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1111.4959

i

we have shown that the physics of systems with heavy fermions is determined by the extended quasiparticle paradigm . in contrast to the paradigm that the quasiparticle effective mass is a constant , within the extended quasiparticle paradigm the effective mass of new quasiparticles strongly depends on the temperature , magnetic field , pressure , and other parameters . the quasiparticles are well defined and can be used to describe the scaling behavior of the thermodynamic hf metals in a wide range of both temperatures @xmath3 and magnetic fields @xmath5 . it was demonstrated that the phase diagram of systems located near the fermion condensation quantum phase transition are strongly influenced by control parameters such as chemical pressure , pressure , the number density or magnetic field . analyzing the phase diagram of @xmath36 , we have found that under the application of the chemical pressure ( positive / negative ) qcp is destroyed or converted into the quantum critical line , correspondingly . we have analyzed the thermodynamic properties of @xmath36 in both the low and the high magnetic fields . our calculations allow us to conclude that in magnetic field the hf system of @xmath36 evolves continuously without a metamagnetic transition and possible localization of heavy @xmath307 electrons . at low temperatures and under the application of magnetic field the hf system demonstrates the lfl behavior , at elevated temperatures the system enters the transition region followed by the nfl behavior . our observations are in good agreement with experimental facts and show that the fermion condensation quantum phase transition is indeed responsible for the observed nfl behavior and quasiparticles survive both high temperatures and high magnetic fields .

in contrast to the landau paradigm stating that the quasiparticle effective mass is a constant , the effective mass of new quasiparticles strongly depends on temperature , magnetic field , pressure , and other parameters . our observations are in good agreement with experimental facts and show that fcqpt is responsible for the observed nfl behavior and quasiparticles survive both high temperatures and high magnetic fields .

strongly correlated fermi systems are among the most intriguing , best experimentally studied and fundamental systems in physics . there is , however , lack of theoretical understanding in this field of physics . the ideas based on the concepts like kondo lattice and involving quantum and thermal fluctuations at a quantum critical point have been used to explain the unusual physics . alas , being suggested to describe one property , these approaches fail to explain the others . this means a real crisis in theory suggesting that there is a hidden fundamental law of nature . it turns out that the hidden fundamental law is well forgotten old one directly related to the landau migdal quasiparticles , while the basic properties and the scaling behavior of the strongly correlated systems can be described within the framework of the fermion condensation quantum phase transition ( fcqpt ) . the phase transition comprises the extended quasiparticle paradigm that allows us to explain the non - fermi liquid ( nfl ) behavior observed in these systems . in contrast to the landau paradigm stating that the quasiparticle effective mass is a constant , the effective mass of new quasiparticles strongly depends on temperature , magnetic field , pressure , and other parameters . our observations are in good agreement with experimental facts and show that fcqpt is responsible for the observed nfl behavior and quasiparticles survive both high temperatures and high magnetic fields .

1407.2757

r

figure [ fig - sp ] shows spectra of the supermaser observed in 18 epochs of the regular astrometry observations from 2011 to 2012 , and figure [ fig - time ] shows time variations of the flux density , velocity width , and peak velocity for all the observed epochs including both 18 epochs of the regular astrometry and 53 epochs of the spectral line monitoring observations . first , these parameters are determined by fitting a single gaussian to the observed profile . however , there are two distinct velocity components at @xmath46.9 km s@xmath5 and @xmath47.5 km s@xmath5 as reported in @xcite . these components can be clearly seen in spectral profiles such as the double - peaked structure on 2011/121 and 2011/137 and red - shifted shoulder on 2011/208 ( figure [ fig - sp ] ) . this results in a significant deviation from the observed line profile in the fitting . thus , we next fit two gaussians to the observed profiles for these epochs . although these line parameters show slightly larger error bars as shown in figure [ fig - time ] , we can see time variations of flux density , velocity width , and peak velocity for the @xmath47.5 km s@xmath5 component continuously changing even during this phase . in contrast , the velocity component that appeared later at @xmath46.9 km s@xmath5 shows a different time variation . according to characteristics of the time variation in figure [ fig - time ] , we can divide the monitoring period of the current h@xmath0o maser burst into four phases ; a moderately active phase in 2009 followed by a relatively quiescent phase in 2010 , a start of the burst with rapid variation in 2011 , the maximum phase in 2012 , and a quiescent / possible initial phase of the next burst in 2013 . in 2009 , there is a moderately active phase slowly increasing and decreasing in the flux density both in total power and cross power spectra . timescales of both rising and falling phases , which are defined as periods from minimum to maximum and maximum to minimum flux densities , respectively , are almost equal , 10 months and 11 months , respectively ( figure [ fig - flux](a ) ) . during this phase , the peak velocity is also slightly changing from 7.4 to 7.3 km s@xmath5 while the velocity width , @xmath40.8 km s@xmath5 , is almost stable with time . after this moderately active phase in 2009 , the maser activity becomes a quiescent phase , whereas the total and correlated flux densities are as high as 2400 jy and 500 jy , respectively , at the minimum phase on 2010/227 . toward this minimum phase , the velocity width of the total - power spectrum gradually increases although that of the cross - power spectrum shows a decreasing trend . at the minimum phase on 2010/227 , the velocity width and peak velocity change drastically . furthermore , these parameters show significant differences between total - power and cross - power spectra but with larger uncertainties than other epochs . this could be caused by other velocity components as their contributions become more and more significant relative to that of the 7.5 km s@xmath5 component . before and after this minimum phase , there were breaks of monitoring observations each for 100 days due to the maintenance of the vera antennas , and hence , we could not trace time variations in this quiescent phase . the h@xmath0o maser burst has started in the end of 2010 or the beginning of 2011 @xcite . the flux density of the total - power spectrum at @xmath47.5 km s@xmath5 has started to increase since 2010/350 while that of the cross power spectrum is temporarily halted on 2010/360 followed by the brightening from 2011/023 . although there is a lack of maser images , this might reflect a variation in the spatial structure of the emitting region . at the beginning of the current burst phase in 2011 , there are two maximum phases on 2011/60 - 2011/121 and 2011/296 - 2011/311 with the total flux density of about 50000 jy ( figure [ fig - time ] ) . the timescales of rising and falling phases are 7 months and 3 months , respectively , for the maximum phase of 2011/60 - 2011/121 ( figure [ fig - flux](b ) ) , although the flux density in this phase shows a variability rather than a monotonic increase or decrease . the timescales for the subsequent maximum phase of 2011/296 - 2011/311 ( figure [ fig - flux](c ) ) are 2 months for both rising and falling phases . apart from the different timescales , the behaviors in rising and falling phases seem to be symmetric as seen in the active phase in 2009 ( figure [ fig - flux ] ) . as discussed above , the burst appears to occur in two different velocity components at 6.9 km s@xmath5 and 7.5 km s@xmath5 @xcite as seen in figures [ fig - time](b ) and ( c ) . the burst activity is temporarily stopped at the end of 2011 , but more active burst has started in early 2012 . the maximum total flux density of 135000 jy is recorded on 2012/154 at the peak velocity of 7.4 km s@xmath5 . in this most active phase , the flux density monotonically increases with the timescale of 5 months . the velocity width is about 0.60 - 0.75 km s@xmath5 , which is the narrowest value observed in our monitoring as shown in figure [ fig - time](b ) . on 2012/123 , the derived velocity widths show the minimum values of 0.50@xmath110.02 km s@xmath5 and 0.46@xmath110.02 km s@xmath5 for the total - power and cross - power spectra , respectively . only in this epoch , the velocity widths are significantly narrower than those observed just before and after this epoch ( 2012/107 and 2012/145 ) . due to the lack of maser images on 2012/123 , we do not discuss what is the true reason for these narrower velocity widths only at this epoch . the flux density of the maser decreases with the timescale of 4 months after this maximum phase . it should be noted that the time variations in rising and falling phases again seem to be symmetric as seen in figure [ fig - flux](d ) . at the end of the burst phase in 2012/265 and 2012/269 , the peak velocities of cross - power spectra show significant differences from those of the total - power spectra . they are thought to be the results of significant contributions from other velocity components and/or effects of structure changes in maser features . this effect is seen particularly in less active phases such as in 2010 . finally , the burst activity seems to end around 2012/269 while it again appears to be brightening from 2013/138 . it is most likely an ignition of a newly occurred burst event . we will continue monitoring observations with vera of the time variation of the supermaser in orion kl . still , the activity of the 22 ghz h@xmath0o maser burst in 2011 - 2012 is relatively lower by a factor of 10 in comparison with the previous bursts in which the peak flux densities reached 10@xmath6 jy . we note that the fluxes reported in figures [ fig - time ] and [ fig - flux ] are those integrated over the whole region including both the supermaser and other features . we investigate possible contribution from other maser features at almost the same velocity with the supermaser feature in the 18 epochs of our vlbi imaging . although it is difficult to make full channel maps with a wide field of view of an order of 10 , we search for positions of the maser features detected by @xcite . as a result , we detect one maser feature around the position offset of ( @xmath43.175 , @xmath4 - 1.850 ) in right ascension and declination , respectively , with respect to the supermaser feature . @xcite detected two maser features near this position at the velocities of 6.3 km s@xmath5 and 7.6 km s@xmath5 with the flux densities of 21.0 jy and 897.7 jy , respectively . figure [ fig - se ] shows the flux density of this maser feature ( we call this feature `` se feature '' ) and the flux density ratio relative to the supermaser feature . the flux density of the se feature increases with time and the maximum phase is observed on 2012/244 . it is about 2 months after the maximum phase of the supermaser . even around the maximum phase of the se feature , a possible contribution to the total flux density is as large as 8% as shown in figure [ fig - se ] ( b ) . therefore , we conclude that the contamination from other maser features including the se features are not significant in figures [ fig - time ] and [ fig - flux ] . the time variation of the linewidth of the supermaser implies an anti - correlation with the flux density as shown in figure [ fig - dv ] . according to model calculations , the line profile of the maser first tends to be narrower as its intensity increases as long as the maser is unsaturated @xcite . then the maser line starts to rebroaden when it becomes saturated @xcite . under the condition of an unsaturated maser , the logarithm of the flux density of the maser line , @xmath12 , is predicted to be proportional to the inverse square of the linewidth , @xmath13 . in figure [ fig - dv ] , we also show best - fit results ; @xmath14 our results may suggest that the supermaser in the current burst phase is still unsaturated . it is consistent with the observed narrow linewidths , 0.40 - 0.48 km s@xmath5 , of the supermaser in 1998 - 1999 possibly attributed to the line narrowing for an unsaturated maser @xcite . in contrast , no clear relationship between the flux density and linewidth is found in the burst in 1979 - 1985 @xcite , suggesting a saturated maser emission . the difference in the degree of saturation could be attributed to the lower flux density , @xmath410@xmath15 jy in the current burst phase than those in the previous bursts , @xmath310@xmath6 jy @xcite . we note that the line narrowing is predicted to occur even for a saturated maser if a stimulated emission rate is not large compared with the cross - relaxation rate @xcite . this means that the above relation holds when the maser flux density is not enough large regardless of saturated or unsaturated cases . thus , we can not firmly estimate the degree of saturation of the supermaser by judging from the linewidth - flux density relation only . figure [ fig - map ] represents channel maps of the phase - referenced images of the supermaser in 2011/137 . three spatially distinct components are found in the initial phase of the burst from 2011/068 to 2011/137 as reported previously @xcite . it is well known that the 22 ghz h@xmath0o line ( 6@xmath16 - 5@xmath17 ) has a hyperfine structure with 3 main components and that the @xmath18=7 - 6 and 5 - 4 components appear with the separation of + 0.45 km s@xmath5 and -0.58 km s@xmath5 with respect to the central component , @xmath18=6 - 5 @xcite . the velocity separation of -0.58 km s@xmath5 is consistent with that observed for two bursting features . however , our results suggest that the two velocity components observed at 6.9 km s@xmath5 and 7.5 km s@xmath5 in the supermaser are not emitted from the same masing gas clump . thus , these two velocity components are unlikely due to the hyperfine structure but they corresponds to distinct masing gas clumps with different positions and velocities . we conduct two - dimensional gaussian fittings on the phase - referenced images to measure the absolute position of each maser spot . hereafter , we define a `` spot '' as a maser emission identified in a single velocity channel and a `` feature '' as a group of spots that are spatially coincident in two or more consecutive velocity channels . by using these results , we derive the absolute proper motions of the detected spots as summarized in table [ tab - proper ] and figure [ fig - position ] . we find that the northern feature , feature 1 ( or spots 1 , 3 , and 5 ) , is detectable only until 2011/296 ( table [ tab - proper ] ) . the lifetime of the northern feature 1 is about 8 months . given the typical monitoring interval and detection criterion , in which a spot is regarded as real when it is detected for more than three contiguous epochs , we might miss a short - term variation of a maser spot on phase - referenced images within a lifetime of less than @xmath42 months . according to the absolute proper motion measurements , the supermaser features are apparently moving toward south and southwest directions as shown in the gray arrows in figure [ fig - map ] . the derived proper motions are consistent but are more reliable than those previously obtained @xcite because we have continued the proper motion measurements in a longer observing period . when we subtract a modulation of an annual parallax of 2.39 mas @xcite and the absolute proper motion of a possible powering source of the low - velocity outflow , source i ( @xmath19 , @xmath20)=(6.3 mas yr@xmath5 , -4.2 mas yr@xmath5 ) , measured by astrometric observations with the very large array ( vla ) @xcite , the derived proper motion vectors with respect to source i point toward west and southwest directions as drawn in the black arrows in figure [ fig - map ] . the magnitude of the proper motions range from 2.7 to 11.4 mas yr@xmath5 or from 5 to 23 km s@xmath5 ( table [ tab - proper ] ) . similar to the previous reports @xcite the supermaser features are elongated along the northwest - southeast direction perpendicular to the low - velocity outflow @xcite . observed proper motions with respect to source i are almost perpendicular to the major axis of each feature . the size of the maser spot at the peak channel on the maximum epoch , 2012/164 , is 2.265@xmath110.014 mas@xmath210.950@xmath110.006 mas ( 0.95 au@xmath210.40 au ) obtained from a gaussian fitting on the self - calibrated image . the peak flux density is ( 1.029@xmath110.010)@xmath22 jy , corresponding to the brightness temperature of 1.2@xmath23 k. the isotropic luminosity is estimated to be 2.4@xmath2110@xmath24 by assuming a linewidth of 0.6 km s@xmath5 . to study physical and chemical properties of the supermaser , we utilize alma cycle 0 data to make images of submillimeter continuum emissions and molecular lines at band 7 . first , we have searched for any 321.225656 ghz h@xmath0o line signal toward the compact ridge where the supermaser resides for the 321.20 - 321.25 ghz range , as shown in figure [ fig - alma ] . several spectral lines are seen , but they are identified as the hcooch@xmath1 lines . if the 321 ghz h@xmath0o line is excited by the maser action like that at 22 ghz , it should be much more compact than those of other molecular lines . with this in mind , we then investigate spectra of the h@xmath0o lines by using the visibility data with the baseline length longer than 100 k@xmath25 , corresponding to the angular size of the emission region of @xmath22 . as a result , we can resolve out all of the lines in the compact ridge while a significant fraction of the 321 ghz h@xmath0o line . in contrast , the broad 321 ghz h@xmath0o line is clearly seen in source i with a double peaked profile @xcite . the 321 ghz h@xmath0o line remains in source i even with the baselines longer than 200 k@xmath25 suggesting a compact structure @xcite . thus , we conclude that no clear evidence of the 321 ghz h@xmath0o maser is detected at the position of the supermaser in spite of the extraordinary strong emission of the 22 ghz h@xmath0o maser . we note that in the observed spectral range a vibrationally excited ( @xmath26=1 , 5@xmath27 - 6@xmath28 ) h@xmath0o line at 336.227931 ghz is not detected in the compact ridge . non - detection of the 321 ghz and 336 ghz h@xmath0o lines implies that the physical conditions around the compact ridge are certainly different from those in source i @xcite . we next compare the distribution of the molecular gas in the compact ridge which hosts the supermaser . for this purpose , we employ the hcooch@xmath1 line at 321.22338 ghz ( @xmath29=0 , 28@xmath30 - 27@xmath31 a ) , which is close to the frequency of the 321 ghz h@xmath0o line ( figure [ fig - alma ] ) , as a tracer of the dense molecular gas in the compact ridge @xcite . the 321.223 ghz hcooch@xmath1 line is not blended with other hcooch@xmath1 transitions unlike those at 321.229 ghz ( @xmath29=1 ) lines , and hence , it is more suitable to analyze the velocity structure of the molecular gas . figure [ fig - moment](a ) shows the moment 0 ( integrated intensity ) map of the 321.223 ghz hcooch@xmath1 line superposed on the alma band 7 continuum emission . the supermaser is located at 8 southwest of source i and is coincident with the compact ridge . the position of the supermaser is close to the hcooch@xmath1 peak but is rather located at the edge of the hcooch@xmath1 condensation . as can be seen in the moment 1 ( peak velocity ) map in figure [ fig - moment ] ( b ) , the velocity of the supermaser @xmath46.9 - 7.5 km s@xmath5 is slightly blue - shifted compared with that of the hcooch@xmath1 line . furthermore , the moment 2 ( velocity width ) map in figure [ fig - moment ] ( c ) implies that the linewidth of the hcooch@xmath1 line tends to be broader around the supermaser . we stress that the velocity structure seems to change abruptly around the supermaser . these apparent velocity structures are caused by two different velocity components of the molecular gas traced by the hcooch@xmath1 line . in figure [ fig - pv ] , we can see detailed velocity structures in the compact ridge by the position - velocity diagram along the x and y axes as indicated in figure [ fig - moment ] ( a ) . it is clear that there exist two different velocity components at 7.5 km s@xmath5 and 9.0 km s@xmath5 . these two components were identified in the previous observations @xcite , but we can resolve both the velocity and spatial structures by higher spectral and spatial resolutions with alma . the supermaser is thought to be associated with one of them at 7.5 km s@xmath5 . interestingly , the velocity of the weak emission from the hcooch@xmath1 line in figure [ fig - pv ] ranges from @xmath46 to 12 km s@xmath5 , although the linewidths of the hcooch@xmath1 lines are only about 1 km s@xmath5 as shown in figure [ fig - alma ] . the velocity range of the weak hcooch@xmath1 emission is significantly broader at x=0 and y=0 , corresponding to the position of the supermaser ( see figure [ fig - pv ] ) . this is probably an evidence of a shock front at the position close to the supermaser . indeed , possible effects of shocks in the compact ridge have been suggested by the enhancement of organic molecules such as hcooh @xcite , hcooch@xmath1 @xcite , and ch@xmath1och@xmath1 @xcite . figure [ fig - cont ] shows a close - up view of distributions of the alma band 7 continuum emission superposed on the integrated intensity map of the 321.223 ghz hcooch@xmath1 line ( figure [ fig - moment](a ) ) . positions of the 22 ghz h@xmath0o masers @xcite including that of the supermaser are also indicated . we detect the compact continuum emission both at alma bands 6 and 7 @xcite . the accurate position of the supermaser is significantly shifted from the continuum peak by 0.3 southeast . we also indicate positions of other possible counterparts observed previously . their relationship will be discussed in the next section .

the supermaser is located close to the methylformate ( hcooch ) line and continuum emission peaks in the orion compact ridge detected by alma , atacama large millimeter / submillimeter array . the broader velocity range of the weak hcooch emission at the supermaser position would be an evidence of a shock front . on the other hand , the 321 ghz ho line is not detected at the position of the supermaser .

the 22 ghz ho maser in orion kl has shown extraordinary burst events in 1979 - 1985 and 1998 - 1999 , sometimes called supermaser . we have conducted monitoring observations of the supermaser in orion kl using vera , vlbi exploration of radio astrometry , in the current third burst since 2011 march . three flux maxima are detected in 2011 and 2012 with rising and falling timescales of 2 - 7 months . time variations of the supermaser seem symmetric for all of the active phases . the maximum total flux density of 135000 jy is observed in 2012 june while it is still one order of magnitude lower than those in previous bursts . the supermaser consists of two spatially different components at different velocities . they are elongated along a northwest - southeast direction perpendicular to the low - velocity outflow driven by source i. proper motions of the supermaser features with respect to source i are measured toward west and southwest directions , almost parallel to the low - velocity outflow . the flux density and linewidth show an anti - correlation as expected for an unsaturated maser emission . the supermaser is located close to the methylformate ( hcooch ) line and continuum emission peaks in the orion compact ridge detected by alma , atacama large millimeter / submillimeter array . the broader velocity range of the weak hcooch emission at the supermaser position would be an evidence of a shock front . on the other hand , the 321 ghz ho line is not detected at the position of the supermaser . it can be explained qualitatively by one of the theoretical ho excitation models without extraordinary conditions . our results support a scenario that the supermaser is excited in the dense gas interacting with the low - velocity outflow in the compact ridge . the extremely high flux density and its symmetric time variation for rising and falling phases could be explained by a beaming effect during the amplification process rather than changes in physical conditions .

1407.2757

c

in this paper , we report results of continued monitoring observations of the supermaser with vera for more than 5 years . we also acquire follow - up observational data with alma of submillimeter continuum emissions and h@xmath0o lines at 321 ghz to reveal characteristics of the supermaser and their environments . in this section , we will address following issues related to the supermaser : what is the powering source of the supermaser and what makes the 6.9 and 7.5 km s@xmath5 features in the compact ridge only such a special burst event ? why there is no bursting h@xmath0o maser feature at 321 ghz despite the extraordinary high flux density in the 22 ghz h@xmath0o maser ? how the drastic burst of the h@xmath0o maser can be explained ? is there a periodicity of the burst event ? according to the absolute position of the supermaser derived from our vera observations , we propose that the supermaser would be excited in the shocked molecular gas interacting between the low - velocity outflow driven by source i and ambient dense gas in the compact ridge @xcite . proper motions and elongations of the supermaser features ( figure [ fig - map ] ) and the broader hcooch@xmath1 line at the position of the supermaser ( figure [ fig - pv ] ) support this scenario . it has also been suggested by the fact that the h@xmath0o maser tends to be distributed in the interface of the shocked molecular gas in the compact ridge traced by hcooh @xcite and hcooch@xmath1 @xcite lines . furthermore , @xcite point out a possible relation between the compact ridge and an explosive outflow traced by the co lines @xcite . indeed , the supermaser is found to be located at the edge of the low - velocity bipolar molecular outflow traced by the thermal sio lines @xcite as well as the explosive outflow @xcite . the latter one is thought to be the result of a recent close encounter of source i and bn object @xcite , although a relationship between these two outflows is still unclear . note that an infrared source irc 5 is located at 1 southeast of the supermaser . the position of irc 5 corresponds to a nearby 3 mm continuum peak , c29 @xcite , and an hcooch@xmath1 peak , mf14 @xcite and hence , it is more closely related to these sources . since irc 5 is thought to be a shocked molecular gas heated externally @xcite , it would not be directly related to the excitation of the supermaser . alternatively , both of them are thought to be heated by the common outflow . as discussed previously @xcite , however , it has been still unknown why only the 6.9 km s@xmath5 and 7.5 km s@xmath5 features show such an extraordinary burst phenomenon . one of the possible explanations is a special physical or geometrical condition of the maser excitation in this region . an anomalous amplification of the h@xmath0o maser burst might need a long path length . such a condition could be achieved only in the systemic velocity component . because it can supply plenty of ambient molecular gas within a narrow velocity range , maser emission would be efficiently amplified only close to the systemic velocity @xcite . millimeter and submillimeter continuum emissions are detected by @xcite , smm1 in @xcite and cb1 in @xcite with spatial resolution of @xmath40.8 - 3 . the mass of the submillimeter core in the compact ridge is estimated to be 4@xmath32 @xcite , and hence , they could provide the dense gas required to form new stars . a similar conclusion is obtained from the alma science verification continuum data that have been analyzed by @xcite . to account for a necessary condition for the supermaser , it is also suggested that the maser burst could occur as a result of an interaction with outflows and a pre - existing yso in the compact ridge @xcite . as discussed in detail by @xcite , there are possible candidate sources physically associated with the supermaser ; a radio continuum source labeled r detected with vla @xcite , 3 mm continuum emission sources detected with the combined array for research in millimeter - wave astronomy ( carma ) @xcite , molecular peaks traced by hcooch@xmath1 lines with the iram plateau de bure interferometer ( pdbi ) @xcite , and optical source parenago 1822 , which is also identified from millimeter , near infrared , optical and x - ray ( see simbad ) , in the compact ridge ( figure [ fig - cont ] ) . @xcite detect a compact 1.3 mm continuum source named hc 438 in the compact ridge with a flux density of 67.8@xmath1114.2 mjy by using carma . we also detect a compact continuum source at alma band 7 ( see contours in the middle of figure [ fig - cont ] ) which is also detected at band 6 @xcite . these observations achieve much higher spatial resolution of @xmath40.5 than those reported above @xcite . the flux density at alma bands 6 and 7 are 57@xmath115 mjy and 129@xmath1114 mjy , respectively @xcite . the alma band 6 result is consistent with that of the carma 230 ghz observation @xcite . the supermaser is located within the submillimeter core detected by alma but is shifted by 0.3 from the peak position . taking into account positional uncertainties , they are identical to hc 438 @xcite , the 3 mm continuum source c32 @xcite and hcooch@xmath1 peak mf1 @xcite . the circumstellar mass of hc 438 is derived to be 0.085 @xmath32 with the assumed dust temperature of 20 k @xcite . if we assume a higher temperature of 100 k derived from the hcooch@xmath1 data @xcite , the smaller mass of 0.01@xmath32 is obtained . these mass estimates would be a lower limit of the dust continuum source possibly associated with the supermaser because most of the flux is filtered out by alma and carma with extended configurations . we speculate that an embedded yso associated with jet / outflow / disk @xcite would play an important role to realize special conditions required for the supermaser . we notice that the h@xmath0o maser features near the supermaser detected with vla @xcite are distributed around the submillimeter continuum peak as seen in figure [ fig - cont ] . it may imply an expanding shell ejected by an embedded yso , which are sometimes seen in massive ysos @xcite . as discussed in section [ sec - vera ] , we tried to search for other maser features in orion kl region previously detected with vla @xcite . we made channel maps of the h@xmath0o maser features with vera within an 1@xmath211 field of view around the supermaser in the compact ridge . however , we found no maser emission because of the limited dynamic range seriously affected by the extremely strong supermaser . further observations of continuum emission and h@xmath0o masers with higher dynamic range will unveil the exact location of the embedded yso in the compact ridge . it is proposed that the pumping mechanism of the h@xmath0o maser is dominated by collisional excitation @xcite . the burst of the h@xmath0o maser in orion kl is proposed as the result of collisional pumping in the magnetohydrodynamic shock wave caused by the outflow @xcite . on the other hand , alternative mechanisms are also considered to account for the extraordinary h@xmath0o maser burst , such as overlapping of two maser gas clumps @xcite and accidental beaming of radiation toward the earth rather than a change in excitation @xcite . to constrain the physical properties of the supermaser , we have carried out observations of the submillimeter h@xmath0o lines which could be masing @xcite by using alma . among a number of h@xmath0o lines , we employ the 10@xmath33 - 9@xmath34 transition at 321 ghz which is proposed to be a good indicator of some key parameters including temperature , density , and h@xmath0o abundance in the masing gas clump @xcite . however , there is no significant emission of the 321 ghz h@xmath0o line at the position around the supermaser . the upper limit of the flux density of the 321 ghz h@xmath0o line is @xmath40.1 jy . if we assume physical properties of the masing gas are common for both the 22 ghz and 321 ghz lines , then a photon luminosity ratio , @xmath35(22 ghz)/@xmath35(321 ghz ) , is identical to the observed flux density ratio , @xmath18(22 ghz)/@xmath18(321 ghz ) . then , an upper limit of @xmath35(22 ghz)/@xmath35(321 ghz)@xmath310@xmath6 is obtained from the flux density of the 22 ghz maser of @xmath310@xmath15 jy . when the beaming angle of the 22 ghz maser is also the same as that of 321 ghz , an emissivity ratio @xmath36(22 ghz)/@xmath37(321 ghz ) @xcite is also equal to the photon luminosity ratio and flux density ratio , @xmath38 . as demonstrated in the model calculations @xcite , the lower limit of @xmath38 can be achieved when the temperature is @xmath4200 - 400 k or the parameter @xmath39 is @xmath40.4 - 1.8 depending on the temperature within the calculated range below 2000 k ( see their figure 3 ) . the parameter @xmath40 is defined as @xmath41(h@xmath0o ) @xmath42/@xmath43 , in which @xmath44(h@xmath0o ) , @xmath45 , and @xmath43 are a fractional abundance of h@xmath0o relative to hydrogen nuclei in units of 10@xmath46 , a number density of hydrogen nuclei in units of 10@xmath47 @xmath48 , and a velocity gradient in units of 10@xmath49 cm s@xmath5 cm@xmath5 @xcite . we note that the model employed here is calculated under the assumption of a saturated maser @xcite and hence , the estimated parameters may be different from an unsaturated case as adopted for the supermaser . furthermore , the model calculation only considers collisional pumping of h@xmath0o molecules ignoring infrared pumping . in addition , the collision rates used in these works are now superseded by newer calculations @xcite . despite these uncertainties , we use the model of @xcite to roughly interpret the supermaser burst at 22 ghz and the non - detection of the 321 ghz line . as a result , we find the supermaser burst at 22 ghz and the non - detection at 321 ghz could still be explained by the theoretical model @xcite without extraordinary physical conditions . thus , under the condition of the unsaturated 22 ghz h@xmath0o maser , the lower temperature and larger value of @xmath40 would also be expected according to a qualitative consideration . to explain the non - detection of the 321 ghz maser line ( high value of @xmath51 ) , either high h@xmath0o abundance , high h@xmath0 density , small velocity gradient , or low temperature of 200 - 400 k would be required . the h@xmath0o abundance in the compact ridge is estimated from the herschel data to be 2.6@xmath2110@xmath52 with the source size of 6 @xcite . if a local abundance enhancement occurs around the supermaser , the higher h@xmath0o abundance up to 6.5@xmath2110@xmath46 as observed in the hot core region @xcite may be possible . the average h@xmath0 number density of the dust continuum source in the compact ridge is estimated to be ( 0.5 - 5)@xmath2110@xmath47 @xmath48 assuming a diameter ( fwhm ) of 0.43 or 90 au @xcite and a total mass of 0.01 - 0.1 @xmath32 @xcite . if we assume a velocity width of 0.6 km s@xmath5 and a path length of 1 au as obtained from a gaussian fitting for a bursting maser spot , the velocity gradient @xmath43 is calculated to be 0.4 . although the above results contain large uncertainties by a factor of 10 or more , these parameters seem reasonable to explain estimated range of @xmath39 of 0.4 - 1.8 unless the h@xmath0o abundance is the lowest estimate of @xmath44(h@xmath0o)=0.026 @xcite . it is also conceivable that the supermaser is the result of strong beaming effects @xcite . if only the 22 ghz maser emission has a smaller beaming angle compared with that of the 321 ghz line , the emissivity ratio @xmath53 is proportional to the flux density ratio , @xmath18(22 ghz)/@xmath18(321 ghz ) , and the ratio of beaming angles , @xmath54(22 ghz)/@xmath54(321 ghz ) , which reduces the upper limit of @xmath53 estimated from the observed flux density ratio . the smaller beaming angle of the 22 ghz maser line than that of 321 ghz by a factor of @xmath4100 would enable a large @xmath54(22 ghz)/@xmath54(321 ghz ) value of @xmath410000 . this may result in the lower @xmath53 value by a factor of 10000 which can be achieved under wider range of physical conditions as seen in figure 3 of @xcite . in spite of the presence or absence of a beaming effect , the condition for the h@xmath0o maser burst only at the 22 ghz transition , @xmath38 , does not require extreme physical properties but rather those typical in hot molecular cores @xcite . we suggest that the symmetric time variation in the flux density ( figure [ fig - flux ] ) could be explained by a change in the beaming angle of the maser rather than changes in the physical properties such as h@xmath0o abundance , h@xmath0 density , and/or temperature . on the other hand , a change in a velocity gradient caused by a length of the maser cloud and/or velocity structure might happen such as those in the overlapping maser model @xcite . nevertheless , it is still uncertain how such an accidental overlapping and/or a beaming effect could occur in two spatially distinct clouds for several times during our monitoring period of @xmath45 years . comparing the basic properties such as the peak lsr velocity , the spatial structure of each feature , and the location coincident with the compact ridge , all of the burst events in 1979 - 1985 , 1998 - 1999 , and 2011 - 2012 could have a common origin . it is also suggested that the h@xmath0o maser burst may have periodicity of 13 years @xcite . however , the current burst shows less activities in terms of the maximum flux density . furthermore , no such burst event is reported in 1973 @xcite , in which the burst event is expected if 13 year - periodicity is valid ( i.e. 1972 - 1973 , 1979 - 1985 , 1998 - 1999 , and 2011 - 2012 ) . in 1973 july , the observed flux density of the h@xmath0o maser at 7.4 km s@xmath5 was only about 100 jy and was weaker than the 11.0 km s@xmath5 component @xcite . this component was probably identical to the second brightest component in the current burst phase ( figure [ fig - sp ] ) . the position of the 7.4 km s@xmath5 component was measured to be r.a.=05h35m14.22s and decl.=-05@xmath552237.0 ( j2000 ) and was consistent with that of the current bursting feature located in the compact ridge . in 1975 - 1976 , the h@xmath0o maser feature at 7.6 km s@xmath5 was detected at the position of r.a.=05h35m14.07s and decl.=-05@xmath55d2238.0 ( j2000 ) . the position of this feature was again in good agreement with that of the current h@xmath0o maser burst , whereas it was rather weak ( much less than 1000 jy ) compared with another strong feature at 10.8 km s@xmath5 . although the h@xmath0o maser feature at @xmath47.5 km s@xmath5 could be excited by a common origin in the compact ridge , it is not very likely that the maser burst occurs regularly at a period of 13 years . more archive data of past observations will be helpful to investigate a long - term variability of the h@xmath0o maser activities since early 1970s . the flux increase started in 2013 is now on - going and hence , further monitoring will also provide some hints to understand a possible relation with previous bursts . along with the 22 ghz h@xmath0o maser lines , it could be useful to continue monitoring observations of the 321 ghz h@xmath0o lines in orion kl with alma in order to see whether the compact ridge and source i , which is a powering source of the outflow interacting with the compact ridge , behave in the same way . figures [ fig - sp]-[fig - flux ] imply that the current burst in 2011 and 2012 sometimes shows variations in the flux density and velocity structure with the timescales of 2 - 7 months . it is comparable to those of typical h@xmath0o masers in orion kl @xcite . although the spectral component of the supermaser seems to survive for more than 5 - 10 years @xcite , a spatial structure of each bursting feature is found to be changing within a timescale of a few months to @xmath22 years at the longest lifetime ( table [ tab - proper ] ) . thus , it is unlikely that the bulk of the bursting maser gas is identical for longer than @xmath42 years .

three flux maxima are detected in 2011 and 2012 with rising and falling timescales of 2 - 7 months . it can be explained qualitatively by one of the theoretical ho excitation models without extraordinary conditions . our results support a scenario that the supermaser is excited in the dense gas interacting with the low - velocity outflow in the compact ridge . the extremely high flux density and its symmetric time variation for rising and falling phases could be explained by a beaming effect during the amplification process rather than changes in physical conditions .

the 22 ghz ho maser in orion kl has shown extraordinary burst events in 1979 - 1985 and 1998 - 1999 , sometimes called supermaser . we have conducted monitoring observations of the supermaser in orion kl using vera , vlbi exploration of radio astrometry , in the current third burst since 2011 march . three flux maxima are detected in 2011 and 2012 with rising and falling timescales of 2 - 7 months . time variations of the supermaser seem symmetric for all of the active phases . the maximum total flux density of 135000 jy is observed in 2012 june while it is still one order of magnitude lower than those in previous bursts . the supermaser consists of two spatially different components at different velocities . they are elongated along a northwest - southeast direction perpendicular to the low - velocity outflow driven by source i. proper motions of the supermaser features with respect to source i are measured toward west and southwest directions , almost parallel to the low - velocity outflow . the flux density and linewidth show an anti - correlation as expected for an unsaturated maser emission . the supermaser is located close to the methylformate ( hcooch ) line and continuum emission peaks in the orion compact ridge detected by alma , atacama large millimeter / submillimeter array . the broader velocity range of the weak hcooch emission at the supermaser position would be an evidence of a shock front . on the other hand , the 321 ghz ho line is not detected at the position of the supermaser . it can be explained qualitatively by one of the theoretical ho excitation models without extraordinary conditions . our results support a scenario that the supermaser is excited in the dense gas interacting with the low - velocity outflow in the compact ridge . the extremely high flux density and its symmetric time variation for rising and falling phases could be explained by a beaming effect during the amplification process rather than changes in physical conditions .

1407.2757

i

we have carried out astrometric monitoring observations of the bursting 22 ghz h@xmath0o maser feature , called supermaser , in orion kl using vera since 2011 march . combined with spectral line data obtained as a fringe - finder , we reveal a time variation of the supermaser for more than 5 years . in addition , we utilize alma cycle 0 data at band 7 ( 320 - 330 ghz ) for both spectral lines and continuum emissions to investigate physical and chemical properties of the supermaser . the main findings are summarized as follows : 1 . within the monitoring period in 2011 and 2012 , we detect three active phases with rising and falling timescales ranging from 2 to 7 months . we also find a smaller burst in 2009 with a slightly longer rising and falling timescales of @xmath410 months . the flux variations of the supermaser seem to be symmetric in time for all of the active phases . 2 . the maximum phase of the current burst is observed on 2012/154 with the total flux density of 135000 jy , which is one order of magnitude lower than those in previous bursts . although the burst events may occur with a possible periodicity of 13 years , ( i.e. 1979 - 1985 , 1998 - 1999 , and 2011 - 2012 ) , a lower flux density by a factor of 10 in the current burst , as well as no significant burst event in 1973 @xcite would make the claimed periodicity of 13 years still unconvincing . the outburst of the maser emission can be seen in two velocity components at @xmath46.9 km s@xmath5 and @xmath47.5 km s@xmath5 as reported in @xcite and @xcite . the 6.9 km s@xmath5 feature is alive only in 2011 with the lifetime of @xmath48 months . note that we detect two spatially distinct features at 6.9 km s@xmath5 and 7.5 km s@xmath5 , and hence , these two velocity components are unlikely due to the hyperfine structure of the h@xmath0o molecule . 4 . the flux density and linewidth show an anti - correlation as expected for an unsaturated maser emission @xcite , in which the logarithm of the flux density of the maser line , @xmath12 , is proportional to the inverse square of the linewidth , @xmath13 . however , we can not rule out a possibility of a saturated maser case because such a line narrowing is also predicted to occur even for a saturated maser if a stimulated emission rate is not large compared with that of the cross - relaxation @xcite . as reported in previous papers @xcite the bursting maser features are elongated along the northwest - southeast direction perpendicular to the low - velocity outflow driven by source i. absolute proper motions of the bursting maser features are measured based on a longer monitoring period than that in the previous paper @xcite . their proper motions with respect to a powering source of the low - velocity outflow , source i , are almost perpendicular to the elongation of the maser features , suggesting that they are related to the low - velocity outflow . the size of the maser spot at the peak channel on the maximum epoch , 2012/164 , is 2.265 mas@xmath210.950 mas , and the total flux density is 1.029@xmath2110@xmath15 jy . these values correspond to the brightness temperature and the isotropic luminosity of 1.2@xmath23 k and 2.4@xmath2110@xmath24 , respectively . the supermaser is located at the compact ridge region in orion kl . continuum peaks detected by alma bands 6 and 7 are located 0.3 northwest of the supermaser . as suggested by @xcite , there are a radio continuum source labeled r @xcite , 3 mm continuum source c32 @xcite , hcooch@xmath1 core mf1 @xcite , and optical source parenago 1822 , which are probably identical or closely related to the compact continuum sources detected by alma and the supermaser . the position of the supermaser is coincident with the dense gas traced by the hcooch@xmath1 line . the velocity of the supermaser agrees well with one of the two velocity components of the hcooch@xmath1 line detected by alma and pdbi @xcite . a slightly broader velocity range of the weak hcooch@xmath1 emission would imply a shock front at the position of the supermaser . the 321 ghz h@xmath0o line is not detected around the 22 ghz supermaser features , although the strong maser emission is found to be associated with source i @xcite . given the high emissivity ratio , the maser burst at 22 ghz could occur under conditions of the temperature of @xmath2200 - 400 k and/or the parameter @xmath56 , suggesting a high abundance of h@xmath0o , a high number density of h@xmath0 , and/or a small velocity gradient . meanwhile , these physical properties are not extraordinary values but are very similar to typical hot molecular cloud cores . thus , the supermaser burst at 22 ghz with non - detection of the 321 ghz maser emission could be explained by the theoretical model qualitatively @xcite . further detailed calculations would be required to interpret the observed flux ratios of the masers @xcite . alternatively , the supermaser may be caused by an accidental beaming only for the 22 ghz h@xmath0o maser @xcite . the symmetric time variation in the flux density is consistent with a result of the beaming rather than changes in physical properties of the masing gas . however , it still remains a matter of debate how accidental overlapping and/or beaming occur repetitively for more than @xmath430 years since the discovery of the supermaser . we are grateful to alain baudry for useful comments , which is essential to improve our scientific discussion . we thank the staff of the vera stations and alma observatory to support our project . this paper makes use of the following alma data : ads / jao.alma#2011.0.00199.s . alma is a partnership of eso ( representing its member states ) , nsf ( usa ) and nins ( japan ) , together with nrc ( canada ) and nsc and asiaa ( taiwan ) , in cooperation with the republic of chile . the joint alma observatory is operated by eso , aui / nrao and naoj . this research has made use of the simbad database , operated at cds , strasbourg , france . t.h . is supported by the mext / jsps kakenhi grant numbers 21224002 , 24684011 , and 25108005 , and the alma japan research grant of naoj chile observatory , naoj - alma-0006 . is supported by the mext / jsps kakenhi grant numbers 24540242 and 25120007 . allen , d. a. & burton , m. g. 1993 , nature , 363 , 54 bally , j. 2008 , in handbook of star forming regions , vol . 1 , ed . b. reipurth ( asp monograph publications , vol . 4 ; san francisco , ca : asp ) , 459 bally , j. , cunningham , n. j. , moeckel , n. , burton , m. g. , smith , n. , frank , a. , & nordlund , a. 2011 , apj , 727 , 113 baudry , a. , forster , j. r. , & welch , w. j. 1974 , a&a , 36 , 217 beuther , h. , & nissen , h. d. 2008 , apjl , 679 , l121 brouillet , n. , despois , d. , baudry , a. , et al . 2013 , a&a , 550 , 46 brouillet , n. et al . 2014 , in preparation chen , p. , pearson , j. c. , pickett , h. m. , matsuura , s. , & blake , g. a. 2000 , apjs , 128 , 371 churchwell , e. , felli , m. , wood , d. o. s. , & massi , m. 1987 , apj , 321 , 516 daniel , f. & cernicharo , j. 2013 , a&a , 553 , a70 deguchi , s. & watson , w. d. 1989 , apjl , 340 , l17 eisner , j. a. , plambeck , r. l. , carpenter , j. m. , corder , s. a. , qi , c. , & wilner , d. 2008 , apj , 683 , 304 elitzur , m. , hollenbach , d. j. , mckee , c. f. 1989 , apj , 346 , 983 favre , c. , despois , d. , brouillet , n .. , baudry , a. , combes , f. , gulin , m. , wootten , a. , & wlodarczak , g. 2011 , a&a , 532 , a32 felli , m. , churchwell , e. , wilson , t. l. , taylor , g. b. 1993 , a&as , 98 , 137 forster , j. r. , welch , w. j. , wright , m. c. h. , & baudry , a. , 1978 , apj , 221 , 137 friedel , d. n. & widicus weaver , s. l. 2011 , apj , 742 , 64 garay , g. , moran , j. m. , & haschick , a. d. 1989 , 338 , 244 gaume , r. a. , wilson , t. l. , vrba , f. j. , johnston , k. j. , schmid - burgk , j. 1998 , apj , 493 , 940 genzel , r. , reid , m. j. , moran , j. m. , & downes , d. 1981 , apj , 244 , 884 genzel , r. , & stutzki , j. 1989 , araa , 27 , 41 goddi , c. , humphreys , e. m. l. , greenhill , l. j. , chandler , c. j. , & matthews , l. d. 2011 , apj , 728 , 15 goldreich , p. & kwan , j. 1974 , apj , 190 , 27 greenhill , l. j. , goddi , c. , chandler , c. j. , matthews , l. d. , humphreys , e. m. l. 2013 , apj , 770 , 32 hirota , t. , tsuboi , m. , fujisawa , k. et al . 2011 , apj , 739 , l59 hirota , t. , bushimata , t. , choi , y. k. et al . 2007 , pajs , 59 , 897 hirota , t. , kim , m. k. , kurono , y. , & honma , m. 2014a , apjl , 782 , l28 hirota , t. , kim , m. k. , kurono , y. , & honma , m. 2014b , in preparation kaifu , n. , usuda , t. , hayashi , s. et al . 2000 , pasj , 52 , 1 kim , m. k. , hirota , t. , honma , m. , et al . 2008 , pasj , 60 , 991 kim , m. k. , hirota , t. , honma , m. , & kobayashi , h. 2014 , in preparation kukolich , s.g . 1969 , j. chem . phys . , 50 , 3751 liu , s. -y . , girart , j. m. , remijan , a. , & snyder , l. e. 2002 , apj , 576 , 255 ma , c. , arias , e. f. , eubanks , t. m. , et al . 1998 , aj , 116 , 516 matthews , l. d. , greenhill , l. j. , goddi , c. , chandler , c. j. , humphreys , e. m. l. , & kunz , m. w. 2010 , apj , 708 , 80 matveenko , l. i. , graham , d. a. , & diamond , p. j. 1988 , sov . , 14 , 468 matveyenko , l. i. , zhakharin , k. m. , diamond , p. j. , & graham , d. a. 2004 , astron . lett . , 30 , 100 matveyenko , l. i. , demichev , v. a. , ipatov , a. v. , melnikov , a. e. , & surkis , i. f. 2012a , astl , 38 , 575 matveyenko , l. i. , demichev , v. a. , ipatov , a. v. , melnikov , a. e. , & surkis , i. f. 2012b , astl , 38 , 764 menten , k. m. , & reid , m. j. 1995 , apj , 445 , l157 menten , k.m . , reid , m. j. , forbrich , j. , & brunthaler , a. 2007 , a&a , 474 , 515 neill , j. , l. , wang , s. , bergin , e. a. , crockett , n. r. , favre , c. , plume , r. , melnick , g. j. 2013 , apj , 770 , 142 neufeld , d. a. & melnick , g. j. 1990 , apjl , 352 , l9 neufeld , d. a. & melnick , g. j. 1991 , apj , 368 , 215 niederhofer , f. , humphreys , e. m. l. , & goddi , c. 2012 , a&a , 548 , a69 okumura , s. , yamashita , t. , sako , s. , miyata , t. , honda , m. , kataza , h. , okamoto , y. k. 2011 , pasj , 63 , 823 omodaka , t. , maeda , t. , miyoshi , m. , et al . 1999 , pasj , 51 , 333 otto , s. & gaylard , m. j. 2012 , in iau symp . , 287 , cosmic masers from oh to h@xmath57 , ed . r. s. booth , e. m. l. humphreys , & w. h. t. vlemmings ( cambridge : cambridge univ . press ) , 110 plambeck , r. l. , wright , m. c. h. , friedel , d. n. , et al . 2009 , apj , 704 , l25 shimoikura , t. , kobayashi , h. , omodaka , t. , diamond , p. j. , matveyenko , l. i. , & fujisawa , k. 2005 , apj , 634 , 459 tang , y. w. , ho , p. t. p. , koch , p. m. , & rao , r. 2010 , apj , 717 , 1262 torrelles , j. m. et al . 2003 , apjl , 598 , l115 tolmachev , a. 2011 , atel , 3177 zapata , l. a. , rodrguez , l. f. , schmid - burgk , j. , loinard , l. , menten , k. m. , & curiel , s. 2012 , apj , 754 , l17 zapata , l. a.,schmid - burgk , j. , ho , p. t. p. , rodrguez , l. f. , menten , k. m. 2009 , apj , 704 , l45 zapata , l. a. , schmid - burgk , j. , & menten , k. m. 2011 , a&a , 529 , a24 cccccc feature & spot & @xmath58 & @xmath19 & @xmath20 & + id@xmath59 & id@xmath60 & [ km s@xmath5 ] & [ mas yr@xmath5 ] & [ mas yr@xmath5 ] & epoch + 1 & 1 & 6.74 & -2.0(0.4 ) & -1.8(0.4 ) & 2011/068 - 2011/296 + 1 & 3 & 6.95 & -2.2(0.5 ) & -1.7(0.6 ) & 2011/068 - 2011/296 + 1 & 5 & 7.16 & -2.7(1.2 ) & -1.0(1.4 ) & 2011/068 - 2011/250 + 2 & 2 & 6.74 & 5.2(0.9 ) & -10.2(0.8 ) & 2011/296 - 2012/164 + 2 & 4 & 6.95 & 4.8(0.6 ) & -9.7(0.5 ) & 2011/250 - 2012/207 + 2 & 6 & 7.16 & 4.0(0.3 ) & -9.0(0.2 ) & 2011/068 - 2012/207 + 2 & 7 & 7.37 & 4.0(0.2 ) & -9.1(0.2 ) & 2011/068 - 2012/207 + 2 & 8 & 7.58 & 4.0(0.2 ) & -9.1(0.2 ) & 2011/068 - 2012/269 + 2 & 10 & 7.79 & 4.0(0.2 ) & -9.0(0.2 ) & 2011/068 - 2012/269 + 3 & 9 & 7.58 & -2.6(9.2 ) & -4.1(8.3 ) & 2011/121 - 2011/208 + 3 & 11 & 7.79 & 0.6(3.7 ) & -5.5(3.7 ) & 2011/121 - 2011/208 + + +

we have conducted monitoring observations of the supermaser in orion kl using vera , vlbi exploration of radio astrometry , in the current third burst since 2011 march . time variations of the supermaser seem symmetric for all of the active phases . the maximum total flux density of 135000 jy is observed in 2012 june while it is still one order of magnitude lower than those in previous bursts . they are elongated along a northwest - southeast direction perpendicular to the low - velocity outflow driven by source i. proper motions of the supermaser features with respect to source i are measured toward west and southwest directions , almost parallel to the low - velocity outflow . the flux density and linewidth show an anti - correlation as expected for an unsaturated maser emission .

the 22 ghz ho maser in orion kl has shown extraordinary burst events in 1979 - 1985 and 1998 - 1999 , sometimes called supermaser . we have conducted monitoring observations of the supermaser in orion kl using vera , vlbi exploration of radio astrometry , in the current third burst since 2011 march . three flux maxima are detected in 2011 and 2012 with rising and falling timescales of 2 - 7 months . time variations of the supermaser seem symmetric for all of the active phases . the maximum total flux density of 135000 jy is observed in 2012 june while it is still one order of magnitude lower than those in previous bursts . the supermaser consists of two spatially different components at different velocities . they are elongated along a northwest - southeast direction perpendicular to the low - velocity outflow driven by source i. proper motions of the supermaser features with respect to source i are measured toward west and southwest directions , almost parallel to the low - velocity outflow . the flux density and linewidth show an anti - correlation as expected for an unsaturated maser emission . the supermaser is located close to the methylformate ( hcooch ) line and continuum emission peaks in the orion compact ridge detected by alma , atacama large millimeter / submillimeter array . the broader velocity range of the weak hcooch emission at the supermaser position would be an evidence of a shock front . on the other hand , the 321 ghz ho line is not detected at the position of the supermaser . it can be explained qualitatively by one of the theoretical ho excitation models without extraordinary conditions . our results support a scenario that the supermaser is excited in the dense gas interacting with the low - velocity outflow in the compact ridge . the extremely high flux density and its symmetric time variation for rising and falling phases could be explained by a beaming effect during the amplification process rather than changes in physical conditions .

1504.04567

i

[ intro ] in the present work we continue our theoretical studies @xcite of multicharged tungsten ions . the spectroscopic parameters of systems with the open 4d - shell are investigated . extensive interest in highly - charged tungsten ions @xcite is caused by its unique physical properties . metallic tungsten is widely exploited in high - temperature devices , including fusion reactors @xcite . although tungsten is difficult to melt and vaporize , its highly - charged ions emerge in fusion plasma and decrease its temperature . therefore one needs to control the concentration of these ions by monitoring their spectra . unfortunately , the experimental data for the multicharged tungsten ions are very sparse . this fact is very evident from the recent compilation @xcite of the experimental and semi - empirical data for the tungsten ions . it is absolutely clear from that review that the tungsten ions from the rubidium - like to the palladium - like systems , which have an open 4d - shell , are investigated very seldom . for the most ions , only a few levels from the ground @xmath6 configuration are determined . moreover , very few energy levels of the first excited @xmath7 and @xmath8 configurations are determined for some tungsten ions . this situation has encouraged us to perform the theoretical investigation of the spectroscopic parameters for these ions . the calculated data can substantially facilitate experimental studies of the corresponding spectra ; on the other hand , these data can be adopted directly for plasma spectra modelling . the w@xmath0 ion energy spectrum of the @xmath3 , @xmath4 and @xmath5 configurations consists of significantly larger number of energy levels , and the range of possible transition wavelengths is wider compared to the previously studied w@xmath9 @xcite and w@xmath10 @xcite ions . in order to keep the current paper concise , we present only the energy spectra and the characteristics of levels . the remaining spectroscopic parameters will be available from the database adamant ( applicable data of many - electron atom energies and transitions ) which is currently under development . likewise for the ions mentioned above ions , we employ a quasirelativistic ( qr ) approach @xcite with an extensive inclusion of correlation effects to investigate the w@xmath0 ion spectroscopic properties . since application of this approach has produced high - accuracy results for the w@xmath9 and w@xmath10 ions , there is no doubt about its applicability to the tungsten ion of slightly lower ionization degree . in section [ calc ] we provide a description of the adopted calculation method . since this approximation ultimately matches the one applied for the investigation of the w@xmath9 and w@xmath10 spectroscopic data in @xcite , here we provide only a brief summary of our method . produced results are discussed in section [ result ] .

the _ ab initio _ quasirelativistic hartree - fock method developed specifically for the calculation of spectroscopic parameters of heavy atoms and highly charged ions was used to derive spectral data for the multicharged tungsten ion w . the energy level spectra , radiative lifetimes , lande-factors are calculated for the , and configurations of the w ion .

the _ ab initio _ quasirelativistic hartree - fock method developed specifically for the calculation of spectroscopic parameters of heavy atoms and highly charged ions was used to derive spectral data for the multicharged tungsten ion w . the configuration interaction method was applied to include the electron - correlation effects . the relativistic effects were taken into account in the breit - pauli approximation for quasirelativistic hartree - fock radial orbitals . the energy level spectra , radiative lifetimes , lande-factors are calculated for the , and configurations of the w ion .

1111.1603

c

motivated by the fact that our current understanding on the abundances of alkali elements in a - type stars is considerably insufficient , we conducted a comprehensive non - lte analysis to establish the photospheric abundances of na , li , and k for 24 selected sharp - lined a - type stars ( @xmath0 km s@xmath1 , 7000 k @xmath2 10000 k ) , many of which are am stars showing different degree of chemical peculiarity . for this purpose , we primarily invoked the spectra of moderately high - dispersion ( @xmath24 ) and high s / n ratio ( typically a few hundreds ) obtained with boes at boao / korea , though spectra of much higher quality ( @xmath28 and s / n @xmath114 ) secured with hides at oao / japan were additionally used for 7 apparently bright stars ( mostly of early a - type ) . we first carried out spectrum fitting analyses applied to the 61466163 @xmath16 region and derived @xmath18 , @xmath23 , @xmath3(o ) , and @xmath3(fe ) , from which the degree of am characteristics for each star could be confirmed . the abundances of sodium , which were determined by the spectrum fitting method applied to the region comprising na i 5682/5688 lines , revealed a significant trend that @xmath3(na ) tightly scales with @xmath3(fe ) , which means that na becomes enriched similarly to fe in accordance with the degree of am phenomenon . this result should be regarded as important because it seriously contradicts the prediction from the atomic diffusion theory . regarding lithium , @xmath3(li ) derived from the weak li i line at 6708 @xmath16 showed a tendency of @xmath4-dependence for late a - type stars in the sense that @xmath3(li ) gradually decreases from @xmath94 ( @xmath95 k ) to @xmath96 ( @xmath97 k ) , while @xmath3(li ) for early a - type stars ( @xmath14 k ) tends to be around the solar system abundance of @xmath94 . however , several stars apparently deviating from this general trend and showing marked underabundances do exist , though what triggers such a li deficiency is not clear . the abundances of potassium derived from the k i 7699 line revealed a tendency somewhat similar to the case of lithium : an apparent @xmath4-dependence ( and possibly with a weak anti - correlation with am peculiarity ) exists for late - a stars where @xmath3(k ) tend to be mildly subsolar systematically decreasing from @xmath8 ( @xmath9 k ) to @xmath10 ( @xmath11 k ) , whereas those for most early - a stars remain near - solar around @xmath12 5.05.2 . when these observational facts are compared with the theoretical prediction of richer et al . ( 2000 ) or talon et al . ( 2006 ) based on their atomic diffusion calculations , a serious discrepancy is found for na ( almost no anomaly or slightly subsolar tendency is predicted , while an enrichment of na just like fe is suggested from our analysis ) , though the simulated results appear to qualitatively reproduce the general trends observed for li and k. further improvement and development on the theoretical side would be desirably awaited to explain the results concluded in this study , which may serve as important constraints for any theory aiming to account for the origin of chemical anomalies in am stars . this research has made use of the simbad database , operated by cds , strasbourg , france . i. han acknowledges the financial support for this study by kicos through korea ukraine joint research grant ( grant 07 - 179 ) . lee acknowledges the astrophysical research center for the structure and evolution of the cosmos ( arsec , sejong university ) of the korea science and engineering foundation ( kosef ) through the science research center ( src ) program . adelman , s. j. 1996 , mnras , 280 , 130 adelman , s. j. 1988 , mnras , 230 , 671 adelman , s. , & philip , a. g. d. 1996 , mnras , 282 , 1181 anders , e. , & grevesse , n. 1989 , geochim . acta , 53 , 197 burkhart , c. , & coupry , m. f. 1991a , a&a , 249 , 205 burkhart , c. , & coupry , m. f. 1991b , mem . soc . astron . it . , 62 , 91 burkhart , c. , & coupry , m. f. 1995 , mem . astron . it . , 66 , 357 burkhart , c. , & coupry , m. f. 2000 , a&a , 354 , 216 burkhart , c. , coupry , m. f. , faraggiana , r. , & gerbaldi , m. 2005 , a&a , 429 , 1043 caliskan , h. , & adelman , s. j. 1997 , mnras , 288 , 501 coupry , m. f. , & burkhart , c. 1992 , a&as , 95 , 41 esa 1997 , the hipparcos and tycho catalogues , esa sp-1200 , available from nasa - adc or cds in a machine - readable form ( file name : hip_main.dat ) flower , p. j. 1996 , apj , 469 , 355 fossati , l. , bagnulo , s. , landstreet , j. , wade , g. , kochukhov , o. , monier , r. , weiss , w. , & gebran , m. 2008 , a&a , 483 , 891 fossati , l. , bagnulo , s. , monier , r. , khan , s. a. , kochukhov , o. , landstreet , j. , wade , g. , & weiss , w. 2007 , a&a , 476 , 911 fossati , l. , ryabchikova , t. , bagnulo , s. , alecian , e. , grunhut , j. , kochukhov , o. , & wade , g. 2009 , a&a , 503 , 945 gebran , m. , & monier , r. 2007 , in convection in astrophysics , ed . f. kupka , i. w. roxburgh , & k. l. chan , proc . 239 ( cambridge : cambridge university press ) , 160 gebran , m. , & monier , r. 2008 , a&a , 483 , 567 gebran , m. , monier , r. , & richard , o. 2008 , a&a , 479 , 189 gebran , m. , vick , m. , monier , r. , & fossati , l. 2010 , a&a , 523 , 71 girardi , l. , bressan , a. , bertelli , g. , & chiosi , c. 2000 , a&as , 141 , 371 gray , d. f. 2005 , the observation and analysis of stellar photospheres , 3rd ed . ( cambridge : cambridge university press ) , ch.9 grevesse , n. , & noels , a. 1993 , in origin and evolution of the elements , ed . n. prantzos , e. vangioni - flam , & m. cass ( cambridge : cambridge university press ) , 15 hoffleit , d. 1982 , the bright star catalogue , 4th ed . ( new haven , connecticut : yale university observatory ) izumiura , h. 1999 , in proc . 4th east asian meeting on astronomy , observational astrophysics in asia and its future ed . p. s. chen ( kunming : yunnan observatory ) , 77 kamp , i. , & paunzen , e. 2002 , mnras , 335 , l45 kurucz , r. l. 1993 , kurucz cd - rom , no . 13 ( harvard - smithsonian center for astrophysics ) kurucz , r. l. , & bell , b. 1995 , kurucz cd - rom , no . 23 ( harvard - smithsonian center for astrophysics ) landstreet , j. d. , kupka , f. , ford , h. a. , officer , t. , sigut , t. a. a. , silaj , j. , strasser , s. , & townshend , a. 2009 , a&a , 503 , 973 lane , m. c. , & lester , j. b. 1987 , apjs , 65 , 137 lehmann , h. , andrievsky , s. m. , egorova , i. , hildebrandt , g. , korotin , s. a. , panov , k. p. , scholz , g. , & schnberner , d. 2002 , a&a , 383 , 558 monier , r. 2005 , a&a , 442 , 563 napiwotzki , r. , schnberner , d. , & wenske , v. 1993 , a&a , 268 , 653 north , p. , betrix , f. , & besson , c. 2005 , in element stratification in stars , 40 years of atomic diffusion , eds . g. alecian , o. richard , and s. vauclair , eas publication series , vol . 17 , p.333 ( eas ) paunzen , e. 2004 , in the a - star puzzle , proc . 224 , eds . j. zverko , j. @xmath115i@xmath116@xmath117ovsk@xmath118 , s.j . adelman , w.w . weiss ( cambridge : cambridge university press ) , p.443 paunzen , e. , iliev , i. kh . , kamp , i. , & barzova , i. s. 2002 , mnras , 336 , 1030 richer , j. , michaud , g. , & turcotte , s. 2000 , apj , 529 , 338 sadakane , k. 2006 , pasj , 58 , 1023 sadakane , k. , & okyudo , m. 1990 , pasj , 42 , 317 smith , v. v. , lambert , d. l. , & nissen , p. e. 1998 , apj , 506 , 405 takeda , y. 1995 , pasj , 47 , 287 takeda , y. 2008 , mnras , 388 , 913 ( paper i ) takeda , y. , han , i. , kang , d .- i . , lee , b .- , & kim , k .- 2008a , jkas , 41 , 83 takeda , y. , kambe , e. , sadakane , k. , & masuda , s. 2010 . pasj , 62 , 1239 takeda , y. , kang , d .- , han , i. , lee , b .- , & kim , k .- m . 2009 , pasj , 61 , 1165 ( paper ii ) takeda , y. , kato , k. , watanabe , y. , & sadakane , k. 1996 , pasj , 48 , 511 takeda , y. , & kawanomoto , s. 2005 , pasj , 57 , 45 takeda , y. , kawanomoto , s. , & ohishi , n. 2007 , pasj , 59 , 245 takeda , y. , ohkubo , m. , & sadakane , k. 2002 , pasj , 54 , 451 takeda , y. , & sadakane , k. 1997 , pasj , 49 , 367 takeda , y. , sato , b. , & murata , d. 2008b , pasj , 60 , 781 takeda , y. , & takada - hidai , m. 1994 , pasj , 46 , 395 talon , s. , richard , o. , & michaud , g. 2006 , apj , 645 , 634 van leeuwen , f. 2007 , hipparcos , the new reduction of the raw data ( berlin : springer ) varenne , o. , & monier , r. 1999 , a&a , 351 , 247 rrccccrrrrccclhd # & hr # & name & sp.type & @xmath4 & @xmath31 & @xmath18 & @xmath23 & @xmath119 & @xmath120 & @xmath121 & @xmath122 & @xmath123 & remark + + 195725 & 7850 & @xmath124 cep & a7iii & 7816 & 3.74 & 4.45 & 52.0 & 7.60 & 8.47 & 3.27 & 6.35 & 4.81 & + 95418 & 4295 & @xmath35 uma & a1v & 9489 & 3.85 & @xmath1252.50 & 46.8 & 7.73 & 8.45 & ( @xmath1264.34 ) & 6.45 & ( @xmath1265.47 ) & + 27819 & 1380 & @xmath127tau & a7v & 8047 & 3.95 & 3.93 & 46.5 & 7.45 & 8.78 & 3.35 & 6.23 & 4.88 & h + 43378 & 2238 & 2 lyn & a2vs & 9210 & 4.09 & @xmath1252.10 & 45.4 & 7.34 & 8.70 & ( @xmath1264.07 ) & 6.13 & ( @xmath1265.18 ) & + 218396 & 8799 & @xmath128 & a5v & 7091 & 4.06 & @xmath1253.00 & 41.4 & 6.90 & 8.88 & 2.82 & 5.83 & 5.01 & vega - like star + 84107 & 3861 & 15 leo & a2iv & 8665 & 4.31 & 3.57 & 38.1 & 7.50 & 8.62 & ( @xmath1263.44 ) & 6.21 & 4.93 & + 33204 & 1670 & @xmath128 & a5 m & 7530 & 4.06 & 4.14 & 36.4 & 7.76 & 8.46 & 3.11 & 6.47 & 4.72 & h + 204188 & 8210 & @xmath128 & a8 m & 7622 & 4.21 & @xmath1253.90 & 35.3 & 7.50 & 8.74 & ( @xmath1262.77 ) & 6.24 & 4.75 & + 141795 & 5892 & @xmath54 ser & a2vm & 8367 & 4.24 & 4.04 & 34.4 & 7.72 & 8.17 & ( @xmath1263.16 ) & 6.46 & 5.02 & + 173648 & 7056 & @xmath129lyr & a4 m & 8004 & 3.90 & 4.73 & 32.4 & 7.74 & 8.31 & 3.21 & 6.47 & 4.82 & + 27628 & 1368 & 60 tau & a3 m & 7218 & 4.05 & 4.74 & 32.3 & 7.74 & 8.43 & 3.03 & 6.46 & 4.75 & h + 28546 & 1428 & 81 tau & a5 m & 7640 & 4.17 & 3.63 & 28.1 & 7.74 & 8.58 & 3.11 & 6.47 & 4.86 & h + 172167 & 7001 & @xmath25 lyr & a0va & 9435 & 3.99 & 1.85 & 21.9 & 6.96 & 8.63 & ( @xmath1263.84 ) & 6.00 & ( @xmath1265.38 ) & vega - like star + 60179 & 2891 & @xmath25 gem & a1v & 9122 & 3.88 & 2.33 & 19.7 & 7.52 & 8.42 & ( @xmath1263.71 ) & 6.15 & 5.10 & + 95608 & 4300 & 60 leo & a1 m & 8972 & 4.20 & 2.93 & 17.2 & 7.84 & 8.19 & ( @xmath1263.43 ) & 6.46 & 5.32 & + 48915 & 2491 & @xmath25 cma & a1vm & 9938 & 4.31 & @xmath1252.53 & 16.5 & 7.89 & 8.41 & ( @xmath1264.01 ) & 6.52 & ( @xmath1265.19 ) & + 27749 & 1376 & 63 tau & a1 m & 7448 & 4.21 & 3.90 & 12.7 & 7.97 & 8.25 & 3.09 & 6.56 & 4.50 & h + 33254 & 1672 & 16 ori & a2 m & 7747 & 4.14 & 3.07 & 12.2 & 7.99 & 8.18 & ( @xmath1262.53 ) & 6.60 & 4.66 & h + 72037 & 3354 & 2 uma & a2 m & 7918 & 4.16 & 2.48 & 11.6 & 7.89 & 7.98 & ( @xmath1262.55 ) & 6.53 & 4.66 & + 47105 & 2421 & @xmath26 gem & a0iv & 9115 & 3.49 & 1.81 & 10.9 & 7.55 & 8.76 & ( @xmath1263.50 ) & 6.35 & 4.90 & + 27962 & 1389 & 68 tau & a2iv & 8923 & 3.94 & 3.44 & 10.4 & 7.73 & 8.54 & ( @xmath1263.23 ) & 6.46 & 5.22 & h + + 182564 & 7371 & @xmath15 dra & a2iiis & 9125 & 3.80 & 3.43 & 27.3 & 7.83 & 8.48 & 3.47 & 6.65 & 4.98 & + 172167 & 7001 & @xmath25 lyr & a0va & 9435 & 3.99 & 1.90 & 21.9 & 6.97 & 8.63 & 3.21 & 6.05 & 5.13 & vega - like star + 48915 & 2491 & @xmath25 cma & a1vm & 9938 & 4.31 & 2.53 & 16.6 & 7.89 & 8.42 & ( @xmath1263.18 ) & 6.59 & 5.15 & + 47105 & 2421 & @xmath26 gem & a0iv & 9115 & 3.49 & 2.49 & 11.1 & 7.48 & 8.74 & 3.17 & 6.33 & 5.19 & + 189849 & 7653 & 15 vul & a4iii & 7870 & 3.62 & 5.16 & 10.7 & 7.34 & 8.65 & 3.03 & 6.31 & 4.60 & + 27962 & 1389 & 68 tau & a2iv & 8923 & 3.94 & 3.99 & 10.5 & 7.69 & 8.54 & 3.17 & 6.46 & 5.10 & h + 214994 & 8641 & @xmath21 peg & a1iv & 9453 & 3.64 & 3.07 & 6.0 & 7.63 & 8.52 & ( @xmath1262.94 ) & 6.46 & 4.74 & + note . + in columns 1 through 6 are given the hd number , hr number , star name ( with constellation ) , spectral type ( taken from hoffleit 1982 ) , effective temperature ( in k ) , and logarithmic surface gravity ( in cm s@xmath130 ) . columns 7 through 10 show the results derived from 61466163 @xmath16 region fitting : the microturbulent velocity ( in km s@xmath1 ) , projected rotational velocity ( in km s@xmath1 ) , ( lte ) abundance of fe , and ( non - lte ) abundance of o. the non - lte abundances of li , na , and k finally resulting from this investigation are presented in columns 1113 . all abundance results are expressed in the usual normalization of @xmath3(h ) = 12.00 . in each of the boao ans oao samples , the objects are arranged in the descending order of @xmath131 . in the remark in column 14 , hyades cluster stars are denoted with `` h '' . + @xmath125regarding these @xmath18 values , literature values were adopted unlike the others , because the @xmath18-determination from the 61466163 @xmath16 region fitting did not work successfully . see subsection 2.3 for more details . cclrldesig . & species & @xmath132 & @xmath133 ( ev ) & @xmath134 + li 6708 & li i & 6707.756 & 0.00 & @xmath135 + & li i & 6707.768 & 0.00 & @xmath136 + & li i & 6707.907 & 0.00 & @xmath137 + & li i & 6707.908 & 0.00 & @xmath138 + & li i & 6707.919 & 0.00 & @xmath139 + & li i & 6707.920 & 0.00 & @xmath137 + o 6156 & o i & 6155.961 & 10.74 & @xmath140 + & o i & 6155.971 & 10.74 & @xmath141 + & o i & 6155.989 & 10.74 & @xmath138 + o 6157 & o i & 6156.737 & 10.74 & @xmath142 + & o i & 6156.755 & 10.74 & @xmath137 + & o i & 6156.778 & 10.74 & @xmath143 + o 6158 & o i & 6158.149 & 10.74 & @xmath144 + & o i & 6158.172 & 10.74 & @xmath145 + & o i & 6158.187 & 10.74 & @xmath146 + na 5682 & na i & 5682.633 & 2.10 & @xmath147 + na 5688 & na i & @xmath148 & 2.10 & @xmath149 + na 6154 & na i & 6154.226 & 2.10 & @xmath150 + na 6160 & na i & 6160.747 & 2.10 & @xmath151 + si 5684 & si i & 5684.484 & 4.95 & @xmath152 + si 5688 & si ii & 5688.817 & 14.19 & + 0.40 + si 6155 & si i & 6155.134 & 5.62 & @xmath153 + s 7696 & s i & 7696.758 & 7.87 & @xmath154 + k 7699 & k i & 7698.974 & 0.00 & @xmath155 + ca 6162 & ca i & 6162.173 & 1.90 & + 0.10 + sc 5684 & sc ii & 5684.202 & 1.51 & @xmath141 + fe 5686 & fe i & 5686.524 & 4.55 & @xmath156 + fe 6147 & fe ii & 6147.741 & 3.89 & @xmath157 + fe 6149 & fe ii & 6149.258 & 3.89 & @xmath157 + fe 6150 & fe ii & 6150.098 & 11.45 & @xmath158 + fe 6157 & fe i & 6157.725 & 4.08 & @xmath151 + fe 6705 & fe i & 6705.101 & 4.61 & @xmath159 + fe 6708 & fe ii & 6708.885 & 10.91 & @xmath160 + ni 5682 & ni i & 5682.198 & 4.11 & @xmath161 + note . + all data are were taken from kurucz & bell s ( 1995 ) compilation , except for those of li i which were adopted from smith et al . ( 1998 ) as in takeda and kawanomoto ( 2005 ) . + @xmath125since this line comprises two close components of stronger @xmath162 ( at 5688.205 @xmath16 ) and weaker @xmath163 ( at 5688.194 @xmath16 ) , we adopted @xmath164 as the sum of these two . regarding the li i lines , we considered only the lines of @xmath165li , since we neglected @xmath166li in our analysis .

the abundances of alkali elements ( li , na , and k ) were determined from the li i 6708 , na i 5682/5688 , and k i 7699 lines by taking into account the non - lte effect for 24 sharp - lined a - type stars ( km s , 7000 k 10000 k , many showing am peculiarities to different degrees ) , based on high - dispersion and high - s / n spectral data secured at boao ( korea ) and oao ( japan ) . we found a significant trend that(na ) tightly scales with(fe ) irrespective of , which means that na becomes enriched similarly to fe in accordance with the degree of am peculiarity . the abundances of potassium also revealed an apparent-dependence in the sense that(k ) in late - a stars tends to be mildly subsolar ( possibly with a weak anti - correlation with(fe ) ) systematically decreasing from ( k ) to ( k ) , while those for early - a stars remain near - solar around 5.05.2 . these observational facts may serve as important constraints for any theory aiming to explain chemical anomalies of a - type stars .

the abundances of alkali elements ( li , na , and k ) were determined from the li i 6708 , na i 5682/5688 , and k i 7699 lines by taking into account the non - lte effect for 24 sharp - lined a - type stars ( km s , 7000 k 10000 k , many showing am peculiarities to different degrees ) , based on high - dispersion and high - s / n spectral data secured at boao ( korea ) and oao ( japan ) . we found a significant trend that(na ) tightly scales with(fe ) irrespective of , which means that na becomes enriched similarly to fe in accordance with the degree of am peculiarity . regarding lithium ,(li ) mostly ranges between and ( i.e. , almost the same as or slightly less than the solar system abundance of 3.3 ) with a weak decreasing tendency with a lowering of at k , though several stars exceptionally show distinctly larger depletion . the abundances of potassium also revealed an apparent-dependence in the sense that(k ) in late - a stars tends to be mildly subsolar ( possibly with a weak anti - correlation with(fe ) ) systematically decreasing from ( k ) to ( k ) , while those for early - a stars remain near - solar around 5.05.2 . these observational facts may serve as important constraints for any theory aiming to explain chemical anomalies of a - type stars .

1305.3174

i

let @xmath6 be a @xmath7-dimensional closed , connected , oriented manifold with an effective @xmath8-dimensional ( i.e. , half - dimensional ) torus @xmath9-action . we call @xmath6 ( or @xmath10 ) a _ torus manifold _ if @xmath11 ( see @xcite ) , where @xmath12 is the set of fixed points . a toric manifold ( i.e. , a non - singular , complete toric variety viewed as a complex analytic space ) with the restricted @xmath9-action is a typical example of torus manifolds . recall that a toric manifold is a complex @xmath13-manifold with the dense orbit ( see @xcite , @xcite ) , and @xmath9 is the maximal compact subgroup of @xmath13 . a fundamental result of toric geometry tells us that there is a one - to - one correspondence between toric manifolds and combinatorial objects called fans . thus , topological ( more precisely , geometric ) invariants of toric manifolds can be described in terms of combinatorial invarinats of fans , such as equivariant cohomology rings , equivariant characteristic classes and other topological invariants . in 2003 , hattori - masuda introduced a torus manifold as the topological generalization of a toric manifold in @xcite . they also introduced the combinatorial objects , called multi - fans ( see @xcite , @xcite ) , and computed topological invariants ( such as equivariant characteristic classes or todd genus for unitary torus manifolds ) in terms of multi - fans . however , unlike toric geometry , a multi - fan does not contain enough information to determine some topological invariants of torus manifolds ( e.g. equivariant cohomology ) . so , in 2007 , maeda - masuda - panov introduced another combinatorial objects , called torus graphs motivated by gkm graphs introduced by guillemin - zara in @xcite . the combinatorial information of torus graphs can completely determine the equivariant cohomology rings of torus manifolds with vanishing odd degree cohomology , i.e. , @xmath14 ( in this paper , we only consider the integer coefficient ) , see @xcite , @xcite ( and also see section [ sect3 ] in this paper about torus graphs ) . however , in general , there is no one - to - one correspondence between torus manifolds with @xmath2 and torus graphs . so , we are naturally led to ask the following two questions : ( 1 ) which subclasses of torus manifolds are completely determined by combinatorial objects ( like multi - fans or torus graphs ) ; ( 2 ) if we find such a subclass of torus manifolds , how we can classify such torus manifolds . several mathematicians have answered to the 1st question ; for example , davis - januszkiewicz @xcite for the subclass called _ quasitoric manifolds _ ( see @xcite or section [ sect4.3 ] in this paper ) , ishida - fukukawa - masuda @xcite for the subclass called _ topological toric manifolds _ , and wiemeler for the class of simply connected @xmath0-dimensional torus manifolds with @xmath2 in @xcite ( see theorem [ wi2 ] ) . the aim of this paper is to answer to the 2nd question for the class of simply connected @xmath0-dimensional torus manifolds with @xmath2 by using torus graphs . let us briefly recall the classification results for torus manifolds with lower dimensions . if @xmath15 acts on a compact @xmath16-dimensional manifold @xmath6 , then @xmath6 is the @xmath16-dimensional sphere @xmath5 , the @xmath16-dimensional real projectiove space @xmath17 or the @xmath16-dimensional torus @xmath18 . because @xmath11 and @xmath6 is oriented , @xmath6 must be equivariantly diffeomorphic to @xmath5 with @xmath15-action ( also see @xcite ) . when @xmath19 . by orlik - raymond s theorem in @xcite , we have the following fact : [ or - thm ] let @xmath6 be a @xmath20-dimensional simply connected torus manifold . then , @xmath6 is equivariantly diffeomorphic to the @xmath20-sphere @xmath21 or an equivariant connected sum of copies of complex projective spaces @xmath22 , @xmath23 ( reversed orientation ) or hirzebruch surfaces @xmath24 . here , in theorem [ or - thm ] , a hirzebruch surface @xmath24 ( @xmath25 ) is a manifold which is defined by the projectivization of the complex @xmath16-dimensional vector bundle @xmath26 over @xmath27 , where @xmath28 is the tautological and @xmath29 is the trivial complex line bundles over @xmath27 . in this paper , we prove that an orlik - raymond type theorem in theorem [ or - thm ] also holds for simply connected @xmath0-dimensional torus manifolds with @xmath2 . before we state our main results , we introduce the result for non - simply connected torus manifolds . as one of the consequences of masuda - panov s theorem ( see theorem [ 2-equiv ] in section [ sect2.2 ] ) , we have the following proposition ( also see @xcite ) : [ wiemeler ] let @xmath30 be a @xmath0-dimensional torus manifold with @xmath31 ( might not be simply connected ) . then , there are a simply connected , @xmath0-dimensional torus manifold @xmath6 with @xmath2 and a homology @xmath1-sphere @xmath32 such that @xmath33 up to equivariantly diffeomorphism . here , in proposition [ wiemeler ] , the product manifold @xmath34 is the product of @xmath32 and the @xmath1-dimensional torus @xmath35 with the free @xmath36-action on the @xmath16nd factor , and the symbol @xmath37 represents the equivariant gluing along two free orbits of @xmath6 and @xmath34 . because the fundamental groups @xmath38 and @xmath39 are isomorphic in proposition [ wiemeler ] , @xmath30 is simply connected if and only if @xmath32 is simply connected , i.e. , the standard sphere . our main theorem is a classification of simply connected torus manifolds appeared in proposition [ wiemeler ] . [ main1 ] let @xmath6 be a simply connected @xmath0-dimensional torus manifold with @xmath2 . then , @xmath6 is equivariantly diffeomorphic to the @xmath0-sphere @xmath40 or obtained by an equivariant connected sum of copies of @xmath0-dimensional quasitoric manifolds or @xmath21-bundles over @xmath41 equipped with the structure of a torus manifold . this type of classification , i.e. , classification by equivariant connected sum , may be regarded as the @xmath0-dimensional analogue of orlik - raymond s classification in theorem [ or - thm ] . so , in this paper , we call this theorem an _ orlik - raymond type classification _ ( also see the papers @xcite and @xcite ) . in the paper @xcite , izmestiev proves an orlik - raymond type classification for some class of @xmath1-dimensional small covers ( i.e. , the real analogue of quasitoric manifolds , see section [ sect4.2 ] ) , called a linear model . the organization of this paper is as follows . in section [ sect2 ] , we recall the basic facts about torus manifolds . in section [ sect3 ] , we recall a torus graph . in particular , corollary [ key2 ] is the key fact to prove theorem [ main1 ] . in section [ sect4 ] , we introduce the torus graphs of @xmath3 , quasitoric manifolds and @xmath4-bundles over @xmath5 . these torus graphs will be the basic graphs to classify simply connected @xmath0-dimensional torus manifolds with @xmath2 . in section [ sect5 ] , we introduce the `` oriented '' torus graphs and translate the equivariant connected sum around fixed points of torus manifolds to the connected sum around vertices of oriented torus graphs . in section [ sect6 ] and [ sect7 ] , we prove theorem [ main1 ] . the brief outline of the proof is as follows . due to corollary [ key2 ] , there is a one - to - one corresponds between @xmath0-dimensional simply connected torus manifolds with @xmath2 and @xmath1-valent torus graphs . therefore , in order to prove theorem [ main1 ] , it is enough to prove that an ( oriented ) torus graph can be decomposed into basic torus graphs in section [ sect4 ] by the connected sum . we prove this by using combinatorial arguments .

the aim of this paper is to classify simply connected-dimensional torus manifolds with vanishing odd degree cohomology . it is shown that there is a one - to - one correspondence between equivariant diffeomorphism types of these manifolds and-valent labelled graphs , called torus graphs introduced by maeda - masuda - panov . using this correspondence and combinatorial arguments , we prove that a simply connected-dimensional torus manifold with is equivariantly diffeomorphic to the-dimensional sphere or an equivariant connected sum of copies of-dimensional quasitoric manifolds or-bundles over .

the aim of this paper is to classify simply connected-dimensional torus manifolds with vanishing odd degree cohomology . it is shown that there is a one - to - one correspondence between equivariant diffeomorphism types of these manifolds and-valent labelled graphs , called torus graphs introduced by maeda - masuda - panov . using this correspondence and combinatorial arguments , we prove that a simply connected-dimensional torus manifold with is equivariantly diffeomorphic to the-dimensional sphere or an equivariant connected sum of copies of-dimensional quasitoric manifolds or-bundles over .

nucl-th0505007

r

for the wave functions of @xmath2b that form the basis of the cdcc expansion of the three - body system we make the following assumptions . we assume that the ground state wave function of @xmath2b , with the @xmath128-component @xmath143 of the total spin @xmath222 of it , is given by @xmath223_{2m_0 } + w_2 \left[i y_1(\hat{\bf r } ) \otimes \zeta_2 \right]_{2m_0 } \ } \nonumber \\ & & \times f_{\rm r}^{(0)}(r ) \nonumber \\ & \equiv&\ ; w_1 f_{1,m_0}^{(0)}({\bf r})+ w_2 f_{2,m_0}^{(0)}({\bf r } ) \label{f0}\end{aligned}\ ] ] in the channel spin representation , neglecting the @xmath224 components . the values of the coefficients @xmath225 and @xmath226 are obtained from the result of the microscopic calculation @xcite of @xmath2b , @xmath227 , where @xmath228 ( @xmath229 ) is the anc in the proton spin - orbit coupling representation corresponding to the @xmath230 ( 3/2 ) state . we further assume the effective @xmath7-@xmath0be interaction for the ground state of @xmath2b , @xmath231 , to be independent of @xmath125 , hence the same radial dependence @xmath232 of the @xmath233 and @xmath234 components in eq . ( [ f0 ] ) . this assumption is valid since only the tail region , @xmath235 , of @xmath103 contributes to the @xmath2b breakup process concerned . the wave function of the @xmath7-@xmath0be scattering state with outgoing scattered waves is given by @xmath236 where @xmath237 is the incident wave with definite channel spin @xmath125 and its @xmath128-component @xmath238 , @xmath239 is the incident energy in the c.m . frame of the @xmath7-@xmath0be system , and @xmath240 is the incident momentum . the wave function with incoming scattered waves @xmath241 corresponding to @xmath242 used below is defined by @xmath243 . we assume that @xmath244 has no tensor force component . we consider the breakup of @xmath2b to its scattering states at low @xmath239 , and truncate the modelspace by @xmath245 mev . in the experiment we analyze , however , the cross section is measured for @xmath246 in the range of 500 kev @xmath247 kev , and it turns out that only coupling of those states with @xmath239 much lower than 10mev need be taken into account as described in sec . [ ress17 ] , for which only s - waves are affected by the nuclear part of @xmath244 . all the higher partial waves have negligible amplitude inside its range because of the coulomb and centrifugal barriers and there have no coupling with the s - waves . therefore , all the angular momenta @xmath124 , @xmath125 and @xmath126 are conserved in @xmath248 . the channel spin @xmath125 is conserved also in s - waves since @xmath249 that is a good quantum number . thus , one sees that @xmath242 is the pure state of @xmath125 , while @xmath124 and @xmath126 are mixed as in the incident wave @xmath250 . it should be noted , however , that @xmath251 for the s - waves depends on @xmath125 as is evident from the large @xmath125-dependence of the s - wave @xmath7-@xmath0be scattering lengths : @xmath252 fm and @xmath253 fm @xcite . furthermore , it turns out that the spin - dependent part of the @xmath7-@xmath4pb optical potential has no effect on the resulting elastic cross section at forward angles . thus , the channel spin @xmath125 is conserved during the breakup process of @xmath2b by the @xmath4pb target @xcite . under these circumstances , the @xmath125-dependent 3-body @xmath28-matrix element in actual cdcc calculation , @xmath254 , is given by @xmath255 where @xmath256 is the wave matrix given in eq . ( [ wavematrix ] ) . the unpolarized @xmath2b breakup cross section calculated by cdcc , @xmath257 , is given by @xmath258 where @xmath259 ( @xmath260 ) is the @xmath128-component of the spin of @xmath7 ( @xmath0be ) and the orthonormality of the clebsch - gordan coefficient is used . we compare @xmath257 with the unpolarized cross sections measured by riken experiment @xcite . in the calculation of @xmath261 and @xmath262 , we use an @xmath126-independent @xmath7-@xmath0be effective interaction @xmath263 as mentioned above . then , the states of @xmath2b with fixed @xmath125 and @xmath124 and different values of @xmath126 are degenerate , which greatly simplifies numerical calculation . the value of @xmath119 in eq . ( [ s170 ] ) corresponding to the spin - dependent anc analysis is @xcite @xmath264 fm . for @xmath231 , the single - particle potential of esbensen and bertsch ( eb ) @xcite is used , except that we neglect the spin - orbit part of the potential and adjust the depth of the central potential to reproduce the separation energy of @xmath7 , 137 kev . the scattering states for the p - waves are also calculated with this @xmath231 . for d- and f - states with both @xmath233 and @xmath234 , we use the potential of barker @xcite . for the s - state in the @xmath234 channel , we use the potential of barker that gives the s - wave @xmath7-@xmath0be scattering length @xmath265 of @xmath266 fm . for the s - state with @xmath233 , we change the depth of the potential of barker to 25.7 mev so that the resulting scattering length @xmath267 is 25 fm . as for the distorting potential between @xmath7 ( @xmath0be ) and @xmath4pb we adopt the global optical potential by koning and delaroche @xcite ( cook @xcite ) . we neglect the spin - orbit parts of the @xmath7-@xmath4pb potential . the multipoles for nuclear and coulomb coupling - potentials are included up to @xmath268 . the discretized - continuum states of @xmath2b are constructed by the average method @xcite . the maximum excitation energy of @xmath2b is 10 mev and 10 , 20 , 10 , and 5 discretized - continuum states are taken for the @xmath269 , 0 , 2 , and 3 states , respectively . the resulting number of scattering - channels is 138 . the maximum values of @xmath49 , @xmath46 , and @xmath27 are , respectively , 200 fm , 1000 fm , and 12000 . the modelspace described above turns out to give good convergence of the resulting breakup cross sections . b breakup cross section integrated over @xmath239 in the range of 500750 kev , as a function of @xmath65 . the dotted , dash - dotted , and solid lines represent the results of the hybrid calculation of cdcc and e - cdcc with @xmath270 , 1000 , and 1500 , respectively . the result of e - cdcc , i.e. @xmath271 , is also shown by the dashed line . , scaledwidth=45.0% ] figure 2 shows the convergence of the hybrid calculation with cdcc and e - cdcc for the breakup cross section of @xmath2b by @xmath4pb at 52 mev / nucleon . the cross section integrated over the excitation energy of @xmath2b measured from the @xmath7+@xmath0be threshold energy , @xmath239 , from 500 kev to 750 kev is plotted as a function of @xmath65 . the dashed line is the result of the e - cdcc calculation ( @xmath271 ) and the dotted , dash - dotted , and solid lines correspond to the hybrid calculation with @xmath270 , 1000 , and 1500 , respectively . the figure shows that the hybrid calculation converges with @xmath272 . the difference between the dash - dotted and solid lines is only less than about 1% in magnitude . thus , we regard the hybrid calculation of cdcc and e - cdcc with @xmath272 as the fully quantum - mechanical cdcc calculation . b breakup cross sections with ( solid line ) and without ( dashed line ) the resolution and efficiency of the measurement @xcite taken into account . the experimental data are taken from ref . ( b ) decomposition of the smeared @xmath2b breakup cross section into the s- ( dashed line ) , p- ( dotted line ) , d- ( dash - dotted line ) , and f - state ( dash - two - dotted line ) breakup components . , scaledwidth=45.0% ] one sees in fig . 2 the oscillation of the cross section at forward angles around 2@xmath273 , which turns out to be due to the interference between nuclear and coulomb breakup - amplitudes . therefore , it can be concluded that nuclear interactions affect the breakup cross section even at very forward angles . however , as one sees below , this oscillation is not observed in actual experimental data because of the limit of the resolution of @xmath65 in the measurement . figure 3 shows the comparison between cdcc calculation and the experimental data for the @xmath2b breakup . in order to take account of the experimental resolution and efficiency , the theoretical result has been smeared out by using the filtering table @xcite provided by the authors of ref . the upper panel shows the filtering effect on the cross section calculated with cdcc , where the solid and dashed lines represent the results obtained with and without the smearing procedure . in the lower panel , the smeared total breakup cross section is decomposed into the s- ( dashed line ) , p- ( dotted line ) , d- ( dash - dotted line ) , and f - state ( dash - two - dotted line ) breakup components of @xmath2b . one sees the smeared result of cdcc well agrees with the experimental data at forward angles ( @xmath120 ) , while it underestimates the data at backward angles . the lower panel shows the importance of the p - state breakup for @xmath274 , which implies that nuclear breakup is significant in this angular region . thus , careful description of the p - state @xmath2b wave function , the resonance structures of it in particular , will be necessary to reproduce the experimental data at backward angles . the underestimation there may be due also to dynamical roles played by the excited - core component in @xmath2b , @xmath0be(1/2@xmath275)@xmath276(3/2@xmath275 ) , that is neglected in the present work as discussed in sec . although further study in this line will be very interesting , it is beyond the scope of the present paper . additionally , the filtering table used was made with assuming the s - state breakup of @xmath2b . thus , quantitative comparison between the calculation and the experimental data , to extract @xmath3 with high accuracy , can only be done in the region where the s - state breakup cross section is dominant . therefore , below we use the data for @xmath277 to determine @xmath278 by @xmath279 where @xmath257 is given by eq . ( [ sigcal ] ) and @xmath280 is the corresponding experimental data . -fit of the breakup cross section calculated with the @xmath2b single - particle potential of esbensen and bertsch ( eb ) @xcite . the solid line is the same as that in each panel in fig . 3 but multiplied by the spectroscopic factor @xmath281 . the result with @xmath282 is also shown by the dashed line for comparison . for the eight data points below @xmath64 , which are used in the fitting procedure , we have put the horizontal bar that represents the resolution of @xmath65 @xcite of the measurement . , scaledwidth=45.0% ] figure 4 shows the result of the @xmath283-fit of the theoretical calculation to the experimental data . the solid line is the same as that in each panel in fig . 3 but multiplied by the spectroscopic factor @xmath281 . the dashed line represents the result before being fitted , i.e. with @xmath282 . each horizontal bar put on the eight data points below @xmath64 does not represent a statistical error but it shows the range of @xmath65 in which the breakup cross sections contribute to each data point @xcite . the value of @xmath283 per datum obtained is 8.5 . although the quality of the fit is not good , it should be noted that estimation of error - propagation in the present case , i.e. comparison between smeared experimental data and a smeared numerical result , is very complicated ; the value of @xmath283 per datum shown above takes account of no error with respect to @xmath65 . the value of @xmath110 in eq . ( [ alpha ] ) for the eb @xmath2b wave - function is 0.704 @xmath284 . with the values of @xmath102 and @xmath110 , the anc @xmath39 is obtained from eq . ( [ c ] ) as @xmath285 @xmath284 . one can then determine @xmath3 by inserting this result into eq . ( [ s170 ] ) , together with @xmath286 fm , i.e. @xmath287 ev b. in the next subsection we quantitatively evaluate uncertainties of the extracted @xmath3 . first , we evaluate the uncertainty of @xmath3 that comes from the use of the anc method , just in the same way as in refs . we show in fig . 5 the result of cdcc calculation with the p - state single - particle potential of @xmath2b by kim _ et al . @xcite ( the dashed line ) and that multiplied by @xmath288 ( the solid line ) ; the latter agrees with the result shown in fig . 4 within 1% . one sees that @xmath102 indeed depends on the p - state potential . b ; the spectroscopic factor @xmath102 obtained is 0.867 . the result with kim s potential before @xmath283-fitting , namely with @xmath282 , is also shown by the dashed line for comparison . , scaledwidth=45.0% ] actually , @xmath110 in eq . ( [ alpha ] ) for kim s potential is 0.796 @xmath284 , which is quite different from the value for the eb potential , 0.704 @xmath284 , because of the difference in the geometry of the two potentials of about 20% . on the contrary , the value of @xmath39 in eq . ( [ c ] ) calculated with kim s potential is 0.741 @xmath284 that agrees very well with the result obtained with the eb potential shown in sec . [ ress17 ] . this result shows that the anc method works with very high accuracy in the present analysis , i.e. the error of the anc method is negligible . second , we estimate the effect of ambiguity of the distorting potentials used in the cdcc calculation on the obtained @xmath3 . for this purpose we use alternative optical potentials for @xmath7-@xmath4pb and @xmath0be-@xmath4pb . for the @xmath7-@xmath4pb potential , we modify the parameter set of koning and delaroche so that the calculated elastic cross section without spin - orbit terms reproduces the one obtained with the full components of the optical potential . the parameter set thus obtained is @xmath289 mev , @xmath290 mev , and @xmath291 mev , with the same notation as in ref . @xcite ; all other parameters are not changed . for the @xmath0be-@xmath4pb potential , we use a single - folding model with the nucleon-@xmath4pb potential of koning and delaroche , neglecting the spin - orbit terms . the density distribution of @xmath0be is assumed to be of the gaussian form with the range that reproduces the rms matter radius of @xmath0be of 2.48 fm @xcite . the difference between the results calculated with the original and alternative optical potentials is found to be negligibly small ( not shown ) . we conclude , therefore , that the error of @xmath3 that comes from the ambiguity of the distorting potentials in the present case is negligibly small . b breakup cross section on the s - state single - particle potentials of @xmath2b for the @xmath233 and @xmath234 channels . the solid line represents the result with the choice of the potentials that corresponds to the s - wave @xmath7-@xmath0be scattering lengths @xmath292 . the dashed ( dotted ) line shows the result with the s - state potentials corresponding to @xmath293 ( @xmath294 ) . , scaledwidth=45.0% ] finally , we estimate the uncertainty of @xmath3 due to the ambiguity of the s - state single - particle potentials of @xmath2b for the @xmath233 and @xmath234 channels by changing the depth of the potential for the @xmath233 ( @xmath234 ) channel ranging from 23.3 mev ( 52.8 mev ) to 30.5 mev ( 57.6 mev ) , which gives the range of the resulting s - wave @xmath7-@xmath0be scattering length @xmath267 ( @xmath265 ) from @xmath295 fm ( @xmath296 fm ) to @xmath297 fm ( @xmath298 fm ) ; these values of @xmath267 and @xmath265 are within the range of errors of the experimental values of them @xcite . in fig . 6 the solid , dashed , and dotted lines represent the results with the s - state potentials corresponding to @xmath299 , @xmath300 , and @xmath301 , respectively . one sees the breakup cross section slightly depends on the choice of the s - state potentials of @xmath2b ; the resulting @xmath3 is found to vary from 20.3 ev b to 21.9 ev b. thus , we evaluate the error of @xmath3 to be @xmath302/@xmath303 . summarizing the discussion given above , the result of the present paper is as follows . the central value of @xmath3 is 20.9 ev b. the theoretical error of the extracted @xmath3 concerned with the s - wave @xmath7-@xmath0be scattering length is @xmath302/@xmath303 . after including the 8.4% systematic experimental error , we obtain @xmath304 the main result of the present paper is @xmath305 ( theo ) @xmath306 ( expt ) ev b derived from @xmath4pb(@xmath2b , @xmath5be)@xmath4pb at 52 mev / nucleon . this value is significantly larger than @xmath23 ev b @xcite obtained in the previous analysis of the same experiment with the first - order perturbation theory . in order to clarify the reason for the difference , we discuss roles of nuclear interaction , e2 transitions , and higher - order processes . in fig . 7 the solid line is the same as in the upper panel in fig . 3 that shows the result of full cdcc . the dashed line corresponds to the calculation without breakup components of nuclear coupling potentials . it should be noted that their diagonal components are included in the calculation to take account of the absorption of the flux of the incident particle by the target nucleus . one sees that the dashed line agrees with the solid line below @xmath307 but deviates from it for @xmath308 . as a result , the value of @xmath3 obtained , @xmath309 ev b , is smaller than @xmath305 ( theo ) @xmath306 ( expt ) ev b obtained with the full cdcc calculation mentioned above . the dash - dotted line in fig . 7 represents the result of first - order iterative solutions of cdcc , designated as one - step cdcc , without nuclear breakup , including only @xmath310 ( e1 ) component of the coulomb interaction ; this calculation is essentially the same as the first - order perturbation theory ( virtual photon theory ) used in the previous analysis of the experimental data @xcite . it overestimates the solid line above 1.5@xmath273 and the resulting value of @xmath3 is @xmath311 ev b , which agrees well with the value @xmath8 ev b obtained in ref . @xcite . if one includes the @xmath312 ( e2 ) component in the one - step cdcc calculation of coulomb breakup , the dotted line in fig . 7 is obtained ; the coupling potentials with @xmath312 are artificially multiplied by 0.7 , following the analysis of the msu data @xcite . one sees from fig . 7 that inclusion of the reduced e2 component somewhat increases the breakup cross section , which results in further decrease of @xmath3 to @xmath313 ev b. this result is consistent with the conclusion of ref . @xcite , in which @xmath314 ev b was derived with first - order perturbation theory including both e1 and the reduced e2 components . if the e2 component is not scaled , the resulting value of @xmath3 is 16.7 ev b. this value is about 20% less than the result of full cdcc , 20.9 ev b. the difference is due to the nuclear and higher - order coulomb processes since the coupling potentials with @xmath315 are found to have little effect on the total breakup - cross - section at @xmath277 . thus , description of @xmath2b breakup process with nuclear and coulomb breakup processes of both the e1 and e2 transitions and higher - order processes is a key to solve a puzzle recognized so far of the discrepancy between the values of @xmath3 extracted from direct @xmath7-capture reactions , @xmath10 ( expt ) @xmath11 ( theo ) ev b , and indirect @xmath2b dissociation experiments . in order to clarify the role of these components in @xmath2b breakup reaction in general , it is necessary to carry out analyses to wider range of data , such as those measured at msu @xcite and gsi @xcite , including the data on other quantities than that dealt with in the present work . analysis of parallel momentum ( @xmath316 ) distribution of @xmath0be - fragment after breakup of @xmath2b is particularly important , since the role of e2 component was determined from it @xcite . in the analysis in ref . @xcite the result of first - order perturbation theory with an adjustable parameter was compared with cdcc calculation that is essentially the same as in the present paper . because of the agreement of the two results , it was concluded that higher order processes were unimportant without quantitative evaluation of the nuclear and higher - order coulomb processes as done in the present work . actually , the contribution is about 20% of the total as already described . a cdcc analysis of the @xmath316 distribution has been done by mortimer _ et al . _ @xcite , where the dependence of the calculated result on the strength of the coulomb @xmath312 ( e2 ) coupling potentials was discussed . they found that the e2 potentials must be multiplied by 1.6 to reproduce the experimental data , although the origin of the enhancement was not clear . therefore , further investigation of the accuracy of the enhancement factor 1.6 seems necessary . unfortunately , filtering table for the msu experiment is not available to the present authors . at this stage , therefore , we can quantitatively extract @xmath3 with cdcc and the anc method only from the @xmath2b breakup experiment done at riken . nevertheless , comparison of our pure theoretical result with that shown in ref . @xcite is very interesting , which will be a subject of our future work . in this subsection we report on our application of the anc method to the @xmath7-capture reaction , @xmath0be(@xmath1)@xmath2b , at energies of 116362 kev @xcite . we assume direct capture of @xmath7 by @xmath0be to the ground state of @xmath2b by a pure e1 transition . a simple potential - model is assumed for the bound and the scattering states of the @xmath7+@xmath0be system , using the single - particle potential of sec . [ input ] . the s- and d - state components in the initial scattering - state wave - function are taken into account , and the intrinsic spins of @xmath7 and @xmath0be are included in the channel spin representation described in sec . [ input ] . in fig . 8 the solid line shows the calculated @xmath317 as a function of the incident energy @xmath318 of the reaction in the c.m . frame of the @xmath7-@xmath0be system . the plotted @xmath21 has been multiplied by the spectroscopic factor @xmath319 obtained by the @xmath283-fit to the data below 362 kev . as a function of the incident energy @xmath318 of the reaction in the c.m . frame of the @xmath7-@xmath0be system . the solid line is the result of the calculation with a simple potential model , multiplied by @xmath319 . the experimental data are taken from ref . @xcite . , scaledwidth=43.0% ] the calculated @xmath21 is not reliable at high energies , say @xmath320 kev , since the inner part of the @xmath2b wave function plays an important role . at low energies , however , the anc method works very well and a reliable value of the anc @xmath39 , and consequently @xmath3 , can be derived from the @xmath283-fitting procedure . the value of @xmath3 thus obtained is 21.7 ev b. uncertainties of the @xmath3 are evaluated in the same way as in sec . [ errors17 ] and found to be @xmath321/@xmath322 ev b , almost all of which is due to the ambiguity of the s - state potentials for the @xmath233 and @xmath234 channels of the @xmath7-@xmath0be system . including the 2.3% systematic experimental error , we obtain the following result : @xmath323 ( theo ) @xmath324 ( expt ) ev b. this result is consistent with both the value extracted from @xmath2b dissociation , @xmath305 ( theo ) @xmath306 ( expt ) ev b , described in the previous subsections , and the result obtained in ref . @xcite , @xmath10 ( expt ) @xmath11 ( theo ) ev b , although no evaluation of the ambiguity due to the uncertainty of the s - wave @xmath7-@xmath0be scattering lengths , as the one described in sec . [ errors17 ] , is made in ref .

the main result of the present paper is ev b. the error consists of 8.4% experimental systematic error and the error due to the ambiguity in the s - wave-be scattering length . this value of differs from the one extracted with the first - order perturbation theory including coulomb breakup by dipole transitions : ev b. it turns out that the difference is due to the inclusion of the nuclear and coulomb - quadrupole transitions and multi - step processes of all - order in the present work . thus , the agreement between the values of obtained from directbe()b and indirectb - breakup measurements is significantly improved .

the astrophysical factor forbe()b at zero energy , , is determined from an analysis ofpb(b ,be)pb at 52 mev / nucleon by means of the method of continuum - discretized coupled - channels ( cdcc ) taking account of all nuclear and coulomb breakup processes . the asymptotic normalization coefficient ( anc ) method is used to extract from the calculated breakup cross section . the main result of the present paper is ev b. the error consists of 8.4% experimental systematic error and the error due to the ambiguity in the s - wave-be scattering length . this value of differs from the one extracted with the first - order perturbation theory including coulomb breakup by dipole transitions : ev b. it turns out that the difference is due to the inclusion of the nuclear and coulomb - quadrupole transitions and multi - step processes of all - order in the present work . the p-be interaction potential used in the cdcc calculation is also used in the anc analysis ofbe()b . the value of ev b obtained is consistent with the previous one obtained from a precise measurement of the-capture reaction cross section extrapolated to zero incident energy , ( expt ) ( theo ) ev b , where ( theo ) stands for the error in the extrapolation . thus , the agreement between the values of obtained from directbe()b and indirectb - breakup measurements is significantly improved .

nucl-th0505007

i

the principal result of the present paper is the value of @xmath3 of @xmath325 ( theo ) @xmath306 ( expt ) ev b obtained by an analysis of the cross section of the @xmath2b breakup reaction @xmath4pb(@xmath2b , @xmath5be)@xmath4pb at 52 mev / nucleon measured at riken @xcite by means of the method of continuum - discretized coupled - channels @xcite ( cdcc ) combined with the asymptotic normalization coefficient ( anc ) method @xcite . the value is consistent with the one extracted from the precise measurement of the cross section of direct capture @xmath0be(@xmath1)@xmath2b , @xmath10 ( expt ) @xmath11 ( theo ) ev b @xcite . the cdcc calculation is based on the three - body model of @xmath7 , @xmath0be , and the target @xmath4pb nucleus , with @xmath0be staying in the ground state throughout the reaction process . this model is shown to be adequate in the breakup reaction in which the fragments @xmath7 and @xmath0be are ejected in very forward angles , less than 4@xmath273 , which is the case for the experimental data analyzed in this work . nuclear and coulomb e1 and e2 transitions and multi - step processes of all - order are included in the calculation . the calculated cross section is shown to be proportional to the squared asymptotic amplitude of the overlap of the ground state wave functions of @xmath0be and @xmath2b , which is a necessary condition for the applicability of the anc method . the cdcc calculation is made efficient by the use of the eikonal cdcc method @xcite ( e - cdcc ) for large angular momentum partial waves . improvements of e - cdcc are made to cope with the coulomb distortions of the incident and scattered waves of relative motion and intrinsic spins of the projectile and the ejectiles . the main source of the error in the obtained @xmath3 is the ambiguity of the s - wave @xmath7-@xmath0be interaction potentials for the channel spin @xmath326 and @xmath327 states . the errors associated with the use of the anc method and the ambiguity of the distorting potentials are both negligible . extracted by the anc method are shown by open symbols : the circles are obtained from three - types of cdcc analysis of @xmath2b breakup and the triangle is the result of analysis of @xmath0be(@xmath1)@xmath2b with a simple potential model . the error of each result is obtained by adding the theoretical and experimental errors in quadrature . the results are compared with @xmath3 extracted from the precise measurement of direct capture @xmath328 cross section @xcite ( closed triangle ) and those obtained from @xmath2b dissociation with first - order perturbation theory ( closed circles ) . , scaledwidth=48.0% ] calculations of @xmath3 with some simplified assumptions are summarized in fig . the results of first - order iterative solutions of cdcc , designated as one - step cdcc , correspond to and agree with those of first - order perturbation theory in the previous work @xcite . the inclusion of the coulomb quadrupole ( e2 ) transitions , scaled by 0.7 , in the one - step calculation decreases @xmath3 by about 6% , and multistep processes increase it by about 20% . this shows the crucial importance of accurate description of the @xmath2b breakup process by cdcc including nuclear and coulomb e1 and e2 transitions and all higher - order processes . it will be interesting to apply the method of the present paper to analyses of wider range of experiments such as those in refs . it may , however , be that the three - body cdcc used in the present paper is not valid in general and the use of cdcc with four - body model such as the one in ref . @xcite becomes necessary .

the astrophysical factor forbe()b at zero energy , , is determined from an analysis ofpb(b ,be)pb at 52 mev / nucleon by means of the method of continuum - discretized coupled - channels ( cdcc ) taking account of all nuclear and coulomb breakup processes . the value of ev b obtained is consistent with the previous one obtained from a precise measurement of the-capture reaction cross section extrapolated to zero incident energy , ( expt ) ( theo ) ev b , where ( theo ) stands for the error in the extrapolation .

the astrophysical factor forbe()b at zero energy , , is determined from an analysis ofpb(b ,be)pb at 52 mev / nucleon by means of the method of continuum - discretized coupled - channels ( cdcc ) taking account of all nuclear and coulomb breakup processes . the asymptotic normalization coefficient ( anc ) method is used to extract from the calculated breakup cross section . the main result of the present paper is ev b. the error consists of 8.4% experimental systematic error and the error due to the ambiguity in the s - wave-be scattering length . this value of differs from the one extracted with the first - order perturbation theory including coulomb breakup by dipole transitions : ev b. it turns out that the difference is due to the inclusion of the nuclear and coulomb - quadrupole transitions and multi - step processes of all - order in the present work . the p-be interaction potential used in the cdcc calculation is also used in the anc analysis ofbe()b . the value of ev b obtained is consistent with the previous one obtained from a precise measurement of the-capture reaction cross section extrapolated to zero incident energy , ( expt ) ( theo ) ev b , where ( theo ) stands for the error in the extrapolation . thus , the agreement between the values of obtained from directbe()b and indirectb - breakup measurements is significantly improved .

1202.0134

i

historically , radio source counts has been a key observational probe of cosmology , more specifically of the geometry of the universe . in a euclidean universe the volume scales with distance as @xmath7 whereas the flux density scales as @xmath8 , which means that the integral number of sources ( for a population of non - evolving sources with constant comoving number density ) above any flux density scales as @xmath9 . departures from this expectation was key evidence for non - euclidean geometry . more recently , the geometry of the cosmos has been established with precision , and source counts represent a measure of cosmological evolution in radio source populations . the behavior of counts at sub - mjy flux density , the nature and evolution of these sources and the question of whether they constitute a new population are unclear . at flux densities of @xmath10 mjy a ` flattening ' of normalized differential source counts has been widely reported in literature ( windhorst et al . 1985 ( wmo85 henceforth ) , @xcite , @xcite and references therein ) . the rms noise level in the latter studies are : @xmath11jy for wmo85 , varying between @xmath12 to about @xmath13jy for hopkins et al . ( 2003 ) ( see fig.9 from hopkins et al . ( 2003 ) ) and approximately @xmath14jy for huynh et al . the flattenning is observed as an apparent change of slope from @xmath15 at @xmath16 mjy to about @xmath17 in the @xmath18 mjy range . wmo85 examined the optical identifications of faint radio sources and found that the sub - mjy radio source population is dominated by blue spiral galaxies . later studies , however , have arrived at discordant results and identify the sub - mjy sources with different populations : starburst galaxies ( @xcite , @xcite , @xcite ) , early type galaxies @xcite , low ( radio ) luminosity active galactic nuclei ( agns ) @xcite or a mixture of these . since spectroscopically complete samples of sub - mjy sources are not available , the exact nature of the population observed as sub - mjy radio sources remains uncertain ; however , it is widely agreed that flattening below @xmath19 mjy requires an evolving population that is different from those that dominate counts at higher flux densities . it may be noted here that the literature is not consistent in observing a flattening in counts at sub - mjy flux density ; for example , the counts in @xcite and @xcite are consistent with a continuation in the slope of the differential counts below mjy flux density . potential causes for the discrepancy are that deep radio surveys often suffer from inadequate sky coverage that is necessary to average over clustering , wide - field surveys often do not go sufficiently deep and so biases arising from the proximity of the detection threshold to the image noise may distort measured counts . additional uncertainly arises from lack of understanding of the radio structures in sub - mjy radio sources , which may lead to biases related to the ability of the survey to catalog sources from detections of source components . the atlbs is a moderately wide - field radio survey , covering @xmath20 square degrees in the southern sky at @xmath21 ghz . the survey has been carried out using the australia telescope compact array ( atca ) , which is a fourier imaging interferometer array . the radio observations for the low - brightness survey were designed for complete u - v coverage up to @xmath22 m ( for details of these observations , see @xcite ) . the work presented herein is based on the combination of the initial low resolution survey and more recent radio observations with the atca in multiple expanded array configurations that extended the u - v coverage to @xmath23 km , giving a synthesized beam with fwhm of @xmath0 and images with rms noise @xmath24jy beam@xmath2 . the high resolution observations are critical in better estimation of the source structures and for removing the effects of blending(source confusion ) in the low resolution survey . see @xcite for details on a sample of extended sources and classification of sources from the atlbs survey , which has been carried out using both the high resolution and low resolution images . the improved imaging of the atlbs survey regions has been used to revisit the 1.4 ghz source counts : the survey has sufficient sensitivity to probe the sub - mjy regime , and the relatively large sky coverage avoids clustering related uncertainties . a specific improvement in this work is the care taken to identify sources with low surface brightness by making use of low resolution images , and using multiple indicators to identify components of sources . the low resolution images were used to make initial identifications so that the sources which might be resolved into multiple components at higher resolution are identified correctly . the blending issues inherent in using low resolution images have been avoided using higher resolution images to identify blends . in addition , the use of low resolution images ( beam fwhm = @xmath6 ) almost completely removes effects of resolution bias ( for a detailed discussion , see section . [ section_resolution_bias ] ) . these strategies , together with use of optical imagesto locate candidate galaxy hosts and a careful visual examination of resolved and complex sources instead of automated classification ensures that the atlbs catalog is a ` source catalog ' as opposed to a ` component catalog ' . the distinction between ` sources ' ( which are single sources ) as opposed to components ( which may be parts of a single source or unrelated sources which are close to each other due to projection effects ) is crucial in estimating the true source counts . the organization of the paper is as follows . in the next section , we give details of the new high resolution radio observations of the atlbs survey regions . in section ( [ section_source_detection ] ) we give details of the procedure adopted for source detection and the estimation of source flux densities . in section ( [ section_source_counts ] ) we present the source counts along with the corrections necessary to derive the true counts from the observations . next , in section ( [ section_comparison ] ) , we compare the atlbs source counts with previous work . finally , in section ( [ section_conclusions ] ) , the conclusions are presented .

the australia telescope low - brightness survey ( atlbs ; ) regions have been mosaic imaged at a radio frequency of 1.4 ghz with angular resolution and 72 jy beam rms noise . , they do not require any changes in the radio source population down to the limit of the survey .

the australia telescope low - brightness survey ( atlbs ; ) regions have been mosaic imaged at a radio frequency of 1.4 ghz with angular resolution and 72 jy beam rms noise . the images ( centered at ra : , dec : and ra : , dec : ( j2000 epoch ) ) cover 8.42 square degrees sky area and have no artifacts or imaging errors above the image thermal noise . multi - resolution radio and optical r - band images ( made using the 4-m ctio blanco telescope ) were used to recognize multi - component sources and prepare a source list ; the detection threshold was 0.38 mjy in a low resolution radio image made with beam fwhm of . radio source counts in the flux density range 0.4 - 8.7 mjy are estimated , with corrections applied for noise bias , effective area correction and resolution bias . the resolution bias is mitigated using low resolution radio images , while effects of source confusion are removed by using high resolution images for identifying blended sources . below 1 mjy the atlbs counts are systematically lower than the previous estimates . showing no evidence for an upturn down to 0.4 mjy , they do not require any changes in the radio source population down to the limit of the survey . the work suggests that automated image analysis for counts may be dependent on the ability of the imaging to reproduce connecting emission with low surface brightness and on the ability of the algorithm to recognize sources , which may require that source finding algorithms effectively work with multi - resolution and multi - wavelength data . the work underscores the importance of using source lists as opposed to component lists and correcting for the noise bias in order to precisely estimate counts close to the image noise and determine the upturn at sub - mjy flux density .

1202.0134

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high - resolution radio images of the atlbs survey regions are presented , with beam fwhm of @xmath0 . the wide field mosaic images covering @xmath20 square degrees sky area with rms noise @xmath24jy beam@xmath2 are of exceptional quality in that there are no imaging errors or artifacts above the thermal noise over the entire field of view . the images have excellent surface brightness sensitivity - the visibility coverage is complete out to 750 m and hence provides good representation of extended emission components associated with radio sources . the images are , therefore , an excellent resource for examining with automated algorithms for source finding , parameter fitting , and morphological classification , and as a resource for testing such algorithms that would be used on upcoming all - sky continuum surveys with the lofar and askap . we make the high - resolution atlbs images available at the website www.rri.res.in/ atlbs . we have generated a source list from the atlbs images . this is a carefully made source list as opposed to a component list . the images were initially examined using automated algorithms , which used representations with different resolutions , to identify sources and distinguish unresolved and single component sources and complex sources . all complex sources were carefully examined by eye to recognize blends and classify appropriately . optical surveys of the atlbs fields were also examined for candidate host galaxies to aid in the classification of complex sources . the integrated flux densities of the sources were derived in a variety of methods - the method appropriate for the source structural classification was adopted in each case . we emphasize the use of multi - resolution images , which may complement each other , as well as the need to use data from other wavebands such as optical , infrared etc . the source list is also presented online along with the integrated flux densities and classification . the source list was used to estimate the radio source counts down to 0.4 mjy . the counts have been corrected for noise bias , resolution bias , and effective area . it may be noted that considerable care has been taken to ensure that the counts correspond to sources and not components . the counts presented in fig . [ submil_source_counts_new ] and table ( [ submil_counts_table_new ] ) above have been self - calibrated for the noise bias in that the counts derived in a first iteration have been used to derive the noise bias correction . comparing the counts with previous work - the athdfs and pds counts - shows that the atlbs counts are systematically lower . this is attributed to our counts representing sources as opposed to components , as well as corrections for noise bias . we have demonstrated the substantial difference in counts that results from using component catalogs as opposed to source catalogs : at 1 mjy flux density component counts may be as much as 50% above true source counts . this implies that automated image analysis for counts may be dependent on the ability of the imaging to reproduce connecting emission with low surface brightness and on the ability of the algorithm to recognize sources , which may require that source finding algorithms effectively work with multi - resolution and multi - wavelength data . the work presented herein underscores the importance of noise bias correction , in particular for deriving counts close to the limit of the survey sensitivity and for correctly estimating the faint end slope and upturn in the source counts at sub - mjy flux density . finally , the lack of an upturn in the source counts at faint flux densities implies that down to the faintest flux densities we have probed ( approximately 0.4 mjy ) there is no evidence for any new population . the upturn reported in the literature may be due to a combination of small survey areas and identification of radio sources as opposed to components , as well as effects of noise bias close to the detection limit . the atca is part of the australia telescope , which is funded by the commonwealth of australia for operation as a national facility managed by csiro . we thank anant tanna for his assistance with the initial processing of the visibility data . becker , r. h. , white , r. l. , & helfand , d. j. 1994 , aspc , 61 , 165 benn , c. r. , rowan - robinson , m. , mcmahon , r. g. , broadhurst , t. j. , & lawrence , a. 1993 , mnras , 263 , 98 bondi , m. , ciliegi , p. , schinnerer , e. , et al . 2008 , astrophys . j. , 681 , 1129 clark , b.g . 1980 a&a , vol . 89 , no . 3 , 377 - 378 condon , j. j. , 1989 , apj , 338 , 13 condon , j. j. , cotton , w. d. , greisen , e. w. , yin , q. f. , perley , r. a. , taylor , g. b. , and broderick , j. j. 1998 , aj , 115 , 1693 eddington , a. , 1913 , mnras , 73 , 359 gruppioni , c. , mignoli , m. , & zamorani , g. 1999 , mnras , 304 , 199 hopkins , a. m. , afonso , j. , chan , b. , et al . 2003 , aj , 125 , 465 huynh , m. t. , jackson , c. a. , norris , r. p. , & prandoni , i. 2005 , aj , 130 , 1373 huynh , m. t. , jackson , c. a. , norris , r. p. , & fernandez - soto , a. 2008 , aj , 135 , 2470 jauncey , d. l. , 1968 , apj , 152 , 647 mitchell , k. j. , condon , j. j. 1985 , aj , 90 , 1957 murdoch , h.s.,crawford , d.f . , jauncey , r.l . , 1917 , apj.,118,1 prandoni , i. , gregorini , l. , parma , p. , de ruiter , h. r. , vettolani , g. , wieringa , m. h. , ekers , r. d. , 2001 , a&a , 365 , 392 - 399 richards , e.a . , 2000 , aj , 533 , 611 saripalli , l. , subrahmanyan , r. , thorat , k. , ekers , r.d . , hunstead , r.w . , johnston , h.m . , sadler , e.m . , 2011 , apj . , in press sault , r.j . , tueben , p. j. and wright , m. c. h. 1995 , astronomical data analysis software and systems iv , asp conference series , vol . shaw , h.e . payne , and j.j.e . hayes , 433 sault , r.j . & wieringa , m.h . 1994 a&as , 108 , 585 subrahmanyan , r. , ekers , r. d. , saripalli , l. , sadler , e. m. , 2010 , mnras , 402 , 2792 thorat , k. , saripalli , l. , subrahmanyan , r. , 2012 , in preparation . windhorst , r. a. , van heerde , g. m. , & katgert , p. , 1984 , a&as , 58 , 1 windhorst , r.a . , miley , g.k . , owen , f.n . , kron , r.g . and koo , d.c.,1985 , aj , 289 , 494 windhorst , r.a . , mathis , d. , neuschaefer , l.,1990 , pasp , vol . 10 , evolution of the universe of galaxies , ed . kron , r.j . , 389 - 403

the images ( centered at ra : , dec : and ra : , dec : ( j2000 epoch ) ) cover 8.42 square degrees sky area and have no artifacts or imaging errors above the image thermal noise . the work suggests that automated image analysis for counts may be dependent on the ability of the imaging to reproduce connecting emission with low surface brightness and on the ability of the algorithm to recognize sources , which may require that source finding algorithms effectively work with multi - resolution and multi - wavelength data . the work underscores the importance of using source lists as opposed to component lists and correcting for the noise bias in order to precisely estimate counts close to the image noise and determine the upturn at sub - mjy flux density .

the australia telescope low - brightness survey ( atlbs ; ) regions have been mosaic imaged at a radio frequency of 1.4 ghz with angular resolution and 72 jy beam rms noise . the images ( centered at ra : , dec : and ra : , dec : ( j2000 epoch ) ) cover 8.42 square degrees sky area and have no artifacts or imaging errors above the image thermal noise . multi - resolution radio and optical r - band images ( made using the 4-m ctio blanco telescope ) were used to recognize multi - component sources and prepare a source list ; the detection threshold was 0.38 mjy in a low resolution radio image made with beam fwhm of . radio source counts in the flux density range 0.4 - 8.7 mjy are estimated , with corrections applied for noise bias , effective area correction and resolution bias . the resolution bias is mitigated using low resolution radio images , while effects of source confusion are removed by using high resolution images for identifying blended sources . below 1 mjy the atlbs counts are systematically lower than the previous estimates . showing no evidence for an upturn down to 0.4 mjy , they do not require any changes in the radio source population down to the limit of the survey . the work suggests that automated image analysis for counts may be dependent on the ability of the imaging to reproduce connecting emission with low surface brightness and on the ability of the algorithm to recognize sources , which may require that source finding algorithms effectively work with multi - resolution and multi - wavelength data . the work underscores the importance of using source lists as opposed to component lists and correcting for the noise bias in order to precisely estimate counts close to the image noise and determine the upturn at sub - mjy flux density .

1502.02524

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it is generally believed that there is a supermassive black hole ( bh ) at the center of an active galactic nucleus ( agn ) ; the gravitational potential of the bh is the ultimate energy source of the agn . the accreted matter of a bh forms an accretion disk and loses angular momentum through viscous or turbulent processes ( rees 1984 ) . broad emission lines are one of the dominant features of many agn spectra , which are produced in a ` broad line region ' ( blr ) nearby the bh . the blr is widely acknowledged to be photoionized by the continuum from the accretion disk ( e.g. , kwan & krolik 1981 ; ferland et al . 1992 ) . in order to explain the special radiation properties of bl lac objects ( bl lacs ) , blandford & rees ( 1978 ) proposed that there are relativistic jet structures in these sources . the jet launching is reported to be connected with the central bh , accretion disk , and corona in a source ( armitage & natarajan 1999 ; merloni & fabian 2002 ; wang et al . 2004 ; cao 2004 , 2014 ; yuan & narayan 2014 ; wilkins & gallo 2015 ; chen et al . the jets may be powered via the blandford@xmath5payne ( bp ; blandford & payne 1982 ) process by releasing the gravitational energy of accreting matter that moves toward the bh , and/or via blandford@xmath5znajek ( bz ; blandford & znajek 1977 ) mechanism by extracting the rotational energy of bh . so far , most confirmed extragalactic gev - tev emitters are blazars , a sub - sample of radio - loud agns with relativistic jets . blazars are divided into bl lacs and flat spectrum radio quasars ( fsrqs ) according to their emission line features . generally , the broadband spectral energy distributions ( seds ) of bl lacs can be well explained with the synchrotron radiation and the synchrotron self - compton ( ssc ) scattering of the relativistic electrons in jets ( maraschi et al . 1992 ; ghisellini et al . 1996 , 2010 ; zhang et al . 2012 ; liao et al . 2014 ; yan et al . 2014 ) ; however , fsrqs need a black body spectrum component and a component from inverse compton ( ic ) scattering of the external photons to fit their broadband seds ( e.g. , sikora et al . 1994 ; ghisellini et al . 1996 , 2010 ; zhang et al . 2014 ; cao & wang 2013 ; chen et al . 2010 , 2012 ) . compared with bl lacs , fsrqs have prominent emission lines in their spectra , and sometimes there are significant blue bumps at @xmath7 hz in their observed broadband seds , which is believed to be the thermal emission of accretion disk . however , often no significant blue bump is observed in the seds since the nonthermal radiation from jet overwhelms the thermal mission from accretion disk , especially when the sources are in the high state ( e.g. , for 3c 454.3 , jorstad et al . hence , the gev fsrqs in which the broadband seds are dominated by the jet emission and the significant blue bumps of the thermal emission from accretion disk are observed in their seds , are the good candidates for investigating the correlations among their jet power , accretion disk radiation , and blr luminosity . the flux ratios of emission lines from blr are suggested to be approximately constant among different agns ( francis et al . 1991 ; vanden berk et al . 2001 ) . if setting the emission line luminosity of ly@xmath8 to 100 , the relative luminosities of h@xmath9 , h@xmath8 , mg ii , and c iv lines are 22 , 77 , 34 , and 63 , respectively , and then the total emission line luminosity is 555.8 ( francis et al . 1991 ; celotti et al . therefore , the luminosity of blr can be roughly estimated with the luminosities of one or some emission lines . using the continuum luminosity and the emission line luminosity in shen et al . ( 2011 ) , calderone et al . ( 2013 ) calculated @xmath1 and @xmath2 , respectively , and reported that @xmath10 , i.e. , the covering factor of blr is probably equal to 10 percent ; therefore , the value of @xmath11 is always used as a proxy to the accretion disk luminosity ( @xmath1 ) . sometimes @xmath12 is also used to estimate the luminosity of blr in blazars when authors have obtained @xmath1 and want to calculate the energy density of blr ( e.g. , ghisellini et al . 2010 ; zhang et al . however , so far it has not be examined whether the @xmath13 relation is still valid for blazars , especially for the gev tev blazars . in this paper , a sample of seds for gev fsrqs is compiled to study their jet and accretion disk relations and their covering factors of blrs . the sample selection and data are presented in section 2 . the models and results of sed fitting are described in section 3 . the study of the covering factors of blrs is in section 4 . the possible connection between the jet and accretion disk is shown in section 5 . further investigation to the correlations among the jet , blr , and accretion disk is described in section 6 . a simple discussion on the anisotropic radiation of accretion disk , the jet formation mechanism for gev agns , and the implications of unification for radio loud agns is given in section 7 . a summary for our results is in section 8 . throughout , @xmath14=73 km s@xmath15 mpc@xmath15 , @xmath16 and @xmath17 are adopted .

the broadband spectral energy distributions ( seds ) of 18 gev flat spectrum radio quasars ( fsrqs ) are collected and compiled from literature , in which both the jet emission and the accretion disk radiation can be observed , in order to investigate the correlations among their jet power ( ) , accretion disk luminosity ( ) , and luminosity of broad line region ( blr , ) . on the basis of the sed fits with the jet radiation and accretion disk radiation models , we calculate and .

the broadband spectral energy distributions ( seds ) of 18 gev flat spectrum radio quasars ( fsrqs ) are collected and compiled from literature , in which both the jet emission and the accretion disk radiation can be observed , in order to investigate the correlations among their jet power ( ) , accretion disk luminosity ( ) , and luminosity of broad line region ( blr , ) . on the basis of the sed fits with the jet radiation and accretion disk radiation models , we calculate and . no correlation between with either or is found . with a sub - sample of for 13 gev fsrqs , it is observed that is strongly correlated with their . we also study the blr covering factors ( ) of the gev fsrqs in our sample , averagely which are smaller than that of the large samples of radio - loud and radio - quiet quasars . of some gev fsrqs is higher than , but of all the gev fsrqs is lower than the accretion power of black hole ( bh ) , which is estimated by , indicating that the total accretion power of bh is sufficient to drive the jets in these sources ; however the uncorrelation between and of the gev fsrqs may suggest that their jets are launched by the blandfordznajek process via extracting the rotational energy of bh . using the relation of the gev fsrqs , we estimate of a bl lac sample with their . a comparison of and eddington ratio ( ) among bl lacs , very radio - loud nls1 galaxies , and fsrqs is also presented . it is found that along with the bl lac nls1fsrq sequence and increase , which may correspond to the change of the accretion disk structure and the transformation of the dominant mechanism for jet launching . this is also consistent with the division of their parent populations , i.e. , low - excitation radio galaxies and high - excitation radio galaxies .

1502.02524

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a sed sample of 18 gev - fsrqs , in which the significant blue bumps from the accretion disk radiation are observed and the blr luminosities ( @xmath2 ) of 13 gev - fsrqs are available , is collected and compiled from literature . on the basis of the sed fits with the jet radiation and accretion disk radiation models , we calculate the jet power ( @xmath0 ) and the accretion disk luminosity ( @xmath1 ) , investigate the correlations of the jet power and disk luminosity as well as the blr luminosity , and also make a comparison of the blr covering factor ( @xmath3 ) with the large rlq and rqq samples from shen et al . our results are summarized below . * @xmath2 of the 13 gev - fsrqs is strongly correlated with @xmath1 , and thus @xmath2 can be used to estimate @xmath1 when the radiation of accretion disk is overwhelmed by the jet emission . the mean of @xmath3 for the 13 gev - fsrqs is 0.043 , which is smaller than that of the rlqs ( @xmath330.082 ) and rqqs ( @xmath330.076 ) in shen et al . ( 2011 ) . considering the inclination effect and anisotropic radiation of accretion disk , the @xmath3 distribution of the 13 gev - fsrqs would be same as that of rlqs and rqqs in shen et al . ( 2011 ) . * no correlation between @xmath0 with @xmath1 and @xmath2 is found for the gev fsrqs . @xmath0 for most of the gev fsrqs is lower than @xmath1 and all of them are lower than the accretion power of bh ( @xmath4 ) , indicating that the total accretion power of bh is sufficient to drive the jets in these sources , but the uncorrelation between @xmath1 and @xmath0 of the gev fsrqs in our sample may suggest that their jets are launched by the bz process via extracting the rotational energy of bh . * using the @xmath2@xmath1 relation of the 13 gev - fsrqs , we estimate @xmath1 of a bl lac sample with their @xmath2 ; a very rl nls1 galaxy sample from yuan et al . ( 2008 ) is also taken into account . it is found that along with the bl lac nls1fsrq sequence @xmath2 and the eddington ratio ( @xmath6 ) increase , which may correspond to the change of the accretion disk structure and the transformation of the dominant mechanism for jet launching . this is also consistent with the division of their parent populations , i.e. , bl lacs / lergs and fsrqs / hergs . we thank the anonymous referee for his / her valuable suggestions . we appreciate helpful discussion with yuan liu , wei cui , bi - fang liu , wei - min yuan , er - lin qiao . this work is supported by the national basic research program ( 973 programme ) of china ( grant 2014cb845800 ) , the national natural science foundation of china ( grants 11373036 , 11133002 , 11025313 ) , the strategic priority research program the emergence of cosmological structures " of the chinese academy of sciences ( grant xdb09000000 ) , the guangxi science foundation ( 2013gxnsffa019001 ) , and the young researcher grant of national astronomical observatories , chinese academic of science . shuang - nan zhang acknowledges support from the qianren start - up grant 292012312d1117210 .

no correlation between with either or is found . with a sub - sample of for 13 gev fsrqs of some gev fsrqs is higher than , but of all the gev fsrqs is lower than the accretion power of black hole ( bh ) , which is estimated by , indicating that the total accretion power of bh is sufficient to drive the jets in these sources ; however the uncorrelation between and of the gev fsrqs may suggest that their jets are launched by the blandfordznajek process via extracting the rotational energy of bh . using the relation of the gev fsrqs , we estimate of a bl lac sample with their . a comparison of and eddington ratio ( ) among bl lacs , very radio - loud nls1 galaxies , and fsrqs is also presented . it is found that along with the bl lac nls1fsrq sequence and increase , which may correspond to the change of the accretion disk structure and the transformation of the dominant mechanism for jet launching . this is also consistent with the division of their parent populations , i.e. , low - excitation radio galaxies and high - excitation radio galaxies .

the broadband spectral energy distributions ( seds ) of 18 gev flat spectrum radio quasars ( fsrqs ) are collected and compiled from literature , in which both the jet emission and the accretion disk radiation can be observed , in order to investigate the correlations among their jet power ( ) , accretion disk luminosity ( ) , and luminosity of broad line region ( blr , ) . on the basis of the sed fits with the jet radiation and accretion disk radiation models , we calculate and . no correlation between with either or is found . with a sub - sample of for 13 gev fsrqs , it is observed that is strongly correlated with their . we also study the blr covering factors ( ) of the gev fsrqs in our sample , averagely which are smaller than that of the large samples of radio - loud and radio - quiet quasars . of some gev fsrqs is higher than , but of all the gev fsrqs is lower than the accretion power of black hole ( bh ) , which is estimated by , indicating that the total accretion power of bh is sufficient to drive the jets in these sources ; however the uncorrelation between and of the gev fsrqs may suggest that their jets are launched by the blandfordznajek process via extracting the rotational energy of bh . using the relation of the gev fsrqs , we estimate of a bl lac sample with their . a comparison of and eddington ratio ( ) among bl lacs , very radio - loud nls1 galaxies , and fsrqs is also presented . it is found that along with the bl lac nls1fsrq sequence and increase , which may correspond to the change of the accretion disk structure and the transformation of the dominant mechanism for jet launching . this is also consistent with the division of their parent populations , i.e. , low - excitation radio galaxies and high - excitation radio galaxies .

1402.1425

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leaf powers are a family of graph classes that has been introduced by nishimura etal . @xcite to model the problem of reconstructing phylogenetic trees . in particular , a given finite simple graph @xmath2 is called the @xmath1-leaf power of a tree @xmath3 for some @xmath17 , if @xmath4 is the set of leaves in @xmath3 and any two distinct vertices @xmath18 are adjacent , that is @xmath5 , if and only if the distance of @xmath6 and @xmath7 in @xmath3 is at most @xmath1 . for all @xmath17 , the class of graphs that are a @xmath1-leaf power of some tree , is simply called @xmath1-leaf powers and denoted by @xmath0 . the general problem , from a graph theoretic point of view , is to structurally characterize @xmath0 for all fixed @xmath17 and to provide efficient recognition algorithms . obviously , a graph @xmath14 is a @xmath8-leaf power , if and only if it is the disjoint union of cliques , that is , @xmath14 does not contain a chordless path of length @xmath8 . dom etal . @xcite prove that @xmath9-leaf powers are exactly the graphs that do not contain an induced bull , dart , or gem . brandstdt etal . @xcite contribute to the characterization of @xmath9-leaf powers by showing that they are exactly the graphs that result from substituting cliques into the nodes of a tree . moreover , they give a linear time algorithm to recognize @xmath9-leaf powers building on their characterization . a characterization of @xmath10-leaf powers in terms of forbidden subgraphs is yet unknown . however , basic @xmath10-leaf powers , the @xmath10-leaf powers without true twins , are characterized by eight forbidden subgraphs @xcite . the structure of basic @xmath10-leaf powers has further been analyzed by brandstdt etal . @xcite , who provide a nice characterization of the two - connected components of basic @xmath10-leaf powers that leads to a linear time recognition algorithm even for @xmath10-leaf powers . for @xmath11-leaf powers , a polynomial time recognition was given in @xcite . however , no structural characterization is known , even for basic @xmath11-leaf powers . only for distance - hereditary basic @xmath11-leaf powers a characterization in terms of @xmath19 forbidden induced subgraphs has been discovered @xcite . except from the result in @xcite that @xmath20 is not true for every @xmath1 , there have not been any more essential advances in determining the structure of @xmath1-leaf powers for @xmath21 since 2007 . instead , research has focused on generalizations of leaf powers @xcite , which also turned into dead ends , very soon . on the other hand , if we push @xmath1 to infinity , then it turns out that not every graph is a @xmath1-leaf power for some @xmath17 . in particular , a @xmath1-leaf power is , by definition , the subgraph of the @xmath1-th power of a tree @xmath3 induced by the leaves of @xmath3 . since trees are sun - free chordal and as taking powers and induced subgraphs do not destroy this property , it follows trivially that every @xmath1-leaf power , despite the value of @xmath1 , is strongly chordal @xcite . but even not every strongly chordal graph is a @xmath1-leaf power for some @xmath17 . in fact , we are aware of exactly one counter example , which has been found by bibelnieks etal . @xcite and is shown as @xmath22 in figure [ fig : counterexamples ] . insofar , it is reasonable to ask for a precise characterization of the graphs that are not a @xmath1-leaf power for any @xmath17 . this problem can equivalently be formulated as to describe the graphs in the class @xmath23 , which we call leaf powers , for short . interestingly , brandstdt etal . @xcite show that @xmath16 coincides with the class of fixed tolerance nest ( neighborhood subtree tolerance ) graphs , a well - known graph class with an absolutely different motivation given by bibelnieks etal . @xcite . naturally , characterizations and an efficient recognition algorithms for this class are also open questions today . however , by brandstdt etal . @xcite , it is know that @xmath16 is a superclass of ptolemaic graphs , that is , gem - free chordal graphs @xcite , and even a superclass of directed rooted path graphs , introduced by gavril @xcite . recently , we introduced the clique arrangement in @xcite , a new data structure that is especially valuable for the analysis of strongly chordal graphs . the clique arrangement @xmath24 of a chordal graph @xmath14 is a directed acyclic graph that has certain vertex subsets of @xmath14 as a node set and describes the mutual inclusion of these sets by arcs . in particular , for every set @xmath25 of maximal cliques of @xmath14 there is a node in @xmath26 for @xmath27 and two nodes @xmath28 are joined by an arc @xmath29 , if @xmath30 and there is no @xmath31 with @xmath32 . in @xcite , we give a new characterization of strongly chordal graphs in terms of a forbidden cyclic substructure in the clique arrangement , called bad @xmath1-cycles for @xmath33 , and we show how to construct the clique arrangement of a strongly chordal graph in nearly linear time . it is known that the clique arrangements of ptolemaic graphs are even directed trees @xcite . since all ptolemaic graphs are leaf powers and all leaf powers are strongly chordal , it appears likely that the degree of acyclicity in clique arrangements of leaf powers is between forbidden bad @xmath1-cycles , @xmath34 , and the complete absence of cycles . this paper describes a cyclic substructure that is forbidden in the clique arrangement of leaf powers . for convenience , we call these substructures bad @xmath8-cycles , although they are not the obvious continuation of the concept of bad @xmath1-cycles for @xmath34 . as the main result of this paper , we show that bad @xmath8-cycles occur in @xmath13 , if and only if @xmath14 contains at least one of seven induced subgraphs @xmath35 depicted in figure [ fig : counterexamples ] . we leave it as an open question , if these seven graphs are sufficient to characterize @xmath16 in terms of forbidden subgraphs . however , we conjecture that this is the case . this would imply a polynomial time recognition algorithm for @xmath16 , by using the possibility of efficiently recognizing strongly chordal graphs and checking the containment of a finite number of forbidden induced subgraphs .

the class of-leaf powers consists of graphs that have a-leaf root , that is , a tree with leaf set , where , if and only if the-distance between and is at most . structure and linear time recognition algorithms have been found for- ,- ,- , and , to some extent ,-leaf powers , and it is known that the union of all-leaf powers , that is , the graph class , forms a proper subclass of strongly chordal graphs . despite from that , no essential progress has been made lately . in this paper , we use the new notion of clique arrangements to suggest that leaf powers are a natural special case of strongly chordal graphs . the clique arrangement of a chordal graph is a directed graph that represents the intersections between maximal cliques of by nodes and the mutual inclusion of these vertex subsets by arcs . recently , strongly chordal graphs have been characterized as the graphs that have a clique arrangement without bad-cycles for . we show that the clique arrangement of every graph of is free of bad-cycles . the question whether this characterizes the class exactly remains open .

the class of-leaf powers consists of graphs that have a-leaf root , that is , a tree with leaf set , where , if and only if the-distance between and is at most . structure and linear time recognition algorithms have been found for- ,- ,- , and , to some extent ,-leaf powers , and it is known that the union of all-leaf powers , that is , the graph class , forms a proper subclass of strongly chordal graphs . despite from that , no essential progress has been made lately . in this paper , we use the new notion of clique arrangements to suggest that leaf powers are a natural special case of strongly chordal graphs . the clique arrangement of a chordal graph is a directed graph that represents the intersections between maximal cliques of by nodes and the mutual inclusion of these vertex subsets by arcs . recently , strongly chordal graphs have been characterized as the graphs that have a clique arrangement without bad-cycles for . we show that the clique arrangement of every graph of is free of bad-cycles . the question whether this characterizes the class exactly remains open .

astro-ph0007262

i

in paper i ( wielen et al . 1999b ) , we have shown that the combination of the data of the hipparcos astrometric satellite ( esa 1997 ) with ground - based results ( such as the fk5 ) is able to provide for many stars individual proper motions which are significantly more accurate than the hipparcos proper motions themselves . the method has been already successfully applied in the construction of the fk6 , the sixth catalogue of fundamental stars ( part i of the fk6 : wielen et al . 1999d , part iii of the fk6 : wielen et al . 2000a ) . the method of combination presented in paper i is , however , strictly valid for single stars only . in the fk6 , we call this procedure therefore the ` single - star mode ' . in reality most of the stars are members of binaries or of multiple systems . if the duplicity of an individual object is already definitely known , either from ground - based investigations or from hipparcos observations , then the method of combination has to be changed properly in order to obtain meaningful results . we call such procedures ` special solutions ' . paper iii of this series of papers will discuss the special solutions for visual binaries and other types of double stars . the present paper ( paper ii ) describes an appropriate method of the combination of hipparcos results with ground - based observations for ` apparently single stars ' . even if we have removed from such a sample of apparently single stars all the objects with known duplicity , there remains beside the truly single - stars a large number of hitherto undetected astrometric binaries . the measured photo - center of an unresolved astrometric binary moves on the sky on a wavy curve , in contrast to the linear motion of single stars ( fig . 1 ) . in such a case , an ` instantaneously ' measured proper motion deviates from a ` mean ' proper motion , averaged over a long interval of time . the proper motions provided by hipparcos ( esa 1997 ) are essentially such instantaneously measured quantities , since they are derived from positional measurements spread over about three years only . in contrast , the proper motions given in the fk5 ( fricke et al . 1988 , 1991 ) are long - term averages over up to about 200 years . we have called the difference between the instantaneous proper - motion and the mean one the ` cosmic error ' of the instantaneous proper motion ( wielen 1995a , b , 1997 , wielen et al . 1997 ) . in some cases , the individual cosmic error is so large that the duplicity of an apparently single star is strongly indicated by this fact . we have called such objects ` @xmath2 binaries ' ( wielen et al . 1999a ) . in most cases , however , the cosmic error in the hipparcos proper motion of a hitherto undetected astrometric binary is not _ individually _ significant , but can be shown to exist only _ statistically _ in a larger sample of apparently single stars . nevertheless , an appropriate combination method should not neglect the statistical consequences of these cosmic errors . our comparison of hipparcos proper motions with ground - based results has shown that , at least for brighter stars , the average cosmic error in a hipparcos proper motion is often larger than the hipparcos measuring error , typically by a factor of three ( wielen 1995a , b , wielen et al . 1997 , 1998 , 1999c ) . wielen ( 1997 , henceforth called paper wpsa ) has developed a coherent scheme of ` statistical astrometry ' for handling the effects of cosmic errors in high - precision astrometry . in the following sections , we shall apply the concepts of statistical astrometry to the problem of combining the hipparcos results with ground - based measurements for a sample of apparently single stars . the main results will be solutions which we call the ` long - term prediction mode ( ltp ) ' and the ` short - term prediction mode ( stp ) ' . our results have already been applied for the ltp and stp solutions given in part i and part iii of the fk6 ( wielen et al . 1999d , 2000a ) . it is clear that in principle the most desirable solution for our problem would be to treat each star individually and fully correctly . this would mean ( 1 ) for truly single stars : to use the ` single - star mode ( si ) ' described in paper i , and ( 2 ) for binaries : to apply individual orbital corrections , as e.g. done for polaris by wielen et al . . however , since for ` apparently single stars ' the true nature ( single or double ) of the individual objects is unknown , we _ have _ to rely on statistical methods in order to handle such a sample of stars properly . the treatment of a sample of apparently single stars by our statistical procedures gives _ on average _ the best astrometric prediction , and it provides the most realistic error budget for such a sample . in this sense , our statistical treatment is certainly much more appropriate than to ignore the binary nature of a large fraction of a sample of apparently single stars altogether . in paper i , we have already pointed out that the older observations carry a high weight in the combination of ground - based measurements with hipparcos data , and that therefore the gc ( boss et al . 1937 ) should be also considered here because of its high number of rather well - measured stars . we call the result of the combination of the gc with hipparcos the combination catalogue gc+hip .

the combination of ground - based astrometric compilation catalogues , such as the fk5 or the gc , with the results of the esa astrometric satellite hipparcos produces for many thousands of stars proper motions which are significantly more accurate than the proper motions derived from the hipparcos observations alone . in paper i ( wielen et al . 1999 , a&a 347 , 1046 ) we have presented a method of combination for single stars ( si mode ) .

the combination of ground - based astrometric compilation catalogues , such as the fk5 or the gc , with the results of the esa astrometric satellite hipparcos produces for many thousands of stars proper motions which are significantly more accurate than the proper motions derived from the hipparcos observations alone . in paper i ( wielen et al . 1999 , a&a 347 , 1046 ) we have presented a method of combination for single stars ( si mode ) . the present paper ii derives a combination method which is appropriate for an ensemble of ` apparently single - stars ' which contains undetected astrometric binaries . in this case the quasi - instantaneously measured hipparcos proper motions and positions are affected by ` cosmic errors ' , caused by the orbital motions of the photo - centers of the undetected binaries with respect to their center - of - mass . in contrast , the ground - based data are ` mean values ' obtained from a long period of observation . we derive a linear ` long - term prediction ' ( ltp mode ) for epochs far from the hipparcos epoch , and a linear ` short - term prediction ' ( stp mode ) for epochs close to . the most accurate prediction for a position at an arbitrary epoch is provided by a smooth , non - linear transition from the stp solution to the ltp solution . we present an example for the application of our method , and we discuss the error budget of our method for the fk6 ( a combination of the fk5 with hipparcos ) and for the combination catalogue gc+hip . for the basic fundamental stars , the accuracy of the fk6 proper motions in the ltp mode is better than that of the hipparcos proper motions ( taking here the cosmic errors into account ) by a factor of more than 4 .

math0702892

i

let @xmath3 be a convex body in @xmath7 . the _ covariogram _ @xmath5 of @xmath3 is the function @xmath8 where @xmath9 and @xmath10 denotes volume in @xmath7 . this functional , which was introduced by matheron in his book @xcite on random sets , is also sometimes called the _ set covariance _ , and it coincides with the _ autocorrelation _ of the characteristic function of @xmath3 : @xmath11 the covariogram @xmath5 is clearly unchanged by a translation or a reflection of @xmath3 . ( the term _ reflection _ will always means reflection in a point . ) matheron @xcite and , independently , adler and pyke @xcite asked the following question . does the covariogram determine a convex body , among all convex bodies , up to translations and reflections ? matheron conjectured a positive answer for the case @xmath12 but this conjecture has not been completely settled . matheron @xcite observed that , for @xmath13 and for all @xmath14 , the derivatives @xmath15 give the distribution of the lengths of the chords of @xmath3 parallel to @xmath16 . such information is common in _ stereology , _ _ statistical shape recognition _ and _ image analysis , _ when properties of an unknown body are to be inferred from chord length measurements ; see @xcite , @xcite and @xcite , for example . blaschke ( cf . @xcite ) asked whether the distribution of the lengths of chords ( in all directions ) of a convex body characterizes the body , up to rigid motions , but mallows and clark @xcite proved that this is false even for convex polygons . in fact ( see @xcite ) the covariogram problem is equivalent to the problem of determining a convex body from all its separate chord length distributions , one for each direction @xmath13 . adler and pyke @xcite asked matheron s question in probabilistic terms . does the distribution of the difference @xmath17 of independent random variables @xmath18 and @xmath19 uniformly distributed over @xmath3 determine @xmath3 , up to translations and reflections ? since the convolution in is , up to a multiplicative factor , the probability density of @xmath17 , this problem is equivalent to the covariogram one . matheron s problem is also relevant in _ x - ray crystallography , _ where the atomic structure of a _ crystal _ ( or _ quasicrystal _ ) is to be found from _ diffraction images . _ a convenient way of describing many important examples of quasicrystals is via the _ cut and project scheme_. here to the atomic structure , represented by a discrete set @xmath20 contained in a space @xmath21 , is associated a _ lattice _ @xmath22 in a higher dimensional space @xmath23 and a _ window _ @xmath24 ( which in many cases is a convex set ) . in this setting @xmath20 coincides with the projection on @xmath21 of the points of the lattice @xmath22 which belong to @xmath25 . in many examples the lattice @xmath22 can be determined by the diffraction image . to determine @xmath20 it is however necessary to know @xmath26 : the covariogram problem enters at this point , since the covariogram of @xmath26 can be obtained by the diffraction image ; see @xcite . enns and ehlers @xcite express in terms of the covariogram the distributions of random line segments in a convex body , under different types of randomness with which they are generated . the monograph @xcite contains an extensive discussion of retrieval problems for convex bodies , while the survey @xcite deals with algorithmic aspects of reconstruction problems in convex geometry . the first contribution to matheron s question was made in 1993 by nagel @xcite , who gave a positive answer when @xmath3 is a planar convex polygon ; see also schmitt @xcite . matheron s conjecture is still unsettled for general planar convex bodies , but it has been confirmed for @xmath27 convex bodies , non - strictly convex bodies , and convex bodies that are not @xmath28 ; see @xcite . it has been recently shown that every convex polytope in @xmath29 is determined by its covariogram , up to translations and reflections ( cf . @xcite ) . for @xmath30 there exist examples of convex polytopes that are not determined by their covariogram ( cf . however @xcite proves that , if @xmath31 is a @xmath32-dimensional simplicial convex polytope in general relative position with respect to @xmath33 , the determination by the covariogram data is unique for every @xmath34 ( see next section for all unexplained definitions ) . the paper @xcite discusses various open retrieval problems related to the covariogram . one of the purposes of this paper is to sharpen some of the known results on matheron s conjecture , indicating how much of the covariogram information is needed to get the uniqueness of determination . we indicate some subsets of the support of the covariogram , with arbitrarily small lebesgue measure , such that the covariogram , restricted to those subsets , identifies certain geometric properties of the body . these results are more precise in the planar case , but some of them , both positive and negative ones , are proved for bodies of any dimension . moreover some results regard _ most _ convex bodies , in the _ baire category sense . _ another purpose is to extend the class of convex bodies for which matheron s conjecture is confirmed by including all planar convex bodies possessing two non - degenerate boundary arcs being reflections of each other . given two convex bodies @xmath3 and @xmath35 in @xmath7 and a closed set @xmath36 we introduce the following property involving @xmath37 and @xmath38 @xmath39 is a shorthand notation standing for `` covariogram coincidence '' ( where covariogram is traditionally referred to by the letter @xmath40 ) . @xmath41 : : the equality @xmath42 holds for all @xmath43 in some neighbourhood of @xmath44 the following theorem presents two choices of the set @xmath18 for which @xmath41 implies the coincidence of @xmath3 and @xmath35 up to translations and reflections , under the assumption @xmath45 before stating the theorem we need to introduce the notion of local symmetry and give some related explanations . a pair of closed boundary arcs of a planar convex body @xmath3 is said to be a _ local symmetry _ of @xmath3 if they are reflections of each other in a point , have disjoint and nonempty relative interiors , and they are not properly contained in a pair of boundary arcs with the same properties . a planar convex body @xmath3 is called _ locally symmetric _ if it possesses a local symmetry . planar convex bodies without local symmetries are called _ globally non - symmetric . _ it is known that the support of @xmath5 is the _ difference body _ of @xmath3 , @xmath46 , and that @xmath47 is @xmath48-symmetric . if @xmath49 and @xmath50 are arcs of @xmath51 which compose a local symmetry , then the set @xmath52 , translated in such a way to be @xmath48-symmetric , is the union of two arcs @xmath53 and @xmath54 of @xmath55 . we say that these arcs of @xmath55 correspond to the local symmetry @xmath56 ( see figs . [ 06.05.23,21:46 ] and [ 05.12.19,11:36 ] ) . a convex body @xmath3 is said to belong to the class @xmath57 if its boundary is a two - times continuously differentiable manifold and all its principal curvatures are non - zero ( for detailed information see ( * ? ? ? * section 2.5 ) ) . [ 05.08.10,15:35 ] let @xmath3 and @xmath35 be planar convex bodies and let @xmath3 be @xmath57 regular . let @xmath58 be the collection of all the arcs of @xmath55 which correspond to local symmetries of @xmath3 . by @xmath59 we denote the midpoint of the segment joining the endpoints of the arc @xmath60 let @xmath61 and let @xmath62 or @xmath63 ( see figs . [ 06.05.23,21:46 ] and [ 05.12.19,11:36 ] ) . then @xmath41 implies the coincidence of @xmath3 and @xmath64 up to translations and reflections . @xmath65 cc ( 40,30 ) ( 12,8 ) ( 11,20)@xmath3 & ( 40,30 ) ( 4,4 ) ( 21,16)@xmath48 ( 3,25)@xmath47 + & we remark that the two choices of @xmath18 defined in the statement of theorem [ 05.08.10,15:35 ] are in some sense minimal for the assertion of the theorem to hold ( for further details see remark [ 06.05.16,16:17 ] below ) . moreover the set @xmath66 depends only on @xmath5 and not on @xmath3 , in the sense that if @xmath35 and @xmath3 satisfy @xmath67 or @xmath68 then the same set @xmath66 corresponds to @xmath35 and @xmath3 . this is the content of the second part of theorem [ 06.05.16,15:21 ] . the following corollary is a direct consequence of theorem [ 05.08.10,15:35 ] . [ 06.05.16,17:58 ] let @xmath3 and @xmath35 be planar convex bodies and let @xmath3 be @xmath57 regular . then the following statements hold . a. there exists a closed and at most countable subset @xmath18 of @xmath69 with no accumulation points in @xmath70 such that @xmath71 implies the coincidence of @xmath3 and @xmath64 up to translations and reflections . furthermore , @xmath18 can be chosen lying on a strictly convex curve . b. if @xmath3 is globally non - symmetric and @xmath18 is either @xmath72 or @xmath73 then @xmath41 implies the coincidence of @xmath3 and @xmath64 up to translations and reflections . @xmath65 it is an open question whether part ii of the above theorem holds for all strictly convex @xmath3 not necessarily @xmath74 the positive answer to this question would imply the confirmation of matheron s conjecture for all planar convex bodies . the following theorem presents determination results involving locally symmetric and symmetric convex bodies . [ 06.05.16,15:21 ] let @xmath3 and @xmath35 be planar convex bodies with @xmath3 strictly convex . then the following statements hold true a. if @xmath3 is @xmath48-symmetric and @xmath53 is a closed simple curve in @xmath70 bounding an open region in @xmath47 that contains the origin , then the conditions @xmath75 and @xmath76 imply the coincidence of @xmath3 and @xmath64 up to translations and reflections . b. if @xmath18 is either @xmath72 or @xmath73 then @xmath41 implies the coincidence of all local symmetries of @xmath3 and @xmath64 up to translations . @xmath65 the statement of the following corollary follows directly from the second part of theorem [ 06.05.16,15:21 ] and two results from ( * ? ? ? * theorem 1.1 and proposition 1.4 ) . [ 06.05.24,09:59 ] every locally symmetric convex body in @xmath77 is determined uniquely , up to translations and reflections , by its covariogram function . @xmath65 let @xmath78 denote the closed unit ball in @xmath7 centered at the origin . further on , we introduce the condition @xmath79 a relaxation of @xmath80 and the `` local coincidence '' condition @xmath81 @xmath82 : : the equality @xmath83 holds for all @xmath43 in some neighbourhood of @xmath18 and a suitable constant @xmath84 @xmath85 : : for every boundary point @xmath86 of @xmath3 there exists a boundary point @xmath87 of @xmath35 such that for some @xmath88 the bodies @xmath89 and @xmath90 coincide , up to translations and reflections ; the same statement also holds with the roles of @xmath3 and @xmath35 interchanged . in the following theorem the relationship between the conditions @xmath91 @xmath92 @xmath93 and @xmath85 is discussed . [ 06.05.15,12:36 ] let @xmath3 and @xmath35 be convex bodies in @xmath94 then the following statements hold true . a. if @xmath3 is strictly convex , then @xmath85 implies @xmath95 b. if @xmath96 and @xmath3 is @xmath97 then @xmath85 is equivalent to @xmath95 c. if @xmath96 and @xmath3 is strictly convex , then @xmath98 is equivalent to @xmath95 d. there exist planar convex bodies @xmath3 and @xmath35 belonging to the class @xmath57 such that @xmath67 holds , while @xmath99 does not . e. there exist @xmath3 and @xmath64 which are convex @xmath32-polytopes , such that the conditions @xmath75 and @xmath99 hold , while @xmath67 does not . @xmath65 it is an open problem whether for @xmath57 convex bodies in @xmath100 @xmath101 the condition @xmath67 implies @xmath81 the space @xmath102 endowed with the hausdorff metric is locally compact and by this a baire space ( see @xcite and @xcite ) . thus , we may speak about statements that hold for most convex bodies , i.e. , for all convex bodies with at most a meager set of exceptions . we recall that a set is said to be _ meager _ if it is a countable union of nowhere dense sets and _ residual _ if it is a complement of a meager set . trivially , a finite intersection of residuals is a again a residual . furthermore , every set possessing a residual subset is also a residual . [ 06.05.08,17:28 ] in the baire category sense , for most convex bodies @xmath3 and all convex bodies @xmath35 in @xmath7 the following statements hold true . a. if @xmath3 and @xmath35 satisfy @xmath93 then @xmath3 and @xmath35 coincide , up to translations and reflections . b. if @xmath96 and @xmath3 and @xmath35 satisfy @xmath91 then @xmath3 and @xmath35 coincide , up to translations and reflections . furthermore , the above two statements can not be extended to all pairs of convex bodies @xmath3 and @xmath64 since there exist bodies @xmath3 and @xmath35 not coinciding , up to translations and reflections , and such that @xmath103 holds . in addition , the bodies @xmath3 and @xmath35 satisfying the above conditions can be chosen belonging to the class @xmath74 @xmath65 it is an open question whether part ii of the statement can be carried over to convex bodies of higher dimensions . the previous theorem is related to ( * ? ? ? * theorem 2 ) and ( * ? ? ? * theorem 6.2 ) . theorem 2 from @xcite states that most convex bodies @xmath3 in @xmath7 , for any @xmath6 , are determined by the combined knowledge of the _ width _ of @xmath3 in direction @xmath16 and of the @xmath104-dimensional volume of @xmath105 , for each @xmath13 . here @xmath106 denotes the orthogonal complement to @xmath107 and @xmath105 stands for the orthogonal projection of @xmath3 onto the hyperplane @xmath108 ( see also @xcite , where `` local versions '' of some results from @xcite are obtained , as well as ( * ? ? ? * theorems 3.3.17 and 3.3.18 ) . ) the relation with the covariogram comes from the fact that knowing its support @xmath109 is equivalent to knowing the width of @xmath3 in all directions , and that the knowledge of @xmath5 in a neighbourhood of @xmath48 gives the volumes of all @xmath110-dimensional projections of @xmath3 . this follows from the formula @xmath111 proved in @xcite and @xcite . here @xmath112 stands for right derivative . theorem 6.2 from @xcite is another result related to theorem [ 06.05.08,17:28 ] , which states that most convex planar bodies are determined by the covariogram function over its entire support . in section 3 we prove theorem [ 06.05.15,12:36 ] . sections 4 and 5 are independent of each other and present proofs of theorem [ 05.08.10,15:35 ] and theorem [ 06.05.16,15:21 ] , respectively . in section 6 we prove theorem [ 06.05.08,17:28 ] .

positive answers to matheron s question have been obtained for large classes of planar convex bodies , while for there are both positive and negative results . one of the purposes of this paper is to sharpen some of the known results on matheron s conjecture indicating how much of the covariogram information is needed to get the uniqueness of determination . we indicate some subsets of the support of the covariogram , with arbitrarily small lebesgue measure , such that the covariogram , restricted to those subsets , identifies certain geometric properties of the body . these results are more precise in the planar case , but some of them , both positive and negative ones , are proved for bodies of any dimension . moreover some results regard most convex bodies , in the baire category sense . another purpose is to extend the class of convex bodies for which matheron s conjecture is confirmed by including all planar convex bodies possessing two non - degenerate boundary arcs being reflections of each other . 52a20 , 52a22 , 52a38 , 60d05 .

the covariogram of a convex body is the function which associates to each the volume of the intersection of with matheron asked whether determines , up to translations and reflections in a point . positive answers to matheron s question have been obtained for large classes of planar convex bodies , while for there are both positive and negative results . one of the purposes of this paper is to sharpen some of the known results on matheron s conjecture indicating how much of the covariogram information is needed to get the uniqueness of determination . we indicate some subsets of the support of the covariogram , with arbitrarily small lebesgue measure , such that the covariogram , restricted to those subsets , identifies certain geometric properties of the body . these results are more precise in the planar case , but some of them , both positive and negative ones , are proved for bodies of any dimension . moreover some results regard most convex bodies , in the baire category sense . another purpose is to extend the class of convex bodies for which matheron s conjecture is confirmed by including all planar convex bodies possessing two non - degenerate boundary arcs being reflections of each other . 52a20 , 52a22 , 52a38 , 60d05 . convex body , convex polytope , covariogram , genericity result , geometric tomography , set covariance , quasicrystal .

0704.2706

i

in this paper , we present a number of results concerning a dynamical version of coalescing random walks , which was recently introduced in @xcite . our results concern times of hausdorff dimension less than one where the system of coalescing walks behaves exceptionally . the results are analogous to and were motivated by the model of dynamical percolation and its exceptional times @xcite . in this section , we define the basic model treated in this paper , which we call the dynamical discrete web ( ddw ) , recall some facts about dynamical percolation , and then briefly describe our main results . the justification for calling this model a discrete web is that there is a natural scaling limit , which is one of our main motivations for analyzing the discrete web ( as it is in @xcite ) ; we also discuss in this section that scaling limit , which is a dynamical version of the brownian web ( see @xcite ) . a paper is in preparation @xcite on the construction of that model , which is closely related to the brownian net of sun and swart @xcite . we note that conjectures conerning ways to construct scaling limits of dynamical percolation ( in two - dimensional space ) appear in @xcite . we further note that exceptional times for dynamical versions of random walks in various spatial dimensions have been studied in @xcite and elsewhere , but these are quite different from the random walks of the ddw , as we note in subsection [ mainresults ] below . let @xmath4 for @xmath5 denote a simple symmetric random walk on @xmath6 starting at @xmath7 , i.e. at @xmath8 at @xmath9 . ( for real @xmath10 , we set @xmath11)$ ] , where @xmath12 $ ] denotes the integer part of @xmath13 . ) if we also consider other simple symmetric random walks starting from arbitrary points on the even space - time sublattice @xmath14 , which are independent of each other except that they coalesce when they meet , that is the system of ( one - dimensional ) coalescing random walks that is closely related to the one - dimensional ( discrete time ) voter model ( see @xcite ) and may be thought of as a one plus one dimensional directed percolation model . the percolation structure is highlighted by defining @xmath15 for @xmath16 to be the increment between times @xmath17 and @xmath18 of the random walker at location @xmath19 at time @xmath17 . these bernoulli variables are symmetric and independent and the paths of all the coalescing random walks can be reconstructed by assigning to any point @xmath20 an arrow pointing from @xmath20 to @xmath21 and considering all the paths starting from arbitrary points in @xmath22 and following the arrows . we note that there is also a set of dual ( or backward ) paths defined by the same @xmath15 s with arrows from @xmath23 to @xmath24 . the collection of all dual paths is a system of backward ( in time ) coalescing random walks that do not cross any of the forward paths . the ddw is a very simple stochastic process @xmath25 in a new dynamical time parameter @xmath0 whose distribution at any deterministic @xmath0 is exactly that of the static coalescing random walk model just described . specifically , let @xmath26 be a family of independent continuous time cadlag markov processes with state space @xmath27 and rate @xmath28 for changing state in either direction , with the initial condition that @xmath29 is a family of independent bernoulli random variables with @xmath30 . although this dynamical version of coalescing random walks sounds quite trivial at first hearing , it turns out that it can have interesting behavior at exceptional values of the dynamical time parameter s. this is a feature that it shares in common with dynamical percolation . static percolation models are defined also in terms of independent bernoulli variables @xmath31 , indexed by points @xmath32 in some @xmath33-dimensional lattice , which in general are asymmetric with parameter @xmath34 . there is a critical value @xmath35 when the system has a transition from having infinite clusters ( connected components ) with probability zero to having them with probability one . it is expected that at @xmath36 there are no infinite clusters and this is proved for @xmath37 and for high @xmath33 ( see , e.g. , @xcite ) . in dynamical percolation one extends @xmath31 to time varying functions @xmath38 , as in the case of coalescing walks , except that the transition rates for the jump processes @xmath38 are chosen to have the critical asymmetric @xmath39 distribution to be invariant . the question raised in @xcite was whether there were exceptional times when an infinite cluster ( say , one containing the origin ) occurs , even though this does not occur at deterministic times . this was answered negatively in @xcite for large @xmath33 and , more remarkably , was answered positively by schramm and steiff for @xmath37 in @xcite , where they further obtained upper and lower bounds on the hausdorff dimension ( as a subset of the dynamical time axis ) of these exceptional times . we apply in this paper the approaches used for dynamical percolation to the dynamical discrete web . although we restrict attention to one - dimensional random walks whose paths are in two - dimensional space - time and hence analogous to @xmath37 dynamical percolation , by considering different possible exceptional phenomena , we use both the high @xmath33 and @xmath37 approaches of @xcite . a natural initial question was whether there might be exceptional dynamical times @xmath0 for which the walk from the origin @xmath40 is transient ( say to @xmath41 ) . our first main result ( see theorem [ th1 ] in section [ tameness ] below ) , modeled after the high-@xmath33 dynamical percolation results , is that there are no such exceptional times . as we explain in remark [ remtame ] in section [ tameness ] , a small modification of the proof of theorem [ th1 ] shows that there are also no exceptional times where some pair of walks avoids eventually coalescing . our other two main results are modelled after the @xmath37 dynamical percolation results . one of them ( see theorem [ violation ] below ) concerns a kind of violation of the central limit theorem , or more accurately a kind of weak subdiffusivity , by the random walk @xmath40 for exceptional dynamical times @xmath0 ; namely , that @xmath42 for all @xmath43 . the other ( see theorem [ dimension ] ) gives upper and lower bounds on the hausdorff dimension of these exceptional times , that depend nontrivially on the constant @xmath3 so that the dimension tends to zero ( respectively , one ) as @xmath44 ( respectively , @xmath45 ) . this is strikingly in contrast with the dynamical random walks of @xcite where there are no exceptional times for which the law of the iterated logarithm fails . to explain why the walks of @xcite can behave so differently from those of the discrete web , we note that a single switch in the former case affects only a single increment of the walk while some switches in the discrete web change the path of the walker by a `` macroscopic '' amount , as discussed in the next subsection on scaling limits see also figure 1 where switching has changed one of the paths macroscopically . by an obvious symmetry argument , there are also exceptional dynamical times @xmath0 for which @xmath46 . one may ask whether there are exceptional @xmath0 for which @xmath47 . as discussed in remark [ twosided ] below , it can be shown , at least for small @xmath3 , that there are no such exceptional times . the case of large @xmath3 is unresolved . [ fixeds ] be the random walk at dynamical time @xmath0 starting from @xmath48 . this graph , with @xmath13 the horizontal and @xmath49 the vertical coordinate , represents simultaneously the family of functions @xmath50 ( @xmath51 ) . the lowest path , say for @xmath13 greater than about @xmath52 , differs `` macroscopically '' from the others.,title="fig : " ] there is a natural scaling limit of the ( static ) coalescing random walks model , the brownian web ( see @xcite ) . here one does a usual diffusive scaling in which the random walk time @xmath13 is scaled by @xmath53 , and space by @xmath54 so that the random walk path starting from @xmath55 $ ] at time @xmath56 $ ] scales to a brownian motion starting from @xmath57 at time @xmath58 . the collection of all random walk paths from all space - time starting points scales to a collection of coalescing brownian motion paths starting from all points of continuum space - time . now taking the rate of switching to be of order @xmath59 , rescaling time and space respectively by @xmath53 and @xmath54 , and then letting @xmath60 go to @xmath8 leads to a nontrivial limit @xmath61 , the dynamical brownian web . the idea of taking a scaling limit of the dynamical discrete web to obtain a dynamical continuum model is a natural one , which is at the heart of @xcite , although their approach appears to be somewhat different than the one we had already been taking . both approaches are closely related to the brownian net construction of sun and swart @xcite as will be extensively explored in @xcite . as we shall discuss in the next subsection , our approach is based on the construction of a certain poissonian marking of special space - time points of the ( static ) brownian web . these are the so - called @xmath62 points where a single brownian web path enters the point from earlier times and then two paths leave to later times , one to the left and one to the right with exactly one of the those two paths the continuation of the path from earlier time and the other one `` newly - born '' ; see figure 2 . neither the idea of doing a poissonian marking of special points for the brownian web nor the idea of using those marked points to construct a scaling limit of a dynamical discrete model is completely new . in particular , we note that a different type of marking ( of @xmath63 points ) was used in @xcite to study the scaling limits of noisy voter models . also the idea of using marked double points of @xmath64 to construct the scaling limit of two - dimensional dynamical percolation is discussed in @xcite . one motivation for the proposed marking in the @xmath64 context was the analogy with markings of @xmath62 as well as of @xmath63 points of the brownian web . in the dynamical brownian web @xmath65 , one can also consider exceptional dynamical times @xmath0 where the path @xmath66 starting from the origin at continuous time @xmath9 behaves differently than an ordinary brownian motion path . the results of @xcite are very similar to those of this paper for the discrete web . indeed , in some respects , the proofs are simpler since calculations with brownian motions are often easier than those with random walks . there is however one substantial complication , which is the main focus of @xcite and the reason we do not present the dynamical brownian web exceptional time results already in this paper . that complication is the actual construction of the dynamical brownian web a construction that is considerably less trivial than that of the dynamical discrete web , as we explain in the next subsection . [ changedirections ] is the vertical and @xmath49 the horizontal coordinate . if a @xmath67 ( left ) point of the original web ( left side of the figure ) is marked to switch at some @xmath68 $ ] , then the direction of that @xmath62 point in the web @xmath69 is changed at @xmath70 so that it becomes a @xmath71 ( right ) point as on the right side of the figure with the incoming path joined to the rightmost of the two paths starting from that point.,title="fig : " ] at the discrete level the scaling is chosen in such a way that between the dynamical times @xmath8 and @xmath0 , in a macroscopic box ( i.e. , one with size of order @xmath72 in the original lattice ) , the number of arrows that change direction will be of order @xmath53 . the situation can be simplified by focusing on switchings with `` macroscopic '' effects ( i.e. , switchings that will lead to a macroscopic alteration of a walker s trajectory in the initial web @xmath73 ) . a priori , one should also consider combinations of switchings that have macroscopic effects , but it turns out ( this will be proved rigorously in @xcite ) that the probability of macroscopic effects from switching two or more arrows is negligible compared to switching single arrows , and can be neglected . there is a natural way of characterizing those critical switchings . for example , let us consider the forward ( rescaled ) path @xmath74 starting from the origin in @xmath73 and assume that the arrow located at some @xmath75 is orginally oriented to the left . now we ask whether a switching of this single arrow will alter the path in such a way that the altered path will be to the right of @xmath76 , where @xmath77 are both positive macroscopic quantities . this will happen if and only if the backward path @xmath78 starting from @xmath79 hits @xmath74 at time @xmath13 ( more precisely , hits @xmath80 at time @xmath81 ) . more generally , the critical arrows leading to similar alterations are the `` contact '' points between @xmath74 and the backward path @xmath78 at which a switching occurs on @xmath82 $ ] . but it is now fairly easy to see what the statistics of such a set of points are . in fact , let @xmath83 be the random variable counting the number of such switchings up to the macroscopic time @xmath13 . the distribution of @xmath83 is simply given by : @xmath84 where @xmath85 are i.i.d . bernoulli random variables with @xmath86 , which is @xmath87 as @xmath88 . as @xmath88 , @xmath89 converges to the `` local time '' @xmath90 of the forward brownian path @xmath91 starting from the origin along a backward brownian path @xmath92 starting on the right of the path @xmath93 ( the joint distribution of @xmath93 and @xmath92 is analysed in @xcite and this `` local time '' will be defined precisely in @xcite ) . further , it is a standard fact that @xmath94 converges to a poisson process . hence , @xmath83 will converge to a poisson process run by the random clock @xmath95 . in other words , this set of points will consist of a two - dimensional ( @xmath13 and @xmath0 ) poisson point process with intensity measure @xmath96 , where @xmath97 is lebesgue measure and @xmath98 is the local time measure ( note that @xmath99 will be a locally finite measure so that the poisson process is well defined ) . so far , we have only selected the critical switchings inducing a specific type of macroscopic effect . namely , the ones altering the path @xmath93 in such a way that a point originally on one side of @xmath93 will be on the opposite side after switching occurs . but in order to select all the critical arrows leading to any kind of macroscopic changes , we should not only consider a poisson process run by the local time of a single forward path @xmath93 against a single backward path @xmath92 , but rather a poisson process run by the `` local time of the entire forward web along the entire backward web '' multiplied by the intensity @xmath100 . in other words , the set of marked points will be a three - dimensional poisson point process with intensity measure @xmath101 , where @xmath97 is lebesgue measure ( in the variable @xmath0 ) and @xmath102 is the local time measure of the forward web along the backward web . would not be a locally finite measure i.e. , the set of marked points in space - time is actually dense in @xmath103 . however , like what is presented in @xcite ( see p. 11 there ) , one can add an extra coordinate and lift @xmath102 to be a @xmath104-finite measure , or equivalently approximate @xmath102 by a sequence of locally finite measures @xmath105 , do the markings using @xmath105 , and then let @xmath106 . ] since the @xmath62 points of the continuum web are precisely those at which a forward and a backward path meet ( see , e.g. , @xcite ) , the measure @xmath107 will be supported by this set of points . from our previous description of them , it should be clear that each @xmath62 point has a preferred left or right `` direction '' . for example , a @xmath71 ( right ) point is one for which the continuing path ( coming in from earlier time ) is to the right of the `` newly - born '' path . hence , at the continuum level , the analog of an arrow switching will simply be a change of direction of all marked @xmath62 points ( see figure 2 ) . the web @xmath69 at time @xmath108 will be `` simply '' deduced from @xmath109 by switching the direction of all marked @xmath62 points whose @xmath0-coordinate is in @xmath110 $ ] . a last comment concerns the nature of the dependence of the two continuum paths @xmath111 and @xmath112 . these turn out to be a pair of `` sticky '' brownian motions , which are independent except when they touch each other . this is one of the major observations in @xcite ; we give a brief derivation of this fact in section [ pairsofpaths ] by analyzing pairs of paths in the discrete setting to see what must occur in the continuum scaling limit . in section [ tameness ] , we state our main theorem about tameness ; i.e. , that there are no exceptional dynamical times when the random walkers are transient . we also give there some other results about tameness in two extended remarks one about non - coalescence and the other about two - sided bounds of order @xmath113 . then in section [ existence ] , we show that there are exceptional dynamical times when the walkers are ( weakly ) subdiffusive i.e. , have one - sided bounds of order @xmath113 . in section [ hausdorff ] we derive upper and lower bounds on the hausdorff dimension of the set of such exceptional dynamical times . some estimates for random walks that are needed for our arguments are given in appendix [ appendix ] .

the dynamical discrete web ( ddw ) , introduced in recent work of howitt and warren , is a system of coalescing simple symmetric one - dimensional random walks which evolve in an extra continuous dynamical time parameter . the evolution is by independent updating of the underlying bernoulli variables indexed by discrete space - time that define the discrete web at any fixed . in this paper our results are motivated by those about exceptional times for dynamical percolation in high dimension by hggstrom , peres and steif , and in dimension two by schramm and steif . the exceptional behavior of the walks in the ddw is rather different from the situation for the dynamical random walks of benjamini , hggstrom , peres and steif . in particular , we prove that there are exceptional values of for which the walk from the origin has with a nontrivial dependence of the hausdorff dimension on . we also discuss how these and other results extend to the dynamical brownian web , a natural scaling limit of the ddw . the scaling limit is the focus of a paper in preparation ; it was also studied by howitt and warren and is related to the brownian net of sun and swart .

the dynamical discrete web ( ddw ) , introduced in recent work of howitt and warren , is a system of coalescing simple symmetric one - dimensional random walks which evolve in an extra continuous dynamical time parameter . the evolution is by independent updating of the underlying bernoulli variables indexed by discrete space - time that define the discrete web at any fixed . in this paper , we study the existence of exceptional ( random ) values of where the paths of the web do not behave like usual random walks and the hausdorff dimension of the set of exceptional such . our results are motivated by those about exceptional times for dynamical percolation in high dimension by hggstrom , peres and steif , and in dimension two by schramm and steif . the exceptional behavior of the walks in the ddw is rather different from the situation for the dynamical random walks of benjamini , hggstrom , peres and steif . in particular , we prove that there are exceptional values of for which the walk from the origin has with a nontrivial dependence of the hausdorff dimension on . we also discuss how these and other results extend to the dynamical brownian web , a natural scaling limit of the ddw . the scaling limit is the focus of a paper in preparation ; it was also studied by howitt and warren and is related to the brownian net of sun and swart .

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gamma - ray bursts ( grbs ) are brief , intense flashes of @xmath0-rays originating at cosmological distances , and they are the most luminous objects in the universe . they also have broadband afterglows long - lasting after the @xmath0-ray radiation has ceased . it has been established that the bursts and afterglows are emitted from outflows moving towards us at highly relativistic speeds @xcite , and at least some grbs are associated with the collapse of massive stars ( e.g. , * ? ? ? * ; * ? ? ? observations suggest that the burst is produced by internal dissipation within the relativistic jet that is launched from the center of the explosion , and the afterglow is the synchrotron emission of electrons accelerated in a collisionless shock driven by the interaction of the jet with the surrounding medium ( for recent reviews , * ? ? ? * ; * ? ? ? * ; * ? ? ? in spite of extensive observational and theoretical efforts , several key questions concerning the nature of the central engines of the relativistic jets and the jets themselves remain poorly understood . in fact , some of these questions are very difficult or even impossible to answer with the spectral and lightcurve information currently collected . on the other hand , polarization information , if retrieved , would lead to unambiguous answers to these questions . in particular , polarimetric observations of grbs can address the following : _ magnetic composition of grb jets _ it is highly speculated that strong magnetic fields are generated at the grb central engine , and may play an essential role in the launch of the relativistic jets . however , it is unclear whether the burst emission region is penetrated by a globally structured , dynamically important magnetic field , and whether the burst is due to shock dissipation or magnetic reconnection ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? . _ emission mechanisms of the bursts _ the leading model for the emission mechanism of the prompt burst emission is synchrotron emission from relativistic electrons in a globally ordered magnetic field carried from the central engine , or random magnetic fields generated in - situ in the shock dissipation region @xcite . other suggestions include compton drag of ambient soft photons @xcite , synchrotron self - compton emission @xcite , and the combination of a thermal component from the photosphere and a non - thermal component ( e.g. , synchrotron ) @xcite . _ geometric structure of grb jets _ although it is generally believed that grb outflows are collimated , the distribution of the jet opening angles , the observer s viewing direction , and whether there are small - scale structures within the global jet are not well understood @xcite . to date , robust positive detections of grb polarization have been made only in the optical band in the afterglow phase . varying linear polarizations have been observed in several optical afterglows several hours after the burst trigger , with a level of @xmath6 , which is consistent with the synchrotron emission mechanism of grb afterglow ( for reviews , see * ? ? ? * ; * ? ? ? an upper limit @xmath7 has been obtained for the early @xmath8 optical afterglow of grb 060418 @xcite . also for radio afterglows , we have several upper limits for the polarization degree @xcite ( for some implications , see * ? ? ? as for the prompt burst emission , strong linear polarization of the @xmath0-ray emission at a level of @xmath9 was claimed for grb 021206 based on an analysis of _ rhessi _ data @xcite , although this claim remains controversial because of large systematic uncertainties @xcite . several other reports of high levels of polarization in the prompt burst emission are also statistically inconclusive @xcite . recently , more sensitive observational techniques for x - ray and @xmath0-ray polarimetry have been developed , and there are several polarimeter mission concepts . these include polarimeters for energetic transients ( _ poet _ , * ? ? ? * ; * ? ? ? * ) , polarimeter of gamma - ray observer ( _ pogo _ , * ? ? ? * ) , _ polar _ @xcite , advanced compton telescope ( _ act _ , * ? ? ? * ) , gravity and extreme magnetism ( _ gems _ , * ? ? ? * ) _ xpol _ @xcite , gamma - ray burst investigation via polarimetry and spectroscopy ( _ grips _ , * ? ? ? * ) , and so on . several of these missions , if launched , would provide definitive detections of the burst polarizations and enable us to discuss the statistical properties of the polarization degrees and polarization spectra . although there are several polarimetry mission concepts described in the literature , _ poet _ is the only one to date that incorporates a broadband capability for measuring the prompt emission from grbs , and for this reason it provides a good case study for our simulations . _ poet _ will make measurements with two different polarimeters , both with wide fields of view . the gamma - ray polarimeter experiment ( grape ; 60 - 500 kev ) and the low energy polarimeter ( lep ; 2 - 15 kev ) provide a broad energy range for the observations . suborbital versions of both _ poet _ instruments are currently being prepared for flight within the next few years . grape will fly on a sub - orbital balloon in 2011 , and the gamma - ray burst polarimeter ( grbp , a smaller version of lep ) will fly on a sounding rocket . theoretically , it has been shown that similarly high levels of linear polarization can be obtained in several grb prompt emission models ; the synchrotron model with a globally ordered magnetic field , the synchrotron model with a small - scale random magnetic field @xcite , and the compton drag model @xcite . thus the detections of grb prompt emission polarization would support these three models . in this paper , we show that these models can be distinguished by their statistical properties of observed polarizations . we performed detailed calculations of the distribution of polarization degrees by including realistic spectra of grb prompt emission and assuming realistic distributions of the physical parameters of grb jets , and show that _ poet _ , or other polarimeters with similar capabilities , can constrain the grb emission models . we use the limits of _ poet _ for grb detection and polarization measurements as realistic and fiducial limits . this paper is organized as follows . we first introduce the _ poet _ mission concept in [ sec : poet ] . in [ sec : theory ] , we summarize the properties of the observed linear polarization from uniform jets within the three emission models . based on these models , we perform monte carlo simulations of observed linear polarizations and show how the statistical properties of observed polarization may constrain grb emission mechanisms in [ sec : simulation ] . a summary and discussion are given in [ sec : summary ] .

the emission mechanism and the origin and structure of magnetic fields in gamma - ray burst ( grb ) jets are among the most important open questions concerning the nature of the central engine of grbs . in spite of extensive observational efforts , these questions remain to be answered and are difficult or even impossible to infer with the spectral and lightcurve information currently collected . polarization measurements will lead to unambiguous answers to several of these questions . recent developments in x - ray and-ray polarimetry techniques have demonstrated a significant increase in sensitivity enabling several new mission concepts , e.g. _ poet _ ( polarimeters for energetic transients ) , providing wide field of view and broadband polarimetry measurements .

the emission mechanism and the origin and structure of magnetic fields in gamma - ray burst ( grb ) jets are among the most important open questions concerning the nature of the central engine of grbs . in spite of extensive observational efforts , these questions remain to be answered and are difficult or even impossible to infer with the spectral and lightcurve information currently collected . polarization measurements will lead to unambiguous answers to several of these questions . recent developments in x - ray and-ray polarimetry techniques have demonstrated a significant increase in sensitivity enabling several new mission concepts , e.g. _ poet _ ( polarimeters for energetic transients ) , providing wide field of view and broadband polarimetry measurements . if launched , missions of this kind would finally provide definitive measurements of grb polarizations . we perform monte carlo simulations to derive the distribution of grb polarizations in three emission models ; the synchrotron model with a globally ordered magnetic field ( so model ) , the synchrotron model with a small - scale random magnetic field ( sr model ) , and the compton drag model ( cd model ) . the results show that _ poet _ , or other polarimeters with similar capabilities , can constrain the grb emission models by using the statistical properties of grb polarizations . in particular , the ratio of the number of grbs for which the polarization degrees can be measured to the number of grbs that are detected ( ) and the distributions of the polarization degrees ( ) can be used as the criteria . if and is clustered between 0.2 and 0.7 , the so model will be favored . if instead , then the sr or cd model will be favored . if several events with are observed , then the cd model will be favored .

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recently there has been an increasing interest in the measurement of x - ray and @xmath0-ray polarization , and the observational techniques can now achieve significant sensitivity in the relevant energy bands . several polarimetry mission concepts , such as _ poet _ , are being planned . the _ poet _ concept has two polarimeters , grape ( 60 - 500 kev ) and lep ( 2 - 15 kev ) both of which have wide fields of view . if launched , missions of this type would provide the first definitive detection of the polarization of grb prompt emission . this would enable the discussion of the statistical properties of the polarization degree and polarization spectra , which will give us diagnostic information on the emission mechanism of grbs and the nature of the grb jets that can not be obtained from current spectra and lightcurve observations . we have performed monte carlo simulations of the linear polarization from grb jets for three major emission models : synchrotron model with globally ordered magnetic field ( so model ) , synchrotron model with small - scale random magnetic field ( sr model ) , and compton drag model ( cd model ) . we assumed that the physical quantities for the emission of the jets are uniform on the emitting surface and that the jets have sharp edges . our jet angle distribution allows the detections of grbs with very small opening angles ( i.e. , smaller than 1 degree ) as suggested by several _ bursts @xcite . we have shown that the _ poet _ mission or other polarimeters with similar capabilities , i.e. , broadband spectral capabilities for the determination of @xmath33 and sensitive broadband polarimetric capabilities to minimize mdp , can constrain the emission models of grbs . furthermore , these simulations indicate that an increase in the lep effective area would be beneficial to compensate for the lower expected polarization at lower energies . as shown in figures [ fig : atorob ] , [ fig : arndb ] , and [ fig : acomp ] , the sr and cd models require off - axis observations of the jets to achieve a high level of polarization , while the so model does not . in this sense the sr and cd models are categorized as _ geometric _ models , and the so model as an _ intrinsic _ model @xcite . the distribution of observed polarizations obtained by our simulations show that the geometric sr / cd models will be ruled out if the number ratio of the @xmath2-measurable bursts to detected bursts is larger than @xmath256 , and in this case the so model will be favored if the measurable polarizations are clustered at @xmath253 . if the number ratio is smaller than @xmath257 , the so model may be ruled out , but we can not distinguish between the sr and cd models with different distributions of @xmath150 , @xmath35 , and @xmath36 , where @xmath0 and @xmath48 are the bulk lorentz factor and the opening angle of the grb jet , respectively , and @xmath35 and @xmath36 are lower and higher indices of the energy spectrum . however , if several bursts with @xmath5 are detected , the cd model which includes an adequate number of small @xmath111 bursts will be favored . if the cumulative distribution of the measurable polarizations favors the so model , the globally ordered magnetic field would be advected from the central engine . if we understand the strength of the magnetic field in the emitting region from the luminosity and the spectrum of the emission , we can constrain the strength of the field at the central engine . if the geometric sr / cd models are favored from the observations , it will be established , independently of the afterglow observations , that grb outflows are not spherical but highly collimated . if the cd model is favored by the observations , we may constrain the distribution of the parameter @xmath258 of grb jets . the cd model needs a dense optical / uv photon field interacting within the relativistic jets @xcite . we have made some simplifications in our simulations , and there are some caveats . we have assumed that the jets are uniform on the emitting surfaces and have sharp edges . to compare the simulations and the observations further , more sophisticated modeling is required ( e.g. , * ? ? ? * ; * ? ? ? we have interpreted bursts as a simple combination of pulses , without taking account of the temporal variation of the lorentz factor @xmath0 of the jet . if this is accounted for , each pulse may have different @xmath150 but the same @xmath149 . we should then average the polarization with respect to fluence of each pulse having different @xmath111 @xcite . however , in the so model , the cumulative distribution of measurable @xmath2 will not be changed significantly as long as @xmath259 , because @xmath2 is clustered into a small range for @xmath129 and @xmath251 . to average the polarization in the case of @xmath219 , the relation between the luminosity and the lorentz factor for each pulse is required to predict the polarization distribution . for the sr model we have assumed that the directions of the magnetic field are confined within the shock plane . they may be more isotropic in reality , in which case the polarization degree in the sr model will be reduced . in the synchrotron model with a combination of the globally ordered magnetic field and the locally random field , @xmath260 , the linear polarization can be calculated by @xmath261 , where @xmath262 and @xmath263 are the stokes parameters from the ordered and random fields , respectively . @xmath264 and @xmath265 are described by equations ( [ eq : atorob ] ) and ( [ eq : arndb ] ) , and @xmath266 . this model will reduce the number ratio of @xmath2-measurable bursts to detected bursts to less than 30% and the clustering of measurable polarizations will be at @xmath267 . this work is supported in part by the grant - in - aid from the ministry of education , culture , sports , science and technology ( mext ) of japan , no.19047004 ( ry , ki , and tn ) , no.18740153 ( ry ) , no.18740147 ( ki ) , and in part by the grant - in - aid for the global coe program _ the next generation of physics , spun from universality and emergence _ from the ministry of education , culture , sports , science and technology ( mext ) of japan . bz acknowledges nasa nng05gb67 g and nnx08ae57a ( nevada nasa epscor program ) and kt acknowledges nasa nnx08al40 g for partial supports . amati , l. 2002 , a&a , 390 , 81 band , d. l. , et al . 1993 , apj , 413 , 281 begelman , m. c. , & sikora , m. 1987 , apj , 322 , 650 black , j. k. , et al . 2007 , nima , 581 , 755 bloser , p. f. , et al . 2006 , chjas , 6 , 393 bloser , p. f. , et al . 2008 , accepted in nima ( arxiv:0812.0782 ) boggs , s. e. , et al . 2006 , arxiv : astro - ph/0608532 coburn w. , & boggs , s. e. 2003 , nature , 423 , 415 costa , e. , et al . 2007 , in proc . of spie vol.6686 , 30 covino , s. , ghisellini , g. , lazzati , d. , & malesani , d. 2004 , in asp conf . 312 , 169 dai , x. , & zhang , b. 2005 , apj , 621 , 875 donaghy , t. q. 2006 , apj , 645 , 436 eichler , d. , & levinson , a. 2003 , apj , 596 , l147 fendt , c. , & ouyed , r. 2004 , apj , 608 , 378 frail , d. a. , et al . 2001 , apj , 562 , l55 genet , f. , daigne , f. , & mochkovitch , r. 2007 , mnras , 381 , 732 ghisellini , g. , & lazzati , d. 1999 , mnras , 309 , l7 ghisellini , g. , ghirlanda , g. , nava , l. , & firmani , c. 2007 , apj , 658 , l75 granot , j. , piran t. , & sari , r. 1999 , apj , 513 , 679 granot , j. 2003 , apj , 596 , l17 granot , j. , & taylor , g. b. 2005 , apj , 625 , 263 greiner , j. , et al . 2008 , in aip conference proceedings , volume 1000 , 620 . gruzinov , a. , & waxman , e. 1999 , apj , 511 , 852 hill , j. e. , et al . 2008 , in proc . of 2008 nanjing grb conference ( arxiv : 0810.2499 ) hjorth , j. 2003 , nature , 423 , 847 ioka , k. , & nakamura , t. 2001 , apj , 554 , l163 ioka , k. , & nakamura , t. 2002 , apj , 570 , l21 ioka , k. , et al . 2007 , apj , 670 , l77 jahoda , k. , et al . 2007 , arxiv : astro - ph/0701090 jason , l. , et al . 2005 , in proc . of spie vol.5898 , 413 kalemci , e. , et al . 2007 , apjs , 169 , 75 lazzati , d. , ghisellini , g. , celotti , a. , & rees , m. j. 2000 , apj , 529 , l17 lazzati , d. , rossi , e. , ghisellini , g. , rees , m. j. 2004 , mnras , 347 , l1 lazzati , d. 2006 , new journal of physics , 8 , 131 levinson , a. , & eichler , d. 2004 , apj , 613 , 1079 lithwick , y. , & sari , r. 2001 , apj , 555 , 540 lyutikov , m. , pariev , v. i. , & blandford , r. d. 2003 , apj , 597 , 998 matsumiya , m. , & ioka , k. 2003 , apj , 595 , l25 mcglynn , s. , et al . 2007 , a&a , 466 , 895 medvedev , m. v. , & loeb , a. 1999 , apj , 526 , 697 mszros , p. 2006 , rep . , 69 , 2259 mizuno , t. , et al . 2005 , nucl . instrum . methods . a , 540 , 158 mundell , c. g. , et al . 2007 , science , 315 , 1822 nakar , e. , piran , t. , & waxman , e. 2003 , jcap , 10 , 5 panaitescu , a. , & mszros , p. 2000 , apj , 544 , l17 piran , t. 2005 , rev . , 76 , 1143 porciani , c. , & madau , p. 2001 , apj , 548 , 522 preece , r. d. , et al . 2000 , apjs , 126 , 19 produit , n. , et al . 2005 , nucl . instrum . methods . res . sec . a , 550 , 616 racusin , j. l. , et al . 2008 , nature , 455 , 183 rees , m. j. , & mszros , p. 1994 , apj , 430 , l93 rutledge , r. e. , & fox , d. b. 2004 , mnras , 350 , 1288 rybicki , g. b. , & lightman , a. p. 1979 , radiative processes in astrophysics ( new york : wiley interscience ) ryde , f. , et al . 2006 , apj , 652 , 1400 sagiv , a. , waxman , e. , & loeb , a. 2004 , apj , 615 , 366 sakamoto , t. , et al . 2005 , apj , 629 , 311 sari , r. 1999 , apj , 524 , l43 schady , p. , et al . 2007 , mnras , 380 , 1041 shaviv , n. j. , & dar , a. 1995 , apj , 447 , 863 spruit , h. c. , daigne , f. , & drenkhahn , g. 2001 , a&a , 369 , 694 stanek , k. z. , et al . 2003 , apj , 591 , l17 taylor , g. b. , frail , d. a. , berger , e. , & kulkarni , s. r. 2004 , apj , 609 , l1 taylor , g. b. , momjian , e. , philstrom , y. , ghosh , t. , & salter , c. 2005 , apj , 622 , 986 thompson , c. , mszros , p. , & rees , m. j. 2007 , apj , 666 , 1012 toma , k. , yamazaki , r. , nakamura , t. 2005 , apj , 635 , 481 toma , k. , ioka , k. , & nakamura , t. 2008 , apj , 673 , l123 uhm , z. l. , & beloborodov , a. m. 2007 , apj , 665 , l93 waxman , e. 2003 , nature , 423 , 388 wigger , c. , et al . 2004 , apj , 613 , 1088 willis , d. r. , et al . 2005 , a&a , 439 , 245 woods , e. , & loeb , a. 1999 , apj , 523 , 187 yamazaki , r. , ioka , k. , & nakamura , t. 2004 , apj , 606 , l33 yonetoku , d. , yamazaki , r. , nakamura , t. , & murakami , t. 2005 , mnras , 362 , 1114 zeh , a. , klose , s. , & kann , d. a. 2006 , apj , 637 , 889 zhang , b. , & mszros , p. 2002 , apj , 581 , 1236 zhang , b. , dai , x. , lloyd - ronning , n. m. , & mszros , p. 2004 , apj , 601 , l119 zhang , b. 2007 , chin . j. astron . astrophys . ,

if launched , missions of this kind would finally provide definitive measurements of grb polarizations . we perform monte carlo simulations to derive the distribution of grb polarizations in three emission models ; the synchrotron model with a globally ordered magnetic field ( so model ) , the synchrotron model with a small - scale random magnetic field ( sr model ) , and the compton drag model ( cd model ) .

the emission mechanism and the origin and structure of magnetic fields in gamma - ray burst ( grb ) jets are among the most important open questions concerning the nature of the central engine of grbs . in spite of extensive observational efforts , these questions remain to be answered and are difficult or even impossible to infer with the spectral and lightcurve information currently collected . polarization measurements will lead to unambiguous answers to several of these questions . recent developments in x - ray and-ray polarimetry techniques have demonstrated a significant increase in sensitivity enabling several new mission concepts , e.g. _ poet _ ( polarimeters for energetic transients ) , providing wide field of view and broadband polarimetry measurements . if launched , missions of this kind would finally provide definitive measurements of grb polarizations . we perform monte carlo simulations to derive the distribution of grb polarizations in three emission models ; the synchrotron model with a globally ordered magnetic field ( so model ) , the synchrotron model with a small - scale random magnetic field ( sr model ) , and the compton drag model ( cd model ) . the results show that _ poet _ , or other polarimeters with similar capabilities , can constrain the grb emission models by using the statistical properties of grb polarizations . in particular , the ratio of the number of grbs for which the polarization degrees can be measured to the number of grbs that are detected ( ) and the distributions of the polarization degrees ( ) can be used as the criteria . if and is clustered between 0.2 and 0.7 , the so model will be favored . if instead , then the sr or cd model will be favored . if several events with are observed , then the cd model will be favored .

astro-ph0501182

i

clusters of galaxies have received intensive observational study over the last decades . this effort has lead to clear results on the way galaxy properties , such as morphology and star formation rate , vary within clusters and how these properties evolve between clusters at different redshifts ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * see bower & balogh 2004 for a recent review ) . in contrast , comparably detailed studies of galaxy groups and their evolution have only recently begun in earnest . the group environment is likely to have a significant impact on star formation rates in the member galaxies @xcite and recent work has emphasied that even for galaxies now in rich clusters , much of the transformation of the galaxies properties may have taken place in groups embedded in the filamentary structure @xcite . in addition , while few galaxies in the local universe are located in clusters , up to 50 per cent @xcite may be located in galaxy groups . furthermore , this number is strongly redshift dependent , as a larger and larger fraction of galaxies become members of groups as the large - scale structure of the universe develops . thus the properties of galaxies in groups and the impact of the group environment on the evolution of galaxies can have an important bearing on the decline of the cosmic star formation rate from @xmath0 to the present - day @xcite . studies of nearby groups show that their galaxy populations exhibit properties which vary from cluster - like ( mostly early - type ) to field - like ( mostly late type ) @xcite . however we know that groups span a wide range in local density , upon which the morphological composition @xcite and the mean star forming properties @xcite strongly depend ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the wide range of galaxy populations found in nearby groups is likely to be a natural consequence of these correlations . conversely , the powerful dependence of galaxy properties on local densities typical of groups suggests that groups provide the ideal environment for galaxy transformations . this may result in the strong dependence of early type fraction and passive dwarf galaxy abundance on group velocity dispersion and x - ray luminosity , observed in nearby groups @xcite . in particular , galaxy interactions are expected to be common in groups , in which the velocity dispersion is typically not much larger than that of the constituent galaxies @xcite . groups have a much lower density contrast against the background galaxy population , so most work has concentrated on groups which are either unusually compact @xcite or x - ray luminous @xcite . more recently , the advent of large field galaxy redshift surveys has made it possible to study galaxy groups selected purely on the basis of their three dimensional galaxy density . in the local universe , early redshift surveys and more recently the extensive 2df galaxy redshift survey ( 2dfgrs ) and sloan digital sky survey ( sdss ) have generated large group catalogues which can be used as the basis for studies of galaxies in the group environment @xcite however , the properties of higher redshift groups have been relatively little explored . this is largely because of the difficulty in finding suitable systems , and the low success rate of spectroscopic follow - up of group members . @xcite used radio galaxies to preselect groups in order to study the evolution of the blue galaxy fraction with redshift , while @xcite have presented a group catalogue based on the cnoc2 galaxy redshift survey . in this paper , we present new data obtained in the region of 26 cnoc2 groups at @xmath3 with ldss2 on magellan . in sections [ sec : cnoc2groupdata ] and [ sec : whyoiiforsf ] we introduce the data and explain why we have chosen to use the [ oii ] emission line to study statistical trends in star formation . in section [ sec : cnoc2dataprocessing ] we begin by describing the data reduction procedure and our method for determination of redshifts and emission line equivalent widths for each galaxy . section [ sec : grpmem ] then goes on to explain our procedure for group membership allocation . in section [ sec : indivgrps ] we present the properties of the 26 individual groups in order to examine any trends of structural group properties with star formation . finally , in section [ sec : stackedgrp ] groups are stacked to enable detailed statistical analaysis , and we investigate the link between the group environment and star formation by contrasting the stacked group with our sample of field galaxies selected from the same redshift range . in a second paper ( * hereafter known as paper ii ) , we present a comparison of the star forming properties of these intermediate redshift groups with local groups selected from the 2pigg catalogue at @xmath4 @xcite . throughout this paper we assume a @xmath5cdm cosmology of @xmath6 , @xmath7 and @xmath8 .

the evolution of galaxies in groups may have important implications for the evolution of the star formation history of the universe , since many processes which operate in groups may suppress star formation and the fraction of galaxies in bound groups grows rapidly between and the present day . in this paper , we present an investigation of the properties of galaxies in galaxy groups at intermediate redshift ( ) . the groups were selected from the cnoc2 redshift survey as described in , with further spectroscopic follow - up undertaken at the magellan telescope in order to improve the completeness and depth of the sample . we stack the galaxy groups in order to compare the properties of group galaxies with those of field galaxies at the same redshift . the groups contain a larger fraction of passive galaxies than the field , this trend being particularly clear for galaxies brighter than in the higher velocity dispersion groups . these trends are qualitatively consitent with the differences between group and field galaxies seen in the local universe . galaxies : fundamental parameters galaxies : evolution galaxies : stellar content catalogues

the evolution of galaxies in groups may have important implications for the evolution of the star formation history of the universe , since many processes which operate in groups may suppress star formation and the fraction of galaxies in bound groups grows rapidly between and the present day . in this paper , we present an investigation of the properties of galaxies in galaxy groups at intermediate redshift ( ) . the groups were selected from the cnoc2 redshift survey as described in , with further spectroscopic follow - up undertaken at the magellan telescope in order to improve the completeness and depth of the sample . we present the data for the individual groups , and find no clear trend in the fraction of passive galaxies with group velocity dispersion and group concentration . we stack the galaxy groups in order to compare the properties of group galaxies with those of field galaxies at the same redshift . the groups contain a larger fraction of passive galaxies than the field , this trend being particularly clear for galaxies brighter than in the higher velocity dispersion groups . in addition , we see evidence for an excess of bright passive galaxies in the groups relative to the field . in contrast , the luminosity functions of the star forming galaxies in the groups and the field are consistent . these trends are qualitatively consitent with the differences between group and field galaxies seen in the local universe . galaxies : fundamental parameters galaxies : evolution galaxies : stellar content catalogues

cond-mat0406202

i

quantum turbulence , the seemingly chaotic motion of quantized vortex lines in a disordered network , is a prominent characteristic of superfluid @xmath1he - ii , where it has been known to exist for almost half a century.@xcite up to recently , @xmath1he - ii was the only superfluid system in which this phenomenon has been investigated . @xmath1he - ii is believed to display turbulence in the entire superfluid temperature range which so far has been probed with measurements . in superconductors friction in vortex motion is always high and turbulence is not observed : only in the extreme clean limit one might hope to see any signs of other behavior . at present the closest superconducting analogues are dynamically driven vortex avalanches.@xcite superfluid @xmath0he is an intermediate case between these two extremes . the dynamics of vortex motion in the @xmath0he superfluids has primarily been studied in rotating cryostats . in the past the generally accepted view was that the high mutual friction leads to exponentially damped motion and forces vortices to evolve rapidly along well defined trajectories , so that the number of vortex lines remains conserved in dynamic processes . a large number of measurements over the years has proven this to be the case in both @xmath0he - a and @xmath0he - b at @xmath4.@xcite even at low temperatures ( @xmath5 ) a duplication of the classic vinen - vibrating - wire measurement@xcite verified that in @xmath0he - b stable vortex motion persists for hours in the absence of applied flow . in this experiment superfluid circulation was trapped around a thin wire suspended along the symmetry axis of a cylindrical container while the cryostat was rotating . when rotation was stopped , the trapped circulation started to unwind while a vortex filament , stretched between the wire and the cylinder wall , precessed around the wire and spiraled down along the whole length of the 15 mm long cylinder . the precessing spiral motion lasted for more than 35h and the precession frequency remained constant with a precision of 0.5% . the first indications of rapid non - linear vortex proliferation in @xmath0he - b came from measurements of the critical velocity of vortex formation at temperatures @xmath6 ( ref . , see p. 140141 ) . instead of the usual single - vortex formation at a reproducible critical velocity , sudden avalanches of vortices were observed in accelerating rotation . these bursts were interpreted to mean that at lower temperatures mutual - friction damping had decreased sufficiently so that turbulence became possible . the first evidence for tangled vorticity was reported from vibrating wire measurements in a non - rotating cryostat at temperatures below @xmath7.@xcite a vortex network was found to be produced with a vibrating wire resonator when it was driven at high level above a critical velocity of vortex formation . this was inferred by studying the damping of a second wire , vibrating at low level and probing the density of quasiparticle excitations which are andreev retro - reflected by the superflow fields in the vortex tangle . similar later measurements have allowed a determination of the vortex density in the wire - generated network . at zero externally applied pressure and at a temperature of @xmath8 the tangle localized around the vibrating wire turned out to have extremely low density , corresponding to an average inter - vortex distance of 0.2 mm , and to decay away rapidly in about 5s , when the generator wire was switched off.@xcite there exist no immediately obvious techniques by which turbulence can be easily generated and detected in @xmath0he - b . the above two examples suggest two ways which are supplementary , since they work in different temperature regimes . as outlined below in sec . [ experiment ] , nmr on a rotating sample can be used at temperatures down to about @xmath9 . in the zero temperature limit , where the density @xmath10 of the normal component approaches zero , moving objects can be used to generate vortices and , when driven in a high - quality resonance mode , to detect them . in this report we outline the techniques by which turbulence is generated and detected in the intermediate temperature regime 0.4 @xmath11 , where mutual friction damping and @xmath10 are still finite . recently a practical technique was discovered for injecting vortex loops into vortex - free flow.@xcite it then became possible to monitor the nature of vortex dynamics as a function of temperature and flow velocity in a controlled fashion.@xcite the transition , which separates regular vortex motion from turbulence , could now be mapped . the foundation , on which the interpretation of these results is built , was laid down by an earlier set of important hydrodynamic measurements@xcite on mutual friction which provided both the dissipative and reactive mutual friction coefficients @xmath12 and @xmath13 as a function of temperature @xmath14 and pressure @xmath15 . it turns out that in @xmath0he - b the variation of mutual friction with temperature happens to be such that the transition falls in the middle of the experimental temperature range , to 0.5 @xmath11 . these techniques have been employed in three recent studies investigating turbulence in @xmath0he - b.@xcite the first@xcite reports on the flight time of the vorticity when it expands along the rotating column . the second@xcite describes how turbulence starts in rotating vortex - free flow in the presence of neutron radiation . the third@xcite discusses the mutual - friction dependence of the transition from regular to turbulent vortex dynamics , _ i.e. _ the transition line as a function of @xmath16 and @xmath17 at high flow velocities , where the transition is velocity independent . these transition properties will also be illuminated in sec . [ turbtransition ] of this report , but from a different point of view . nmr measurements from the transient period , when the turbulent vorticity decays into the equilibrium rotating state of rectilinear vortex lines , will be analyzed in a forthcoming report.@xcite according to current view no similar kind of turbulence as in @xmath1he - ii or @xmath0he - b exists in the anisotropic superfluid @xmath0he - a . here vortex motion is highly damped at all experimentally accessible temperatures and fast vortex motion is supported by the appearance of a different structure of vorticity , the vortex sheet.@xcite

the experimental investigation of superfluid turbulence inhe - b is generally not possible with the techniques which have been developed forhe - ii . we describe a new method by which a transient burst of turbulent vortex expansion can be generated inhe - b . pacs numbers : 47.37 , 67.40 , 67.57 .

the experimental investigation of superfluid turbulence inhe - b is generally not possible with the techniques which have been developed forhe - ii . we describe a new method by which a transient burst of turbulent vortex expansion can be generated inhe - b . it is based on the injection of a few vortex loops into rotating vortex - free flow . the time - dependent evolution of the quantized vorticity is then monitored with nmr spectroscopy . using these techniques the transition between regular ( _ i.e. _ vortex number conserving ) and turbulent vortex dynamics can be recorded at and a number of other characteristics of turbulence can be followed down to a temperature of . pacs numbers : 47.37 , 67.40 , 67.57 .

nucl-ex0412039

i

an in - flight fragment separation apparatus can be used in two ways : * as a recoil spectrometer , to measure production cross sections or kinematics properties of the fragments ; * as a separation device , aiming at producing high - purity secondary beams of nuclides . the fragment recoil separator ( frs ) @xcite of gsi has been very successfully used for both purposes for more than ten years . by now , several projects across the world are dedicated to the construction of more powerful devices , in terms of larger fragment acceptance ( spectrometer for fission products ) , and/or increased selectivity and high - intensity secondary - beam production . the upper energy range covered by such devices seems to be mostly a technological ( and financial ) question , as increasing the energy requires more powerful magnets and a longer flight path , not even talking about the accelerator itself . but the lower range is determined by physics : it is assumed that only a very low proportion of non - fully stripped fragments can be tolerated in order to obtain a clean separation of fragments and to measure production cross sections . therefore , a whole energy range is somehow forbidden to fragmentation experiments . this low - energy limit has been faced by a recent experiment conducted at the gsi spectrometer frs . the aim of this experiment was to use the inverse - kinematics method to measure production cross sections from residues of the spallation of lead by protons with an incident energy of 500a mev . the results of this experiment will be the subject of a separate , forthcoming publication . this paper is dedicated to the description of the experimental and analysis techniques which were developed for this experiment and to discuss whether or not they proved to be successful . part of these techniques may be used more generally than for the frs setup from gsi . first we will briefly remind the main characteristics of the frs ( section [ chap : frs ] ) . the fragment recoil separator and its set of detectors have been designed using the hypothesis that most , if not all the fragment one wishes to study are fully stripped @xcite . this is of course less and less true with decreasing energy . in section [ chap : qst ] we will discuss the variations of the charge - state probabilities with energy and their consequences on the selectivity of the spectrometer , as well as the possible choices of so - called stripping materials . with a lead beam energy as low as 500a mev , no stripper is efficient enough so that the fraction of non - fully stripped fragments would be negligible . the response of the ionization chambers ( used for the determination of the atomic number of the fragments ) in this situation will be discussed in section [ chap : z ] , as well as a new setup , developed for this experiment , based on an increased gas thickness . in section [ chap : deg ] we will describe a method to use a thick matter of layer as a passive measurement device in order to estimate the atomic number and the charge state of the fragments . we will also discuss , how unexpected problems prevented the measurement of the ionic charge state of ions ( and thus of the mass ) in the above - mentioned experiment . the final sections will be dedicated to new analysis techniques aiming at obtaining production cross sections , even in the case of an incomplete event - by - event mass identification . section [ chap : a ] will present a method to determine the most - likely mass of each fragment and to reduce the number of possible contaminating charge states . then , in section [ chap : cs ] , we will explain how to account for the large fraction of non fully - stripped ions and how to obtain isotopic production rates with low uncertainties despite the ambiguities in the mass determination . we will then conclude and try to answer whether or not the widely admitted low - energy limit has been pushed downwards .

three topics are covered . first , a specific set - up for ionization chambers , based on a very large gas thickness , is presented . the possibility to use a thick layer of matter ( a degrader ) as a passive measurement device to identify the nuclear charge and the ionic charge state of fragments is discussed . the combination of those new experimental and analysis techniques made the 500a mev spallation experiment a success .

the feasibility of low - energy fragmentation experiments using a magnetic spectrometer is discussed . the main challenge is the multiplicity of the ionic charge states , which can hamper the identification in both z and a of the fragments . three topics are covered . first , a specific set - up for ionization chambers , based on a very large gas thickness , is presented . its satisfactory performances are discussed in light of the observations during a 500a mev pb+p experiment performed at the frs ( gsi ) . as a second topic , the possibility to use a thick layer of matter ( a degrader ) as a passive measurement device to identify the nuclear charge and the ionic charge state of fragments is discussed . this method , successfully used for z identification in experiments such as pb+p at 1a gev , fails to measure the charge states at 500a mev for the same system . it is shown that surface defects of the degrader are probably responsible for this failure . the third topic is the description of new analysis techniques developed in order to account for and subtract the contribution of polluting charge states in the spectrometer , thus making possible a clean estimation of the production cross sections of all fragments . the combination of those new experimental and analysis techniques made the 500a mev spallation experiment a success . , , , , , magnetic spectrometer , ionic charge state , production cross section , degrader , ionization chambers 29.30.aj , 29.40.cs , 34.50.bw , 25.40-h , 25.70-z

1509.05427

i

a major outstanding goal in cosmology is to piece together the history of the universe between cosmic dawn , the emergence of the first stars and galaxies , and the end of reionization , when the radiation from these objects had ionized the intergalactic medium ( igm ) . advances in numerical techniques , combined with exquisite measurements of the `` initial '' conditions ( at a redshift @xmath6 ; @xcite , @xcite ) , have led to remarkable simulations ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) of the conditions leading up to the former milestone , occurring at @xmath7 , when the universe was @xmath8 old . however , reconstructing the subsequent several hundred myr of cosmic history has proved far more challenging , due to the difficulties in reliably modeling the numerous forms of feedback from the first astrophysical objects ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in particular , x - rays from the first galaxies can act as a powerful source of feedback ( e.g. * ? ? ? * ; * ? ? ? * ) that exerts influence over a wide range of distance scales . because hard x - rays ( energies @xmath9 ) have mean free paths comparable to the hubble horizon , they can isotropically heat and partially reionize the early igm ( e.g. @xcite ) . in fact , they are expected to be the dominant agent in heating the igm . such heating may suppress star formation @xcite and massive black hole ( bh ) growth @xcite inside low - mass dark matter haloes by raising the jeans and filtering masses of the igm @xcite . on galactic and circum - galactic scales , soft x - rays ( @xmath10 ) can affect the formation of stars and possibly massive black holes ( bhs ) by promoting the formation of molecular hydrogen via electron - catalyzed reactions ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? in addition to their suspected roles in early galaxy evolution , x - rays are important also because they can leave an observable signature that can be exploited to probe the cosmological epoch in question @xcite . their thermal impact on the early universe should be measurable through the redshifted @xmath11 transition line of neutral hydrogen , which is observed in emission or absorption depending on the relative temperature of the igm with respect to that of the cosmic microwave background ( cmb ) . several studies have investigated how forthcoming observations of the sky - average amplitude and power spectrum of the relic @xmath11 line ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) could be used to constrain the astrophysical agent ( or agents ) responsible for heating the early igm . there are sound reasons to expect that the first galaxies produced x - rays in abundance , and rapidly heated the igm . there are two dominant x - ray sources in present - day galaxies both powered by gas accretion onto bhs , and both plausibly prominent shortly after cosmic dawn : gas feeding massive bhs shining as active galactic nuclei ( agn ) , and x - ray binaries , powered by a stellar - mass bh gradually cannibalizing a companion star . estimates of the mass accumulated by nuclear bhs prior to @xmath12 @xcite , the existence of very massive bhs at @xmath13 ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , as well as the observed ( e.g. * ? ? ? * ) and theoretically expected @xcite increase in their duty cycles toward higher redshifts , all hint that x - ray agn may have been much more common during this epoch . likewise , high - mass x - ray binaries ( hmxbs ) dominate the x - ray emission of star - forming galaxies ; the low metallicity and rapid baryonic mass accretion of the earliest galaxies both lend credence to the notion that they were rife with hmxbs . theoretical models suggest that either type of x - ray source could heat the igm to above the cmb temperature as early as @xmath14 , and that this transition should be measurable by the planned @xmath11 experiments . at present , there are too many theoretical uncertainties to determine from the future data which type of x - ray source agn or hmxbs was responsible for driving the thermal evolution of the @xmath15 igm . modeling the early agn x - ray emission is particularly difficult , because the conditions for triggering agn activity are not fully understood even at low redshifts ( e.g. * ? ? ? * ; * ? ? ? because of the uncertainty in the fraction of x - ray photons that is released into the igm as opposed to being trapped inside the accretion flow or reprocessed into the infrared ( e.g. * ? ? ? * ; * ? ? ? * ) ; and because the epoch , initial masses , and birthplaces of the massive bh `` seeds '' are not yet constrained by observations ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? similarly , studies usually estimate the x - ray contribution from early hmxbs by simply inferring empirical relations between x - ray luminosity and star formation rate ( sfr ) in local galaxies ( and modeling the sfr using a semi - analytic cosmological model ) , or combining such relations with one or more free parameters ( e.g. * ? ? ? * ; * ? ? ? the goal of this study is to alleviate the uncertainties in the formation rate and x - ray output of hmxbs in the early universe , by using @xmath1-body simulations of nascent groups of the first ( population iii , henceforth pop iii ) stars . we choose the properties of the star groups in our simulations to reflect those found in hydrodynamical simulations of pop iii star formation at @xmath16 ( @xcite , @xcite ) . we follow the formation and dynamical evolution of compact binaries over thousands to millions of years , including the effects of the background gravitational potential and dynamical friction . this allows us to compute the fraction of pop iii stars that form stable , compact binaries , and eventually undergo an x - ray bright phase . the end result is an estimate of the formation rate of hmxbs in the first protogalaxies , as well as the amount of x - rays they generate per unit star formation . to our knowledge , this is the first published estimate of this type . our simulations predict a binary formation rate which is similar to what is observationally inferred in present - day galaxies . however , we derive a hmxb energy output ( normalized to the star formation rate ) that is a factor @xmath17 higher than in present - day star - forming galaxies , if the hmxb duty cycle is similar to the one in the local universe . we find that the x - ray output does not change significantly within the wide variety of simulation setups considered such as different orientations for collisions between star groups , and ambient gas density and submit that this is a robust estimate . the findings of this study can be used as model inputs in estimating the @xmath11 global signature and power spectrum , but have wider applications . as stated above , the x - ray output of the first galaxies are also of interest for studying feedback on smaller scales , such as subsequent star formation and massive bh formation . our work is also relevant for predicting the rates of long - duration gamma - ray bursts ( lgrbs ) from pop iii stars . lgrbs are important probes that can shed light on the universe out to @xmath18 ( e.g. * ? ? ? according to the collapsar model @xcite , progenitors of lgrbs require rapid rotation of the he core and removal of the h envelope . both criteria are satisfied by pop iii hmxbs , and it is plausible that massive pop iii stars in binary systems are dominant lgrb progenitors in the early universe @xcite . our results on hmxb formation rates can therefore be used to predict and interpret observations of high - redshift lgrbs . the paper is organized as follows . we start in [ sec : dynamics ] by discussing the problem to be solved beginning with the equations of motion , followed by the description of our @xmath1-body code , our choices for the initial conditions , and how the data is interpreted for hmxb formation . we present our results in [ sec : results ] . in [ sec : discussion ] , we discuss the implication of our work for the x - ray output of the first galaxies , as well as for other topics such as lgrbs and smbh formation . we conclude with a summary of our findings in [ sec : summary ] .

the first astrophysical objects shaped the cosmic environment by reionizing and heating the intergalactic medium ( igm ) . in particular , x - rays are very efficient at heating the igm before it became completely ionized , an effect that can be measured through the redshifted 21 cm line of neutral hydrogen . high - mass x - ray binaries ( hmxbs ) , known to be prolific x - ray sources in star - forming galaxies at lower redshifts , are prime candidates for driving the thermal evolution of the igm at redshifts . despite their importance , the formation efficiency of hmxbs from the first stellar populations is not well understood as such , their collective x - ray emission and the subsequent imprint on the 21 cm signature are usually evaluated using free parameters . using-body simulations , we estimate the rate of hmxb formation via mutual gravitational interactions of nascent , small groups of the first stars ( population iii stars ) . we discuss broader implications of our results , such as the rate of long gamma - ray bursts from population iii stars and the direct collapse channel for massive black hole formation . [ firstpage ] cosmology : theory early universe cosmology : dark ages , reionization , first stars stars : population iii intergalactic medium x - rays : binaries stars : kinematics and dynamics

the first astrophysical objects shaped the cosmic environment by reionizing and heating the intergalactic medium ( igm ) . in particular , x - rays are very efficient at heating the igm before it became completely ionized , an effect that can be measured through the redshifted 21 cm line of neutral hydrogen . high - mass x - ray binaries ( hmxbs ) , known to be prolific x - ray sources in star - forming galaxies at lower redshifts , are prime candidates for driving the thermal evolution of the igm at redshifts . despite their importance , the formation efficiency of hmxbs from the first stellar populations is not well understood as such , their collective x - ray emission and the subsequent imprint on the 21 cm signature are usually evaluated using free parameters . using-body simulations , we estimate the rate of hmxb formation via mutual gravitational interactions of nascent , small groups of the first stars ( population iii stars ) . we run two sets of calculations : one in which stars form in small groups of five in nearly keplerian initial orbits , and another in which two such groups collide ( an expected outcome of mergers of host protogalaxies ) . we find that hmxbs form at a rate of one per in newly born stars , and that they emit with a power of in the kev band per solar mass per year of star formation . this value is a factor larger than what is observed in star forming galaxies at lower redshifts ; the x - ray production from early hmxbs would have been even more copious , if they also formed _ in situ _ or via migration in protostellar disks . combining our results with earlier studies suggests that early hmxbs were highly effective at heating the igm and leaving a strong 21 cm signature . we discuss broader implications of our results , such as the rate of long gamma - ray bursts from population iii stars and the direct collapse channel for massive black hole formation . [ firstpage ] cosmology : theory early universe cosmology : dark ages , reionization , first stars stars : population iii intergalactic medium x - rays : binaries stars : kinematics and dynamics

1509.05427

r

here , we summarize the findings of our @xmath1-body simulations , focusing in particular on the properties of the most compact binaries found for each set of runs . [ sec : results ] we ran 20 simulations for @xmath97 and 23 for @xmath99 . for @xmath97 , in 12 out of 20 runs , the two most massive stars ( @xmath113 and @xmath114 , where @xmath115 is the @xmath53-th most massive star ) form the most compact binary we denote such a binary with the notation @xmath116 . similarly , binaries of type @xmath117 ( i.e. made up of the most massive star @xmath113 and the third most massive star @xmath118 ) form the most compact binary in 6 of the runs . the left panel of figure [ fig:1 ] shows a sample set of stellar trajectories for one of the large scale @xmath119 runs . throughout the simulation , the compact binary tends to remain near the center of the halo , as less massive stars repeatedly undergo 3-body interactions with the binary . the fact that they do not stray far from the center of the halo is a combined effect of the background potential and the gravitational potential of the massive binary . it is these 3-body encounters that cause the most compact binary in the simulations to end up as type @xmath116 or @xmath117 . in two of the runs , the most compact binaries after @xmath104 consist of less massive stars . the average value of the semimajor axis after @xmath120 in the large scale , @xmath119 runs is @xmath121 , and the minimum value of @xmath64 across the 20 runs is 60 au . these values for @xmath64 are much larger than that necessary for rlof to take place , @xmath122 au . their characteristic dynamical friction time scales are roughly @xmath123 yrs , which is much longer than their lifetimes ( see equation [ eq7 ] when @xmath124 and equation [ eq11 ] ) . we therefore conclude that in systems of @xmath109 stars and @xmath125 , with the stars initially separated at hundreds of au , hmxbs are unlikely to form . 1c c c large scale & @xmath97 & @xmath99 + number of runs & 20 & 23 + @xmath126 $ ] & 0.60(0.90 ) & 0.56(0.74 ) + @xmath127[au ] & 270 & 340 + for the @xmath99 case , the fraction of runs where the most compact binary after @xmath104 is type @xmath116 or @xmath117 are similar to the @xmath119 simulations : @xmath128 for @xmath116 , and @xmath129 for @xmath116 _ or _ @xmath117 . however , the dynamical evolution is quite different , as can be seen by the right panel of figure [ fig:1 ] . the lower gas densities lead to weaker forces due to dynamical friction and background potential , and stars ( especially less massive ones ) tend to be scattered farther from their initial position , as far as @xmath130 . this also results in less frequent three - body interactions in general , and may explain the larger average value of the semi - major axis after @xmath104 , @xmath131 . the formation of hmxbs appears even more intractable for the @xmath132 case . sample stellar trajectories for the @xmath119 and @xmath132 large scale cases are shown in figure [ fig:1 ] , and a summary of the results is given in table [ tab : tab1 ] . 0.7c c c small scale & @xmath97 & @xmath99 + runs & 86 & 86 + @xmath133 [ au ] & 1.37 & 1.42 + @xmath134[yr ] & @xmath135 & @xmath136 + companion stars & + @xmath137 & 0.070 & 0.070 + @xmath138 [ @xmath139 & 4.6 & 4.6 + for the small scale case , we performed 86 runs of 5-body simulations for each of the number density values @xmath119 and @xmath132 . due to the smaller initial separations of the stars , we run the simulations for a shorter amount of time . we run each simulation for a minimum of @xmath140 , but stop the run if a stable binary forms , and if no further significant dynamical changes are observed . if such a binary does not form , we run the simulations to a maximum duration of @xmath141 . in order to properly compare the results from the @xmath97 calculations with those from the @xmath99 calculations , we use the same initial conditions for each set of runs . in the @xmath97 calculations , the most common scenario is that @xmath113 always forms the most compact binary almost immediately , while stellar scatterings are most common during the first few years to about 40 years . thereafter , a multiple system usually survives and stabilizes , while less massive stars are ejected . a difference between the large - scale and the small - scale scenarios is that , whereas most cases in the large - scale calculations end up with one binary and unbound single stars ( in @xmath142 out of @xmath143 cases ) , in the small - scale runs a multiple system such as triple or quartet ( rather than a simple binary ) forms ( in 59 of 86 cases ) less massive stars take some energy from the multiple system and convert it into their kinetic energies while causing the binary to harden . as an example , figure [ fig:7 ] shows the evolution in the semi - major axis of a compact binary in one of the runs . one can easily notice the quick decrease in the semi - major axis during violent stellar interactions ( before 10 years ) , which clearly indicates the hardening . after a couple of stars are cast away and the multiple system is stabilized and isolated ( after about 10 years ) , dynamical friction plays the main role in the decrease of the semi - major axis ; after this point , we do not expect further dramatic hardening of the binary . in our 86 runs , the last surviving binary is typically of type @xmath144 ( pairing of the most massive and third most massive stars ) . with total mass of @xmath145 and @xmath146 . @xmath147 and the minimum semi - major axis is @xmath148 . the corresponding dynamical friction time scale ( equation [ eq11 ] ) is @xmath149 yr . the ejected stars have speeds of @xmath150 , and @xmath151 . six of the hmxb candidates ( hmxbc hereafter ) have been formed in all runs ( @xmath137 = 0.070 ) . for later use , let us define @xmath138 as the number of hmxbc formed across all simulations , normalized by the total mass of the stars . then @xmath152 ( this term will be used to estimate the x - ray luminosity and is one of the primary results of our study ) . the outcomes of the @xmath132 simulations are quite similar : a triple or higher multiple forms in 65 of 86 runs , and @xmath153 . furthermore , due to the same number of hmxbc , @xmath137 and @xmath154 are the same . one notable difference is that for @xmath132 , the dynamical friction time scale is longer by 2 orders of magnitude compared to @xmath97 , because this quantity is inversely proportional to the number density . interestingly , there are four runs ( for each density value ) in which the most compact binary is eccentric , and inside the requisite separation for rlof at pericenter but outside it at apocenter . we consider only two of them as hmxbc and rule out the other two binaries since the mass of the more massive star is smaller than @xmath155 @xcite . we present the distribution of eccentricity for pericenter distance in figure [ fig:8 ] . in particular , the _ left _ panel shows the distribution for @xmath97 calculations and the _ right _ panel for @xmath99 . the circled point indicates hmxbc with distance at pericenter shorter than the corresponding roche - lobe radius . how accretion proceeds in a highly eccentric binary system under these conditions remains an unsettled issue to date , as studies have claimed that the orbital semimajor axis and eccentricity can either increase or decrease depending on the binary properties at pericenter ( @xcite and @xcite ) . if the rlof does induce circularization , then accretion proceeds normally ( i.e. steadily ) . however , if the rlof instead increases the eccentricity of the system , then , whether accretion can proceed steadily rather than intermittently will depend on the relative timescale between the disk lifetime @xmath156 ( on the order of the viscous timescale ) , and the orbital period of the binary @xmath157 . we computed these timescales for all the eccentric binaries in our simulations ( for which the roche - lobe radius straddles the pericenter and apocenter ) , and found that @xmath158 in all cases but one . this implies that the fraction of binaries whose eccentricities cause intermittent rlof is small , and that as a global average , rlof is steady to a good approximation . the magnitude of the gas density considerably influences the characteristics of the dynamical interactions . while on the one hand @xmath159 of the simulations end up forming the same triples for both density values , on the other hand their trajectories and the center of mass movements differ significantly . figure [ fig:4 ] shows two sample trajectories of 5 stars with low number density ( left panel ) and high number density ( right panel ) after 1000 yr . they were given identical initial conditions for the run , but their trajectories have developed differently . in figure [ fig:3 ] , at 800 yr , even though the same stars form a triple and the same star is ejected for both number densities , their trajectories are clearly different . as can be seen in figure [ fig:2 ] , which shows the change of forces per unit mass exerted on a typical kicked - off star , @xmath160 and @xmath161 are negligible compared to @xmath162 before about 5 years . note that @xmath160 and @xmath161 are synchronized at early times because the motions of the stars are close to the keplerian motion , @xmath163 . the star in figure [ fig:2 ] is ejected at @xmath164 for the high number density ( and at @xmath165 for the low number density ) . this can be understood from the fact that @xmath162 monotonically decreases and @xmath161 increases ( @xmath166 where @xmath88 is the distance from the center of mass ) . at the same time , @xmath167 barely changes since the star moves in the supersonic regime and the speed decreases slowly . there is no noticeable difference in the overall results between the @xmath132 and @xmath119 runs quantities such as @xmath168 , the dynamical friction time scale @xmath169 , the total mass of the most compact binary ( or which star forms the compact binary with @xmath113 ) as summarized in table [ tab : tab2 ] . for both number densities , the companion star of the binary is typically the third most massive star @xmath118 . to sum up , we find that @xmath170 of our simulations form hmxbc , regardless of the gas density value . normalized to the total stellar mass in the simulations , the number of hmxbc formed per stellar mass is @xmath171 . we now explore several different configurations for the star group , and run several sets of simulations with 10 stars ( instead of 5 ) . these are : ( 1 ) 10-body version of the small scale calculation presented above ; ( 2 ) head - on crash of two star groups containing 5 stars each ; ( 3 ) a close encounter and subsequent inspiral and merger of two star groups containing 5 stars each . the latter two scenarios are motivated by the fact that the merger timescales and mass accretion timescales of pop iii host haloes , as well as the lifetimes of the massive pop iii stars themselves , are of the same order , @xmath172 . this suggests that merging haloes will be continuously forming new stars ( perhaps pop ii instead of pop iii ) as they merge with other haloes , and that close interactions and mergers of nascent star groups may be relatively common . we generate stellar masses in the same way as for the 5-body case , but with a larger value for the parameter @xmath173 . we have run each simulation for 500 yr . the results of these simulations are summarized in table [ tab : tab3 ] . we briefly discuss each one , as follows . 0.6c c c c c c scenario & 1 & 2 & 3 & 4a & 4b + runs & 54 & 30 & 30 & 30 & 30 + @xmath174 @xmath175 $ ] & 1.0 & 1.1 & 0.90 & 1.8 & 1.6 + @xmath176 @xmath175 $ ] & 1.6 & 1.5 & 1.8 & 2.4 & 2.0 + @xmath177 @xmath175 $ ] & 0.72 & 0.15 & 0.42 & 1.2 & 0.23 + @xmath178 & 0.33 & 0.33 & 0.27 & 0.13 & 0.27 + @xmath179 [ @xmath139 & 15 & 11 & 9.0 & 4.2 & 8.4 + we set up the simulations as in the 5-body calculations , but with 10 stars . we find that @xmath180 . interestingly , there are 18 out of 54 cases in which @xmath181 . there is a large difference in scale between @xmath182 and @xmath183 , where @xmath182 is the semi - major axis of @xmath116 ( binary made up of the two most massive stars ) and @xmath183 is the semi - major axis of the binary stars other than @xmath113 and @xmath114 . this is a common feature of the 10-body simulations : they often end up with triples whose inner binary is @xmath184 while the outer binary is @xmath185 . our simulations yield @xmath186 and @xmath187 . also note that , in 14 out of 18 hmxbc , the binary is @xmath188 ( i.e. it is not made up of the two most massive stars ) . since the compact binaries in these simulations form quickly and we only follow them for 500 years , it is technically possible that they will be disrupted before one of the stars turns into a bh . however , our simulations for the 5-body scenario showed that compact , quasi - steady binaries are unlikely to be disrupted , and for practical purposes we extrapolate this qualitative result to the 10-body case . we find that a hmxbc forms in a larger fraction of these simulations than in the 5-body case , @xmath189 , for the obvious reason that there are more stars . per unit stellar mass in the simulations , the number of hmxb candidates is @xmath190 , which is a factor @xmath191 higher than we found for the 5-body case . two groups of 5 stars are set up with random initial conditions , in the same manner as for the previous simulations of 5-body groups . the two groups are then arranged to collide head - on , as follows : they are placed at a separation of two to three times their sizes and their disks are aligned so that the mutual inclination is zero . the initial relative speed of the groups is roughly the speed of sound and the center of mass of one group is set to move directly toward the center of mass of the other group . we find that prior to colliding , each group forms a compact binary of type @xmath116 ( the most and second - most massive star ) . when the two groups collide , those two binaries that existed before the collision were broken and the two most massive stars of each group form a new compact binary with high chances . the average @xmath192 is @xmath193 , but @xmath194 and @xmath195 , meaning that the most compact binaries are not formed from the most massive stars . the shorter average separations may be a result of a larger number of early 3-body scatterings , which act to harden the group as a whole . hmxbc form in 10 out of 30 runs , and they are not of type @xmath116 . however , we find a rate of hmxb formation per stellar mass @xmath196 ; this is higher than in the 5-body case and comparable to scenario 1 above . sample trajectories for one of the simulations of scenario 2 are depicted in figure [ fig:10 ] . we have used the same input parameters for the two groups as in scenario 2 , except that we now set the impact parameter to be of order the size of the group , whereas it was set to zero in scenario 2 . the groups are given opposite velocities of @xmath197 along the @xmath198-direction , and are offset by a displacement along the @xmath199-direction that is @xmath200 times the typical size of the star group ( @xmath201 ) so that they merge with a spiral motion . we find that @xmath202 , @xmath203 and @xmath204 . the average separation lies between what we find in scenarios 1 and 2 . this can be interpreted as being due to the fact that these simulations ( in which the two groups merge gradually via inspiral ) have more close 3-body interactions than in scenario 1 ( in which 10 stars in quasi - keplerian orbits evolve in isolation ) but fewer such interactions than in scenario 2 ( in which the two groups merge head - on ) . hmxbs form in 8 out of 30 runs and , as with scenarios 1 and 2 , none of the hmxbs are made up of the two most massive stars . we find a similar hmxb formation rate per stellar mass , @xmath205 . sample trajectories from one of the simulations for scenario 3 are shown in figure [ fig:11 ] . in these two scenarios , we again set two groups of five stars each on a collision course . the difference is that the orbital plane of one star group is tilted , so that the two stellar disks have a mutual inclination @xmath53 . we set the inclination at @xmath206 ( nearly co - rotating ) for scenario 4a , and @xmath207 ( nearly counter - rotating ) for scenario 4b . the groups are initially placed at a separation of two to three times their sizes , and set in motion at the same speeds as for the inspiral case ( scenario 3 ) . we find that @xmath208 , @xmath209 , and @xmath210 for scenario 4a . in scenario 4b , we find @xmath211 , @xmath212 , and @xmath213 . in @xmath214 of the runs for both scenarios , the two most massive stars form the most compact binary . stellar binaries end up with somewhat closer separations in the nearly counter - rotating case , due to the fact that the net angular momentum of the merged star group is smaller . indeed , we find a total of four hmxbc across all the @xmath206 simulations , and eight in a same number of @xmath207 simulations . for the same reason , we find a larger fraction of hmxb candidates per stellar mass simulated in the nearly counter - rotating case ( @xmath215 ) compared to the nearly co - rotating case ( @xmath216 ) . the overall formation rate of hmxb candidates is lower for both cases than the cases in which all the stellar orbits were nearly coplanar ( scenarios 1 , 2 and 3 ) , plausibly due to the additional degree of freedom in the stellar orbits . still , the value of @xmath138 is within a factor of a few for all of our simulations . sample trajectories from runs for scenarios 4a and 4b are depicted in figure [ fig:12 ] and figure [ fig:13 ] , respectively .

we run two sets of calculations : one in which stars form in small groups of five in nearly keplerian initial orbits , and another in which two such groups collide ( an expected outcome of mergers of host protogalaxies ) . we find that hmxbs form at a rate of one per in newly born stars , and that they emit with a power of in the kev band per solar mass per year of star formation .

the first astrophysical objects shaped the cosmic environment by reionizing and heating the intergalactic medium ( igm ) . in particular , x - rays are very efficient at heating the igm before it became completely ionized , an effect that can be measured through the redshifted 21 cm line of neutral hydrogen . high - mass x - ray binaries ( hmxbs ) , known to be prolific x - ray sources in star - forming galaxies at lower redshifts , are prime candidates for driving the thermal evolution of the igm at redshifts . despite their importance , the formation efficiency of hmxbs from the first stellar populations is not well understood as such , their collective x - ray emission and the subsequent imprint on the 21 cm signature are usually evaluated using free parameters . using-body simulations , we estimate the rate of hmxb formation via mutual gravitational interactions of nascent , small groups of the first stars ( population iii stars ) . we run two sets of calculations : one in which stars form in small groups of five in nearly keplerian initial orbits , and another in which two such groups collide ( an expected outcome of mergers of host protogalaxies ) . we find that hmxbs form at a rate of one per in newly born stars , and that they emit with a power of in the kev band per solar mass per year of star formation . this value is a factor larger than what is observed in star forming galaxies at lower redshifts ; the x - ray production from early hmxbs would have been even more copious , if they also formed _ in situ _ or via migration in protostellar disks . combining our results with earlier studies suggests that early hmxbs were highly effective at heating the igm and leaving a strong 21 cm signature . we discuss broader implications of our results , such as the rate of long gamma - ray bursts from population iii stars and the direct collapse channel for massive black hole formation . [ firstpage ] cosmology : theory early universe cosmology : dark ages , reionization , first stars stars : population iii intergalactic medium x - rays : binaries stars : kinematics and dynamics

astro-ph9710182

i

what has been presented in the preceding sections represents the first comprehensive hi study of the _ isolated _ , edge - on , infrared - bright galaxy ngc 3044 . the ir brightness is partly due to proximity , since the massive star formation rate is a factor of 5 lower than that of m 82 ( 5.1 ) . the hi distribution in the galaxy was modelled using all available data points , i.e. hi spectral lines were modelled over the entire galaxy in order to determine the best global density and velocity distributions in the galaxy as well as the best geometrical parameters . the resulting quantities are listed in table [ tab : model ] . a gaussian ring density distribution in the plane was found to be the best fit overall . an important result derived from the model is that the galaxy has a moderately thick hi disk with a gaussian vertical scale height of @xmath138 . this is consistent with previous observations which have also revealed a thick radio continuum disk . ngc 3044 shows a very asymmetric distribution optically , in hi , and in the radio continuum , with excellent agreement between the radio continuum and hi column density distributions ( see [ subsec : asymmetry ] ) . in hi , the asymmetry is particularly apparent from the global profile , which shows a lopsided double - horned structure . otherwise , however , derived global parameters tell the story of a normal sbc galaxy . the column density map confirms the asymmetric distribution of the hi in the galaxy . this is clear from the 27@xmath16 offset of the hi peak to the east of the radio continuum peak . the major - axis rotation curve also shows the asymmetry in that the approaching side of the galaxy appears to be `` truncated '' before reaching terminal velocity while the receding side stays flat for about @xmath139 after reaching terminal velocity . while the galaxy is asymmetric in hi , it also shows an extremely straight disk ( i.e. , no obvious disk warp ) . it is not clear what could have caused the asymmetry in this apparently isolated galaxy . it is likely , though , that the mechanism would have to act on the galaxy after its formation , since it is difficult to explain how the galaxy would form asymmetrically in the first place . it is noted here that asymmetries in isolated galaxies are not uncommon , which indicates that a common mechanism such as past minor mergers may be responsible for it . if this is the case for ngc 3044 , the merger likely took place over 10@xmath105 yrs ago . the velocity channel maps reveal a host of high - latitude hi extensions . we have catalogued a total of 12 such features that appear in at least two consecutive velocity channels . these features are distributed uniformly across the disk of the galaxy and above and below the plane . we derive a lower limit for mass flow to the halo of @xmath109 , = @xmath110 . there is also some correlation between high - latitude hi features and high - latitude radio continuum features ( @xmath140 5.2.3 ) . four of the high latitude features exhibit the signature of an expanding shell and have radii of order a few kpc . based on the assumption that the shells were formed by supernovae energy input , the required input energies are in the range 4 @xmath19 10@xmath115 to 7 @xmath19 10@xmath114 @xmath141 ergs . these values vary somewhat depending on the adopted model , but it is clear , even from the kinetic energies of expansion of the individual supershells , that large numbers ( e.g. up to tens of thousands ) of correlated supernovae are required to form them . this means that ngc 3044 would have to harbour a number of such superclusters ( such as the cluster r136 in the 30 doradus region in the lmc ) , something which is not supported by the current massive star formation rate . the alternative model , that of impacting external clouds , is even less attractive as a formation mechanism for the supershells because of the absence of companions , the fact that the supershells are young ( of order the age of a typical ob association ) and because hi clouds which are massive enough to produce these shells would have been easily detected in our data . we suggest that the supershells are indeed formed internally , but that some additional energy - boost ( e.g. through magnetic fields ) is needed to explain their large energies . the authors wish to thank the staff at the vla for obtaining the hi data and kathy perrett for coordinating the remote observation . thanks also go to denise giguere and jayanne english for many useful discussions on various data reduction techniques . we have also made used of the nasa / ipac extragalactic database ( ned ) . this work is supported by the national research council of canada . bosma , a. 1981 , , 86 , 1825 bottinelli , l. , gouguenheim , l. , paturel , g. , and de vaucouleurs , g. 1984 , , 56 , 381 brinks , e. , and bajaja , e. 1986 , , 169 , 14 burton , w. b. , and gordon , m. a. 1978 , , 63 , 7 chevalier , r. a. 1974 , , 188 , 501 condon , j. j. 1992 , , 30 , 575 frei , b. d. , henriksen , r. n. , irwin , j. a. , and king , d. l. 1997 , , submitted van gorkom , j. h. , and ekers , r. d. 1994 , in synthesis imaging in radio astronomy , ed . perley , r. a. , schwab , f. r. , and bridle , a. h. , ( astronomical society of the pacific conference series , vol . 6 ) , 341 haynes , m. p. , and giovanelli , r. 1984 , , 89 , 758 heiles , c. , 1979 , , 229 , 533 heiles , c. , 1984 , , 55 , 585 heiles , c. , 1990 , , 354 , 483 hernquist , l. , and mihos , j. c. 1995 , , 448 , 41 irwin , j. a. , and seaquist , e. r. 1990 , , 353 , 469 irwin , j. a. , and seaquist , e. r. 1991 , , 371 , 111 irwin , j. a. 1994 , , 429 , 618 kamaya , h. , mineshige , s. , shibata , k. , matsumoto , r. 1996 , , 458 , l25 van der kruit , p. c. 1981 , , 99 , 298 krumm , n. , and salpeter , e. e. 1980 , , 85 , 1312 lequeux , j. 1983 , , 125 , 394 lockman , f. j. 1984 , , 283 , 90 mihos , j. c. , and hernquist , l. 1994 , , 425 , l13 mac low , m .- m . , mccray , r. , & norman . m. l. 1989 , , 337 , 141 norman , c. a. , and ikeuchi , s. 1989 , , 345 , 372 perley , r. a. 1994 , in very large array observational status summary , published by the national radio astronomy observatory quinn , p. j. , hernquist , l. and fullagar , d. p. 1993 , , 403 , 74 rand , r. j. , and van der hulst , j. m. 1993 , , 105 , 2098 rand , r. j. 1994 , , 285 , 833 rand , r. j. , and stone , j. m. 1996 , , 111 , 190 richter , o. -g . , and sancisi , r. 1994 , , 290 , l9 rix , h .- w . , and zaritsky , d. 1995 , , 447 , 82 roberts , m. s. , and haynes , m. p. 1994 , , 32 , 115 snchez - saavedra , m. l. , battaner , e. , and florido , e. 1990 , , 246 , 458 shapiro , p. r. , and field , g. b. 1976 , , 205 , 762 soifer , b. t. , sanders , d. b. , madore , b. f. , neugebauer , g. , and danielson , g. e. 1987 , , 320 , 238 soifer , b. t. , boehmer , l. , neugebauer , and sanders , d. b 1989 , , 98 , 766 solomon , p. m. , and sage , l. j. 1988 , , 334 , 613 sorathia , b. 1994 , m.sc . thesis : a radio continuum survey of edge - on spiral galaxies , queen s university spitzer , l. , jr . 1978 , in physical processes in the interstellar medium , ( new york : john wiley and sons ) staveley - smith , l. , and davies , r. d. 1988 , , 231 , 833 tenorio - tagle , g. , and bodenheimer , p. 1988 , , 26 , 145 tully , r. b. 1988 , nearby galaxies catalog , ( cambridge university press ) vader , j. p. , and chaboyer , b. 1995 , , 445 , 691 de vaucouleurs , g. , de vaucouleurs , a. , corwin , h. g. , jr . , buta , r. j. , paturel , g. , and fouqu@xmath142 , p. 1991 , third reference catalogue of bright galaxies , ( new york : springer - verlag)(rc3 ) visser , h. c. d. 1980 , , 88 , 159 zaritsky d. 1995 , , 448 , l17

the first detailed vla mapping of the neutral hydrogen distribution in the _ isolated _ , edge - on spiral galaxy ngc 3044 is presented . we have modelled the hi spectra in order to derive its global density and velocity distributions . an hi scale height of 420 pc is thus found . the approaching ( northwest ) side of the galaxy is 14% less massive than the receding side and its rotation curve does not reach terminal velocity . the rotation curve of the receding ( southeast ) side however resembles that of a normal galaxy . twelve high - latitude features were catalogued , of which four exhibit the signature of an expanding shell . we have investigated the possibility that the supershells could have been produced by external impacting clouds , but conclude that this scenario is unattractive , given the age of the shells , the isolation of the galaxy , and the lack of any observed features sufficiently massive to form the shells in the vicinity of the galaxy . since the implied input energies from supernovae are extremely high ( e.g. from , corresponding to 400 74,000 supernovae ) , we suggest that some additional energy ( e.g. from magnetic fields ) may be needed to produce the observed supershells .

the first detailed vla mapping of the neutral hydrogen distribution in the _ isolated _ , edge - on spiral galaxy ngc 3044 is presented . physical parameters such as , , etc . determined for this galaxy are typical for galaxies of its morphological class ( sbc ) . we have modelled the hi spectra in order to derive its global density and velocity distributions . an hi scale height of 420 pc is thus found . this can be compared to the impressive radio continuum halo , previously found to extend to above the midplane . the present study reveals an asymmetry in the hi distribution as well as numerous high - latitude hi structures at various galactocentric radii . the approaching ( northwest ) side of the galaxy is 14% less massive than the receding side and its rotation curve does not reach terminal velocity . the rotation curve of the receding ( southeast ) side however resembles that of a normal galaxy . twelve high - latitude features were catalogued , of which four exhibit the signature of an expanding shell . there is some correlation of these features with features observed in the radio continuum from independent data . the most massive shell ( feature 10 ) extends out to 6 kpc above the galactic disk . the radii and masses of these shells range from and , respectively . we have investigated the possibility that the supershells could have been produced by external impacting clouds , but conclude that this scenario is unattractive , given the age of the shells , the isolation of the galaxy , and the lack of any observed features sufficiently massive to form the shells in the vicinity of the galaxy . therefore , an internal origin is suggested . since the implied input energies from supernovae are extremely high ( e.g. from , corresponding to 400 74,000 supernovae ) , we suggest that some additional energy ( e.g. from magnetic fields ) may be needed to produce the observed supershells .

1510.03486

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in the hierarchical structure formation paradigm , merging is among the dominant mechanisms by which galaxy clusters grow . therefore , detailed studies of merging clusters shed light on the growth of cosmological structures . apart from cosmological interests , merging clusters are also receiving growing attention as astrophysical laboratories , providing rare and invaluable opportunities to investigate the origin of cosmic rays ( e.g. , volk et al . 1996 ; berezinsky et al . 1997 ; feretti et al . 2012 ; brunetti & jones 2014 ) , generation of nonthermal energy in plasma ( e.g. , cassano & brunetti 2005 ) , properties of dark matter ( kahlhoefer et al . 2014 ) , star formation and galaxy evolution driven by merging ( e.g. , stroe et al . 2015 ) , etc .. radio relic " clusters are a subclass of merging clusters that exhibit elongated diffuse radio emissions at the periphery of the systems . these radio relics " often occur in pairs and in most cases stretch nearly perpendicular to observed merger axes . now many observational and theoretical studies support the premise that the relics trace the locations of shock fronts induced by cluster mergers ( e.g. , ensslin et al . detailed analysis of the radio relic data enables us to put independent constraints on the key parameters necessary in our reconstruction of the merging scenario , including the direction of the merger , the projection angle between the merger axis and the plane of the sky , the shock velocity , and the time since the impact ( e.g. , ng et al . 2015 ) . because of the limited observational time window set by both development and deterioration of mature shocks , only a few tens of radio relic clusters are known to date ( e.g. , van weeren et al . 2010 ; 2012 ; 2013 , govoni et al . 2001 , brunetti et al . 2008 ) . the cluster rx j0603.3 + 4214 is a remarkable cluster at @xmath0 whose radio relic stretches over @xmath1 mpc ( figure [ fig_tb ] ) . because of its peculiar morphology composed of the western short ( @xmath7 mpc ) thick band ( brush " ) and a long ( @xmath8 mpc ) thin stripe ( handle " ) , rx j0603.3 + 4214 is nicknamed the toothbrush cluster " ( van weeren et al . together with the much fainter relic found near the southern cluster edge , this asymmetric and remarkably linear feature implies that perhaps the merger might have been complex , involving more than two subclusters ( bruggen et al . this unusual radio morphology is different from that of the ciza j2242.8 + 5301 cluster ( van weeren et al . 2010 ) , possessing a similarly giant but more symmetric sausage "- like radio relic . the toothbrush " relic of rx j0603.3 + 4214 was discovered with the westerbork synthesis radio telescope ( wsrt ) and the giant metrewave radio telescope ( gmrt ) by van weeren et al . for the toothbrush " relic , van weeren et al . ( 2012 ) detected a spectral index gradient from the front ( northern edge ) of the toothbrush " relic toward the back ( southern edge ) . the frontal part of this relic is highly polarized ( @xmath9% at 4.9 ghz ) , which indicates that the merger might be happening nearly in the plane of the sky ( ensslin et al . 1998 ) . van weeren et al . ( 2012 ) also found a north - south elongated x - ray morphology at the location of the cluster based on archival rosat data . bruggen et al . ( 2012 ) carried out a numerical simulation of rx j0603.3 + 4214 by modeling the cluster with two large ( @xmath10 ) and one small ( @xmath11 ) halos and demonstrated that the simulation can generate a giant relic with a similar morphology . ogrean et al . ( 2013 ) studied the cluster with _ xmm - newton _ data , which reveal two distinct x - ray peaks . at both northern and southern edges ( near the relics ) of the cluster , they detected density discontinuities indicating the presence of potential shocks . itahana et al . ( 2015 ) constrained the mach number to be @xmath12 based on this density discontinuity , which is consistent with their independent measurement @xmath13 from the temperature jump obtained from _ suzaku _ data . however , these x - ray - based mach numbers are lower than what the radio data imply ( @xmath14 ; van weeren et al . correlations between the cluster galaxy star formation and the merger environment were studied by stroe et al . ( 2014 ; 2015 ) . despite a number of studies mentioned above on this remarkable system , no reliable mass estimation of the system has been carried out , and little is known about the spatial distribution of its mass and member galaxies . the cluster s underlying mass distribution is one of the critical pieces of information in order to infer the merger scenario responsible for the radio relic morphology ( e.g. , ng et al . 2015 ; dawson 2013 ) . hence , in this paper , as part of our merging cluster collaboration ( mc@xmath15 ) project , we present detailed weak - lensing analysis of rx j0603.3 + 4214 with subaru / suprime cam and _ hubble space telescope ( hst ) _ imaging data . because of the low galactic latitude @xmath2 of the system , some observational challenges , including severe extinction and stellar obscuration , are present . however , in the weak - lensing study of ciza j2242.8 + 5301 ( jee et al . 2015 ) , we already demonstrated that a successful weak - lensing study is still possible when high - resolution imaging observations are carefully planned and analyzed with the state - of - the - art technique . we launched the mc@xmath15 project to study a large sample of merging clusters with a coherent approach . our immediate goals for the current paper are ( 1 ) to map the underlying mass distribution and compare the result with the galaxies and x - ray emission and ( 2 ) to quantify the matter content of the system . these mass properties are among the critical parameters necessary to constrain the merging scenario of the system leading to such an unusual morphology in radio emission . our long - term goals of the mc@xmath15 project include detailed studies of dark matter properties through systematic investigation of the large sample and careful numerical simulations . we present our study as follows . in [ section_observation ] we describe our data and reduction . in [ section_wl ] we review the basic lensing theory of weak lensing and our technique . we present our mass reconstruction results in [ section_mass_reconstruction ] , discussing the source selection , mass distribution , and mass estimation . discussions of our results will follow in [ section_discussion ] before we conclude in [ section_conclusion ] . we assume a flat @xmath16 cold dark matter ( @xmath16cdm ) cosmology with @xmath17 , @xmath18 , and @xmath19 . at the redshift of rx j0603.3 + 4214 , @xmath20 , the plate scale is @xmath21 ( @xmath22 ) . the @xmath23 value that we adopt here as a halo mass is a spherical mass within @xmath24 , inside which the mean density becomes 200 times the critical density of the universe at the redshift of the cluster .

the galaxy cluster rx j0603.3 + 4214 at is one of the rarest clusters boasting an extremely large ( mpc ) radio relic . because of the remarkable morphology of the relic , the cluster is nicknamed the toothbrush cluster " . although the cluster s underlying mass distribution is one of the critical pieces of information needed to reconstruct the merger scenario responsible for the puzzling radio relic morphology , its proximity to the galactic plane has imposed significant observational challenges . we present a high - resolution weak - lensing study of the cluster with subaru / suprime cam and _ hubble space telescope _ imaging data .

the galaxy cluster rx j0603.3 + 4214 at is one of the rarest clusters boasting an extremely large ( mpc ) radio relic . because of the remarkable morphology of the relic , the cluster is nicknamed the toothbrush cluster " . although the cluster s underlying mass distribution is one of the critical pieces of information needed to reconstruct the merger scenario responsible for the puzzling radio relic morphology , its proximity to the galactic plane has imposed significant observational challenges . we present a high - resolution weak - lensing study of the cluster with subaru / suprime cam and _ hubble space telescope _ imaging data . our mass reconstruction reveals that the cluster is composed of complicated dark matter substructures closely tracing the galaxy distribution , in contrast , however , with the relatively simple binary x - ray morphology . nevertheless , we find that the cluster mass is still dominated by the two most massive clumps aligned north - south with a:1 mass ratio ( and for the northern and southern clumps , respectively ) . the southern mass peak is offset toward the south with respect to the corresponding x - ray peak , which has a bullet "- like morphology pointing south . comparison of the current weak - lensing result with the x - ray , galaxy , and radio relic suggests that perhaps the dominant mechanism responsible for the observed relic may be a high - speed collision of the two most massive subclusters , although the peculiarity of the morphology necessitates involvement of additional subclusters . careful numerical simulations should follow in order to obtain more complete understanding of the merger scenario utilizing all existing observations .

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because we make an approximation that the mass of rx j0603.3 + 4214 is dominated by the two halos associated with the two x - ray peaks , it is useful to examine the validity of the assumption by an independent method . we employ aperture mass densitometry , which allows us to estimate total projected masses within a given aperture without any assumption on the number of halos and their profiles . we will compare this projected mass from aperture mass densitometry with the results from our two halo model by projecting the 3d nfw mass distribution onto the plane of sky . aperture mass densitometry ( fahlman et al . 1994 ; clowe et al . 2000 ) is computed through the following equation : @xmath161 where @xmath162 is the azimuthal average of tangential shears , @xmath163 is the aperture radius , and @xmath164 and @xmath165 are the inner and the outer radii of the annulus , respectively . @xmath166 provides a density contrast of the region inside @xmath167 with respect to the control annulus @xmath168 . we choose @xmath169 and @xmath170 for the control annulus . projecting our nfw fitting results , we estimate the density within this annulus to be @xmath171 . because the control annulus radius is large and the density there is small , the impact of adopting the nfw results on the aperture mass densitometry becomes negligible . the input to the equation of the densitometry is a shear @xmath172 , not a reduced shear @xmath173 . therefore , we need to determine the aperture mass using the relation @xmath174 . we find that the density converges after three or four iterations . the resulting aperture mass is displayed in figure [ fig_aperture_mass ] . also displayed in figure [ fig_aperture_mass ] is the aperture mass estimated by projecting the nfw fitting results above . in order to obtain this estimation , we first projected each nfw profile along the line - of - sight direction and summed the two - halo results . the aperture mass density masses are within the 1@xmath135 upper limits of the nfw masses , which may hint at the possibility that the two - halo representation may not be a perfect choice . however , because the 1@xmath135 error bars from both methods overlap , we argue that the difference should not be considered statistically significant . range of statistical uncertainties . the two results are consistent with each other , and we conclude that no significant mass is excluded by modeling rx j0603.3 + 4214 with two nfw profiles . , width=321 ] a diffuse hot plasma within a cluster is well traced by x - ray emission because the emissivity is in general proportional to the plasma density squared ( given the same plasma temperature ) . since the plasma consists of charged particles subject to ram pressure , the x - ray morphology of merging clusters reveals critical information that can not be probed otherwise . here we compare the x - ray morphology of rx j0603.3 + 4214 with the weak - lensing mass distribution and discuss the implication in the context of the merging scenario responsible for the observed toothbrush " radio relic . rx j0603.3 + 4214 has been observed with both _ xmm - newton _ and _ chandra_. the 82 ks _ xmm - newton _ data were studied by ogrean et al . ( 2013 ) , and van weeren et al . ( 2015 ) analyzed the 237 ks @xmath175 data ( obsid : 15171 , 15172 , and 15323 ) . ogrean et al . ( 2013 ) showed that the intracluster medium of rx j0603.3 + 4214 is dominated by two components , which is confirmed by the chandra study of van weeren et al . in addition , a few new remarkable features are revealed in the high - resolution chandra observation . first , a density jump indicating a shock is detected in the southern edge . this location coincides with the southern edge of the radio halo . across the shock a temperature jump is also found . the two mach numbers derived by both density and temperature jumps are consistent ( @xmath176 and @xmath177 , respectively ) . second , the high - resolution chandra data show that the southern x - ray component has a triangular bullet "- like shape . according to their further temperature analysis , the density jump at the southern edge of the bullet indicates a cold front . the comparison of these x - ray findings with the current weak - lensing results provides a consistent picture regarding the merging scenario of rx j0603.3 + 4214 . we display the comparison in figure [ fig_massoverxray ] , where we illustrate our hypothesized merger axis . despite the somewhat complex galaxy distribution , the x - ray and weak - lensing results suggest that the dominant merger may be approximated by a north - south collision of two components . we find offsets between x - ray and mass peaks . the northern mass peak is offset toward the northwest with respect to the corresponding x - ray peak by @xmath178 whereas the the southern mass peak is offset to the south by @xmath6 . similar to the bullet cluster , the direction of the offsets favors a scenario wherein the two components passed through each other and are still separating . our weak - lensing analysis shows that the northern component is more massive than the southern component by a factor of three . we believe that this mass inequality is consistent with the offset inequality , since the less massive southern component should experience more ram pressure . another supporting evidence for this mass inequality is the location of the toothbrush "- relic . the simulation by van weeren et al . ( 2011 ) predicts that two radio - relics are generated in a two - body encounter and travel along the merger axis with the larger relic associated with the more massive halo . the observation that the @xmath179mpc toothbrush "- relic is located near the northern edge of rx j0603.3 + 4214 is consistent with the northern component being more massive in our weak - lensing analysis . the same trend has been observed in our weak - lensing study of the sausage " cluster ciza j2242.8 + 5301 ( jee et al . 2015 ) and zwcl0008.8 + 5215 ( n. golovich et al . in prep . the study of zwcl0008.8 + 5215 shows that the x - ray emission of the less massive system appears as a clear bullet "- like feature , similar to the bullet " cluster ( clowe et al . 2006 ) , whereas the larger radio relic is found near the edge of the more massive system . the exact physical mechanism is unknown as to the question why does the larger radio relic occur on the higher mass side ? " on the other hand , x - ray observations show that distinct shock features such as density discontinuities , temperature jumps , etc . , are more prominent on the lower - mass side unlike radio relics , which are also believed to trace the location of shock fronts . some may argue that the above mass inequality argument may be challenged by the x - ray luminosity of the southern peak being much higher . needless to say , in general x - ray luminosity is positively correlated with mass . however , in active merging clusters , it is natural to suspect that this correlation between mass and x - ray luminosity can temporarily be altered for many reasons ( e.g. , randall et al . 2002 ; skillman et al . 2013 ) . for example , a cool core ( associated with a lower - mass component ) can survive a head - on collision , whereas a hot core ( associated with a higher - mass component ) can severely be disrupted after a core pass - through . the deep chandra x - ray image of the el gordo " cluster at @xmath180 is a good example . the weak - lensing study shows that the system is composed of two halos with a 2:1 mass ratio , whereas only the cool core associated with the less massive system ( south ) is clearly visible in x - ray ( jee et al . 2014 ; menanteau et al . the hydrodynamical simulation by molnar & broadhurst ( 2015 ) reproduces this asymmetry in brightness between the two x - ray peaks of el gordo " . another example is zwcl0008.8 + 5215 ( n. golovich et al . in prep . ) at @xmath181 mentioned above . by and large the zwcl0008.8 + 5215 cluster is also a binary merging system with one of two x - ray peaks resembling a bullet "- like shape . the bullet " component is brighter than the other component in x - ray , whereas the mass associated with the bullet " is found to be approximately a factor of five smaller . one of the goals of the mc@xmath15 collaboration is to enable quantitative comparisons between observations and simulations for interesting merging clusters . rx j0603.3 + 4214 is a remarkably interesting system and should be followed up by careful numerical analysis . here we discuss some of the puzzling issues of rx j0603.3 + 4214 that future hydrodynamic simulations should address . first , we believe that the extremely high icm temperature of rx j0603.3 + 4214 deserves our attention . van weeren et al . ( 2015 ) constrain the temperatures of the northern and southern x - ray peaks to be @xmath182 kev and @xmath183 kev , respectively . these temperatures are substantially higher than what our weak - lensing masses imply _ if _ we neglect nonthermal energy injection into icm . with the assumption of the isothermal @xmath56 model with @xmath184 kpc and @xmath185 , the weak - lensing masses are converted to @xmath186 kev and @xmath187 kev for the northern and southern halos , respectively . even when we treat rx j0603.3 + 4214 as a single halo with @xmath188 ( i.e. , the sum of the two halos using the values in table 3 ) , the implied temperature ( again with an isothermal @xmath56 model ) becomes only @xmath189 kev , significantly smaller than the global x - ray temperature @xmath190 kev . although this discrepancy may not be considered surprising , given the common understanding that x - ray temperatures of merging clusters are biased indicators of the cluster masses , the level of discrepancy that we witness in rx j0603.3 + 4214 is somewhat extreme when we consider results for other clusters in the literature . for example , even for the bullet "- cluster , clowe et al . ( 2006 ) find that the temperature levels of the system are consistent with their weak - lensing masses . second , although we argue that the two subclusters of rx j0603.3 + 4214 played the dominant roles in creating the current observational features such as the galaxy - mass - relic alignments , the offsets between mass / galaxy and x - ray peaks , etc . , the long asymmetrically linear feature of the toothbrush " relic strongly suggests that a smaller third component might have been involved , as suggested by bruggen et al . ( 2012 ) . however , the mass , path , and timing of this third component are unclear . it is our hope that the weak - lensing substructures revealed in the current study will aid us to reduce the volume of the parameter space that future simulations should explore . third , the implied collision velocity is very high . the high polarization fraction @xmath191% ( van weeren et al . 2012 ) suggests that the merger may be happening in the plane of the sky . according to our redshift analysis ( w. dawson et al . in prep ) , the line - of - sight velocity difference between the northern and southern subclusters is @xmath192 km s@xmath37 . even with the polarization prior @xmath193% , the implied collision velocity is as high as @xmath33500 km s@xmath37 , which exceeds the escape velocity of the rx j0603.3 + 4214 system and thus is hard to accommodate within the current @xmath16cdm paradigm . more detailed discussions will appear in w. dawson et al . ( in prep ) .

our mass reconstruction reveals that the cluster is composed of complicated dark matter substructures closely tracing the galaxy distribution , in contrast , however , with the relatively simple binary x - ray morphology . the southern mass peak is offset toward the south with respect to the corresponding x - ray peak , which has a bullet "- like morphology pointing south .

the galaxy cluster rx j0603.3 + 4214 at is one of the rarest clusters boasting an extremely large ( mpc ) radio relic . because of the remarkable morphology of the relic , the cluster is nicknamed the toothbrush cluster " . although the cluster s underlying mass distribution is one of the critical pieces of information needed to reconstruct the merger scenario responsible for the puzzling radio relic morphology , its proximity to the galactic plane has imposed significant observational challenges . we present a high - resolution weak - lensing study of the cluster with subaru / suprime cam and _ hubble space telescope _ imaging data . our mass reconstruction reveals that the cluster is composed of complicated dark matter substructures closely tracing the galaxy distribution , in contrast , however , with the relatively simple binary x - ray morphology . nevertheless , we find that the cluster mass is still dominated by the two most massive clumps aligned north - south with a:1 mass ratio ( and for the northern and southern clumps , respectively ) . the southern mass peak is offset toward the south with respect to the corresponding x - ray peak , which has a bullet "- like morphology pointing south . comparison of the current weak - lensing result with the x - ray , galaxy , and radio relic suggests that perhaps the dominant mechanism responsible for the observed relic may be a high - speed collision of the two most massive subclusters , although the peculiarity of the morphology necessitates involvement of additional subclusters . careful numerical simulations should follow in order to obtain more complete understanding of the merger scenario utilizing all existing observations .

1510.03486

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we have presented detailed weak - lensing studies of the toothbrush " relic cluster rx j0603.3 + 4214 with _ hst _ and subaru imaging . together with the sausage " relic cluster ciza j2242.8 + 5301 , rx j0603.3 + 4214 has been known for its giant ( @xmath1mpc ) radio relic , whose peculiar morphology gives the system the nickname toothbrush " . our weak - lensing study provides a high - resolution map of the cluster dark matter , which helps us to constrain the merging scenario responsible for the toothbrush " relic . we find that although the cluster substructure is more complicated than that of ciza j2242.8 + 5301 , the global mass distribution can be approximated by a bimodal distribution with a 3:1 mass ratio . the northern mass clump encloses @xmath194 and coincides with the galaxy luminosity peak . the southern mass component contains @xmath195 and is also in an excellent spatial agreement with the southern luminosity peak . however , the southern mass peak is @xmath6 offset with respect to the southern x - ray peak . the two mass peaks , two x - ray peaks , two luminosity peaks , and the brush " of the toothbrush " relic are collinear , which strongly suggests that the violent merger responsible for the giant radio relic was mainly derived by the collision of the two components . however , the long handle " relic extended northeast from the brush " indicates that a third ( or more ) component might have been involved in this merger . it is interesting that our weak - lensing mass reconstruction reveals a mass clump southwest of the northern mass peak . we find that a galaxy luminosity peak coincides with this mass overdensity . nevertheless , we have yet to carry out detailed simulations in order to quantify the possibility that this observed component might have been involved in the creation of the peculiar radio - relic morphology . the shape of the southern x - ray peak is triangular and is reminiscent of the bullet " in the bullet cluster . a recent chandra study reveals a shock south of this feature traced by both density and temperature jumps . together with the aforementioned offset , these x - ray features show that we may be witnessing a post - collision , where the two cluster components are separating from each other . the high x - ray temperatures of rx j0603.3 + 4214 are discrepant with what the weak - lensing masses imply . we attribute the large differences to substantial departure from the hydrostatic equilibrium . these severe discrepancies support the consensus that using x - ray temperatures is an unreliable way to infer cluster masses in violent merging systems . galaxy clusters are receiving growing attention as cosmic particle accelerators . although every merger case is special and deserves scrutiny , radio - relic clusters are particularly useful thanks to strong constraints on both the geometry and stage of the mergers , which enables us to reduce the parameter search space by substantial factors . of course , careful numerical simulations should follow up the observations in order to come up with quantitatively coherent scenarios , wherein all the observed features fit together within the observational uncertainties . + support for program number hst - go-13343.01-a was provided by nasa through a grant from the space telescope science institute , which is operated by the association of universities for research in astronomy , incorporated , under nasa contract nas5 - 26555 . mjj acknowledges support from nrf of korea to cger . as acknowledges financial support from an nwo top subsidy ( 614.001.006 ) . hr gratefully acknowledges support from the european research council under the european union s seventh framework programme ( fp/2007 - 2013)/erc advanced grant newclusters-321271 . part of this work performed under the auspices of the u.s . doe by llnl under contract de - ac52 - 07na27344 abazajian , k. n. , adelman - mccarthy , j. k. , ageros , m. a. , et al . 2009 , , 182 , 543 akamatsu , h. , & kawahara , h. 2013 , , 65 , 16 bartelmann , m. , & schneider , p. 2001 , , 340 , 291 bertin , e. , & arnouts , s. 1996 , , 117 , 393 berezinsky , v. s. , blasi , p. , & ptuskin , v. s. 1997 , , 487 , 529 clowe , d. , luppino , g. a. , kaiser , n. , & gioia , i. m. 2000 , , 539 , 540 clowe , d. , brada , m. , gonzalez , a. h. , et al . 2006 , , 648 , l109 dahlen , t. , mobasher , b. , dickinson , m. , et al . 2010 , , 724 , 425 dawson , w. a. , wittman , d. , jee , m. j. , et al . 2012 , , 747 , l42 dawson , w. a. 2013 , , 772 , 131 duffy , a. r. , schaye , j. , kay , s. t. , & dalla vecchia , c. 2008 , , 390 , l64 ensslin , t. a. , biermann , p. l. , klein , u. , & kohle , s. 1998 , , 332 , 395 evrard , a. e. , bialek , j. , busha , m. , et al . 2008 , , 672 , 122 fahlman , g.,kaiser , n.,squires , g . & woods , d . 1994 , , 437 , 56 feretti , l. , giovannini , g. , govoni , f. , & murgia , m. 2012 , , 20 , 54 fischer , p. , & tyson , j. a. 1997 , , 114 , 14 giavalisco , m. , et al . 2004 , , 600 , l93 govoni , f. , feretti , l. , giovannini , g. , et al . 2001 , , 376 , 803 hoekstra , h. , herbonnet , r. , muzzin , a. , et al . 2015 , , 449 , 685 ilbert , o. , capak , p. , salvato , m. , et al . 2009 , , 690 , 1236 itahana , m. , takizawa , m. , akamatsu , h. , et al . 2015 , , 248 jee , m. j. , blakeslee , j. p. , sirianni , m. , martel , a. r. , white , r. l. , & ford , h. c. 2007a , , 119 , 1403 jee , m. j. , et al . 2007b , , 661 , 728 jee , m. j. , rosati , p. , ford , h. c. , et al . 2009 , , 704 , 672 jee , m. j. , & tyson , j. a. 2011 , , 123 , 596 jee , m. j. , mahdavi , a. , hoekstra , h. , et al . 2012 , , 747 , 96 jee , m. j. , tyson , j. a. , schneider , m. d. , et al . 2013 , , 765 , 74 jee , m. j. , hoekstra , h. , mahdavi , a. , & babul , a. 2014a , , 783 , 78 jee , m. j. , hughes , j. p. , menanteau , f. , et al . 2014b , , 785 , 20 jee , m. j. , stroe , a. , dawson , w. , et al . 2015 , , 802 , 46 kaiser , n. , & squires , g. 1993 , , 404 , 441 kahlhoefer , f. , schmidt - 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comparison of the current weak - lensing result with the x - ray , galaxy , and radio relic suggests that perhaps the dominant mechanism responsible for the observed relic may be a high - speed collision of the two most massive subclusters , although the peculiarity of the morphology necessitates involvement of additional subclusters . careful numerical simulations should follow in order to obtain more complete understanding of the merger scenario utilizing all existing observations .

the galaxy cluster rx j0603.3 + 4214 at is one of the rarest clusters boasting an extremely large ( mpc ) radio relic . because of the remarkable morphology of the relic , the cluster is nicknamed the toothbrush cluster " . although the cluster s underlying mass distribution is one of the critical pieces of information needed to reconstruct the merger scenario responsible for the puzzling radio relic morphology , its proximity to the galactic plane has imposed significant observational challenges . we present a high - resolution weak - lensing study of the cluster with subaru / suprime cam and _ hubble space telescope _ imaging data . our mass reconstruction reveals that the cluster is composed of complicated dark matter substructures closely tracing the galaxy distribution , in contrast , however , with the relatively simple binary x - ray morphology . nevertheless , we find that the cluster mass is still dominated by the two most massive clumps aligned north - south with a:1 mass ratio ( and for the northern and southern clumps , respectively ) . the southern mass peak is offset toward the south with respect to the corresponding x - ray peak , which has a bullet "- like morphology pointing south . comparison of the current weak - lensing result with the x - ray , galaxy , and radio relic suggests that perhaps the dominant mechanism responsible for the observed relic may be a high - speed collision of the two most massive subclusters , although the peculiarity of the morphology necessitates involvement of additional subclusters . careful numerical simulations should follow in order to obtain more complete understanding of the merger scenario utilizing all existing observations .

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the study of the emission characteristics from rotation powered pulsars has been a subject of long standing interest . our knowledge of the fundamental properties ( e.g. , mass , spin , and magnetic field ) of the underlying neutron star stems from detailed spectral and timing investigations . to facilitate an understanding of the mechanism by which the loss of rotational energy is converted into high energy radiation , many observational and theoretical studies have sought to determine the relationship between the x - ray luminosity , @xmath0 , and the rate of rotational energy loss or spin down power , @xmath1 . indeed , a correlation of the form @xmath9 was found in einstein data by seward & wang ( 1988 ) . subsequent studies using a larger sample of pulsars led to a relation of the form , @xmath10 based on rosat data ( see becker & trmper 1997 ) and @xmath11 based on asca data ( see saito 1998 ) . recently , a reanalysis of 39 pulsars based on data obtained from several x - ray satellites by possenti et al . ( 2002 ) led to an intermediate relation @xmath12 , similar to that of seward & wang ( 1988 ) . while the deduced existence of a correlation between @xmath0 and @xmath1 suggests that the observed x - rays are produced by a process which taps the rotational energy of the neutron star , a detailed description of the mechanism remains elusive . this is , in part , a result of the fact that the data from different satellites are obtained in different energy ranges . the results can be affected , for example , by interstellar absorption especially for those pulsars studied in the soft x - ray regime of rosat ( 0.1- 2.4 kev ) . in addition , the total x - ray luminosity is composed of contributions from both the pulsed and non - pulsed components , and these components are likely to reflect physical conditions in diverse spatial environments . the x - rays radiated by rotation powered pulsars could include contributions from 5 distinct components with different origins : + 1 . non - thermal non - pulsed diffuse radiation can be emitted from a pulsar wind nebula . the radiation will be discussed in 2 , and we suggest that this emission component is the major contribution to the non - pulsed x - ray radiation in the asca observations of pulsars . non - thermal non - pulsed radiation from the pulsar magnetosphere could be important as suggested by becker et al . ( 2004 ) if the angular resolution of x - ray detector is sufficiently high to separate this contribution from that of the nebula . although such a component may be present in the asca data that we use , due to its low angular resolution , it is not likely to dominate the contribution from the pulsar wind nebula . for example , tennant et al . ( 2001 ) have found a non - thermal non - pulsed component from the crab pulsar by using the high - resolution camera of the chandra x - ray observatory . they estimate that the x - ray luminosity of this component is @xmath13 , whereas , the non - thermal non - pulsed x - ray luminosity from the crab nebula detected by asca ( saito et al . 1997a ) is @xmath14 . the specific origin of the non - thermal non - pulsed component , not associated with the nebula , is not clear . although it contaminates the emission of the nebula , it is small . provided that this contribution is small for all the pulsars we study in this investigation , this component should not affect our analysis . the non - thermal pulsed radiation component is generally believed to be produced from the pulsar magnetosphere . this follows from the fact that the motion of charged particles within the light cylinder is strongly affected by the magnetic field , and the radiation of charged particles in the open field lines should be pulsed . this component could be produced in the vicinity of the polar cap as a result of inverse compton scattering of higher order generation pairs of particles on soft photons emitted by the neutron star ( zhang & harding 2000 ) or in the outer magnetosphere as a result of synchrotron radiation of downward cascades from the outer gap electron / positron particles ( cheng & zhang 1999 ) . the thermal non - pulsed radiation from the pulsar surface can contribute to the soft x - ray bands , typically , characterized by @xmath15 kev ( cheng & zhang 1999 ) . in this paper , we have used the asca data on pulsars so this component will not contribute to the 2 - 10 kev asca energy band . the thermal pulsed radiation from the pulsar surface likely originates in a polar cap on the neutron star surface and can contribute to the hard x - ray band ( @xmath16 kev ) . in analyzing the pulsed emission from pulsars , we follow the model of cheng & zhang ( 1999 ) where the thermal pulsed x - ray emission is included in their model prediction . thus , the x - ray emission observed from pulsars in the asca sample primarily consists of contributions from components 1 , 3 , and 5 . we have assumed that component 2 is not important and component 4 does not significantly contribute to the 2 - 10 kev energy band . on the other hand , becker & trmper(1997 ) have used rosat data and obtained a linear relation between the x - ray luminosity consisting of components 2 and 3 and spin - down power . in the present paper , we concentrate on the x - ray properties in the energy band of asca ( 2 - 10 kev ) . the x - rays , then , consists of a thermal component from the polar cap , a non - thermal pulsed component from the magnetosphere and a non - thermal , non - pulsed emission from the nebula . that is , we have explicitly assumed that the pulsar magnetosphere and the pulsar wind nebula are primarily responsible for the pulsed and non - thermal non - pulsed component respectively . since the pulsed and non - pulsed emission have different origins , the relationship between the total x - ray luminosity and spin down power is not expected , in general , to be represented by a single power law . in fact , the non - thermal pulsed and non - pulsed emission components are distinguished by different spectral signatures and conversion efficiencies . to determine their relative importance and their relationship to the spin down power , we have reexamined the pulsar data obtained in the 2 - 10 kev energy band of the asca satellite , focusing on separating the non - pulsed and pulsed emission data . in the next section , we provide a simplified description of the emission from a pulsar wind nebula , based upon earlier work by chevalier ( 2000 ) , where the relativistic pulsar wind interacts with the interstellar medium . in 3 , the x - ray properties of the pulsed and non - pulsed components are collected and the relation between their luminosities with spin down power and photon spectral index are determined . with these results in hand , the pulsar wind nebula model is used to explain the occurrence of the tail - like emission morphology in geminga and psr b 1757 - 24 in 4 . finally , we summarize and conclude in the last section .

the relation for the pulsed component , on the other hand , is consistent with a magnetospheric emission model . such wind nebulae can contribute to the non - thermal symmetric emission morphology ( point - like ) and elongated emission morphology ( tail - like ) from sources similar to geminga and psr b1757 - 24 .

the general properties of the non - thermal non - pulsed x - ray emission of rotation powered pulsars are investigated in the context of a pulsar wind nebula model . an examination of the observed x - ray emission from a sample of 23 pulsars in the energy range between 2 - 10 kev reveals that the relation of x - ray luminosity , , to the pulsar spin down power , , is steeper for the non - pulsed component than for the pulsed component . specifically , for the non - pulsed component , whereas for the pulsed component . the former relation is consistent with emission from a pulsar wind nebula model in which where is the power law index of the electron energy distribution . the relation for the pulsed component , on the other hand , is consistent with a magnetospheric emission model . in addition , the photon spectral index , , was found to be correlated to the conversion efficiency of spin down power to non - pulsed x - ray emission with greater efficiencies for than for . such a relation is naturally understood within the framework of a pulsar wind nebula model with the former relation corresponding to the emission of x - rays in the fast cooling regime and the latter relation corresponding to emission in the slow cooling regime . the x - ray properties of pulsar wind nebulae are sensitive to the physical conditions ( e.g. , the density and magnetic field ) of the interstellar medium and can lead to important differences between the x - ray emission characteristics ( luminosity , photon spectral index and emission morphology ) of pulsars in various environments . such wind nebulae can contribute to the non - thermal symmetric emission morphology ( point - like ) and elongated emission morphology ( tail - like ) from sources similar to geminga and psr b1757 - 24 . # 1 # 1#2#1 # 2

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the non - thermal non - pulsed x - ray emission of rotation powered pulsars has been investigated in the context of emission from a pulsar wind nebula . we have confirmed that this emission can significantly contribute to the total x - ray emission , thereby , increasing the x - ray emission above that produced in the pulsar magnetosphere . a reexamination of asca data for pulsars separated into the non - pulsed and pulsed emission components indicates that their non - thermal components , individually , are correlated with spin down power . in particular , the dependence is steeper for the non - pulsed component with @xmath173 as compared to the relation , @xmath174 for the pulsed component . our results are similar to that discovered by becker & trmper(1997 ) , who found that the non - thermal ( pulsed and non - pulsed ) component satisfied the linear relation , @xmath175 , based on rosat data in 0.1 - 2.4 kev range . in this paper , we have used the asca data in the 2 - 10 kev range , which includes the contribution of the additional thermal pulsed component with @xmath176 kev from the polar cap ( cheng & zhang 1999 ) . in this case , the dependence of the x - ray luminosity on spin down power is steeper . because of the poor angular resolution of asca , the possible contribution of non - thermal non - pulsed emission from the magnetosphere is mixed in with that of the nebula . within the framework of a one zone model for the pulsar wind developed by chevalier ( 2000 ) , the power law relation between the non - pulsed luminosity and spin down power provides an important diagnostic for the electron energy distribution in the shock resulting from the interaction of the relativistic wind with the interstellar medium . specifically , @xmath177 where @xmath5 is the power law index of the electron energy distribution , suggesting that the index characterizing these pulsars is relatively high , @xmath178 . the observational results also show that the conversion efficiency of spin down power to x - ray luminosity is a function of spin down power varying from @xmath119 to 0.1 . the efficiencies in the lower ( upper ) end of the range can be understood in terms of emission in the slow ( fast ) cooling regime where the x - ray frequency is less ( greater ) than the electron synchrotron cooling frequency . the spectra from pulsar wind nebulae are distinctly non - thermal , described by a photon power law index , @xmath179 or @xmath180 for the fast or slow cooling regime respectively . this implies a correlation between the photon index and efficiency of conversion of spin down power to non - pulsed x - ray luminosity with steeper photon power law indices associated with higher conversion efficiencies . although the photon power law indices inferred from the pulsars studied have large uncertainties , there are hints from the observed data that such a correlation exists . we note that the low values of @xmath6 and @xmath181 inferred for the extended emission observed from geminga and b 1757 - 24 are consistent with such an interpretation . future observed determinations of the photon power law indices could further verify this correlation , thereby , providing an additional diagnostic tool for probing the pulsar and its environment . finally , the pulsar wind nebula interpretation may also apply to the spatially extended x - ray emission observed in binary systems containing a pulsar . for example , the extended x - ray emission associated with the millisecond pulsar b1957 + 20 ( stappers et al . 2003 ) may be interpreted within such a framework . the application of such models to recycled pulsars in the galaxy will be the subject of a future investigation . we are grateful to the anonymous referee for the fruitful suggestions . this work is partially supported by the nsf through grant ast-0200876 , by a rgc grant of the hong kong government , and by the national natural science foundation of china under grant 10273011 . achterberg , a. , gallant , y.a . , kirk , j.g . & guthmann , a.w . 2001 , , 328 , 393 arons , j. 1983 , in electron - positron pairs in astrophysics , ed . m. l. burns , a. k. harding , & r. ramaty ( new york : aip ) , 113 becker , w. , & trmper , j. 1997 , , 326 , 682 becker , w. et al . , 2004 , astro - ph/0405180 bednarz , j. & ostrowski , m. 1998 , phys . rev . lett . , 80 , 3911 bignami , g. f. , & caraveo , p.a . 1993 , , 361 , 704 bignami , g. f. , & caraveo , p.a . 1996 , ann . astron . astrophys . 34 , 331 blumenthal , g. & gould , k. 1970 , rev . mod . phys . , 42 , 237 camilo , f. et al . 2002 , , 579 , l25 caraveo , p.a . 2003 , science , 301 , 1345 cheng , k. s. , gil , j. & zhang , l. 1998 , , 493 , l35 cheng , k. s. , & zhang , l. 1999 , , 515 , 337 chevalier , r. a. 2000 , , 539 , l45 coroniti , f. v. 1990 , , 349 , 538 finley , j.p . 1998 , , 493 , 884 frail , d. a. , kassim , n. e. , & weiler , k. w. 1994 , aj , 107 , 1120 gaensler , b. m. , & frail , d. a. 2000 , nature , 406 , 158 gaensler , b. m. et al . 2003a , , 588 , 441 gaensler , b. m. et al . 2003b , , 594 , l111 gaensler , b. m. et al . 2004 , , submitted ( astro - 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1926 & 0.065 & @xmath192 & 5.0 & 7.0@xmath193 & 1.6@xmath194 & 1.9@xmath195 & 1.4@xmath196 & 2,3 + b0531 + 21 & 0.033 & 4.2@xmath197 & 2.0 & 4.5@xmath198 & 1.1@xmath199 & 6.8@xmath200 & 1.0@xmath201 & 4 + b0833 - 45 & 0.089 & 1.25@xmath197 & 0.3 & 6.9@xmath193 & 1.9@xmath195 & 1.5@xmath202 & 1.8@xmath203 & 4,5,6 + b0633 + 17 & 0.237 & 1.1@xmath204 & 0.16 & 3.2@xmath196 & 8.2@xmath205 & 4.6@xmath205 & 3.6@xmath206 & 7,8 + b1706 - 44 & 0.1025 & 9.3@xmath204 & 1.82 & 3.4@xmath193 & 6.8@xmath202 & 4.1@xmath202 & 2.7@xmath207 & 4 + b1509 - 58 & 0.150 & 1.54@xmath208 & 4.3 & 1.8@xmath199 & 4.0@xmath194 & 1.3@xmath194 & 2.7@xmath194 & 4 + b1951 + 32 & 0.0395 & 5.8@xmath209 & 2.5 & 3.7@xmath193 & 6.2@xmath195 & 6.2@xmath202 & 5.6@xmath203 & 4 + b1046 - 58 & 0.124 & 9.6@xmath204 & 2.98 & 2.0@xmath193 & 9.5@xmath202 & 5.5@xmath202 & 4.5@xmath202 & 4,9 + b1929 + 10 & 0.227 & 1.16@xmath209 & 0.17 & 3.9@xmath203 & 1.54@xmath210 & 5.6@xmath205 & 9.8@xmath205 & 10 + b0656 + 14 & 0.385 & 5.5@xmath204 & 0.76 & 3.8@xmath196 & 1.7@xmath211 & 1.0@xmath211 & 7.0@xmath212 & 4 + b0540 - 69 & 0.05 & 4.8@xmath197 & 49.4 & 1.5@xmath198 & 8.3@xmath213 & 1.3@xmath213 & 7.0@xmath193 & 11 + b0950 + 08 & 0.253 & 2.3@xmath214 & 0.12 & 5.6@xmath207 & 4.6@xmath205 & 1.6@xmath205 & 3.0@xmath206 & 10 + b1610 - 50 & 0.232 & 4.93@xmath197 & 7.26 & 1.6@xmath193 & 9.6@xmath195 & 3.0@xmath195 & 6.6@xmath203 & 9 + b1055 - 52 & 0.197 & 5.83@xmath209 & 1.53 & 3.0@xmath196 & 2.7@xmath210 & 2.0@xmath210 & 7.0@xmath206 & 12 + b1853 + 01 & 0.267 & 5.4@xmath197 & 2.02 & 8.0@xmath215 & 1.4@xmath195 & 1.4@xmath202 & 1.3@xmath203 & 4 + j2229 + 6114 & 0.0516 & 7.8@xmath204 & 3.0 & 2.2@xmath201 & 1.7@xmath195 & 4.0@xmath202 & 1.3@xmath203 & 13 + b0537 - 69 & 0.016 & 5.13@xmath204 & 47 & 4.8@xmath198 & 2@xmath213 & 1.7@xmath200 & 1.8@xmath193 & 14,15 + j1846 - 0258 & 0.32 & @xmath216 & 19 & 1@xmath199 & 1@xmath213 & 4@xmath194 & 1@xmath213 & 16 + b1937 + 21 & 0.00156 & 1.05@xmath217 & 3.6 & 1.1@xmath193 & 5.7@xmath202 & 2.5@xmath202 & 3.2@xmath207 & 17 + j2124 - 3358 & 0.005 & 1.08@xmath217 & 0.25 & 3.5@xmath203 & 4.8@xmath205 & 1.6@xmath205 & 3.2@xmath206 & 18 + b1821 - 24 & 0.003 & 1.6@xmath218 & 5.1 & 2.2@xmath193 & 6.5@xmath195 & 9.4@xmath202 & 5.5@xmath195 & 19 + j0437 - 47 & 0.0058 & 2.0@xmath217 & 0.18 & 4.2@xmath203 & 1.3@xmath210 & 4.0@xmath205 & 9.0@xmath206 & 4 + l c c c c c l psr & @xmath1 & @xmath219 & @xmath220 & @xmath221 & @xmath222 & reference + b1823 - 13 & 2.8@xmath213 & @xmath223 & @xmath224 & @xmath225 & @xmath226 & 1 + j0537 - 6910 & 4.8@xmath227 & @xmath228 & @xmath229 & @xmath230 & @xmath231 & 2 + b0540 - 69 & 1.5@xmath227 & 0.01 & 0.05 & @xmath232 & @xmath233 & 3 + b1509 - 58 & 1.8@xmath199 & @xmath234 & @xmath235 & @xmath236 & @xmath237 & 4 + j0218 + 4232 & 2.5@xmath200 & 4.8@xmath238 & 2@xmath239 & 0.61@xmath240 & @xmath241 & 5 + j0631 + 1036 & 5.4@xmath194 & @xmath242 & @xmath243 & 2.3@xmath244 & @xmath245 & 6 + j1811 - 1926 & @xmath246 & 3@xmath238 & @xmath247 & 1.65@xmath248 & @xmath249 & 7 + b0531 + 21 & 4.5@xmath227 & 1.6@xmath250 & 0.03 & 1.6@xmath251 & 2.1@xmath252 & 8 + b0833 - 45 & @xmath253 & 2@xmath254 & 3@xmath239 & 1.5@xmath255 & 1.67@xmath256 & 9 + b0633 + 17 & 3.2@xmath194 & 1.4@xmath254 & 1.1@xmath257 & 1.0@xmath244 & 1.6@xmath251 & 10,11 + b1055 - 52 & 3@xmath194 & 7@xmath254 & 2@xmath257 & 1.5@xmath255 & 1.9@xmath251 & 12 + b1937 + 21 & 1.1@xmath213 & 2@xmath238 & @xmath258 & 1.71@xmath259 & 0.8@xmath260 & 13 + b1821 - 24 & 2.2@xmath213 & 5@xmath238 & 3@xmath261 & 1.2@xmath244 & @xmath262 & 14 + j2229 + 6114 & 2.2@xmath199 & 2@xmath254 & @xmath80 & 1.51@xmath263 & 1.6@xmath251 & 15 + j1105 - 6107 & 2.5@xmath213 & 6@xmath238 & 1.6@xmath261 & 1.8@xmath264 & 2.2@xmath264 & 16 + b1706 - 44 & 3.4@xmath213 & 1.4@xmath238 & @xmath80 & 1.9@xmath260 & 1.7@xmath244 & 17 + b1757 - 24 & 2.6@xmath213 & @xmath163 & @xmath80 & 1.6@xmath265 & 1.0@xmath260 & 18 + j0205 + 6449 & 2.6@xmath199 & @xmath119 & @xmath266 & 1.1@xmath264 & 1.9@xmath251 & 19 + b1929 + 10 & 3.9@xmath195 & 3@xmath238 & @xmath267 & 1.79@xmath268 & & 20 + b0656 + 14 & 3.8@xmath194 & 3@xmath238 & 2@xmath239 & 1.5@xmath269 & & 21 + j2021 + 3651 & @xmath270 & 3@xmath238 & @xmath243 & 1.5@xmath255 & 1.7@xmath255 & 22 + j1747 - 2958 & 2.5@xmath213 & @xmath163 & 0.02 & 1.8@xmath269 & 2.1@xmath269 & 23 + b1853 + 01 & @xmath271 & @xmath242 & 1.5@xmath261 & @xmath272 & @xmath273 & 24 + l c c c c c c c c l psr & @xmath1 & @xmath274 & @xmath275 & @xmath276 & @xmath277 & @xmath18 & @xmath71 & @xmath278 & reference + & & cm & cm & & & @xmath74 & km s@xmath63 & cm & + b1823 - 13 & 2.8@xmath213 & 6@xmath279 & & 3@xmath195 & 2@xmath195 & 1 & & 7@xmath280 & 1 + j0537 - 6910 & 4.8@xmath227 & 4@xmath279 & & 1.8@xmath213 & 3@xmath213 & & & & 2 + b0540 - 69 & 1.5@xmath227 & 3@xmath279 & & 7@xmath213 & 4@xmath213 & & & & 3 + j1811 - 1926 & @xmath246 & 2@xmath279 & & 1.4@xmath194 & @xmath66 & & & & 4 + b0531 + 21 & 4.5@xmath227 & 4@xmath279 & 3@xmath281 & @xmath282 & 4@xmath213 & 10 & 123 & @xmath283 & 5 + b0833 - 45 & @xmath253 & @xmath284 & 2@xmath281 & 1.8@xmath195 & @xmath285 & 1 & 65 & 8@xmath286 & 6 + b0633 + 17 & 3.2@xmath194 & 5@xmath286 & 4@xmath287 & 4@xmath205 & @xmath288 & 1 & 120 & 4@xmath279 & 7 + j2229 + 6114 & 2.2@xmath199 & 4@xmath279 & & 1.3@xmath195 & 3@xmath195 & & & & 8 + j1105 - 6107 & 2.5@xmath213 & 4@xmath286 & & 4@xmath195 & 3@xmath195 & & & & 9 + b1706 - 44 & 3.4@xmath213 & 3@xmath279 & & 3@xmath202 & 4@xmath202 & & & & 10 + b1757 - 24 & 2.6@xmath213 & 4@xmath286 & @xmath289 & 3@xmath202 & 5@xmath202 & 1 & @xmath290 & @xmath283 & 11 + j0205 + 6449 & 2.6@xmath199 & @xmath284 & & 3@xmath194 & 3@xmath194 & & & & 12 + b1957 + 20 & @xmath291 & 5@xmath286 & 4@xmath286 & 1.6@xmath211 & @xmath292 & 1 & 220 & 4@xmath279 & 13 + j2021 + 3651 & @xmath270 & 8@xmath279 & & 3@xmath203 & 2@xmath195 & & & & 14 + j1747 - 2958 & 2.5@xmath213 & 3@xmath286 & 7@xmath287 & 5@xmath194 & @xmath66 & 0.3 & 600 & 2@xmath280 & 15,16 + j1124 - 5916 & @xmath282 & @xmath284 & 2@xmath279 & 4@xmath196 & @xmath66 & 0.5 & 450 & 6@xmath279 & 17 + b1853 + 01 & @xmath271 & 10@xmath293 & 3@xmath286 & 6@xmath202 & 4@xmath202 & 5 & 375 & @xmath283 & 18 + j1930 + 1852 & 2@xmath213 & @xmath284 & & @xmath285 & 7@xmath202 & 1 & & @xmath283 & 19 + b0453 - 685 & @xmath282 & 6@xmath279 & & 6@xmath194 & 2@xmath194 & 0.4 & & @xmath294 & 20 + j0538 + 2817 & 4@xmath194 & 8@xmath286 & 3@xmath287 & 6@xmath211 & 5@xmath211 & 0.5 & 385 & & 21 +

the general properties of the non - thermal non - pulsed x - ray emission of rotation powered pulsars are investigated in the context of a pulsar wind nebula model . in addition , the photon spectral index , , was found to be correlated to the conversion efficiency of spin down power to non - pulsed x - ray emission with greater efficiencies for than for . such a relation # 1 # 1#2#1 # 2

the general properties of the non - thermal non - pulsed x - ray emission of rotation powered pulsars are investigated in the context of a pulsar wind nebula model . an examination of the observed x - ray emission from a sample of 23 pulsars in the energy range between 2 - 10 kev reveals that the relation of x - ray luminosity , , to the pulsar spin down power , , is steeper for the non - pulsed component than for the pulsed component . specifically , for the non - pulsed component , whereas for the pulsed component . the former relation is consistent with emission from a pulsar wind nebula model in which where is the power law index of the electron energy distribution . the relation for the pulsed component , on the other hand , is consistent with a magnetospheric emission model . in addition , the photon spectral index , , was found to be correlated to the conversion efficiency of spin down power to non - pulsed x - ray emission with greater efficiencies for than for . such a relation is naturally understood within the framework of a pulsar wind nebula model with the former relation corresponding to the emission of x - rays in the fast cooling regime and the latter relation corresponding to emission in the slow cooling regime . the x - ray properties of pulsar wind nebulae are sensitive to the physical conditions ( e.g. , the density and magnetic field ) of the interstellar medium and can lead to important differences between the x - ray emission characteristics ( luminosity , photon spectral index and emission morphology ) of pulsars in various environments . such wind nebulae can contribute to the non - thermal symmetric emission morphology ( point - like ) and elongated emission morphology ( tail - like ) from sources similar to geminga and psr b1757 - 24 . # 1 # 1#2#1 # 2

1512.01473

c

as mentioned in the introduction , the glg model is a very flexible family of distributions which is used to describe asymmetrically distributed data in many real applications . in this paper , we considered estimators which are simultaneously robust and efficient for aft models , when the errors follow a glg distribution and the data may contain censored observations . the estimation procedures have two main components : an initial highly robust but not necessarily efficient estimator and a final efficient estimator which starts with the initial one . we first considered the case , where no covariables are present and , in this case , we proposed an initial estimator that minimizes a @xmath0 scale of the differences between theoretical an empirical quantiles of order smaller than @xmath346 , where @xmath115 is a trimming fraction . the final estimator is a one step weighted likelihood estimator , where the weights penalizing the outliers are derived from the initial estimator . for the case , where covariables are present , the proposed estimators were derived in three steps . in a first step we used a regression mm - estimator as proposed in @xcite to obtain initial slope estimates and to compute the corresponding residuals . in a second step , we computed an initial estimator of the glg parameters by applying the procedure for the no covariables case to these residuals . in the third step we obtained a final estimator of all the parameters using a one step truncated ml starting with the initial estimator . we provided asymptotic results and extensive monte carlo results showing that the final estimators are highly efficient and maintain the same robustness level as the initial ones .

the generalized log - gamma ( glg ) model is a very flexible family of distributions to analyze datasets in many different areas of science and technology . in this paper , we propose estimators which are simultaneously highly robust and highly efficient for the parameters of a glg distribution in the presence of censoring .

the generalized log - gamma ( glg ) model is a very flexible family of distributions to analyze datasets in many different areas of science and technology . in this paper , we propose estimators which are simultaneously highly robust and highly efficient for the parameters of a glg distribution in the presence of censoring . we also introduced estimators with the same properties for accelerated failure time models with censored observations and error distribution belonging to the glg family . we prove that the proposed estimators are asymptotically fully efficient and examine the maximum mean square error using monte carlo simulations . the simulations confirm that the proposed estimators are highly robust and highly efficient for finite sample size . finally , we illustrate the good behavior of the proposed estimators with two real datasets . * keywords * : censored data . quantile distance estimates . estimators . truncated maximum likelihood estimators . weighted likelihood estimators .

astro-ph0509028

r

as mentioned above , our strategy in testing our jet models against the data was to allow the maximum number of model parameters to vary freely during the fit . this allowed us to explore which parameters had the greatest influence on the fits . several parameters settled on fairly similar values for both sources and all observations , which suggests that those parameters could be fixed in future applications of this model . we will discuss this possibility explicitly below . fits with a complicated model can easily lead to false , local minima ; therefore , we began the fitting procedure outside of isis , using unfolded data sets in order to find a set of starting parameters that would yield reduced @xmath34 . for this paper we have chosen to explore only models with rough equipartition between the magnetic and radiating particle pressures ( @xmath35 ) . this assumption is obviously not applicable for poynting flux dominated jets ; however , we consider the very weak acceleration required by observations to be an indication that magnetic domination ( which would generally imply stronger acceleration mechanisms ) is not likely to be very extreme . we use the results of @xcite as a rough guide for consistency , and only consider models with reflection fractions @xmath19 for jet nozzle radii @xmath36 to be ` successful ' fits . for smaller values of the radii , slightly lower values for the reflection fraction would be expected . in all cases the jet models seemed to naturally prefer reflection fractions @xmath37 , so in practice this restriction on reflection fraction was not an issue . [ gx339_comps ] shows a representative model for gx 339@xmath04 in order to illustrate the contribution from the various components which go into the later figures showing actual fits . the radio through ir originates exclusively from self - absorbed synchrotron radiation beginning at @xmath38 and continuing outwards along the jet . optically thin synchrotron emission from the accelerated power - law tail of leptons also contributes to the soft x - ray band . the base of the jet radiates direct synchrotron photons , giving a slight hump in the optical / uv , which are then included as seed photons ( along with disk photons ) for upscattering by the emitting electrons into an ssc / ec `` hump '' in the hard x - rays . the shape of this hump is rounded , due to the quasi - thermal particle distribution assumed in the base , and thus reduces the need for a large fraction of disk - reflected photons to contribute to the spectral break / hardening at @xmath1810 kev . the possibility that there are two correlated continuum components in the x - ray band is supported by our ensemble of simultaneous radio / x - ray observations of cyg x-1 , whose spectra are very well - described by exponentially cut - off , broken power - laws ( @xcite ) . in these models , the soft x - ray spectral slope is very well - correlated with the break of the hard x - ray spectral slope , and the hard x - rays are very well - correlated with the radio @xcite . the multicolor blackbody included in the jet model is also shown in the soft x - ray band . the photons from this component are included in the inverse compton upscattering within the jet . the statistical fits are shown in figs . [ gx339_all ] & [ cyg_all ] , for gx 339@xmath04 and cyg x-1 , respectively . each figure encompasses nine panels , with each row representing a single simultaneous radio and x - ray observation of the source . the first column shows the entire radio through x - ray jet model + soft disk + reflection fit , and the second column focuses just on the x - ray band . the last column shows the thermal compton corona model from eqpair for comparison . values for all fitted parameters are given in tables 24 . the results presented in figs . [ gx339_all ] & [ cyg_all ] and tables [ tab : mffjeti ] , [ tab : mffjetii ] , & [ tab : eqpair ] immediately demonstrate three important results of this work . * * jet models describe the data equally well as pure compton corona models , even when employing the broad - band and high statistics of the rxte data . * there has been question in the literature ( e.g. , @xcite ) as to whether or not jet models can adequately describe the spectral cutoff of the hard tail . while pure synchrotron jet models may not be able to describe the steep cutoff present in some ( but not all ) observations , jets can also successfully account for this hard tail cutoff via comptonization . the primary differences between ` traditional ' coronal models and jet coronal models are that the coronal temperatures are higher in the latter ( @xmath39k vs. @xmath40k ) , and the disk seed photons in jet models are significantly augmented if not dominated by synchrotron seed photons . * * the jet models , similar to the compton corona models , describe a complex continuum with curvature specifically , a hardening above 10kev . * again , the hardening often predominantly ascribed to a ` reflection hump ' is being somewhat subsumed by continuum emission . in the jet model , the steeper slope of the soft x - rays is primarily due to synchrotron emission from the jet , rather than being influenced by the disk photons , while the hardening is due to the ssc / ec component . reflection is present , but represents a smaller fraction of the total hard flux compared to the corona models . note that the fits discussed here are in contrast to earlier incarnations of the jet model which attempted to describe observations solely via the synchrotron component ( e.g. , the studies of xte j1118 + 480 ; @xcite ) . for xte j1118 + 480 , the lack of any discernible break or hardening near 10kev in the continuum spectrum was used to argue for the lack of a reflection component @xcite , which would be consistent with a jet spectrum dominated by the synchrotron component @xcite . in contrast , the fact that all of the xrb spectra shown here harden above 10kev argue for the importance of both the synchrotron and ssc / ec components of the jet spectrum for these fits , as well as the presence of reflection . * * although the jet and compton coronal models describe the x - ray data equally well , only the jet model naturally describes both the amplitude and slope of the radio data without the need for additional free parameters . * it is important to note that the radio spectrum , as well as the bulk of the 3 - 200kev x - ray continuum ( i.e. , the overall amplitude and continuum curvature ) , are almost solely driven by the parameters of the jet : energy input to the jet ( @xmath41 ) , radius of the jet base ( @xmath10 ) , electron temperature at the jet base ( @xmath42 ) , slope of the power - law component of the electron energy distribution ( @xmath43 ) , the equipartition parameter ( @xmath44 ) , and the location of the particle acceleration zone in the jet ( @xmath45 ) . if one begins instead with a corona model and attempts to fit the amplitude and slope of the radio data by assuming a relationship to an extant jet model , this will in essence require the addition of many more parameters to describe just two physical quantities . we argue that nothing can be gained by this approach , which is why we have chosen to study the test case of full coupling . from our set of jet model fits that successfully describe the gx 339@xmath04 and cyg x-1 data , we can now explore the implications of the fitted parameters . cyg x-1 and gx 339@xmath04 are somewhat different sources while in their hard states . the luminosity of gx 339@xmath04 varies much more than that of cyg x-1 . this is apparent in the fitted values for the power normalization @xmath12 and output power @xmath46 shown in the first two columns of table [ tab : mffjeti ] . both sources show best fit @xmath12 in the range of @xmath47 @xmath48 , but gx 339@xmath04 shows significantly more variation in this parameter . differences can also be seen in the other main parameters , for instance on average gx 339@xmath04 favors slightly larger values of the nozzle radius , @xmath10 . this reflects the slightly higher ratio of x - ray to radio flux observed in cyg x-1 . a smaller scale jet base , for a given jet power , increases the jet compactness which in turn gives a slightly higher flux ( with the x - ray flux being more sensitive to this effect ) and pushes all jet emission to slightly higher frequencies . other fit parameters also indicate differences between these two sources ; however , the parameters surprisingly fall roughly in the same range given the _ a priori _ possibility for much greater parameter variations . note that the lowest luminosity gx 339@xmath04 observation , obs i d 40108 - 02 - 03 , has poor enough statistics that the following general statements about the gx 339@xmath04 fits will be based mostly on the brighter two observations . for example , both the electron temperature , @xmath42 , and the location of the start of the acceleration zone , @xmath38 , tend to be larger in gx 339@xmath04 than in cyg x-1 . ( although we were unable to find adequate error bars for the latter parameter , the trend of finding larger values in gx 339@xmath04 was persistent . ) additionally , we note that the electron power law index , @xmath43 , shows more variation in gx 339@xmath04 than in cyg x-1 . although the range in electron temperatures at the base of the jets falls within a range of a factor of @xmath49 for both sources , one of the criticisms of this class of models has been that @xmath50-@xmath51 k is not as `` natural '' a value as the @xmath52kev typically used in thermal comptonization models . the jet model electron temperature , however , is comparable to or slightly greater than the value typically derived for radiatively inefficient accretion flows ( e.g. , * ? ? ? if some fraction of the accreting plasma is fed directly into the jets , and also perhaps heated slightly in the process , we would expect such a temperature . on the other hand , several jet model free parameters seemed to settle quite quickly into similar values for both cyg x-1 and gx 339@xmath04 : the equipartition factor @xmath44 , the fraction of accelerated particles @xmath53 , and the ratio of nozzle length to radius @xmath54 . physically , this suggests that these jets either are close to equipartition , or we have found a local minima of solutions for @xmath55 , and we may find other reasonable minima for @xmath56 , e.g. , magnetically - dominated jets . we plan to explore this particular question in a future work . it seems reasonable , however , to freeze the fraction of accelerated particles at @xmath57 and make the statement that reasonably efficient acceleration is expected to occur in hard state bhc jets . similarly , a compact base / corona region with scale height similar to the radius seems a reasonable assumption . it is likely that this parameter can also be frozen in future applications of the jet model . we listed the two `` acceleration parameters '' , the shock speed relative to the bulk plasma flow , @xmath58 , and the ratio of the scattering mean free path to the gyroradius , @xmath59 , as separate fit parameters . however , as discussed in the appendix , these parameters are perhaps not physically meaningful as currently defined , since we are no longer as convinced that the acceleration process is diffusive fermi acceleration . these parameters enter into the acceleration rate as the factor @xmath60 , which is compared to the sum of the cooling rates from synchrotron and inverse compton radiation , and adiabatic expansion in order to calculate the local maximum accelerated lepton energy . therefore , this parameter can be loosely interpreted as a factor related to the efficiency of the acceleration process and merged for future fits into a single parameter . for the current fits , the individual components were left free to vary , with mixed results . for cyg x-1 , @xmath61 , suggesting a meaningful range of fits . however , for gx 339@xmath04 , @xmath62 ranges over two orders of magnitude , and we suspect that we did not fully explore parameter space meaningfully for this source . in future applications of the model , it is likely that we will combine these two parameters into a single parameter that will absorb our uncertainty about the acceleration process . while we list best fit values for the multicolor blackbody disk model parameters @xmath63 and @xmath64 , as well as the derived inner radius @xmath65 , it is important to keep in mind that because the data only extend down to a few kev , we can not meaningfully constrain this component from spectral fitting . as described in the appendix , the disk photons are not as important to the overall photon field as the locally produced synchrotron photons and thus can mainly be constrained by their direct spectral contribution . this contribution , although weak , is in fact required for a good fit , but it is not unique . @xcite have also fit some of the x - ray data presented here , and for similar reasons fixed the thermal disk parameters . on the other hand , for the disk emission plus comptonization models presented here ( as well as for those presented in @xcite ) , the temperature of the disk was tied to the temperature of the seed photons i.e . , the thermal photons were the _ only _ source of seed photons for comptonization . thus by virtue of these imposed restrictions , much more stringent formal limits for the disk components were attainable . the main result to take away about the accretion flow modeling is that our fits are generally consistent with a sub - eddington accretion disk with temperatures somewhat less than 1 kev . similarly , the total power entering into the jets is roughly consistent with being of the same order as the observed luminosity required in the disk to be consistent with the data . the presence of a weak disk component is necessary for a good fit , and thus disk photons will contribute to the inverse compton component from the jet . we do not , however , feel we can confidently make any statements about the disk geometry and thus the accretion rate at the inner radius assumedly feeding the jets . for both gx 339@xmath04 and cyg x-1 , the amount of reflection required by the jet models is roughly comparable to , although in general slightly lower than , that required by comptonization models . this trend can be understood by the fact that the jet base ssc / ec component dominates above 10kev , and to some extent subsumes the role played by the `` compton hump '' normally attributed to disk reflection . this effect of course brings up an interesting point : there is a clear degeneracy in how the spectral hardening above 10kev can be understood in terms of continuum models . the fact that the jet ssc / ec component has a similar appearance to the compton reflection hump does not preclude the presence of both . clearly , the fluorescent fe line implies that there must be a degree of reflection . what these results ( as well as the comptonization fits ; @xcite ) do suggest is that one can not uniquely determine a reflection fraction independently of the presumed continuum model .

the hard state of x - ray binaries ( xrbs ) is characterized by a power law spectrum in the x - ray band , and a flat / inverted radio / ir spectrum associated with occasionally imaged compact jets . are very similar to the derived plasma conditions at the jet footpoints . here we explore the question of whether the ` corona ' and ` jet base ' are in fact related , starting by testing the strongest premise that they are synonymous . the conditions at the jet base fix the conditions along the rest of the jet , thus creating a direct link between the x - ray and radio emission .

the hard state of x - ray binaries ( xrbs ) is characterized by a power law spectrum in the x - ray band , and a flat / inverted radio / ir spectrum associated with occasionally imaged compact jets . it has generally been thought that the hard x - rays result from compton upscattering of thermal accretion disk photons by a hot , coronal plasma whose properties are inferred via spectral fitting . interestingly , these properties especially those from certain magnetized corona models are very similar to the derived plasma conditions at the jet footpoints . here we explore the question of whether the ` corona ' and ` jet base ' are in fact related , starting by testing the strongest premise that they are synonymous . in such models , the radio through the soft x - rays are dominated by synchrotron emission , while the hard x - rays are dominated by inverse compton at the jet base with both disk and synchrotron photons acting as seed photons . the conditions at the jet base fix the conditions along the rest of the jet , thus creating a direct link between the x - ray and radio emission . we also add to this model a simple iron line and convolve the spectrum with neutral reflection . after forward - folding the predicted spectra through the detector response functions , we compare the results to simultaneous radio / x - ray data obtained from the hard states of the galactic xrbs gx 339 and cygnus x-1 . results from simple compton corona model fits are also presented for comparison . we demonstrate that the jet model fits are statistically as good as the single - component corona model x - ray fits , yet are also able to address the simultaneous radio data .

1108.3764

i

diphoton final states represent a very important testing ground for the standard model ( sm ) , for example they may be one of the main discovery channels for the higgs boson searches at the cern lhc . moreover , similar to the case of dileptons , the inclusive production of two - photon high mass resonance states at the lhc : @xmath2 is considered as a powerful , clean test of new physics ( np ) , would an excess of @xmath3 events be observed with respect to the prediction from the sm cross section . one np scenario of particular importance is the case of the spin-2 kaluza - klein ( kk ) graviton excitations predicted by the randall - sundrum ( rs ) model of gravity in one warped spatial extra dimension @xcite . this model suggests a rich phenomenology that includes the production of diphoton resonances , to be explored at collider energies , see , for example , refs . @xcite . the existence of such graviton excitations can be signalled by the occurrence of peaks in the invariant mass distribution of the photon pairs and , indeed , the lowest lying predicted diphoton peak has recently been searched for in experiments at the @xmath4 fermilab tevatron collider @xcite , and at the 7 tev @xmath5 lhc collider with time - integrated luminosity of the order of 40 @xmath6 @xcite . in these experiments , exclusion mass limits on the lightest rs resonance of the tev order have been set , and graviton mass scales larger than 1 tev will certainly be in the kinematical reach of lhc . assuming that a diphoton peak at an invariant mass value @xmath7 is observed , its association to a specific np scenario would be possible only if we are able to discard other competitor models , potential sources of the peak itself with same @xmath7 and same number of events . basically , for any nonstandard model one can define , on the basis of the foreseeable statistics and uncertainties , a _ discovery reach _ on the relevant heavy resonance @xmath8 as the upper limit of the range in @xmath7 where , in a specific domain of the model parameters called `` signature space '' , the peak is expected to give a signal observable over the sm prediction to a prescribed confidence level . instead , the _ identification reach _ on the model is the upper limit of the range in @xmath7 where it can be identified as the source of the peak , once discovered , or , equivalently , the other competitor models can be excluded for all values of their respective parameters . of course , for many models , identification should be possible only in a subdomain of their signature space . the determination of the spin of an observed resonance clearly represents an important selection among different classes of nonstandard interactions . in the case of the inclusive diphoton production ( [ proc ] ) , the tool to directly test the spin-2 of the rs graviton resonance or , equivalently , exclude the hypothesis of a spin-0 scalar particle exchange , would be provided by the distinctive angular distributions in the angle @xmath9 between the incident quark or gluon and the final photon in the diphoton center - of - mass frame . this is similar to dilepton production , the difference being that in this case the hypotheses of both the spin-0 and the spin-1 exchanges must simultaneously be excluded . the spin-2 test of the lowest - lying rs graviton in lepton - pair collider events , through the direct comparison of the angular distributions for the various spin hypotheses , was earlier discussed in several papers , see , e.g. , refs . @xcite , and experimental angular analysis were attempted at the tevatron in ref . a potential difficulty of the direct - fit angular analysis at the lhc is that generally , due to the symmetry of the proton - proton initial configuration , the determination on an event - by - event basis of the direction of the initial parton , hence of the sign of @xmath10 , is in principle not fully unambiguous , so that cuts in phase space must be applied in this regard . the spin-2 rs graviton analysis of lhc dilepton events proposed in ref . @xcite , makes use of a `` center - edge '' angular asymmetry @xmath0 where the above mentioned ambiguity should not be present @xcite . essentially , in this observable the dilepton events are weighted according to the @xmath10 differential distributions , and the asymmetry is defined between cross sections symmetrically integrated over `` center '' and `` edge '' angular intervals . recently , asymmetries conceptually analogous to @xmath0 , have been applied to heavy quantum states spin identification in refs . @xcite , and a comparison of the performances of different methods for heavy resonances identification has been presented in ref . angular analyses for different spin - mediated drell - yan processes have been applied to a variety of np models in ref . @xcite . here , we propose the application of @xmath11 to the angular analysis of the diphoton production process ( [ proc ] ) at the lhc . as remarked previously , the selection of the spin-2 rs graviton amounts in practice to exclude the hypothesis of a spin-0 particle exchange with same mass @xmath7 and producing the same number of diphoton events . ideally , one advantage of the diphoton channel over dileptons can be represented by the doubled statistics expected in the former case @xcite . also , the automatic exclusion of the spin-1 hypothesis @xcite , should in any case allow a simplification of the analysis from the phenomenological point of view . finally , the consideration of process ( [ proc ] ) , in addition to dilepton production , is needed for an exhaustive test of model @xcite . for our analysis we have used the calculations of the required differential cross sections to next - to - leading order ( nlo ) in qcd , and this is essential at a hadron collider as the theoretical uncertainties get reduced when higher order corrections are included . furthermore , as a result of new interactions in a np model , there will be additional subprocesses that contribute at leading order ( lo ) itself ( e.g. , @xmath12 in the rs model ) and hence the signal can receive enhanced contributions due to the nlo corrections . specifically , in sec . ii we review the definitions of the basic cross sections involved in the asymmetry @xmath0 ; sec . iii will be devoted to the relevant properties and the characteristic angular distributions for the rs graviton and for the competitor scalar particle exchanges in process ( [ proc ] ) , for which we will adopt the model recently proposed in ref.@xcite . in sec . iv we discuss the nlo qcd effects to the diphoton production rates and to the angular distributions , for both kinds of spin exchange . v contains an outline of the @xmath0-based angular analysis and the consequent numerical results for rs identification , in the lhc center - of - mass running configurations @xmath13 tev and @xmath14 tev . finally , sec . vi contains some conclusive remarks .

the high mass neutral quantum states envisaged by theories of physics beyond the standard model can at the hadron colliders reveal themselves through their decay into a pair of photons . once such a peak in the diphoton invariant mass distribution is discovered , the determination of its spin through the distinctive photon angular distributions is needed in order to identify the associated nonstandard dynamics . we here discuss the discrimination of the spin-2 randall - sundrum graviton excitation against the hypothesis of a spin-0 exchange giving the same number of events under the peak , by means of the angular analysis applied to resonant diphoton events expected to be observed at the lhc .

the high mass neutral quantum states envisaged by theories of physics beyond the standard model can at the hadron colliders reveal themselves through their decay into a pair of photons . once such a peak in the diphoton invariant mass distribution is discovered , the determination of its spin through the distinctive photon angular distributions is needed in order to identify the associated nonstandard dynamics . we here discuss the discrimination of the spin-2 randall - sundrum graviton excitation against the hypothesis of a spin-0 exchange giving the same number of events under the peak , by means of the angular analysis applied to resonant diphoton events expected to be observed at the lhc . the spin-0 hypothesis is modelled by an effective interaction of a high mass gauge singlet scalar particle interacting with the standard model fields . the basic observable of our analysis is the symmetrically integrated angular asymmetry , calculated for both graviton and scalar-channel exchanges to next - to - leading order in qcd . desy 11 - 139

astro-ph0301394

i

at visual wavelengths , the dusty bipolar `` homunculus '' ejecta structure around @xmath0 car is primarily a hollow reflection nebula ( see thackeray 1961 ; visvanathan 1967 ; meaburn 1987 ; hillier & allen 1992 ; hamann et al . 1994 ; etc . ) . therefore , by observing localized parts of the homunculus , _ we can indirectly see the star s spectrum from a range of directions in space _ potentially allowing us to reconstruct the shape of @xmath0 car s wind , which is expected to lack spherical symmetry . independent of the large - scale bipolar morphology , hints of non - sphericity have been noted by , e.g. , viotti et al . ( 1989 ) , hillier & allen ( 1992 ) , davidson et al . ( 1995 ) , davidson & humphreys ( 1997 ) , and zethson et al . indeed , hillier & allen ( 1992 ) found a difference between direct and reflected he i emission that originates in the stellar wind , and early space telescope imaging spectrograph ( _ hst_/stis ) observations showed that the reflected h@xmath1 profile depends on location within the homunculus . departures from spherical symmetry are obviously critical for theories of winds and instabilities in the most massive stars ( see lamers & cassinelli 1999 , and papers in wolf , stahl , & fullerton 1998 ) . asphericity in @xmath0 car s wind may also be critical for understanding its 5.5 year cycle ( damineli 1996 ) , its long term variability , and excitation of its ejecta . in addition to its classic status as a very massive unstable star , @xmath0 car is uniquely favorable for this problem because the dusty homunculus has a fairly definite three - dimensional structure ; each projected location on the nebula provides reflected light from a viewing direction whose stellar latitude is approximately known ( davidson et al . 2001 ; smith 2002 ) . we have obtained long - slit stis spectra optimized for studies of the reflected latitude - dependent effects . we find that some features do in fact depend on viewing direction . wind velocities are highest around the pole , as one might expect if stellar rotation reduces the effective gravity and escape velocity at the equator . dominant outflow velocities in the stellar wind are 400 to 600 km s@xmath2 , but some faster material ( @xmath31000 km s@xmath2 ) had been seen ( viotti et al . 1989 ; damineli et al . 1998 ) , and our data now show that these high velocities are polar . we also find a much less anticipated phenomenon : broad p cyg absorption components of h@xmath1 and h@xmath4 , usually weak in our direct view of @xmath0 car , _ are quite deep at higher ( not lower ) latitudes_. traditionally , a slow equatorial wind is supposed to be denser than the associated fast polar wind and the mass - loss rate may increase with decreasing @xmath5 ( friend & abbott 1986 ) ; some examples are b[e ] stars ( zickgraf et al . 1986 ) , wind - compressed disks or zones ( bjorkman & cassinelli 1993 ; ignace , cassinelli , & bjorkman 1996 ; owocki , cranmer , & blondin 1994 ) , and bistable winds ( lamers & pauldrach 1991 ) . our observations of @xmath0 car , however , suggest that its wind is densest near the poles despite higher velocities there . other interpretations are conceivable , but require detailed models of line transfer . if @xmath0 car s wind densities are highest near the poles as one might guess from the deeper hydrogen p cyg absorption , then this tends to support recent comments by owocki and others concerning the importance of non - radial forces and gravity darkening in line - driven winds of massive stars ( owocki , cranmer , & gayley 1996 ; owocki & gayley 1997 ; owocki , gayley , & cranmer 1998 ; maeder & meynet 2000 ; meader & desjacues 2001 ) . specifically , these studies predict that if a luminous star is rotating fast enough for gravity darkening to be important ( i.e. , at @xmath670% of the `` critical '' rotation speed ) , then stronger radiative flux at the hot poles will tend to drive a higher mass flux . glatzel ( 1998 ) and maeder ( 1999 ) have discussed modifications to the `` critical '' rotation rate near the eddington luminosity . we describe new stis observations in 2 below , hydrogen line profiles in 3 , and helium profiles in 4 . in 5 we discuss various likely implications of the observed wind geometry . then in 6 we examine older stis spectra and discuss temporal variability of the wind structure . finally , in 7 we mention consequences that a variable , bipolar wind may have for interpretations of @xmath0 car s 5.5-year spectroscopic cycle .

the homunculus reflection nebula around carinae provides a rare opportunity to observe the spectrum of a star from more than one direction . in the case of car , we present stis spectra of several positions in the homunculus , showing directly that car has an aspherical stellar wind . . the wind geometry and its variability have critical implications for understanding the 5.5 year cycle and long - term variability , but do not provide a clear alternative to the binary hypothesis for generating car s x - rays .

the homunculus reflection nebula around carinae provides a rare opportunity to observe the spectrum of a star from more than one direction . in the case of car , the nebula s geometry is known well enough to infer how line profiles vary with latitude . we present stis spectra of several positions in the homunculus , showing directly that car has an aspherical stellar wind . p cygni absorption in balmer lines depends on latitude , with relatively high velocities and strong absorption near the polar axis . stronger absorption at high latitudes is surprising , and it suggests _ higher mass flux toward the poles _ , perhaps resulting from radiative driving with equatorial gravity darkening on a rotating star . reflected profiles of he i lines are more puzzling , offering clues to the wind geometry and ionization structure . during car s high - excitation state in march 2000 , the wind was fast and dense at the poles , with higher ionization at low latitudes . older stis data obtained since 1998 reveal that this global stellar - wind geometry changes during car s 5.5 year cycle , and may suggest that this star s _ spectroscopic events are shell ejections_. whether or not a companion star triggers these outbursts remains ambiguous . the most dramatic changes in the wind occur at low latitudes , while the dense polar wind remains relatively undisturbed during an event . the apparent stability of the polar wind also supports the inferred bipolar geometry . the wind geometry and its variability have critical implications for understanding the 5.5 year cycle and long - term variability , but do not provide a clear alternative to the binary hypothesis for generating car s x - rays .

math0303218

i

in a series of two papers , the present one and the second one by the second author @xcite , we continue the study of the hurwitz problem @xcite concerning counting ramified coverings of the @xmath1-sphere . roughly speaking , this problem can be formulated as follows : _ given a set of fixed ramification points on the target @xmath1-sphere and a set of ramification types over these points , count the number of non - isomorphic ramified coverings @xmath2 by a @xmath1-surface @xmath3 , having the prescribed ramification types over the prescribed ramification points_. two coverings are considered to be isomorphic if there is a homeomorphism of the covering surfaces taking the first covering to the second one . in fact , we count isomorphism classes with the weight equal to the inverse order of the group of automorphisms of the class ; in this form the problem is more natural , and admits a lot of applications . in a more modern setting this problem can be reformulated as the computation of the gromov witten invariants of the complex projective line . a detailed exposition of the history of the problem and a description of various approaches to its solution can be found in @xcite . hurwitz @xcite himself gave an explicit answer to the problem in the case , where the covering surface is also a sphere , and there is one ramification point with arbitrary ramification , while all others are points of simple ramification . in spite of the importance of the problem , only recently hurwitz s original results were extended to more general cases and treatable answers were obtained : * i. goulden and d. jackson @xcite solved the combinatorial problem that allows one to give the answer to hurwitz s problem for polynomials ( that is , ramified coverings of the sphere by a sphere having a point with a single preimage and arbitrary ramification over other points ) ; later their results were reestablished in @xcite and @xcite by absolutely different methods ; * t. ekedahl , s. lando , m. shapiro , and a. vainshtein @xcite gave an expression for the number of ramified coverings of the sphere by a surface of arbitrary genus with a single point of arbitrary ramification type and all other points of simple ramification , in terms of intersection indices on moduli spaces of curves ( when the covering surface is the sphere , the answer given by the formula coincides with hurwitz s one ) ; another proof of the formula was given in @xcite . here we address the special case of the hurwitz problem , where the covering surface is also a sphere , but in contrast to the hurwitz case , ramification points of arbitrary type are allowed . we are far from solving the problem in this generality , but we suggest a general approach , and show how it works in some special cases , thus producing new enumerative results . to a ramification point (= a critical value ) of multiplicity @xmath4 we assign a partition @xmath5 of @xmath4 , called the _ ramification type_. the elements of @xmath5 are the multiplicities of the critical points that correspond to our critical value . recall the hurwitz theorem . the number @xmath6 of degree @xmath7 coverings of the sphere by the sphere , having the ramification type @xmath8 over one point , @xmath9 , while all other ramification points are fixed and simple , is @xmath10 here @xmath11 is the order of the automorphism group of the partition @xmath5 , @xmath12 is the number of nondegenerate ramification points , and @xmath13 is the number of simple preimages of the multiple ramification point . as a consequence of our approach we obtain , in the second part of this paper @xcite , for example , the following result . the number @xmath14 of degree @xmath7 coverings of the sphere by the sphere , having two double critical points and @xmath15 simple critical points , all the @xmath16 critical values being fixed , is @xmath17 as far as we know , this formula , as well as similar formulas for some other ramification types , is new . first of all we reduce the problem to the calculation of the degree of some map , called the lyashko looijenga map . this step is now standard . the lyashko looijenga map ( below , the @xmath18 map ) takes a meromorphic function to the set of its critical values . its source space can be chosen in a variety of ways ; here we define the @xmath18 map on the hurwitz space @xmath19 constructed in @xcite . it is the space of stable maps from genus zero complex curves to the projective line , having trivial ramification over infinity . all spaces of functions possessing degenerate ramification are considered as subvarieties in this space . these subvarieties form a stratification of the hurwitz space . [ thmml ] the number @xmath20 of ramified coverings of the sphere , having the ramification types @xmath21 over prescribed ramification points with multiplicities @xmath22 , is given by the formula @xmath23 where @xmath24 is the degree of the @xmath18 map restricted to the stratum @xmath25 consisting of functions with these ramification types . this is an instance of a general situation , see e.g. @xcite . indeed , if we fix a ramified covering @xmath26 and choose a complex structure on the target sphere @xmath27 , then there exists a unique complex structure on the covering surface @xmath3 making the function @xmath28 into a meromorphic function . this complex structure is produced by the riemann construction . hence , there is a one - to - one correspondence between ramified coverings with fixed ramification points of given types and meromorphic functions with fixed critical values of the same types . the latter number is exactly the degree of the @xmath18 map on the corresponding moduli space . the coefficient @xmath29 results from the fact that in our construction of the space @xmath19 we choose a numbering of the @xmath7 poles of each rational function . the factor @xmath30 is due to the fact that if we permute the ramification types @xmath31 preserving the multiplicities @xmath22 , we obtain a new set of ramified coverings that lie on the same stratum @xmath25 and have the same image under the @xmath18 map . the space @xmath19 is , in fact , a vector bundle over the deligne mumford moduli space @xmath32 of stable genus zero curves . the latter space is a smooth projective variety . the multiplicative group @xmath33 of nonzero complex numbers acts on this bundle fiberwise . this action consists in just multiplying a meromorphic function by a constant . it preserves the stratification of the space @xmath19 because the multiplication does not change the type of singularities . deleting the zero section of the bundle and taking the quotient modulo this action we reduce the variety to the projectivization @xmath34 of the vector bundle @xmath19 . the projectivization @xmath34 carries the tautological line bundle @xmath35 , and a natural cohomology class @xmath36 , @xmath37 , the class of a hyperplane section . the degree of the lyashko looijenga map restricted to a subvariety in @xmath19 is related to the intersection index of the subvariety with the complementary power of the class @xmath38 . namely , the following statement is true . [ thm1.4 ] the degree @xmath24 of the @xmath18 map restricted to the stratum @xmath25 is equal to @xmath39 here @xmath4 is the dimension of the stratum @xmath40 , @xmath41 is the multiplicity of the @xmath42th ramification point ( or the sum of the elements of @xmath43 ) , and @xmath44 is the coupling between a homology and a cohomology class . this theorem is proved in section [ ssec : strathur ] . theorem [ thm1.4 ] implies that our approach requires the study of the cohomology ring @xmath45 . all cohomology groups we consider are with complex coefficients , and we do not specify the coefficients explicitly . we need * a reasonable description of this ring , say , in terms of generators and relations ; * reasonable expressions for the cohomology classes of the strata and the class @xmath38 in terms of the generators . the solution of the first problem is known since the space @xmath19 is a vector bundle over the moduli space of stable rational curves , whose cohomology is known . the second problem seems to be much more difficult . in fact , we need less than the whole cohomology ring . the symmetric group @xmath46 acts on the space @xmath19 by permuting the indices , whence it acts on the cohomology space @xmath45 . all the cohomology classes we are interested in are symmetric with respect to this action . therefore , we only need to know the @xmath46-symmetric part of the cohomology algebra @xmath45 . this is an additional problem , but its solution can lead to a simplification of the decompositions of the strata . the situation would become even easier if we restrict ourselves to the subalgebra in the cohomology algebra @xmath45 generated by the classes of the strata . consider two closed codimension 1 subvarieties @xmath47 and @xmath48 in @xmath19 ; the first of them is called the _ caustic _ and it is the closure of the space of functions having a critical point of order @xmath1 , the second one is the _ maxwell stratum _ and it is the closure of the space of functions having two distinct critical points with coinciding critical values . [ conj : kazarian ] the subalgebra of the cohomology algebra @xmath45 generated by the cohomology classes of the strata is generated by the two classes @xmath47 and @xmath48 in @xmath49 . up to now , the basis of this conjecture is not too solid . but it does not contradict our sample calculations , and it has a nonformal justification coming from kazarian s theory . kazarian s theory concerns cohomology classes of multisingulatities of a map @xmath50 of two complex manifolds , @xmath51 . its main statement claims that there is a universal way to express these cohomology classes in terms of the characteristic classes of the tangent bundles over the two manifolds @xmath52 and @xmath53 , more precisely in terms of the class @xmath54 , where @xmath55 is the total chern class . it is a development of the theory of the thom polynomial . up to now , only a preliminary version @xcite of the text describing the theory is available , and we are not going to refer directly to statements from it . however , the ideology of the theory seems to be applicable in the situation we are studying , and it leads to a number of conjectures concerning the part of the cohomology ring of the hurwitz spaces we are interested in . in our situation , the variety @xmath52 is the universal curve @xmath56 over the hurwitz space @xmath34 , while the variety @xmath53 is the quotient of @xmath57 by the natural @xmath33 action . the map @xmath28 is the universal map over @xmath34 . it is easy to see that the map @xmath28 almost identifies the tangent spaces @xmath58 and @xmath59 ; more precisely , one has @xmath60 , where @xmath61 and @xmath62 are first chern classes of some linear bundles . however , new complications arise , since we are interested in cohomology classes of @xmath34 and not of @xmath56 . kazarian s ideology leads to conjecture [ conj : kazarian ] . if the conjecture is true , then the computation of intersection numbers of the strata in the hurwitz space with the complementary powers of the class @xmath36 can be split into two independent stages : * express the cohomology class of the required stratum as a ( homogeneous ) polynomial in the classes @xmath48 and @xmath47 ; * find the intersection index of each monomial in @xmath48 and @xmath47 with the complementary degree of the class @xmath38 . another cohomology class in @xmath49 is also distinguished . this is the class @xmath63 dual to the subvariety of functions defined on singular curves . this class also can be expressed in terms of the classes @xmath47 and @xmath48 . this means that the subring in @xmath45 generated by the classes @xmath47 and @xmath48 coincides with that generated by @xmath38 and @xmath63 . the linear relations relating these four classes are as follows : @xmath64 the coefficients in these linear relations are polynomial in @xmath7 , which ( together with the informal support of kazarian s theory ) allows us to sharpen conjecture 1.5 in the following way : each cohomology class dual to a stratum in @xmath34 can be expressed as a homogeneous polynomial in @xmath65 whose coefficients that are polynomials in @xmath7 . therefore the calculations must even be simplified . in section 2 we give precise definitions of notions mentioned in this introduction . section 3 is devoted to the description of the lyashko looijenga map . in section 4 the structure of cohomology of the hurwitz spaces is analyzed . we are greatful to a. zorich who invited us both to rennes , where the main part of this work was accomplished . the work was completed during our participation in the mini - workshop on hurwitz theory and its ramifications , and we thank its organizers j. h. kwak and a. d. mednykh for inviting us . we also thank b. shapiro and m. shapiro for their interest and m. kazarian for explaining the basics of his theory .

the hurwitz space is a compactification of the space of rational functions of a given degree . the lyashko - looijenga map assigns to a rational function the set of its critical values . it is known that the number of ramified coverings of by with prescribed ramification points and ramification types is related to the degree of the lyashko looijenga map on various strata of the hurwitz space . _ [ cols= " > , < " , ]

the hurwitz space is a compactification of the space of rational functions of a given degree . the lyashko - looijenga map assigns to a rational function the set of its critical values . it is known that the number of ramified coverings of by with prescribed ramification points and ramification types is related to the degree of the lyashko looijenga map on various strata of the hurwitz space . here we explain how the degree of the lyashko - looijenga map is related to the intersection theory on this space . we describe the cohomology algebra of the hurwitz space and prove several relations between the homology classes represented by various strata . _ _ [ cols= " > , < " , ]

1312.0832

i

spontaneous breakdown of chiral symmetry ( @xmath4ssb ) @xmath5 characterizes the vacuum and low - energy dynamics of quantum chromodynamics ( qcd ) @xcite . the non - vanishing chiral condensate @xmath6 is considered as one of the order parameters of @xmath7ssb and gives a characteristic scale for hadron physics . @xmath7ssb is considered to be responsible for the origin of constituent quark mass after the current quark mass is given by the higgs condensate slightly . according to the spontaneous breakdown , the pseudoscalar mesons such as @xmath8 appear as the nambu - goldstone ( ng ) bosons . recently , in order to investigate the mechanism of the dynamical mass generation , partial restoration of the chiral symmetry in the nuclear medium has gained considerable attention . this phenomenon is incomplete restoration of chiral symmetry with sufficient reduction of the absolute value of the chiral condensate in the medium and will lead to various changes of hadron properties . once we understand the partial restoration of chiral symmetry , we can predict other in - medium hadronic quantities through low energy theorems and vice versa . from this point of view , vast theoretical and experimental efforts are devoted for this topic . the density dependence of the chiral condensate is evaluated in various approaches , for example , the well - known linear density approximation providing the model - independent low density theorem @xcite , the relativistic bruckner - hartree - fock theory approach@xcite and systematic calculations by in - medium chiral perturbation theory beyond the linear density calculation @xcite . according to the model - independent linear density approximation , the leading density correction to the chiral condensate is determined by the @xmath9n sigma term @xmath10 and with the empirical value of the sigma term it has been found that the leading correction gives enough large contribution at the normal nuclear density : @xmath11 where @xmath12 , @xmath13 is the in - medium and in - vacuum condensate and @xmath14 is the normal nuclear density . recently , an in - medium sum rule satisfied in any density region has been derived model - independently by current algebra method and the low energy theorems , such as the gell mann oakes renner relation , the glashow weinberg relation and the weinberg tomozawa relation , are discussed within the linear density order @xcite . to investigate the pion properties in nuclei , deeply bound pionic atoms have received much attention @xcite . theoretically , the binding energies and decay widths of the 1s and 2p deeply - bound pionic atom states are estimated @xcite and in refs . @xcite hadronic quantities , such as pion optical potential , have been calculated beyond the linear density . experimentally the reduction of the chiral condensate is estimated quantitatively through reduction of the @xmath15-wave isovector parameter @xmath16 in the @xmath17-nucleus optical potential @xcite . the @xmath18 parameter is regarded as an in - medium isovector @xmath17n scattering length . these results show that the reduction of @xmath16 means the repulsive enhancement of the @xmath15-wave @xmath17-nucleon interaction in nucleus . another examples are low energy @xmath17-nucleus scattering and @xmath19 interaction in nuclei in the scalar - isoscalar channel . the low energy @xmath17-nucleus scattering also show that s - wave @xmath17-nucleus interaction are enhanced repulsively @xcite . according to the theoretical discussion given in refs . @xcite , the in - medium @xmath19 interaction in the scalar - isoscalar part will also has attractive enhancement thanks to the partial restoration of chiral symmetry in nuclear medium and the experimental observation of the invariant mass spectrum of the @xmath20 production off nuclear targets performed in refs . @xcite could have a hint of such a enhancement . in particular the pion decay constant is a fundamental quantity of chiral symmetry breaking . the in - medium decay constant also has been investigated in the linear density approximation @xcite and recently the chiral condensate and the decay constant have been evaluated in the next - to - leading order based on chiral order counting @xcite . in this paper , we discuss a general in - medium pion state and evaluate in - medium pionic quantities such as the decay constant , mass and the pseudo scalar coupling beyond linear density approximation . this paper is organized as follows . in sec.[in - medium chpt ] , we explain the general formulation of the in - medium chiral perturbation theory and discuss an expansion by fermi momentum counting . in sec.[decayconst ] , we discuss in - medium pion state and define the in - medium pionic quantities . here we will find that the pion wave function renormalization plays an important role for the in - medium pionic quantities . in sec.[results ] , we evaluate the in - medium pion self energy , wave function renormalization , pion decay constant and pseudo - scalar coupling and show the numerical results of the density dependence of them up to @xmath21 in fermi momentum expansion in symmetric nuclear matter and in isospin limit . we also discuss whether the in - medium low energy theorems , the gell - mann oakes renner relation and the glashow weinberg relation , are satisfied or not . finally we discuss the in - medium @xmath22 process caused by chiral anomaly . in sec.[summary ] , we summarize our paper .

we show that the linear density correction is dominant and the next - to - leading corrections are not so large at the saturation density , while their contributions can be significant in higher densities . we also discuss whether the low energy theorems , the gell - mann oakes renner relation and the glashow

the in - medium pion properties , _ i.e. _ the temporal pion decay constant , the pion mass and the wave function renormalization , in symmetric nuclear matter are calculated in an in - medium chiral perturbation theory up to the next - to - leading order of the density expansion . the chiral lagrangian for the pion - nucleon interaction is determined in vacuum , and the low energy constants are fixed by the experimental observables . we carefully define the in - medium state of pion and find that the pion wave function renormalization plays an essential role for the in - medium pion properties . we show that the linear density correction is dominant and the next - to - leading corrections are not so large at the saturation density , while their contributions can be significant in higher densities . the main contribution of the next - to - leading order comes from the double scattering term . we also discuss whether the low energy theorems , the gell - mann oakes renner relation and the glashow weinberg relation , are satisfied in nuclear medium beyond the linear density approximation . we also find that the wave function renormalization is enhanced as largely as 50% at the saturation density including the next - to - leading contribution and the wave function renormalization could be measured in the in - medium decay .

1312.0832

i

we have discussed the in - medium pion properties , such as the pion decay constant , the pion mass and the wave function renormalization based on the in - medium chiral perturbation theory . first , we have provided a general formalism of the in - medium chiral perturbation theory and have discussed an expansion in terms of fermi momentum . assuming that the renormalization for the in - vacuum quantities is performed in an appropriate way , we use the observed values to determine the low energy constants ( lecs ) in the chiral lagrangian . since we have used the physical values , the higher order corrections for the momentum expansion are implicitly included in the calculation . thus , we focus on the expansion of the fermi momentum of the physical quantities , which are calculated by the qcd current green functions . to calculate the in - medium quantities , we carefully define the in - medium pion state , and we have found that the in - medium wave function renormalization plays an essential role to define the in - medium coupling constants , such as the decay constant and pseudo - scalar coupling constant . we have evaluated the density dependence of the decay constant , the pion mass , the pion wave function renormalization and the pseudo - scalar coupling including the next - to - leading order of the density expansion beyond the well - known linear density approximation based on the in - medium chiral perturbation theory . we have found that the @xmath2 corrections give a few percents changes in the low density region for the decay constant and the pion mass , while in higher density such as three times saturation density , the corrections can be as the order of 10 to 20 percents and can give significant contribution . we have also found that the wave function renormalization is enhanced as largely as 50 percents at the saturation density . the main contribution among the corrections comes from the double scattering term . in addition , we have checked whether the low energy theorems , the gell - mann oakes renner relation and the glashow weinberg relation are satisfied in medium beyond the linear density approximation . we have found that these relations are not satisfied at @xmath2 off the chiral limit . the origin of the breaking is that we use the different energy values to evaluate the pion quantities and the chiral condensate ; we take the soft limit to obtain the chiral condensate , while we take the pion on shell point , that is @xmath296 , to evaluate the pion quantities . finally , we have discussed the density dependence of the @xmath297 decay width . considering the spinor and flavor vertex structure of the chiral interactions , we have found that the density dependence of the @xmath274 width comes from the wave function renormalization alone at linear density order . with this observation , the wave function renormalization @xmath136 would be measured directly in the decay process .

i.e. _ the temporal pion decay constant , the pion mass and the wave function renormalization , in symmetric nuclear matter are calculated in an in - medium chiral perturbation theory up to the next - to - leading order of the density expansion . we carefully define the in - medium state of pion and find that the pion wave function renormalization plays an essential role for the in - medium pion properties . the main contribution of the next - to - leading order comes from the double scattering term . weinberg relation , are satisfied in nuclear medium beyond the linear density approximation .

the in - medium pion properties , _ i.e. _ the temporal pion decay constant , the pion mass and the wave function renormalization , in symmetric nuclear matter are calculated in an in - medium chiral perturbation theory up to the next - to - leading order of the density expansion . the chiral lagrangian for the pion - nucleon interaction is determined in vacuum , and the low energy constants are fixed by the experimental observables . we carefully define the in - medium state of pion and find that the pion wave function renormalization plays an essential role for the in - medium pion properties . we show that the linear density correction is dominant and the next - to - leading corrections are not so large at the saturation density , while their contributions can be significant in higher densities . the main contribution of the next - to - leading order comes from the double scattering term . we also discuss whether the low energy theorems , the gell - mann oakes renner relation and the glashow weinberg relation , are satisfied in nuclear medium beyond the linear density approximation . we also find that the wave function renormalization is enhanced as largely as 50% at the saturation density including the next - to - leading contribution and the wave function renormalization could be measured in the in - medium decay .

0806.0552

c

in the present work a new study has been undertaken of the effects expected from isospin - mixing in nuclear ground - state wave functions on elastic parity - violating electron scattering at momentum transfers extending up to about 1.5 @xmath11 . four n = z 0@xmath7 nuclei have been considered , @xmath1c , @xmath2 mg , @xmath3si , and @xmath4s , each expected to be very close to eigenstates of isospin with @xmath5 in their ground states . however , as first discussed in @xcite ( dds ) , the coulomb interaction occurs asymmetrically between pp and pn / nn nucleon pairs in the nucleus , thereby giving rise to small isospin mixing and thus the nuclear ground states considered here have small admixtures with t@xmath2210 . while such effects are essentially negligible in the parity - conserving cross section , they can play a measurable role in the parity - violating asymmetry , and accordingly , whether the focus is placed on isospin mixing itself or on how these effects may confuse interpretations of the pv asymmetry in terms of standard model tests or with respect to strangeness content in the weak neutral current , it is important to evaluate their influence . in the older work of dds a limited - model - space shell model was employed to estimate the isospin mixing and the mixing via the coulomb interaction was handled perturbatively via a simple two - level approximation . furthermore , in the study of dds the idea of using pv elastic electron scattering to determine ground - state neutron distributions as in the case of @xmath9pb ( which forms the basis of the prex experiment ) was put forward ; here the focus has been limited to a few special n = z nuclei and n@xmath221z cases such as lead have not been re - considered . in the present work a self - consistent axially - symmetric mean - field approximation with density - dependent effective two - body skyrme interactions , including coulomb interactions between pp pairs , has been used in direct determinations of the ground state wave functions . the small differences between the proton and neutron density distributions thereby obtained yield both isoscalar and isovector ground - state coulomb monopole matrix elements and produce modifications in the pv asymmetry from the model - independent result obtained in the absence of isospin - mixing and strangeness contributions . additionally , the effects of pairing in this mean - field approximation have also been investigated , as have effects from strangeness contributions in the single - nucleon form factors and from subtle spin - orbit contributions in the coulomb monopole operators . * in the present work one observes considerably larger effects from isospin mixing than were found in dds , especially since here important matrix elements both diagonal and off - diagonal are naturally included , whereas in the earlier study the restriction of the shell - model space to a single major shell yielded a special constraint on the @xmath12-dependences of the isovector matrix elements . * specific influences of nuclear dynamics ( different forces , different pairing gaps ) and of subtleties in the current operators ( spin - orbit effects ) were investigated and seen not to affect the pv asymmetry at low-@xmath12 significantly . * results using either plane or distorted electron waves were obtained and , for the relatively light nuclei considered in the present work , their differences were seen to be small at low momentum transfers except in the vicinity of a diffraction minimum where the cross section is also small . * kinematic ranges where potential future measurements might be undertaken are discussed by studying both the deviations in the pv asymmetry ( the differences seen with / without isospin mixing ) and the experimental figure - of - merit . we have shown that the isospin mixing effects considered in this work will have a measurable effect on the asymmetries , even for the light nuclei considered . * furthermore , in going from the lightest n = z nuclei to heavier cases one sees that the asymmetry deviations increase making the isospin - mixing effects all the more evident . * in exploring the interplay between the isospin - mixing effects and those effects that may arise from electric strangeness contributions one sees an interesting constructive / destructive interference scenario : with positive electric strangeness the two contributions add at low momentum transfers , whereas when negative they subtract . presently the sign of the electric strangeness form factor is unknown ( the form factor is , in fact , consistent with zero ) and so such interferences may provide information on isospin mixing , namely the main focus of the present work , but also on strangeness . this work was supported by ministerio de ciencia e innovacin ( spain ) under contracts no . fis2005 - 00640 and no . fis2008 - 01301 . thanks ministerio de ciencia e innovacin ( spain ) for financial support . j.m.u . acknowledges support from intas open call grant no 05 - 1000008 - 8272 , and ministerio de ciencia e innovacin ( spain ) under grants fpa-2007 - 62616 and fpa-2006 - 07393 , and ucm and comunidad de madrid under grant grupo de fsica nuclear ( 910059 ) . this work was also supported in part ( twd ) by the u.s . department of energy under contract no . de - fg02 - 94er40818 . twd also wishes to thank ucm - gruposantander for financial support at the universidad complutense de madrid . ccccc isotope & @xmath223 = 0 & @xmath223 = 1 mev & @xmath223 from mass diff . & @xcite @xmath1c & @xmath2240 & @xmath2240 & @xmath2240 & - @xmath2 mg & 56.67 & 54.70 & 38.54 & 58.1 @xmath3si & -45.35 & -43.41 & -28.62 & -57.75 @xmath4s & @xmath2240 & @xmath2240 & @xmath2240 & - cccccccc & & & & @xmath225 & @xmath226 & @xmath227 & @xmath228 & @xmath229 & & @xmath230 = 0.1 @xmath231 & @xmath230 = 0.5 @xmath231 & @xmath230 = 1 @xmath231 & & 0 & 0 & 0.058 & * 0.208 * & 0.229 & 0.145 & & 0 & 1 & 0.168 & 0.005 & 0.136 & * 0.346 * 0 & 1/2 & 0 & 2 & 0.052 & 0.000 & 0.005 & 0.048 & & 1 & 1 & 0.028 & 0.100 & 0.079 & 0.024 & & 1 & 2 & * 0.203 * & 0.011 & * 0.244 * & 0.304 & & 0 & 0 & 0.093 & * 0.335 * & 0.309 & 0.078 & & 0 & 1 & * 0.349 * & 0.013 & * 0.329 * & * 0.555 * 1 & 1/2 & 0 & 2 & 0.048 & 0.000 & 0.006 & 0.048 & & 1 & 1 & 0.093 & 0.330 & 0.217 & 0.047 & & 1 & 2 & 0.018 & 0.001 & 0.023 & 0.018 & & 0 & 0 & 0.184 & * 0.662 * & * 0.610 * & 0.016 & & 0 & 1 & * 0.628 * & 0.024 & 0.592 & * 1.000 * 1 & 3/2 & 0 & 2 & 0.137 & 0.000 & 0.018 & 0.137 & & 1 & 1 & 0.186 & 0.659 & 0.434 & 0.094 & & 1 & 2 & 0.031 & 0.002 & 0.040 & 0.032 & & 0 & 0 & 0.044 & * 0.156 * & * 0.119 * & 0.007 & & 0 & 1 & * 0.061 * & 0.003 & 0.061 & * 0.060 * 2 & 3/2 & 0 & 2 & 0.008 & 0.000 & 0.001 & 0.007 & & 1 & 1 & 0.001 & 0.004 & 0.002 & 0.000 & & 1 & 2 & 0.002 & 0.000 & 0.002 & 0.001 & & 0 & 0 & 0.142 & 0.506 & 0.386 & 0.024 & & 0 & 1 & * 1.000 * & 0.045 & * 1.000 * & * 0.986 * 2 & 5/2 & 0 & 2 & 0.048 & 0.000 & 0.008 & 0.044 & & 1 & 1 & 0.284 & * 1.000 * & 0.541 & 0.075 & & 1 & 2 & 0.379 & 0.003 & 0.049 & 0.021 ccisotope & for @xmath163 @xmath1c & 0.74 @xmath232 q @xmath232 1.42 & 838 @xmath232 @xmath233 @xmath232 1607 & 8.38 @xmath232 @xmath210 @xmath232 16.07 @xmath2 mg & 0.51 @xmath232 q @xmath232 1.10 & 577 @xmath232 @xmath233 @xmath232 1245 & 5.77 @xmath232 @xmath210 @xmath232 12.45 @xmath3si & 0.48 @xmath232 q @xmath232 1.08 & 543 @xmath232 @xmath233 @xmath232 1222 & 5.43 @xmath232 @xmath210 @xmath232 12.22 @xmath4s & 0.45 @xmath232 q @xmath232 1.05 & 509 @xmath232 @xmath233 @xmath232 1188 & 5.09 @xmath232 @xmath210 @xmath232 11.88

their ground - state wave functions have been obtained using a self - consistent axially - symmetric mean - field approximation with density - dependent effective two - body skyrme interactions . some differences from previous shell - model calculations appear for the isovector coulomb form factors which play a role in determining the parity - violating asymmetry . results are obtained not only within the plane - wave born approximation , but also using the distorted - wave born approximation for comparison with potential future experimental studies of parity - violating electron scattering . to this end , for each nucleus the focus is placed on kinematic ranges where the signal ( isospin - mixing effects on the parity - violating asymmetry ) and the experimental figure - of - merit are maximized .

the influence of nuclear isospin mixing on parity - violating elastic electron scattering is studied for the even - even , nucleic , mg ,si , ands . their ground - state wave functions have been obtained using a self - consistent axially - symmetric mean - field approximation with density - dependent effective two - body skyrme interactions . some differences from previous shell - model calculations appear for the isovector coulomb form factors which play a role in determining the parity - violating asymmetry . to gain an understanding of how these differences arise , the results have been expanded in a spherical harmonic oscillator basis . results are obtained not only within the plane - wave born approximation , but also using the distorted - wave born approximation for comparison with potential future experimental studies of parity - violating electron scattering . to this end , for each nucleus the focus is placed on kinematic ranges where the signal ( isospin - mixing effects on the parity - violating asymmetry ) and the experimental figure - of - merit are maximized . strangeness contributions to the asymmetry are also briefly discussed , since they and the isospin mixing contributions may play comparable roles for the nuclei being studied at the low momentum transfers of interest in the present work .

1609.01050

i

finding first integrals is fundamental for characterizing a dynamical system . the motion is confined to submanifolds of lower dimensions on which the orbits evolve , providing an intuitive interpretation of the dynamics and reducing the complexity of the system . in addition , conserved quantities are good candidates when applying the second method of lyapunov for stability analysis . conservative systems related to central forces are typical examples of ( liouville ) integrability , and provide useful analytic results . hamiltonian systems have been widely analyzed in the classical and modern literature to determine adequate integrability conditions . the existence of first integrals under the action of small perturbations occupied ( * ? ? ? * chap . v ) back in the 19th century . later , emmy @xcite established in her celebrated theorem that conservation laws can be understood as the system exhibiting dynamical symmetries . in a more general framework , @xcite analyzed the conditions that yield algebraic first integrals of generic systems . he relied on the kowalevski exponents for characterizing the singularities of the solutions and derived the necessary conditions for existence of first integrals exploiting similarity transformations . conservation laws are sensitive to perturbations and their generalization is not straightforward . for example , the jacobi integral no longer holds when transforming the circular restricted three - body problem to the elliptic case @xcite . nevertheless , @xcite was able to find approximate conservation laws for orbits of small eccentricities . @xcite benefited from the similarities between the elliptic and the circular problems in order to define transformations connecting them . @xcite deepened in the nature of conservation laws and reviewed the concepts of isolating and nonisolating integrals . their study introduced a similarity transformation that embeds one of the constants of motion and transforms the original problem into a simplified one , reducing the degrees of freedom @xcite . @xcite proposed a numerical method for finding the dimension of the manifold in which orbits evolve , i.e. the number of isolating integrals that the system admits . the conditions for existence of integrals of motion under nonconservative perturbations received important attention in the past due to their profound implications . @xcite advanced on noether s theorem and included nonconservative forces in the derivation . relying on hamilton s variational principle , they not only extended noether s theorem , but also its inverse form and the noether - bessel - hagen and killing equations . later studies by @xcite sought integrating factors that yield conservation laws upon integration . examples of application of noether s theorem to constrained nonconservative systems can be found in the work of @xcite . @xcite arrived to a compact formulation using what was later called the neutral action method . remarkable applications exploiting noether s symmetries span from cosmology @xcite to string theory @xcite , field theory @xcite , and fluid models @xcite . in the book by ( * ? ? ? * chaps . 4 and 5 ) , an exhaustive review of the connection between symmetries and conservation laws is provided within the framework of lie algebras . we refer to ( * ? ? ? 3 ) for a formal derivation of noether s theorem , and a discussion on the connection between conservation laws and dynamical symmetries . integrals of motion are often useful for finding analytic or semi - analytic solutions to a given problem . the acclaimed solution to the satellite main problem by @xcite is a clear example of the decisive role of conserved quantities in deriving solutions in closed form . by perturbing the delaunay elements , @xcite solved the dynamics of a satellite subject to atmospheric drag and the oblateness of the primary . they proved the usefulness of canonical transformations even in the context of nonconservative problems . @xcite approached the problem of a central force depending on powers of the radial distance , @xmath0 , and found that there are only fourteen values of @xmath1 for which the problem can be integrated in closed form using elementary functions or elliptic integrals . later , he discussed the solvability conditions for equations involving square roots of polynomials @xcite . @xcite advanced on whittaker s results and found six potentials that are a generalization of the integrable central forces discussed by the latter . these potentials include the referred fourteen values of @xmath1 as particular cases . numerical techniques for shaping the potential given the orbit solution were published by @xcite . classical studies on the integrability of systems governed by central forces are based strongly on newton s theorem of revolving orbits . the problem of the orbital precession caused by central forces was recently recovered by @xcite , who considered potentials involving both powers and logarithms of the radial distance , and the special case of the yukawa potential @xcite . @xcite relied on hamilton s vector to simplify the analytic solutions found by @xcite . more elaborated potentials have been explored for modeling the perihelion precession @xcite . the dynamics of a particle in schwarzschild space - time can also be regarded as orbital motion perturbed by an effective potential depending on inverse powers of the radial distance @xcite . potentials depending linearly on the radial distance appear recursively in the literature because they render constant radial accelerations , relevant for the design of spacecraft trajectories propelled by continuous - thrust systems . the pioneering work by @xcite provided the explicit solution to the problem in terms of elliptic integrals , as predicted by @xcite . by means of a special change of variables , @xcite arrived to an elegant solution in terms of the weierstrass elliptic functions . these functions were also exploited by @xcite when he solved the dynamics of a particle attracted by a central force decreasing with @xmath2 . @xcite solved the tsien problem using the dromo formulation , which models orbital motion with a regular set of elements @xcite . advances on dromo can be found in the works by @xcite and @xcite . the case of a constant radial force was approached by @xcite from an energy - driven perspective . they studied in detail the roots of the polynomial appearing in the denominator of the equation to integrate , and connected their nature with the form of the solution . general considerations on the integrability of the problem can be found in the work of @xcite . another relevant example of an integrable system in celestial mechanics is the stark problem , governed by a constant acceleration fixed in the inertial frame . @xcite provided the complete solution to the motion relying extensively on elliptic integrals and jacobi elliptic functions . a compact form of the solution involving the weierstrass elliptic functions was later presented by @xcite , who also exploited this formalism for building a secular theory for the post - newtonian model @xcite . the stark problem provides a simplified model of radiation pressure . in the more general case , the dynamics subject to this perturbation can not be solved in closed form . an intuitive simplification that makes the problem integrable consists in assuming that the force due to the solar radiation pressure follows the direction of the sun vector . the dynamics are equivalent to those governed by a keplerian potential with a modified gravitational parameter . the present paper introduces a new class of integrable system , governed by a biparametric nonconservative perturbation . this acceleration unifies various force models , including special cases of solar radiation pressure , low - thrust propulsion , and some particular configurations in general relativity . the problem is formulated in sec . [ sec : dynamics ] , where the biparametric acceleration is defined and then reduced to a uniparametric forcing thanks to a similarity transformation . the conservation laws for the energy and angular momentum are generalized to the nonconservative case by exploiting known symmetries of kepler s problem . before solving the dynamics explicitly , we will prove that there are four cases that can be solved in closed form using elementary or elliptic functions . sections [ sec : conic][sec : sinusoidal ] present the properties of each family of orbits and the corresponding trajectories are derived analytically . section [ sec : summary ] is a summary of the solutions , which are unified in sec . [ sec : weierstrass ] introducing the weierstrass elliptic functions . finally , sec . [ sec : connection ] discusses the connection with known solutions to similar problems , and with schwarzschild geodesics .

keplerian orbits appear naturally as particular solutions to the problem . after characterizing the orbits independently , a unified form of the solution these orbits can represent the motion of particles perturbed by solar radiation pressure , of spacecraft with continuous thrust propulsion , and some instances of schwarzschild geodesics . finally , the problem is connected with other known integrable systems in celestial mechanics . [ firstpage ] celestial mechanics methods : analytical radiation : dynamics acceleration of particles

the invariance of the lagrangian under time translations and rotations in kepler s problem yields the conservation laws related to the energy and angular momentum . noether s theorem reveals that these same symmetries furnish generalized forms of the first integrals in a special nonconservative case , which approximates various physical models . the system is perturbed by a biparametric acceleration with components along the tangential and normal directions . a similarity transformation reduces the biparametric disturbance to a simpler uniparametric forcing along the velocity vector . the solvability conditions of this new problem are discussed , and closed - form solutions for the integrable cases are provided . thanks to the conservation of a generalized energy , the orbits are classified as elliptic , parabolic , and hyperbolic . keplerian orbits appear naturally as particular solutions to the problem . after characterizing the orbits independently , a unified form of the solution is built based on the weierstrass elliptic functions . the new trajectories involve fundamental curves such as cardioids and logarithmic , sinusoidal , and cotes spirals . these orbits can represent the motion of particles perturbed by solar radiation pressure , of spacecraft with continuous thrust propulsion , and some instances of schwarzschild geodesics . finally , the problem is connected with other known integrable systems in celestial mechanics . [ firstpage ] celestial mechanics methods : analytical radiation : dynamics acceleration of particles

1309.2669

i

in the past decade ultra - cold quantum gases have emerged as ideal candidates for clean and controllable simulation of condensed matter physics @xcite . ultra - cold quantum gases are now created in a variety of configurations in laboratories worldwide . in particular , both bosonic and fermionic atoms can be trapped and manipulated on optical lattice potentials @xcite . the lack of thermal phonons coupled with the tunability of the interactions by means of feschbach resonances @xcite has allowed for the detailed study of a multitude of phase diagrams , the most celebrated example is perhaps the bose - hubbard model @xcite . + equilibrium properties aside , over the past number of years there has been a surge in interest in the out of equilibrium behavior of closed quantum systems following a quench of a hamiltonian parameter . fundamentally , this is due to a series of spectacular experiments in ultra - cold atoms whereby the high degree of isolation and long coherence times permits the study of dynamics over long timescales @xcite . these experiments have raised a number of important theoretical issues such as the relationship between thermalisation and integrability and the universality of defect generation following evolution across a critical point @xcite . + given the controllability of ultra - cold atomic systems and the current interest in quench dynamics , it is a natural question to ask if there are any out of equilibrium condensed matter physics problems which could be simulated . unfortunately , due to their intrinsic complexity , there are very few examples of exactly solvable problems in the out - of - equilibrium domain . a worthy exception is the phenomenon of orthogonality catastrophe @xcite and the fermi - edge singularity . this problem was first pointed out by p. w. anderson over 40 years ago when he showed that the overlap of two many - body wave - functions , which describe deformed and undeformed fermi seas , vanishes in the thermodynamic limit @xcite . the corresponding ` quench ' problem , was investigated a few years later with the prediction of a universal absorption - edge singularity in the x - ray spectrum of metals , the ` fermi - edge ' singularity @xcite . + the universal physics of the anderson orthogonality catastrophe and the fermi - edge singularity was recently explored by goold _ _ in the context of ultra - cold quantum gases @xcite . in this work it was suggested that the physics maybe simulated in a controlled fashion by the appropriate embedding of a single probe qubit . the approach was further formalized in @xcite where the authors solved the dynamical problem in the inhomogeneous system by means of a linked cluster expansion . this qubit probe approach was further suggested as a mechanism to probe the physics of the orthogonality catastrophe in @xcite . + interestingly enough , a connection was made by heyl and kehrein @xcite between the absorption and emission spectrum in the original x - ray experiments and the so called quantum work distribution and corresponding fluctuation relations in classical and quantum statistical mechanics @xcite . treating a quench problem in manybody physics as a thermodynamic transformation and analyzing the statistics of work done has recently shown to be a useful approach to understand the intrinsic out of equilibrium dynamics in manybody systems @xcite . the approach is based on the study of the moments of a quantity known as the quantum work distribution @xcite which have been found to encode both thermodynamic and universal features of the model in question . + in this work this relationship will be explored in detail in the context of a locally quenched trapped fermi gas . in particular , in section [ sec100 ] the general problem of a system hamiltonian depending on a work - parameter will be introduced , adopting the description based on the grand canonical ensemble @xcite . the formalism provided by the work distribution and its characteristic function will be discussed , and the concept of irreversible work will be explored . in section [ sec200 ] the focus will be moved to a fermi gas in equilibrium with a harmonic trap , being suddenly perturbed by a spatially structure - less perturbation . in section [ lce ] the vacuum persistence amplitude and the linked cluster expansion will be used to reduce the calculation of the characteristic function of work to the sum of connected feynman diagrams . the relation of these diagrams to the characteristic function of work will be covered and an analytic approximation holding at low temperature will be presented . in section [ sec500 ] the first three cumulants of the work distribution will be computed and their link with thermodynamics will be discussed . finally , in section [ sec600 ] the irreversible work will be calculated using a perturbative and a numerical approaches , while section [ concluse ] will provide some further comments and conclusions .

the local quench of a fermi gas , giving rise to the fermi edge singularity and the anderson orthogonality catastrophe , is a rare example of an analytically tractable out of equilibrium problem in condensed matter . it has recently been proposed that the effect could be efficiently simulated in a controlled manner using the tunability of ultra - cold atoms . in this work , the statistics of work are shown to provide an accurate insight into the fundamental physics of the process .

the local quench of a fermi gas , giving rise to the fermi edge singularity and the anderson orthogonality catastrophe , is a rare example of an analytically tractable out of equilibrium problem in condensed matter . it describes the universal physics which occurs when a localized scattering potential is suddenly introduced in a fermi sea leading to a brutal disturbance of the quantum state . it has recently been proposed that the effect could be efficiently simulated in a controlled manner using the tunability of ultra - cold atoms . in this work , we analyze the quench problem in a gas of trapped ultra - cold fermions from a thermodynamic perspective using the full statistics of the so called _ work _ distribution . the statistics of work are shown to provide an accurate insight into the fundamental physics of the process . _ keywords _ : work distribution , non - equilibrium thermodynamics , quantum quench , orthogonality catastrophe .

0908.0650

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a flaring activity during the afterglow ( ag ) phase of a gamma ray burst ( grb ) was first observed in the late - time ag of grb 970508 with the narrow field instrument ( nfi ) aboard the bepposax satellite in the x - ray band @xcite , and with ground based telescopes in the optical band @xcite . it was interpreted in the framework of the fireball ( fb ) model of grbs as a delayed burst from the central grb engine @xcite . alternatively , in the cannonball ( cb ) model of grbs it was interpreted as a synchrotron radiation ( sr ) flare from an encounter of the highly relativistic jetted ejecta from an underlying supernova ( sn ) explosion with a density jump in the interstellar medium @xcite . late - time flares were later discovered in the broadband ag of several other grbs that were localized by the bepposax satellite , most notably in grb 000301c at @xmath0 days after burst @xcite where the flare was attributed to gravitational microlensing @xcite and in grb 030329 @xcite where the flare was interpreted in the framework of the fb model as due to ` refreshed shocks ' generated by a late activity of the central engine @xcite . in the cb model , however , these flares were well reproduced by the emission of sr from encounters of the jetted ejecta from an underlying sn explosion in a star formation region with density jumps within or at the border of a super bubble created by the star formation region @xcite . early - time x - ray flares ending the prompt emission phase were also detected by the wide field camera ( wfc ) aboard bepposax in a few grbs such as grb 011121 . in the fb model they were attributed to the onset of the external shock in the circumburst material . in the cb model they were interpreted as being due to the last episodes of bipolar cb ejections from a shutting off central engine . shortly after the launch of the swift satellite in november 2004 , data collected with its x - ray telescope ( xrt ) showed that x - ray flares are quite common in all the phases of the emission from grbs . in more than 50% of the grbs observed with the swift x - ray telescope ( xrt ) , flares were observed at the end of the prompt emission and/or the early ag phase @xcite . in some cases x - ray flares were observed also at very late times , of the order of several days after the prompt emission . although the information on flares is much more sketchy compared to that on the prompt gamma ray pulses , their spectral and temporal behaviours show clearly that the x - ray flares during the prompt @xmath1-ray emission follow the pattern of the @xmath1-ray pulses , suggesting they are the low energy part of these pulses . the x - ray flares ending the prompt emission and those superimposed on the early - time afterglow have a fast spectral evolution . their peak intensities decrease with time , and their spectral and temporal behaviours are similar to those of the prompt x/@xmath1-ray pulses , except that they are progressively softer and last longer . in most cases their @xmath1-ray emission probably is below the detection sensitivity of the swift broad alert telescope ( bat ) . in some cases their fluence in the xrt band exceeded that of the prompt emission in the bat 15 - 150 kev band @xcite . late - time ( @xmath2 s ) x - ray flares , however , seem to exhibit temporal and spectral behaviours that are different from those of most of the early - time flares . their power - law decline is more moderate , they are `` achromatic '' with a power - law spectrum almost identical to that of the late - time ag , and they show very little spectral evolution ( see , e.g. , the late time broad band flares in grbs 060614 @xcite and 081028 @xcite , and the hardness ratio during late time flares in swift grbs reported in the swift - xrt lightcurve repository , @xcite ) . flares in the x - ray lightcurve of swift grbs were studied phenomenologically by various observer groups @xcite . modifications of previously suggested models and new theoretical models were proposed and discussed by several authors @xcite , but none of these proposed models was shown to actually derive the observed lightcurves and spectral evolution of either early - time or late - time flares from underlying physical assumptions . flares are a natural consequence of the cannonball ( cb ) model of grbs , which was motivated by a grb - microquasar analogy @xcite . in the cb model , _ long - duration _ grbs and their ags are produced by bipolar jets of highly relativistic plasmoids of ordinary matter ejected in accretion episodes on the newly formed compact stellar object @xcite in core - collapse supernova ( sn ) explosions @xcite . it is hypothesized that an accretion disk or a torus is produced around the newly formed compact object , either by stellar material originally close to the surface of the imploding core and left behind by the explosion - generating outgoing shock , or by more distant stellar matter falling back after its passage @xcite . as observed in microquasars @xcite , each time part of the accretion disk falls abruptly onto the compact object , two jets of cannonballs ( cbs ) made of _ ordinary - matter plasma _ are emitted with large bulk - motion lorentz factors in opposite directions along the rotation axis , wherefrom matter has already fallen back onto the compact object due to lack of rotational support . the entire radiation emitted from a grb is produced by the interaction of the jet of cbs with the environmemt along its path , as illustrated in fig . the prompt @xmath1-ray and x - ray emission is dominated by inverse compton scattering ( ics ) of photons of the sn light filling the cavity produced by the pre - supernova wind / ejecta blown from the progenitor star long before the grb . the cbs electrons compton up - scatter this ` glory ' light into a narrow conical beam of @xmath1 rays along the cbs direction of motion . each cb produces a single grb pulse . an x - ray ` flare ' coincident in time with a prompt @xmath1-ray pulse is simply its low - energy part . the natural explanation of flares ending the prompt emission and during the early time afterglow is the same : ics of glory photons by the electrons of cbs ejected in late accretion episodes of fall - back matter on the newly formed central object . early - time x - ray flares without an accompanying detectable @xmath1-ray emission are usually ic flares ( icfs ) produced by cbs with relatively smaller lorentz factors , due to weakening activity of the engine : as the accretion material is consumed , one may expect the ` engine ' to have a few progressively - weakening dying pangs . like the lightcurves of the prompt grb pulses , the lightcurves of icfs exhibit a rapid softening during their fast decline phase ( see , e.g. , the xrt hardness ratio reported for swift grbs in the swift lightcurve repository , @xcite ) . in the cb model , each ic flare ( icf ) is followed by the emission of sr flare ( srf ) from the encounter of the cb with the wind / ejecta , which was blown from the progenitor star long before the grb ( see fig . [ fig1 ] ) . because of time - aberration in the observer frame , these srfs appear to have only short lag - times relative to the corresponding icfs . below their peak energy , the spectral behaviour of the ics pulses / flares is roughly @xmath3 , while the sr emission from fast cooling electrons has typically @xmath4 . thus , while the prompt kev - mev pulses / flares are dominated by ics of glory light , the ` prompt ' optical emission is dominated by sr . as the glory extends into the wind , often the sr emission begins before the ics pulse / flare has ended . the initial expansion of the cbs and the slow - down of the leading ones by the circumburst matter may merge most of them into a single leading cb @xcite during the afterglow phase . its collimated beam of the prompt gamma rays ionizes the matter in front of it . the ions continuously impinging on a cb with a relative lorentz factor @xmath5 , where @xmath5 is the bulk motion lorentz factor of the cb , generate within it an equipartition turbulent magnetic field . the intercepted electrons are isotropized and fermi accelerated by these fields and emit isotropic synchrotron radiation in the cb s rest frame , which is doppler boosted and beamed relativistically into a narrow cone with a typical opening angle @xmath6 in the observer s rest frame . late srfs are produced mainly when the cbs encounter winds or density bumps along their path first from the progenitor star and later in the interstellar medium ( ism ) . the lightcurve of these flares depends on the unknown density profile of the encountered wind / density bump that can not be predicted a - priori . but , both the early - time and the late - time srfs have a typical sr spectrum and a weak spectral evolution that are quite different from those of the accretion induced icfs and can be used to identify their origin late ejection episodes from the central engine or density bumps . in the cb model , short hard bursts ( shbs ) are also produced by bipolar jets of plasmoids ejected in mergers of compact objects in close binary systems such as neutron stars merger @xcite or in mass accretion episodes on compact objects in close binary systems , or in phase transitions in compact stars ( neutron stars , hyper stars and strange quark stars ) @xcite . bipolar ejections in late accretion episodes or phase transitions after cooling and loss of angular momentum probably produce the observed icfs in shbs , and sr radiation from encounters with winds / density bumps produces srfs . flares were routinely included in the cb model description of the afterglows of grbs and shbs @xcite . they were calculated from the master formulae of the model , which describe well the prompt ics emission and the emission of sr at all times . it was shown that ics explains successfully both the prompt kev - mev pulses and the x - ray flares ending the prompt emission , while the sr emitted in the collision of the jet of cbs with the wind / ejecta from the progenitor star explains well the prompt optical flares measured with robotic telescopes in very bright grbs @xcite . however , attention was focused there on the general properties of the prompt emission and the smooth afterglow , rather than on flares during the afterglow phase . moreover , in many grb afterglows , flares are weak , or are blended , or are not well sampled , and their properties could neither be inferred reliably from the ag lightcurve nor used reliably to test theoretical models . the situation concerning prominent x - ray flares observed by the swift xrt is different . they are well resolved and their spectral properties are much better measured . in this paper we focus our attention on grb x - ray and optical lightcurves with prominent flares . in particular , we compare the cb model lightcurves and their spectral evolution with representatives set of x - ray and optical lightcurves measured with the swift xrt , and with ground - based robotic telescopes and swift uvo in space , respectively , which have prominent flares that are well sampled . such a comparison provides stringent tests of both the cb model and its interpretation of the origin of prompt emission pulses in grbs , their afterglows and the early and late time flares in their lightcurves . we show that the cb model correctly predicts their main observed properties , and reproduces well their entire lightcurves and spectral properties . for completeness , we first summarize the relevant master formula of the cb model and their simplified forms that we later use in our analysis of the x - ray and optical lightcurve of grbs .

the many similarities between the prompt emission pulses in gamma ray bursts ( grbs ) and x - ray flares during the fast decay and afterglow phases of grbs suggest a common origin . in the cannonball ( cb ) model of grbs , this common origin is mass accretion episodes of fall - back matter on a newly born compact object . the prompt emission pulses are produced by a bipolar jet of highly relativistic plasmoids ( cbs ) ejected in the early , major episodes of mass accretion . as the accretion material is consumed , one may expect the engine s activity to weaken . x - ray flares ending the prompt emission and during the afterglow phase are produced in such delayed episodes of mass accretion . the common engine , environment and radiation mechanisms ( inverse compton scattering and synchrotron radiation ) produce their observed similarities . flares in both long grbs and short hard gamma ray bursts ( shbs ) can also be produced by bipolar ejections of cbs following a phase transition in compact objects due to loss of angular momentum and/or cooling . optical flares , however , are mostly produced in collisions of cbs with massive stellar winds / ejecta or with density bumps along their path . in this paper

the many similarities between the prompt emission pulses in gamma ray bursts ( grbs ) and x - ray flares during the fast decay and afterglow phases of grbs suggest a common origin . in the cannonball ( cb ) model of grbs , this common origin is mass accretion episodes of fall - back matter on a newly born compact object . the prompt emission pulses are produced by a bipolar jet of highly relativistic plasmoids ( cbs ) ejected in the early , major episodes of mass accretion . as the accretion material is consumed , one may expect the engine s activity to weaken . x - ray flares ending the prompt emission and during the afterglow phase are produced in such delayed episodes of mass accretion . the common engine , environment and radiation mechanisms ( inverse compton scattering and synchrotron radiation ) produce their observed similarities . flares in both long grbs and short hard gamma ray bursts ( shbs ) can also be produced by bipolar ejections of cbs following a phase transition in compact objects due to loss of angular momentum and/or cooling . optical flares , however , are mostly produced in collisions of cbs with massive stellar winds / ejecta or with density bumps along their path . in this paper we show that the master formulae of the cb model of grbs and shbs , which reproduce very well their prompt emission pulses and their smooth afterglows , seem to reproduce also very well the lightcurves and spectral evolution of the prominent x - ray and optical flares that are well sampled . -1 cm

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in the cb model , grbs , xrfs and shbs and their afterglows are produced by the interaction of bipolar jets of highly relativistic plasmoids ( cannonballs ) of ordinary matter , which are ejected in mass accretion episodes on a newly formed compact stellar object , with the radiation and matter that they encounter along their path . as observed in microquasars , each time part of the accretion disk falls abruptly onto the compact object , two jets of cannonballs ( cbs ) made of _ ordinary - matter plasma _ with large bulk - motion lorentz factors are emitted in opposite directions along the rotation axis , wherefrom matter has already fallen back onto the compact object due to lack of rotational support . the prompt @xmath1-ray and x - ray emission is dominated by inverse compton scattering ( ics ) of photons of the glory - a quasi isotropic optical light emitted by the supernova and scattered by the wind / ejecta blown from the progenitor star long before the grb . the cbs electrons compton up - scatter the glory photons into a narrow conical beam of @xmath1 rays along the cbs direction of motion . an x - ray ` flare ' coincident in time with a prompt @xmath1-ray pulse is simply its low - energy part . the early - time x - ray flares without a detectable accompanying @xmath1-ray emission are usually icfs produced by cbs with relatively smaller lorentz factors due to a weakening activity of the central engine : as the accretion material is consumed , the ` engine ' has a few progressively - weakening dying pangs . the lightcurves of icfs , like those of the prompt emission pulses , exhibit a rapid softening during their fast decline phase . roughly , the lightcurves are a function of the product @xmath21 and not of the individual values of the photon energy @xmath165 and the time @xmath7 after the beginning of the flare . the peak energy , isotropic equivalent energy and peak luminosity of the icfs are correlated like those of the prompt grb pulses . in the cb model , each icf is followed by srf from the encounter of the cb with the wind / ejecta that was blown from the progenitor star long before the grb . because of time - aberration , in the observer frame , these srfs lag after their preceding icfs by a short time of the order of the ics pulse duration . optical flares are usually much wider than their corresponding gamma / x - ray pulses and overlap , which makes it difficult to associate the early time optical flares with their preceding gamma / x - ray pulses / flares and measure their lag - time . only in single - pulse grbs that are bright enough to be detected with robotic telescopes and/or swift uvo and in very bright grbs , such as 080319b and 071031 , where the optical flares were partially resolved with robotic telescopes , could the predicted association between early time optical flares following gamma / x - ray pulses / flares be tested . often the fast decay of an x - ray icf is taken over by sr of x - rays from the cb encounter with the wind enclosing the glory light before it disappears under the plateau / shallow decay phase of the ag ( see , e.g. , figs . 3a , b , c in @xcite ) . late - time flares are usually srfs produced by cb encounters with the bumpy boundary of the star formation region , or with density bumps within this region where the grb took place . their exact profile is not known apriori but a wind - like profile seems to be a good working hypothesis , unlike the empirical parametrizations ( such as band function @xcite , cut - off power - law , beuermann function @xcite , broken power - law , segmented power - law , etc . ) used in most of the published standard analyses of grb lightcurves , which have never been properly derived from underlying physical assumptions , the master formulae of the cb model were derived in fair approximations from its underlying physical assumptions . as shown in this paper , the lightcurves and spectral evolution of x - ray flares and optical flares in grbs , xrfs and shbs are well described by the master formulae of the cannonball model of grbs . so far , no new assumptions or modifications of these formulae were needed when applied to well sampled flares in the grb lightcurves . probably , in the future , when much more refined data and better sampled lightcurves of grbs and their ags will become available , the cb model with its current simplifying assumptions , which were introduced in order to avoid ` over parametrization ' and make it predictive and falsifyable , will have to be refined in order to reproduce such data with sufficient accuracy . llllc grb050502b & 674 & 0.73 & 0.96 & 0.945 ( + 0.077 , -0.100 ) + shb050724 & & & & 0.81 ( + 0.14 , -0.17 ) + grb050820a & 9545 & 1.19 & 1.10 & 0.966 ( + 0.051 , -0.050 ) + grb050916 & 2178 & 0.74 & 0.90 & + grb060206 & 9402 & 1.04 & 1.12 & 1.21 ( + 0.27 , -0.24 ) + grb060418 & 123 & 1.73 & 1.05 & 0.96 ( + 0.15 , -0.14 ) + grb060526 & 4828 & 1.35 & 1.02 & 0.931 ( + 0.086 , -0.084 ) + grb060729 & 32665 & 2.52 & 1.10 & 1.067 ( + 0.038 , -0.037 ) + grb060929 & 5383 & 1.27 & 0.91 & 1.22 ( + 0.25 , -0.25 ) + grb061007 & 40 & 0.15 & 1.08 & 1.018 ( + 0.087 , -0.083 ) + grb070704 & 5183 & 1.27 & 0.90 & 0.98 ( + 0.18 , -0.33 ) + grb071003 & 1214 & 1.94 & 1.08 & 0.984 ( + 0.107 , -0.059 ) + xrf071031 & 5451 & 2.56 & 0.74 & 0.86 ( + 0.14 , -0.15 ) + grb080319b & 86 & 0.14 & 1.08 & 1.03 ( + 0.064 , -0.063 ) + xrf080330 & 541 & 4.61 & 0.89 & 0.89 ( + 0.13 , -0.12 ) + grb080506 & 7801 & 1.76 & 0.91 & 0.990 ( + 0.122 , -0.077 ) + grb080607 & 2904 & 0.53 & 0.91 & 1.102 ( + 0.098 , -0.092 ) + grb080810 & 3452 & 0.63 & 1.25 & 1.156 ( + 0.099 , -0.089 ) + grb080906 & 5790 & 0.90 & 0.96 & 1.049 ( + 0.069 , -0.164 ) + grb081102 & 1891 & 0.47 & 0.92 & 0.921 ( + 0.079 , -0.114 ) + grb081203a & 436 & 0.91 & 1.15 & 1.096 ( + 0.089 , -0.081 ) + grb090102 & 348 & 0.80 & 0.95 & 0.858 ( + 0.078 , -0.076 ) + grb090417b & 1259 & 0.63 & 1.04 & 1.09 ( + 0.11 , -0.11 ) + grb090618 & 1540 & 1.10 & 1.04 & 1.008 ( + 0.047 , -0.046 ) + grb090621a & 1309 & 0.83 & 0.94 & 1.01 ( + 0.18 , -0.18 ) + grb090709a & 1098 & 0.51 & 1.08 & 1.081(+0.076 , -0.074 ) + grb090812 & 598 & 1.34 & 0.92 & 0.914 ( + 0.138 , -0.089 ) + grb091029 & 5753 & 2.32 & 1.01 & 1.197 ( + 0.077 , -0.070 ) + [ t1 ] lllllllc grb050502b & icf , srf , & 485.7 & 308.3 & 0.27 kev & 13750 & 28950 & 6013 s + & srf & 58950 & 18911 & 3350 s & & & + grb060418 & icf , icf & 60 & 12 & 0.13kev & 9.9 & 118 & 0.13kev + grb060206 & srf , srf & 1.19 & 32.2 & 235 s & 653 & 3427 & 3645 s + & srf & 609359 & 245909 & 1980979 s & & & + shb050724 & icf , icf & 1.58 & 114 & 1.08 kev & 469 & 1422 & 1.32 kev + & icf & 9757 & 49512 & 3.53 kev & & & + grb050916 & srf , icf & & & & 17836 & 1335 & 91 kev + & icf & 9757 & 49512 & 3.53 kev & & & + grb050916 & srf , icf & & & & 17836 & 1335 & 91 kev + grb060526 & srf , icf & & & & 233 & 42.5 & 0.15 kev + & icf , srf & 280 & 25.7 & 60.2 kev & 85 & 106 & 288 s + grb060929 & srf , icf & & & & 472 & 45 & 117 kev + grb071031 & icf , icf & 84.8 & 46.2 & 13.2 kev & 131 & 33.8 & 0.74 kev + & icf , icf & 181.7 & 30.5 & 4.3 kev & 228 & 40.6 & 14.63 kev + & icf , icf & 328 & 176 & 2.74 kev & 572 & 173.6 & 19,74 kev + & icf & 4351 & 1201 & 4.5 kev & & & + & srf , srf & 16743 & 5463 & 4.2 s & 33241 & ( 53238 ) & @xmath166 + grb070704 & srf , icf & ( 63 ) & ( 0.35 ) & ( 25 s ) & 472 & 45.22 & 117 kev + grb080506 & icf , srf & 130 & 36.7 & 14.4 kev & 211 & 43 & 171 s + & icf , icf & 433 & ( 41 ) & ( 159 kev ) & 684 s & ( 160 ) & ( 156 kev ) + grb080607 & ics , icf & 65.9 & 8.6 & 145 kev & 113.9 & ( 15.4 ) & ( 350 kev ) + & srf , srf & 222 & 332 & 0.6 s & 652 & 1018 & 335 s + grb081203a & srf & 79 & 10.8 & ( 0 ) & & & + grb080810 & icf , srf , & 74 & 16 & 25.5 kev & 98.6 & 4.6 & 34 s + & icf , srf & 196 & ( 14 ) & ( 203 kev ) & 265 & 208 & ( 7.2 s ) + grb080906 & srf , srf , & ( 49 ) & ( 1 ) & ( 47.7 s ) & 157 & 27.5 & 10.75 s + & srf , icf & 490 & 8.58 & 200 s & 836 & 78 & 145 kev + grb081102 & srf , icf & 63 & 11 & 42.7 s & 914 & 88 & 111 kev + grb090417b & srf , icf & 336.2 & 203 & 82.6 s & 1227.8 & 431 & 1.96 kev + grb090618 & icf , srf & 65.9 & 12.9 & & ( 0 ) & 884 & ( 0 ) + grb090621a & srf , icf & 150.6 & 2.6 s & 215 & 217.9 & 50.4 & 0.95 kev + grb090709a & icf , srf , & 70.3 & 20.61 & 2.38 kev & 75.5 & 14.3 & 116 s + & srf , icf & 165.8 & 110.2 & 149 & 324.6 & 37 & 187 s + grb091029 & icf , icf & 0 & 38.8 & 9.8 kev & 218.6 & 102.5 & 10.9 kev + & srf & 209360 & 245909 & & & & + [ t2 ] llllc -5.cm grb 080319b : & & & & + srf1 & 9.50 & 3.52 & 10.24 & 0.70 + srf2 & 32.37 & 3.52 & 5.83 & 0.70 + srf3 & 39.54 & 3.52 & 6.96 & 0.70 + grb 060206 : & & & & + srf1 & @xmath167 & 548 & @xmath166 & 0.50 + srf2 & 2526 & 1214 & 887 & 0.80 + srf3 & 4286 & 3113 & 31 & 0.87 + grb 071003 : & & & & + srf1 & 4.11 & @xmath168 & 16.7 & 0.79 + srf2 & 125 & 139 & 14.6 & 1.03 + srf3 & 441 & 348 & @xmath169 & 0.75 + grb 071031 : & & & & + srf1 & 90 & 97 & 1875 & 0.62 + srf2 & 540 & @xmath168 & 43 & 0.63 + srf3 & 2335 & 7900 & 158 & 0.63 + srf4 & 10318 & 13372 & 134 & 0.63 + grb 080330 : & & & & + srf1 & 0.29 & 32 & 946 & 0.67 + srf2 & 3.40 & 1716 & 235 & 0.67 + srf3 & 3416 & 1491 & 18337 & 0.67 + [ t3 ] llllc -2.cm 1 & -5.57 & 15.4 & 300 & @xmath170 + 2 & 19.42 & 4.28 & 1450 & @xmath171 + 3 & 29.88 & 0.87 & 500 & @xmath172 + 4 & 32.95 & 5.43 & 800 & @xmath173 + 5 & 43.67 & 4.99 & 500 & @xmath174 + 6 & 52.77 & 4.30 & 450 & @xmath175 + 7 & 61.09 & 4.10 & 450 & @xmath176 + 8 & 70.35 & 5.63 & 600 & @xmath177 + 9 & 85.50 & 1.86 & 200 & @xmath178 + [ t4 ] lllllc grb990123 & srf & 22 & @xmath179 & 1.67 & 0.50 + grb030418 & srf & 200 & 4097 & @xmath166 & 0.56 + grb050820a & srf & 109 & 479 & @xmath166 & + grb061007 & srf & 15.8 & 90.37 & @xmath166 & 0.60 + grb081203a & srf & 0 & 316 & 368 & 0.90 + grb090102 & srf & 1.65 & 0.13 & 2.16 & 0.53 + grb090618 & srf & 118 & @xmath167 & 61 & 0.51 + [ t5 ]

we show that the master formulae of the cb model of grbs and shbs , which reproduce very well their prompt emission pulses and their smooth afterglows , seem to reproduce also very well the lightcurves and spectral evolution of the prominent x - ray and optical flares that are well sampled . -1 cm

the many similarities between the prompt emission pulses in gamma ray bursts ( grbs ) and x - ray flares during the fast decay and afterglow phases of grbs suggest a common origin . in the cannonball ( cb ) model of grbs , this common origin is mass accretion episodes of fall - back matter on a newly born compact object . the prompt emission pulses are produced by a bipolar jet of highly relativistic plasmoids ( cbs ) ejected in the early , major episodes of mass accretion . as the accretion material is consumed , one may expect the engine s activity to weaken . x - ray flares ending the prompt emission and during the afterglow phase are produced in such delayed episodes of mass accretion . the common engine , environment and radiation mechanisms ( inverse compton scattering and synchrotron radiation ) produce their observed similarities . flares in both long grbs and short hard gamma ray bursts ( shbs ) can also be produced by bipolar ejections of cbs following a phase transition in compact objects due to loss of angular momentum and/or cooling . optical flares , however , are mostly produced in collisions of cbs with massive stellar winds / ejecta or with density bumps along their path . in this paper we show that the master formulae of the cb model of grbs and shbs , which reproduce very well their prompt emission pulses and their smooth afterglows , seem to reproduce also very well the lightcurves and spectral evolution of the prominent x - ray and optical flares that are well sampled . -1 cm

1209.0393

i

the recent discovery of a particle consistent with the standard model ( sm ) higgs boson , announced by the atlas @xcite and cms @xcite collaborations at cern , is a milestone in particle physics ; adding in quadrature statistical and systematic errors , the mass of the particle turns out to be in the range @xmath1 gev at @xmath2 . here we assume that the new particle is actually the sm higgs boson and study the implications that its mass value , together with other relevant parameters such as the top quark mass and the strong gauge coupling , has on the behavior of the higgs potential at very high energy scales and , in particular , for the sake of electroweak vacuum stability . the project of extrapolating the higgs potential up to the planck scale is a long standing one @xcite , and was revamped in the fall of 2011@xcite after the first lhc hints of a higgs boson were reported@xcite . recently , the tools for a next - to - next - to - leading order ( nnlo ) renormalization procedure were derived @xcite . so , there are now all the ingredients necessary to carry out this long standing project . clearly , the extrapolation is based on the assumption that there is a desert up to the planck scale or , better , that possible new physics do not significantly affect the running of the higgs quartic coupling , which dominates the higgs potential at high energy . it is interesting that the recently discovered experimental higgs mass range , combined with the experimental top mass range , indicates a particularly intriguing high energy behavior of the higgs potential , close to the transition between electroweak vacuum stability and metastability . this is due to the fact that , for these higgs and top mass values , the higgs quartic coupling can be very small or even negative . since the dependence on the top mass is strong and quite subtle , it is not surprising that different groups slightly disagree in the interpretation of the results , some of them favoring @xcite and some others disfavoring @xcite electroweak vacuum stability . traditionally the top pole mass was used in the analysis ; however it has been pointed out @xcite that the top pole mass value used in previous analyses and taken to be the one measured at the tevatron , @xmath3 gev @xcite , is not unambiguously derived and that a more careful derivation should be based instead on the running top mass in the @xmath4 scheme , @xmath5 gev . as was shown in @xcite , the top pole mass range consistently derived from the running one , @xmath6 gev , is plagued by a larger error than the tevatron measurement considered in @xcite , rescuing electroweak vacuum stability . in our analysis we keep as a free parameter the running top mass , rather than the pole one . in this way we completely avoid the theoretical uncertainties associated with the top yukawa matching procedure . as we are going to discuss , the theoretical error associated with the higgs quartic coupling matching @xcite turns out to be smaller than the one induced by the experimental uncertainty in the strong gauge coupling , @xmath7 . given the above mentioned range for the running top mass @xcite , we find that electroweak stability is allowed in the whole higgs mass range @xcite . stability could soon be excluded if values of the running top mass @xmath8 gev are excluded by the lhc . otherwise , testing electroweak vacuum stability would become very challenging , since this would require precision measurements of the higgs and top masses , and also of @xmath7 . a stable higgs potential configuration which deserves particular interest is a shallow false minimum close to the planck scale , which could have been relevant for primordial inflation@xcite . we show that such a configuration is realized only if the higgs quartic coupling and its derivative satisfy very specific boundary conditions , possibly having a deep origin in quantum gravity . as is well know , new physics in addition to the sm is required to explain the neutrino masses and mixings , as well as dark matter . the mechanism responsible for the neutrino masses could affect the higgs quartic coupling ; as an example , we consider the impact that the inclusion of neutrino masses via a type i seesaw has on electroweak stability , discussing in some detail the shallow false minimum configuration . the paper is organized as follows . in sec.[sec-1 ] we discuss the input parameters and the nnlo renormalization procedure used to extrapolate the higgs potential up to the planck scale . an analysis of electroweak vacuum stability and the associated constraints on the top and higgs masses , with a detailed discussion of the theoretical errors and the prospects for the future , are presented in sec.[sec-2 ] . in sec.[sec-3 ] we investigate the boundary conditions leading to the particularly interesting configuration of a shallow false minimum below the planck scale . sec.[sec-4 ] is devoted to the upper bound on the seesaw right - handed neutrino masses following from the requirement of electroweak vacuum stability . conclusions are drawn in sec.[sec - concl ] . appendix[app - a ] contains the relevant formulas for the nnlo running procedure in the sm and , and those to incorporate the type i seesaw mechanism are found in appendix[app - b ] .

the measurements of the higgs boson and top quark masses can be used to extrapolate the standard model higgs potential at energies up to the planck scale . adopting a nnlo renormalization procedure , we : i ) find that electroweak vacuum stability is at present allowed , discuss the associated theoretical and experimental errors and the prospects for its future tests ; ii ) determine the boundary conditions allowing for the existence of a shallow false minimum slightly below the planck scale , which is a stable configuration that might have been relevant for primordial inflation ; iii ) derive a conservative upper bound on type i seesaw right - handed neutrino masses , following from the requirement of electroweak vacuum stability . * higgs boson and top quark masses + as tests of electroweak vacuum stability * isabella masina + + +

the measurements of the higgs boson and top quark masses can be used to extrapolate the standard model higgs potential at energies up to the planck scale . adopting a nnlo renormalization procedure , we : i ) find that electroweak vacuum stability is at present allowed , discuss the associated theoretical and experimental errors and the prospects for its future tests ; ii ) determine the boundary conditions allowing for the existence of a shallow false minimum slightly below the planck scale , which is a stable configuration that might have been relevant for primordial inflation ; iii ) derive a conservative upper bound on type i seesaw right - handed neutrino masses , following from the requirement of electroweak vacuum stability . * higgs boson and top quark masses + as tests of electroweak vacuum stability * isabella masina + + +

0803.4125

i

transport phenomena in random media have remained a very active field of research since the discovery of the anderson localization fifty years ago @xcite . for classical systems also , the presence of quenched disorder can induce completely new transport behaviors with respect to pure systems in some regions of parameters . it turns out that even the dynamics of a single particle in one - dimensional random media ( see the review @xcite and references therein ) can already present a very rich phase diagram as a function of the temperature @xmath0 and the external applied force @xmath1 . as an example , we shown on fig . 1 the exactly known phase diagram for the biased sinai model @xcite : one needs to introduce a dimensionless parameter @xmath15 ( where we have chosen to fix the disorder strength at some simple value to simplify the notations and emphasize the dependence upon @xmath0 and @xmath1 we are interested in ) . for @xmath5 , the motion is logarithmically slow @xmath16 . for @xmath17 , the diffusion is anomalous with a sub - linear displacement @xmath18 ; for @xmath19 , the velocity becomes finite @xmath20 , but the dispersion remains anomalous of order @xmath21 . finally for @xmath22 , both the velocity and the diffusion coefficient are finite . so already in simple one - dimensional systems , various dynamical properties can undergo phase transitions at various thresholds . and the external force @xmath1 of the one - dimensional sinai model @xcite : the important dimensionless parameter is @xmath23 ( the disorder strength has been fixed at some simple value ) . from the point of view of strong disorder renormalization @xcite , the logarithmic behavior @xmath24 for @xmath5 corresponds to an `` infinite disorder fixed point '' , whereas the anomalous diffusion phase @xmath25 for @xmath26 corresponds to a `` strong disorder fixed point '' . a finite - velocity @xmath27 appears only for @xmath28 , i.e. when the force is above some temperature - dependent value . , height=302 ] and the external force @xmath1 is not exactly known . however one expects physically two very different regimes : ( i ) near the zero - temperature depinning critical point @xmath29 , the transport at small temperature is dominated by depinning events . ( ii ) in the regime where @xmath0 is finite and @xmath1 is small , the roughness exponent @xmath13 of the equilibrium case @xmath5 is expected to describe the polymer roughness up to some large scale ( that diverges as @xmath4 ) . the transport is then dominated by thermal jumps of finite segments of the polymer between quasi - equilibrated metastable states . in this paper , we focus only on the regime ( ii ) and discuss the center - of - mass motion and the roughness at the largest scales . , height=302 ] the case of more complex systems like interfaces or manifolds in random media has attracted a lot of attention in relation with many important applications , and various approaches have been developed to elucidate the structure of the dynamical phase diagram ( see the reviews @xcite and references therein ) . the simplest model within this class of systems is the directed polymer in a two - dimensional random medium ( see @xcite for a review ) , first introduced to model an interface in the low - temperature phase of two - dimensional disordered ferromagnets @xcite . the statics of this model is rather well understood with exactly known critical exponents : at any temperature @xmath0 , the directed polymer is in a disordered - dominated phase characterized by the roughness exponent @xmath13 and the droplet exponent @xmath30 @xcite . in comparison , the dynamics is much harder to study , and no exact result exists . even numerically , the computational complexity changes completely between the statics that can be studied via exact transfer matrix methods that are polynomial in the size of the polymer @xcite , and the dynamics where the determination of barriers is an np - complete problem @xcite . as a consequence , a complete characterization of the dynamical properties as a function of the temperature and external force ( here we consider that the disorder strength is fixed ) has remained a very challenging issue . an essential novelty with respect to the dynamics of the sinai model described above , is the presence of the chain constraint of the polymer , so that even at zero temperature @xmath31 , the dynamics is already non trivial : the competition between interaction and disorder gives rise to a non - equilibrium depinning phase transition , between a pinned phase @xmath32 where the interface remains blocked forever in some configuration , and a moving phase for @xmath33 . this type of depinning transition has motivated a lot of experimental and theoretical studies ( see the reviews @xcite ) , and an exact mean - field solution has been obtained in @xcite . the critical region with a small temperature around the depinning transition of an elastic line has been studied in @xcite . in the present paper , we focus on the opposite region of the dynamical phase diagram ( see fig . 2 ) where the temperature is finite and the external force is small . in this regime , one expects that the dynamics is dominated by thermal activations between locally quasi - equilibrated metastable states . in particular , the polymer is expected to keep during the motion its equilibrium roughness exponent @xmath13 up to some large scale ( that diverges as @xmath4 ) . this equilibrium roughness has been measured in dynamic simulations in @xcite , and in @xcite when the temperature remains larger that some disorder - dependent threshold . however in other regimes , larger roughness exponents have been measured at larger scales @xcite . this issue of the roughness at the largest scales will be rediscussed later in the paper . but we first need to better understand the statistical properties of the barriers between the locally quasi - equilibrated metastable states . in the regime of finite temperature and small external force , the standard picture in the field ( see the review @xcite and references therein ) seems to be that the dynamics then corresponds to a creep motion , where the center - of - mass moves linearly in time as soon as the temperature is positive @xmath34 with a very non - linear force - velocity relation of the form @xmath35 where the exponent @xmath36 involves the dimension @xmath37 of the interface ( the directed polymer we are interested in corresponds to @xmath38 ) , the equilibrium roughness exponent @xmath39 , and the barrier exponent @xmath40 of the dynamics without external force @xmath41 note that this relation is usually written in the form @xmath42 after using the additional assumption concerning the identity between the barrier exponent @xmath40 and the droplet exponent @xmath43 . however , in our opinion , there is no convincing evidence of the equality @xmath44 neither theoretically ( see @xcite for a recent summary on the debate ) nor numerically ( the best numerical results presently available @xcite points towards an exponent of order @xmath45 rather different from the exactly known droplet exponent @xmath46 ) , we will consider in the following that the barrier @xmath40 is an independent exponent satisfying the bound @xmath47 the usual qualitative argument given in favor of a finite velocity in eq . [ defvitesse ] as soon as @xmath48 is that any barrier can be passed by thermal activation. this is of course true , but this is not sufficient to conclude that the asymptotic velocity is finite , since the motion can also exhibit anomalous behavior as shown by the sinai model at small external force ( see the beginning of the introduction ) . to determine the asymptotic motion of the center - of mass at large times , one needs to study the time needed to travel over a given large distance . the more quantitative argument in favor of the finite velocity of eq . [ defvitesse ] is a scaling argument where the barrier landscape existing in the absence of bias is tilted to take into account the bias contribution : this scaling argument yields that the relevant barriers for the large - time dynamics corresponds to a barrier scale @xmath49 and to a length scale @xmath50 that are finite as soon as @xmath51 ( and that diverge as @xmath4 ) . we fully agree with this scaling argument that will be rediscussed below in section [ scalingarg ] . however again , this is not sufficient to conclude that the velocity is finite , since exactly the same argument can be made for the sinai model where an anomalous diffusion phase exists ( see section [ scalingarg ] for more details ) . the crucial property to determine whether the velocity is finite or not is the probability distribution of barriers @xmath52 around this typical value @xmath49 . in the present paper , we explain that within the strong disorder renormalization in configuration space that we have introduced recently @xcite ( see @xcite for a more detailed presentation ) , one obtains an exponential tail for the distribution of renormalized barriers @xmath53 as is well known in the field of disordered systems since derrida s random energy model @xcite , other disordered models sharing the same low - energy states statistics @xcite and related bouchaud s trap models @xcite ( see also @xcite for one of the first mention of exponentially distributed barriers in connection with extremal statistics ) , this innocent exponential distribution for the barriers corresponds via the change of variable @xmath54 to a very broad power - law decay for the distribution of the trapping times @xmath55 @xmath56 the exponent depends continuously on the external force and on the temperature ( we consider here that the disorder remains fixed ) @xmath57 since the characteristic barrier scale @xmath49 grows with @xmath1 and diverges as @xmath4 as @xmath58 the exponent @xmath7 vanishes as @xmath4 as @xmath59 as a consequence , the region of small external force where @xmath60 corresponds to a very broad distribution of trapping times with a diverging averaged value @xmath61 . this invalidates the usual creep formula that is obtained by replacing all trapping times by the typical value @xmath62 to obtain @xmath63 ( see eq . [ vitessecreep ] ) . we obtain instead that for @xmath60 , the center - of - mass displacement then grows only sub - linearly in time @xmath64 i.e. the asymptotic velocity vanishes @xmath12 . although the vast majority of papers on the subject never mentions the possibility of a zero - velocity phase , we are aware of three papers where the question of the probability distribution of barriers around the typical value has been raised : \(i ) twenty years ago , ioffe and vinokur @xcite have proposed the anomalous sub - linear motion of eq . [ powerlaw ] . but for reasons that are very unclear to us , this possibility seems to have completely disappeared in the more recent literature . \(ii ) fifteen years ago , bouchaud has pointed out in @xcite that the usual creep argument might lead to incorrect results because of problem of strong fluctuations , and cites the sinai model as an example where the transport is indeed harder than anticipated from the typical barrier alone . \(ii ) ten years ago , vinokur , marchetti and chen @xcite have proposed an exponential distribution of barriers , based on extremal statistics argument , and the corresponding power - law distribution for trapping times . however , these authors have supplemented this power - law distribution by a sharp cut - off to recover the usual finite velocity behavior of eq . [ defvitesse ] . in our opinion , there is no good reason to impose this sharp cut - off , since the same procedure for the exactly soluble sinai model would give a wrong answer . to summarize this long introduction , the aim of the present paper is to justify the existence of the anomalous diffusion phase of eq . [ sublinear ] in the region of the phase diagram corresponding to finite temperature and small external force ( see fig . 2 ) , via the use of some strong disorder renormalization procedure on the barriers . the paper is organized as follows . in section [ infinite ] , we briefly recall the main idea of strong disorder renormalization , and we describe the statistical properties of the `` infinite disorder '' fixed point that describes the thermal dynamics of the directed polymer without external force . in section [ strong ] , we explain how the presence of a small external force @xmath1 transforms this `` infinite disorder fixed point '' into a `` strong disorder fixed point '' with an exponential distribution of renormalized barriers , and we describe the consequences for distribution of trapping times and the large - time dynamics . in section [ numerics ] , we present detailed numerical simulations for a directed polymer driven in a traps landscape . in section [ previous ] , we compare our results concerning the roughness with previous works . our conclusions are summarized in section [ conclusion ] . in appendix a , we recall the subtleties associated to the type of the interactions ( metric constraint versus elastic energy ) to justify our choice to consider the metric constraint .

we obtain that for small , this `` infinite disorder fixed point '' becomes a `` strong disorder fixed point '' with an exponential distribution of renormalized barriers . our conclusion is that in the small force region , the divergence of the averaged trapping time induces strong non - self - averaging effects that invalidate the usual creep formula obtained by replacing all trapping times by the typical value .

the motion of driven interfaces in random media at finite temperature and small external force is usually described by a linear displacement at large times , where the velocity vanishes according to the creep formula as for . in this paper , we question this picture on the specific example of the directed polymer in a two dimensional random medium . we have recently shown ( c. monthus and t. garel , arxiv:0802.2502 ) that its dynamics for can be analyzed in terms of a strong disorder renormalization procedure , where the distribution of renormalized barriers flows towards some `` infinite disorder fixed point '' . in the present paper , we obtain that for small , this `` infinite disorder fixed point '' becomes a `` strong disorder fixed point '' with an exponential distribution of renormalized barriers . the corresponding distribution of trapping times then only decays as a power - law , where the exponent vanishes as as . our conclusion is that in the small force region , the divergence of the averaged trapping time induces strong non - self - averaging effects that invalidate the usual creep formula obtained by replacing all trapping times by the typical value . we find instead that the motion is only sub - linearly in time , i.e. the asymptotic velocity vanishes . this analysis is confirmed by numerical simulations of a directed polymer with a metric constraint driven in a traps landscape . we moreover obtain that the roughness exponent , which is governed by the equilibrium value up to some large scale , becomes equal to at the largest scales . # 1#2 # 1#2

0803.4125

c

in this paper , we have considered the dynamics of the directed polymer in a two - dimensional random potential in the regime where the temperature @xmath0 is finite and the external force @xmath1 is small . we have explained how the `` infinite disorder fixed point '' that describes the dynamics for @xmath5 becomes a `` strong disorder fixed point '' for small @xmath1 with an exponential distribution of renormalized barriers . since the corresponding distribution of trapping times then only decays as a power - law @xmath6 , where the exponent @xmath7 vanishes as @xmath294 as @xmath4 , we have concluded that the motion is only sub - linearly in time @xmath11 in the region @xmath9 , i.e. that the asymptotic velocity vanishes @xmath12 , in contrast with the usual creep scenario where the velocity is finite as soon as @xmath295 . all along the paper , we have discussed the similarities with the sinai model with bias , where an analogous zero - velocity phase has been established long ago by rigorous methods @xcite and where the asymptotic exactness of the strong disorder renormalization has been demonstrated explicitly by a direct comparison with the available rigorous results @xcite . we have then checked the presence of the predicted zero - velocity phase by numerical simulations of a directed polymer with a metric constraint driven in a traps landscape . we have moreover obtained that the roughness , which is governed by the equilibrium exponent @xmath13 up to the large scale @xmath288 , is equal to @xmath14 at the largest scales . an important issue is of course whether such a zero - velocity phase also exists for interfaces of higher dimensionalities @xmath84 driven in a random medium of dimension @xmath296 , and more generally for other classes of driven extended systems . since `` collective transport in random media is an impossibly broad subject '' @xcite , a general answer clearly goes beyond the present work . however we think that the essential property needed to have a zero - velocity phase at small force is the presence of a positive barrier exponent @xmath92 for the dynamics at @xmath5 , and this should be the case for a broad class of disordered systems in finite dimensions . then the dynamics for @xmath5 will be logarithmically slow and should correspond to some `` infinite disorder fixed point '' for the renormalized barriers , that transforms into a `` strong disorder fixed point '' at small @xmath1 , with an exponentially distribution of renormalized barriers . another argument in favor of this general scenario is the extremal statistics argument on the barriers @xcite that also lead to an exponential tail for the probability distribution of large barriers , and thus to a power - law decay for the trapping time distribution .

the corresponding distribution of trapping times then only decays as a power - law , where the exponent vanishes as as . we find instead that the motion is only sub - linearly in time , i.e. the asymptotic velocity vanishes . this analysis is confirmed by numerical simulations of a directed polymer with a metric constraint driven in a traps landscape . we moreover obtain that the roughness exponent , which is governed by the equilibrium value up to some large scale , becomes equal to at the largest scales .

the motion of driven interfaces in random media at finite temperature and small external force is usually described by a linear displacement at large times , where the velocity vanishes according to the creep formula as for . in this paper , we question this picture on the specific example of the directed polymer in a two dimensional random medium . we have recently shown ( c. monthus and t. garel , arxiv:0802.2502 ) that its dynamics for can be analyzed in terms of a strong disorder renormalization procedure , where the distribution of renormalized barriers flows towards some `` infinite disorder fixed point '' . in the present paper , we obtain that for small , this `` infinite disorder fixed point '' becomes a `` strong disorder fixed point '' with an exponential distribution of renormalized barriers . the corresponding distribution of trapping times then only decays as a power - law , where the exponent vanishes as as . our conclusion is that in the small force region , the divergence of the averaged trapping time induces strong non - self - averaging effects that invalidate the usual creep formula obtained by replacing all trapping times by the typical value . we find instead that the motion is only sub - linearly in time , i.e. the asymptotic velocity vanishes . this analysis is confirmed by numerical simulations of a directed polymer with a metric constraint driven in a traps landscape . we moreover obtain that the roughness exponent , which is governed by the equilibrium value up to some large scale , becomes equal to at the largest scales . # 1#2 # 1#2

hep-ph0701151

i

among the remaining unknowns in neutrino physics , resolving the neutrino mass hierarchy may be one of the key importance to our understanding of physics of neutrino masses and the lepton flavor mixing @xcite . given the significance of the problem , it is natural that many methods are proposed for determining the mass hierarchy . the most conventional one would be to do neutrino and antineutrino comparison in long - baseline ( lbl ) accelerator based oscillation experiments @xcite . because of the difference in how the matter effect interferes with the vacuum oscillation effect it can signal the sign of @xmath3 , and hence the mass hierarchy . other less conventional ideas include the methods using atmospheric neutrinos @xcite , @xmath4 and @xmath5 disappearance channels @xcite , supernova neutrinos @xcite , and neutrino - less double beta decay @xcite . these lists of references can not be complete , and some of the other relevant references are quoted therein . in this paper , we discuss yet another way of determining the neutrino mass hierarchy by a neutrino oscillation disappearance experiment using _ a single neutrino flavor _ in vacuum whereas in previous works @xcite the method required the use of two different disappearance channels close to the first oscillation maximum . the possibility that the neutrino survival probability in vacuum can be sensitive to the neutrino mass hierarchy was first suggested in @xcite using reactor neutrinos in the context of high-@xmath6 large mixing angle ( lma ) solar neutrino solution . it was also pursued recently in the hanohano project using a fourier transform technique @xcite . we present here a complete formulation and physics understanding of the new method to determine the neutrino mass hierarchy . this method utilizes the feature that the atmospheric-@xmath7 scale oscillation `` interferes '' with the solar-@xmath7 scale oscillation in a different way depending upon the mass hierarchy . we first carefully re - formulate the difference as an advancement or retardation of the phase of the atmospheric - scale neutrino oscillation relative to the solar - scale oscillation ; for the @xmath8 and @xmath9 disappearance probabilities , the atmospheric oscillation is continuously advanced ( retarded ) for the normal ( inverted ) hierarchy . since the core of the problem exists in extracting long wavelength solar oscillation out of the two short wavelength atmospheric scale oscillations due to @xmath10 and @xmath3 , it is the critical matter to identify which quantity to be held fixed in defining the mass hierarchy reversal from the normal to the inverted , or vice versa . to our understanding , the only known appropriate quantity to hold is the effective neutrino mass squared difference @xmath11 ( see eq.([eqn : dmsqee ] ) ) , the one which is actually observed in @xmath4 ( or @xmath0 ) disappearance measurement at the first few oscillation maxima and/or minima @xcite . we find it important to have the proper formalism because otherwise the sensitivity to the mass hierarchy resolution can be significantly overestimated . then , we point out that an experiment using the resonant @xmath0 absorption reaction @xcite enhanced by mssbauer effect recently proposed by raghavan @xcite gives the first concrete realization of the idea . ( see @xcite for earlier proposals of mssbauer enhanced experiments . ) because of the monochromaticity of the @xmath0 beam from the bound state beta decay @xcite , the phase advancement or retardation of atmospheric - scale neutrino oscillation is detectable after 20 or more oscillations if the source and the target are made sufficiently compact in size . the unique feature of this method is the use of this ultra - monochromatic neutrino source thereby sidestepping the very high energy resolution requirement requested with reactor or accelerator neutrinos . a concrete plan for the experiment may be as follows ; in the first stage the atmospheric @xmath11 must be accurately measured in a way described in @xcite by a measurement at @xmath1210 m baseline . as we will see , the precision of the measurement must reach sub - percent level in order for this method to work . then , in the second stage relative phase advancement or retardation of the atmospheric - scale neutrino oscillation must be detected by moving the detector to @xmath12350 m , this is just beyond the solar - scale oscillation distance for 18.6 kev neutrinos . based on this plan we give a detailed estimate of the sensitivity to the resolution of the mass hierarchy . upon finishing the above measurement , it is natural to think about the continuation of the experiment by moving the detector to distances tuned for precision measurement of the oscillation parameters relevant for solar neutrinos , @xmath1 and @xmath2 . we also give a detailed estimate of the accuracy for the determination of these parameters . it is notable that a resonant @xmath13 absorption experiment could allow to make precise measurements of _ all mixing parameters _ that appear in the @xmath14 oscillation channel : @xmath15 , @xmath2 , @xmath1 , the effective atmospheric @xmath16 and the neutrino mass hierarchy . in sec . [ sec : how ] , we first describe the essence of the method in an explanatory way . we then define our theoretical machinery using the effective @xmath11 . we also clarify the basic requirement for the measurement . in sec . [ sec : exp ] , we discuss the concrete set up of the experiment and describe our statistical method for the analysis . we then give the analysis results on sensitivity to the mass hierarchy resolution . in sec . [ sec : solar ] , we describe the analysis for the determination of the solar oscillation parameters . in sec . [ sec : conc ] , we finish by giving our concluding remarks . in appendix [ appendixa ] , we give a different interpretation of the phenomena in terms of the effective mass squared differences whereas in appendix [ appendixb ] , we discuss how this method can be applied to the @xmath17 disappearance channel . this possibility has been discussed in @xcite however the baseline required is @xmath18 km .

, we give a complete description and physics understanding of the method . the key feature of the method is to detect advancement ( normal ) or retardation ( inverted ) of the phase of the atmospheric - scale oscillation relative to the solar - scale oscillation . the unique feature of this setup is the ultra - monochromaticity of the observed s . because of this feature the phase advancement or retardation of atmospheric - scale neutrino oscillation is detectable after 20 or more oscillations if the source and the target are made sufficiently compact in size .

the neutrino mass hierarchy can be determined , in principle , by measuring a phase in the disappearance oscillation probability in vacuum , without relying on the matter effect , using a single channel . this phase is not the same for the normal and inverted neutrino mass spectra . in this paper , we give a complete description and physics understanding of the method . the key feature of the method is to detect advancement ( normal ) or retardation ( inverted ) of the phase of the atmospheric - scale oscillation relative to the solar - scale oscillation . we then show that this method can be realized with the recently proposed resonant absorption reaction enhanced by mssbauer effect . the unique feature of this setup is the ultra - monochromaticity of the observed s . because of this feature the phase advancement or retardation of atmospheric - scale neutrino oscillation is detectable after 20 or more oscillations if the source and the target are made sufficiently compact in size . a quantitative estimate of the sensitivity to mass hierarchy resolution is given . we have also examined how a possible continuation of such experiment can be carried out in order also to achieve high precision ( few % ) determination of the solar - scale oscillation parameters and . 1.6 cm

hep-ph0701151

c

in this paper , we have shown that the neutrino mass hierarchy can be determined only by _ a single experiment _ based on resonant @xmath28 absorption reaction enhanced by the mssbauer effect . in its first stage , @xmath11 must be accurately determined by @xmath18910 m measurements . in the second stage of the experiment , the relative phase of the atmospheric oscillation ( wiggles ) between the normal vs. inverted mass hierarchies , phase advancement or retardation must be discriminated by measurements at @xmath190350 m. it can be executed thanks to the ultra monochromatic nature of neutrino beam which would allow us to detect relative phase of atmospheric oscillation even after 20 oscillations . we stress that the monochromaticity is special to the resonant @xmath28 absorption reaction , most probably the unique experimental way to realize this principle . we concluded that assuming @xmath157 % , the hierarchy can be determined at 90 ( 99 ) % cl for @xmath49 down to 0.035 ( 0.06 ) for 1000 events collected at five different positions and down to 0.025 ( 0.04 ) for 2000 events . for a larger error @xmath162% , the critical value of @xmath49 will be @xmath12 0.08 ( 0.11 ) at 90 ( 99 ) % cl approximately independent of the number of events for more than @xmath12 1000 events . we have also shown that in a third stage of the experiment , by positioning detectors in different locations , it is possible to determine the solar - scale parameters too . the precision one can achieve with 1000 events in each detector for @xmath191 is about 1.6 ( 4.0 ) % at 68.27 ( 99.73 ) % cl whereas that for @xmath1 is about 0.9 ( 2.2 ) % at 68.27 ( 99.73 ) % cl , all for 2 dof . the accuracies improve as data taking proceeds and the errors would reduce by a factor of @xmath192 when an order of magnitude larger number of events is taken . it is in fact remarkable that the experimental set up considered in this paper allows us to make a precise measurement of all the mixing parameters appear in the oscillation probability for @xmath14 channel , @xmath2 , @xmath15 , @xmath1 , @xmath11 and the neutrino mass hierarchy only by a single experiment , independent of any other experiments . the only parameters inaccessible by the method are @xmath193 and the cp phase @xmath194 , but precision measurement of the other mixing parameters will certainly help in determining these parameters by other experiments . some remarks are in order : * as noted in sec . [ subsec : theo ] , our method of determining the mass hierarchy can be confused by the cpt violation of the type with @xmath2 in different octants in the neutrino and the antineutrino sectors . it in turn implies that once the mass hierarchy is determined by some other means , the measurement we propose in this paper can be regarded as testing that particular type of cpt violation . * due to the capability of resolving atmospheric wiggles even after 20 atmospheric oscillations away from the source , this experiment could be sensitive to other dynamics @xcite which differ from the standard three flavor mass induced oscillation one . in particular , one can perhaps probe mechanisms such as : neutrino decay @xcite , decoherence @xcite , mixing with sterile neutrinos @xcite , violation of lorentz invariance or the equivalence principle @xcite , long - range leptonic forces @xcite , extra - dimensions @xcite . finally , we emphasize that realizing the proposed mssbauer @xmath28 experiment is crucial in order to make all the discussions in this paper meaningful . the principle of the experiment is well formulated by having the decay producing source @xmath28 and the absorption reaction in the target as t - conjugate channels with each other , allowing mutual cancellation of large part of the atomic shift @xcite . nonetheless , it still remains unclear to what extent the @xmath124he atom in the target experiences exactly the same environment as the @xmath124h atom in the source @xcite . this point has to be ( and will be ) investigated in a systematic way . if the experiment is indeed realizable it will certainly open a new window for neutrino experiments which can explore the neutrino properties in otherwise inaccessible manner . one of the authors ( h.m . ) thanks the abdus salam international center for theoretical physics , where part of this work was done , for the hospitality . two of us ( h.n . and r.z.f ) are grateful for the hospitality of the theory group of the fermi national accelerator laboratory during the summer of 2006 . this work was supported in part by the grant - in - aid for scientific research , nos . 16340078 and 19340062 , japan society for the promotion of science , by fundao de amparo pesquisa do estado de so paulo ( fapesp ) , fundao de amparo pesquisa do estado de rio de janeiro ( faperj ) and conselho nacional de cincia e tecnologia ( cnpq ) . fermilab is operated under doe contract no . de - ac02 - 76ch03000 .

the neutrino mass hierarchy can be determined , in principle , by measuring a phase in the disappearance oscillation probability in vacuum , without relying on the matter effect , using a single channel . we then show that this method can be realized with the recently proposed resonant absorption reaction enhanced by mssbauer effect . we have also examined how a possible continuation of such experiment can be carried out in order also to achieve high precision ( few % ) determination of the solar - scale oscillation parameters and .

the neutrino mass hierarchy can be determined , in principle , by measuring a phase in the disappearance oscillation probability in vacuum , without relying on the matter effect , using a single channel . this phase is not the same for the normal and inverted neutrino mass spectra . in this paper , we give a complete description and physics understanding of the method . the key feature of the method is to detect advancement ( normal ) or retardation ( inverted ) of the phase of the atmospheric - scale oscillation relative to the solar - scale oscillation . we then show that this method can be realized with the recently proposed resonant absorption reaction enhanced by mssbauer effect . the unique feature of this setup is the ultra - monochromaticity of the observed s . because of this feature the phase advancement or retardation of atmospheric - scale neutrino oscillation is detectable after 20 or more oscillations if the source and the target are made sufficiently compact in size . a quantitative estimate of the sensitivity to mass hierarchy resolution is given . we have also examined how a possible continuation of such experiment can be carried out in order also to achieve high precision ( few % ) determination of the solar - scale oscillation parameters and . 1.6 cm

1607.05205

i

the cold atom community has revived the study of the approach to thermal equilibrium for large isolated quantum systems . we refer to @xcite and references therein on previous work . most accessible , both numerically and experimentally , are lattice systems in one dimension . one dimension is peculiar , since there are models with an extensive number of locally conserved fields . examples of such quantum integrable systems are the xxz spin chain and the continuum lieb - liniger @xmath1-bose gas . obviously the pathway to equilibrium will depend crucially on whether the system is integrable or not @xcite . but in addition there is also the dependence on initial conditions which is potentially overwhelming . one could prepare the system already in thermal equilibrium and study the response to small initial perturbations @xcite . these are the much investigated time response and correlation functions in equilibrium . the initial state could be translation invariant , to some extent thereby suppressing the mostly slow spatial variations @xcite . recently initial domain - wall states have become very popular @xcite . such a state is obtained by joining two distinct thermal states at a single point ( and at two points in case of periodic boundary conditions ) . domain - wall states will be the main focus of our contribution . browsing the introductions to the papers mentioned above , one might have the impression that the approach to equilibrium for classical systems in one dimension is a well - covered topic . we study here fermi - pasta - ulam type anharmonic chains with domain - wall initial conditions and are not aware of any previous systematic study . the structure of equilibrium time - correlations for such chains has been elucidated only recently @xcite . in particular one now understands the link to anomalous transport which is most directly observed when coupling the chain to thermal reservoirs at distinct temperatures , see @xcite . as in the quantum world , there are integrable chains , in our context the most famous one being the toda chain . but the kam theorem signals in addition the possibility that , as a function of the energy , the structure may change from integrable to chaotic . this energy threshold is fascinating from the perspective of nonlinear dynamics and has attracted considerable attention @xcite . we hope that a better understanding of classical models also serves as an incentive to look for related phenomena in quantum systems . the parameters of the initial domain - wall state will be chosen such that in the accessible part of phase space the chain dynamics is sufficiently chaotic . then one would expect that the conserved fields as computed from the chain dynamics are approximated by the respective solution of the macroscopic euler equations , for times limited by diffusive effects . how well such expectations work out will have to be studied . the euler equations are based on the notion of local thermodynamic equilibrium . the microscopic local conservation laws are deduced from the chain dynamics and are then averaged in the stipulated local equilibrium state so to arrive at a closed set of equations for the conserved fields . in particular , to reach non - trivial predictions , the thermal average of the microscopic currents is not allowed to vanish . this is ensured if the interaction potential depends only on positional differences , as @xmath2 , implying momentum conservation . upon adding an on - site potential , @xmath3 , momentum conservation would be broken , all euler currents would vanish , and the evolution of the initial step profile is determined by diffusive effects only . the euler equations are a system of @xmath4 hyperbolic conservation laws , @xmath5 for our case of anharmonic chains . they are of the generic form @xmath6 @xmath7 , @xmath8 , with given current functions @xmath9 . in the mathematical literature the domain - wall initial data are known as riemann problem for eq . , which means @xmath10 for a wide class of current functions , there is a unique entropy solution to with initial conditions , see the exposition @xcite , sections 48 . this solution scales ballistically as @xmath11 where @xmath12 is bounded and continuous except for isolated jumps , possibly . there is a well developed theory of how to compute @xmath12 , at least in principle @xcite , sections 13 . in our case the current functions are determined through the microscopic particle model , and hence of a very particular form . thus our task is twofold . firstly we have to investigate the solution to the riemann problem . secondly such predictions should be compared with numerical simulations of the dynamics . let us return for a moment to the distinction between integrable and non - integrable systems , both starting from a domain - wall initial state . as supported by a variety of studies on quantum integrable models @xcite , one expects that still holds in the integrable case . thus at first sight there seems to be little difference . of course , the macroscopic profiles are computed by using completely different methods for the two cases . but the real distinguishing feature is the appearance of shocks . an ideal gas with step - initial conditions shows ballistic spreading but no shocks . the entropy solution for the euler equations is a mathematical shorthand for the limit of small dissipation , which is meaningful only if the underlying dynamics is sufficiently chaotic . merely invoking the conservation laws , the euler equations admit stable and unstable shocks . such unphysical solutions to are removed by requiring a positive entropy production at the shock , as will be illustrated in the examples below . in a local region away from the shock , the local state is ( to very good approximation ) in thermal equilibrium . our study adds current fluctuations as an item , which can no longer be based on the euler equations . most simple - mindedly , one would consider the fluctuations of the time - integrated current across the origin . for anharmonic chains the current is a three - vector . in most cases one would find gaussian fluctuations of size @xmath13 , thus not so interesting from a theoretical perspective . a more global picture emerges by considering the current integrated along the ray @xmath14 for some prescribed velocity @xmath15 . the ray is chosen to lie in the interior of a rarefaction wave . in addition , one has to consider a computable but particular linear combination of the three currents . as will be discussed , then the integrated current fluctuations are of size @xmath0 , smaller as for all other linear combinations , and the statistics is given by the tracy - widom distribution known from random matrix theory . our paper consists of three , at first sight somewhat unrelated parts . we start with a stochastic model with two conserved fields , as always with domain - wall initial conditions . for our particular system the validity of the euler equations has been established mathematically @xcite . thus the model is used to explain the method by which one obtains the solution of the riemann problem and as a numerical benchmark . we proceed to anharmonic chains , first with a general interaction potential . analytically and numerically we then consider two specific choices for the potential , which generate sufficiently chaotic dynamics ( as known from previous studies ) . in the third part we discuss the fluctuations of time - integrated currents .

the nonequilibrium dynamics of anharmonic chains is studied by imposing an initial domain - wall state , in which the two half lattices are prepared in equilibrium with distinct parameters . their typical fluctuations should be of size and have a tracy - widom gue distributed amplitude . the proper extension to anharmonic chains is explained and tested through molecular dynamics .

the nonequilibrium dynamics of anharmonic chains is studied by imposing an initial domain - wall state , in which the two half lattices are prepared in equilibrium with distinct parameters . we analyse the riemann problem for the corresponding euler equations and , in specific cases , compare with molecular dynamics . additionally , the fluctuations of time - integrated currents are investigated . in analogy with the kpz equation , their typical fluctuations should be of size and have a tracy - widom gue distributed amplitude . the proper extension to anharmonic chains is explained and tested through molecular dynamics . our results are calibrated against the stochastic leroux lattice gas .

1603.05463

i

analysis of the nonlinear schrdinger ( nls ) and wave equations with double - well , multi - well , or periodic potentials constitutes a continuously developing subject @xcite . these nonlinear partial differential equations ( pdes ) have potential applications to many realistic problems such as bose einstein condensation , nano - technology , and photonic optics . in many applications , a specific waveguide geometry of the spatial domain suggests the use of metric graphs as suitable way to approximate dynamics of the nonlinear pdes on such spatial domains @xcite . at the vertex points , where different edges of the metric graphs are connected , boundary conditions are given to define the coupling between the wave functions along the edges . kirchhoff boundary conditions are commonly used to ensure continuity of the wave functions and the flow conservation through the vertex point @xcite . the subject of the nls and wave equations on metric graphs has seen many developments in the recent years . at the rigorous mathematical level , the emphasis has been placed on the case of star graphs , where existence , variational properties , stability , and scattering of nonlinear waves have been studied , e.g. in @xcite . nonlinear waves in more complex graphs have been studied only very recently . variational results on the non - existence of ground states in unbounded graphs with closed cycles is given in @xcite under a set of certain topological conditions . bifurcation and stability of nonlinear waves on tadpole and dumbbell graphs were studied in @xcite by using methods of bifurcation theory . periodic metric graphs arise in many contexts such as carbon nanotubes and graphene . spectral properties of the periodic graphs were studied in many details @xcite . generalized floquet bloch theory is introduced for periodic graphs in a similar fashion to the study of schrdinger operators with bounded periodic potentials @xcite . however , the periodic graphs represent a more challenging and fascinating subject since the effective periodic potentials are defined in spaces of lower regularity . as a result , more exotic phenomena arise such as the presence of embedded eigenvalues of infinite multiplicities inside the floquet bloch spectral bands @xcite . in our recent work @xcite , we showed how to apply the spectral floquet bloch decomposition for the periodic graphs in order to analyze propagation of nonlinear waves on such graphs . in nonlinear pdes with smooth periodic potentials , localization of standing waves is quite common for the frequencies occurring in the spectral gaps of the associated linear operators @xcite . mathematical justification of such standing localized waves in the smooth periodic potentials is now well - understood in the tight - binding approximation @xcite and in the envelope approximation near the spectral edges @xcite . in the present work , we are interested to characterize standing localized waves on periodic graphs near the bifurcation points . however , compared to the tight - binding and envelope approximations , we would like to explore the discrete nature of the periodic graphs . consequently , we reduce the existence of standing localized waves in the nls equation on the periodic graph to the existence of homoclinic orbits of the two - dimensional discrete map . we will establish the equivalence between the differential equations on the periodic graphs and the difference equations , which holds for all frequencies below the lowest spectral band of the associated linear operator . in order to deduce definite results on existence of standing localized waves on the periodic graphs , we will use the proximity of the frequencies of the standing waves to those for the spectral edge . let us consider the following nls equation @xmath0 on the periodic graph @xmath1 shown in figure [ qgfig1 ] . the same periodic graph and its modifications was considered in the previous literature within the linear spectral theory of the associated stationary schrdinger operator @xcite . .,width=384 ] in the recent work @xcite , using the floquet bloch spectral transform and energy methods , we have addressed the time evolution problem associated with the nls equation ( [ nls ] ) on the periodic graph @xmath1 and justified the most universal approximation of the modulated wave packets given by the homogeneous nls equation @xmath2 where @xmath3 and @xmath4 are specific numerical coefficients computed by means of the floquet bloch spectral theory and @xmath5 is the envelope function in slow spatial and temporal variables @xmath6 for the leading - order term in the floquet bloch decomposition . in the present work , we will consider bound states of the stationary nls equation @xmath7 which arise for the standing waves @xmath8 of the time - dependent nls equation ( [ nls ] ) on the periodic graph @xmath1 . the stationary nls equation ( [ statnls ] ) is the euler lagrange equation of the energy functional @xmath9 , where @xmath10 and @xmath11 are two conserved quantities in the time evolution of the nls equation ( [ nls ] ) . quantities @xmath12 and @xmath13 have the physical meaning of the hamiltonian and mass , respectively . in the definitions ( [ energy ] ) and ( [ charge ] ) , the integrals are defined piecewise along each edge of the periodic graph @xmath1 . the critical points of @xmath14 are defined in the energy space @xmath15 given by @xmath16 here and in what follows , @xmath17 , @xmath18 is defined by using piecewise integration along each edge of the graph @xmath1 , whereas @xmath19 means that @xmath20 is continuous not only along the edges but also across the vertex points of the graph @xmath1 . compared to the weak energy space @xmath15 , strong solutions of the stationary nls equation ( [ statnls ] ) are defined in the domain space @xmath21 , which is a subspace of @xmath22 closed with the continuity conditions as well as with the kirchhoff boundary conditions for derivatives across the vertex points , see equations ( [ keq1 ] ) and ( [ keq4 ] ) below . by theorem 1.4.11 in @xcite , although the energy space @xmath15 is only defined by the continuity boundary conditions , the kirchhoff boundary conditions for the derivatives are natural boundary conditions for critical points of the energy functional @xmath14 in the space @xmath15 . by bootstrap arguments , any critical point of the energy functional @xmath14 in @xmath15 is also a solution of the stationary nls equation ( [ statnls ] ) in @xmath21 . on the other hand , solutions of the stationary nls equation ( [ statnls ] ) in @xmath21 are immediately the critical points of the energy functional @xmath14 . therefore , the set of bound states of the stationary nls equation ( [ statnls ] ) is equivalent to the set of critical points of the energy functional @xmath14 . in the context of the stationary nls equation ( [ statnls ] ) , we consider small bound states @xmath23 bifurcating for small negative @xmath24 . in this asymptotic limit , we prove the existence of two families of small , positive , exponentially decaying bound states , one of which is centered at the midpoint of the horizontal link connecting two rings in the periodic graph @xmath1 and the other one is centered symmetrically at the midpoints in the upper and lower semicircles of one ring , see the periodic graph @xmath1 in figure [ qgfig1 ] . by discrete translational invariance , the two bound states can be translated to the midpoints of every horizontal link and every ring in @xmath1 . on a technical side , we show that the two families of the bound states can be obtained from the symmetric solutions of the two - dimensional discrete map . the two families of bound states of the stationary nls equation ( [ statnls ] ) on the periodic graph @xmath1 bifurcate from the point @xmath25 , which coincides with the bottom of the spectrum of the linear operator @xmath26 in @xmath27 . the following theorem presents the main result of this work . [ theorem - main ] there are positive constants @xmath28 and @xmath29 such that for every @xmath30 , the stationary nls equation ( [ statnls ] ) admits two bound states @xmath23 ( up to the discrete translational invariance ) such that @xmath31 one bound state satisfies @xmath32 and the other one satisfies @xmath33 where @xmath34 is the length of the horizontal link and @xmath35 is the arc length of the upper and lower semicircles in @xmath1 . moreover , it is true for both bound states that * @xmath36 is symmetric in upper and lower semicircles of @xmath1 , * @xmath37 for every @xmath38 , * @xmath39 as @xmath40 exponentially fast . we conjecture that the bound state satisfying ( [ branch-1 ] ) is the ground state of the nls equation ( [ nls ] ) in the sense that it is a standing wave of smallest energy @xmath12 at a fixed value of @xmath13 in the limit of small positive @xmath13 . indeed , both bound states correspond to the values of @xmath24 near the bottom of the spectrum of the linear operator @xmath26 in @xmath27 . both bound states have properties ( ii)(iii ) , which are standard properties of the ground states in the nls equation . however , in comparison , the bound state satisfying ( [ branch-1 ] ) has a single hump at @xmath41 , whereas the bound state satisfying ( [ branch-2 ] ) has two humps at @xmath42 in the upper and lower semicircles due to property ( i ) . the bound state with two humps is expected to have bigger energy @xmath12 at a fixed value of @xmath13 . unfortunately , the energy difference between the two bound states is exponentially small in terms of small parameter @xmath43 , see section 5 below . [ remark-1 ] using the asymptotic method developed in @xcite , one can prove existence of two bound states of the stationary nls equation ( [ statnls ] ) in the limit of large negative @xmath24 . one bound state represents a narrow solitary wave symmetric about @xmath44 . the other bound state represents two narrow solitary waves symmetric about @xmath45 in the upper and lower semicircles . it becomes then obvious from the methods developed in @xcite that the former solution is a ground state of the nls equation ( [ nls ] ) . connection between the limits of small and large negative @xmath24 was considered numerically in @xcite . similar results are expected for the periodic graph @xmath1 , as is suggested by numerical approximations in section 5 . [ remark-2 ] the rest of the paper is organized as follows . the linear spectral analysis on the periodic graph @xmath1 involving a two - dimensional linear discrete map is developed in section 2 . existence of the two bound states stated in theorem [ theorem - main ] is obtained in section 3 by using a two - dimensional nonlinear discrete map . properties ( i)(iii ) stated in theorem [ theorem - main ] are proved in section 4 by using geometric theory of stable and unstable manifolds in two - dimensional discrete maps . section 5 reports numerical approximations of the two bound states obtained in theorem [ theorem - main ] .

the nonlinear schrdinger ( nls ) equation is considered on a periodic graph subject to the kirchhoff boundary conditions . bifurcations of standing localized waves for frequencies lying below the bottom of the linear spectrum of the associated stationary schrdinger equation are considered by using analysis of two - dimensional discrete maps near hyperbolic fixed points . we prove existence of two distinct families of small - amplitude standing localized waves , which are symmetric about the two symmetry points of the periodic graph . we also prove properties of the two families , in particular , positivity and exponential decay .

the nonlinear schrdinger ( nls ) equation is considered on a periodic graph subject to the kirchhoff boundary conditions . bifurcations of standing localized waves for frequencies lying below the bottom of the linear spectrum of the associated stationary schrdinger equation are considered by using analysis of two - dimensional discrete maps near hyperbolic fixed points . we prove existence of two distinct families of small - amplitude standing localized waves , which are symmetric about the two symmetry points of the periodic graph . we also prove properties of the two families , in particular , positivity and exponential decay . the asymptotic reduction of the two - dimensional discrete map to the stationary nls equation on an infinite line is discussed in the context of the homogenization of the nls equation on the periodic graph .

1105.5222

i

the determination of the equation of state ( eos ) of asymmetric nuclear matter ( nm ) has been the main object of numerous nuclear structure and reaction studies involving unstable nuclei lying close to the neutron or proton driplines @xcite . the knowledge about the eos of asymmetric nm is vital for any model of neutron star @xcite , and the nuclear mean - field potential is the most important input for the determination of the nuclear eos . many microscopic studies of the eos have been done based on the nuclear mean field given by both nonrelativistic and relativistic nuclear many - body approaches , using realistic two - body and three - body nucleon - nucleon ( nn ) forces or interaction lagrangians ( see recent reviews @xcite ) . these many - body studies have shown the important role played by the pauli blocking effects as well as higher - order nn correlations at different nm densities . these medium effects are normally considered as the physics origin of the density dependence that has been introduced into various versions of the effective nn interactions used in the modern mean - field approaches . among them , very popular is the so - called m3y interaction which was originally constructed to reproduce the g - matrix elements of the reid @xcite and paris @xcite nn potentials in an oscillator basis . several realistic density dependences have been added later on to the m3y interactions @xcite to properly account for the nm saturation properties as well as the ground - state structure of finite nuclei @xcite . these density dependent versions of the m3y interaction have been used in the nonrelativistic hartree - fock ( hf ) studies of symmetric and asymmetric nm . some of them have been successfully used in the folding model studies of the nucleon - nucleus and nucleus - nucleus scattering @xcite . in attempt to find a realistic version of the effective nn interaction for consistent use in the mean - field studies of nm and finite nuclei as well as in the nuclear reaction calculations , we have performed recently a systematic hf study of nm @xcite using the cdm3y@xmath2 interactions , which have been used mainly in the folding model studies of the nuclear scattering @xcite , and the m3y - p@xmath2 interactions carefully parametrized by nakada @xcite for use in the hf studies of nuclear structure . for comparison , the same hf study has also been done with the d1s and d1n versions of the gogny interaction @xcite and sly4 version of the skyrme interaction @xcite . while these effective nn interactions give more or less the same description of the saturation properties of the symmetric nm , the hf results for the asymmetric nm @xcite show that they are divided into two families , which are associated with two different ( _ soft _ and _ stiff _ ) behaviors of the nm symmetry energy at high nucleon densities . as a result , these two families predict very different behaviors of the proton - to - neutron ratio in the @xmath1-equilibrium that can imply two drastically different mechanisms for the neutron star cooling ( with or without the direct urca process ) @xcite . as a further step in this direction , we try to find out in the present work how such a difference in the nm symmetry energy can affect the eos of the @xmath1-stable neutron star ( ns ) matter as well as the main ns properties like the maximum mass , radius , central density and moment of inertia . for this purpose , the tolman - oppenheimer - volkov ( tov ) equations have been solved using different eos s of the ns matter that are associated with the nuclear mean - field potentials given by different in - medium nn interactions under study . given the complex , inhomogeneous structure of the ns crust , it is a tremendous task to develop a consistent structure model for the inner and outer ns crusts using all versions of the in - medium nn interaction considered here . therefore , we have used the eos of the ns crust given by the compressible liquid drop model ( cldm ) @xcite with the model parameters determined by the sly4 interaction @xcite . different eos s of the uniform ns core are then calculated for the np@xmath0 composition in the @xmath1-equilibrium at zero temperature and extended to the supranuclear densities , using the mean - field potentials given by different density - dependent nn interactions . in this way , any difference found in the solutions of the tov equations is entirely due to the choice of the eos of the ns core , i.e. , to the choice of the in - medium nn interaction . the main ns properties obtained in each case are compared with the empirical data given by the recent astronomical observation of neutron stars .

the eos of the uniform ns core has been calculated for the np composition in the-equilibrium at zero temperature , using version sly4 of the skyrme interaction as well as two density - dependent versions of the finite - range m3y interaction ( cdm3y and m3y - p ) , and versions d1s and d1n of the gogny interaction .

the nuclear mean - field potentials obtained in the hartree - fock method with different choices of the in - medium nucleon - nucleon ( nn ) interaction have been used to study the equation of state ( eos ) of the neutron star ( ns ) matter . the eos of the uniform ns core has been calculated for the np composition in the-equilibrium at zero temperature , using version sly4 of the skyrme interaction as well as two density - dependent versions of the finite - range m3y interaction ( cdm3y and m3y - p ) , and versions d1s and d1n of the gogny interaction . although the considered effective nn interactions were proven to be quite realistic in numerous nuclear structure and/or reaction studies , they give quite different behaviors of the symmetry energy of nuclear matter at supranuclear densities that lead to the _ soft _ and _ stiff _ scenarios discussed recently in the literature . different eos s of the ns core and the eos of the ns crust given by the compressible liquid drop model have been used as input of the tolman - oppenheimer - volkov equations to study how the nuclear symmetry energy affects the model prediction of different ns properties , like the cooling process as well as the gravitational mass , radius , and moment of inertia .

1105.5222

i

the eos of the np@xmath0 matter of neutron star in @xmath1-equilibrium has been studied in details using the nuclear mean - field potentials obtained in the hf method with different choices of the effective ( in - medium ) nn interactions that give two different behaviors of the nm symmetry energy at supranuclear densities ( the _ soft _ and _ stiff _ scenarios ) . the fast decrease of the soft nm symmetry energy to zero at @xmath57 @xmath21 results on a drastic decrease of the proton and lepton components in the uniform ns core that then becomes the _ @xmath1-unstable _ , pure neutron matter at @xmath58 @xmath21 . very small proton fraction in the ns matter given by the soft - type interactions excludes the direct urca process in the ns cooling , whereas the du process is well possible for the _ @xmath1-equilibrated _ ns matter predicted by the stiff - type cdm3y@xmath2 interactions . the ns pressure obtained with different in - medium nn interactions are compared with the empirical ns pressure deduced from the recent astronomical observation . in general , the eos given by the soft - type interactions tend to give pressure lower the empirical values at high densities . in particular , the d1s version of the gogny interaction gives negative pressure at baryon densities @xmath72 and violates , therefore , le chatelier s principle that ensures the ns stability . the adiabatic sound velocity estimated from the ns pressure given by two versions of the soft - type m3y - p@xmath2 interaction becomes superluminal at high baryon densities and violates , therefore , the causality condition , and the eos has been corrected by hand in this case for further use in the tov equations . it seems , therefore , likely that there could be uncertainties in a well parametrized effective ( density dependent ) nn interaction that are not visible at low nuclear densities , and its success in the nuclear structure study is not sufficient to validate its extrapolation to supranuclear densities . different eos s of the ns core supplemented by the sly4 eos of the ns crust given by the compressible liquid drop model have been used for the input of the tolman - oppenheimer - volkov equations to study how different behaviors of the symmetry energy affect the model prediction of the ns properties . the eos s obtained with the stiff - type interactions were found to give consistently reasonable description of the empirical data for the ns mass and radius , and to comply well with the causality condition . in comparison with the same empirical ns data , the soft - type interactions were found less successful , especially , the two versions of the famous gogny interaction certainly need an appropriate modification before they can be used in the tov equations to study structure of neutron star . the vital role of the nm symmetry energy has been demonstrated in our specific test of the cdm3y@xmath2 interactions , where we found a significant reduction of the maximum gravitational mass @xmath89 and radius @xmath90 away from the empirical boundaries when the slope of the nm symmetry energy is changed from the _ stiff _ behavior to the _ soft _ one . it is natural to expect that if hyperons ( and other hypothetical constituents like kaons or quark matter ) are included at high baryon densities , the @xmath89 and @xmath90values given by the soft - type interactions could be driven to region lying well below all existing empirical estimates .

the nuclear mean - field potentials obtained in the hartree - fock method with different choices of the in - medium nucleon - nucleon ( nn ) interaction have been used to study the equation of state ( eos ) of the neutron star ( ns ) matter . although the considered effective nn interactions were proven to be quite realistic in numerous nuclear structure and/or reaction studies , they give quite different behaviors of the symmetry energy of nuclear matter at supranuclear densities that lead to the _ soft _ and _ stiff _ scenarios discussed recently in the literature . different eos s of the ns core and the eos of the ns crust given by the compressible liquid drop model have been used as input of the tolman - oppenheimer - volkov equations to study how the nuclear symmetry energy affects the model prediction of different ns properties , like the cooling process as well as the gravitational mass , radius , and moment of inertia .

the nuclear mean - field potentials obtained in the hartree - fock method with different choices of the in - medium nucleon - nucleon ( nn ) interaction have been used to study the equation of state ( eos ) of the neutron star ( ns ) matter . the eos of the uniform ns core has been calculated for the np composition in the-equilibrium at zero temperature , using version sly4 of the skyrme interaction as well as two density - dependent versions of the finite - range m3y interaction ( cdm3y and m3y - p ) , and versions d1s and d1n of the gogny interaction . although the considered effective nn interactions were proven to be quite realistic in numerous nuclear structure and/or reaction studies , they give quite different behaviors of the symmetry energy of nuclear matter at supranuclear densities that lead to the _ soft _ and _ stiff _ scenarios discussed recently in the literature . different eos s of the ns core and the eos of the ns crust given by the compressible liquid drop model have been used as input of the tolman - oppenheimer - volkov equations to study how the nuclear symmetry energy affects the model prediction of different ns properties , like the cooling process as well as the gravitational mass , radius , and moment of inertia .

1005.5424

i

to summarize , we have carried out a study of calculating overlap fermion propagators and hadron correlators on the @xmath0 flavor domain wall fermion configurations on @xmath115 , and @xmath3 lattices with both deflation in the inversion and low - mode substitution in constructing the correlators . with hyp smearing and low - mode deflation , we find a speed up from @xmath238 23 for the @xmath1 lattice with 200 pairs of eigenmodes and @xmath291 51 for the @xmath2 lattice with 200 pairs of eigenmodes to @xmath292 for the larger @xmath3 lattice with 400 pairs of eigenmodes . the cost of the overhead for calculating eigenmodes is 4.5 , 4.9 and 7.9 propagators for the above lattices , respectively , which will be amortized with calculation of propagators for more sources . we have calculated the quark mass dependence of the hyperfine splitting and find that one can accommodate charm quarks with small @xmath6 error . since this is a mixed action approach with overlap on dwf sea , we use the finite volume boundary condition property of the scalar correlator to estimate the low - energy constant @xmath7 for finite lattice spacing which is needed for the mixed action partially quenched chiral perturbation theory extrapolation to the physical point and the continuum limit . the preliminary result of @xmath293 turns out to be small . it only shifts the 300 mev mixed valence - sea pion mass by @xmath8 mev at @xmath167 gev for the @xmath3 lattice and @xmath294 mev at @xmath236 gev for the @xmath2 lattice . we have examined the signal - to - noise issue for the connected hadron correlators from the noise source on a time slice and found that the noise wall source is worse than the point source for all mesons except the pion . it is worse still for the baryon ( and multi - quark systems ) by a @xmath295 factor where @xmath252 is the 3-volume of the time slice . the situation can be ameliorated by reducing the contamination from neighboring sites with less source points . this introduces the idea of a noise grid source with support on some uniformly spaced grid points on a time slice . on the other hand , we find that the low - frequency part of the multiple hadron source with exact eigenmodes is highly correlated so that , beyond 64 grid points on a time slice of the @xmath3 lattice , the relative errors of the meson correlators do not decrease . these observations led to a suggestion of a new algorithm for the grid noise with low - mode substitution to reduce the variance from noise contamination while addressing the low - mode correlation at the same time . we decide to use 64 @xmath9 grid noise and low - mode substitution with 400 pairs of eigenmodes on the @xmath3 lattice with the light sea mass @xmath119 to calculate both the meson and baryon correlators . we find that for light quarks ( pion masses at 200 - 300 mev ) , the errors of the mesons and nucleon masses can be reduced by a factor of @xmath238 3 to 4 as compared to the point source . in the strange quark region , the statistical errors of the pion and nucleon masses can be improved by a factor @xmath12 , but it is not much improved for the vector meson . we find that the results from low - mode substitution start to degrade beyond the strange quark region . this is due to the fact that the signal falls off quickly at large @xmath186 and yet the variance of the noise estimation of the high - frequency and the mixed high- and low - frequency parts of the correlator does not fall . luckily , the @xmath9 grid results are still better than the the point source and can reduce the errors of the charmonium masses by a factor of @xmath12 . one can use it to address the hadrons involving the charm quark . we should point out that the interplay between the noise grid source and low - mode substitution is quite general and is not restricted to a particular fermion action . so far the study of two - point functions has been favorable . the three - point function with @xmath9 grid source and low - mode substitution will undoubtedly pose a different set of challenges .

the overlap fermion propagator is calculated on flavor domain wall fermion gauge configurations on , and lattices . with hyp smearing and low eigenmode deflation the overhead cost for calculating eigenmodes ranges from 4.5 to 7.9 propagators for the above lattices . through the study of hyperfine splitting , we found that the error is small and these dynamical fermion lattices can adequately accommodate quark mass up to the charm quark . a preliminary calculation of the low energy constant which characterizes the discretization error of the pion made up of a pair of sea and valence quarks in this mixed action approach we have studied the signal - to - noise issue of the noise source for the meson and baryon . we introduce a new algorithm with grid source and low eigenmode substitution to study the the many - to - all meson and baryon correlators . , it can reduce the statistical errors of the light quark ( mev ) meson and nucleon correlators by a factor of as compared to the point source . the grid source itself can reduce the errors of the charmonium correlators by a factor of .

the overlap fermion propagator is calculated on flavor domain wall fermion gauge configurations on , and lattices . with hyp smearing and low eigenmode deflation , it is shown that the inversion of the overlap operator can be expedited by times for the lattice and times for the lattice . the overhead cost for calculating eigenmodes ranges from 4.5 to 7.9 propagators for the above lattices . through the study of hyperfine splitting , we found that the error is small and these dynamical fermion lattices can adequately accommodate quark mass up to the charm quark . a preliminary calculation of the low energy constant which characterizes the discretization error of the pion made up of a pair of sea and valence quarks in this mixed action approach is carried out via the scalar correlator with periodic and anti - periodic boundary conditions . it is found to be small which shifts a 300 mev pion mass by to 19 mev on these sets of lattices . we have studied the signal - to - noise issue of the noise source for the meson and baryon . we introduce a new algorithm with grid source and low eigenmode substitution to study the the many - to - all meson and baryon correlators . it is found to be efficient in reducing errors for the correlators of both mesons and baryons . with 64-point grid source and low - mode substitution , it can reduce the statistical errors of the light quark ( mev ) meson and nucleon correlators by a factor of as compared to the point source . the grid source itself can reduce the errors of the charmonium correlators by a factor of .

astro-ph0703475

c

the pan - starrs project has developed the first integrated asteroid detection , intra and inter - night linking , attribution , precovery , orbit identification and orbit determination system in the world . it is known as the moving object processing system ( mops ) . for testing and monitoring purposes during operations we have developed a peudo - realistic simulation of the system including a realistic survey strategy incorporating simple weather factors , s / n - dependent astrometric noise and false detections at a sky - plane density expected for the four telescope pan - starrs system . the simulation does not include additional important factors such as the camera fill factor or probabilistic detections near the detection threshold . we have developed new algorithms based on kd - tree and variable - trees to link detections within and between nights that dramatically improve the speed of identification and that scale as @xmath81 where @xmath0 is the sky - plane density of objects . the implementation of the algorithms is trivially parallelizable on a set of cpu nodes . using these algorithms we have demonstrated nearly 100% efficiency for intra - night linking of synthetic detections with realistic properties into ` tracklets ' . furthermore , we have demonstrated the ability to obtain nearly 100% efficiency for linking those tracklets over many nights into ` tracks ' . the accuracy of the algorithm , the fraction of identified tracks that are actually synthetic in the presence of noise , depends on and decreases with the sky - plane density of detections . tests of the mops intra and inter - night linking algorithms on real data provided by the spacewatch facility show that the system is capable of handling real data with all its inherent systematic problems that are otherwise not explored in our synthetic surveying model .

here we describe new kd - tree and variable - tree algorithms that allow fast , efficient , scalable linking of intra and inter - night detections . using a pseudo - realistic simulation of the pan - starrs survey strategy incorporating weather , astrometric accuracy and false detections successful tests of the mops on real source detections from the spacewatch asteroid survey indicate that the mops is capable of identifying asteroids in real data . 27 manuscript pages + 14 figures + 7 tables keywords : : : asteroids * running head : + * efficient linking of asteroid detections + * editorial correspondence and proofs : + * robert jedicke + institute for astronomy + university of hawaii + honolulu , hi , 96822

the panoramic survey telescope and rapid response system ( pan - starrs ) under development at the university of hawaii s institute for astronomy is creating the first fully automated end - to - end moving object processing system ( mops ) in the world . it will be capable of identifying detections of moving objects in our solar system and linking those detections within and between nights , attributing those detections to known objects , calculating initial and differentially - corrected orbits for linked detections , precovering detections when they exist , and orbit identification . here we describe new kd - tree and variable - tree algorithms that allow fast , efficient , scalable linking of intra and inter - night detections . using a pseudo - realistic simulation of the pan - starrs survey strategy incorporating weather , astrometric accuracy and false detections we have achieved nearly 100% efficiency and accuracy for intra - night linking and nearly 100% efficiency for inter - night linking within a lunation . at realistic sky - plane densities for both real and false detections the intra - night linking of detections into ` tracks ' currently has an accuracy of 0.3% . successful tests of the mops on real source detections from the spacewatch asteroid survey indicate that the mops is capable of identifying asteroids in real data . 27 manuscript pages + 14 figures + 7 tables keywords : : : asteroids * running head : + * efficient linking of asteroid detections + * editorial correspondence and proofs : + * robert jedicke + institute for astronomy + university of hawaii + honolulu , hi , 96822 + + tel : 808.956.9841 + fax : 808.988.8972 + e - mail : jedicke@ifa.hawaii.edu

1612.00106

i

electric vehicles ( evs ) have several advantages over the traditional gasoline powered vehicles . for example , evs are more environment friendly and more energy efficient . realizing the above , regulators ( e.g. federal energy regulator commission ( ferc ) ) are providing incentives to the consumers to switch to electric vehicles . manufacturers ( e.g. tesla , nissan ) are increasingly developing evs equipped with superior technologies . as a result , electric vehicles are increasingly become popular . however , a wide deployment of evs requires an extensive network of charging stations which can be capable of charging large number of vehicles . vehicle - to - grid ( v2 g ) service has been proposed @xcite to enhance the profitability of the evs . in the v2 g service , evs can inject energies to the grid by discharging from their batteries . thus , this bidirectional power flow where evs can both charge and discharge has a lot of potential . hence , a lot of effort is going on for developing bidirectional evs@xcite . however , the higher amount of charging and discharging cycles will degrade the battery life . hence , the owners of the evs have to be compensated adequately for the v2 g service . thus , though a charging station can gain an additional profit using the v2 g service of the evs , however without a proper pricing mechanism , the owners of the evs will not prefer the v2 g service in the first place which may nullify the profit of the charging station . without a proper control mechanism , the cost of the charging station and the peak energy consumption may increase . without a profitable charging station , the wide - scale deployment of the evs will remain a distant dream . the charging station needs to select prices in order to earn profits by allocating resources in an intelligent manner among the evs . the charging station also needs to provide adequate compensation to the owners if the ev is used for the v2 g service . however , high prices or low compensation may not provide incentives to the owners which may reduce the profit . hence , a proper pricing mechanism for charging the evs and the v2 g service is imperative for a charging station . we propose a menu based pricing scheme for charging an ev . whenever an ev arrives at the charging station , the charging station offers a variety of contracts @xmath0 to the ev s owner ( or , user ) at a price @xmath1 to the user where the user will be able to charge at least @xmath2 units of energy within the deadline @xmath3 for completion , and the battery usage will be limited to @xmath4 amount . the battery usage is the total amount of charging and discharging of the ev . the user either accepts one of the contracts by paying the specified price or rejects all of those based on its payoff . we assume that the user gets a utility for consuming @xmath2 amount of energy within the deadline @xmath3 . however , the user also has to incur a cost for battery utilization @xmath5 . the payoff of the user ( or , user s surplus ) for a contract is the difference between the utility and the sum of the cost incurred , and the price to be paid for the contract . the user will select the option which fetches the highest payoff . the various advantages of the above pricing scheme should be noted . first , it is an online pricing scheme . it can be adapted for each arriving user . second , since the charging station offers prices for different levels of charging required and the deadline , the charging station can prioritize one contract over the others depending on the energy resources available . third , the charging station also provides options of the maximum battery utilization to the users . the user who is not interested in the v2 g service is entitled to do that by selecting the contract with @xmath5 as @xmath6 . finally , the user s decision is much simplified . she only needs to select one of the contracts ( or , reject all ) . we consider that the charging station is equipped with renewable energy harvesting devices and a storage device for storing energies . the charging station may also buy conventional energy from the market to fulfill the contract of the user if required . hence , if a new user accepts the contract @xmath0 , a cost is incurred to the charging station . this cost may also depend on the existing evs and their resource requirements . a contract also specifies the maximum battery utilization which restricts the v2 g service generated from an ev . hence , the charging station needs to find the optimal cost for each contract . we show that obtaining the cost of fulfilling a contract is a _ linear programming _ problem . we also show that if a user accepts a contract with a higher battery utilization , the cost of the contract is lower ( lemma 1 ) . we consider two optimization problems i ) social welfare maximization , and ii ) the ev charging station s profit maximization . we investigate the existence of a pricing mechanism which maximizes the ex - post social welfare , _ i.e. _ , maximizes the social welfare for every possible realization of the utility function . we show that there exists such a pricing strategy . the pricing scheme is simple to compute , as the charging station selects a price which is equal to the marginal cost for fulfilling a certain contract for a new user ( theorem [ thm : max_socv2 g ] ) . however , the above pricing scheme only provides _ zero _ profit to the charging stations . thus , such a pricing scheme may not be useful to the charging station . we show that when a charging station is _ clairvoyant _ ( i.e. , the primary knows the utilities of the users ) , there exists a pricing scheme which satisfies both the objectives ( lemma [ thm : profit_max ] ) . though in the above pricing mechanism , the user s surplus becomes @xmath6 . a _ clairvoyant _ charging station may not be beneficial for the user s surplus . in the scenario where the charging station does not know the exact utilities of the users , we show that _ there may not exist a pricing strategy which simultaneously maximizes the ex - post social welfare and the expected profit_. one has to give away the ex - post social welfare maximization in order to achieve expected profit maximization . _ however , the user s surplus becomes higher compared to the clairvoyant scenario_. hence , an uncertainty of the utility enhances the user s surplus . we propose a pricing strategy which can fetch the highest possible profit to the charging station under the condition that it maximizes the ex - post social welfare ( theorem [ thm : profitmax_uncertainty ] ) . above pricing strategy provides a _ worst case _ maximum profit to the charging station . since the above pricing strategy may not yield the _ maximum expected _ profit to the charging station , we have to relax the constraint the social welfare to be maximized in order to yield a higher profit to the charging station . whether a contract will be selected by the user does not depend on the price of the contract , but also , the prices of other contracts . thus , achieving a pricing scheme which maximizes the expected profit is difficult because of the discontinuous nature of the profits . we propose a pricing strategy which yields a fixed ( say @xmath7 ) amount of profit to the charging station . further , we show that a suitable choice of @xmath7 can maximize the profit of the charging station for a class of utility functions ( theorem [ thm : aclassutility ] ) . in section [ sec : v2g_profitability ] we characterize the conditions which will yield higher profits to the charging station in the v2 g service . we show that if the conventional energy price is high , the charging station selects more preferable prices for enticing v2 g services if the renewable energy harvested is low . when the charging station s storage capacity is low and the renewable energy harvesting is low , the user s incentives for the v2 g service also increases . the v2 g service also increases the profit of the charging station . finally , we , empirically provide insights how a trade - off between the profit of the charging station and the social welfare can be achieved for various pricing schemes ( section [ sec : simulation_results ] ) . our numerical analysis shows that both the user s surplus and the charging station s profit increase with the v2 g service . the energy consumption during the peak period decreases as users provide more v2 g services during the peak period . charging schedule for evs using price signals for _ unidirectional _ service have been considered@xcite . the above papers did not consider the optimal discharging schedule of the evs as these papers only considered unidirectional power flow . as a result , these paper did not consider the battery degradation cost incurred in the v2 g service . few papers considered the _ bidirectional _ power flow @xcite . however , their focus was scheduling of the charging and discharging pattern of the evs , rather than the pricing aspects . naturally , these papers did not consider whether users will prefer the amount of battery degradation found in the optimal scheduling process . the social welfare maximizing and profit maximizing prices are also not considered . @xcite considered the optimal pricing to the evs in a day - ahead setting for residential charging . the users control the charging and discharging pattern at each instance for the price selected by the aggregator in a pre - specified manner . however , the users can arrive randomly in the charging station , the charging station needs to select a price for each arriving user using an online algorithm . the users can not control the charging and discharging schedule at each instance in the charging station . compared to _ all _ the above papers , in our approach , the charging station specifies the amount of battery utilization for each contract . the charging station also selects prices for different deadlines in our approach . hence , the user can now choose its own deadline and can specify the v2 g service it is willing to commit based on its own need . deadline differentiated prices have been considered @xcite . in our previous work @xcite , we also considered a menu - based pricing scheme where the charging station provides prices for different deadlines and prices to the new user . however , the above papers did not consider the _ bidirectional _ power flow problem . thus , in this setting the charging station now also needs to select different prices for different amounts of battery utilization . _ to the best of our knowledge , this is the first attempt to consider menu - based pricing which considered the bidirectional power flow from the evs . _ further , this is the first work that incentivizes the users to participate in the v2 g service by finding optimal prices for different amounts of battery degradation while maximizing the social welfare or profit of the charging station .

the paper considers a bidirectional power flow model of the electric vehicles ( evs ) in a charging station . the evs can inject energies by discharging via a vehicle - to - grid ( v2 g ) service which can enhance the profits of the charging station . however , frequent charging and discharging degrade battery life . the user can accept one of the contracts or rejects all depending on their utilities . we propose a pricing strategy which provides a guaranteed fixed profit to the charging station and it also maximizes the expected profit for a wide range of utility functions . our analysis shows that when the harvested renewable energy is small the users have higher incentives for the v2 g service . we , numerically , show that the charging station s profit and the user s surplus both increase as v2 g service is efficiently utilized by the pricing mechanism .

the paper considers a bidirectional power flow model of the electric vehicles ( evs ) in a charging station . the evs can inject energies by discharging via a vehicle - to - grid ( v2 g ) service which can enhance the profits of the charging station . however , frequent charging and discharging degrade battery life . a proper compensation needs to be paid to the users to participate in the v2 g service . we propose a menu - based pricing scheme , where the charging station selects a price for each arriving user for the amount of battery utilization , the total energy , and the time ( deadline ) that the ev will stay . the user can accept one of the contracts or rejects all depending on their utilities . the charging station can serve users using a combination of the renewable energy and the conventional energy bought from the grid . we show that though there exists a profit maximizing price which maximizes the social welfare , it provides no surplus to the users if the charging station is aware of the utilities of the users . if the charging station is not aware of the exact utilities , the social welfare maximizing price may not maximize the expected profit . in fact , it can give a zero profit . we propose a pricing strategy which provides a guaranteed fixed profit to the charging station and it also maximizes the expected profit for a wide range of utility functions . our analysis shows that when the harvested renewable energy is small the users have higher incentives for the v2 g service . we , numerically , show that the charging station s profit and the user s surplus both increase as v2 g service is efficiently utilized by the pricing mechanism .

1612.00106

c

this paper proposed a menu - based pricing approach for v2 g service where the charging station selects prices to the arriving users for different charging amounts , additional amount of battery utilization , and the deadline . the user either selects one of the contracts or rejects all based on her utility function . when the charging station is aware of the utilities , there exists a profit maximizing pricing strategy which can also maximize the social welfare , however , it provides zero user s surplus . however , when the charging station is not aware of the utilities there is _ no _ profit maximizer pricing strategy which can maximize the ex - post social welfare . this paper also considered a pricing strategy which gives a fixed positive profit to the charging station irrespective of the contract chosen . the conditions where the users have incentives to participate in the v2 g service are characterized , and it is seen that the v2 g service is more preferable when the harvested energy is low , and the storage capacity of the charging station is low . this work can be extended in several directions . for example , the characterization of the optimal price in the non - myopic setting remain open . this paper considered a fixed price for selling the energy to the grid . the optimal price that the grid should set to enhance the v2 g service or reduce the peak consumption constitutes a future research direction . e. sortomme , m. m. hindi , s. d. j. macpherson , and s. s. venkata , `` coordinated charging of plug - in hybrid electric vehicles to minimize distribution system losses , '' _ ieee transactions on smart grid _ , vol . 2 , no . 1 , pp . 198205 , march 2011 . m. alizadeh , h. t. wai , m. chowdhury , a. goldsmith , a. scaglione , and t. javidi , `` optimal pricing to manage electric vehicles in coupled power and transportation networks , '' _ ieee transactions on control of network systems _ , vol . pp , no . 99 , pp . 11 , 2016 . j. xu and v. w. s. wong , `` an approximate dynamic programming approach for coordinated charging control at vehicle - to - grid aggregator , '' in _ smart grid communications ( smartgridcomm ) , 2011 ieee international conference on _ , oct 2011 , pp . 279284 . h. xing , m. fu , z. lin , and y. mou , `` decentralized optimal scheduling for charging and discharging of plug - in electric vehicles in smart grids , '' _ ieee transactions on power systems _ , vol . 31 , no . 5 , pp . 41184127 , sept 2016 . b. g. kim , s. ren , m. van der schaar , and j. w. lee , `` bidirectional energy trading and residential load scheduling with electric vehicles in the smart grid , '' _ ieee journal on selected areas in communications _ , vol . 31 , no . 7 , pp . 12191234 , july 2013 . a. nayyar , m. negrete - pincetic , k. poolla , and p. varaiya , `` duration - differentiated energy services with a continuum of loads , '' _ corr _ , vol . abs/1408.5825 , 2014 . [ online ] . available : http://arxiv.org/abs/1408.5825 a.ghosh and v.aggarwal , `` control of charging of electric vehicles through menu based pricing , '' 2016 . [ online ] . available : http://arxiv.org/abs/1609.09037 m. a. delucchi and t. e. lipman , `` an analysis of the retail and lifecycle cost of battery - powered electric vehicles , '' _ transportation research part d : transport and environment _ , vol . 6 , no . 6 , pp . 371 404 , 2001 . c. zhou , k. qian , m. allan , and w. zhou , `` modeling of the cost of ev battery wear due to v2 g application in power systems , '' _ ieee transactions on energy conversion _ , 26 , no . 4 , pp . 10411050 , dec 2011 . w. shuai , p. maill , and a. pelov , `` charging electric vehicles in the smart city : a survey of economy - driven approaches , '' _ corr _ , vol . abs/1601.03925 , 2016 . [ online ] . available : http://arxiv.org/abs/1601.03925 l. gan , u. topcu , and s. h. low , `` optimal decentralized protocol for electric vehicle charging , '' _ ieee transactions on power systems _ , vol . 28 , no . 2 , pp . 940951 , may 2013 . `` evaluating electric vehicle charging impacts and customer charging behaviors- experiences from six smart grid investment grant projects , '' https://www.smartgrid.gov/files/b3_revised_master-12-17-2014_report.pdf , december , 2014 . now , since @xmath209 , and @xmath210 , thus , @xmath211 . thus , @xmath212 . hence , @xmath213 the other constraints are independent of @xmath214 , hence , it will be feasible . thus , with the modified @xmath215 , @xmath216 , and @xmath217 , with the other unchanged solution the value of the optimization problem is _ lower_. hence , this leads to a contradiction . now , we show that @xmath28 in an optimal solution of ( [ eq : vlt ] ) . suppose that in an optimal solution we have @xmath218 and @xmath219 for some @xmath29 and @xmath3 . now , consider the following modification for each @xmath29 . @xmath220 note that because of the above modification @xmath221 hence , the constraints in ( [ eq : charged ] ) , ( [ eq : chargeeachev ] ) , ( [ eq : dischargelimit ] ) , ( [ eq : limit ] ) , ( [ eq : battery_utilization ] ) are satisfied for this modified solution . now , consider the following @xmath222 since @xmath223 , and @xmath224 for all @xmath29 and @xmath225 for at least index @xmath30 , thus , @xmath226 . thus , if @xmath227 and @xmath228 are modified as follows @xmath229 then the constraints in ( [ eq : battery_capacity ] ) , ( [ eq : battery_level ] ) are also satisfied when the rest of the solution are unchanged . however , the cost decreases as @xmath230 with the modified values of @xmath231 , @xmath232 , @xmath233 . this contradicts that @xmath234 are optimal . hence , the result follows . the above theorem also shows the transformation of the optimal solution requires to get @xmath53 ( cf.([eq : transformse ] ) , ( [ eq : lowervaluee ] ) ) and @xmath28 ( cf.([eq : transformr ] ) , ( [ eq : transformrtch ] ) , ( [ eq : lowervaluer ] ) ) in case if @xmath235 are bounded . the modified solution will still be bounded . suppose the statement is false . without loss of generality , assume that @xmath236 where @xmath237 for some @xmath5 , @xmath2 and @xmath3 achieves a strictly higher expected payoff than the pricing strategy @xmath238 . the expected profit of the charging station for pricing strategy @xmath236 is given by @xmath239 now , we evaluate the expression @xmath240 . the user @xmath8 will select the menu @xmath10 with a positive probability if @xmath241 and for every @xmath242 , @xmath243 since @xmath244 are fixed , hence , the above inequality is either satisfied or not satisfied with probability @xmath135 . more specifically , the user selects the menu @xmath0 if @xmath241 and @xmath245 without loss of generality , assume that @xmath246 be the maximum value for which the above inequality is satisfied i.e. @xmath247 the random variable @xmath152 only affects the probability whether @xmath248 or not . hence , the charging station s expected profit is upper bounded by @xmath249 note that by the definition of @xmath147 ( definition [ defn : alpha ] ) , @xmath250 however by theorem [ thm : expected_payoff ] the expected payoff of the charging station when it selects the price @xmath251 is given by the expression in the left - hand side of the inequality in ( [ eq : compare ] ) . hence , this leads to a contradiction . thus , the result follows .

we propose a menu - based pricing scheme , where the charging station selects a price for each arriving user for the amount of battery utilization , the total energy , and the time ( deadline ) that the ev will stay . the charging station can serve users using a combination of the renewable energy and the conventional energy bought from the grid . we show that though there exists a profit maximizing price which maximizes the social welfare , it provides no surplus to the users if the charging station is aware of the utilities of the users .

the paper considers a bidirectional power flow model of the electric vehicles ( evs ) in a charging station . the evs can inject energies by discharging via a vehicle - to - grid ( v2 g ) service which can enhance the profits of the charging station . however , frequent charging and discharging degrade battery life . a proper compensation needs to be paid to the users to participate in the v2 g service . we propose a menu - based pricing scheme , where the charging station selects a price for each arriving user for the amount of battery utilization , the total energy , and the time ( deadline ) that the ev will stay . the user can accept one of the contracts or rejects all depending on their utilities . the charging station can serve users using a combination of the renewable energy and the conventional energy bought from the grid . we show that though there exists a profit maximizing price which maximizes the social welfare , it provides no surplus to the users if the charging station is aware of the utilities of the users . if the charging station is not aware of the exact utilities , the social welfare maximizing price may not maximize the expected profit . in fact , it can give a zero profit . we propose a pricing strategy which provides a guaranteed fixed profit to the charging station and it also maximizes the expected profit for a wide range of utility functions . our analysis shows that when the harvested renewable energy is small the users have higher incentives for the v2 g service . we , numerically , show that the charging station s profit and the user s surplus both increase as v2 g service is efficiently utilized by the pricing mechanism .

1208.6478

i

contact problems of elasticity are widely used in many fields of science and engineering , especially in machine science , structural mechanics , geology and biomechanics . the brief overview of existing numerical and analytical methods for the solution of contact problems can be found in @xcite . efficient approach to the solution of multibody contact problems is the use of domain decomposition methods ( ddms ) . ddms are well developed for the solution of linear boundary value problems , particularly for linear poisson and linear elasticity problems @xcite . the construction of ddms for unilateral contact problems , which are nonlinear , are much more complicated . among domain decomposition methods for unilateral two - body contact problems obtained on continuous level , one should mention signorini neumann @xcite , signorini dirichlet @xcite and signorini signorini @xcite iterative algorithms . all of these methods in each iteration require to solve a nonlinear one - sided contact problem with a rigid surface ( signorini problem ) for one of the bodies , and a linear elasticity problem with neumann @xcite or dirichlet @xcite boundary conditions on possible contact area for other body , or require to solve nonlinear signorini problems for both of the bodies @xcite . moreover , to increase the convergence rate of signorini dirichlet and signorini signorini algorithms , it is recommended to perform an additional iteration , in which we have to solve linear elasticity problems with neumann boundary conditions for both of the bodies @xcite . domain decomposition method presented in work @xcite for two - body unilateral contact problem , is also obtained on continuous level . it is based on the use of augmented lagrangian variational formulation and uzawa block relaxation method . this domain decomposition method in each iteration require to solve linear elasticity problems for both of the bodies . on contrary , ddms can be constructed on discrete level , after a discretization of corresponding continuous boundary - value problem . among discrete ddms for unilateral contact problems , one should mark out substructuring and feti methods @xcite . in works @xcite we have proposed on continuous level a class of penalty parallel robin robin type domain decomposition methods for the solution of unilateral multibody contact problems of elasticity . these methods are based on penalty method for variational inequalities and some stationary and nonstationary iterative methods for nonlinear variational equations . in each iteration of proposed ddms we have to solve in parallel some linear variational equations in subdomains , which correspond to elasticity problems with robin boundary conditions , prescribed on some subareas of possible contact zones . these ddms do not require the solution of nonlinear one - sided contact problems in each step . the main result of this paper is that we have proved theorems about convergence of proposed penalty robin robin domain decomposition methods . the paper is organized as follows . in section 2 the classical formulation of multibody contact problem in the form of the system of second order elliptic partial differential equations with inequality and equality constrains is given . in section 3 we consider the variational formulation of this problem in the form of convex minimization problem and in the form of elliptic variational inequality at closed convex set , and formulate theorem about a unique existence of the solution of this inequality . in section 4 we use the penalty method to reduce the variational inequality to an unconstrained minimization problem , which is equivalent to a nonlinear variational equation in the whole space . later , we prove a theorem about a unique existence of the solution of the penalty variational equation and a theorem about strong convergence of this solution to the solution of initial variational inequality . in section 5 we consider stationary and nonstationary iterative methods for the solution of abstract nonlinear variational equations in reflexive banach spaces . we prove theorems about convergence of these methods , and show that the convergence rate of stationary methods in some energy norm is linear . we also prove theorem about stability of stationary iterative methods to errors which may occur in each iteration . in section 6 we present parallel stationary and nonstationary penalty robin robin domain decomposition methods for the solution of nonlinear penalty variational equations of multibody unilateral contact problems . we prove theorem about convergence of these methods , and show that the convergence rate of stationary robin robin methods in some energy norm is linear . in section 7 we provide numerical investigations of proposed domain decomposition methods using finite element approximations . the penalty parameter and mesh refinement influence on the numerical solution , as well as the dependence of the convergence rate of domain decomposition methods on iterative parameters are investigated . in conclusion section we summarize all results presented in the paper .

the paper is devoted to penalty robin robin domain decomposition methods ( ddms ) , proposed by us for the solution of unilateral multibody contact problems of elasticity . these ddms are based on the penalty method for variational inequalities and some stationary and nonstationary iterative methods for nonlinear variational equations . the main result of the paper is that we give mathematical justification of proposed ddms and prove theorems about their convergence . we also provide numerical investigations of the efficiency of these methods using finite element approximations .

the paper is devoted to penalty robin robin domain decomposition methods ( ddms ) , proposed by us for the solution of unilateral multibody contact problems of elasticity . these ddms are based on the penalty method for variational inequalities and some stationary and nonstationary iterative methods for nonlinear variational equations . the main result of the paper is that we give mathematical justification of proposed ddms and prove theorems about their convergence . we also provide numerical investigations of the efficiency of these methods using finite element approximations . * key words : * elasticity , multibody contact , variational inequalities , penalty method , iterative methods , domain decomposition * msc2010 : * 65n55 , 74s05

1609.02638

i

from motion ( sfm ) is the process to find three - dimensional ( 3d ) structure and camera motion parameters from a set of 2d image sequences . the classical method for 3d reconstruction is stereo vision using two or three images @xcite . stereo vision , due to limited information , is sensitive to image noise . given a sequence of images , structure from motion is a powerful method to build a consistent 3d map with the knowledge of multiple - view geometry . over the past two to three decades , tremendous progress has been made in sfm @xcite@xcite@xcite@xcite@xcite , the results of this research have a wide range of potential applications , including robot navigation and obstacle avoidance , autonomous driving , video surveillance , and environment modeling . structure and motion factorization algorithm , pioneered by tomasi and kanade @xcite , is an effective approach for sfm . based on a bilinear formulation using singular value decomposition ( svd ) with low - rank approximation , the method decomposes image measurement directly into the 3d structure and the camera motion components , given a set of tracked features across the sequence . by dealing uniformly with the data from all images , the algorithm achieves a more robust and more accurate solution than stereo vision - based methods @xcite@xcite@xcite@xcite . a linear affine camera has been adopted by most research in sfm due to its simplicity @xcite . it was extended to a more accurate nonlinear perspective camera model in @xcite by incrementally performing the affine factorization of a scaled tracking matrix . triggs @xcite proposed a full projective factorization algorithm with projective depths recovered from epipolar geometry . the method was further studied and different iterative schemes were proposed to recover the projective depths by minimizing image reprojection errors @xcite . oliensis and hartley @xcite provided a complete theoretical convergence analysis for the iterative extensions . because full perspective model is computational intensive , a quasi - perspective model was proposed in @xcite as a trade - off of efficiency and accuracy . by assuming deformation constraints that the nonrigid 3d structure lies in a span of rigid bases , the factorization algorithm was extended to handle nonrigid deformation @xcite , where the shape bases , combination coefficients , and camera motions are solved simultaneously in a svd framwork . this idea has been extensively investigated and developed in @xcite@xcite@xcite@xcite . a manifold - learning framework was proposed in @xcite to relax the deformation assumption . @xcite proposed a sequential approach for nonrigid sfm . yan and pollefeys @xcite developed a similar factorization framework to recover the structure and motion of articulated objects . in a dual trajectory space , @xcite proposed a duality solution to this problem based on basis trajectories . most factorization algorithms are based on the svd decomposition of the tracking matrix composed by all features tracked across the sequence . in the presence of missing data , however , svd factorization could not be performed directly . different alternative factorization approaches have been proposed to handle incomplete data , such as power factorization @xcite , alternative factorization @xcite , and factor analysis @xcite . in practical application , the tracked features are usually corrupted by outliers or larger errors , in this case , most algorithms will degrade or even fail . the most popular strategies to handle outliers are random sample consensus ( ransac ) @xcite and its variations , least median of squares ( lmeds ) @xcite , and other similar framework based on hypothesis - and - test @xcite . most of these methods are computational intensive and only work well for two or three views . in recent years , some robust structure and motion factorization algorithms have been proposed @xcite@xcite@xcite@xcite . a scalar - weighted svd algorithm was proposed by aguitar and moura @xcite through minimizing weighted square errors . gruber and weiss @xcite enhanced the robustness to missing data and uncertainties using a factor analysis in an expectation maximization ( em ) framework . zelnik - manor _ @xcite defined a new type of motion consistency based on temporal consistency , and applied it to multi - body factorization with directional uncertainty . a gaussian mixture model with the em algorithm was introduced by zaharescu and horaud @xcite . @xcite proposed to correct the outliers with pseudo observations through iterations . ke and kanade @xcite dealt the outliers by minimizing a l1 norm of the reprojection errors . eriksson and hengel @xcite utilized the l1 norm to the wiberg algorithm to handle missing and outlying features . alternatively , okatani _ @xcite solved the problem by introducing a damping factor into the wiberg algorithm . more recently , yu _ @xcite presented a quadratic program formulation for robust multi - model fitting of geometric structures . @xcite proposed an adaptive kernel - scale weighted hypotheses to segment multiple - structure data with a large number of outliers . an alternating bilinear approach was proposed by paladini _ _ @xcite to solve nonrigid structure from motion by introducing a globally optimal projection step of the motion matrices onto the manifold of metric constraints . _ @xcite designed a spatial - and - temporal - weighted factorization algorithm to deal with significant noise in the measurement . @xcite developed an optimal approach based on branch - and - bound . in this paper , by exploring the fact that the reprojection residuals are in general proportional to measurement errors of the tracking data , we propose to handle the outlying data through a new viewpoint via the distribution of image reprojection residuals . the proposed approach is based on a new augmented factorization formulation , which circumvents the problem of image registration in the presence of missing data and outliers . an alternative weighted factorization algorithm is developed to handle the missing data and measurement uncertainties . finally , a robust factorization scheme is proposed to handle outlying and missing data in both rigid @xcite and nonrigid @xcite structure and motion recovery . in addition , the proposed scheme can be directly applied to handle nonrigid structure and motion factorization . the remainder of this paper is organized as follows . some background on affine factorization is offered in section [ sec : background ] . the augmented factorization algorithm is elaborated in section [ sec : rank4 ] . section [ sec : pf ] presents the alternative factorization algorithm for incomplete data . an outlier detection scheme and the robust factorization algorithm are discussed in section [ sec : outliers ] . section [ sec : nonrigid ] discusses the extension to nonrigid factorization . experimental evaluations and comparisons on synthetic and real images are described in sections [ sec : experiment1 ] and [ sec : experiment2 ] , respectively . finally , a short conclusion is drawn in section [ sec : conclusions ] .

the paper preposes a new scheme to promote the robustness of 3d structure and motion factorization from uncalibrated image sequences . first , an augmented affine factorization algorithm is proposed to circumvent the difficulty in image registration with imperfect data . then , an alternative weighted factorization algorithm is designed to handle the missing data and measurement uncertainties in the tracking matrix . finally , a robust structure and motion factorization scheme is proposed to deal with outlying and missing data .

the paper preposes a new scheme to promote the robustness of 3d structure and motion factorization from uncalibrated image sequences . first , an augmented affine factorization algorithm is proposed to circumvent the difficulty in image registration with imperfect data . then , an alternative weighted factorization algorithm is designed to handle the missing data and measurement uncertainties in the tracking matrix . finally , a robust structure and motion factorization scheme is proposed to deal with outlying and missing data . the novelty and main contribution of the paper are as follows : ( i ) the augmented factorization algorithm is a new addition to previous affine factorization family for both rigid and nonrigid objects ; ( ii ) it is demonstrated that image reprojection residuals are in general proportional to the error magnitude in the tracking data , and thus , the outliers can be detected directly from the distribution of image reprojection residuals , which are then used to estimate the uncertainty of inlying measurement ; ( iii ) the robust factorization scheme is proved empirically to be more efficient and more accurate than other robust algorithms ; and ( iv ) the proposed approach can be directly applied to nonrigid scenarios . extensive experiments on synthetic data and real images demonstrate the advantages of the proposed approach . computer vision , structure from motion , robust factorization , weighted factorization , reprojection residual , outlier detection .

cond-mat0505148

i

lanthanide based heavy fermion ( hf ) metals constitute a major , long studied class of correlated electron materials @xcite . their behaviour is quite distinct from conventional clean metals , the basic physics being driven by strong spin - flip scattering from essentially localised @xmath3-levels , generating the large effective mass and attendant low - energy scale indicative of strong interactions . the low - temperature ( @xmath4 ) state is a lattice - coherent fermi liquid with well defined quasiparticles and coherently screened @xmath3-spins , crossing over with increasing @xmath4 to essentially incoherent screening via independent kondo scattering , before attaining characteristic clean metallic behaviour . physical properties of hf are in consequence typically ` anomalous ' : e.g. the resistivity @xmath5 shows a strong non - monotonic @xmath4-dependence , while optics often exhibit rich structure from the microwave to the near infrared , and pronounced evolution on low temperature scales @xcite . theoretical treatments of hf centre on the periodic anderson model ( pam ) , in which a non - interacting conduction band hybridizes locally with a correlated @xmath3-level in each unit cell of the lattice ; or on its strong coupling limit , the kondo lattice model . the absence of exact results ( save for some in one dimension , see e.g. @xcite ) has long spurred the search for suitable approximation schemes . one such framework , which has had a major impact in recent years , is provided by dynamical mean field theory ( dmft , for reviews see @xcite ) . formally exact in the large - dimensional limit , the self - energy within dmft becomes momentum independent and hence spatially local , but still retains full temporal dynamics ; such that all lattice models map onto an effective single - impurity model with a self - consistently determined host @xcite . that raises an immediate question , easier asked than answered : to what extent are the properties of real hf materials captured within a dmft approach to the pam ? to answer this clearly requires direct quantitative comparsion of theory to experiment . and a prerequisite to that in turn is a method to solve the pam which dmft does not _ per se _ provide . the latter has of course been studied extensively using a wide variety of techniques . full scale numerical methods include the numerical renormalization group ( nrg ) @xcite , quantum monte carlo @xcite and exact diagonalization @xcite , while theoretical approaches encompass finite - order perturbation theory in the interaction @xmath6 @xcite , iterated perturbation theory @xcite , the lattice non - crossing approximation @xcite and the average @xmath7-matrix approximation @xcite , large-@xmath8 mean - field theory / slave bosons @xcite , the gutzwiller variational approach @xcite and the recently developed local moment approach @xcite . all of these methods naturally have their own virtues . but most possess significant , well known limitations @xcite , be it the general inability of perturbative approaches ( and in practice quantum monto carlo ) to handle strong interactions ; failure to recover fermi liquid behaviour at low - energies as arises in nca - based approaches , restriction to the lowest - energy fermi liquid behaviour as in large-@xmath8/slave boson mean - field theories , finite - size effects limiting exact diagonalization , and so on . to enable viable comparison to experiment requires an approach that can adequately handle all experimentally relevant energy and/or temperature scales in the strongly correlated hf regime of primary interest ; and indeed ideally also across the full spectrum of interaction strengths , such that intermediate valence and related behaviour can likewise be treated . one such is employed here , the local moment approach ( lma ) @xcite . via study of the generic asymmetric pam , our essential aims are ( i ) to provide a many - body description of dynamical and transport properties of paramagnetic hf , notably single - particle dynamics , d.c . transport and optical conductivities ; as considered here . ( ii ) to make direct quantitative comparison with experiment . that is taken up in the following paper where comparison to transport / optical properties of @xmath9 , @xmath10 , @xmath11 and @xmath12 is made . some remarks on the lma are apposite at this point since the paper will focus mainly on results obtained using the approach , with minimal technical details . intrinsically non - perturbative and as such capable of handling strong interactions , the lma @xcite introduces the physically intuitive notion of local moments @xcite from the outset . this leads directly to a ` two - self - energy ' description in which , post mean - field level , the key correlated spin - flip dynamics is readily captured ; corresponding in physical terms to dynamical tunneling between initially degenerate local moment configurations , which lifts the erstwhile spin degeneracy and restores the local singlet symmetry characteristic of a fermi liquid state . as with all techniques for lattice models within dmft , the lma originated in study of the single - impurity anderson model ( aim ) @xcite , where results for dynamics are known to give good agreement with nrg calculations @xcite , and for static magnetic properties with known exact results @xcite the approach has recently been developed to encompass the anderson lattice ( pam ) ; initially for the particle - hole symmetric limit @xcite appropriate to the kondo insulating sub - class of heavy electron materials , where for all interaction strengths the system is an ` insulating fermi liquid ' that evolves continuously from its simple non - interacting limit of a hybridization - gap insulator @xcite . from this a rich description of transport and optical properties of kondo insulators arises @xcite , particularly in strong coupling where the system is characterized by an exponentially small indirect gap scale @xmath13 , such that dynamics / transport exhibit scaling as functions of @xmath14 . exploiting that scaling enables direct comparison to experiment with minimal use of ` bare ' material / model parameters ; and in particular for three classic kondo insulators @xmath15 , @xmath16 and @xmath17 , leads to what we regard as excellent agreement between theory and experiment on essentially all relevant energy and temperature scales @xcite . the particle - hole symmetric pam is of course special , confined as it is to the case of kondo insulators . most recently the lma has been non - trivially extended to handle the generic asymmetric pam @xcite and hence hf metals ( with the insulating symmetric limit recovered simply as a particular case ) . single - particle dynamics at @xmath18 were considered in @xcite , with a natural emphasis on the strongly correlated kondo lattice regime of localised @xmath3-electrons but general conduction ( ` @xmath19 ' ) band filling @xmath20 . the problem was found to be characterized by a _ single _ low - energy coherence scale @xmath1 the precise counterpart of the insulating indirect gap scale @xmath21 , and likewise exponentially small in strong coupling in terms of which dynamics exhibit one - parameter universal scaling as a function of @xmath22 , independently of either the interaction strength or local @xmath23 hybridization . with increasing @xmath24 dynamics cross over from the low - energy quasiparticle behaviour required by and symptomatic of the coherent fermi liquid state , to essentially incoherent single - impurity kondo scaling physics at high-@xmath24 but still in the @xmath24-scaling regime and as such incompatible @xcite with a two - scale ` exhaustion ' scenario @xcite . in this paper we extend the work of @xcite to finite temperature , thereby enabling access to d.c . transport and optics . our primary focus is again the strongly correlated hf regime and attendant issues of scaling / universality ( that play a key role in comparing to experiment ) , the paper being organised as follows . the model and a bare bones description of background theory is introduced in section 2 , together with preliminary consideration of transport / optics . results for the thermal evolution of single - particle dynamics and scattering rates , and the connection between the two , are given in section 3 . the d.c . resistivity is considered in section 4 , with particular emphasis in this context on the crossover from the low-@xmath25 coherent fermi liquid to the high-@xmath26 incoherent regime , and explicit connection to single - impurity scaling behaviour . optical conductivities on all relevant @xmath27- and @xmath4-scales are investigated in section 5 ; and the paper concludes with a brief summary .

the paramagnetic phase of heavy fermion systems is investigated , using a non - perturbative local moment approach to the asymmetric periodic anderson model within the framework of dynamical mean field theory . transport and optics are found to exhibit scaling in terms of a single underlying low - energy coherence scale .

the paramagnetic phase of heavy fermion systems is investigated , using a non - perturbative local moment approach to the asymmetric periodic anderson model within the framework of dynamical mean field theory . the natural focus is on the strong coupling kondo - lattice regime wherein single - particle spectra , scattering rates , d.c . transport and optics are found to exhibit scaling in terms of a single underlying low - energy coherence scale . dynamics / transport on all relevant ()-scales are encompassed , from the low - energy behaviour characteristic of the lattice coherent fermi liquid , through incoherent effective single - impurity physics likewise found to arise in the universal scaling regime , to non - universal high - energy scales ; and which description in turn enables viable quantitative comparison to experiment .

cond-mat0505148

c

we have considered here the periodic anderson lattice , the canonical model for understanding heavy fermion metals , kondo insulators , intermediate valence and related materials . optical conductivities , d.c . transport and single - particle dynamics of the paramagnetic phase have been investigated , using the local moment approach within a dmft framework . for obvious physical reasons our main focus has been the strongly correlated kondo lattice regime , where we find the problem to be characterised by a single , exponentially small coherence scale @xmath1 ; in terms of which the frequency and temperature dependence of physical properties scale being universally dependent on @xmath344 and/or @xmath25 regardless of the interaction or hybridization strengths . all relevant energy / temperature scales are handled by the theory , from the low - energy coherent fermi liquid domain out to large ( and in the strict scaling limit arbitrarily large ) multiples of @xmath1 where incoherent many - body scattering dominates the physics ; followed by the crossover out of the scaling regime to non - universal , high energy / temperature scales dictated by ` bare ' model / material parameters . and while our emphasis has been on strong correlations we add that all interaction strengths from weak to strong coupling are encompassed by the lma @xcite , such that intermediate valence behaviour in particular can also be addressed . the first question posed in the introduction nonetheless remains : to what extent does the model , and our theory for it , capture experiment ? we turn to that in the following paper where direct comparison of theory and experiment is made for three heavy fermion materials and a classic intermediate valence compound . we are grateful to the epsrc for supporting this research .

dynamics / transport on all relevant ()-scales are encompassed , from the low - energy behaviour characteristic of the lattice coherent fermi liquid , through incoherent effective single - impurity physics likewise found to arise in the universal scaling regime , to non - universal high - energy scales ; and which description in turn enables viable quantitative comparison to experiment .

the paramagnetic phase of heavy fermion systems is investigated , using a non - perturbative local moment approach to the asymmetric periodic anderson model within the framework of dynamical mean field theory . the natural focus is on the strong coupling kondo - lattice regime wherein single - particle spectra , scattering rates , d.c . transport and optics are found to exhibit scaling in terms of a single underlying low - energy coherence scale . dynamics / transport on all relevant ()-scales are encompassed , from the low - energy behaviour characteristic of the lattice coherent fermi liquid , through incoherent effective single - impurity physics likewise found to arise in the universal scaling regime , to non - universal high - energy scales ; and which description in turn enables viable quantitative comparison to experiment .

gr-qc0112002

i

spin foam models have been proposed as candidates for a quantum theory of space - time geometry @xcite and therefore form candidates for a quantum theory of gravity . spin foam models also play a central role in the construction of invariants of piecewise - linear three- and four - manifolds @xcite . they arise as the models that are strong - weak dual to non - abelian lattice gauge theory @xcite and form a possible starting point for the generalization of gauge theories from lie groups to quantum groups @xcite . for reviews on the subject , see , for example @xcite . a spin foam @xcite whose symmetry group is a compact lie group @xmath6 , is an abstract oriented @xmath5-complex consisting of faces , edges and vertices , together with a colouring of the faces with representations of @xmath6 and a colouring of the edges with compatible intertwiners ( representation morphisms ) of @xmath6 . a spin foam model is a discrete model in the framework of statistical mechanics whose partition function is a sum over spin foams each of which is assigned a boltzmann weight . if the boltzmann weight factors into contributions for each vertex , edge and face , these factors are usually called vertex , edge and face amplitudes . barrett , crane and baez @xcite have developed a particular spin foam model whose partition function can be understood as the sum over all quantized euclidean geometries that can be assigned to a given triangulation of a four - manifold . the spin foam model is usually defined on the @xmath5-complex dual to that triangulation . several versions of this model are studied in the literature @xcite which differ in their boltzmann weights ( amplitudes ) , in particular in their edge amplitudes . some of the models are formulated on a fixed @xmath5-complex while others include a sum over @xmath5-complexes . in the following , we call all these models barrett crane models . in this article , we study a generalized version which encompasses all interesting choices of amplitudes , but we restrict ourselves to a fixed @xmath5-complex . the partition function of our model is a sum over all possible assignments of _ balanced _ irreducible representations of the lie group @xmath0 to the faces . the balanced representations are of the form @xmath7 where @xmath8 is an irreducible representation of @xmath9 . they are also called the _ simple _ representations . each edge is then assigned a unique intertwiner , the barrett crane intertwiner @xcite . we allow quite generic edge and face amplitudes , but the vertex amplitude is always the generalized @xmath10-symbol @xcite consisting of one barrett crane intertwiner for each edge attached to the vertex . we make use of the fact that the barrett crane intertwiner can be written in terms of an integral over the sphere @xmath2 @xcite and of the techniques familiar from the duality transformation for non - abelian lattice gauge theory @xcite and derive a dual expression for the partition function of the barrett crane model in which the fundamental variables are pairs of @xmath2-values associated to the edges . the partition sum is then given by an integral over @xmath2 for each of these variables . provided that the edge amplitude of the original model is of a particular form , the dual model has local interactions , its boltzmann weight factors into one contribution for each face , and it depends on the @xmath2-variables at the edges in the boundary of that face . this reformulation of the barrett crane model has the following geometric interpretation if the @xmath5-complex is chosen to be dual to a triangulation of a four - manifold . the @xmath2-variables are then associated to the tetrahedra . they parameterize the ( normalized ) normal vectors of the hyperplanes spanned by the tetrahedra where the tetrahedra are locally embedded in @xmath3 . the factorized boltzmann weight provides an interaction term for each triangle so that the interaction depends on the @xmath2-values associated to all tetrahedra that contain the triangle in their boundaries . however , there are two @xmath2-values associated to each tetrahedron one of which belongs to either one of the two four - simplices that contain the tetrahedron in their boundaries . this suggests that there exists an @xmath0-valued parallel transport along the tetrahedron which maps the first @xmath2-value to the second one . however , this parallel transport is defined only up to elements of @xmath0 that stabilize the first of the @xmath2-values . following this idea , we show that the barrett crane model can be obtained from @xmath0 lattice @xmath4-theory ( the @xmath0 ooguri model @xcite ) if we impose a constraint at the quantum level by averaging over this stabilizer in a suitable way . this means that of the @xmath0-valued parallel transport only the action of @xmath0 on @xmath2 is physically relevant . finally , we consider the boltzmann weight of the dual formulation of the barrett crane model and list possible face and edge amplitudes for which the partition function is well defined ( not just divergent ) . we outline how one can analyze this model in the context of statistical mechanics , for example in order to study its ground state and fluctuations around it . in addition , one can expect that the dual formulation of the barrett crane model is well suited for numerical studies . the present article is organized as follows . in section [ sect_prelim ] , we review some mathematical background material on the algebra of representation functions of a compact lie group , we construct the spherical functions of @xmath2 , and we introduce our notation for abstract @xmath5-complexes . the barrett crane model and @xmath0 lattice @xmath4-theory are introduced in section [ sect_bcmodel ] . in section [ sect_transform ] , we present the duality transformation for the barrett crane model in detail and show how this model is related to @xmath0 lattice @xmath4-theory subject to a suitable constraint . we also discuss its geometric interpretation and the possible choices of face and edge amplitudes . section [ sect_conclusion ] finally contains our concluding comments . note added : the barrett crane model is often understood as a path integral in the ` real time ' picture , using an integrand of the form @xmath11 for some action @xmath12 . however , baez and christensen @xcite have shown that for the common choices of edge amplitudes , the integrand of the partition function is always positive so that the path integral admits an interpretation in the framework of statistical mechanics in terms of probabilities . in this article , we use the language of statistical mechanics .

the partition function of the- or-symmetric euclidean barrett crane model can be understood as a sum over all quantized geometries of a given triangulation of a four - manifold . in the original formulation , we present an exact duality transformation for the full quantum theory and reformulate the model in terms of new variables which can be understood as variables conjugate to the quantized areas .

the partition function of the- or-symmetric euclidean barrett crane model can be understood as a sum over all quantized geometries of a given triangulation of a four - manifold . in the original formulation , the variables of the model are balanced representations of which describe the quantized areas of the triangles . we present an exact duality transformation for the full quantum theory and reformulate the model in terms of new variables which can be understood as variables conjugate to the quantized areas . the new variables are pairs of-values associated to the tetrahedra . these-variables parameterize the hyperplanes spanned by the tetrahedra ( locally embedded in ) , and the fact that there is a pair of variables for each tetrahedron can be viewed as a consequence of an-valued parallel transport along the edges dual to the tetrahedra . we reconstruct the parallel transport of which only the action of on is physically relevant and rewrite the barrett crane model as an lattice-theory living on the-complex dual to the triangulation subject to suitable constraints whose form we derive at the quantum level . our reformulation of the barrett crane model in terms of continuous variables is suitable for the application of various analytical and numerical techniques familiar from statistical mechanics .

1309.3957

i

following ( * ? ? ? * example 6.3 ) , consider the reaction network in the species @xmath0 and @xmath1 with the reactions @xmath2{\,k_1\ , } 2x , & & 2y \xrightleftharpoons[k_4]{\,k_3\ , } x\end{aligned}\ ] ] let @xmath3 represent concentrations at time @xmath4 of the species @xmath5 respectively . then * mass - action kinetics * is described by the system of ordinary differential equations @xmath6 does there exists a trajectory @xmath7 originating in the positive orthant ( i.e. , @xmath8 ) that can get arbitrarily close to the boundary @xmath9 as time @xmath10 ? that is , for each @xmath11 , does there exist a time @xmath12 such that the distance of @xmath13 from @xmath14 is less than @xmath15 ? the * persistence conjecture * @xcite asserts that so long as the reaction network is _ weakly - reversible _ ( definition [ def : rnprop ] ) , this can not happen . this conjecture has a history going back to 1974 @xcite . it remains open , even when all reactions are reversible , _ even for as few as @xmath16 species _ ! the @xmath17 species case was settled only very recently @xcite . the notion of * critical siphon * @xcite provides a powerful and easy combinatorial way of proving persistence for a certain subclass of networks . the idea is that the existence of a trajectory violating persistence has certain combinatorial implications , i.e. , the existence of critical siphons . conversely , the absence of critical siphons which can be combinatorially checked has dynamical implications , i.e. , persistence . for example , consider the following network in the species @xmath0 and @xmath1 with reactions given by @xmath18 this is persistent . the idea is that if @xmath0 were ever at zero concentration , it would be produced from nothing , and similarly for @xmath1 . only the first reaction @xmath19 matters for this analysis . the other reactions can be replaced arbitrarily , and so long as they remain reversible , we can prove persistence . the notion of _ siphon _ helps to make this idea into a proof . a siphon is a set of species that , once absent , remain absent . it turns out that reaction networks without siphons are persistent . another example is @xmath20 . here if @xmath0 and @xmath1 are both absent , they remain absent , so @xmath21 is a siphon . however , there is a conservation law : @xmath22 is time - invariant , because whenever an @xmath0 is destroyed , a @xmath1 is created , and vice versa . therefore , if the initial conditions are @xmath23 then the point @xmath24 where both @xmath0 and @xmath1 are absent is unreachable . the idea is that if there is a positive conservation law whose support is contained in a siphon then that siphon can not be drained . hence , among siphons , the challenge to persistence comes only from _ critical _ siphons , i.e. , siphons that do not contain the support of a positive conservation law . the example with reactions @xmath25 and @xmath26 has the critical siphon @xmath21 . so , though it is persistent , showing this requires a different argument that proceeds by exhibiting a lyapunov function @xcite . a different approach to the persistence conjecture is to try to identify a subclass of weakly - reversible systems which are somehow _ physical _ , and exploit this extra structure to obtain a proof for the persistence conjecture . this program was initiated in @xcite and @xcite , where the notion of systems where every species is made up of _ atoms _ in a unique way was made precise , and it was shown that atomic systems have no critical siphons , and hence are persistent . later , in @xcite , this result was extended to all _ saturated _ or non - catalytic systems , a larger class of systems properly containing the atomic systems . the biological motivation for our work comes from synthetic biology , specifically from the dna molecular programming community @xcite , where reaction networks are being viewed as programming languages for the synthesis of desired behaviour . one would like to have a programming language that is natural with respect to chemical reaction dynamics , so that there are meaningful ways to separately test , and then compose , different subsystems . the petri net view of reaction networks makes a connection with process algebras , and connects to work on concurrent programming languages . our work may be viewed as setting down a mathematical bridge between these two different areas , by making explicit the combinatorial foundations of reaction network notions like catalysis , self - replication , and persistence . we hope to exploit these connections more in future to describe ways of programming chemical reaction networks that will take advantage of advances in concurrent programming language design . our contributions in this paper are the following : we give an explicit combinatorial characterization of the minimal critical siphons . specifically , we introduce the notions of * drainable * and * self - replicable * sets in definition [ def : siphon ] , and prove in theorem [ minimal - siphon ] that every minimal critical siphon is either drainable or self - replicable . conjecture 1 from @xcite asserted a link between a certain notion of autocatalysis and critical siphons . we provide a counterexample ( example [ ex : counter ] ) to this conjecture . our notion of self - replicable siphons captures a more nuanced notion of autocatalysis . with this notion , we show in the spirit of ( * ? ? ? * conjecture 1 ) that the weakly - reversible networks that have critical siphons are precisely the autocatalytic systems ( theorem [ minimal - siphon ] ) . in particular , all non - autocatalytic ( i.e. , without self - replicable siphons ) weakly - reversible networks are persistent . as a special case , in section [ sec : catalysis ] we obtain a combinatorial proof for the persistence of non - catalytic networks , the main result in @xcite which was originally proved using algebraic geometric methods . angeli et al . @xcite have shown that conservative reaction networks without critical siphons are persistent . we show that reaction networks without drainable siphons are persistent ( theorem [ thm : persistence ] ) . since networks with drainable siphons are a proper subclass of networks with critical siphons ( theorem [ minimal - siphon ] ) , our result sharpens angeli s result , and brings out that the obstruction to proving the persistence conjecture comes from a competition between the drainable and self - replicable natures of a siphon ( remark [ rmk : compete ] ) . in section [ sec : dm ] , towards proving theorem [ minimal - siphon ] , we prove the convex rank - nullity theorem ( theorem [ rank - nullity ] ) , a trichotomy result for matrices that have a sign pattern with all diagonal terms are negative , and all off - diagonal terms positive . though this result is very suggestive of farkas lemma and its variants , to our best knowledge it has neither appeared before , nor is it an immediate corollary of farkas lemma ( remark [ rmk : notfarkas ] ) . all our results are in the setting of _ positive _ reaction networks ( definition [ def : rn ] ) . this means our results hold for reactions like @xmath27 with fractional stoichiometric coefficients . we introduce the notion of a _ critical _ set ( definition [ def : siphon ] ) , so that a critical siphon is a set of species which is both critical and a siphon . together with the notion of _ critical point _ ( definition [ def : critpt ] ) , this decoupling of the two notions simplifies the analysis ( theorem [ critical - equivalence ] ) , and allows us to obtain slightly stronger results ( theorem [ minimal - siphon ] ) . figure [ fig:1 ] provides a summary of all the results at a glance . @xmath28{newpresentation1.pdf}\ ] ]

the idea is that if all reactions are reversible in a weak sense , then no species can go extinct . a notion that has been found useful in thinking about persistence is that of `` critical siphon . '' we explore the combinatorics of critical siphons , with a view towards the persistence conjecture . we introduce the notions of `` drainable '' and `` self - replicable '' ( or autocatalytic ) siphons . we show that : every minimal critical siphon is either drainable or self - replicable ; reaction networks without drainable siphons are persistent ; and non - autocatalytic weakly - reversible networks are persistent . our results clarify that the difficulties in proving the persistence conjecture are essentially due to competition between drainable and self - replicable siphons .

the persistence conjecture is a long - standing open problem in chemical reaction network theory . it concerns the behavior of solutions to coupled ode systems that arise from applying mass - action kinetics to a network of chemical reactions . the idea is that if all reactions are reversible in a weak sense , then no species can go extinct . a notion that has been found useful in thinking about persistence is that of `` critical siphon . '' we explore the combinatorics of critical siphons , with a view towards the persistence conjecture . we introduce the notions of `` drainable '' and `` self - replicable '' ( or autocatalytic ) siphons . we show that : every minimal critical siphon is either drainable or self - replicable ; reaction networks without drainable siphons are persistent ; and non - autocatalytic weakly - reversible networks are persistent . our results clarify that the difficulties in proving the persistence conjecture are essentially due to competition between drainable and self - replicable siphons .

astro-ph0510335

c

damping on cosmic rays may terminate the slow kraichnan - type cascade in the interstellar medium at @xmath261 @xmath8 . our estimates were made for the level of mhd turbulence which produces the empirical value of cosmic - ray diffusion coefficient . this finding suggests a possible explanation for the peaks in secondary / primary nuclei ratios at about 1 gev / n observed in cosmic rays : the amplitude of short waves is small because of damping and thus the low energy particles rapidly exit the galaxy without producing many secondaries . there is no other obvious reasons for a sharp cut off in the wave spectrum . if the concept of mhd turbulence by @xcite works for interstellar turbulence , the mhd waves we are dealing with in this context are the fast magnetosonic waves . the alfven waves propagate predominantly perpendicular to the magnetic field and because of this they do not significantly scatter cosmic rays . it also explains why radio scintillation observations show no sign of the termination of electron density fluctuations at wave numbers between @xmath262 to @xmath263 @xmath8 . according to @xcite these fluctuations are produced by the slow magnetosonic waves with @xmath264 which are almost not damped on cosmic rays . an alternative explanation is that the wave damping on cosmic rays and the radio scintillations mainly occur in separate regions of the interstellar medium ( see below in the discussion on the `` sandwich '' model of cosmic ray propagation in the galaxy ) . some minor contribution to the observed scintillations is possible from fast magnetosonic waves interacting with energetic particles , and in this respect it is of interest that the observations may need an enhancement in the power on large `` refractive '' scales @xmath265 cm relative to the power on small `` diffractive '' scales @xmath266 cm @xcite . this may indicate the cutoff of the spectrum of fast magnetosonic waves due to cosmic ray action . while the mere fact of a wave spectrum steepening under the action of damping on cosmic rays can be described by a simple eq . ( [ eq9 ] ) with some characteristic time for nonlinear wave interactions @xmath267 $ ] , the exact form of the function @xmath91 at large @xmath112 where the damping is significant depends critically on the form of the equation for waves . it involves in particular to the vanishing of @xmath91 at some @xmath268 ( @xmath26@xmath269 @xmath8 ) and the corresponding singularity of @xmath165 at some @xmath217 ( @xmath261 gv ) found in our calculations . less significant in this sense is our approximation of the resonant wave number in eq . ( [ eq5 ] ) , which does not include the particle pitch angle in an explicit form . ( if it were included , the term with @xmath162 in eq . [ [ eq9 ] ] would have a third integration over the pitch angle . ) we note however that this effect was included in the derivation of eq . [ [ eq10 ] ] for the attenuation rate . in the context of the approximations adopted in the present work , the problem of cosmic - ray transport at @xmath160 arises . the free streaming of cosmic rays from the galaxy leads to an instability and to the growth of waves which scatter particles and thus slow down the streaming , see e.g. @xcite . we shall consider the processes at low energies in a separate work . here we note only that the streaming instability develops above the galactic disk at @xmath270@xmath271 cm@xmath4/s ( if the wave damping is absent ) and leads to the diffusive - convective transport of cosmic rays . the given estimate of the diffusion coefficient at 1 gv follows from the condition of cosmic ray streaming instability @xmath272 where @xmath273 is the bulk velocity of cosmic ray gas . the bulk velocity is @xmath274 where the cosmic ray anisotropy perpendicular to galactic disk is @xmath275 . the alfven velocity in galactic halo is about @xmath276 cm / s . it is important that the magnetic rigidity @xmath6 gv corresponds to a kinetic energy @xmath277 gev for protons , and @xmath278 gev / n for nuclei with charge to mass ratio @xmath279 . the galactic spectrum of cosmic - ray protons and nuclei at such low energies can not be derived from direct observations at the earth because of strong modulation in the solar wind . dissipation other than on cosmic rays has been neglected in the present work , though it may completely destroy the mhd cascade or considerably change its angular distribution and thus affect @xmath165 in a large part of the interstellar medium , see @xcite , @xcite , @xcite . the region of the cosmic ray halo is the most `` safe '' in this sense @xcite . in particular , dissipation on ion - neutral collisions may destroy mhd turbulence in the galactic disk but not in the halo where neutrals are absent . we then come to the `` sandwich '' model for cosmic - ray propagation , with different diffusion coefficients in the galactic disk , @xmath280 , and in the halo , @xmath281 ( it is assumed here that some scattering is present in the galactic disk and the diffusion approximation works ) . in this case , the mean matter thickness traversed by cosmic rays does not depend on diffusion inside the disk even at zero gas density in the halo : @xmath282 @xcite . the energy dependence of secondary to primary ratios in cosmic rays is determined by the diffusion coefficient in the cosmic ray halo where the model developed in the present paper is applied . the estimate based on the empirical value of the diffusion coefficient for gev particles ( see section 1 ) gives the level of turbulence at the principal scale @xmath283 @xmath284 for a kraichnan - type spectrum @xmath115 , and @xmath285 for a kolmogorov - type spectrum @xmath114 , if @xmath286 @xmath8 . at the same time , the data on faraday rotation angles favor the kolmogorov spectrum with @xmath285 and @xmath286 @xmath8 . the cascades of alfven waves ( with the scaling @xmath287 ) and the fast magnetosonic waves ( @xmath288 ) are independent in the @xcite model of mhd turbulence , and the amplitude of alfven wave cascade may dominate at the principle scale . also , in the `` sandwich '' model described in a previous paragraph , the turbulence , which determines the confinement of cosmic rays in the galaxy , is distributed in the halo of size @xmath289 kpc whereas the observations of interstellar turbulence refer to the galactic disk and the adjacent region , where it can be much stronger .

we find that the dissipation of waves due to the resonant interaction with cosmic ray particles may terminate the kraichnan - type cascade below wavelengths cm . the energy - dependence of the cosmic - ray diffusion coefficient found in the resulting self - consistent model may explain the peaks in the secondary to primary nuclei ratios observed at about 1 gev / nucleon .

the physical processes involved in diffusion of galactic cosmic rays in the interstellar medium are addressed . we study the possibility that the nonlinear mhd cascade sets the power - law spectrum of turbulence which scatters charged energetic particles . we find that the dissipation of waves due to the resonant interaction with cosmic ray particles may terminate the kraichnan - type cascade below wavelengths cm . the effect of this wave dissipation has been incorporated in the galprop numerical propagation code in order to asses the impact on measurable astrophysical data . the energy - dependence of the cosmic - ray diffusion coefficient found in the resulting self - consistent model may explain the peaks in the secondary to primary nuclei ratios observed at about 1 gev / nucleon .

1108.2534

i

the young stellar object ( yso ) was first noted to be an erupting source when it brightened suddenly in november 2003 , illuminating a new nebula now known as mcneil s nebula . this deeply embedded , low - mass yso is typically considered to be an ex lupi - type object ( an exor " ) though it shares some spectral characteristics with fu orionis @xcite , the prototype of a similar class of erupting pre - main sequence ( pms ) stars ( fuors " ) . exors are observed to brighten irregularly at optical wavelengths up to several times per decade ; these outbursts persist for weeks to months @xcite . fuors are ysos that erupt less often than exors , perhaps only once per century , and fade much more slowly , i.e. , on timescales of years to decades @xcite . the general consensus is that these eruptions are the result of massive accretion events that occur irregularly as young protostars grow ; such accretion episodes may be the primary process through which young stars accrete most of their mass @xcite . the mechanisms underlying exor and fuor outbursts remain very poorly understood ; however , models generally invoke the rapid onset of disk instabilities that lead to sudden inward migration of the inner disk truncation radius and dramatic changes in the star / disk magnetic field configuration ( e.g. , @xcite ) . soft x - ray ( @xmath10.3 kev ) generation via shock - heating of plasma at the bases of pms accretion streams has been proposed for some objects from x - ray grating observations ( see review by * ? ? ? * ) using plasma diagnostics based on helium - like ions , a prime example being tw hydrae @xcite . on the other hand , studies such as the chandra orion ultradeep project ( coup ) indicate that coronal activity , and not accretion , is likely the primary production mechanism for the harder x - rays that are characteristic of most pre - main sequence stars @xcite . debate still lingers as to the primary x - ray generation mechanism in ysos during optical outbursts . since 2003 , v1647 ori has been observed to undergo two distinct outbursts that have been detected in the optical and near - infrared @xcite as well as at x - ray wavelengths @xcite . the magnitudes and timescales for brightening and fading displayed by v1647 ori do not match those of exors . furthermore , the duration of the initial outburst was shorter than those of fuors @xcite . however , spectroscopic data do show signatures of accretion , such as strong h@xmath6 and br@xmath7 emission @xcite , confirming that the eruptions of v1647 ori do resemble those of fuors and exors . v1647 ori has been observed in x - rays before and during both of the eruptions ( as well as after the first of the two eruptions ) detected in the optical / near - infrared since 2003 . although other fuor- or exor - like ysos have been observed in x - rays ( v1118 ori @xcite ; ex lup @xcite ; z cma @xcite ; fu ori @xcite ; v1735 cyg @xcite ) , v1647 ori is the only eruptive yso to undergo such extensive x - ray monitoring . during the 2003 eruption , the sudden rise in flux and subsequent decline in both the optical and near - infrared correlated strongly with a sharp increase and then decline in the x - ray flux , which suggests a common origin @xcite . in this paper , we present and analyze x - ray spectra obtained with the chandra x - ray observatory ( cxo ) during the 20082009 outburst . in [ obs ] , we describe the observations and data reduction . in [ results ] , we examine the trends and patterns seen in the x - ray emission from v1647 ori over the past two outbursts , present modeling results for each of the five recent cxo observations , and compare these results to those obtained from previous ( 20032005 ) cxo and xmm - newton observations . finally , in [ discussion ] we discuss the implications of the results , and we argue that the measured properties of the x - ray emitting plasma are best understood within the framework of the accretion - generated x - ray hypothesis .

the pre - main sequence star v1647 ori has recently undergone two optical / near - infrared ( oir ) outbursts that are associated with dramatic enhancements in the stellar accretion rate . our analysis of all fourteen chandra x - ray observatory observations of v1647 ori demonstrate that variations in the x - ray luminosity of v1647 ori are correlated with similar changes in the oir brightness of this source during both ( 20032005 and 2008 ) eruptions , strongly supporting the hypothesis that accretion is the primary generation mechanism for the x - ray outbursts .

the pre - main sequence star v1647 ori has recently undergone two optical / near - infrared ( oir ) outbursts that are associated with dramatic enhancements in the stellar accretion rate . our intensive x - ray monitoring of this object affords the opportunity to investigate whether and how the intense x - ray emission is related to pre - ms accretion activity . our analysis of all fourteen chandra x - ray observatory observations of v1647 ori demonstrate that variations in the x - ray luminosity of v1647 ori are correlated with similar changes in the oir brightness of this source during both ( 20032005 and 2008 ) eruptions , strongly supporting the hypothesis that accretion is the primary generation mechanism for the x - ray outbursts . furthermore , the chandra monitoring demonstrates that the x - ray spectral properties of the second eruption were strikingly similar to those of the 2003 eruption . we find that x - ray spectra obtained immediately following the second outburst during which v1647 ori exhibited high x - ray luminosities , high hardness ratios , and strong x - ray variability are well modeled as a heavily absorbed ( n 4 ) , single - component plasma with characteristic temperatures ( kt 26 kev ) that are consistently too high to be generated via accretion shocks but are in the range expected for plasma heated by magnetic reconnection events . we also find that the x - ray absorbing column has not changed significantly throughout the observing campaign . since the oir and x - ray changes are correlated , we hypothesize that these reconnection events either occur in the accretion stream connecting the circumstellar disk to the star or in accretion - enhanced protostellar coronal activity .

1108.2534

c

figure [ overall ] suggests that the overall x - ray flux of v1647 ori is strongly correlated with optical / near - infrared flux . this correlation is revealed more clearly in figure [ longtermhvsx ] , in which we plot the x - ray luminosity versus the i@xmath19-band luminosity . we interpolated i@xmath19-band luminosities for the 20022005 x - ray observation dates . we did not extrapolate i@xmath19-band luminosities for the two 2006 x - ray observation dates due to the highly uncertain flux behavior of v1647 ori . of the 2008 - 2009 x - ray observations , we could only interpolate an i@xmath19-band luminosity for obsid 9916 . with these eight interpolated luminosities , we derived a correlation coefficient between x - ray luminosity and i@xmath19-band luminosity of 0.65 . dramatic increases in optical / near - infrared flux for ysos , such as fu ori , have long been thought to be associated with enhanced accretion @xcite . in such an environment , material is channeled through magnetic funnels from the co - rotation radius of the circumstellar disk down to the photosphere @xcite . hence , when the x - ray flux from a pre - main - sequence star or protostar is elevated and the rapid rise in x - ray emission is directly correlated with large - scale optical outbursts , the correlation itself strongly suggests that accretion is the mechanism responsible for generating the increase in x - ray output @xcite . one way in which accretion - generated x - ray emission could be identified observationally would be through the relatively soft x - rays emitted by the plasma when it plunges onto the stellar surface at free - fall velocities and is shock heated to temperatures of a few million kelvin ( kt@xmath5 @xmath10.3 kev ) @xcite . we can speculate that a second such signature would be much hotter ( kt@xmath5 @xmath1few to tens of kev ) and harder x - rays generated in magnetic reconnection events @xcite within the accretion streams . whether the soft or hard x - ray generating plasma is observable likely depends on the observing geometry . if we have an unobscured line of sight to the footprint of the accretion column , our observations should be sensitive to the cooler plasma ; if the accretion column obscures our view of the accretion - column footprint , our observations should be sensitive only to the hotter plasma in the accretion stream ; and if the obscuration of the accretion footprint is partial , we might detect both plasmas . in between periods of dramatically enhanced accretion , previous studies such as coup @xcite and the xmm - newton extended survey of the taurus molecular cloud ( xest ) @xcite , suggest that the x - ray signature of young stars should be that of normal coronal emission . such emission would be similar to but much fainter than the hot , hard plasma seen from reconnection events in the accretion funnel . during quiescence , the x - ray flux of v1647 ori has a low count rate , low median photon energy , and negative hardness ratio ; in contrast , when the x - ray flux is elevated , the count rate increases by a factor of 25 or greater , the median photon energy doubles , and the hardness ratio becomes strongly positive . most of the v1647 ori light curves reveal that this yso also experiences what appear to be short - term ( few kilosecond ) variability in its x - ray flux . since most of the cxo observations show this short - duration variability when the x - ray count rate is high , the short - term variations are likely part of the normal behavior for v1647 ori . for all 20082009 cxo observations , the x - ray variability is almost entirely seen in hard ( @xmath142.8 kev ) x - rays . our model fits of the v1647 ori spectra indicate that the x - ray signature of the plasma we observe from this source during optical eruptions is predominantly a bright , hot , hard , single - temperature plasma heated to temperatures of 26 kev , which is also consistent with x - rays generated from reconnection events in an accretion funnel @xcite . we must keep in mind , however , that the intervening hydrogen column density will play a significant role in our ability to detect x - ray flux from accretion hotspots at temperatures of a few million kelvin , especially when dealing with column densities as high as those modeled in v1647 ori observations . an accretion - footprint ( shocked ) plasma at a temperature of kt@xmath5 @xmath1 0.3 kev subject to an intervening absorbing column density of a few times 10@xmath3 @xmath4 would have @xmath198% of its x - ray flux extinguished . even given the smallest hydrogen column density found via spectral modeling of the 20042005 v1647 ori observations when the hydrogen column density was allowed to vary freely ( @xmath11 @xmath2 10@xmath3 @xmath4 ) , such a soft component still has @xmath196% of its x - ray flux absorbed . if the hydrogen column density decreased dramatically to n@xmath0 of a few times 10@xmath20 @xmath4 the accretion shock emission could dominate the observed flux . this seems a plausible scenario to explain the softer plasma detected in late 2004 march , especially if the large intervening hydrogen column density inferred at other observing epochs was due mostly to the accretion streams . an alternative explanation is that we observed v1647 ori when it was in the midst of a large accretion episode that pushed the star - disk boundary inward to the point where the accretion became non - magnetospheric @xcite , effectively reducing the amount of hard x - ray flux produced by magnetic reconnection events in the accretion stream . during the 20082009 epoch , when the x - ray luminosity of v1647 ori increased , the spectrum hardened and the emitting plasma increased in temperature ( fig . [ v1647orilumhrtemp ] , right panel ) ; also , when the overall x - ray luminosity decreased , the x - ray spectrum softened and the x - ray generating plasma cooled . these correlations are also seen in the chandra observations following the 2003 eruption ( fig . [ v1647orilumhrtemp ] , left panel ) . however , between 2008 september and 2008 november , the spectrum appeared to harden slightly as the x - ray luminosity decreased slightly . if we are observing x - rays generated predominantly by the @xmath11 kev plasma in the accretion footprint , then a decline in accretion should result in a decline in total x - ray luminosity , particularly in the lower energy flux , resulting in a hardening of the spectrum . therefore , the hardening of the spectrum and decrease in x - ray luminosity observed between 2008 september and november might be a time when cxo was able to see plasma closer to the protostellar surface . in fact , this epoch showed a low temperature ( @xmath12 kev ) plasma , consistent with what could be a mixture of hotter ( 46 kev ) and cooler ( 1 kev ) plasmas . these data may offer evidence that the x - ray flux includes an emission component from the cooler plasma in the footprint of the accretion funnel located in the stellar photosphere . because the cooler plasma suffers greater extinction and because cxo is less sensitive to softer x - ray emission than xmm - newton , cxo would likely only detect the cooler plasma when the viewing geometry is favorable . our modeling work for the x - ray observations obtained in 20042005 and 20082009 , when the mean x - ray count rates were greater than 1 cts ks@xmath15 yield a best fit value for @xmath21 of about 4.1 @xmath2 10@xmath3 @xmath4 , consistent with the results derived by @xcite and a visual extinction of @xmath22 @xmath1 20 @xcite . we were unable to fit @xmath21 in our modeling work for the low count - rate observations during the quiescent period in 20052006 ; however , @xcite obtained a best fit value for @xmath22 of 19 @xmath13 2 , based on their optical , near - infrared , and mid - infrared observations obtained in february 2007 , which was also during the quiescent period ( based on the optical and near - infrared photometry reported by @xcite ) . the observed value of @xmath22 for february 2007 lends strong support to our use of @xmath21 = 4.1 @xmath2 10@xmath3 @xmath4 for our modeling of the quiescent epoch observations . in addition , together these data suggest that @xmath21 and , by implication , @xmath22 , remained essentially unchanged as inferred from the x - ray observations , whether v1647 ori was in the quiescent or elevated x - ray state . on the other hand , as seen at longer wavelengths , the extinction toward v1647 ori has changed . @xcite derive @xmath22 = 13 from near - infrared data obtained in 1998 by 2mass . during the outburst in 20042005 , @xcite found @xmath22 = 810 on 2004 february 18 , @xcite found @xmath23 = 1.26 , @xmath24 = 0.81 , and @xmath25 = 0.5 on 2004 feburary 18 , all of which are consistent with @xmath22 of @xmath15 @xcite , @xcite obtained @xmath22 = 11 from measurements of the 3.1 @xmath26 m water band on 2004 march 9 , and @xcite , who made optical and near - infrared observations from 2004 into very late 2005 , reported @xmath22 of @xmath15 during the 2004 outburst . @xcite then report that @xmath22 increased to @xmath110 by the end of 2005 , when v1647 ori had dramatically faded , and @xcite reported @xmath22 was as high as 19 by early 2007 . clearly , the extinction , as measured via optical and near - infrared measurements , changed first from quiescence to outburst and then from outburst back to quiescence . these apparently discordant results have a straightforward and consistent explanation in the context of an accretion episode . in x - rays , we are essentially detecting v1647 ori along a direct line of sight to the stellar photosphere . our results therefore indicate that the absorption along this direct line of sight which likely includes at least part of a thick circumstellar disk that is tilted about 30 degrees from edge - on @xcite does not change significantly as a function of time , despite the evident changes in x - ray luminosity . the optical and near - infrared photons we observe , however , emerge from the near - photosphere environment of v1647 ori along two paths . one path , along our direct line of sight to the photosphere , produces heavily reddened and extincted light . the second path takes photons nearly perpendicular to our line of sight , through an evacuated polar cavity , where they then scatter into our line of sight @xcite . these photons are bluer and much less heavily extincted than the line - of - sight photons . when v1647 ori is in the quiescent state ( 1998 , late 20052007 ) , we see a faint , reddened , heavily extincted source because the contribution from scattered light is minimal . during the outburst state ( 20042005 ; 20082009 ) , we see a brighter , bluer source because the contribution to the continuum of scattered photons is large . though the plasma temperature of v1647 ori strongly correlates with the x - ray luminosity and hardness ratio ( fig . [ v1647orilumhrtemp ] ) , it is unclear whether we are observing a single - component plasma that increases or decreases in temperature and thus causes the observed changes in x - ray luminosity or if a second , lower - temperature plasma is also present and whose contribution to the total spectrum is overwhelmed by the hotter temperature plasma during outbursts . other sources , such as v710 tau @xcite and ex lupi @xcite have spectra that can be modeled as two - temperature plasmas , with one component fading as the star returns to quiescent levels . @xcite was able to model the xmm - newton observation of v1647 ori in 2004 april with a single - temperature plasma but also found a better fit using a two - component model . however , this observation of v1647 ori was at least twice as long as most of the chandra observations from 20042009 . in addition , xmm - newton is more sensitive to lower - energy photons than cxo / acis . therefore , it may be the case that v1647 ori does have two plasmas that contribute to the x - ray spectra but that acis was unable to consistently detect the lower - temperature component due to the inherit limitations of its design , the shorter observation times of the cxo observations , and the high degree of softer x - ray absorption by the intervening hydrogen column . in order to test whether cxo would be able to detect two distinct plasma temperatures in 5 ks and 20 ks observations , we simulated a two - component plasma ( using _ fakeit _ ) with a normalization ratio and plasma temperatures identical to those found by @xcite and suffering extinction by the same hydrogen column density . the simulated spectra were then convolved with the responses of the front - illuminated acis - i3 and back - illuminated acis - s3 ccds . the simulations incorporated appropriately - scaled normalization parameters so that the resultant count rates were comparable to those of the 2005 and 20082009 cxo observations . each of the simulated spectra was first fit with a single - component model and then with a two - component model . all of the 20 ks observations were found to be fit better using two - component models with each fit yielding values for plasma temperatures and normalization that were close to the original simulation parameters . f - tests also suggested a slight improvement in the model fits if the 75%/25% normalization ratio between the low / high components , as found by @xcite , was forced . when fit with a two - component model , the simulated 5 ks observation of the more sensitive acis - s3 ccd yielded a best fit ( using the 75%/25% normalization ratio ) that converged to a model with two nearly - identical temperature plasmas , i.e. , to a single - temperature plasma , and thus does not lead to a better fit . thus , it appears that cxo should have the sensitivity to detect a two - component plasma such as that found by @xcite if the observations are long enough and the lower - temperature plasma flux is strong enough compared to the higher - temperature plasma flux . the spectral models for each of the five chandra observations obtained in 20082009 consistently converge to fits with a single - temperature plasma that , to within the errors , is @xmath14 kev . as seen with the correlation between x - ray luminosity and the mean hardness ratio , median photon energy , and mean count rate , we also find that when the x - ray luminosity increases or decreases , so does the plasma temperature . this single - component model is consistent with the single - component model of the 2005 april 11 xmm - newton data @xcite . finally , the second ( 2008 ) eruption of v1647 ori has very similar spectral characteristics to that of the first ( 20032005 ) eruption . from tables [ tab-1 ] , [ tab-3 ] , and [ tab-2 ] , the five 20082009 observations of v1647 ori , which span a period of approximately seven months , show * mean hardness ratios that are consistently as hard ( to within the errors ) as the hardest value of any observation following the previous eruption ; * median photon energies at levels that are very similar to the greatest median photon energy of any observation from the previous eruption ; * mean count rates that are 2050 times higher than those observed during x - ray quiescence and that are typically 12 times the highest mean count rate of the 20032006 observations ; * plasma emission measures that are usually 12 times greater than any modeled from the 2003 - 2005 observations ; * and x - ray luminosities that are consistently greater than 1.5 @xmath2 10@xmath27 ergs s@xmath15 , 12 times the x - ray luminosity of v1647 ori during any of the 2003 - 2005 cxo observations . given that the spectral characteristics of v1647 ori are so similar in observations in which the x - ray flux is elevated above the x - ray quiescent level , it appears that the same x - ray generation mechanism was at work during both eruptions and that the plasma characteristics were very similar during the two eruption epochs . the derived x - ray luminosities suggest that the second eruption was more energetic than the first , and given that the modeled emission measures are greater for the observations following the second eruption , it is reasonable to conclude that we observed the same phenomenon in both eruptions but that a larger mass of x - ray emitting plasma was active during the outburst that began in 2008 .

furthermore , the chandra monitoring demonstrates that the x - ray spectral properties of the second eruption were strikingly similar to those of the 2003 eruption . since the oir and x - ray changes are correlated , we hypothesize that these reconnection events either occur in the accretion stream connecting the circumstellar disk to the star or in accretion - enhanced protostellar coronal activity .

the pre - main sequence star v1647 ori has recently undergone two optical / near - infrared ( oir ) outbursts that are associated with dramatic enhancements in the stellar accretion rate . our intensive x - ray monitoring of this object affords the opportunity to investigate whether and how the intense x - ray emission is related to pre - ms accretion activity . our analysis of all fourteen chandra x - ray observatory observations of v1647 ori demonstrate that variations in the x - ray luminosity of v1647 ori are correlated with similar changes in the oir brightness of this source during both ( 20032005 and 2008 ) eruptions , strongly supporting the hypothesis that accretion is the primary generation mechanism for the x - ray outbursts . furthermore , the chandra monitoring demonstrates that the x - ray spectral properties of the second eruption were strikingly similar to those of the 2003 eruption . we find that x - ray spectra obtained immediately following the second outburst during which v1647 ori exhibited high x - ray luminosities , high hardness ratios , and strong x - ray variability are well modeled as a heavily absorbed ( n 4 ) , single - component plasma with characteristic temperatures ( kt 26 kev ) that are consistently too high to be generated via accretion shocks but are in the range expected for plasma heated by magnetic reconnection events . we also find that the x - ray absorbing column has not changed significantly throughout the observing campaign . since the oir and x - ray changes are correlated , we hypothesize that these reconnection events either occur in the accretion stream connecting the circumstellar disk to the star or in accretion - enhanced protostellar coronal activity .

1108.2534

i

our x - ray monitoring demonstrates that the two optical / near - ir outbursts undergone by the enigmatic v1647 ori in less than a decade were accompanied by strong x - ray outbursts . during these two outbursts ( 20032005 and 2008present ) , we see that the x - ray flux rose to peak luminosity over a span of a few weeks and then remained elevated for approximately two years during the first eruption and for at least one year during the second eruption . given that there is very strong evidence that the outbursts observed in the optical and near - infrared regimes are driven by accretion , we conclude that the correlated outbursts in x - rays are also driven by accretion . we find that all of the cxo spectra of v1647 ori are best modeled with a single , moderate - temperature ( 26 kev ) plasma . in almost all cases , the plasma temperature that emerges from models of the cxo spectra is too high to be generated via accretion hotspots on the stellar photosphere but is reasonable for a plasma generated via magnetic reconnection events . however , the x - ray - emitting plasma could also be located in a strongly enhanced stellar corona , or at the inner edge of the circumstellar disk . given that accretion is ongoing , lower - temperature plasma generated by shocks at the accretion footprint is very likely present ; however , during these cxo observations , any such soft component contributed much less flux than the moderate - temperature plasma and so usually did not leave a distinct signature in the x - ray spectra . with the elevated hard x - ray flux lasting the duration of the 20082009 epochs , we conclude that the x - ray flux is not the result of typical coronal flares generated via reconnection events . we believe that since the optical / near - infrared flux remains elevated throughout this observation epoch , we are instead observing the x - rays generated from reconnection events in the accretion stream , with the softer x - ray flux possibly being generated by accretion hotspots at the stellar photosphere . we find no significant change in x - ray absorbing column , indicating that varying optical / ir color measurements , which have previously been interpreted as evidence for variable reddening toward v1647 ori , may instead be indicative of varying contributions from scattered vs. direct photospheric emission from the yso . two of the spectra obtained during the most recent ( 2008 ) outburst appear to show the 6.4 kev neutral iron feature indicating fluorescence from cold ( presumably circumstellar disk ) gas surrounding v1647 ori . with v1647 ori being observed intensely during both outbursts at x - ray , optical , and infrared wavelengths , this objects stands as one of the best characterized systems that exhibits such a close correspondence between x - ray output and accretion rate . as a result of intense monitoring at x - ray , optical , and infrared wavelengths during two successive accretion - driven outbursts , v1647 ori stands as the best characterized yso in terms of the correspondence between x - ray output and accretion rate . we have shown , furthermore , that this yso exhibited strikingly similar x - ray behavior and spectral properties during its recent accretion bursts . these results underscore the need for x - ray monitoring of additional eruptive ysos , so as to evaluate whether the remarkable consistency of v1647 ori is the exception or the norm . we thank nuria calvet for providing early access to the data in cxo obsids 10763 and 8585 . this research was supported via awards numbers go8 - 9016x and go9 - 0006x to vanderbilt university issued by the chandra x - ray observatory center , which is operated by the smithsonian astrophysical observatory for and on behalf of nasa under contract nas8 - 03060 . brahm , p. , kspl , a. , csizmadia , s. , mor , a. , kun , m. , & stringfellow , g. 2004 , , 419 , l39 acosta - pulido , j. a. , et al . 2007 , , 133 , 2020 anthony - twarog , b.j . the h 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, & ozawa , h. 2003 , , 408 , 581 zhu , z. , hartmann , l. , gammie , c. , & mckinney , j. c. 2009 , , 701 , 620 llcccccccc 2539 & 2002 nov 14 & 2452593 & s2 & 62.8 & 17 & 0.3 @xmath13 0.1 & 2.0 @xmath13 0.3 & @xmath120.34 @xmath13 0.31 & @xmath120.28 @xmath13 0.28 + 5307 & 2004 mar 07 & 2453072 & s3 & 5.5 & 64 & 11.7 @xmath13 1.5 & 3.6 @xmath13 0.3 & 0.46 @xmath13 0.15 & 0.45 @xmath13 0.14 + 5308 & 2004 mar 22 & 2453087 & s3 & 4.9 & 12 & 2.5 @xmath13 0.8 & 2.0 @xmath13 0.5 & @xmath120.45 @xmath13 0.33 & @xmath120.46 @xmath13 0.33 + 5382 & 2005 apr 11 & 2453472 & i3 & 18.2 & 86 & 4.8 @xmath13 0.5 & 3.5 @xmath13 0.1 & 0.51 @xmath13 0.19 & 0.46 @xmath13 0.12 + 5383 & 2005 aug 27 & 2453610 & i3 & 19.9 & 18 & 0.9 @xmath13 0.2 & 3.0 @xmath13 0.8 & 0.01 @xmath13 0.29 & 0.34 @xmath13 0.25 + 5384 & 2005 dec 09 & 2453714 & i3 & 19.7 & 2 & 0.1 @xmath13 0.1 & 2.2 @xmath13 1.1 & 0.0 @xmath13 0.20 & @xmath120.07 @xmath13 0.92 + 6413 & 2005 dec 14 & 2453719 & i3 & 18.1 & 4 & 0.2 @xmath13 0.1 & 1.7 @xmath13 0.3 & @xmath120.36 @xmath13 0.26 & @xmath121.0 @xmath13 0.75 + 6414 & 2006 may 01 & 2453857 & i3 & 21.6 & 3 & 0.1 @xmath13 0.1 & 1.3 @xmath13 0.3 & 0.09 @xmath13 0.23 & 0.07 @xmath13 0.92 + 6415 & 2006 aug 07 & 2453955 & i3 & 20.5 & 4 & 0.2 @xmath13 0.1 & 2.4 @xmath13 0.4 & @xmath120.27 @xmath13 0.21 & @xmath121.0 @xmath13 0.73 + 9915 & 2008 sep 18 & 2454728 & i3 & 19.9 & 466 & 23.6 @xmath13 1.1 & 3.5 @xmath13 0.1 & 0.36 @xmath13 0.07 & 0.37 @xmath13 0.05 + 10763 & 2008 nov 27 & 2454798 & i2 & 19.7 & 217 & 11.0 @xmath13 0.7 & 3.9 @xmath13 0.1 & 0.65 @xmath13 0.09 & 0.64 @xmath13 0.08 + 8585 & 2008 nov 28 & 2454799 & i2 & 28.5 & 160 & 5.8 @xmath13 0.4 & 3.4 @xmath13 0.1 & 0.40 @xmath13 0.10 & 0.43 @xmath13 0.09 + 9916 & 2009 jan 23 & 2454855 & i3 & 18.4 & 245 & 13.6 @xmath13 0.9 & 3.7 @xmath13 0.2 & 0.41 @xmath13 0.08 & 0.43 @xmath13 0.07 + 9917 & 2009 apr 21 & 2454943 & i3 & 29.8 & 260 & 8.8 @xmath13 0.5 & 3.5 @xmath13 0.2 & 0.28 @xmath13 0.08 & 0.37 @xmath13 0.07 + 9915 & 2008 sep 18 & 0.85 & 77 & 4.1@xmath28 & 3.7@xmath29 & 15.0@xmath30 & 4.2@xmath31 & 8.1@xmath32 + 10763 & 2008 nov 27 & 1.24 & 39 & 4.1 ( fixed ) & 4.0 ( fixed ) & 6.1@xmath33 & 1.8@xmath34 & 3.5@xmath35 + 8585 & 2008 nov 28 & 0.71 & 26 & 5.9@xmath36 & 2.0@xmath37 & 8.2@xmath38 & 1.0@xmath39 & 1.8@xmath40 + 9916 & 2009 jan 23 & 0.79 & 42 & 4.1@xmath41 & 6.0@xmath42 & 6.8@xmath43 & 2.6@xmath44 & 5.0@xmath45 + 9917 & 2009 apr 21 & 0.88 & 44 & 4.1@xmath46 & 3.4@xmath47 & 5.9@xmath48 & 1.5@xmath49 & 2.9@xmath40 + lcccccccc 2539 & 2002 nov 14 & 1.37 & 13 & 0.9@xmath50 & 0.6@xmath51 & 0.03@xmath52 & 0.05@xmath53 + 5307 & 2004 mar 7 & 1.19 & 10 & 4.0 ( f ) & 5.4 @xmath13 1.3 & 1.6 @xmath13 0.5 & 3.1 @xmath13 0.9 + 5308 & 2004 mar 22 & 1.45 & 10 & 1.1@xmath54 & 3.9@xmath55 & 0.2 @xmath13 0.1 & 0.4 @xmath13 0.1 + 5382 & 2005 apr 11 & 0.98 & 14 & 3.4@xmath56 & 3.1@xmath57 & 0.8@xmath58 & 1.5@xmath59 + 5383 & 2005 aug 27 & 1.99 & 16 & 3.2@xmath60 & 0.8@xmath61 & 0.2@xmath62 & 0.4@xmath58 + 5384 & 2005 dec 9 & 1.67 & 1 & 0.86 ( f ) & 0.2@xmath63 & 0.01 @xmath13 0.01 & 0.01 @xmath13 0.01 + 6413 & 2005 dec 14 & 0.87 & 3 & 0.86 ( f ) & 0.9@xmath64 & 0.02 @xmath13 0.01 & 0.05 @xmath13 0.03 + 6414 & 2006 may 1 & 2.83 & 2 & 0.86 ( f ) & 0.3@xmath65 & 0.01 @xmath13 0.01 & 0.02 @xmath13 0.02 + 6415 & 2006 aug 7 & 1.45 & 3 & 0.86 ( f ) & 0.9@xmath65 & 0.01 @xmath13 0.01 & 0.01 @xmath13 0.01 +

our intensive x - ray monitoring of this object affords the opportunity to investigate whether and how the intense x - ray emission is related to pre - ms accretion activity . we find that x - ray spectra obtained immediately following the second outburst during which v1647 ori exhibited high x - ray luminosities , high hardness ratios , and strong x - ray variability are well modeled as a heavily absorbed ( n 4 ) , single - component plasma with characteristic temperatures ( kt 26 kev ) that are consistently too high to be generated via accretion shocks but are in the range expected for plasma heated by magnetic reconnection events .

the pre - main sequence star v1647 ori has recently undergone two optical / near - infrared ( oir ) outbursts that are associated with dramatic enhancements in the stellar accretion rate . our intensive x - ray monitoring of this object affords the opportunity to investigate whether and how the intense x - ray emission is related to pre - ms accretion activity . our analysis of all fourteen chandra x - ray observatory observations of v1647 ori demonstrate that variations in the x - ray luminosity of v1647 ori are correlated with similar changes in the oir brightness of this source during both ( 20032005 and 2008 ) eruptions , strongly supporting the hypothesis that accretion is the primary generation mechanism for the x - ray outbursts . furthermore , the chandra monitoring demonstrates that the x - ray spectral properties of the second eruption were strikingly similar to those of the 2003 eruption . we find that x - ray spectra obtained immediately following the second outburst during which v1647 ori exhibited high x - ray luminosities , high hardness ratios , and strong x - ray variability are well modeled as a heavily absorbed ( n 4 ) , single - component plasma with characteristic temperatures ( kt 26 kev ) that are consistently too high to be generated via accretion shocks but are in the range expected for plasma heated by magnetic reconnection events . we also find that the x - ray absorbing column has not changed significantly throughout the observing campaign . since the oir and x - ray changes are correlated , we hypothesize that these reconnection events either occur in the accretion stream connecting the circumstellar disk to the star or in accretion - enhanced protostellar coronal activity .

astro-ph0005182

i

dwarf irregular galaxies often have relatively large and bright hii regions indicative of active star formation in dense neighboring clouds . normal spiral galaxies have equally bright hii regions , but the background stellar disks in spiral galaxies are usually bright too , giving the hii regions less contrast than they have in dwarfs . this difference leads to the well - known patchy and apparent starburst quality of dwarf galaxies . here we point out that the difference also translates into a pressure anomaly that may have important implications for the distribution of matter or the origin of giant shells . the pressures in the largest hii regions of 6 dwarf irregular galaxies are found to be @xmath0 times larger than the pressures from the average gravitational binding of the disk in the vertical direction , unlike the case for spiral galaxies where these two pressures are comparable ( sects . [ sect : press ] , [ sect : p ] ) . either the hii regions are actively expanding to fill the disk volume and part of the halo ( their volumes have to increase by a factor of @xmath3 before they reach pressure equilibrium ) , or there is additional mass in the star - forming regions that increases the ambient disk pressure . we show below that this additional mass corresponds to a factor of @xmath4 enhancement in column density if it is in the form of gas , and a factor of @xmath0 enhancement in column density if it is in the form of non - interacting cosmological particles . we first consider the possibility that there might be additional mass in a pervasive dark form ( sects . [ sect : ddm ] ) . the factor of @xmath0 needed to account for the disk pressure anomaly is comparable to the mass factor needed to account for dwarf galaxy rotation curves . disk dark matter was previously considered for dwarf galaxies based on the gravitational instability threshold for star formation and on the need for a cool atomic phase of interstellar matter ( hunter , elmegreen , & baker 1998 ; hereafter paper i ) . there seems to be a problem with scale heights in this case , however : if pervasive dark matter in any form explains the hii region pressure anomaly , then the interstellar scale heights would be 3 to 10 times smaller than the values usually inferred for dwarf galaxies ( sect . [ sect : prob ] ) . a better solution is to have the visible matter distributed non - uniformly , with large concentrations of gas around the hii regions and relatively small column densities elsewhere ( sect . [ sect : local ] ) . observations of dwarfs already suggest that most of the inner - disk hi gas is concentrated directly in the regions of star formation ( see also van zee et al . this raises the pressure locally , and provides some resistance to hii region expansion . a comparison with the gas distributions in spiral galaxies ( sect . [ sect : spiral ] ) suggests that the same physical processes may be at work in the formation of clouds , but the presence of shear and spiral waves in the larger systems makes the morphology , and possibly the ages , of the equivalent gas concentrations different . any systematic concentration of gas in the immediate vicinity of star formation raises the possibility that enriched outflows from dwarf galaxies may be less likely than previously believed ( dekel & silk 1986 ) . the outflow would not feel the weak potential of the galaxy at first , allowing its easy escape , but the deep potential well of the star - forming concentration and the enhanced drag from all of the additional gas around it . only if the outflow can get around this local resistance may it get a chance to leave the galaxy . another possibility is that the hii regions are only the brightest and highest - pressure members of a larger population of hii regions that are still expanding into an anomalously low pressure interstellar medium ( sect . [ sect : shell ] ) . this is consistent with our detection limitations , and also has interesting implications for the origin of giant hi shells . distinctions between these possibilities can be determined by independent measures of the turbulent pressures and disk dark matter contents of dwarf galaxies , by observations of the kinematics and morphology of extremely faint hii regions , and by any correlation between old and dispersed ob associations and giant hi shells .

the pressures of giant hii regions in 6 dwarf irregular galaxies are found to be a factor of larger than the average pressures of the corresponding galaxy disks , obtained from the stellar and gaseous column densities . this is unlike the situation for spiral galaxies where these two pressures are approximately equal . there is a problem with both of these solutions , however : the vertical scale heights inferred for irregular galaxies are consistent with the luminous matter alone . these peaks also explain the anomalously low average column density thresholds for star formation that were found earlier for irregular galaxies , and they permit the existence of a cool hi phase as the first step toward dense molecular cores . the third possibility is that all of the visible hii regions in these dwarf galaxies are strongly over - pressured and still expanding .

the pressures of giant hii regions in 6 dwarf irregular galaxies are found to be a factor of larger than the average pressures of the corresponding galaxy disks , obtained from the stellar and gaseous column densities . this is unlike the situation for spiral galaxies where these two pressures are approximately equal . either the hii regions in these dwarfs are all so young that they are still expanding or there is an unexpected source of disk self - gravity that increases the background pressure . we consider first whether any additional self - gravity might come from disk dark matter that is either cold h gas in diffuse or self - gravitating clouds with weak co emission , or is the same material as the halo dark matter inferred from rotation curves . the h solution is possible because cold molecular clouds would be virtually invisible in existing surveys if they were also co - weak from the low metal abundances in these galaxies . cosmological dark matter might be possible too because of the relatively large volume fraction occupied by the disk within the overall galaxy potential . there is a problem with both of these solutions , however : the vertical scale heights inferred for irregular galaxies are consistent with the luminous matter alone . the amount of disk dark matter that is required to explain the high hii region pressures would give gas and stellar scale heights that are too small . the anomalous pressures in star - forming regions are more likely the result of local peaks in the gravitational field that come from large gas concentrations . these peaks also explain the anomalously low average column density thresholds for star formation that were found earlier for irregular galaxies , and they permit the existence of a cool hi phase as the first step toward dense molecular cores . the evidence for concentrations of hi in regions of star formation is summarized ; the peak column densities are shown to be consistent with local pressure equilibrium for the hii regions . strongly self - gravitating star - forming regions should also limit the dispersal of metals into the intergalactic medium . the third possibility is that all of the visible hii regions in these dwarf galaxies are strongly over - pressured and still expanding . the mean time to pressure equilibrium is times their current age , which implies that the observed population is only 7% of the total if they live that long ; the rest are presumably too faint to see . the expansion model also implies that the volume filling factor can reach times the current factor , in which case faint and aging hii regions should merge and occupy nearly the entire dwarf galaxy volume . this would explain the origin of the giant hi shells seen in these galaxies as the result of old , expanded hii regions that were formerly driven by ob associations . the exciting clusters would now be so old and dispersed that they would not be recognized easily . the shells are still round because of a lack of shear . received 16 february 2000 ; accepted 13 april 2000

0805.3824

i

the problem of error correction for a network implementing linear network coding has been an active research area since 2002 @xcite . the crucial motivation for the problem is the phenomenon of error propagation , which arises due to the recombination characteristic at the heart of network coding . a single corrupt packet occurring in the application layer ( e.g. , introduced by a malicious user ) may proceed undetected and contaminate other packets , causing potentially drastic consequences and essentially ruling out classical error correction approaches . in the basic multicast model for linear network coding , a source node transmits @xmath0 packets , each consisting of @xmath1 symbols from a finite field @xmath2 . each link in the network transports a packet free of errors , and each node creates outgoing packets as @xmath2-linear combinations of incoming packets . there are one or more destination nodes that wish to obtain the original source packets . at a specific destination node , the received packets may be represented as the rows of an @xmath3 matrix @xmath4 , where @xmath5 is the matrix whose rows are the source packets and @xmath6 is the transfer matrix of the network . errors are incorporated in the model by allowing up to @xmath7 error packets to be added ( in the vector space @xmath8 ) to the packets sent over one or more links . the received matrix @xmath9 at a specific destination node may then be written as @xmath10 where @xmath11 is a @xmath12 matrix whose rows are the error packets , and @xmath13 is the transfer matrix from these packets to the destination . under this model , a coding - theoretic problem is how to design an outer code and the underlying network code such that reliable communication ( to all destinations ) is possible . this coding problem can be posed in a number of ways depending on the set of assumptions made . for example , we may assume that the network topology and the network code are known at the source and at the destination nodes , in which case we call the system _ coherent network coding_. alternatively , we may assume that such information is unavailable , in which case we call the system _ noncoherent network coding_. the error matrix @xmath11 may be random or chosen by an adversary , and there may be further assumptions on the knowledge or other capabilities of the adversary . the essential assumption , in order to pose a meaningful coding problem , is that the number of injected error packets , @xmath7 , is bounded . error correction for coherent network coding was originally studied by cai and yeung @xcite . aiming to establish fundamental limits , they focused on the fundamental case @xmath14 . in @xcite ( see also @xcite ) , the authors derive a singleton bound in this context and construct codes that achieve this bound . a drawback of their approach is that the field size required can be very large ( on the order of @xmath15 , where @xmath16 is the number of edges in the network ) , and no efficient decoding method is given . similar constructions , analyses and bounds appear also in @xcite . in section [ sec : coherent - network - coding ] , we approach this problem ( for general @xmath1 ) under a different framework . we assume the pessimistic situation in which the adversary can not only inject up to @xmath7 packets but can also freely choose the matrix @xmath13 . in this scenario , it is essential to exploit the structure of the problem when @xmath17 . the proposed approach allows us to find a metric the rank metric that succinctly describes the error correction capability of a code . we quite easily obtain bounds and constructions analogous to those of @xcite , and show that many of the results in @xcite can be reinterpreted and simplified in this framework . moreover , we find that our pessimistic assumption actually incurs no penalty since the codes we propose achieve the singleton bound of @xcite . an advantage of this approach is that it is _ universal _ , in the sense that the outer code and the network code may be designed independently of each other . more precisely , the outer code may be chosen as any rank - metric code with a good error - correction capability , while the network code can be designed as if the network were error - free ( and , in particular , the field size can be chosen as the minimum required for multicast ) . an additional advantage is that encoding and decoding of properly chosen rank - metric codes can be performed very efficiently @xcite . for noncoherent network coding , a combinatorial framework for error control was introduced by ktter and kschischang in @xcite . there , the problem is formulated as the transmission of subspaces through an operator channel , where the transmitted and received subspaces are the row spaces of the matrices @xmath5 and @xmath9 in ( [ eq : matrix - model ] ) , respectively . they proposed a metric that is suitable for this channel , the so - called subspace distance @xcite . they also presented a singleton - like bound for their metric and subspace codes achieving this bound . the main justification for their metric is the fact that a minimum subspace distance decoder seems to be the necessary and sufficient tool for optimally decoding the disturbances imposed by the operator channel . however , when these disturbances are translated to more concrete terms such as the number of error packets injected , only decoding guarantees can be obtained for the minimum distance decoder of @xcite , but no converse . more precisely , assume that @xmath7 error packets are injected and a general ( not necessarily constant - dimension ) subspace code with minimum subspace distance @xmath18 is used . in this case , while it is possible to guarantee successful decoding if @xmath19 , and we know of specific examples where decoding fails if this condition is not met , a general converse is not known . in section [ sec : noncoherent - network - coding ] , we prove such a converse for a new metric called the _ injection distance_under a slightly different transmission model . we assume that the adversary is allowed to arbitrarily select the matrices @xmath6 and @xmath13 , provided that a lower bound on the rank of @xmath6 is respected . under this pessimistic scenario , we show that the injection distance is the fundamental parameter behind the error correction capability of a code ; that is , we can guarantee correction of @xmath7 packet errors _ if and only if _ @xmath7 is less than half the minimum injection distance of the code . while this approach may seem too pessimistic , we provide a class of examples where a minimum - injection - distance decoder is able to correct more errors than a minimum - subspace - distance decoder . moreover , the two approaches coincide when a constant - dimension code is used . in order to give a unified treatment of both coherent and noncoherent network coding , we first develop a general approach to error correction over ( certain ) adversarial channels . our treatment generalizes the more abstract portions of classical coding theory and has the main feature of mathematical simplicity . the essence of our approach is to use a single function called a _ discrepancy function_to fully describe an adversarial channel . we then propose a distance - like function that is easy to handle analytically and ( in many cases , including all the channels considered in this paper ) precisely describes the error correction capability of a code . the motivation for this approach is that , once such a distance function is found , one can virtually forget about the channel model and fully concentrate on the combinatorial problem of finding the largest code with a specified minimum distance ( just like in classical coding theory ) . interestingly , our approach is also useful to characterize the error detection capability of a code . the remainder of the paper is organized as follows . section [ sec : preliminaries ] establishes our notation and review some basic facts about matrices and rank - metric codes . section [ sec : adversarial - model ] presents our general approach to adversarial error correction , which is subsequently specialized to coherent and noncoherent network coding models . section [ sec : coherent - network - coding ] describes our main results for coherent network coding and discusses their relationship with the work of yeung et al . @xcite . section [ sec : noncoherent - network - coding ] describes our main results for noncoherent network coding and discusses their relationship with the work of ktter and kschischang @xcite . section [ sec : conclusion ] presents our conclusions .

is succinctly described by the rank metric ; as a consequence , it is shown that universal network error correcting codes achieving the singleton bound can be easily constructed and efficiently decoded . all of these results are based on a general approach to adversarial error correction , which could be useful for other adversarial channels beyond network coding .

the problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model . for coherent network coding , where knowledge of the network topology and network code is assumed at the source and destination nodes , the error correction capability of an ( outer ) code is succinctly described by the rank metric ; as a consequence , it is shown that universal network error correcting codes achieving the singleton bound can be easily constructed and efficiently decoded . for noncoherent network coding , where knowledge of the network topology and network code is not assumed , the error correction capability of a ( subspace ) code is given exactly by a new metric , called the _ injection metric _ , which is closely related to , but different than , the subspace metric of ktter and kschischang . in particular , in the case of a non - constant - dimension code , the decoder associated with the injection metric is shown to correct more errors then a minimum - subspace - distance decoder . all of these results are based on a general approach to adversarial error correction , which could be useful for other adversarial channels beyond network coding . adversarial channels , error correction , injection distance , network coding , rank distance , subspace codes .

0805.3824

c

we have addressed the problem of error correction in network coding under a worst - case adversarial model . we show that certain metrics naturally arise as the fundamental parameter describing the error correction capability of a code ; namely , the rank metric for coherent network coding , and the injection metric for noncoherent network coding . for coherent network coding , the framework based on the rank metric essentially subsumes previous analyses and constructions , with the advantage of providing a clear separation between the problems of designing a feasible network code and an error - correcting outer code . for noncoherent network coding , the injection metric provides a measure of code performance that is more precise , when a non - constant - dimension code is used , than the so - called subspace metric . the design of general subspace codes for the injection metric , as well as the derivation of bounds , is left as an open problem for future research .

the problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model . for coherent network coding , where knowledge of the network topology and network code is assumed at the source and destination nodes , the error correction capability of an ( outer ) code adversarial channels , error correction , injection distance , network coding , rank distance , subspace codes .

the problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model . for coherent network coding , where knowledge of the network topology and network code is assumed at the source and destination nodes , the error correction capability of an ( outer ) code is succinctly described by the rank metric ; as a consequence , it is shown that universal network error correcting codes achieving the singleton bound can be easily constructed and efficiently decoded . for noncoherent network coding , where knowledge of the network topology and network code is not assumed , the error correction capability of a ( subspace ) code is given exactly by a new metric , called the _ injection metric _ , which is closely related to , but different than , the subspace metric of ktter and kschischang . in particular , in the case of a non - constant - dimension code , the decoder associated with the injection metric is shown to correct more errors then a minimum - subspace - distance decoder . all of these results are based on a general approach to adversarial error correction , which could be useful for other adversarial channels beyond network coding . adversarial channels , error correction , injection distance , network coding , rank distance , subspace codes .

1301.7455

c

we considered a setting where opinions of individuals in a social network evolve through processes of social dynamics , reaching a nash equilibrium . adopting a standard social and economic model of such dynamics we addressed the following natural question : given a social network of individuals who have their own internal opinions about an information item , which are the individuals that need to be convinced to adopt a positive opinion so that in the equilibrium state , the network ( as a whole ) has the maximum positive opinion about the item ? we studied the computational complexity of this problem and proposed algorithms for solving them exactly or approximately . our theoretical analysis and the algorithm design relied on a connection between opinion dynamics and random walks with absorbing states . our experimental evaluation on real datasets demonstrated the efficacy of our algorithms and the effect of the structural characteristics of the underlying social networks on their performance . 10 benchmark folksonomy data from bibsonomy . technical report , knowledge and data engineering group , university of kassel , 2007 . d. acemoglu and a. ozdaglar . opinion dynamics and learning in social networks . , 2011 . d. bindel , j. m. kleinberg , and s. oren . how bad is forming your own opinion ? in _ focs _ , 2011 . s. brin and l. page . the anatomy of a large - scale hypertextual web search engine . in _ www _ , 1998 . n. chen . on the approximability of influence in social networks . in _ soda _ , 2008 . m. h. degrout . reaching consensus . , 1974 . p. m. demarzo , d. vayanos , and j. zweibel . persuasion bias , social influence , and unidimensional opinions . , 2003 . p. doyle and j. snell . . mathematical association of america , 1984 . e. even - dar and a. shapira . a note on maximizing the spread of influence in social networks . in _ wine _ , 2007 . u. feige . vertex cover is hardest to approximate on regular graphs . , 2003 . n. e. friedkin and e. johnsen . social influence and opinions . , 1990 . b. golub and m. o. jackson . naive learning in social networks : convergence , influence and the wisdom of the crowds . , 2010 . m. o. jackson . . princeton university press , 2008 . d. kempe , j. m. kleinberg , and . tardos . maximizing the spread of influence through a social network . in _ kdd _ , 2003 . d. e. knuth . . addison - wesley , 1993 . d. krackhardt . a plunge into networks . , 2009 . j. leskovec , a. krause , c. guestrin , c. faloutsos , j. m. vanbriesen , and n. s. glance . cost - effective outbreak detection in networks . in _ kdd _ , 2007 . d. lusseau , k. schneider , o. j. boisseau , p. haase , e. slooten , and s. m. dawson . , 54:396405 , 2003 . g. nemhauser , l. wolsey , and m. fisher . an analysis of the approximations for maximizing submodular set functions . , 1978 . m. richardson and p. domingos . mining knowledge - sharing sites for viral marketing . in _ kdd _ , 2002 . w. w. zachary . an information flow model for conflict and fission in small groups . , 33:452473 , 2003 .

, we adopt a well - established model for social - opinion dynamics and formalize the campaign - design problem as the problem of identifying a set of target individuals whose positive opinion about an information item will maximize the overall positive opinion for the item in the social network . we study the complexity of the campaign problem , and design algorithms for solving it . our experiments on real data demonstrate the efficiency and practical utility of our algorithms .

the process of opinion formation through synthesis and contrast of different viewpoints has been the subject of many studies in economics and social sciences . today , this process manifests itself also in online social networks and social media . the key characteristic of successful promotion campaigns is that they take into consideration such opinion - formation dynamics in order to create a overall favorable opinion about a specific information item , such as a person , a product , or an idea . in this paper , we adopt a well - established model for social - opinion dynamics and formalize the campaign - design problem as the problem of identifying a set of target individuals whose positive opinion about an information item will maximize the overall positive opinion for the item in the social network . we call this problem campaign . we study the complexity of the campaign problem , and design algorithms for solving it . our experiments on real data demonstrate the efficiency and practical utility of our algorithms .

hep-ph0606205

i

the evolution of cosmic string networks is a challenging problem . the need to consider large ratios of length and time scales makes a complete numerical analysis impossible , while the nonlinearity of the process defeats a purely analytic treatment . thus a full understanding of most of the signatures of cosmic strings will require a careful combination of analytic and numerical approaches . this is needed both to establish precisely the current bounds on the dimensionless cosmic string tension @xmath0 , and to anticipate what will be the most sensitive future measurements . also , if cosmic strings are one day discovered , a precise understanding of the network properties will be needed in order to distinguish different microscopic models . on scales close to the horizon size , the networks are reasonably well understood from simulations @xcite . in particular , there are a few dozen long strings crossing any horizon volume . on shorter scales , however , the situation is far less clear . there is a nontrivial short distance structure on the strings , which arises because the intercommutation process produces kinks @xcite . there have been many previous analytic and numerical studies of this , but there is no general consensus as to its nature . in particular , the size at which typical loops form is uncertain to tens of orders of magnitude . one widely - held assumption has been that gravitational radiation is necessary in order for cosmic string networks to scale @xcite , and that it determines the size of loops . if so , the loops will be parametrically smaller than the horizon scale , by a power of @xmath0 @xcite ( even shorter scales have been suggested @xcite ) . more recent work appears to be converging on loop sizes at a fixed fraction of the horizon scale , but even here there are significant differences . ref . @xcite suggests that loops form at around @xmath1 times the horizon scale , whereas refs . @xcite ( and some portion of the conventional wisdom ) suggest a scale several orders of magnitude smaller . the larger loops would lead to enhanced signatures of several types , and tighter bounds on @xmath0 @xcite . in a system with a large hierarchy of scales , one might hope that analytic methods would be particularly useful in separating the processes occurring at different scales , while numerical methods would be needed to understand the nonlinearities at a given scale . this is the philosophy that we will attempt to implement . we focus on a microscopic description , similar in spirit to ref . @xcite and in particular ref . an important difference from ref . @xcite is that we are less ambitious : that work was largely directed at understanding the horizon - scale structure quantitatively , whereas we are only interested in shorter scales . also , we do not attempt to reduce the dynamics to a parameterized model but rather focus on the full two - point function ; this two - point function appears to be characterized by a critical exponent , which did not enter into previous work . finally , our ( tentative ) conclusions are opposite to ref . @xcite , in that we believe that the network scales even without gravitational radiation . the full microscopic equations for the string network @xcite appear to be too complicated to solve , and so we model what we hope are the essential physical processes . we have had some success in matching results from simulations , but there are also some discrepancies which may indicate additional processes that must be included . in section 2 we consider the evolution of a small segment on a long string . if the rate of string intercommutations is fixed in horizon units , then over a range of scales the only important effect would be stretching due to the expansion of the universe . we are then able to determine the two - point functions characterizing the small scale structure . we find that the string is actually rather smooth , in agreement with recent simulations @xcite : its fractal dimension approaches one as we go to smaller scales . there is a nontrivial power law , but this appears in the _ approach _ of the fractal dimension to one ; that is , the critical exponent @xmath2 is related to the power spectum of perturbations on the long string . the two - point functions depend on two parameters that must be taken from simulations . one of these is the mean @xmath3 of an element of the long string ; this determines the exponent @xmath2 . the second parameter is the normalization of the two - point function . our results for the two - point function match reasonably well with the simulations @xcite over a range of scales , but there is substantial deviation at the shortest scales . it remains to be seen whether this is due to transient effects in the simulations , or real effects that we have omitted . in section 3 we study the effects of the small scale structure on string lensing . because the string is fairly smooth , these effects are not as dramatic as has been considered in some previous work . however , there are calculable deviations from perfect lensing . we also consider , for lensing by a long string , the likely trajectory of the string relative to the axis of a given lensed object . we discuss some deviations from gaussianity in the small scale structure , due to kinks . in section 4 we add in loop production as a perturbation . even though the strings are relatively smooth at short distance , we find that the total rate of loop production diverges for small loops ; the rate of divergence appears to agree with recent simulations @xcite . this divergence does not invalidate our stretching model , because the loop production is localized to regions where the left- and right - moving tangents @xmath4 are approximately equal , but it points to a complicated fragmentation process , cascading to smaller and smaller loops . we are not able to follow the fragmentation process analytically at present , but we give an analytic argument as to why the cascade should terminate , leaving loops at some small but fixed multiple of the horizon scale . we also point out an interesting puzzle related to loop velocities , which again points to a complicated fragmentation process . in section 5 we discuss various applications and future directions . the behavior of string networks is notoriously complicated , and it appears to remain so even when one focusses on small scales . thus we view our work as part of an ongoing dialogue between analytic calculations and simulations , which we hope will lead to a more complete and precise picture .

we then add in loop production as a perturbation and find that it diverges at small scales . this need not invalidate the stretching model , since the loop production occurs in localized regions , but it implies a complicated fragmentation process . our ability to model this process is limited , but we argue that loop production peaks a few orders of magnitude below the horizon scale , without the inclusion of gravitational radiation . we find agreement with some features of simulations , and interesting discrepancies that must be resolved by future work . * analytic study of small scale structure on cosmic strings * joseph polchinski _ kavli institute for theoretical physics _ _ university of california _ _ santa barbara , ca 93106 - 4030 _ joep@kitp.ucsb.edu santa barbara , ca 93106 _ jrocha@physics.ucsb.edu = 16pt

the properties of string networks at scales well below the horizon are poorly understood , but they enter critically into many observables . we argue that in some regimes , stretching will be the only relevant process governing the evolution . in this case , the string two - point function is determined up to normalization : the fractal dimension approaches one at short distance , but the rate of approach is characterized by an exponent that plays an essential role in network properties . the smoothness at short distance implies , for example , that cosmic string lensing images are little distorted . we then add in loop production as a perturbation and find that it diverges at small scales . this need not invalidate the stretching model , since the loop production occurs in localized regions , but it implies a complicated fragmentation process . our ability to model this process is limited , but we argue that loop production peaks a few orders of magnitude below the horizon scale , without the inclusion of gravitational radiation . we find agreement with some features of simulations , and interesting discrepancies that must be resolved by future work . * analytic study of small scale structure on cosmic strings * joseph polchinski _ kavli institute for theoretical physics _ _ university of california _ _ santa barbara , ca 93106 - 4030 _ joep@kitp.ucsb.edu jorge v. rocha _ department of physics _ _ university of california _ santa barbara , ca 93106 _ jrocha@physics.ucsb.edu = 16pt

0906.5576

i

with the advent of quantum field theory our idea of vacuum has been strongly modified with respect to that of classical physics . vacuum is no more intended as a literal nothing but as a physical entity with a complex structure . within the framework of quantum electrodynamics ( qed ) , the interest in investigating the properties of quantum vacuum has been growing considerably in the last years , mostly due to the advancement of the strong field laser technique . in particular , many experimental schemes have been put forward to measure these properties ( see the recent reviews @xcite and the references therein ) . in fact , qed predicts that in the presence of very intense electromagnetic fields quantum vacuum manifests dielectric properties due to the polarization of the virtual electron - positron background and even breaks down in stronger fields when virtual electron - positron pairs , acquiring sufficient energy from the field , become real @xcite . the strength scale of the electromagnetic field where the qed vacuum effects become apparent is determined by the so - called critical fields : @xmath0 and @xmath1 ( here @xmath2 and @xmath3 are the electron charge and mass , respectively and natural units with @xmath4 are used ) . the investigation of the properties of qed vacuum is closely connected with the possibility of testing qed in the presence of strong background electromagnetic fields . however , the values of the critical fields are far beyond the strength of electromagnetic fields that can be produced in terrestrial laboratories . a remarkable exception to this fact are highly charged nuclei . in the context of qed , `` highly charged nuclei '' are nuclei with a charge number @xmath5 such that @xmath6 , with @xmath7 the fine structure constant . in fact , the electric field of highly charged nuclei at the typical qed length @xmath8 ( compton length ) is comparable with the critical field @xmath9 . this explains the recent experimental successes in measuring the delbrck scattering @xcite , i. e. the scattering of a high - energy photon by the field of a highly charged ion , and the photon splitting in a coulomb field @xcite confirming the theoretical predictions @xcite . the development of laser technology is opening up the possibility of probing the properties of qed vacuum and of testing qed in the presence of intense wave fields . although the next generation of petawatt laser systems is expected to reach an intensity of `` only '' @xmath10 @xcite , different theoretical schemes have been put forward to approach the so - called schwinger intensity of @xmath11 @xcite . a significant step towards the schwinger intensity will be realized in the near future at the extreme light infrastructure ( eli ) where unprecedented intensities of the order of @xmath12 will be attained @xcite . the ever - increasing available laser intensities have stimulated numerous theoretical proposals to observe `` refractive '' vacuum polarization effects ( vpes ) induced by strong laser fields @xcite , while the observation of `` absorptive '' vpes in colliding laser beams , namely electron - positron pair creation , requires field intensities of the order of @xmath13 @xcite . however , laser - assisted pair production was observed about ten years ago at the stanford linear accelerator center ( slac ) in the collision of a high - energy electron beam ( @xmath14 ) and an optical laser beam with an intensity of the order of @xmath15 @xcite . due to the large electron energy , the effective laser field amplitude and frequency in the rest frame of the electron are much larger than their value in the laboratory frame and this has allowed electron - positron pair creation . a qed process in a strong laser field , that is characterized by a typical four - momentum of a particle @xmath16 and by a laser field with four - vector potential amplitude @xmath17 , field tensor amplitude @xmath18 , electric field amplitude @xmath19 and frequency @xmath20 , depends on the two invariant parameters @xmath21 and @xmath22 ( the metric @xmath23 is employed ) @xcite . the classical field parameter @xmath24 can be interpreted as the work done by the laser field on the electron in the compton length @xmath8 in units of the laser photon energy and , therefore , determines the role of multiphoton processes ( at @xmath25 the process is multiphoton ) . the same parameter @xmath24 also determines the adiabaticity of the process ( the limit @xmath26 and @xmath27 fixed corresponds to the constant crossed field case ) @xcite . the quantum field parameter @xmath27 determines the magnitude of the quantum nonlinear effects . when @xmath28 multiphoton effects play a minor role and the probability of the process goes to its perturbative weak field limit described by the feynman diagram(s ) of lowest order in the laser field . in the opposite case of @xmath26 the process is adiabatic , the laser field is almost constant and the photon picture does not hold anymore . in this limit another perturbative weak field regime exists when the parameter @xmath27 is much smaller than unity . in the following , by `` perturbative regime '' we mean that either @xmath29 or @xmath30 when the process probability can be represented as a power expansion in the corresponding small parameter . in the case of two equal , counterpropagating laser beams , the parameter @xmath27 results from the @xmath18 of one laser beam and from the @xmath31 of a photon of the other laser beam : @xmath32 . the schemes proposed in @xcite to observe vpes in colliding laser beams are limited to _ perturbative _ processes . this is because for usual parameters of strong optical lasers , though the condition @xmath33 is easily fulfilled , nevertheless , @xmath34 since @xmath35 and @xmath36 , and , consequently , the nonperturbative effects are suppressed @xcite . however , the vpes can be increased if a strong laser beam collides with a high - energy proton beam . analogously to the slac experiment @xcite , this is due to the lorentz boost of the laser field amplitude and frequency in the rest frame of the relativistically fast moving proton . the perturbative regime ( @xmath34 and @xmath37 ) of scattering of a strong laser field with arbitrary polarization by a coulomb field has been considered in @xcite . the first attempt to go beyond the perturbative regime of vpes in this process has been done in the early work of ref . @xcite , where the laser photon merging was considered in the scattering of a strong _ circularly _ polarized laser field by a coulomb field . due to the symmetry of the system , however , only two laser photons can merge if the laser field is circularly polarized , i. e. the possibility of multiphoton vpes is in principle ruled out in this case . moreover , the author explicitly considers only regions of parameters where nonperturbative effects either are completely negligible or cancel out each other , in such a way that the final results are , in fact , perturbative . already in ref . @xcite it was pointed out that the large lorentz boost of a high - energy proton beam enhances the cross - section of the photon merging process in the perturbative case . moreover , the enhancement of the laser field amplitude and frequency may open a way to nonperturbative regimes : @xmath33 and @xmath38 . in @xcite we have done the first calculation of probabilities of nonperturbative refractive vpes in the collision of a high - energy proton beam with a linearly polarized , strong laser field and proposed a setup that will allow an observation of the merging of multiple pairs of laser photons into a single high - energy photon due to vpe induced by the proton field and the laser field . the proton features fit very well the requirements of this setup . in fact , on the one hand it is light enough to be accelerated to very high energies like up to @xmath39 at the tevatron or even up to @xmath40 at the forthcoming large hadron collider ( lhc ) @xcite , such that the laser field amplitude and frequency in the proton rest frame are significantly larger than their values in the laboratory frame . on the other hand , the proton is heavy enough that multiphoton thomson scattering of the laser photons by the proton itself is strongly suppressed . this is of great advantage with respect to employing , for example , an electron beam because , as we will see , multiphoton thomson scattering represents a background of our process of laser photon merging . the nonperturbative vpes during a proton and a laser beam collision manifest themselves in two ways . first , the scaling of the photon merging probability is very sensitive to the laser field parameters . thus , in the limit @xmath33 the probability @xmath41 of the merging of @xmath42 photons scales as @xmath43 if @xmath44 , while in the perturbative case ( @xmath30 ) the scaling is @xmath45 . second , the multiphoton processes ( merging of @xmath42 laser photons with @xmath46 ) , while being negligibly small in the perturbative regime , become significant and observable in the nonperturbative regime . in our previous letter @xcite we have investigated the most favorable case for observation of multiphoton vpes by employing proton accelerators already available and the next generation of petawatt optical laser systems . accordingly , we have calculated the probabilities of the photon merging in the domain of @xmath26 and @xmath27 fixed . however , there are other interesting regimes of parameters which show peculiarities in the amplitudes of the process and which are connected with the possibility of the experimental observation of laser photon merging with the next generation of x - ray - free electron lasers ( x - fels ) like those available in the near future at desy @xcite and at slac @xcite . the investigation of these regimes is carried out in the present paper . in the present paper we thoroughly investigate the laser photon merging process during the proton and laser beam collision in nonperturbative regimes , taking into account exactly the influence of the laser field . starting from the general expressions of the amplitudes of the process , we obtain analytical asymptotics valid in different parameters regions and analyze ranges of parameters not considered yet . in particular , additionally to the previous results , we obtain new analytical expressions for the amplitudes of the process in the domain of @xmath28 and for any @xmath47 , as well in the regime of @xmath48 and @xmath25 that are relevant for x - fel . we also analyze the experimental feasibility of the process with different possible experimental devices . attention is devoted to the question of how advantageous for the photon merging process could be the complementary virtues of an x - fel with respect to an optical laser , namely , the high photon energy , the high repetition rate and the relatively large space - time volume of the laser beam . as we will see , the use of optical strong laser fields is much more favorable from an experimental point of view . for this reason , in addition to the results in @xcite , we also investigate in this case the polarization and the complete angular distribution of the emitted photons . the paper is organized as follows : the theoretical model is considered in sec . the asymptotics of the probability of the process are analyzed in sec . iii . in the same section , in each asymptotic limit the corresponding physical situations are considered and the process feasibility is discussed . the summary of sec . iv concludes the paper . for the sake of completeness , we have reported in an appendix the expression of the polarization operator found in @xcite that will be our starting point here .

the quantum electrodynamical vacuum polarization effects arising in the collision of a high - energy proton beam and a strong , linearly polarized laser field are investigated . the probability that laser photons merge into one photon by interacting with the protons electromagnetic field is calculated taking into account the laser field exactly .

the quantum electrodynamical vacuum polarization effects arising in the collision of a high - energy proton beam and a strong , linearly polarized laser field are investigated . the probability that laser photons merge into one photon by interacting with the protons electromagnetic field is calculated taking into account the laser field exactly . asymptotics of the probability are then derived according to different experimental setups suitable for detecting perturbative and nonperturbative vacuum polarization effects . the experimentally most feasible setup involves the use of a strong optical laser field . it is shown that in this case measurements of the polarization of the outgoing photon and and of its angular distribution provide promising tools to detect these effects for the first time .

nucl-ex0006012

r

1 and 2 show typical singles particle and @xmath3-ray spectra obtained at 125 mev bombarding energy . figs . 3 and 4 show similar spectra obtained at 135 mev beam energy . from the measured @xmath4-particle and @xmath3-ray energies and lifetimes , production cross sections for various evaporation residue nuclei , with estimated errors of @xmath3825% , were deduced and are summarized in table 1 . ( cross sections for some isomeric states ( see below ) , are also given in table 1 . ) figs . 5 and 6 give respective @xmath4-@xmath3 coincidence plots from measurements i and ii , corresponding to irradiations i and ii . . 7 and 8 are one dimensional projection plots on the @xmath4-particle axis of figs . 5 and 6 , respectively , for e@xmath3 @xmath7 25 kev . 9 presents a particle-@xmath3 coincidence spectrum from measurement iii , corresponding to irradiation iii.e - e system of ref . @xcite was performed and gave negative results with an upper limit of about 0.5 nb for half - lives of between 20 hours to 70 days . on the other hand , in the 135 mev experiment ( fig . 9 ) we most probably saw protons in the particle-@xmath3 coincidences . ( see further below ) . ] the estimated numbers of random coincidences in the 3 10 mev particle energy and 10 250 kev @xmath3-energy are 5.4 x 10@xmath39 , 4.4 x 10@xmath39 , and 0.4 in figs . 5 , 6 , and 9 , respectively . some of the coincidence events in figs . 5 , 6 and 9 , between 5 - 6 mev @xmath4-particles and various @xmath3-rays , may perhaps be due to a contamination from an emanated @xmath40pb source from @xmath41th , which was used in the same chamber about 4 months earlier @xcite . despite the long time delay to our present long term measurements of 77 to 235 days , and careful cleaning of the chamber , we might have picked up some residual contamination . also , indication for k x - rays of rn is seen in this region . while in principle their origin may be from some reaction products , they also may be from the decay of @xmath42ra , which belongs to the @xmath43u chain . although it is not likely , but because of this ambiguity , we will not try to make a claim about this region . a two - dimensional background measurement , taken for 8 days , before the @xmath40pb source was used in the chamber , gave zero events in the whole region of 3.5 10 mev particles and 0 250 kev @xmath3 s . it is seen in figs . 5 and 6 , and figs . 7 and 8 , that while the region of @xmath4-particles of 6 8 mev is relatively empty , coincidence events are seen between various @xmath3-rays and @xmath4-particles of 8 9 mev . in fig . 5 , 13 coincidence events between 7.99 - 8.61 mev @xmath4-particles and various @xmath3-rays of e @xmath7 20 kev are observed , where 8 of them fall within a narrow range of 190 kev particle energy , between 8.42 - 8.61 mev . ( the estimated @xmath4-particle full line width for the 200 @xmath27g/@xmath44 c foil is around 340 kev ) . from the intensities of the singles in the @xmath4- and @xmath3-ray spectra ( 339 @xmath4-particles and 2.14x10@xmath45 gamma - rays in 76.8 days ) , and the resolving time of 1 @xmath27s of the coincidence system , the total number of random coincidences in the 8 - 9 mev region was estimated to be 2.2x10@xmath46 . in fig . 6 one finds 8 coincidence events between 8.19 9.01 mev , where 5 of them fall within 70 kev , between 8.55 8.62 mev , and one at 9.01 mev . ( the @xmath4-particle full line width for a 60 @xmath27g/@xmath44 c foil is about 100 kev ) . the corresponding estimated total number of random coincidences between 8 to 9 mev is 1.4x10@xmath46 . one does not see such concentration of events in the same energy region in fig . 9 which was taken for about 2.7 times longer period than figs . 5 and 6 . 3 events are seen in the 8 - 9 mev region in fig . 9 which sets an upper limit on the background in figs . 5 and 6 to be aroud 1 count as compared to the respective 13 and 8 counts seen experimentally . it was estimated that in the 8 9 mev range of @xmath4-particles , at most 0.8 events in fig . 5 and 0.3 events in fig . 6 may be due to the contamination mentioned above of coincidences between @xmath47 and @xmath3-rays from @xmath40bi and the 8.78 mev @xmath4-particles from @xmath40po ( t@xmath5 = 0.3 @xmath27s ) . shows time sequence plots for the @xmath4-@xmath3 coincidences with @xmath4-energies of 89 mev obtained in measurements i and ii and seen in figs . 5 and 6 , respectively . in measurement ii a growth in the intensity of the 89 mev group was found from the beginning up to 97 days after the end of irradiation . in measurement i no significant change in decay rate was observed between 77 to 154 days and , by binning the data , t@xmath5 @xmath7 40 days was estimated for the lower limit of the decaying half - life . an additional measurement , taken about 4.5 y after the one presented in fig . 5 and measurement i of fig . 10 , gave 0 counts in 22.0 d. an upper limit for the half - life of t@xmath5 @xmath30 2.1 y is deduced from this measurement . table 2(a ) and fig . 11 show that almost all the coincidence events in figs . 5 and 6 with 7.8 - 8.61 mev @xmath4-particles ( the encircled ones ) fit very nicely with a j(j+1 ) law assuming e@xmath48 = 4.42xj(j+1 ) kev and @xmath29j = 1 . this fit is very significant from a statistical point of view @xcite . all the gamma - rays in fig . 5 ( 7 out of 7 events ) , and almost all of them in fig . 6 ( 6 out of 7 events ) , which are above 90 kev , fit , to within @xmath380.5 kev on the average , with this formula . the probability for 13 out of 14 events which are distributed evenly ( for instance due to compton effect from higher energy gamma - rays ) , to fall into 13 specified energy positions , within 1 kev is : @xmath49 . p is equal to 36x1.0/(250 - 90 ) . 36 is the number of possible gamma - transitions between states of both integer and half integer spins with e@xmath48 = 4.42 x j(j+1 ) , in the range of 90 to 250 kev . ( the four low energy events of e@xmath50 @xmath30 60 kev in fig . 5 and the one event in fig . 6 which do not fit with the j(j+1 ) rule may be due to compton events ) . it is also seen in fig . 6 and in table 2(b ) that the @xmath3-rays of the 3 coincidence events in the region of 6 - 7 mev @xmath4-energy of 6.16 mev - 176.1 kev , 6.94 mev - 207.4 kev and 6.41 mev - 242.3 kev , fit with 20 @xmath51 19 ( 176.4 ) , 47/2 @xmath51 45/2 ( 207.3 ) and 55/2 @xmath51 53/2 ( 242.6 ) j @xmath51 j-1 transitions , assuming e@xmath48 = 4.41xj(j+1 ) kev . the probability in this case that this fit is accidental due to a chance coincidence of evenly distributed events is 1.2x10@xmath46 , taking into account that p = 18x0.47/(250 - 170 ) . 18 is the number of possible gamma - transitions in the range of 170 to 250 kev , and 0.47 kev is twice the average deviation from the specified energies . ( this probability increases to 1.1x10@xmath39 if , instead of 0.47 kev , the value which was used before of 1.0 kev is assumed in the calculation ) . it should be mentioned that rotational constants around 4.4 kev correspond to superdeformed bands [ sdb ] in this region of nuclei @xcite . in fig . 9 one sees about 10 scattered events in the 6.5 9 mev region . some of them may also fit with a j(j+1 ) law . however , the statistical significance of the fit in this case is not so good and we will not discuss them further . the appearance in table 2a of both integer and half - integer spins at low @xmath3-ray energies indicates that bands in both even and odd nuclei were formed . ( at high energies the observed transitions are probably sum events . see the following paragraphs . ) @xmath52rn , produced via pn evaporation , and its daughters , are , from the kinematic point of view , the best candidates for the half - integer transitions . the 8.42 mev @xmath4-particle in coincidence with a photon of 67.1 kev ( seen in fig . 5 and table 3 below ) , which fits with k@xmath14 x - ray of pt ( known energy 66.832 kev ) , may indicate that the @xmath4-transition is from @xmath53hg to @xmath54pt . @xmath53hg is the daughter after 3 @xmath4-particle decays from @xmath52rn . it should be mentioned that the high energy @xmath3-rays ( above about 120 kev , table 2 ) are most probably sum events rather than photo - peak events . if , for instance , the three coincidence events in fig . 6 at e@xmath34 of 247.0 ( 2 events ) and 225.3 kev are photo - peak events , then 9.5@xmath385.5 compton events below 120 kev ( the position of the compton edge ) should have been seen in coincidence with @xmath4-particles of 8.55 - 8.61 mev , but only one event is seen . similarly if the @xmath3-rays which are in coincidence with 6 - 7 mev @xmath4-particles , seen in the same figure and mentioned above , are photo - peak events , then 7.6@xmath55 compton events should have been seen in this @xmath4-energy range at e@xmath50 @xmath30 120 kev , while only one event is seen . on the other hand , for a de - excitation of a superdeformed band with @xmath29j = 1 , a measured energy which fits a transition between high - spins , may be due to many sum combinations of lower energy transitions between lower spins , for which low - energy compton events should not be observed . for instance , an energy of 225.4 kev which fits a 51/2 @xmath51 49/2 transition ( assuming e@xmath48 = 4.42@xmath56j ( j+1 ) kev , table 2 ) may be due to one of 17 different combinations of 3-fold events , if only the first 14 levels of the band up to maximum spin of 27/2 , and maximum transition energy of 119.3 kev are considered , for which the photo - peak to total ratio is 100% . ( 119.3 ( 27/2 @xmath51 25/2 ) + 92.8 ( 21/2 @xmath51 19/2 ) + 13.3 ( 3/2 @xmath51 1/2 ) = 225.4 , or 84.0 ( 19/2 @xmath51 17/2 ) + 75.1 ( 17/2 @xmath51 15/2 ) + 66.3 ( 15/2 @xmath51 13/2 ) = 225.4 are two examples out of these 17 possible combinations ) . because of the large solid angle of the @xmath3-detector ( 0.16 ) and the large number of possible 3-fold combinations , the probability p@xmath57 to see a 3-fold event is larger than the probability p@xmath58 to see a 1-fold event . ( these probabilities for the above example are : p@xmath58 = @xmath59(1-@xmath59)@xmath60 = 0.042(1 - 0.16)@xmath61 = 6.4 x 10@xmath62 , and p@xmath57 = n@xmath57@xmath59@xmath13(1-@xmath59)@xmath63 = 17x0.16@xmath13(1 - 0.16)@xmath64 = 1.2x10@xmath39 , about 20 times larger . @xmath59 is the photo - peak efficiency of the detector for the particular energy , @xmath59 is the geometrical efficiency , n is the number of transitions in the band counting from the level to which the @xmath4-particle is decaying , and n@xmath57 is the number of 3-fold combinations ) . many combinations of 2- or 4- fold events of a half - integer spin band will give energies which fit with those of a band of an integer spin . for instance , the two events at 247.0 kev ( table 2 ) which fit in energy to a 28 @xmath51 27 transition , and the 186.5 kev event which fits with a 21 @xmath51 20 transition , may be due to such combinations , since the @xmath4-particle energy is the same as that of the half - integer transitions of 225.3 and 171.8 kev , and therefore they presumably belong to the same band . ( in an integer - spin band of @xmath29j = 1 various combinations of 2- , 3- and 4-fold events of low energy transitions have large efficiencies and give energies which fit with those of transitions between higher spins . this property , both for half - integer and integer spin bands , does not exist for @xmath29j = 2 transitions ) . as shown above the detection of sum events which are energetically degenerate with the diagram line leads to a substantially increased effective detection efficiency ( dependent , however , on the maximum available spin ) for this energy . the minimum spin which is consistent with the data is 19/2 . the largest efficiency of the detector ( which corresponds to the smallest production cross section ) , taking into account 2- and 4-fold sum events of transitions between half - integer spins in order to get the 247.0 kev transition , is obtained with a spin of 35/2 . the lower limit for the production cross section estimated from irradiation ii and taking into account the detector efficiency for various possible combinations of sum events , as described above , is about 130 nb ( table 1).-particles , are photo - peak events due to known transitions in @xmath53hg and @xmath16tl . however , in this case 12.6@xmath386.3 compton events below 120 kev should have been seen in fig . 6 in coincidence with @xmath4-particles of 8.55 - 8.62 mev , but only one event is seen.]-energies are compton events due to higher energy @xmath3-rays . but then the probability @xcite to have two events in the same position ( within the energy resolution ) is only a few percent , and this occurred twice , at 247.0 ( fig . 6 ) and 225.3 kev ( figs . 5 and 6 ) . ] as shown above , the observation in table 2 of gamma rays which fit in energies with transitions between high spin sdb states is consistent with various sums of gamma rays due to transitions between lower spin states with @xmath29j = 1 . since the intensity of the characteristic x - rays seen in figs . 5 and 6 in coincidence with 8 - 9 and 6 - 7 mev @xmath4-particles is very low , the observed @xmath3-rays should be due to e1 transitions , with quite low conversion factors , rather than m1 ones . such transitions have been seen before @xcite and were predicted for sd wells in nuclei around z = 86 and n = 116 @xcite . in order to identify some of the coincidence events seen in figs . 5 , 6 , and 9 at lower particle energies below 6 mev , we first looked on groups of events . the existence of groups of 3 or 2 coincidence events in clean regions indicates that they are probably not background . secondly , one looks on their accurately measured photon energies . at low energies the observed photon may be either an x - ray or a @xmath3-ray . the energies of the characteristic x - rays of the elements are known very well @xcite . the k@xmath14 x - rays of the various elements of the evaporation residue nuclei and their daughters are separated one from another by about 2 kev , where the value of a k@xmath14-line of an element with z protons is about the same as the value of the k@xmath65-line of an element with z+1 protons . if the measured energy turns out to be very close to a known x - ray energy , then it is reasonable to assume that the observed photon is an x - ray rather then a @xmath3-ray . ( in the cases found by us and discussed below the deviations from the known values are from 0.03 to 0.28 kev , while the width of one channel in the @xmath3-spectrum is about 0.24 kev and the fwhm is about four channels ) . the x - ray may be emitted if the @xmath4-particle is decaying to an excited state which decays by conversion electrons . such a process is followed by emitting characteristic x - rays of the daughter nucleus . the z - value of the daughter is thus determined . in order to determine its a - value we tried to identify the @xmath3-rays which are in coincidence with @xmath4-particles of about the same energy . a consistency is obtained when the @xmath3-ray fit in energy with the measured value , belongs to an isotope of the determined element , and it is consistent with known or expected values of the conversion factors , and also with the decay scheme . in several cases , as seen below , some of the observed events have been identified as due to characteristic x - rays ( the events surrounded with squares in figs . 5 , 6 and 9 ) and as known @xmath3-transitions in various nuclei ( the events surrounded with triangles in figs . 5 , 6 and 9 ) . in fig . 6 two coincidences between about 5.50 mev @xmath4-particles and 61.1 and 59.4 kev photons are seen , and fit with k@xmath14 and k@xmath65 x - rays of re of 61.140 and 59.718 kev . at about the same @xmath4-energy two 144.0 kev events are observed and can be identified with a known transition in @xmath66re . this identification is supported by the observation in fig . 5 , in the same @xmath4-energy range , of coincidence events with respective 59.7 kev and 140 kev x- and @xmath3-rays . the first fits with k@xmath65 of re , and the second with a transition in @xmath66re , which precedes the above 144.0 kev transition . a coincidence between 5.45 mev @xmath4-particles and 59.4 or 59.7 kev photons may in principle be also due to the known decay of @xmath20am of 5.486 mev @xmath4 and 59.54 kev @xmath3 . however , we did not use and never had in our laboratory a @xmath20am calibration source . under these circumstances the observation of the 61.1 kev photon , which fits very nicely with k@xmath14 of re , and which is very far off ( 1.56 kev ) from the @xmath3-rays of @xmath20am , and of the two consecutive @xmath3-rays of @xmath66re , suggests that the two events at about 59.6 kev are due to k@xmath65 of re and not due to @xmath20am . a 59.6 kev x - ray may in principle be also due to k@xmath14 of w of 59.3182 kev . here also the observation of the other x - rays and @xmath3-rays suggest that it is k@xmath65 of re rather than k@xmath14 of w. out of total number of 3 x - rays , one is expecting to see 1.9 k@xmath14 events and 1.1 k@xmath65 events . the observation of 1 event in the first case and 2 in the second , is well within the statistical error . in fig . 9 , for @xmath4-particles between 5.18 and 5.53 mev , groups of two and three events with photon energies of 66.8 kev and 59.6 kev , respectively , are seen . they may correspond to the known k@xmath14 x - rays of pt of 66.832 kev and of w of 59.318 kev of w. at the same corresponding @xmath4-energies known @xmath3-rays of @xmath67pt and @xmath68w are observed . here the three 59.6 kev events are more likely to be due to k@xmath14 of w , rather than k@xmath65 of re . if they were k@xmath65 of re then 5.2 events of k@xmath14 at 61.140 kev are expected . the observation of zero events when 5 are expected is unlikely . on the other hand , if the 3 observed events are k@xmath14 x - rays of w , then 1.7 events of k@xmath65 of w at 57.98 kev are expected . the observation of zero events when 1.7 are expected is well within the statistical errors . as mentioned above and seen in table 3 , about the same @xmath4-energy corresponds to two different decays . one leads to @xmath66re and was obtained in the e@xmath2 = 125 mev experiment , and the other presumably leads to @xmath68w and was obtained in the e@xmath2 = 135 mev experiment . as seen below ( section iva ) , these data are interpreted as due to transitions from the second well of the potential in the parent nuclei to the normal states in the daughters . there is nothing against having about the same @xmath4-particle energy in two different transitions . because of the low statistics we consider the identifications mentioned above as tentative only , where the identification of @xmath66re is better than of the other . the results are summarized in table 3 together with possible reaction channels and corresponding decay chains which lead to the observed transitions . the deduced production cross sections ( with an accuracy of about a factor of 2 ) are given in table 1 , columns 3 and 5 . in general lower limits were deduced since the branching ratios along the decay chains are not known . some coincidence events between 6.17 9.01 mev @xmath4-particles and identified x - rays with no corresponding @xmath3-rays were seen . they are also given in table 3 . a very well defined coincidence group of three events is seen in fig . 9 at an average particle energy of 3.88 mev and @xmath3-energy of 185.8 kev . because of the low energy of the particles and the very narrow total width of 40 kev , one may conclude that the particles are protons . ( the total estimated widths at this energy are 55 kev for protons and 630 kev for @xmath4-particles . the estimated half - life for 3.88 mev @xmath4-particles decaying to , for instance , @xmath69hg is about 1x10@xmath70 y @xcite ) . the 185.8 kev @xmath3-rays fit with a known transition in @xmath71rn ( table 3 ) . the production cross section of this group is given in table 1 .

the data are interpreted in terms of the production of long - lived ( t of several months ) high spin isomeric states in the second well of the potential in the parent nuclei , which decay to the normal states in the daughters , and in the third well of the potential , which decay to the second well .

the reactionsi +ta has been studied at e=125 and 135 mev . coincidences between high energy particles and various x- and-rays from abnormally long - lived states were observed . e.g. 7.8 - 8.6 mev-particles with-rays of a superdeformed band , 5.1 - 5.5 mev-particles with x- and-rays of w , re , and pt , and 3.88 mev particles ( interpreted as protons ) with 185.8 kev-rays . the data are interpreted in terms of the production of long - lived ( t of several months ) high spin isomeric states in the second well of the potential in the parent nuclei , which decay to the normal states in the daughters , and in the third well of the potential , which decay to the second well . pacs numbers : 23.60.+e , 21.10.re , 21.10.tg , 27.80.+w

1203.3207

i

the outstanding performance of the lhc experiments has led the field of high energy physics into unprecedented territory in the energy and luminosity frontier . major discoveries at the tera - scale are highly anticipated . one of the primary motivations for lhc experiments is the exploration for the mechanism of electroweak symmetry breaking . among the many possibilities for new physics beyond the standard model ( sm ) , supersymmetry ( susy ) provides a natural framework for electroweak symmetry breaking . although the signals for susy are still elusive at the lhc , significant progress has been made in the search for the higgs boson . recently , the atlas and cms collaborations have reported their updated searches for the sm higgs boson @xcite . continuously extending the previous lep2 mass bound for a sm higgs ( 114.4 gev ) @xcite , the lhc search has reached an impressively wide coverage for the mass parameters . the main conclusions are * a sm - like higgs boson was excluded at @xmath11 c.l . in the mass range of @xmath12 gev , in @xmath13 gev @xmath14 gev @xcite and in @xmath15 gev@xmath16 gev @xcite , thus leaving a @xmath11 c.l . mass window @xmath17 * an excess of events above the background expectation was observed in the final state of @xmath1 , at 126 gev with 2.5@xmath18 by the atlas collaboration @xcite and at 125 gev with 2.8@xmath18 by the cms collaboration @xcite , thus giving a tantalizing hint for a higgs boson in the mass range @xmath19 * no significant excess of events above the sm backgrounds was observed in the final states of @xmath20 , however , a small excess has been seen in @xmath21 @xcite . although inconclusive with the current data , each one of the statements above has significant impact on our understanding of electroweak symmetry breaking and thus guides us for the next step of the higgs search . in this paper , we study the consequences of the above findings on the higgs sector within the framework of the minimal supersymmetric standard model ( mssm ) @xcite . we first recollect the existing constraints from all the current bounds of the direct searches from lep2 @xcite , the tevatron @xcite and the lhc @xcite . if we accept the existence of a cp - even higgs boson in the mass range of eq . ( [ eq : mh1 ] ) as observed in the @xmath1 mode , we then find very interesting features for the mssm higgs sector and some other relevant susy parameters . there are two distinctive scenarios , both of which incorporate a sm - like higgs boson . * decoupling " regime with @xmath22 gev @xcite : the light cp - even higgs @xmath23 is in the mass range of eq . ( [ eq : mh1 ] ) and sm - like . the non - sm - like higgs bosons ( heavy cp - even state @xmath24 , cp - odd state @xmath25 and the charged state @xmath26 ) are all heavy and nearly degenerate , with masses around @xmath27 . * non - decoupling " regime with @xmath28 around @xmath29 gev : the heavy cp - even higgs @xmath24 is in the mass range of eq . ( [ eq : mh1 ] ) and sm - like , while the light cp - even higgs @xmath23 is non - sm - like . the masses of the light cp - even higgs and the cp - odd higgs are nearly degenerate while the charged higgs is nearly degenerate with @xmath30 @xcite . each of these two cases predicts unique signatures to establish the nature of the mssm at the lhc . while the current searches continue to improve in the future runs and the standard electroweak production processes @xmath31 are still available , we would like to point out the potential importance of the electroweak processes @xmath32 which are via pure gauge interaction and independent of the susy parameters except for their masses . in addition , there may be sizable contributions from @xmath33 in the low - mass non - decoupling region , which may be used to distinguish the model - parameters . on the other hand , due to the strong positive correlation between the higgs decays to @xmath3 and to @xmath4 predicted in the mssm , the observed @xmath4 signal and the apparent absence of the @xmath3 final state signal near the peak would be mutually exclusive to each other . namely , the suppression of the @xmath3 channel would automatically reduce the @xmath4 channel , in direct conflict with the observed @xmath4 excess . we also found another interesting inverse correlation between the higgs decays to @xmath3 and to @xmath34 . in this case , the suppression to the @xmath3 channel would automatically force the @xmath34 channel to be bigger . if the deficit in the @xmath3 channel persists and the result is strengthened for an extended mass range in the future run at the lhc , it would imply that the sm - like higgs boson has reduced couplings to @xmath35 , rendering it less sm - like . consequently , the other non - sm - like higgs bosons can not be deeply into the decoupling regime , and thus can not be too heavy , typically below 350 gev , making them more accessible at the lhc . moreover , if the excess in the @xmath4 channel and the absence of an excess in the @xmath3 channel continue to be strengthened at the lhc , new physics beyond the mssm will be required could help to enhance the branching fraction of the @xmath36 channel . ] . in the current study , we wish to focus on the essentials of the higgs sector in the mssm and to minimize the effects from other susy sectors @xcite . nevertheless , a few other susy parameters , the higgs mixing @xmath37 , the stop mixing @xmath38 and the stop soft susy masses @xmath39 and @xmath40 , play crucial roles in the higgs sector . we explore the effects of the higgs searches on those susy parameters by scanning them in a wide range and we find clear correlations and thus predictions on them . the rest of the paper is organized as follows . in sec . [ sec : mssmhiggs ] , we give a brief introduction to the mssm higgs sector , focusing on the mass corrections as well as the coupling structures that are relevant for our discussion below . in sec . [ sec : parameterregion ] , we discuss our broad scanning of the relevant mssm parameters by imposing the existing constraints of the direct searches from lep2 , the tevatron and the lhc . we obtain the surviving regions for the higgs mass and the other parameters . with the further improvement expected at the lhc with 8 tev and 14 tev , we discuss the consequence of the sm - like higgs boson searches on the mssm higgs sector in sec . [ sec : future ] . in light of the current direct search , we present the dominant production and decay channels as well as the characteristic channels for the non - sm higgs bosons in sec . [ sec : lhcsearch ] to test the mssm in the future runs . we conclude in sec . [ sec : conclude ] .

the other hand , due to the strong correlation between the higgs decays to and to predicted in the mssm , the apparent absence of a final state signal is in direct conflict with the peak . if both the excess and the absence of a signal continue , new physics beyond the mssm will be required . a similar correlation exists between the and channels : a reduced channel would force the channel to be larger . future searches for the sm - like higgs boson at the lhc will provide critical tests for the mssm prediction . we also study the signals predicted for the non - sm - like higgs bosons and emphasize the potential importance of the electroweak processes , which are independent of the susy parameters except for their masses . we allow variations of the relevant susy parameters in a broad range and demonstrate the correlations and constraints on these parameters and associated susy particles .

the recent results on higgs boson searches from lhc experiments provide significant guidance in exploring the minimal supersymmetric ( susy ) standard model ( mssm ) higgs sector . if we accept the existence of a sm - like higgs boson in the mass window of 123 gev gev as indicated by the observed events , there are two distinct mass regions ( in ) left in the mssm higgs sector : ( a ) the lighter cp - even higgs boson being sm - like and the non - sm - like higgs bosons all heavy and nearly degenerate above 300 gev ( an extended decoupling region ) ; ( b ) the heavier cp - even higgs boson being sm - like and the neutral non - sm - like higgs bosons all nearly degenerate around 100 gev ( a small non - decoupling region ) . on the other hand , due to the strong correlation between the higgs decays to and to predicted in the mssm , the apparent absence of a final state signal is in direct conflict with the peak . if we consider the channel on its own , the absence of the signal would imply that the sm - like higgs boson has reduced coupling to , and that the other non - sm - like higgs bosons should not be too heavy and do not decouple . if both the excess and the absence of a signal continue , new physics beyond the mssm will be required . a similar correlation exists between the and channels : a reduced channel would force the channel to be larger . future searches for the sm - like higgs boson at the lhc will provide critical tests for the mssm prediction . we also study the signals predicted for the non - sm - like higgs bosons and emphasize the potential importance of the electroweak processes , which are independent of the susy parameters except for their masses . in addition , there may be sizable contributions from and in the low - mass non - decoupling region , which may serve to discriminate the model parameters . we allow variations of the relevant susy parameters in a broad range and demonstrate the correlations and constraints on these parameters and associated susy particles .

1203.3207

c

in light of the powerful results presented by atlas and cms for the sm higgs boson searches at the lhc , along with the data from the lep2 and tevatron , we reexamined the mssm higgs sector for their masses , couplings and other related susy parameters . instead of only presenting benchmark scenarios , we allowed variations of other susy parameters in a broad range . if we accept the existence of a sm - like higgs boson in the mass window of 123 gev@xmath0127 gev as indicated by the observed @xmath1 events , we found that there are two distinctive mass regions left in the mssm higgs sector : ( a ) the lighter cp - even higgs boson being sm - like and the non - sm - like higgs bosons all heavy and nearly degenerate above 300 gev ( an extended decoupling region ) ; ( b ) the heavier cp - even higgs boson being sm - like and the neutral non - sm - like higgs bosons all nearly degenerate around 100 gev ( a small non - decoupling region ) . these features were shown in figs . [ fig : csr](a ) and [ fig : csr](b ) . on the other hand , due to the strong positive correlation between the higgs decays to @xmath3 and to @xmath4 predicted in the mssm , as seen in fig . [ fig : csr](c ) and eq . ( [ eq : r ] ) , the observed @xmath4 signal and the apparent absence of the @xmath3 final state signal near the peak would be mutually exclusive to each other . namely , the suppression to the @xmath3 channel would automatically reduce the @xmath4 channel . in fact , the theoretical expectation for the @xmath4 signal in the mssm relative to that in the sm is even smaller than that for the @xmath3 channel [ @xmath194 eq . ( [ eq : r ] ) ] . to accommodate both the @xmath3 deficit and the @xmath4 enhancement , physics beyond the mssm would be needed . we also found another interesting inverse correlation between the higgs decays to @xmath3 and to @xmath34 , as seen in fig . [ fig : csr](d ) . the suppression to the @xmath3 channel would automatically force the @xmath34 channel to be larger . if the absence of the @xmath3 signal persists and the observation is strengthened for an extended mass range in the future run at the lhc , it would imply that the sm - like higgs boson has reduced couplings to @xmath35 , rendering it less sm - like . although less statistically significant , the lack of the @xmath34 final state signal could also contribute to reach a consistent picture . consequently , the other non - sm - like higgs bosons can not be deeply into the decoupling regime , and thus can not be too heavy , typically below 350 gev , making them more accessible at the lhc . future searches for the sm - like higgs boson at the lhc will provide critical tests for the mssm predictions for those points , as presented in sec . [ sec : future ] . guided by those observations , we studied the signals predicted for the non - sm - like higgs bosons satisfying the current bounds . along with the standard searching processes @xmath195 as shown in fig . [ fig : cs_h](c ) , we emphasize the potential importance of the electroweak processes @xmath8 in fig . [ fig : nondec14tev](e ) , which are independent of the susy parameters except for their masses . in addition , there may be sizable contributions from @xmath9 in the low - mass non - decoupling region , which may serve to discriminate the model parameters . these cross sections can be as large as that of the @xmath196 associated production , which sensitively depends on @xmath85 . the stringent constraints also imply nontrivial correlation and prediction to some other susy parameters relevant to the higgs sector , such as @xmath197 etc . further explorations may lead to predictions for other susy signals for gaugino and stops . over all , the search for the sm higgs boson will prove crucial in understanding the susy higgs sector . we would like to thank s. heinemeyer , t. hahn , c. wagner and h. baer for helpful discussions . the work of n.c . and t.h . was supported in part by pitt pacc , and in part by the lhc - ti under u.s . national science foundation , grant nsf - phy-0705682 . the work of s.s . was supported by the department of energy under grant de - fg02 - 04er-41298 . j. f. gunion , h. e. haber , g. l. kane and s. dawson , front . * 80 * , 1 ( 2000 ) ; j. f. gunion and h. e. haber , nucl . b * 272 * , 1 ( 1986 ) [ erratum - ibid . b * 402 * , 567 ( 1993 ) ] . a. djouadi , phys . rept . * 459 * , 1 ( 2008 ) [ hep - ph/0503173 ] . t. aaltonen _ et al . _ [ cdf collaboration ] , phys . lett . * 103 * , 101803 ( 2009 ) [ arxiv:0907.1269 [ hep - ex ] ] ; v. m. abazov _ et al . _ [ d0 collaboration ] , phys . b * 682 * , 278 ( 2009 ) [ arxiv:0908.1811 [ hep - ex ] ] . cms collaboration , cms - pas - hig-11 - 009 ; g. aad _ et al . _ [ atlas collaboration ] , phys . b * 705 * , 174 ( 2011 ) [ arxiv:1107.5003 [ hep - ex ] ] . cms collaboration on @xmath198 , cms cms - pas - hig-11 - 029 ( 2011 ) . h. e. haber , hep - ph/9505240 . gerard and m. herquet , phys . lett . * 98 * , 251802 ( 2007 ) [ hep - ph/0703051 [ hep - ph ] ] ; e. cervero and j. -m . gerard , arxiv:1202.1973 [ hep - ph ] . m. carena , s. gori , n. r. shah and c. e. m. wagner , arxiv:1112.3336 [ hep - ph ] . some recent papers dealt with the other mssm aspects in light of the recent higgs searches , see , _ e.g. _ h. baer , v. barger and a. mustafayev , arxiv:1112.3017 ; t. moroi and k. nakayama , arxiv:1112.3123 ; o. buchmueller _ et al . _ , arxiv:1112.3564 ; s. akula , b. altunkaynak , d. feldman , p. nath and g. peim , arxiv:1112.3645 ; m. kadastik , k. kannike , a. racioppi and m. raidal , arxiv:1112.3647 ; j. cao , z. heng , d. li and j. m. yang , arxiv:1112.4391 [ hep - ph ] ; p. draper , p. meade , m. reece and d. shih , arxiv:1112.3068 [ hep - ph ] ; n. desai , b. mukhopadhyaya and s. niyogi , arxiv:1202.5190 [ hep - ph ] ; h. baer , v. barger and a. mustafayev , arxiv:1202.4038 [ hep - ph ] . j. l. feng , k. t. matchev and d. sanford , arxiv:1112.3021 . m. s. carena , m. quiros and c. e. m. wagner , nucl . b * 461 * , 407 ( 1996 ) [ arxiv : hep - ph/9508343 ] . m. s. carena , j. r. espinosa , m. quiros and c. e. m. wagner , phys . b * 355 * , 209 ( 1995 ) [ arxiv : hep - ph/9504316 ] . m. s. carena , s. heinemeyer , c. e. m. wagner and g. weiglein , eur . j. c * 26 * , 601 ( 2003 ) [ arxiv : hep - ph/0202167 ] . g. degrassi , s. heinemeyer , w. hollik , p. slavich and g. weiglein , eur . j. c * 28 * , 133 ( 2003 ) [ hep - ph/0212020 ] . s. heinemeyer , w. hollik and g. weiglein , eur . j. c * 9 * , 343 ( 1999 ) [ hep - ph/9812472 ] . m. s. carena , s. mrenna and c. e. m. wagner , phys . d * 62 * , 055008 ( 2000 ) [ arxiv : hep - ph/9907422 ] . m. s. carena , s. mrenna and c. e. m. wagner , phys . d * 60 * , 075010 ( 1999 ) [ arxiv : hep - ph/9808312 ] . l. j. hall , r. rattazzi and u. sarid , phys . d * 50 * , 7048 ( 1994 ) [ arxiv : hep - ph/9306309 ] . r. hempfling , phys . d * 49 * , 6168 ( 1994 ) . m. s. carena , m. olechowski , s. pokorski and c. e. m. wagner , nucl . b * 426 * , 269 ( 1994 ) [ arxiv : hep - ph/9402253 ] . j. a. bagger , k. t. matchev , d. m. pierce and r. j. zhang , phys . * 78 * , 1002 ( 1997 ) [ erratum - ibid . * 78 * , 2497 ( 1997 ) ] [ arxiv : hep - ph/9611229 ] . m. frank , t. hahn , s. heinemeyer , w. hollik , h. rzehak and g. weiglein , jhep * 0702 * , 047 ( 2007 ) [ hep - ph/0611326 ] , and references therein . s. heinemeyer , w. hollik and g. weiglein , comput . commun . * 124 * , 76 ( 2000 ) [ hep - ph/9812320 ] , and references therein . p. bechtle , o. brein , s. heinemeyer , g. weiglein and k. e. williams , comput . commun . * 181 * , 138 ( 2010 ) [ arxiv:0811.4169 [ hep - ph ] ] , and references therein . p. bechtle , o. brein , s. heinemeyer , g. weiglein and k. e. williams , comput . commun . * 182 * , 2605 ( 2011 ) [ arxiv:1102.1898 [ hep - ph ] ] , and references therein . s. heinemeyer , o. stal and g. weiglein , arxiv:1112.3026 . i. low and s. shalgar , jhep * 0904 * , 091 ( 2009 ) [ arxiv:0901.0266 [ hep - ph ] ] . j. cao , z. heng , j. m. yang , y. zhang and j. zhu , arxiv:1202.5821 [ hep - ph ] . d. asner _ [ heavy flavor averaging group ] , arxiv:1010.1589 [ hep - ex ] . m. misiak _ et al . _ , phys . lett . * 98 * , 022002 ( 2007 ) [ arxiv : hep - ph/0609232 ] . m. misiak and m. steinhauser , nucl . b * 764 * , 62 ( 2007 ) [ arxiv : hep - ph/0609241 ] . r. barbieri and g. f. giudice , phys . b * 309 * , 86 ( 1993 ) [ arxiv : hep - ph/9303270 ] . m. duhrssen , s. heinemeyer , h. logan , d. rainwater , g. weiglein and d. zeppenfeld , phys . d * 70 * , 113009 ( 2004 ) [ hep - ph/0406323 ] . s. dittmaier _ et al . _ [ lhc higgs cross section working group collaboration ] , arxiv:1101.0593 [ hep - ph ] . f. maltoni , z. sullivan and s. willenbrock , phys . d * 67 * , 093005 ( 2003 ) [ hep - ph/0301033 ] . j. l. diaz - cruz , h .- j . he , t. m. p. tait and c. p. yuan , phys . lett . * 80 * , 4641 ( 1998 ) [ hep - ph/9802294 ] . a. pukhov , e. boos , m. dubinin , v. edneral , v. ilyin , d. kovalenko , a. kryukov and v. savrin _ et al . _ , hep - ph/9908288 , a. belyaev , n. d. christensen and a. pukhov , arxiv:1207.6082 [ hep - ph ] . s. dawson , s. dittmaier and m. spira , phys . d * 58 * , 115012 ( 1998 ) [ arxiv : hep - ph/9805244 ] . atlas collaboration , atlas - conf-2012 - 014 ( 2012 ) . cao , s. kanemura and c .- p . yuan , phys . d * 69 * , 075008 ( 2004 ) [ hep - ph/0311083 ] . a. belyaev , q .- h . cao , d. nomura , k. tobe and c .- p . yuan , phys . lett . * 100 * , 061801 ( 2008 ) [ hep - ph/0609079 ] . altas collaboration , expected performance of the atlas experiment : detector , trigger and physics , cern - open-2008 - 020 . m. hashemi , s. heinemeyer , r. kinnunen , a. nikitenko and g. weiglein , arxiv:0804.1228 [ hep - ph ] . s. gennai , s. heinemeyer , a. kalinowski , r. kinnunen , s. lehti , a. nikitenko and g. weiglein , eur . j. c * 52 * , 383 ( 2007 ) [ arxiv:0704.0619 [ hep - ph ] ] .

the recent results on higgs boson searches from lhc experiments provide significant guidance in exploring the minimal supersymmetric ( susy ) standard model ( mssm ) higgs sector . if we accept the existence of a sm - like higgs boson in the mass window of 123 gev gev as indicated by the observed events , there are two distinct mass regions ( in ) left in the mssm higgs sector : ( a ) the lighter cp - even higgs boson being sm - like and the non - sm - like higgs bosons all heavy and nearly degenerate above 300 gev ( an extended decoupling region ) ; ( b ) the heavier cp - even higgs boson being sm - like and the neutral non - sm - like higgs bosons all nearly degenerate around 100 gev ( a small non - decoupling region ) . on if we consider the channel on its own , the absence of the signal would imply that the sm - like higgs boson has reduced coupling to , and that the other non - sm - like higgs bosons should not be too heavy and do not decouple . in addition , there may be sizable contributions from and in the low - mass non - decoupling region , which may serve to discriminate the model parameters .

the recent results on higgs boson searches from lhc experiments provide significant guidance in exploring the minimal supersymmetric ( susy ) standard model ( mssm ) higgs sector . if we accept the existence of a sm - like higgs boson in the mass window of 123 gev gev as indicated by the observed events , there are two distinct mass regions ( in ) left in the mssm higgs sector : ( a ) the lighter cp - even higgs boson being sm - like and the non - sm - like higgs bosons all heavy and nearly degenerate above 300 gev ( an extended decoupling region ) ; ( b ) the heavier cp - even higgs boson being sm - like and the neutral non - sm - like higgs bosons all nearly degenerate around 100 gev ( a small non - decoupling region ) . on the other hand , due to the strong correlation between the higgs decays to and to predicted in the mssm , the apparent absence of a final state signal is in direct conflict with the peak . if we consider the channel on its own , the absence of the signal would imply that the sm - like higgs boson has reduced coupling to , and that the other non - sm - like higgs bosons should not be too heavy and do not decouple . if both the excess and the absence of a signal continue , new physics beyond the mssm will be required . a similar correlation exists between the and channels : a reduced channel would force the channel to be larger . future searches for the sm - like higgs boson at the lhc will provide critical tests for the mssm prediction . we also study the signals predicted for the non - sm - like higgs bosons and emphasize the potential importance of the electroweak processes , which are independent of the susy parameters except for their masses . in addition , there may be sizable contributions from and in the low - mass non - decoupling region , which may serve to discriminate the model parameters . we allow variations of the relevant susy parameters in a broad range and demonstrate the correlations and constraints on these parameters and associated susy particles .

1306.2172

i

neutral hydrogen ( hi ) interacts with @xmath0 cm photons through a spin - flip transition @xcite . observing the redshifted @xmath0 cm brightness temperature cm signal or @xmath0 cm brightness temperature we , really mean _ redshifted _ @xmath0 cm signal ] against a background of the cosmic microwave background is a promising tracer of the cosmic dark ages , cosmic dawn , and the epoch of reionization @xcite . detecting the spatial fluctuations of @xmath0 cm brightness requires many hundreds of hours of integration with large radio synthesis telescopes , owing to its faintness as compared to galactic and extragalactic foregrounds @xcite . on the other hand , the sky averaged @xmath0 cm brightness also called the global signal , is bright enough to be measured within a day s worth of integration based on a signal to noise ratio argument @xcite . since the received frequency of redshifted @xmath0 cm photons corresponds to cosmic redshift , accurately estimating the sky averaged brightness temperature as a function of frequency will provide insights into the evolution of hi during the dark ages , cosmic dawn , and the epoch of reionization @xcite . + thermal uncertainties are not the limiting factor in global @xmath0 cm experiments , and spectral contamination due to systematic artifacts have impeded a reliable detection thus far @xcite . in particular , since the signal in such experiments is the variation of @xmath0 cm brightness temperature with frequency , any instrumental or observational systematic that affects the measured bandpass power poses a severe limitation . these systematics are especially limiting since the foregrounds are @xmath10 orders of magnitude larger than the expected @xmath0 cm signal . consequently , measuring the @xmath0 cm signal spectrum requires precise understanding of frequency dependent effects of instrumental gain , instrumental noise contribution , antenna beam shape , and ionospheric effects , coupled with spatially and spectrally varying foregrounds ( galactic and extragalactic ) . the effects of these parameters are not always mutually separable , further complicating calibration and signal extraction efforts . + ongoing global @xmath0 cm experiments have primarily focused on frequencies ranging from @xmath11 mhz to @xmath12 mhz ( @xmath13)@xcite . dark ages and cosmic dawn experiments at lower frequencies are being planned , or are being commissioned dark ages radio explorer ( dare ) @xcite , large - aperture experiment to detect the dark ages @xcite , and broadband instrument for the global hydrogen reionization signal ( bighorns ) experiment @xcite , among others . global @xmath0 cm work especially in the lower frequency band requires a strict assessment of systematic chromatic corruptions . the reasons for this are threefold . ( i ) firstly , the magnitude of ionospheric effects such as refraction and absorption increase rapidly with decreasing frequency . ( ii ) secondly , galactic foreground brightness temperatures increase with decreasing frequency as a power law with a relatively steep spectral index of about @xmath14 . consequently , any systematic corruptions which are multiplicative , which many of the ones in such experiments are , may undermine @xmath0 cm signal detection efforts more severely at lower frequencies . ( iii ) finally , the increased fractional bandwidth in the lower frequency band leads to an increased variation of antenna beams across the measurement bandwidth , giving larger chromatic effects . + receiver gain and noise temperature may be calibrated by switching the receiver between the sky and known man - made noise sources . such techniques have been demonstrated with moderate success in global @xmath0 cm experiments @xcite . however , little attention has been paid in the literature to chromatic ( frequency dependent ) antenna beam and ionospheric effects . these effects have thus far been assumed to be ` spectrally smooth ' and possibly fitted away along with the foregrounds . they have thus escaped qualitative and quantitative treatment one of the primary aims of this paper . + chromatic effects must be studied in conjunction with algorithms that are used to separate the measured sky spectrum into foregrounds and the @xmath0 cm signal . due to the lack of sufficiently accurate foreground models at these frequencies , such algorithms must rely on some priors on the differential properties of foregrounds and the @xmath0 cm signal . these algorithms typically exploit ( i ) the spectral smoothness of power - law - like foregrounds in comparison to less smooth structure expected in the @xmath0 cm signal , and/or ( ii ) the angular structure of foregrounds as opposed to isotropic nature of the global @xmath0 cm signal . spectral smoothness of foregrounds may be exploited by casting the measured sky spectrum in a basis where foregrounds have a sparse representation unlike the @xmath0 cm signal . we may call such techniques spectral - basis methods , since they only use spectral smoothness as a prior . one such basis set suggested in literature , which we will call ` logpolyfit ` , uses polynomials in logarithmic space as basis to represent the time averaged spectrum @xcite . exploiting priors on the angular structure of foregrounds for global @xmath0 cm experiments has not received due attention in literature , save a recent effort by @xcite , who in light of their simulations , recommend measurements with an angular resolution of @xmath10 degrees . practical implications of a narrow beam ( highly chromatic sidelobes etc . ) remain to be evaluated . moreover , ongoing and proposed global @xmath0 cm experiments have near - hemisphere fields of view and lack any meaningful angular resolution . it is then instructive to place limits on the extent to which beam and ionospheric chromatic effects can confuse @xmath0 cm signatures in the context of spectral - basis algorithms another primary aim of this paper . + in this paper , we simulate the contribution of foregrounds ( with chromatic effects ) to the measured antenna temperature and evaluate an optimal set of basis functions for a sparse representation of foregrounds . by casting the foregrounds and the expected @xmath0 cm signal in this basis , we place limits on the amount of @xmath0 cm signal power that will be lost to foreground confusion in any spectral - basis technique . since the optimal basis functions are not known apriori in real measurements , we may resort to predefined analytic basis functions such as polynomials . in this paper , we show that polynomials in logarithmic space ( ` logpolyfit ` ) are incapable of even detecting the presence of a template @xmath0 cm signal in simulated data in the frequency range of @xmath1 mhz to @xmath15 mhz . + in this paper , we propose an alternative spectral - basis method which we call ` svdfit ` , that evaluates a suitable basis using the measured data itself . despite hemispherical fields of view of ongoing experiments , earth rotation couples angular structure of the foregrounds into the time domain , while the global @xmath0 cm signal being isotropic , has no temporal structure . ` svdfit ` uses the time variable component of the measured dynamic spectra to compute an efficient basis in which the foregrounds and chromatic effects have a sparse representation , but not the @xmath0 cm signal itself . we will show that a ` svdfit ` is better than ` logpolyfit ` in ascertaining the presence of a template @xmath0 cm signal in our simulated data . nevertheless , we argue that for complete reconstruction of the @xmath0 cm signal spectrum , spectral smoothness is an inadequate prior in the above frequency range , and ultimately extracting the @xmath0 cm signal spectrum will require modeling of the foregrounds , antenna beam , and ionospheric effects via a full measurement equation . + the rest of the paper is organized as follows . details of the simulations used herein are described in section [ sec : simu ] . in section [ sec : iono ] we describe our two - layered ionospheric model ( f- and d - layers ) . we derive approximate expressions for chromatic effects from these two layers , and also quantify the level at which we expect these effects . in section [ sec : chrom ] we use the results of our simulations to compute an optimal basis to represent the foreground induced antenna temperature , and quantify the extent to which foregrounds and chromatic effects confuse the @xmath0 cm signatures in spectral - basis methods . we then describe a novel foreground removal technique which we call ` svdfit ` , and also evaluate the efficiency with which ` logpolyfit ` and ` svdfit ` remove foregrounds and chromatic effects . finally in section [ sec : concl ] we draw conclusions and recommendations for future work .

the redshifted cm brightness distribution from neutral hydrogen is a promising probe into the cosmic dark ages , cosmic dawn , and re - ionization . lofar s low band antennas ( lba ) may be used in the frequency range mhz to mhz ( ) to measure the sky averaged redshifted cm brightness temperature as a function of frequency , or equivalently , cosmic redshift . we conclude that foregrounds and chromatic mixing may not be subtracted as generic functions of frequency as previously thought , but must rather be carefully modeled using additional priors and interferometric measurements . latexl-.36em.3ex-.15em t-.1667em.7ex-.125emx [ section ] [ firstpage ] cosmology : observational , first stars radiolines : general atmospheric effects methods : observational , numerical

the redshifted cm brightness distribution from neutral hydrogen is a promising probe into the cosmic dark ages , cosmic dawn , and re - ionization . lofar s low band antennas ( lba ) may be used in the frequency range mhz to mhz ( ) to measure the sky averaged redshifted cm brightness temperature as a function of frequency , or equivalently , cosmic redshift . these low frequencies are affected by strong galactic foreground emission that is observed through frequency dependent ionospheric and antenna beam distortions which lead to chromatic mixing of spatial structure into spectral structure . using simple models , we show that ( i ) the additional antenna temperature due to ionospheric refraction and absorption are at a% level to orders of magnitude higher than the expected cm signal , and have an approximate dependence , ( ii ) ionospheric refraction leads to a knee - like modulation on the sky spectrum atplasma frequency . using more realistic simulations , we show that in the measured sky spectrum , more than% of the cm signal variance can be lost to confusion from foregrounds and chromatic effects . we conclude that foregrounds and chromatic mixing may not be subtracted as generic functions of frequency as previously thought , but must rather be carefully modeled using additional priors and interferometric measurements . latexl-.36em.3ex-.15em t-.1667em.7ex-.125emx [ section ] [ firstpage ] cosmology : observational , first stars radiolines : general atmospheric effects methods : observational , numerical

1306.2172

c

single antenna wide field of view experiments that measure the sky spectrum to high degree of accuracy are interesting probes of the cosmic dark ages , cosmic dawn , and the epoch of reionization . such measurements not only require unprecedented accuracy in receiver gain and noise temperature calibration , but also require accurate modeling and removal of contamination along the frequency axis . ionospheric refraction and absorption are highly frequency dependent and are thus a potential limitation in such experiments . additionally , a frequency dependent antenna beam mixes spatial structure of foregrounds into spectral structure providing an additional source of signal contamination . in this paper , we have studied the nature and magnitude of the above spectral contaminants in the frequency range of @xmath103 mhz to @xmath90 mhz that is particularly interesting for cosmic dawn studies . + we have arrived at the following results / conclusions : 1 . a simple ionospheric model that accounts for static chromatic effects consists of two homogeneous layers : the f - layer that accounts for chromatic refraction , and the d - layer that accounts for chromatic absorption . in case of a sky with a global spectral index @xmath184 , and a frequency invariant beam , chromatic refraction due to typical f - layer electron densities ( @xmath185x@xmath186m@xmath52 ) adds a component to the measured antenna dynamic spectrum that has a spectral index of @xmath187 , and is about @xmath120 k at @xmath1 mhz and @xmath4 k at @xmath2 mhz . likewise , typical d - layer absorption for an electron density of @xmath165m@xmath52 , and collisional rate of @xmath188 mhz , adds a ( negative ) component to the dynamic spectrum at the @xmath105% level with spectral shape given by @xmath115 . typical values for additional signal due to d - layer absorption range from @xmath121 k at @xmath103 mhz to @xmath189 k at @xmath2 mhz . we have also shown that high f - layer electron densities lead to low elevation cut - off of incoming rays , and that this leads to a knee - like feature in elevation angle of the horizon ray versus frequency . we have identified the knee to be at @xmath190 times the plasma frequency . we have shown that if the f - layer electron densities approach or exceed @xmath191m@xmath52 during the measurement duration , low elevation cut - off leads to undesirable modulation of the measured spectrum within the bandwidth of interest ( @xmath103-@xmath2 mhz ) . we thus recommend monitoring of ionospheric tec throughout observations with an intention of flagging data during periods with high tec values . to evaluate chromatic effects from more realistic sky and beam models , we have set - up simulations that accept a variety of sky , beam , and ionospheric parameters and produce dynamic spectra of the measured antenna temperature . we have evaluated chromatic effects for the @xcite sky models , for ideal frequency independent , and simulated lofar lba beams . using the results of these simulations we have placed limits on the efficiency of spectral basis methods algorithms that separate foregrounds from the @xmath0 cm signal based on the spectral smoothness of foreground and chromatic effects as compared with the @xmath0 cm signal . in doing so we have shown that even under ideal ionospheric conditions a minimum of @xmath172 parameters are required to sufficiently describe chromatic effects of the lofar lba beam and the ionosphere , and that a minimum of @xmath192% of the variance in the @xmath0 cm signal is typically lost due to confusion with foreground and chromatic effects , rendering such a method ineffective . + 3 . we have also evaluated the efficiency of two practical algorithms : ( i ) ` logpolyfit ` that uses polynomial in logarithmic space as basis functions , and ( ii ) ` svdfit` a novel algorithm proposed herein that uses the dynamic part of the antenna temperature spectrum to compute a near - optimal set of basis vectors that may then be used to separate foreground from the time averaged ( static part ) antenna temperature spectrum . we show that ` logpolyfit ` fails as a spectral basis method in our frequency range of interest , but ` svdfit ` has potential to succeed in case of a near frequency independent beam . we however conclude that ` svdfit ` fails as a spectral basis method in case of the highly chromatic lofar lba . moreover , dynamic ionospheric effects will only decrease the efficiency of any spectral basis method . we conclude that spectral basis methods , though attractive due to their simplicity , do not use many of the strong priors ( that almost always exist ) from independent measurements of the sky brightness temperature , ionospheric conditions , and the dipole beam , all three of which have a large impact on the dynamic spectrum . as part of future work , we plan to improve upon spectral basis methods for single dipole experiments by modeling the observed data using a full measurement equation . we have recently concluded a pilot project with data from the de602 lofar station ( near garching , germany ) , and plan to present results from a measurement equation based modeling of this pilot data in a forthcoming paper . additionally , embedding the dipole into an array gives dipole - dipole visibilities that provide strong constraints on not only receiver bandpass calibration , but also on all the above factors . array based measurements / constraints may be an effective way forward for global @xmath0 cm experiments . consequently , as part of future work , we also plan to develop a framework that exploits priors derived from dipole - dipole visibilities , to address the challenges posed by large foregrounds and chromatic mixing . while we only address single dipole measurements in this paper , our analysis of chromatic lensing in the ionosphere ( see sections [ subsec : flayer ] and [ subsec : leco ] ) may have implication for interferometric @xmath0 cm experiments . this is especially important for observations at epochs when the galactic plane is at low elevations where refraction is at its strongest . refraction may cause bright radio sources to cross the spectrally varying radio - horizon within the observation bandwidth giving insidious frequency structure in the visibilities . as part of future work , we plan to evaluate these effects on techniques presented by @xcite and @xcite that propose to filter out discrete foreground sources in the frequency domain .

these low frequencies are affected by strong galactic foreground emission that is observed through frequency dependent ionospheric and antenna beam distortions which lead to chromatic mixing of spatial structure into spectral structure . using simple models , we show that ( i ) the additional antenna temperature due to ionospheric refraction and absorption are at a% level to orders of magnitude higher than the expected cm signal , and have an approximate dependence , ( ii ) ionospheric refraction leads to a knee - like modulation on the sky spectrum atplasma frequency . using more realistic simulations , we show that in the measured sky spectrum , more than% of the cm signal variance can be lost to confusion from foregrounds and chromatic effects .

the redshifted cm brightness distribution from neutral hydrogen is a promising probe into the cosmic dark ages , cosmic dawn , and re - ionization . lofar s low band antennas ( lba ) may be used in the frequency range mhz to mhz ( ) to measure the sky averaged redshifted cm brightness temperature as a function of frequency , or equivalently , cosmic redshift . these low frequencies are affected by strong galactic foreground emission that is observed through frequency dependent ionospheric and antenna beam distortions which lead to chromatic mixing of spatial structure into spectral structure . using simple models , we show that ( i ) the additional antenna temperature due to ionospheric refraction and absorption are at a% level to orders of magnitude higher than the expected cm signal , and have an approximate dependence , ( ii ) ionospheric refraction leads to a knee - like modulation on the sky spectrum atplasma frequency . using more realistic simulations , we show that in the measured sky spectrum , more than% of the cm signal variance can be lost to confusion from foregrounds and chromatic effects . we conclude that foregrounds and chromatic mixing may not be subtracted as generic functions of frequency as previously thought , but must rather be carefully modeled using additional priors and interferometric measurements . latexl-.36em.3ex-.15em t-.1667em.7ex-.125emx [ section ] [ firstpage ] cosmology : observational , first stars radiolines : general atmospheric effects methods : observational , numerical

1604.06873

i

graphene is a two - dimensional sheet of carbon atoms arranged in a hexagonal lattice , which possesses unusual mechanical , electrical and optical properties . at energies below a few ev the electronic excitations ( quasiparticles ) in graphene are well described by the dirac model , i.e. , display the linear dispersion relation , where the speed of light @xmath0 is replaced with the fermi velocity @xmath1 @xcite . this makes graphene a unique laboratory for testing some effects of quantum electrodynamics and quantum field theory , such as the thermal casimir force @xcite , the klein paradox @xcite , and the creation of particles from vacuum in strong external fields @xcite . it is important also that technological applications of graphene are numerous and diverse . one could mention graphene coatings used in the optical detectors @xcite , solar cells @xcite , transparent electrodes @xcite , corrosium protection @xcite , optical biosensors @xcite , optoelectronic switches @xcite , etc . in order to make the best use of graphene in both fundamental physics and its applications , it is necessary to investigate the reflectivity properties of this novel material over the wide frequency region . as was shown experimentally , in the region of visible light , where the photon energy is much larger than both thermal and fermi energies , the transparency and conductivity of graphene are defined by the fine structure constant @xmath2 @xcite and by the quantity @xmath3 @xcite , respectively . these facts were understood in theoretical studies of the conductivity of graphene using the current - current correlation function and the kubo formula ( see ref . @xcite and review in ref . @xcite ) . the obtained results for the in - plane ( longitudinal ) conductivity have been applied to investigate the reflectivity properties of graphene . this was done in the framework of spatially local approximation , i.e. , with no regard for dependence on the wave vector . the reflection coefficients and reflectivities of graphene with zero mass - gap parameter ( quasiparticle mass ) for the transverse magnetic ( tm ) , i.e. , @xmath4 polarized , electromagnetic waves have been found at both low @xcite and high @xcite frequencies . the case of gapless graphene deposited on a substrate was considered in ref . @xcite . the most fundamental quantity allowing full investigation of the reflectivity properties of graphene over the entire frequency range is the polarization tensor in ( 2 + 1)-dimensional space - time . it was found in refs . @xcite at zero and nonzero temperature , respectively , and used to investigate the casimir effect in graphene systems in refs . @xcite ( several calculations of the casimir force were performed also using the density - density correlation functions of graphene and other methods @xcite ) . we stress , however , that for calculation of the casimir force using the lifshitz theory one should use the reflection coefficients defined at the discrete imaginary matsubara frequencies @xcite . it was shown @xcite that the polarization tensor of ref . @xcite is valid strictly at the matsubara frequencies and can not be immediately continued either to the real or to the entire imaginary frequency axis . the polarization tensor of graphene valid at all complex frequencies , including the real frequency axis , was derived in ref . @xcite . at the imaginary matsubara frequencies it coincides with that of ref . @xcite , but , in contrast to ref . @xcite , allows immediate analytic continuation to the whole complex plane . using this representation for the polarization tensor , the reflectivity properties of gapless graphene were investigated at low , high and intermediate frequencies for both polarizations of the electromagnetic field tm and te ( i.e. , transverse electric or @xmath5 polarization ) . in so doing , some new properties were found which escaped notice in previous literature . the polarization tensor of ref . @xcite , has been also used to find the reflectivities of material plates coated with gapless graphene @xcite . in this paper , the polarization tensor of ref . @xcite is used to investigate the reflectivity properties of graphene with nonzero mass - gap parameter @xmath6 . it is common knowledge that the quasiparticles of pristine ( ideal ) graphene are massless . however , they acquire some small mass @xmath6 under the influence of defects of the structure , electron - electron interaction , and in the presence of substrates @xcite . the exact value of @xmath6 for some specific graphene sample usually remains unknown , but , according to some estimations @xcite , may achieve 0.1ev ( we measure masses and frequencies in the units of energy ) . here , we derive convenient explicit expressions for the polarization tensor of graphene with nonzero mass - gap parameter at any temperature . we demonstrate that under some conditions the nonzero mass - gap parameter may have a dramatic effect on the reflectivity properties of graphene . specifically , we find the resonance behavior of graphene reflectivities at the border frequency of incident electromagnetic waves @xmath7 . this effect occurs at both zero and nonzero temperature . at nonzero temperature the reflectivities of gapped graphene drop to zero at some frequency smaller than the border one . we find the asymptotic expressions for the reflectivities of gapped graphene at both low and high frequencies . at zero temperature the tm and te reflectivities of graphene with @xmath8 take the zero value at zero frequency . this is different from the case of gapless graphene , where both reflectivities at zero temperature are equal to nonzero constants depending on @xmath9 and on the angle of incidence @xcite . at nonzero temperature the reflectivities of gapped graphene go to unity with vanishing frequency . we also perform numerical computations of the reflectivities of gapped graphene over the wide range of frequencies at both zero and nonzero temperature and find the regions , where nonzero value of @xmath6 makes a profound effect on the obtained results . the paper is organized as follows . in sec . ii we derive convenient expressions for the polarization tensor of graphene with nonzero mass - gap parameter and present the general formalism . section iii contains calculation of the reflectivities of gapped graphene at zero temperature . an investigation of the impact of temperature on the reflectivity of gapped graphene is presented in sec . iv . in sec . v the reader will find our conclusions and discussion .

the reflectivity properties of graphene with nonzero mass - gap parameter are investigated in the framework of dirac model using the polarization tensor in ( 2 + 1)-dimensional space - time . for this purpose , a more simple explicit representation for the polarization tensor along the real frequency axis we also find the resonance behavior of the reflectivities of gapped graphene at both zero and nonzero temperature at the border frequency determined by the width of the gap . at nonzero temperature the reflectifities of graphene drop to zero in the vicinity of some frequency smaller than the border frequency .

the reflectivity properties of graphene with nonzero mass - gap parameter are investigated in the framework of dirac model using the polarization tensor in ( 2 + 1)-dimensional space - time . for this purpose , a more simple explicit representation for the polarization tensor along the real frequency axis is found . the approximate analytic expressions for the polarization tensor and for the reflectivities of graphene are obtained in different frequency regions at any temperature . we show that the nonzero mass - gap parameter has a profound effect on the reflectivity of graphene . specifically , at zero temperature the reflectivity of gapped graphene goes to zero with vanishing frequency . at nonzero temperature the same reflectivities are equal to unity at zero frequency . we also find the resonance behavior of the reflectivities of gapped graphene at both zero and nonzero temperature at the border frequency determined by the width of the gap . at nonzero temperature the reflectifities of graphene drop to zero in the vicinity of some frequency smaller than the border frequency . our analytic results are accompanied with numerical computations performed over a wide frequency region . the developed formalism can be used in devising nanoscale optical detectors , optoelectronic switches and in other optical applications of graphene .

1604.06873

c

in the foregoing , we have investigated the reflectivity properties of gapped graphene at both zero and nonzero temperature in the framework of the dirac model . it was shown that the presence of nonzero mass - gap parameter has a profound effect on the reflectivity of graphene . to find this effect , we have employed the polarization tensor of graphene found in ref . @xcite , which was further adapted and simplified for the case of gapped graphene . specifically , it was shown that at zero temperature the reflectivities of gapped graphene go to zero when the frequency vanishes . this is not the case for a gapless graphene , where the reflectivities at zero temperature are nonzero and depend only on the fine structure constant and the angle of incidence . we have shown also that at nonzero temperature the reflectivities of gapped graphene go to unity with vanishing frequency , as it is for a gapless graphene . another distinctive property of gapped graphene is that its reflectivities possess the narrow resonances having the maximum values equal to unity at the border frequency @xmath237 $ ] . this is the case at both zero and nonzero temperature and can be observed experimentally as a jump in the reflectivities of graphene when passing across the border frequency . at frequencies larger than the border frequency there is only minor influence of the mass - gap parameter on the reflectivities of graphene . the next remarkable property of gapped graphene at nonzero temperature is that in the vicinity of some frequency @xmath163 smaller than the border frequency its reflectivities drop to zero . this local minimum also can be observed as a jump in the reflectivities of graphene when passing across the frequency @xmath163 . there is no such effect for a gapless graphene or for a gapped graphene at @xmath141k . it is caused by the fact that the thermal correction to the polarization tensor takes negative values . all the above effects have been derived and investigated analytically in different frequency regions . as a result , the approximate analytic expressions for the reflectivities of graphene and for the frequency @xmath163 have been found . both the cases of the normal incidence and an arbitrary incidence angle were considered . the analytic results have been illustrated by numerical computations over a wide range of frequencies from @xmath238ev to 20ev . from the comparison between approximate analytic and computational results , the exactness of the former was estimated . the developed theory of the reflectivity of gapped graphene at any temperature is based on the first principles of quantum electrodynamics . it can be used in many prospective applications of graphene , such as optical detectors , optoelectronic switches and other mentioned in sec . i. in future it would be interesting to generalize this theory for the case of nonzero chemical potential ( see ref . @xcite for the polarization tensor of graphene taking the chemical potential into account ) and to apply it to graphene - coated substrates .

we show that the nonzero mass - gap parameter has a profound effect on the reflectivity of graphene . specifically , at zero temperature the reflectivity of gapped graphene goes to zero with vanishing frequency . at nonzero temperature our analytic results are accompanied with numerical computations performed over a wide frequency region . the developed formalism can be used in devising nanoscale optical detectors , optoelectronic switches and in other optical applications of graphene .

the reflectivity properties of graphene with nonzero mass - gap parameter are investigated in the framework of dirac model using the polarization tensor in ( 2 + 1)-dimensional space - time . for this purpose , a more simple explicit representation for the polarization tensor along the real frequency axis is found . the approximate analytic expressions for the polarization tensor and for the reflectivities of graphene are obtained in different frequency regions at any temperature . we show that the nonzero mass - gap parameter has a profound effect on the reflectivity of graphene . specifically , at zero temperature the reflectivity of gapped graphene goes to zero with vanishing frequency . at nonzero temperature the same reflectivities are equal to unity at zero frequency . we also find the resonance behavior of the reflectivities of gapped graphene at both zero and nonzero temperature at the border frequency determined by the width of the gap . at nonzero temperature the reflectifities of graphene drop to zero in the vicinity of some frequency smaller than the border frequency . our analytic results are accompanied with numerical computations performed over a wide frequency region . the developed formalism can be used in devising nanoscale optical detectors , optoelectronic switches and in other optical applications of graphene .

hep-ph9711392

i

the study of multiparticle production in hard processes provides one with an important information about both the qcd partonic branching processes and the transition from the coloured partons to the colourless hadrons . the vast amount of experimental data collected in various hard collisions processes convincingly confirms that the inclusive characteristics of qcd jet systems can be successfully described within the analytical perturbative approach to multiparticle production , see e.g. @xcite . this approach is based on the so - called modified leading logarithmic approximation ( mlla ) @xcite and on the concept of local parton hadron duality ( lphd ) @xcite . in particular , the experiment clearly demonstrates that the bright colour coherence effects survive the hadronization stage and are distinctively visible in the data . this has been known for quite a long time for annihilation processes ( see e.g. @xcite ) . recently the very impressive data from hera @xcite and from the tevatron @xcite have become available . the lphd allows one to relate the ( sufficiently ) inclusive hadronic observables to the corresponding quantities computed for the cascading partonic system . one of the well known ( but still striking ) predictions of the perturbative scenario is the depletion of the soft particle production and the resulting approximately gaussian shape of the inclusive distribution in the variable @xmath10for particles with energy @xmath11 in a jet of energy @xmath12 ( the so - called `` hump - backed plateau '' ) @xcite . this behaviour is observed in all inclusive energy distributions ; the charged particle spectrum for not too small momenta prove to be in surprisingly good agreement with the mlla - lphd predictions reflecting the qcd cascading picture of multiple hadroproduction . moreover , the data collected in various hard scattering processes ( , dis , @xmath13 ) clearly demonstrate a remarkable universality of particle spectra assuming the proper ( mlla - based ) choice of the cascading evolution variables , equivalent to the @xmath14 energy @xmath15 . the most challenging is the soft momentum end of the particle spectra ( p @xmath16gev ) where the non - perturbative dynamics could invalidate the perturbatively based expectations . an attempt to stretch the perturbative predictions to the limit of their applicability ( or better to say , beyond it ) has been performed in previous papers of the present authors ( see e.g. @xcite ) . in these papers it was shown that ( after the proper modifications ) the perturbatively based formulae allow a sufficiently smooth transition into the soft momentum domain . the non - perturbative hadronization effects are encoded in the transverse momentum cutoff @xmath17 which can be motivated by the space - time picture of hadroproduction in qcd jets , see e.g. @xcite . explicit predictions for distributions of hadrons in the soft region need some additional assumptions on mass effects . scaling phenomena are expected to be of more general nature . let us recall that the gluons of long wave length are emitted by the total colour current which is independent of the internal structure of the jet and is conserved when the partons split . applying the lphd hypothesis one then expects that the hadron spectrum at very low momenta @xmath18 should be nearly independent of the jet energy @xcite . as discussed in @xcite , the low momentum data support the basic ideas of qcd coherence and lphd . quantitatively , the analysis was performed in terms of the invariant particle density @xmath19 for annihilation into hadrons at low momenta in quite a wide @xmath14 energy region ( from adone to lep-2 ) . the spectra were found to be in a good agreement with the scaling behaviour and with analytical perturbative expectations which became sensitive to the running of the coupling @xmath20 at small scales @xcite . the new h1 data@xcite follow these predictions as well , thus confirming the universality of soft particle production . in this paper we study further the phenomenology of the soft particle production for both the charged and identified hadrons . the analytical calculations are compared with the quantity @xmath21 which has some practical advantages over the invariant density considered before . we derive a scaling prediction for particles at low transverse but arbitrary longitudinal momenta , which generalizes our previous results and which for very small @xmath22 explains the so - called fan - invariance experimentally observed long ago @xcite . an important test of this line of approach towards soft particle production is the sensitivity to the colour charge of the primary emitters : the density of low momentum particles roughly doubles when going from a primary @xmath3 to a @xmath4 antenna . it is interesting to note that this prediction applies to the soft particles already at present energies , whereas for the total multiplicity this doubling needs much higher energies . the sensitivity of the low momentum particle density to the primary colour charges can be studied in experimentally accessible processes , such as in @xmath23 jets @xcite . here this process is discussed further and we derive predictions for the soft particle production in quark and gluon exchange reactions which are observed in photoproduction or dis at hera or in @xmath1 collisions .

they are based upon the difference in the intensity of the soft radiation from primary and antennae . * perturbative universality in soft particle production * valery a. khoze , sergio lupia , wolfgang ochs _ infn - laboratori nazionali di frascati , p.o .

the spectrum of partons in a qcd jet becomes independent of the primary energy in the low momentum limit . this follows within the perturbative qcd from the colour coherence in soft gluon branching . remarkably , the hadrons follow such behaviour closely , suggesting the parton hadron duality picture to be appropriate also for the low momentum particles . more generally , this scaling property holds for particles of low transverse and arbitrary longitudinal momentum , which explains an old experimental observation ( `` fan invariance '' ) . further tests of the perturbatively based picture for soft particle production are proposed for three - jet events in annihilation and di - jet production events in , and collisions . they are based upon the difference in the intensity of the soft radiation from primary and antennae . * perturbative universality in soft particle production * valery a. khoze , sergio lupia , wolfgang ochs _ infn - laboratori nazionali di frascati , p.o . box 13 , + i-00044 frascati , italy _ + + _ th division cern + ch-1211 , geneva 23 _ + + _ max - planck - institut fr physik + ( werner - heisenberg - institut ) + fhringer ring 6 , d-80805 munich , germany _

0907.4388

i

background independence and diffeomorphism invariance are key assumptions in various approaches to quantum gravity @xcite . compared to older canonical approaches @xcite , what makes loop quantum gravity @xcite technically possible and mathematically robust is a further assumption consisting in the choice of the loop algebra as the basis for quantization @xcite@xcite . the kinematical hilbert space of the theory turns out to admit a decomposition into orthogonal subspaces @xmath0 associated to diffeomorphism equivalence classes of graphs @xmath1 . spin network states with graph @xmath1 @xcite provide a complete orthonormal basis of @xmath0 . the motivation for this paper comes from the following remark : the mathematical structure of the hilbert space @xmath0 and its physical interpretation in terms of quantum geometries @xcite are the ones proper to the hilbert space of a system with a finite ( but possibly large ) number of degrees of freedom . therefore , while the full theory has an infinite number of degrees of freedom ( as classical general relativity does ) , actually each subspace @xmath0 captures only a finite number of them . the question we want to explore in this paper is if the state space @xmath0 , together with its physical interpretation , can be obtained directly from the quantization of a classical system with a finite number of degrees of freedom . a classical system that is generally considered for this purpose is a discrete gauge theory on an abstract graph @xmath1 @xcite . this model captures some important features of loop quantum gravity . however , as the graph @xmath1 is not embedded into a @xmath2-manifold , in this model the role played by diffeomorphisms is rather obscure . moreover , potential problems with locality have been identified @xcite . on the other hand , here we look for a model such that a manifold is present and diffeomorphisms act on local fields in the standard way , via pullback . the classical system we investigate is a field theory : we consider a theory of locally - flat connections on a manifold . the manifold is assumed to be non simply - connected because of the presence of a network of defects . we quantize this system relying only on standard field theoretical methods @xcite . in particular , the quantization procedure we discuss does not involve the basic assumption about loop observables which characterizes loop quantum gravity . nevertheless , the resulting state space is surprisingly close to the one of ordinary loop quantum gravity . spin networks arise again and provide the appropriate tool for describing gauge- and diffeomorphism - invariant functionals of the connection . the role played by defects and loops in this approach is analogous to the one played by solenoids and wilson loops in the aharonov - bohm effect @xcite . this justifies the title of the paper . the paper is organized as follows : in section [ sec : foundations ] we introduce our model , in section [ sec : line ] we analyze in detail a simple example and in section [ sec : perspectives ] we discuss some perspectives .

the state space of loop quantum gravity admits a decomposition into orthogonal subspaces associated to diffeomorphism equivalence classes of spin - network graphs . in this paper i investigate the possibility of obtaining this state space from the quantization of a topological field theory with _ degrees of freedom . i quantize this theory using standard field theoretical methods .

the state space of loop quantum gravity admits a decomposition into orthogonal subspaces associated to diffeomorphism equivalence classes of spin - network graphs . in this paper i investigate the possibility of obtaining this state space from the quantization of a topological field theory with _ many _ degrees of freedom . the starting point is a 3-manifold with a network of defect - lines . a locally - flat connection on this manifold can have non - trivial holonomy around non - contractible loops . this is in fact the mathematical origin of the aharonov - bohm effect . i quantize this theory using standard field theoretical methods . the functional integral defining the scalar product is shown to reduce to a finite dimensional integral over moduli space . a non - trivial measure given by the faddeev - popov determinant is derived . i argue that the scalar product obtained coincides with the one used in loop quantum gravity . i provide an explicit derivation in the case of a single defect - line , corresponding to a single loop in loop quantum gravity . moreover , i discuss the relation with spin - networks as used in the context of spin foam models .

1008.4796

i

according to the popular hierarchical clustering @xmath2 cold dark matter ( ) scenario , galaxies form and grow inside evolving dark matter haloes . a central question emerges then about what is the galaxy stellar mass , , associated on average with a given halo of mass , i.e. , the relation . the change with redshift of this relation , ( , @xmath0 ) , resumes the key astrophysical processes of galaxy stellar mass assembly in the context of the scenario . with the advent of large galaxy surveys in the last years , a big effort has been made in constraining the local relation ( 1 ) directly by estimating halo masses with galaxy - galaxy weak lensing , with kinematics of satellite galaxies or with x - ray studies ; and ( 2 ) indirectly by linking the observed statistical galaxy properties ( e.g. , the galaxy stellar mass function , the two point correlation function , galaxy group catalogs ) to the theoretical halo mass function ( hereafter @xmath12 ; for recent reviews on all of these methods see moster et al . 2010 ; behroozi et al . 2010 ; more et al . 2010 , and more references in these papers ) . the latter approach is less direct than the former one , but it allows to cover larger mass ranges , and it can be extended up to the redshifts where observed are reported ( for recent results see conroy & wechsler 2009 ; moster et al . 2010 ; wang & jing 2010 ; behroozi et al . 2010 ) . in moster et al . ( 2010 ) and behroozi et al . ( 2010 ; hereafter bcw10 ) , the ( , @xmath0 ) functionality has been constrained up to @xmath13 . in each case , different observational data sets for the and different methods for statistically assigning halo masses to the galaxies were used . the relation at @xmath10 is similar in both works ( see also baldry et al . 2008 ; drory et al . 2009 ; guo et al . 2010 ; wang & jing 2010 ) . however , the change with @xmath0 of this relation , ( , @xmath0 ) , particularly for @xmath14 , is different in both cases . although the uncertainties in the inferences of ( , @xmath0 ) are still significant , the current determinations can be used for preliminary explorations of the galaxy mass assembly process . an original approach has been introduced by conroy & wechsler ( 2009 ; hereafter cw09 ) , who proposed a parametric form for as function of @xmath0 constrained by both some observational reports of this function and the star formation rate ( sfr) relations to @xmath9 . then , the cumulative at each @xmath0 were matched to the cumulative @xmath12s in order to infer the relations at different @xmath11s ( abundance matching formalism , the simplest of the indirect methods ; e.g. , marinoni & hudson 2002 , kravtsov et al . 2004 , vale & ostriker 2004 ; see 2 ) . finally , the obtained relations at different @xmath11s were connected by using simple parameterizations of the average halo mass aggregation histories ( mahs ) in order to infer the average stellar mass buildup of galaxies as a function of mass . the previous approach has the advantage ( 1 ) of being flexible enough as to allow for explorations covering large mass and redshift ranges , and ( 2 ) of providing a bridge between observational results and theoretical work . one of the bases of this approach is the statistical abundance matching formalism , which has shown to give robust results in agreement with direct inferences of the local relation or with other indirect inferences based on observations of the two - point correlation functions or galaxy group catalogs ( see moster et al . 2010 ; bcw10 ; more et al . 2010 ; dutton et al . 2010a ) . from the purely empirical point of view , recent studies are posing a new conception in our understanding of galaxy stellar mass assembly . for example , drory & alvarez ( 2008 ) used empirical up to @xmath15 ( drory et al . 2005 ) to infer the assembly of large galaxies , and in combination with available observations of the sfr relation at different @xmath11s , they constrained the contribution of star formation ( sf ) and merging to stellar mass build up in galaxies . from this and other studies ( e.g. , bundy et al . 2006,2009 ; hopkins et al . 2007 ; pozzetti et al . 2010 ) , the trend of downsizing ( cowie et al . 1996 ) is clearly shown in the sense that the mass at which the sfr starts to drop strongly decreases with time ( from @xmath16 at @xmath17 to @xmath18 at @xmath19 according to drory & alvarez 2008 ) . this result combined with observationally inferred merger rates , led the latter authors to conclude that the ( massive ) red sequence is built up from top to down . this phenomenon was originally dubbed as _ archaeological downsizing _ ( thomas et al . 2005 ; see also for related results e.g. , daddi et . al 2004,2007 ; drory et al . 2004 ; bundy et al . 2005,2006 ; conselice et al . 2007 ; marchesini et al . 2009 ; perez - gonzalez et al . 2008 and more references therein ) , and it seems that its main driver are internal galaxy processes that efficiently quench sf in massive galaxies ( e.g. , bundy et al . 2006 ; peng et al . 2010 ) . the latter result has been confirmed by recent decompositions of the by galaxy type ( based on color , sfr , morphology , etc . ) up to @xmath9 ( e.g. , borch et al . 2006 ; bell et al . 2007 ; drory et al . 2009 ; ilbert et al . 2010 ; pozzetti et al . 2010 ; for a compilation of early observations , see hopkins et al . a systematic result obtained in these works is that blue / late - type ( active ) galaxies migrate to the red / early - type ( passive ) population involving a sequence of masses that decreases with time , a result in line with the archaeological downsizing phenomenon . the environment plays also an important role . recent observational studies , where the has been divided not only by galaxy types but also by environment , show that the population migration happens more efficiently and earlier in denser environments ( e.g. , peng et al . 2010 ) . at lower masses the inferences of the assembly are difficulted by the incompleteness limit of the samples as higher is @xmath0 . however , at least for @xmath20 , current studies show that the specific sfr ( ssfr ) of low - mass ( blue ) galaxies is surprisingly high , and higher than the ssfrs of more massive galaxies ( e.g. , bauer et al . 2005 ; noeske et al . 2007 ; zheng et al . 2007 ; bell et al 2007 ; elbaz et al . 2007 ; chen et al . 2009 ; damen et al . 2009a , b ; santini et al . 2009 ; oliver et al . 2010 ; rodighiero et al . downsizing in ssfr of low - mass galaxies _ seems to imply a delayed buildup as lower is the mass , something difficult to explain by the moment in -based models ( for models , discussions , and more references see noeske et al . 2007 ; fontanot et al . 2009 ; firmani , avila - reese & rodrguez - puebla 2010 ) . based on the scenario and the new observational inferences discussed above , a unified picture of stellar and halo mass buildup of galaxies of all sizes can be developed . by using relations constrained by bcw10 from @xmath21 to @xmath22 , we generate an analytical ( , @xmath0 ) relationship , which is continuous and differentiable at any @xmath0 . this sequence of relations in @xmath0 is combined with average halo mahs in order to : 1 . calculate the _ average _ stellar mass buildup tracks of galaxies , ( @xmath0 ) , from @xmath23 up to now ( hereafter , galaxian hybrid evolutionary tracks , ghets ) along with their halo mahs , ( @xmath0 ) ; 2 . calculate the average ssfr histories of galaxies from the corresponding specific stellar mass growth rate histories , ; 3 . determine the typical mass at each @xmath0 that marks the transition from active to passive galaxy population ( in terms of growth ) 4 . infer the transition rate in the number density of active to passive galaxies at each @xmath0 . our approach differs from cw09 in several aspects . these authors used observational inferences of the ssfr vs at different @xmath11s for constraining the evolution of their proposed ( up to @xmath9 ) , which is a partial input of their approach for calculating ( , @xmath0 ) . instead , we use more recent and updated direct constraints for this relationship ( bcw10 ) , which extends up to @xmath13 , and then predict the ssfr histories . in cw09 a simple parameterization for the average mahs was used , while we generate them by using an extended press - schechter formalism that gives results similar to those of large n - body cosmological simulations . we differ from cw09 also in several aims and results . the inferences of the quantities listed above constrain in general the multiple astrophysical processes participating in the formation and evolution of galaxies . in particular , we will compare the inferred evolutionary tracks ( ghets ) to predictions of standard @xmath24-based semi - numerical models of disk galaxy evolution and explore whether the so - called downsizing in ssfr is really an issue for models . in 2 , the method to calculate the ghets is explained . the inferred average ghets are presented in different diagrams in 3 . in 3.1 and 3.2 the evolution of the ssfr as a function of mass , the evolution of the transition mass , and the flow of active to passive galaxies at each epoch , are shown and compared with direct observational estimates . the reliability of our approach and the results are discussed in 3.3 . in 4 , -based models of disk galaxy evolution are used to calculate evolutionary tracks for low - mass galaxies and see whether they are able to reproduce or not the ghets , in particular the ssfr downsizing phenomenon . a summary and our conclusions are given in 5 .

this sequence of relations , defined in the range , together with average cold dark matter ( ) halo mass aggregation histories ( mahs ) are used here for inferring _ average _ growth histories , the galaxian hybrid evolutionary tracks ( ghets ) , where hybrid remarks the combination of observational ( ) and theoretical ( ) ingredients . as a result of our approach , a unified picture of stellar and halo mass buildup , population migration , and downsizing of galaxies as a function of mass is presented .

the stellar dark halo mass relation of galaxies at different redshifts , ( , ) , encloses relevant features concerning their physical processes and evolution . this sequence of relations , defined in the range , together with average cold dark matter ( ) halo mass aggregation histories ( mahs ) are used here for inferring _ average _ growth histories , the galaxian hybrid evolutionary tracks ( ghets ) , where hybrid remarks the combination of observational ( ) and theoretical ( ) ingredients . as a result of our approach , a unified picture of stellar and halo mass buildup , population migration , and downsizing of galaxies as a function of mass is presented . the inferred average growth histories ( ghets ) of highest and lowest mass galaxies are definitively quite different from the average mahs , ( ) , of the corresponding dark halos . depending on how a given ( ) compares with the mass at which the -to- ratio curve peaks at the epoch , ( ) , two evolutionary phases are evidenced : ( i ) galaxies in an active regime of growth when , and ( ii ) galaxies in a quiescent or passive regime when . the typical at which galaxies transit from the active ( star - forming ) to the quiescent regime , , increases with , log(/) , making evident a _ population downsizing _ phenomenon . this result agrees with independent observational determinations based on the evolution of the galaxy stellar mass function decomposition into blue and red galaxy populations . the specific star formation rate , ssfr , predicted from the derivative of the ghet is consistent with direct measures of the ssfr for galaxies at different redshifts , though both sets of observational inferences are independent . the average ghets of galaxies smaller than at ( , ) did not reach the quiescent regime , and for them , the lower the mass , the faster the later growth rate ( _ downsizing in ssfr _ ) . the ghets allow us to predict the transition rate in the number density of active to passive population ; the predicted values agree with direct estimates of the growth rate in the number density for the ( massive ) red population up to . we show that based models of disk galaxy evolution , including feedback - driven outflows , are able to reproduce the low - mass side of the relation at , but at highers strongly disagree with the ghets : models do not reproduce the strong downsizing in ssfr and the high ssfr of low mass galaxies .

1008.4796

i

empirically inferred relations from @xmath10 to @xmath25 were connected with average halo mahs in order to infer the corresponding individual _ average _ stellar mass growth histories , called here ghets . we have adopted an ( , @xmath0 ) relationship continuous in the @xmath147 redshift range and in agreement with the inferences by bcw10 , who used the technique of jointly matching the abundances of observed to the theoretical @xmath12s at different @xmath11s . the main results obtained here , which allow to establish a unified description of average galaxy evolutionary tracks for a large range of masses , are as follows . @xmath148 the folding in the @xmath0 surface , reflected mainly as peaks in the ( /) diagram that shift to higher masses as @xmath0 increases , introduces an important feature in the behavior of the ghets . for masses much smaller than the peak mass at a given @xmath0 , ( @xmath0 ) , the ghets are in an active growth phase , whereas masses close to or greater than ( @xmath0 ) are in a quiescent or completely passive ( stagnated ) phase ( figs . [ msmh ] and [ galefficiency ] ) . therefore , at each @xmath0 there is a characteristic stellar mass at which on average galaxies slow down their growth and transit from an active ( star forming blue ) population to a passive ( red ) population . this transition mass decreases with time , giving rise to a phenomenon called here _ population downsizing_. @xmath148 galaxies less massive than at @xmath6 ( @xmath149 , @xmath150 ) have still growing ghets . besides , the lower the mass , the faster the later growth , due likely to a delayed and lately active sf phase , a phenomenon called _ downsizing in ssfr_. @xmath148 the shapes of the average stellar and halo mass assembling histories are quite different ( figure [ ghets ] ) . for galaxies that at @xmath6 have @xmath151 , their dark mahs at later epochs grow slightly slower as smaller is the mass , while their stellar ghets grow much faster . for @xmath152 , the larger the galaxy , the earlier its ghets attain a stellar mass stagnation ; until this epoch , the more massive the galaxy , the faster the growth with respect to the corresponding growth . @xmath148 by neglecting any stellar mass growth by accretion ( dry mergers ) , a ghet allows to find the corresponding ssfr history , ssfr(@xmath0 ) , by calculating and correcting by the stellar mas - loss recycling factor @xmath153 . the inferred ssfrs at different @xmath0 s and as a function of ( figs . [ dotm ] , [ dotmobs ] , and [ ssfr - ms ] ) are reasonably consistent with recent observational studies based on direct measures of the ssfr of star - forming galaxies at different @xmath0 s . the ghet - based ssfrs corresponding to masses that at a given @xmath0 are larger than the transition mass ( @xmath0 ) , are much lower than the measured ssfrs of ( rare ) luminous blue galaxies , but agree or are even slightly larger than the measured ssfrs of red galaxies . the overall consistency between the ghet - based ssfr- relations at different @xmath11s with direct inferences of these relations suggests that the accretion of stellar systems ( mergers ) plays a minor role in the assembling of galaxies , excepting perhaps those that transited to the passive sequence ( the most massive ones ) . @xmath148 by using the ssfr vs. evolutionary tracks , we calculated the characteristic transition mass at each @xmath0 , ( @xmath0 ) , above which the average ghet starts to significantly decrease its growth rate , transiting from the active to the passive galaxy population . the result is roughly described by the relation log(/ ) = @xmath154 ( at least up to @xmath105 ) . this result agrees with recent observational determinations of the evolution of the mass , at which the early- and late - type components cross each other , from @xmath155 to the present ( fig . [ mtran ] ) . @xmath148 we determined also the transition rate in number density of active ( blue ) to quiescent ( red ) galaxy population . at @xmath21 such a rate is @xmath156 gal gyr@xmath31 mpc@xmath126 and up to @xmath46 the rates are within @xmath157 gal gyr@xmath31 mpc@xmath126 , in good agreement with direct observational inferences of growth rate in number density of red galaxies . @xmath148 we further explored whether -based models of galaxy evolution are able to predict galaxy evolutionary tracks ( called here gets ) in agreement with the ghets , in particular at low masses where the downsizing in ssfr is evidenced by the ghets . we have shown that while the models with sn energy driven outflows are able to reproduce the local relation ( see also firmani et al . 2010 ) , they fail in reproducing this relation at higher @xmath0 s . the difference between gets and ghets at low masses is rather large : the former ones show a fast decrease in ssfr with time almost independent of mass , while for the latter ones , the lower the mass , the slower the late decrease of ssfr ( downsizing in ssfr ) . from these results , we conclude that the general description of stellar mass buildup of galaxies provided by our average ghets appears rather successful : the predicted ssfr histories as a function of and the predicted transition mass as a function of @xmath0 , as well as the transition flux at different @xmath11s , are roughly consistent with direct ( but yet limited ) observational estimates of all these quantities . furthermore , our analysis reveals nicely the existence of a galaxy bi - modality related to the growth activity : as @xmath0 decreases , smaller and smaller masses transit on average from the active ( blue star - forming ) to the passive ( red ) population . an important ingredient of our approach is the connection of halos to the observed galaxies . therefore , the underlying hierarchical scenario is successful in the sense that the predictions of the model are in agreement with independent observations . the average stellar and dark mass buildup of galaxies were found to be significantly different , specially for low and high masses . this result is in qualitative agreement with cw09 in spite of the differences in the data , method , and redshift range between their and our work . however , the results from both works are different at a quantitative level , which is seen , for example , in the different conclusions regarding the existence of a characteristic mass at each epoch at which the ssfr of galaxies is truncated . note that the ssfr and the determination of this characteristic mass ( ) are related to the first and second derivatives of the growth , respectively . our results put in a unified picture both the population downsizing ( related to galaxies with @xmath158 at @xmath6 ) and the downsizing in ssfr ( related to smaller galaxies ) . the challenges are now to explain the processes that produce : ( 1 ) the transition from active to passive regimes in growth associated with a sharp cessation of the sfr in massive galaxies , ( 2 ) the fact that the typical mass of ssfr truncation , , decreases with cosmic time ( population downsizing ) , and ( 3 ) the fact that the smaller is the halo , the more is delayed the galaxy s growth ( downsizing in ssfr ) . items ( 1 ) and ( 2 ) seem to find partial explanations in aspects related to the same dark halo clustering ( environment ) evolution ( e.g. , neistein et al . 2006 ) as well as to the introduction of feedback processes due to the agns of massive galaxies ( e.g. , silk & rees 1998 ; kauffmann & haehnelt 2000 ; granato et al . 2004 ; cattaneo et al . 2005 ; de lucia et al . 2005 ; bower et al . 2006 ; croton et al . 2006 ) . item ( 3 ) , as shown here , is a sharp and less understood problem . later re - accretion of the gas ejected by galaxies due to sn - driven outflows does not account for a solution to this issue ( firmani et al . . a better understanding of the astrophysical processes intervening in galaxy formation and evolution as well as the role of environmental processes is necessary . we are grateful to dr . l. pozzetti for kindly making available to us in electronic form the results reproduced in our fig . [ mtran ] . we thank the anonymous referee for his / her careful review of our paper . v. a. acknowledges papiit - unam grant in114509 and conacyt grant 60354 for partial funding .

the stellar dark halo mass relation of galaxies at different redshifts , ( , ) , encloses relevant features concerning their physical processes and evolution . the inferred average growth histories ( ghets ) of highest and lowest mass galaxies are definitively quite different from the average mahs , ( ) , of the corresponding dark halos . depending on how a given ( ) compares with the mass at which the -to- ratio curve peaks at the epoch , ( ) , two evolutionary phases are evidenced : ( i ) galaxies in an active regime of growth when , and ( ii ) galaxies in a quiescent or passive regime when . the typical at which galaxies transit from the active ( star - forming ) to the quiescent regime , , increases with , log(/) , making evident a _ population downsizing _ phenomenon . this result agrees with independent observational determinations based on the evolution of the galaxy stellar mass function decomposition into blue and red galaxy populations . the average ghets of galaxies smaller than at ( , ) did not reach the quiescent regime , and for them , the lower the mass , the faster the later growth rate ( _ downsizing in ssfr _ ) . the ghets allow us to predict the transition rate in the number density of active to passive population ; the predicted values agree with direct estimates of the growth rate in the number density for the ( massive ) red population up to . we show that based models of disk galaxy evolution , including feedback - driven outflows , are able to reproduce the low - mass side of the relation at , but at highers strongly disagree with the ghets : models do not reproduce the strong downsizing in ssfr and the high ssfr of low mass galaxies .

the stellar dark halo mass relation of galaxies at different redshifts , ( , ) , encloses relevant features concerning their physical processes and evolution . this sequence of relations , defined in the range , together with average cold dark matter ( ) halo mass aggregation histories ( mahs ) are used here for inferring _ average _ growth histories , the galaxian hybrid evolutionary tracks ( ghets ) , where hybrid remarks the combination of observational ( ) and theoretical ( ) ingredients . as a result of our approach , a unified picture of stellar and halo mass buildup , population migration , and downsizing of galaxies as a function of mass is presented . the inferred average growth histories ( ghets ) of highest and lowest mass galaxies are definitively quite different from the average mahs , ( ) , of the corresponding dark halos . depending on how a given ( ) compares with the mass at which the -to- ratio curve peaks at the epoch , ( ) , two evolutionary phases are evidenced : ( i ) galaxies in an active regime of growth when , and ( ii ) galaxies in a quiescent or passive regime when . the typical at which galaxies transit from the active ( star - forming ) to the quiescent regime , , increases with , log(/) , making evident a _ population downsizing _ phenomenon . this result agrees with independent observational determinations based on the evolution of the galaxy stellar mass function decomposition into blue and red galaxy populations . the specific star formation rate , ssfr , predicted from the derivative of the ghet is consistent with direct measures of the ssfr for galaxies at different redshifts , though both sets of observational inferences are independent . the average ghets of galaxies smaller than at ( , ) did not reach the quiescent regime , and for them , the lower the mass , the faster the later growth rate ( _ downsizing in ssfr _ ) . the ghets allow us to predict the transition rate in the number density of active to passive population ; the predicted values agree with direct estimates of the growth rate in the number density for the ( massive ) red population up to . we show that based models of disk galaxy evolution , including feedback - driven outflows , are able to reproduce the low - mass side of the relation at , but at highers strongly disagree with the ghets : models do not reproduce the strong downsizing in ssfr and the high ssfr of low mass galaxies .

1301.0166

i

computer simulations of macromolecular liquids described at the atomistic level are extremely useful because they bridge information between the microscopic molecular structure of the polymeric system , at the given thermodynamic conditions , and its macroscopic properties , such as viscosity , diffusion , and dynamical - mechanical response , which are observed experimentally.@xcite it is unfortunate that , despite the progress already occurred in the computational hardware and software , the study of the dynamics of polymeric liquids by atomistic computer simulations is still limited by the impossibility of simulating polymer dynamics in the wide range of time and length scales relevant for these systems . it is known that long simulation trajectories deteriorate with time , following a law defined by the lyapunov exponent characteristic of the system , and the resulting long - time dynamics is affected by errors.@xcite atomistic simulations of polymeric liquids are limited either in the length and number of macromolecules , or in the maximum timescale that can be reached . the long timescale is a regime of great interest for these systems , because of the relevance of dynamical - mechanical properties of macromolecules in that regime for their industrial applications . because the limitation concerns only the region of long - time , large - scale properties , it is possible to shift the focus of a simulation to this region of interest by the reduction of the simulated degrees of freedom through the averaging of local scale properties , i.e. adopting a so - called coarse - graining " procedure . while simulations of coarse - grained systems afford to represent larger length- and longer time - scales than atomistic simulations , they also are marred by the shortcoming that the measured dynamics is unphysically fast . this is the advantage that allows one to perform simulations in the long - time regime , but it is also a problem because the dynamics in the simulation becomes too fast and measured diffusion coefficients are too large . depending on the level of coarse - graining the dynamics can become orders of magnitude faster than the atomistic dynamics.@xcite being aware that the dynamics has to be rescaled to recover the correct timescale,@xcite one resorts to the most conventional method , which is to build a calibration curve calculated by superimposing the long - time dynamics of the coarse - grained and atomistic simulations.@xcite the hope is for this calibration curve to be transferable to other systems , or to be identical , and so applicable , for thermodynamic conditions close to , but different than the phase point for which the curve was optimized in the first place . otherwise , if an atomistic simulation has to be ran every time we need to rescale a coarse - grained simulation there is no advantage in running simulations of coarse - grained ( cg ) systems . the rescaling factor of the conventional calibration curve is , however , purely a numerical correction . there is no physical motivation for one to assume that this correction has to be identical for any system or thermodynamic condition different from the ones in which it was optimized . given that the effective potentials between coarse - grained units are free energies , and as such they are parameter dependent , it is very unlikely that numerically optimized corrections will be identical for different systems . however , if the calibration curve is applied for conditions of temperature , density , and degree of polymerization , very close in the phase diagram to the ones in which the calibration curve was originally optimized , there is hope that the error is very contained . alternatively , in the case that very limited levels of coarse - graining are applied , e.g. combination of a few atoms to obtain a new coarse - grained unit , the error incurred in using the calibration curve in different conditions , can be small enough to be within the numerical error of the calculation . this is in fact the reason for the observed good agreement in the rescaled dynamics of systems with contained level of coarse - graining.@xcite the goal of this paper is orthogonal to the more conventional calculation of an optimized calibration curve for systems with limited level of coarse - graining . in fact our goal is to investigate the physical motivation that leads to the accelerated dynamics in first place and to provide , through our analysis , a theoretical approach to calculate , from first principle equations , the correction factor that needs to be applied to the fast dynamics measured in coarse - grained simulations to recover the slower and more realistic dynamics of the atomistic description . we study the most extreme level of molecular coarse - graining , where one polymer chain is represented as a soft sphere , because i ) the description is analytical allowing the formal study of the rescaling problem , ii ) it provides a solid test of the reconstruction procedure because possible errors would be maximized , iii ) this level of coarse - graining is associated with the largest computational gain , so it is important . recently we have proposed an original procedure to rescale the dynamics measured in simulations of coarse - grained polymer melts.@xcite the procedure we proposed does not require to run atomistic simulations to calibrate the dynamics of the coarse - grained simulation . once one parameter , specifically the diameter of the hard - core monomer potential , is fixed , the rescaling factors are fully determined . the advantage of this method is clear , given that the coarse - grained simulation can reach larger - scale longer - time properties than the atomistic simulation . because no atomistic simulations are needed , the measured dynamics can be directly rescaled to obtain the dynamics of the real system we wanted to study . the method has been formally derived , and then applied to systems of polyethylene ( pe ) melts . the choice of pe as a test system was motivated by the wealth of experimental and simulation data available in the literature . we have shown that the proposed theory is able to predict diffusion coefficients in agreement with both atomistic simulations and experiments for systems in both the unentangled and entangled regimes , for a range of temperatures and densities . for entangled system the approach of dynamical reconstruction includes an extra loop in the calculation of the friction coefficient , which accounts for the fact that in real systems described at the atomistic level , the dynamics is slowed down by the presence of entanglements . we hypothesized for the entanglements to relax in time following the same dynamical mechanism of single chain interdiffusion . in this paper entangled chain dynamics is not investigated as most of the samples in the atomistic simulations are either unentangled or in the region of crossover from the unentangled to the entangled regimes . one of the questions that still needed to be answered was if our method was able to generate high quality predictions also for macromolecular liquids with a more complex monomeric structure than the simple polyethylene . a first study of this issue is presented in this manuscript which investigates the agreement between theoretically predicted diffusion coefficients for _ cis_-1,4-polybutadiene ( pb ) chains and data from molecular dynamics simulations performed by tsolou , mavrantzas and coworkers.@xcite the approach is completely general and can be applied to polybutadiene chains with different tacticity . for these systems the difference in local chain semiflexibility , which corresponds to different overall chain dimension , i.e. a different radius - of - gyration ( @xmath0 ) and statistical segment length ( @xmath1 ) , ultimately leads to a different diffusion coefficients for polybutadienes with different tacticity . in this paper we limit our calculations to _ cis_-1,4-polybutadiene samples because those are the samples investigated by atomistic simulations and provide a effective test of our procedure for dynamical reconstruction . our rescaling method considers two contributions emerging from the consequence of applying the coarse - graining process and derives the theoretical corrections that need to be applied to the dynamics of the coarse - grained description to recover the modalities of the original atomistic system . to calculate the analytical correction we adopt for the atomistic descriptions a simple bead - and - spring description of the chain where each pb polymer of @xmath2 monomeric units is represented as a collection of @xmath2 beads connected by semi flexible springs of length @xmath3 , and the overall chain dimension is defined by the radius - of - gyration of the molecule , @xmath0 . this model is a rouse approach modified to include chain semiflexibility and has been shown to represent well the diffusion of polymer melts in the unentangled regime.@xcite from the comparison of this model and the soft sphere representation of the chain , it is possible to evaluate the two contributions that are responsible for the accelerated dynamics , and which have to be included to correct the measured dynamics and bring it to the realistic values of the atomistic ( here bead - and - spring ) description . the first correction emerges from the consideration that due to the process of averaging the intramolecular degrees of freedom , the coarse - grained system experiences a change in its entropy , because a number of local states are neglected . while the atomistic system devotes time to explore local configurations , the coarse - grained system does nt . to recover the correct dynamics those states need to be included _ a posteriori _ in the form of an entropic contribution to the free energy that rescales the time measured in the cg simulations . the second correction comes from the change of the shape " of the molecule once it is coarse - grained . macromolecules described at the atomistic level become represented by chains of effective atoms , or as bead - and - springs , chains of soft blobs , or even each molecule as a soft sphere . in all these multiple forms the surface of each molecule available to the surrounding molecules , i.e. the solvent " , is different . the hydrodynamic radius , @xmath4 , of the coarse - grained unit in each description is different and so is its friction coefficient , @xmath5 , defined by stokes law as @xmath6 , where @xmath7 is the viscosity of the medium . by solving the memory function for the friction coefficient in each description we are able to calculate the correction factor that has to be applied to each friction coefficient to recover the description at a different level of coarse - graining . in this paper our rescaling method is first briefly summarized and then applied to study the dynamics of cis-1,4-pb and compared with simulation data by tsolou et.al.@xcite who also investigated the effect of temperature and pressure on the simulations.@xcite the global dynamics of the polymer is represented by the diffusion coefficient and the decay of the self - correlation for the end - to - end molecular vector . these dynamical quantities are reconstructed using the method by lyubimov at al.,@xcite from the information contained in the trajectories of the mesocale simulations of the coarse - grained polymer melts and show good agreement with the data from united atom simulations . for the internal dynamics the theory for cooperative motion@xcite is used to predict monomer dynamics and the dynamical structure factors , which compare well with the simulations . if atomistic simulations are not available , the theory of dynamical reconstruction is able to predict the correct dynamics from the rescaling of the mesoscale simulations having as an input the polymer radius - of - gyration , which can be calculated from simple structural models for polymers . the accuracy of adopting a freely rotating chain model for the calculation of the polymer radius of gyration is discussed in the last section . a brief summary concludes the paper .

the rescaling formalism accounts for the corrections in the dynamics due to the change in entropy and the change in friction that are a consequence of the coarse - graining procedure . by including these two corrections the dynamics theoretically predicted time correlation functions show good agreement with simulations in the whole range of length and time scales in which data are available . the theory provides , from data of mesoscale simulations of soft spheres , the correct atomistic - level dynamics , having as solo input static quantities .

the theory to reconstruct the atomistic - level chain diffusion from the accelerated dynamics that is measured in mesoscale simulations of the coarse - grained system , is applied here to the dynamics of _ cis_-1,4-polybutadiene melts where each chain is described as a soft interacting colloidal particle . the rescaling formalism accounts for the corrections in the dynamics due to the change in entropy and the change in friction that are a consequence of the coarse - graining procedure . by including these two corrections the dynamics is rescaled to reproduce the realistic dynamics of the system described at the atomistic level . the rescaled diffusion coefficient obtained from mesoscale simulations of coarse - grained _ cis_-1,4-polybutadiene melts shows good agreement with data from united atom simulations performed by tsolou et al . the derived monomer friction coefficient is used as an input to the theory for cooperative dynamics that describes the internal dynamics of a polymer moving in a transient regions of slow cooperative motion in a liquid of macromolecules . theoretically predicted time correlation functions show good agreement with simulations in the whole range of length and time scales in which data are available . the theory provides , from data of mesoscale simulations of soft spheres , the correct atomistic - level dynamics , having as solo input static quantities .

1501.00266

i

one way of finding rates of reaction is to consider rates of transport in a low dimensional hamiltonian system representing the specific reaction . some of the first examples studied using transition state theory consisted of bimolecular reaction in gaseous phase , i.e. @xmath4 for two ( polyatomic ) molecules @xmath5 and @xmath6 . provided the born - oppenheimer approximation holds , we can pass from the quantum mechanical system to a classical one , namely the hamiltonian system for the motion of the nuclei interacting via a potential given by the ( ground state ) energy of the electrons as a function of the internuclear coordinates . then , if this extremely high dimensional hamiltonian system is , at any instant , the product of `` reacting '' two molecule sub - systems that are independent of each other , we may consider the evolution of an ensemble of individual reactions in this low dimensional hamiltonian sub - system . for this , we require the gas to be sufficiently dilute . see keck @xcite for a nice review of transition state theory and discussion of the assumptions involved . finally , since the low dimensional system is hamiltonian and energy is conserved , we can restrict our attention to the energy levels , and consider the flow of ergode , as a function of the energy . finding ( microcanonical ) reaction rates translates to finding the rate of transport of ergode between regions representing reactants and products . transition state theory provides upper bounds on rates of transport via the flux of ergode through a _ dividing surface _ that separates the regions of interest . the dividing surface approach , which we reviewed in @xcite , can be traced back to the works of marcelin ( * ? ? ? * chapter 2 ) and wigner @xcite . in order to obtain a useful upper bound , the dividing surface is chosen to have locally minimum flux in a given direction . for this to be the case , the dividing surface must be the union of surfaces of unidirectional stationary flux with no local recrossings , which in turn is the case for surfaces spanning a closed , invariant , orientable , codimension-2 submanifold of the energy level , known as a _ transition state_. the simplest transition states and dividing surfaces are found in the basic transport scenario of `` flux over a saddle '' @xcite . these are transition states diffeomorphic to @xmath7 for energies just above the index-1 critical point of the hamiltonian for @xmath8 degree of freedom systems , with dividing surfaces diffeomorphic to @xmath9 . for two degree of freedom systems , these transition states are hyperbolic periodic orbits . as the energy is increased , they may lose normal hyperbolicity and bifurcate . the bifurcations of periodic orbits are well known , see e.g. ( * ? ? ? * section 8.6 ) , and those of periodic orbit transition states have been studied for a long time , see e.g. @xcite . instead , for higher degrees of freedom than two the transition states for the basic scenario are normally hyperbolic @xmath10 spheres ( within the energy levels ) and very little is known about their bifurcations . what had been overlooked , and was explained in @xcite , is that the transition states may lose normal hyperbolicity by becoming singular , i.e. the manifold structure fails , at a higher critical energy value but then regain their normal hyperbolicity for values above the critical energy . these are _ morse bifurcations _ * appendix b ) , leading to a change in diffeomorphism class of the transition states and dividing surfaces spanning them . they occur when the union of transition states over a range of energies forms a smooth normally hyperbolic submanifold of state space , which we call a _ transition manifold _ , and there is a critical value of the hamiltonian function restricted to the transition manifold . by definition , the transition states are the level sets of this restricted hamiltonian and undergo a bifurcation . similarly , the dividing surfaces , which span the transition manifold , undergo a morse bifurcation . actually , they occur because the energy levels undergo a morse bifurcation themselves so the dividing surfaces , and therefore the transition states , must also undergo a change of diffeomorphism class in order to still separate these in two . morse theory tells us that we can continue the transition states and dividing surfaces , with respect to the energy , through critical values , as well as giving the diffeomorphism class of the submanifolds . this is useful , for example , when the transition states above some critical energy are disjoint , which we shall see in the atom - frozen diatom system , as we then know exactly what objects to look for . recently , there has been a lot of interest in general transport problems ( as opposed to the basic one ) , non - minimum energy paths @xcite , and roaming reactions @xcite . these transport scenarios may emerge from the basic one via a morse bifurcation , in which case by considering these bifurcations , we obtain transition states and dividing surfaces that can be used to find the rates of transport . we shall consider transport between the region representing two distant molecules ( reactants ) and the region in which the molecules are close . the latter does not however generally constitute the products . this is the _ capture _ transport problem associated with the necessary first step of the molecules getting close enough to react . the _ capture rate _ ( sometimes also called _ collision rate _ ) provides an upper bound on the reaction rate , as we do not expect all captured trajectories to proceed to the products region @xcite . note that there might actually be multiple product regions , but for a two - body capture process there is only one final region of interest . capture rates are crucial for many physical processes , and have a long history dating back at least to 1905 with langevin s early contribution @xcite , see review by chesnavich and bowers @xcite . two assumptions are usually found in the literature . firstly , the reacting hamiltonian systems are assumed to have euclidean symmetry , that is to be invariant under translations and rotations . this is the case for gas phase reactions with no background ( electro - magnetic ) field . the hamiltonian system can then be reduced to a family of systems , in centre of mass frame , parametrised by the angular momentum . the hamiltonian function then contains both coriolis and centrifugal terms . secondly , the energy is taken to be below those at which the two molecules dissociate and centrifugal and coriolis forces to be sufficiently weak such that the molecules are well defined and in the small vibrations regime . these assumptions allow to distinguish between intermolecular degrees of freedom ( distance and relative attitudes of the molecules ) and intramolecular ones . we too shall consider systems that satisfy these assumptions . we want to find the rate of capture , which we shall assume can be thought of as transport between regions on either side of a non - degenerate maximum @xmath11 of the effective potential ( centrifugal terms plus potential ) with respect to the intermolecular distance @xmath12 . in the literature , this maximum is generally a centrifugal maximum obtained by balancing the repulsive centrifugal terms with the attractive long distance potential energy . alternatively , @xmath11 could be a non - degenerate chemical maximum of the bimolecular potential and therefore of the effective potential for small angular momentum . provided @xmath11 is sufficiently large , such that capture occurs in a region where the potential is only weakly dependent upon the attitudes of the molecules , and sufficiently non - degenerate , we shall see that fixing the intermolecular distance degree of freedom to the maximum value gives a normally hyperbolic transition manifold in state space , which can be spanned by a dividing manifold . the restriction of these manifolds to the energy levels gives dividing surfaces and transition states , which we shall refer to as _ capture _ transition states . the literature often refers to them as _ orbiting _ or _ loose _ transition states @xcite . the central field model , in which the attitudes of the colliding pair are ignored , is attributed to langevin @xcite . in this very early work , one already finds capture periodic orbit transition states . langevin considers the capture process using scattering theory . for an introduction to scattering theory see e.g. ( * ? ? ? * section 3.10 ) , whereas for a comparison with the dividing surface approach see @xcite . non - central fields were considered later , also usually from a scattering theory perspective , starting with the works of pechukas @xcite and chesnavich , su and bowers @xcite . as the energy is increased above the critical energy for first connection between reactants and `` products '' , the intermolecular attitude and angular momentum degrees of freedom will generally be involved in interesting sequences of morse bifurcations causing changes in the diffeomorphism class of the energy levels , as the `` cone of acceptance '' ( i.e. orientations for which capture is possible ) opens up , and therefore changes of the capture transition states and dividing surfaces . instead , the intramolecular degrees of freedom are assumed to consist of small vibrations , thus not playing a role in the morse bifurcations . using morse theory , one can know which the correct transition states and dividing surfaces are , as we shall outline for two examples , and then study rates of transport for larger energies than previously thought possible . here , we shall focus on the morse bifurcations , the reduction and the details of bimolecular capture problems . some analysis of `` reaction dynamics '' of rotating molecules has been done recently in @xcite , but we are interested in the interaction of two rotating molecules . whether captured pairs then go on to react can be thought of as a further transport problem with its own ( _ reaction _ ) transition states and dividing surfaces , possibly ( but not necessarily ) associated to other maxima @xmath13 of the effective potential . these are often referred to as _ tight _ transition states . the capture and reaction transition states are therefore in series . the simplest case will be when these are distant and the level sets of separate transition manifolds . however , even when `` separate '' their stable and unstable manifolds , which act as transport barriers , will intersect , determining the `` reaction channels '' . some trajectories joining reactants and products might roam in the region between the ( capture and reaction ) dividing surfaces , that is follow trajectories with a non - monotonic intermolecular distance in time , before finally crossing the reaction dividing surface . this is to be expected due to coupling between degrees of freedom , and was recently given as an explanation of what has been called _ roaming reactions _ @xcite . reaction rates have an equally long history as capture rates , and bimolecular reactions have played the role of test problems since the early days of transition state theory ( as noted in @xcite ) . the transport problems associated with reaction tend to be harder because the chemical potentials are at best not simple and often degenerate . similarly to how the first capture models were simplified by making the fields central , reaction rates were first , and largely still , considered for collinear and planar systems with zero angular momentum . note that reaction transition states will also generally undergo morse bifurcations . hamiltonian systems with symmetry , such as the molecular @xmath14 body systems with euclidean symmetry considered here , have conserved quantities by noether s theorem ( see e.g. ( * ? ? ? * appendix 5 ) , ( * ? ? ? * section 2.7 ) ) , and can be reduced via symplectic reduction . the euclidean symmetry group of our @xmath14 body systems is a semi - direct product @xmath15 and can be reduced in stages ( * ? ? ? * chapter 4 ) . the translational symmetry and associated linear momentum are easily reduced , whereas the rotational symmetry , which does not act freely on the whole of state space , and the associated angular momentum require singular reduction , see e.g. @xcite , ( * ? ? ? * section 8) . the reduced state space is therefore a stratified symplectic manifold , however the hamiltonian flow leaves the connected components of the strata invariant so the reduced dynamics can be studied on each stratum individually . the stratified symplectic manifold for our reduced molecular @xmath14 body systems is composed of three strata . both singular strata have zero angular momentum , whereas on the principal stratum the angular momentum is arbitrary . this is discussed in @xcite . actually , reactions with initial positions and momenta confined to a plane remain in this plane for all successive times , and reduced planar systems have no angular momentum degree of freedom and no coordinate singularities at collinear configurations . in section [ planaratomdiatom ] , we therefore consider planar capture between an atom and a diatom and find our first examples of morse bifurcations . this example and that of two interacting diatoms were considered in less detail in @xcite . a spatial example , of an atom interacting with a molecule , is considered in section [ spatialbimol ] . we choose to use the coordinates that one obtains via the gauge theoretic approach to cotangent bundle reduction as outlined by littlejohn and reinsch @xcite , and reviewed in appendix [ bigauge ] , where we discuss the symplectic form and consider the transformation to serret - andoyer coordinates on the angular momentum sphere , which is not done in @xcite . this approach gives coordinates , which are furthermore physically meaningful since coordinates and momenta are not mixed , however it involves considering the rotational @xmath16 action on configuration space as opposed to the lifted action in state space , and therefore introduces coordinate singularities . these are avoided by considering non - collinear molecules . ways to deal with them are discussed in the conclusions in section [ conclude ] .

the transition states and dividing surfaces used to find rate constants for bimolecular reactions are shown to undergo morse bifurcations , in which they change diffeomorphism class , and to exist for a large range of energies , not just immediately above the critical energy for first connection between reactants and products . the capture between an atom and a diatom , and then a general molecule are presented , providing concrete examples of morse bifurcations of transition states and dividing surfaces . + bimolecular reactions , collision theories , transition state theory , dividing surfaces , morse bifurcations + published in * nonlinearity * , http://dx.doi.org/10.1088/0951-7715/28/12/4303[28(12):4303-4329 ] +

the transition states and dividing surfaces used to find rate constants for bimolecular reactions are shown to undergo morse bifurcations , in which they change diffeomorphism class , and to exist for a large range of energies , not just immediately above the critical energy for first connection between reactants and products . specifically , we consider capture between two molecules and the associated transition states for the case of non - zero angular momentum and general attitudes . the capture between an atom and a diatom , and then a general molecule are presented , providing concrete examples of morse bifurcations of transition states and dividing surfaces . morse bifurcations of transition states in bimolecular reactions + r s mackay and d c strub + mathematics institute and centre for complexity science , university of warwick , coventry cv4 7al , u.k . + bimolecular reactions , collision theories , transition state theory , dividing surfaces , morse bifurcations + published in * nonlinearity * , http://dx.doi.org/10.1088/0951-7715/28/12/4303[28(12):4303-4329 ] +

1501.00266

c

the purpose of this article was to show that morse bifurcations must be considered when studying transport problems for larger ranges of energies , and more specifically to show the existence of morse bifurcations of capture transition states and dividing surfaces for bimolecular reactions . by considering the different sequences of morse bifurcations we were able to find interesting new transition states and dividing surfaces for general reactions with non - zero angular momentum , thus extending the dividing surface approach beyond the well known basic transport scenario . other choices of molecules than those considered here will have similar capture transport problems and therefore similar transition states and bifurcations . the flux of ergode through a dividing surface as a function of energy and the effect of the morse bifurcations was considered in @xcite and commented upon in section [ atomdiatom ] for planar atom - diatom reactions . seeing as the systems representing these examples have more than 2 degrees of freedom , apart from the unrealistic planar atom - frozen diatom case , the morse bifurcations do not have a significant effect on the flux , which varies @xmath107 smoothly through these . the actual use of capture rates as bounds on reaction rates is debatable , but largely depends on the reaction being considered . however , these were only chosen to provide relatively simple examples of morse bifurcations , and to show the importance of the attitude and angular momentum degrees of freedom in bimolecular reactions . we considered bimolecular reactions with euclidean symmetry and reduced them accordingly . even though ( symplectic ) reduction theory is a highly developed subject , we faced a number of difficulties when considering these examples . setting aside the fact that singular reduction was required , due to the nature of the rotational symmetry , and that singular cotangent bundle reduction is still not a complete theory , there is a large gap between the reduction theory literature and applications . even if one restricts one s attention to the principal non - singular stratum , it is not an easy task to find suitable charts . some of the literature avoids charts altogether , focusing instead on the global geometric properties of the reduced spaces , whereas the celestial mechanics literature considers charts for different regions of the reduced space . the most common approach in the molecular literature is to restrict one s attention to non - collinear configurations such that the gauge theoretic approach to cotangent bundle reduction provides a set of charts , as reviewed in appendix [ bigauge ] . however , here we face the opposite issue , namely the reduced space is an @xmath116 fibre bundle , due to the angular momentum degree of freedom , but the global nature of this bundle is generally not discussed in the literature . we feel that more work is needed , both on charts for the reduced spaces and on their global nature , and that this would improve our understanding of molecular reactions , and also other @xmath14-body systems . by considering normal molecules , with a fixed equilibrium configuration and energies below that at which either of the two molecules dissociates , collinearity becomes a decreasing concern with increasing size of the molecules , namely codimension-@xmath273 where @xmath274 is the number of atoms in the @xmath275th molecule ( @xmath276 ) , and the chemistry of the molecule is not taken into account . however , for smaller molecules , higher energies , or other transport problems we may need to consider collinear configurations . for non - zero angular momentum , collinear configurations are a subset of the principal reduced stratum . however due to collinear configurations having non - trivial configuration space isotropy , we can not find charts via the gauge theoretic approach to cotangent bundle reduction . the issue is therefore not one of reduction per se , but only of finding suitable coordinates . the transport problem and bifurcations of transition states will be the same as those considered in section [ spatialbimol ] . for more than seventy years , chemists have been using charts obtained by modifying gauge theoretic cotangent bundle reduction @xcite . the idea is to pass to a rotating frame in which the collinear ( equilibrium ) configuration is along a chosen axis , say the @xmath132-axis , but retain the remaining rotational symmetry ( about @xmath132 ) as an internal coordinate . then by choosing the eckart convention and the non - gauge invariant form of the kinetic energy , we find that the lagrangian is not a function of the angular velocity about the collinear axis @xmath277 , so we can obtain a hamiltonian that is not a function of the first angular momentum component @xmath278 . that is , @xmath278 is replaced by the canonical momentum conjugate to the `` internal '' rotation about the @xmath132-axis . these charts were first considered by sayvetz @xcite , though nowadays they are often attributed to watson @xcite . this procedure can be justified geometrically by applying the slice theorem ( see e.g. ( * ? ? ? * section 2.3.14 ) ) to configuration space in a neighbourhood of the collinear configurations , and then lifting the charts obtained to the cotangent bundle @xcite . actually , with this understanding , charts can be obtained that are not those of the eckart convention , i.e. other gauges and internal coordinates . this was used in examples by kozin et al . note that this is just the splitting of coordinates into internal coordinates and rotations and not an actual reduction , cf . appendix [ bigauge ] . with these charts , we can not simply pass to serret - andoyer coordinates to reduce the symmetry , seeing as the hamiltonian is not a function of @xmath278 . this is generally not addressed in literature . the transport problems associated with reaction are usually a lot more complicated than the capture ones considered here , so their transition states may undergo a number of different bifurcations . one simple example which should display much the same bifurcations as those seen here is isomerization reactions involving only one molecule . these will be the topic of a future publication . we have concentrated here on how the transition state and dividing surface vary with energy , but the exact dependence of the capture transition states on the angular momentum and the possible loss of normal hyperbolicity for large values should be considered in detail . due to the high degrees of freedom of these systems , this is not a straightforward task . it is also interesting to ask whether the dividing surface method can be extended to consider reactions with a varying external field or laser pulse , which need to be modelled as a non - autonomous hamiltonian system ; or reactions that are not in the ( dilute ) gas phase , for which the product kinetic approximation leading to a low dimensional hamiltonian system is not valid ; or even reactions out of equilibrium . reviews of the dividing surface approach applied to the basic transport scenario of flux over a saddle for non - autonomous systems and langevin systems can be found in @xcite and @xcite , respectively . however , more work is required to consider general transport scenarios and fully understand transport in these systems .

specifically , we consider capture between two molecules and the associated transition states for the case of non - zero angular momentum and general attitudes . morse bifurcations of transition states in bimolecular reactions + r s mackay and d c strub + mathematics institute and centre for complexity science , university of warwick , coventry cv4 7al , u.k .

the transition states and dividing surfaces used to find rate constants for bimolecular reactions are shown to undergo morse bifurcations , in which they change diffeomorphism class , and to exist for a large range of energies , not just immediately above the critical energy for first connection between reactants and products . specifically , we consider capture between two molecules and the associated transition states for the case of non - zero angular momentum and general attitudes . the capture between an atom and a diatom , and then a general molecule are presented , providing concrete examples of morse bifurcations of transition states and dividing surfaces . morse bifurcations of transition states in bimolecular reactions + r s mackay and d c strub + mathematics institute and centre for complexity science , university of warwick , coventry cv4 7al , u.k . + bimolecular reactions , collision theories , transition state theory , dividing surfaces , morse bifurcations + published in * nonlinearity * , http://dx.doi.org/10.1088/0951-7715/28/12/4303[28(12):4303-4329 ] +

1112.6179

i

in his paper @xcite , tutte took advantage of two natural operations on ( finite multi)graphs ( actually on isomorphism classes of multigraphs ) , deletion and contraction of an edge , in order to introduce the ring @xmath0 $ ] and a polynomial in two commuting variables @xmath1 , also known by whitney @xcite , unique up to isomorphism since solutions of a universal problem . this polynomial , since called the tutte polynomial , is a graph invariant in at least two different meanings : first of all , it is defined on isomorphism classes , rather than on actual graphs , in such a way that two graphs with distinct tutte polynomials are not isomorphic ( a well - known functorial point of view ) , and , secondly , it is invariant with respect to a graph decomposition . indeed , let @xmath2 be a graph , and let @xmath3 be an edge of @xmath2 , which is not a loop ( an edge with the same vertex as source and target ) nor a bridge ( an edge that connects two connected components of a graph ) . the edge contraction @xmath4 of @xmath2 is the graph obtained by identifying the vertices source and target of @xmath3 , and removing the edge @xmath3 . we write @xmath5 for the graph where the edge @xmath3 is merely removed ; this operation is the edge deletion . let us consider the graph @xmath6 ( well - defined as isomorphic classes ) which can be interpreted as a decomposition of @xmath2 . then , the tutte polynomial @xmath7 is invariant with respect to this decomposition in the sense that @xmath8 . moreover this decomposition eventually terminates with graphs with bridges and loops only as edges , and the choice of edges to decompose is irrelevant . in his paper @xcite , brylawski observed that the previous construction ( and many others , for instance the tutte polynomial for matroids ) may be explained in terms of an elegant and unified categorical framework ( namely a universal problem of invariants ) . in brief , brylawski considered an abstract notion of decomposition . let @xmath9 be a set , and let @xmath10 be an order relation on ( a part of ) the free commutative semigroup @xmath11 ( actually brylawski considered multisets , nevertheless the choice is here made to deal with semigroups since they play a central rle in this contribution ) , which satisfies a certain number of axioms that are quickly reviewed in informal terms below for the sake of completeness ( appendix [ shortreviewbrylawski ] contains a short review of brylawski s theory in mathematical terms but it may be skipped ) and to show how natural is their translations in terms of rewriting systems . let @xmath12 be a set of formal ( finite ) sums @xmath13 where @xmath14 , @xmath15 not all of them being zero ( an element of the free commutative semigroup @xmath11 on @xmath9 ) partially ordered by @xmath10 . if @xmath16 such that @xmath17 , then we say that @xmath18 _ decomposes _ into @xmath19 or that @xmath19 is a _ decomposition _ of @xmath18 . therefore @xmath12 is seen as a set of commutative _ decompositions_. elements of @xmath9 that belong to @xmath12 are assumed to be minimal with respect to @xmath10 . elements of @xmath20 that are maximal ( and therefore incomparable since also minimal ) are said to be _ irreducible_. according to a second axiom satisfied by the order relation @xmath10 , an element @xmath21 can not be decomposed further into any other element of @xmath12 if , and only if , @xmath18 is a finite linear combination , with non negative integers as coefficients , of incomparable elements , that is , if @xmath22 is the set of all irreducibles , then @xmath18 is not decomposed into another element if , and only if , @xmath18 is a formal ( finite ) sum of elements of @xmath22 with non negative integers as coefficients . this property is similar to the notion of termination in rewriting systems . two other properties ( _ refinability _ and _ finiteness _ ) on @xmath12 ensure that every element of @xmath9 has one , and only one , `` terminal '' decomposition into irreducible elements . they are equivalent to convergence of a rewriting system . for instance , the order @xmath23 on the free commutative semigroup generated by all ( isomorphism classes of ) finite graphs satisfies these axioms and properties . now , to a decomposition @xmath24 with the above properties may be attached a group in a universal way . a function @xmath18 from @xmath9 to an abelian group @xmath2 is said to be _ invariant _ if for every @xmath25 such that @xmath26 ( @xmath14 , and @xmath15 ) , then @xmath27 . recall here that tutte polynomial @xmath7 is invariant because @xmath8 . brylawski proved the following theorem , which was his main result . there exist an abelian group , called _ tutte - grothendieck group _ , and an invariant mapping @xmath28 , called _ universal tutte - grothendieck invariant _ , such that for every abelian group @xmath2 and every invariant mapping @xmath29 , there exists a unique group homorphism @xmath30 with @xmath31 . in addition , @xmath32 is isomorphic to the free abelian group with the irreducible elements as generators . in the classical context of graph theory , as expected , @xmath32 is the additive structure of @xmath0 $ ] and @xmath7 is the tutte polynomial . many other decompositions enter in the scope of brylawski s theory ( see his paper @xcite , examples and references therein ) . in the present contribution , we adapt brylawski s results to the theory of ( string ) rewriting systems which we think is the natural framework to deal with theoretical notions of decomposition . moreover we extend previous works by allowing non commutative , and even partially commutative , decompositions . our main result , theorem [ mainstatement ] , similar to brylawski s main theorem , states the existence and uniqueness of a universal group and a universal invariant associated to some kind of string rewriting systems , even if there are not convergent ( which is beyond the scope of brylawski s work ) . in case of convergence , we prove that the universal group under consideration is the free partially commutative group generated by irreducible letters , which is a generalization of the original result , and that the universal invariant is nothing else than the normal form function that maps an element to its normal form . we mention the fact that in this case , the universal group is proved to be the grothendieck completion of a monoid ( obtained from the semigroup subject to rewriting by free adjunction of an identity ) , which was not seen by brylawski even if he called tutte - grothendieck his universal construction .

the two operations , deletion and contraction of an edge , on multigraphs directly lead to the tutte polynomial which satisfies a universal problem . as observed by brylawski in terms of order relations , these operations may be interpreted as a particular instance of a general theory which involves universal invariants like the tutte polynomial , and a universal group , called the tutte - grothendieck group . in this contribution , brylawski s theory is extended in two ways : first of all , the order relation is replaced by a string rewriting system , and secondly , commutativity by partial commutations ( that permits a kind of interpolation between non commutativity and full commutativity ) . this allows us to clarify the relations between the semigroup subject to rewriting and the tutte - grothendieck group : the later is actually the grothendieck group completion of the former , up to the free adjunction of a unit ( this was even not mention by brylawski ) , and normal forms may be seen as universal invariants . moreover we prove that such universal constructions are also possible in case of a non convergent rewriting system , outside the scope of brylawski s work .

the two operations , deletion and contraction of an edge , on multigraphs directly lead to the tutte polynomial which satisfies a universal problem . as observed by brylawski in terms of order relations , these operations may be interpreted as a particular instance of a general theory which involves universal invariants like the tutte polynomial , and a universal group , called the tutte - grothendieck group . in this contribution , brylawski s theory is extended in two ways : first of all , the order relation is replaced by a string rewriting system , and secondly , commutativity by partial commutations ( that permits a kind of interpolation between non commutativity and full commutativity ) . this allows us to clarify the relations between the semigroup subject to rewriting and the tutte - grothendieck group : the later is actually the grothendieck group completion of the former , up to the free adjunction of a unit ( this was even not mention by brylawski ) , and normal forms may be seen as universal invariants . moreover we prove that such universal constructions are also possible in case of a non convergent rewriting system , outside the scope of brylawski s work .

astro-ph0310592

i

the uninterrupted 7-day _ asca _ observation of the tev blazar mrk 421 in 1998 has revealed that day - scale x ray flares seen in previous observations were probably unresolved superpositions of many smaller flares @xcite . the nearly continuous observation allowed not only the possibility to track the individual flares entirely from the rise to decay , but it also enabled quantitative statistical tests of the time series by employing the power spectrum or the structure function @xcite . the main characteristic of blazars is their high flux observed from radio to @xmath7rays coupled with strong variability and strong polarization . these properties are now successfully explained by the scenario where blazars are active galactic nuclei ( agn ) , possessing jets aligned close to the line of sight , and accordingly the doppler - boosted non - thermal emission from the jet dominates other emission components ( e.g. blandford & knigl 1979 ; urry & padovani 1995 ) . this is what makes blazars critical in understanding jets in agn . the broadband spectra of blazars consist of two peaks , one in the radio to optical uv range ( and in some cases , reaching to the x ray band ) , and the other in the hard x ray to @xmath7ray region . the high polarization of the radio to optical emission suggests that the lower energy peak is produced via the synchrotron process by relativistic electrons in the jet . the higher energy peak is believed to be due to compton up - scattering of seed photons by the same population of relativistic electrons . several possibilities exist for the source of the seed photons ; these can be the synchrotron photons internal to the jet @xcite , but also external , such as from the broad emission line clouds @xcite or from the accretion disk @xcite . the blazars with peak synchrotron output in the x ray range also emit strongly in the @xmath7ray energies , and the brightest of those have been detected in the tev range with ground - based cherenkov arrays . these are the so - called `` tev blazars . '' in tev blazars , variability of the synchrotron flux is measured to be the strongest and most rapid in the x ray band , and thus it provides the best opportunity to study the electrons that are accelerated to the highest energies . in particular , the synchrotron peak is a very important observable in two aspects : first because the flux at the peak represents the total emitted power from the blazar , and secondly because the peak frequency reflects the maximum energy of radiating particles gained in the acceleration process . mrk 421 is among the closest known blazars , at redshift of 0.031 , and was the first blazar ( and also the first extragalactic source ) discovered to be a tev emitter . it was first detected as a weak source by egret @xcite , and 9 months later , _ whipple_detected a clear signal from this object between 0.5 and 1.5 tev @xcite . flux variability on various time scales has been observed , including a very short flare with a duration of @xmath81 hour @xcite . ever since , mrk 421 has been repeatedly confirmed to be a tev source by various ground - based telescopes . it has also been one of the most studied blazars , and have been a target of several multi - wavelength campaigns @xcite . the multi - wavelength campaign of mrk 421 in 1998 was one of the first opportunities to observe a blazar in the tev range using several telescopes located in different locations in the world , so as to have as continuous coverage as possible @xcite . observations in other frequencies included x ray observations by _ asca _ , _ rxte _ @xcite , and _ bepposa@xmath0x _ ( maraschi et al . 1999 ; fossati et al . 2000a , b ) , euv observations by _ euve _ , optical observation with bvri filters organized by the webt collaboration ( http://www.to.astro.it/blazars/webt/ ) , and radio observations at the metshovi radio observatory . in this paper , we present the results of the spectral analysis of x ray and euv data during the 1998 april campaign . in particular , we estimate the location of the synchrotron peak in the @xmath9 spectrum . so far , quantitative studies of the variation of the synchrotron peak have been conducted only for the two brightest blazars , mrk 421 and mrk 501 . the largest variation of the synchrotron peak energy was observed in mrk 501 by _ bepposa@xmath0x _ , where the peak energy shifted @xmath82 orders of magnitude @xcite . collecting data from different epochs ( separated by as long as years ) , @xcite have shown the relation of the form @xmath10 with @xmath112 . a similar analysis was done by @xcite for the mrk 421 data obtained by _ bepposa@xmath0x _ in 1997 and 1998 , which showed a relation of @xmath12 with n=0.55 . in this paper we describe a continuous 7-day variation of the synchrotron peak , which allows us to investigate the dynamical change of the synchrotron spectrum during the flares . we first describe the observations and data analysis in 2 . the results of spectral analysis are described in 3 ; a summary of the results and a discussion of our findings with the emphasis on the temporal evolution of the spectrum are presented in 4 .

the uninterrupted 7-day _ asca _ observations of the tev blazar mrk 421 in 1998 have clearly revealed that x ray flares occur repeatedly . in this paper , we present the results of the time - resolved spectral analysis of the combined data taken by _ asca _ , _ rxte _ , _ bepposax _ , and _ euve_. in this object and in many other tev blazars the precise measurement of the shape of the x ray spectrum , which reflects the high energy portion of the synchrotron component , is crucial in determining the high energy cutoff of the accelerated electrons in the jet . thanks to the simultaneous broadband coverage , we measured the 0.125 kev spectrum resolved on time scales as short as several hours , providing a great opportunity to investigate the detailed spectral evolution at the flares . by analyzing the time subdivided observations , we parameterize the evolution of the synchrotron peak , where the radiation power dominates , by fitting the combined spectra with a quadratic form ( where the flux at the energy obeys ) . in this case , we show that there is an overall trend that the peak energy and peak flux both increase or decrease together . the relation of the two parameters is best described as for the 1998 campaign .

the uninterrupted 7-day _ asca _ observations of the tev blazar mrk 421 in 1998 have clearly revealed that x ray flares occur repeatedly . in this paper , we present the results of the time - resolved spectral analysis of the combined data taken by _ asca _ , _ rxte _ , _ bepposax _ , and _ euve_. in this object and in many other tev blazars the precise measurement of the shape of the x ray spectrum , which reflects the high energy portion of the synchrotron component , is crucial in determining the high energy cutoff of the accelerated electrons in the jet . thanks to the simultaneous broadband coverage , we measured the 0.125 kev spectrum resolved on time scales as short as several hours , providing a great opportunity to investigate the detailed spectral evolution at the flares . by analyzing the time subdivided observations , we parameterize the evolution of the synchrotron peak , where the radiation power dominates , by fitting the combined spectra with a quadratic form ( where the flux at the energy obeys ) . in this case , we show that there is an overall trend that the peak energy and peak flux both increase or decrease together . the relation of the two parameters is best described as for the 1998 campaign . similar results were derived for the 1997 observation , while the relation gave a smaller index when included both 1997 and 1998 data . on the other hand , we show that this relation , and also the detailed spectral variations , differ from flare to flare within the 1998 campaign . we suggest that the observed features are consistent with the idea that flares are due to a appearance of a new spectral component . with the availability of the simultaneous tev data , we also show that there exists a clear correlation between the synchrotron peak flux and the tev flux .

astro-ph0310592

i

we have performed detailed analysis of the combined _ euve _ , _ asca _ , _ bepposa@xmath0x _ , and _ rxte _ data collected during the long look campaign of mrk 421 in 1998 , resulting in the measurement of the time - resolved spectrum in a broad energy range of 0.125 kev in segments as short as several ksec . these are among the highest quality spectra with regard to both photon statistics and energy coverage so far for any blazar , providing the precise spectral shape at the highest energy end of the synchrotron spectrum . we have shown that both curved power - law function and quadratic function in @xmath24@xmath25@xmath9 space reproduce the combined _ euve _ , _ bepposa@xmath0x _ , _ asca _ , and _ rxte _ spectrum . for the epochs where _ bepposa@xmath0x _ data do not exist , we assumed that the spectral gap between @xmath42 and @xmath43 can be extrapolated with a quadratic function , and we showed that the energy and the flux at the synchrotron peak in the @xmath9 spectrum are correlated , showing an overall trend of a higher synchrotron peak energy for higher peak flux , but the details of this relation differed from flare to flare . in particular , within the three flare beginnings , one flare started from a rise in the higher energy while another started from a rise in the lower energy . the relative amplitude of the rise in different energies also differed from flare to flare . an interesting result was shown from the 2nd flare , where it was indicated that this flare started with a hardening at the higher energy . this feature is difficult to describe by a simple cooling or acceleration of a single electron distribution ( see e.g. kataoka 2000 ) , and thus this concave curvature indicates that two different spectral components were likely to co - exist at the beginning of the flare . we remark that such a behavior is observed in only one flare , but the importance is that we observed a flare that could not be explained by a single electron distribution . this suggests an appearance of a new component , which generated the observed flare . recently , many theoretical studies has been performed to model the energy dependence , or time lags observed in the day - scale flares in blazars . one approach considers models with a homogeneous emission region @xcite . for instance , @xcite have suggested that a sudden increase in the maximum energy of the accelerated electrons could result in the x ray and tev flare observed in mrk 421 . similar results were shown by @xcite , in reproducing the soft - lag observed in pks 2155304 . however , most of these models assume a change in some parameter in the emission region ( such as the magnetic field , maximum energy of electrons , number density of electrons , etc . ) . the observational results for mrk 421 described above lead us to suggest a different scenario . an alternative scenario has each flare forming as a result of a separate electron distribution . this was suggested in modeling the high state sed of mrk 501 @xcite . they applied the one - zone homogeneous synchrotron self - compton model to the sed from april 1997 , and concluded that a single electron distribution is insufficient to reproduce the observed synchrotron spectrum . this scenario could work for instance when the jet is emitted intermittently from the central engine , and several separate regions generate different emission components . another viable scenario can be provided by an internal shock model , where the light curve results from a superposition of many flares due to the collisions of shells , which may occur when a faster shell catches up to a slower shell ( ghisellini 2001 , spada et al . 2001 ; sikora et al . 2001 ) in fact , @xcite has shown from simulations that the internal shock model can naturally explain various variability properties observed in tev blazars . one observational fact is that the x ray flares always appear to lie on top of an underlying offset - like component . in the internal shock model , flares can be considered as arising from collisions of shells that had the largest difference in the initial velocity . all other collisions generate smaller amplitude , longer flares , which pile up to generate the offset component . in this case , it was shown that the flares will tend to have a higher synchrotron peak energy as compared with that of the offset component . assuming that flares are due to an emergence of a new component with a higher synchrotron peak energy than the pre - existing component , the synchrotron peak energy in the observed spectrum would appear as shifting to a higher energy . it is interesting to note that our observations are consistent with this , with the overall trend of the synchrotron peak energy being higher during flares . furthermore in this case , the spectral evolution would depend on the relation of the new and pre - existing spectra . this would naturally explain the different spectral evolution among different flares . finally , we remark again that due to the data gap between the _ euve _ and _ asca _ data in our observation , the results concerning the spectrum peak are somewhat tentative . because of the rapid variability of the source in short time scales , the effective area of the instrument is most important . long - look observations by the new observatories such as @xmath44-@xmath45 should provide data allowing a more detailed analysis of the flaring mechanism , leading to the dynamics of the accelerated electrons in blazar jets . we thank the anonymous referee for numbers of constructive comments to improve the paper . support for this work was provided by the fellowship of japan society for promotion of science for young scientists , and by the department of energy contract to slac no . de - ac3 - 76sf00515 . we also acknowledge the nasa chandra grants via sao grant no . go1 - 2113x . aharonian , f. a. et al . 1999 , , 350 , 757 burke , b. e. , et al . 1991 , ieee trans . ed-38 , 1069 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ftp://www.sdc.asi.it/pub/sax/doc/software_docs/saxabc_v1.2.ps.gz_ urry , c. m. , & padovani , p. 1995 , , 107 , 803 yamashita , a. , et al . 1997 , ieee trans nucl . , 44 , 847 yaqoob , t. , & _ asca _ team , _ asca _ gof calibration memo [ asca - cal-00 - 06 - 01.v1.0(06/05/00 ) ] ll ccc ccc c lecs ( 0.12 - 4 ) & pl & 2.20@xmath160.01 & -&-&-&-&- & 2.85 ( 83 ) + mecs ( 1.65 - 10.5 ) & pl & 2.76@xmath160.02 & -&-&-&-&- & 1.28 ( 193 ) + gis ( 0.7 - 7 ) & pl & 2.52@xmath160.01 & -&-&-&-&- & 1.29 ( 124 ) + pca ( 3 - 25 ) & pl & 2.91@xmath160.01 & -&-&-&-&- & 2.63 ( 50 ) + lecs , mecs , gis , pca & broken pl & 2.21@xmath160.01 & 2.90@xmath160.01 & 2.24@xmath160.04 & -&-&- & 1.86 ( 451 ) + lecs , mecs , gis , pca & curved pl & 1.77@xmath160.04 & 1.66@xmath160.03 & 2.5@xmath160.3 & -&-&- & 1.08 ( 451 ) + lecs , mecs , gis , pca & cutoff pl & 2.17@xmath160.01 & - & 7.80@xmath160.14 & -&-&- & 1.74 ( 452 ) + lecs , mecs , gis , pca & quadratic & -&-&- & 0.47@xmath160.02 & 217@xmath163 & 0.42@xmath160.01 & 1.07 ( 452 ) + c| cccl 1 & 0.53@xmath160.02 & 230@xmath162 & 0.39@xmath160.02 & 1.06 ( 66 ) + 2 & 0.51@xmath160.02 & 244@xmath163 & 0.39@xmath160.02 & 0.95 ( 85 ) + 3 & 0.57@xmath160.02 & 266@xmath162 & 0.39@xmath160.01 & 0.95 ( 122 ) + 4 & 0.69@xmath160.02 & 280@xmath162 & 0.48@xmath160.01 & 1.22 ( 106 ) + 5 & 0.62@xmath160.01 & 331@xmath162 & 0.42@xmath160.01 & 1.08 ( 116 ) + 6 & 0.72@xmath160.02 & 372@xmath162 & 0.40@xmath160.01 & 0.97 ( 137 ) + 7 & 0.63@xmath160.04 & 377@xmath165 & 0.41@xmath160.02 & 0.89 ( 145 ) + 8 & 0.60@xmath160.03 & 323@xmath164 & 0.46@xmath160.02 & 1.20 ( 87 ) + 9 & 0.49@xmath160.02 & 277@xmath163 & 0.38@xmath160.02 & 0.80 ( 82 ) + 10 & 0.55@xmath160.02 & 270@xmath162 & 0.36@xmath160.01 & 0.92 ( 79 ) + 11 & 0.58@xmath160.02 & 278@xmath162 & 0.36@xmath160.01 & 1.10 ( 137 ) + 12 & 0.59@xmath160.02 & 307@xmath162 & 0.36@xmath160.01 & 1.04 ( 126 ) + 13 & 0.59@xmath160.02 & 337@xmath162 & 0.38@xmath160.01 & 0.97 ( 125 ) + 14 & 0.66@xmath160.02 & 358@xmath162 & 0.39@xmath160.01 & 1.01 ( 154 ) + 15 & 0.69@xmath160.02 & 324@xmath163 & 0.43@xmath160.02 & 0.73 ( 97 ) + 16 & 0.65@xmath160.02 & 303@xmath162 & 0.37@xmath160.01 & 0.89 ( 87 ) + 18 & 0.71@xmath160.02 & 333@xmath162 & 0.35@xmath160.01 & 0.93 ( 98 ) + 19 & 0.76@xmath160.02 & 364@xmath162 & 0.37@xmath160.01 & 0.92 ( 173 ) + 20 & 0.68@xmath160.02 & 346@xmath162 & 0.38@xmath160.01 & 1.16 ( 144 ) + 21 & 0.77@xmath160.02 & 337@xmath162 & 0.42@xmath160.01 & 1.04 ( 132 ) + 22 & 0.86@xmath160.02 & 391@xmath162 & 0.40@xmath160.01 & 1.14 ( 169 ) + 23 & 0.89@xmath160.02 & 458@xmath162 & 0.43@xmath160.01 & 0.97 ( 184 ) + 24 & 0.73@xmath160.03 & 423@xmath163 & 0.34@xmath160.02 & 1.21 ( 119 ) + 25 & 0.87@xmath160.03 & 379@xmath163 & 0.41@xmath160.02 & 0.85 ( 113 ) + 26 & 0.85@xmath160.02 & 366@xmath162 & 0.36@xmath160.01 & 0.88 ( 95 ) + 27 & 0.71@xmath160.02 & 336@xmath162 & 0.36@xmath160.01 & 1.14 ( 153 ) + 28 & 0.68@xmath160.02 & 397@xmath163 & 0.38@xmath160.01 & 1.09 ( 146 ) + 29 & 0.74@xmath160.02 & 404@xmath163 & 0.39@xmath160.01 & 0.85 ( 125 ) + 30 & 0.70@xmath160.01 & 423@xmath162 & 0.41@xmath160.01 & 1.08 ( 176 ) + 31 & 0.69@xmath160.01 & 442@xmath162 & 0.40@xmath160.01 & 0.88 ( 181 ) + 32 & 0.74@xmath160.02 & 439@xmath163 & 0.41@xmath160.01 & 0.81 ( 124 ) + 33 & 0.66@xmath160.02 & 459@xmath163 & 0.38@xmath160.01 & 1.07 ( 136 ) + 34 & 0.83@xmath160.02 & 390@xmath163 & 0.43@xmath160.01 & 0.97 ( 93 ) + 35 & 0.72@xmath160.02 & 350@xmath162 & 0.34@xmath160.01 & 1.02 ( 135 ) + 36 & 0.73@xmath160.03 & 365@xmath162 & 0.30@xmath160.01 & 0.78 ( 136 ) + 37 & 0.85@xmath160.02 & 388@xmath162 & 0.34@xmath160.01 & 0.96 ( 165 ) + 38 & 0.95@xmath160.02 & 413@xmath162 & 0.33@xmath160.01 & 0.97 ( 187 ) + 39 & 1.11@xmath160.02 & 515@xmath162 & 0.33@xmath160.01 & 1.07 ( 182 ) + 40 & 1.09@xmath160.03 & 469@xmath162 & 0.36@xmath160.01 & 0.96 ( 146 ) + 41 & 1.02@xmath160.04 & 423@xmath162 & 0.32@xmath160.02 & 1.11 ( 153 ) + 42 & 0.88@xmath160.02 & 348@xmath162 & 0.37@xmath160.01 & 0.70 ( 92 ) + 43 & 0.76@xmath160.03 & 352@xmath162 & 0.32@xmath160.01 & 0.98 ( 131 ) + 44 & 0.76@xmath160.03 & 369@xmath163 & 0.30@xmath160.02 & 1.23 ( 84 ) + 45 & 0.94@xmath160.03 & 343@xmath162 & 0.27@xmath160.01 & 0.98 ( 97 ) + 46 & 0.80@xmath160.02 & 293@xmath161 & 0.29@xmath160.01 & 0.96 ( 126 ) + 47 & 0.92@xmath160.02 & 308@xmath162 & 0.33@xmath160.01 & 1.09 ( 138 ) + 48 & 0.88@xmath160.03 & 311@xmath162 & 0.37@xmath160.01 & 1.04 ( 130 ) + 49 & 0.85@xmath160.03 & 378@xmath163 & 0.30@xmath160.02 & 1.13 ( 80 ) + 50 & 1.13@xmath160.03 & 476@xmath162 & 0.32@xmath160.01 & 1.04 ( 132 ) + 51 & 1.12@xmath160.02 & 443@xmath162 & 0.35@xmath160.01 & 0.79 ( 144 ) + 52 & 0.95@xmath160.03 & 416@xmath163 & 0.36@xmath160.02 & 0.86 ( 112 ) + 53 & 0.95@xmath160.02 & 429@xmath162 & 0.36@xmath160.01 & 1.04 ( 171 ) + 54 & 0.85@xmath160.02 & 365@xmath162 & 0.38@xmath160.01 & 1.13 ( 180 ) + 55 & 0.82@xmath160.02 & 341@xmath162 & 0.34@xmath160.01 & 1.02 ( 152 ) + 56 & 0.98@xmath160.02 & 372@xmath162 & 0.35@xmath160.01 & 1.10 ( 157 ) + 57 & 0.99@xmath160.03 & 396@xmath162 & 0.32@xmath160.01 & 1.00 ( 166 ) + ll |cccc | ccc 1997.4.29 & 1 & 0.54@xmath160.03 & 137@xmath163 & 0.48@xmath160.02 & 0.99 ( 126 ) & 0.56@xmath160.02 & 146@xmath166 & 0.96 ( 125 ) + & 2 & 0.46@xmath160.02 & 124@xmath162 & 0.48@xmath160.02 & 1.21 ( 126 ) & 0.49@xmath160.02 & 125@xmath164 & 1.23 ( 125 ) + & 3 & 0.50@xmath160.01 & 131@xmath162 & 0.46@xmath160.01 & 1.16 ( 126 ) & 0.53@xmath160.01 & 134@xmath163 & 1.15 ( 125 ) + 1997.4.30 & 1 & 0.53@xmath160.03 & 132@xmath164 & 0.48@xmath160.02 & 1.24 ( 126 ) & 0.55@xmath160.04 & 127@xmath165 & 1.25 ( 125 ) + & 2 & 0.47@xmath160.02 & 127@xmath163 & 0.47@xmath160.02 & 0.88 ( 126 ) & 0.50@xmath160.02 & 132@xmath165 & 0.85 ( 125 ) + & 3 & 0.55@xmath160.03 & 124@xmath163 & 0.51@xmath160.02 & 0.85 ( 126 ) & 0.58@xmath160.03 & 123@xmath164 & 0.84 ( 125 ) + & 4 & 0.52@xmath160.01 & 129@xmath162 & 0.47@xmath160.01 & 0.81 ( 126 ) & 0.55@xmath160.01 & 130@xmath162 & 0.79 ( 125 ) + 1997.5.1 & 1 & 0.45@xmath160.03 & 129@xmath164 & 0.45@xmath160.02 & 1.11 ( 126 ) & 0.48@xmath160.03 & 131@xmath166 & 1.11 ( 125 ) + & 2 & 0.57@xmath160.03 & 144@xmath163 & 0.44@xmath160.02 & 1.03 ( 126 ) & 0.59@xmath160.03 & 146@xmath164 & 1.03 ( 125 ) + & 3 & 0.58@xmath160.02 & 178@xmath164 & 0.49@xmath160.02 & 0.84 ( 126 ) & 0.61@xmath160.03 & 170@xmath165 & 0.85 ( 125 ) + & 4 & 0.52@xmath160.01 & 143@xmath162 & 0.44@xmath160.01 & 1.03 ( 126 ) & 0.55@xmath160.02 & 145@xmath162 & 1.01 ( 125 ) + 1997.5.2 & 1 & 0.57@xmath160.02 & 171@xmath163 & 0.46@xmath160.01 & 0.86 ( 126 ) & 0.60@xmath160.02 & 174@xmath164 & 0.85 ( 125 ) + 1997.5.3 & 1 & 0.42@xmath160.03 & 120@xmath164 & 0.48@xmath160.02 & 0.97 ( 126 ) & 0.39@xmath160.06 & 116@xmath164 & 0.96 ( 125 ) + & 2 & 0.42@xmath160.02 & 123@xmath163 & 0.44@xmath160.02 & 1.13 ( 126 ) & 0.41@xmath160.05 & 120@xmath164 & 1.14 ( 125 ) + 1997.5.4 & 1 & 0.31@xmath160.02 & 105@xmath164 & 0.50@xmath160.03 & 1.23 ( 126 ) & 0.22@xmath160.09 & 104@xmath165 & 1.25 ( 125 ) + & 2 & 0.32@xmath160.02 & 103@xmath163 & 0.50@xmath160.02 & 1.23 ( 126 ) & 0.32@xmath160.05 & 103@xmath164 & 1.24 ( 125 ) + 1997.5.5 & 1 & 0.38@xmath160.02 & 127@xmath164 & 0.47@xmath160.02 & 1.24 ( 126 ) & 0.42@xmath160.03 & 131@xmath165 & 1.24 ( 125 ) + & 2 & 0.37@xmath160.02 & 127@xmath163 & 0.46@xmath160.02 & 1.24 ( 126 ) & 0.40@xmath160.03 & 129@xmath164 & 1.25 ( 125 ) + 1998.4.21- & 1 & 0.69@xmath160.04 & 341@xmath168 & 0.42@xmath160.02 & 1.04 ( 126 ) & 0.69@xmath160.04 & 357@xmath1613 & 1.01 ( 125 ) + & 2 & 0.85@xmath160.02 & 404@xmath166 & 0.42@xmath160.01 & 1.12 ( 126 ) & 0.93@xmath160.03 & 397@xmath167 & 1.06 ( 125 ) + & 3 & 0.87@xmath160.02 & 378@xmath165 & 0.37@xmath160.01 & 1.03 ( 126 ) & 0.91@xmath160.03 & 379@xmath166 & 1.04 ( 125 ) + & 4 & 0.83@xmath160.03 & 337@xmath165 & 0.37@xmath160.01 & 0.93 ( 126 ) & 0.87@xmath160.04 & 337@xmath167 & 0.94 ( 125 ) + & 5 & 0.74@xmath160.03 & 300@xmath165 & 0.34@xmath160.01 & 0.90 ( 126 ) & 0.72@xmath160.04 & 310@xmath167 & 0.86 ( 125 ) + & 6 & 0.78@xmath160.03 & 274@xmath164 & 0.37@xmath160.01 & 1.31 ( 126 ) & 0.82@xmath160.03 & 274@xmath165 & 1.33 ( 125 ) + & 7 & 0.64@xmath160.03 & 239@xmath164 & 0.33@xmath160.02 & 1.04 ( 126 ) & 0.68@xmath160.03 & 235@xmath165 & 1.02 ( 125 ) + & 8 & 0.67@xmath160.03 & 236@xmath165 & 0.38@xmath160.02 & 0.95 ( 126 ) & 0.70@xmath160.04 & 235@xmath166 & 0.96 ( 125 ) + 1998.4.23- & 1 & 0.65@xmath160.03 & 309@xmath168 & 0.44@xmath160.02 & 1.11 ( 126 ) & 0.70@xmath160.05 & 287@xmath168 & 1.06 ( 125 ) + & 2 & 0.58@xmath160.03 & 257@xmath166 & 0.38@xmath160.02 & 1.07 ( 126 ) & 0.62@xmath160.03 & 257@xmath168 & 1.08 ( 125 ) + & 3 & 0.56@xmath160.02 & 247@xmath165 & 0.40@xmath160.02 & 0.90 ( 126 ) & 0.58@xmath160.02 & 254@xmath167 & 0.88 ( 125 ) + & 4 & 0.58@xmath160.03 & 248@xmath166 & 0.43@xmath160.02 & 1.04 ( 126 ) & 0.61@xmath160.03 & 239@xmath167 & 1.01 ( 125 ) + & 5 & 0.57@xmath160.02 & 253@xmath165 & 0.44@xmath160.02 & 0.86 ( 126 ) & 0.60@xmath160.02 & 251@xmath167 & 0.87 ( 125 ) + & 6 & 0.52@xmath160.02 & 233@xmath165 & 0.44@xmath160.02 & 1.17 ( 126 ) & 0.53@xmath160.03 & 227@xmath166 & 1.18 ( 125 ) + & 7 & 0.49@xmath160.02 & 220@xmath165 & 0.43@xmath160.02 & 1.34 ( 126 ) & 0.51@xmath160.03 & 218@xmath166 & 1.36 ( 125 ) + & 8 & 0.46@xmath160.03 & 219@xmath167 & 0.38@xmath160.02 & 1.07 ( 126 ) & 0.44@xmath160.06 & 213@xmath168 & 1.08 ( 125 ) + & 9 & 0.45@xmath160.03 & 217@xmath167 & 0.42@xmath160.02 & 1.04 ( 126 ) & 0.34@xmath160.09 & 203@xmath167 & 1.01 ( 125 ) + & 10 & 0.44@xmath160.03 & 203@xmath165 & 0.40@xmath160.02 & 1.14 ( 126 ) & 0.39@xmath160.06 & 194@xmath166 & 1.14 ( 125 ) + lc | cc| c c cc 50926.8814 & 11.0 & hegra & 0.46@xmath160.10 & 0.48@xmath160.03 & 226@xmath166 & 0.45@xmath160.04 & 0.75(33 ) + 50927.1390 & 13.7&_whipple_&0.33@xmath160.09 & 0.47@xmath160.01 & 218@xmath162 & 0.42@xmath160.01 & 0.95(216 ) + 50927.8839 & 10.5 & hegra & 0.79@xmath160.12 & 0.74@xmath160.02 & 381@xmath163 & 0.43@xmath160.01 & 1.18(210 ) + 50928.2273 & 5.3 & _ whipple_&0.33@xmath160.07 & 0.56@xmath160.02 & 269@xmath163 & 0.42@xmath160.01 & 0.95(142 ) + 50928.8824 & 10.5 & hegra & 0.58@xmath160.10 & 0.66@xmath160.02 & 316@xmath162 & 0.41@xmath160.01 & 0.90(221 ) + 50929.8848 & 10.1 & hegra & 1.10@xmath160.13 & 0.77@xmath160.02 & 424@xmath162 & 0.36@xmath160.01 & 1.13(205 ) + 50930.1516 & 12.2&_whipple_&0.54@xmath160.05 & 0.81@xmath160.02 & 364@xmath162 & 0.40@xmath160.01 & 0.99(274 ) + 50930.8845 & 9.8 & hegra & 1.41@xmath160.15 & 0.66@xmath160.03 & 472@xmath164 & 0.39@xmath160.01 & 1.15(244 ) + 50931.1467 & 10.3&_whipple_&0.58@xmath160.14 & 0.72@xmath160.02 & 367@xmath163 & 0.38@xmath160.01 & 0.94(229 ) + 50932.2041 & 6.9 & _ whipple_&0.67@xmath160.07 & 0.84@xmath160.02 & 367@xmath162 & 0.34@xmath160.01 & 1.31(239 ) + 50933.2358 & 3.4 & _ whipple_&0.67@xmath160.11 & 0.90@xmath160.02 & 454@xmath162 & 0.38@xmath160.01 & 1.21(238 ) +

similar results were derived for the 1997 observation , while the relation gave a smaller index when included both 1997 and 1998 data . on the other hand , we show that this relation , and also the detailed spectral variations , differ from flare to flare within the 1998 campaign . we suggest that the observed features are consistent with the idea that flares are due to a appearance of a new spectral component . with the availability of the simultaneous tev data ,

the uninterrupted 7-day _ asca _ observations of the tev blazar mrk 421 in 1998 have clearly revealed that x ray flares occur repeatedly . in this paper , we present the results of the time - resolved spectral analysis of the combined data taken by _ asca _ , _ rxte _ , _ bepposax _ , and _ euve_. in this object and in many other tev blazars the precise measurement of the shape of the x ray spectrum , which reflects the high energy portion of the synchrotron component , is crucial in determining the high energy cutoff of the accelerated electrons in the jet . thanks to the simultaneous broadband coverage , we measured the 0.125 kev spectrum resolved on time scales as short as several hours , providing a great opportunity to investigate the detailed spectral evolution at the flares . by analyzing the time subdivided observations , we parameterize the evolution of the synchrotron peak , where the radiation power dominates , by fitting the combined spectra with a quadratic form ( where the flux at the energy obeys ) . in this case , we show that there is an overall trend that the peak energy and peak flux both increase or decrease together . the relation of the two parameters is best described as for the 1998 campaign . similar results were derived for the 1997 observation , while the relation gave a smaller index when included both 1997 and 1998 data . on the other hand , we show that this relation , and also the detailed spectral variations , differ from flare to flare within the 1998 campaign . we suggest that the observed features are consistent with the idea that flares are due to a appearance of a new spectral component . with the availability of the simultaneous tev data , we also show that there exists a clear correlation between the synchrotron peak flux and the tev flux .

1312.3734

i

modern density - functional theory ( dft ) was introduced by hohenberg and kohn in a classic paper @xcite and is now the workhorse of quantum chemistry and other fields of quantum physics . subsequently , dft was put on a mathematically firm ground by lieb using convex analysis.@xcite the central quantity of dft is the universal density functional @xmath11 , which represents the electronic energy of the system consistent with a given density @xmath12 . clearly , the success of dft hinges on the modelling of @xmath0 , an extremely complicated function of the electron density . it is an interesting observation that , over the last two or three decades , @xmath0 has been modelled sufficiently accurately to make dft the most widely applied method of quantum chemistry , in spite of the fact that schuch and verstraete @xcite have shown how considerations from the field of computational complexity place fundamental limits on exact dft : if @xmath11 could be found efficiently , all np hard problems would be solvable in polynomial time , which is highly unlikely.@xcite from a mathematical point of view , dft is neatly formulated using convex analysis@xcite : the universal density functional @xmath11 and the ground - state energy @xmath7 are related by a conjugation operation , with the density @xmath12 and external potential @xmath13 being elements of a certain banach space @xmath14 and its dual @xmath15 , respectively . the functionals @xmath0 and @xmath2 are equivalent in the sense that they contain the same information each can be generated exactly from the other . the universal density functional @xmath0 is convex and lower semi - continuous but otherwise highly irregular and ill behaved . importantly , @xmath0 is everywhere discontinuous and not differentiable in any sense that justifies taking the functional derivative in formal expressions even for the @xmath13-representable densities , as pointed out by lammert.@xcite for example , it is common practice to formally differentiate @xmath0 with respect to the density , interpreting the functional derivative `` @xmath16 '' as a scalar potential at @xmath17 . however , this derivative , a gteaux derivative , does not exist . together with the problem of @xmath13-representability , conventional dft is riddled with mathematically unfounded assumptions that are , in fact , probably false . for example , conventional kohn sham theory assumes , in addition to differentiability of @xmath0 , that , if @xmath12 is @xmath13-representable for an interacting @xmath18-electron system , then @xmath12 is also @xmath13-representable for the corresponding noninteracting system.@xcite while providing excellent predictive results with modelled approximate density functionals , it is , from a mathematical perspective , unclear why kohn sham dft works at all . it is the goal of this article to remedy this situation by introducing a family of regularized dfts based on a tool from convex analysis known as the _ moreau envelope _ or _ yosida regularization_. for @xmath3 , the idea is to introduce a regularized energy functional @xmath19 related to the usual ground - state energy @xmath2 by @xmath20 where @xmath21 is the usual @xmath22-norm . the convex conjugate of @xmath23 is the moreau envelope @xmath24 of @xmath0 , from which the regularized ground - state energy can be obtained by a hohenberg - kohn minimization over densities : @xmath25 where @xmath26 . the usual hohenberg kohn variation principle is recovered as @xmath5 . importantly , the moreau envelope @xmath27 is _ everywhere differentiable _ and converges pointwise from below to @xmath11 as @xmath5 . we use the term `` regularized '' for both @xmath23 and @xmath28 , although it is @xmath28 that , as will be shown below , becomes differentiable through the procedure . a remark regarding the banach spaces of densities and potentials is here in order . if @xmath13 is a coulomb potential , then the regularization term in eq . becomes infinite . moreover , the strongest results concerning the moreau yosida regularization are obtained in a reflexive setting . the usual banach spaces @xmath29 and @xmath30 for densities and potentials , respectively,@xcite are therefore abandoned , and both replaced with the hilbert space @xmath31 , where @xmath32 ^ 3 $ ] is an arbitrarily large but finite box in @xmath33 . as is well known , domain truncation represents a well - behaved approximation : as @xmath34 increases , all eigenvalues converge to the @xmath33-limit . moreover , the continuous spectrum is approximated by an increasing number of eigenvalues whose spacing converges to zero . we observe that , in the box , the difference @xmath35 is arbitrarily small and _ explicitly known_it does not relate to the electronic structure of the system and is easily calculated from @xmath13 . nothing is therefore lost in the transition from @xmath1 to @xmath36 . on the contrary , we obtain a structurally simpler theory that allows taking the derivative of expressions involving the universal functional . moreover , the differentiability of @xmath37 implies @xmath13-representability of any @xmath12 , for noninteracting as well as interacting systems , as needed for a rigorous formulation of kohn sham theory . in this paper , we explore the moreau envelope as applied to dft , demonstrating how every concept of standard dft has a counterpart in the moreau - regularized formulation of dft and vice versa . the remainder of the article is organized as follows : in sec.[sec : prelim ] , we review formal dft and discuss the regularity issues of the universal functional within the nonreflexive banach - space setting of lieb.@xcite in preparation for the moreau yosida regularization , we next reformulate dft in a truncated domain , introducing the hilbert space @xmath31 as density and potential space . the moreau yosida regularization is a standard technique of convex analysis , applicable to any convex function such as the universal density functional . we introduce this regularization in sec.[sec : my ] , reviewing its basic mathematical properties . to establish notation , a review of convex analysis is given in the appendix ; for a good textbook of convex analysis in a hilbert space , with an in - depth discussion of the moreau yosida regularization , see ref . . following the introduction of the moreau yosida regularization , we apply it to dft in sec.[sec : mydft ] and subsequently to kohn sham theory in sec.[sec : ks ] . finally , sec.[sec : conclusion ] contains some concluding remarks .

the universal density functional of density - functional theory is a complicated and ill - behaved function of the density in particular , is not differentiable , making many formal manipulations more complicated . the moreau in particular , taking advantage of the differentiability of , a rigorous formulation of kohn sham theory is presented that does not suffer from the noninteracting representability problem in standard kohn sham theory .

the universal density functional of density - functional theory is a complicated and ill - behaved function of the density in particular , is not differentiable , making many formal manipulations more complicated . whilst has been well characterized in terms of convex analysis as forming a conjugate pair with the ground - state energy via the hohenberg kohn and lieb variation principles , is nondifferentiable and subdifferentiable only on a small ( but dense ) set of its domain . in this article , we apply a tool from convex analysis , moreau yosida regularization , to construct , for any , pairs of conjugate functionals that converge to pointwise everywhere as , and such that is ( frchet ) differentiable . for technical reasons , we limit our attention to molecular electronic systems in a finite but large box . it is noteworthy that no information is lost in the moreau yosida regularization : the physical ground - state energy is exactly recoverable from the regularized ground - state energy in a simple way . all concepts and results pertaining to the original pair have direct counterparts in results for . the moreau yosida regularization therefore allows for an exact , differentiable formulation of density - functional theory . in particular , taking advantage of the differentiability of , a rigorous formulation of kohn sham theory is presented that does not suffer from the noninteracting representability problem in standard kohn sham theory .

0905.4408

i

nonlinear hyperbolic conservation laws on networks have recently attracted a lot of interest in various fields : car traffic @xcite , gas dynamics @xcite , irrigation channels @xcite and supply chains @xcite . a network is modeled by a graph : a finite collection of arcs connected together by vertices . on each arc we consider a scalar conservation law . for instance one may think to the lighthill - whitham - richards model for car traffic @xcite . however , our results applies to the other application domains . it is easy to check that the dynamic at nodes is not uniquely determined by imposing the conservation of mass through vertices . then , to completely describe the network load evolution , the first step is to appropriately define the concept of solution at a vertex . + as in the classical theory of conservation laws , this problem is equivalent to giving the solution riemann problems ( now at vertices ) . more precisely , a riemann problem at a vertex is simply a cauchy problem with constant initial conditions in each arc of the vertex . the map , which associates the solution to each riemann problem at a vertex @xmath0 , is called a riemann solver at @xmath0 . similarly to the case of a real line , one has to resort to the concept of weak solutions in the sense of distributions and there are infinitely many riemann solvers producing weak solutions . first one uses entropy type conditions inside arcs as for the real line . then , in order to select a particular solution ( i.e. a riemann solver ) at the vertex , one has to impose some additional conditions . in @xcite , for example , the authors required some rules about the distribution of the fluxes in the arcs and a maximization condition ; see also @xcite . it is then natural to ask if entropy - like conditions can be imposed also at the vertex and not only inside arcs . in this paper , we focus on a single vertex @xmath0 , composed by @xmath1 incoming and @xmath2 outgoing arcs and we extend the krukov @xcite entropy - type conditions . more precisely , we propose two different entropy conditions for admissibility of solutions , called , respectively , ( e1 ) and ( e2 ) . the condition ( e1 ) is stronger than ( e2 ) , indeed the first asks for krukov entropy condition to be verified for all entropies , while the second asks only for the precise krukov entropy corresponding to sonic point . it is interesting to note that the entropy condition ( e1 ) imposes strong restrictions both on riemann solvers and on the geometry of the vertex . indeed , riemann solvers satisfying ( e1 ) can exist only in the case of vertices with the same number of incoming and outgoing arcs . we then test our conditions on riemann solvers considered in the literature . first we can prove that the riemann solver , introduced in @xcite for data networks , satisfies ( e2 ) and , in special situations , also ( e1 ) . + then we show that the riemann solvers defined in @xcite do not satisfy ( e2 ) . however , at least for the riemann solver in @xcite , the entropy condition and the maximization procedure agree on some particular set , over which the maximization is taken . roughly speaking the solver respects the entropy condition once traffic distribution is imposed . the paper is organized as follows . section [ se : def ] introduces the basic definitions of networks and of solutions . section [ se : riemann_problem ] deals with the solution to the riemann problem at the vertex @xmath0 . moreover , we introduce the entropy conditions ( e1 ) and ( e2 ) for riemann solvers at @xmath0 . in section [ se : rs_e1 ] , we determine which riemann solvers satisfy the entropy condition ( e1 ) . the paper ends with section [ se : examples ] , which considers the riemann solvers @xmath4 , @xmath5 and @xmath6 , introduced respectively in @xcite , and analyzes what entropy conditions these riemann solvers satisfy .

this paper deals with conservation laws on networks , represented by graphs . entropy - type conditions are considered to determine dynamics at nodes . since entropy dispersion is a local concept , we consider a network composed by a single node with incoming and outgoing arcs . we extend at the classical krukov entropy obtaining two conditions , denoted by ( e1 ) and ( e2 ) : the first requiring entropy condition for all krukov entropies , the second only for the value corresponding to sonic point . finally we focus three different riemann solvers , introduced in previous papers . in particular , we show that the riemann solver introduced for data networks is the only one always satisfying ( e2 ) . _ key words : _ scalar conservation laws , traffic flow , riemann solver , networks , entropy conditions . _ ams subject classifications : _ 90b20 , 35l65 .

this paper deals with conservation laws on networks , represented by graphs . entropy - type conditions are considered to determine dynamics at nodes . since entropy dispersion is a local concept , we consider a network composed by a single node with incoming and outgoing arcs . we extend at the classical krukov entropy obtaining two conditions , denoted by ( e1 ) and ( e2 ) : the first requiring entropy condition for all krukov entropies , the second only for the value corresponding to sonic point . first we show that in case , no riemann solver can satisfy the strongest condition . then we characterize all the riemann solvers at satisfying the strongest condition ( e1 ) , in the case of nodes with at most two incoming and two outgoing arcs . finally we focus three different riemann solvers , introduced in previous papers . in particular , we show that the riemann solver introduced for data networks is the only one always satisfying ( e2 ) . _ key words : _ scalar conservation laws , traffic flow , riemann solver , networks , entropy conditions . _ ams subject classifications : _ 90b20 , 35l65 .

1506.07653

i

the dynamics of a wide class of open quantum systems , interacting with the environment , can be described in the framework of the hudson - parthasarathy quantum stochastic calculus @xcite . this approach employs quantum stochastic differential equations ( qsdes ) which are driven by a quantum mechanical analogue of the classical wiener process @xcite . the quantum wiener process models a heat reservoir of external fields and acts on a boson fock space @xcite . the drift vector and the dispersion matrix of the qsdes depend on the system hamiltonian and the system - field coupling operators . these energy operators specify the evolution of the system as a result of its internal dynamics influenced by the interaction with the environment . the hamiltonian and the coupling operators are usually modelled as functions of the system variables . in particular , such functions can be polynomials or weyl quantization integrals @xcite , which affects the complexity of the resulting quantum system . an important role in the linear quantum control and filtering theory @xcite is played by open quantum harmonic oscillators ( oqhos ) @xcite with quadratic hamiltonians and linear system - field coupling operators . the linear - quadratic dependence of the energy operators on the system variables , in combination with the canonical commutation relations ( ccrs ) between the variables , makes the oqho dynamics linear ( and gaussian in the case of vacuum fields and gaussian initial states @xcite ) . despite some similarities to the classical linear sdes , the coherent ( that is , measurement - free ) quantum counterparts @xcite to the classical lqg control and filtering problems @xcite for oqhos are complicated by the physical realizability ( pr ) constraints . the latter are associated with the state - space matrices of the qsdes for fully quantum controllers or filters and are related , in particular , to the ccr preservation . we mention one of the existing variational approaches @xcite to the coherent quantum lqg ( cqlqg ) control and coherent quantum filtering ( cqf ) problems which develops optimality conditions using the frechet differentiation of the lqg cost with respect to the state - space matrices . the quantum nature of the underlying problem enters this approach only through the pr constraints , with all the other aspects of the method being essentially `` classical '' . the latter has certain advantages , such as practical applicability to the numerical optimization algorithms @xcite . however , this approach is limited to linear controllers and filters , and the resulting optimality conditions do not provide insights into whether nonlinear quantum controllers or filters can outperform the linear ones for linear quantum plants . in the present paper , we consider a cqf problem , similar to @xcite , where a quantum observer is cascaded in a measurement - free fashion with a linear quantum plant so as to minimize a mean square error with which the observer variables approximate linear combinations of plant variables of interest . both systems are governed by markovian hudson - parthasarathy qsdes driven by bosonic fields in vacuum state . we employ a recently proposed fully quantum variational method of @xcite based on using a transverse hamiltonian , an auxiliary time - varying operator which encodes the propagation of perturbations through the unitary system - field evolution . we apply the transverse hamiltonian approach to the development of first - order necessary conditions of optimality for the cqf problem in a larger class of observers . the latter is obtained by perturbing the hamiltonian and system - field coupling operators of a linear coherent quantum observer along linear combinations of the unitary weyl operators @xcite . similar trigonometric polynomials of quantum variables have recently been used in @xcite for modelling the uncertainty in system hamiltonians . in the present paper , the weyl variations play a different role which resembles that of the needle variations in the proof of the pontryagin minimum principle @xcite . we show that if the observer is a stationary point of the cost functional in the class of linear observers , then it is also a stationary point with respect to the weyl variations ( with the latter leading to nonlinear observers ) . therefore , in the mean square optimal cqf problem for linear quantum plants , linear coherent quantum observers are locally sufficient at least in the sense of the weyl variations of the energy operators . the paper is organised as follows . section [ sec : not ] outlines notation used in the paper . section [ sec : oqho ] specifies the class of open quantum stochastic plants being considered . section [ sec : cqf ] formulates the mean square optimal cqf problem . section [ sec : var ] employs the transverse hamiltonian approach in order to study the sensitivity of the performance criterion to perturbations in the energy operators of observers . section [ sec : linopt ] applies these results to liner - quadratic perturbations of the observer energy operators and obtains the first - order necessary conditions of optimality in the class of linear observers . section [ sec : weyl ] introduces the weyl variations of the energy operators and establishes the main result of the paper that the stationarity of the quadratic cost functional with respect to linear - quadratic perturbations of a linear observer implies the stationarity with respect to the weyl variations . section [ sec : conc ] provides concluding remarks .

this paper is concerned with the coherent quantum filtering ( cqf ) problem , where a quantum observer is cascaded in a measurement - free fashion with a linear quantum plant so as to minimize a mean square error of estimating the plant variables of interest . both systems are governed by markovian hudson - parthasarathy quantum stochastic differential equations driven by bosonic fields in vacuum state . these quantum dynamics are specified by the hamiltonians and system - field coupling operators . we apply a recently proposed transverse hamiltonian variational method to the development of first - order necessary conditions of optimality for the cqf problem in a larger class of observers . the latter is obtained by perturbing the hamiltonian and system - field coupling operators of a linear coherent quantum observer along linear combinations of unitary weyl operators , whose role here resembles that of the needle variations in the pontryagin minimum principle . we show that if the observer is a stationary point of the performance functional in the class of linear observers , then it is also a stationary point with respect to the weyl variations in the larger class of nonlinear observers . in loving memory of my mother , raisa dmitrievna vladimirova ( 10.05.1933 30.05.2015 )

this paper is concerned with the coherent quantum filtering ( cqf ) problem , where a quantum observer is cascaded in a measurement - free fashion with a linear quantum plant so as to minimize a mean square error of estimating the plant variables of interest . both systems are governed by markovian hudson - parthasarathy quantum stochastic differential equations driven by bosonic fields in vacuum state . these quantum dynamics are specified by the hamiltonians and system - field coupling operators . we apply a recently proposed transverse hamiltonian variational method to the development of first - order necessary conditions of optimality for the cqf problem in a larger class of observers . the latter is obtained by perturbing the hamiltonian and system - field coupling operators of a linear coherent quantum observer along linear combinations of unitary weyl operators , whose role here resembles that of the needle variations in the pontryagin minimum principle . we show that if the observer is a stationary point of the performance functional in the class of linear observers , then it is also a stationary point with respect to the weyl variations in the larger class of nonlinear observers . in loving memory of my mother , raisa dmitrievna vladimirova ( 10.05.1933 30.05.2015 )

1203.4724

i

we are happy to help celebrate stein s stunning , deep and significant contribution to the statistical literature . in 1956 , charles stein ( @xcite ) proved a result that astonished many and was the catalyst for an enormous and rich literature of substantial importance in statistical theory and practice . stein showed that when estimating , under squared error loss , the unknown mean vector @xmath0 of a @xmath1-dimensional random vector @xmath2 having a normal distribution with identity covariance matrix , estimators of the form @xmath3 dominate the usual estimator @xmath0 , @xmath2 , for @xmath4 sufficiently small and @xmath5 sufficiently large when @xmath6 . james and stein ( @xcite ) sharpened the result and gave an explicit class of dominating estimators , @xmath7 for @xmath8 , and also showed that the choice of @xmath9 ( the james stein estimator ) is uniformly best . for future reference recall that `` the usual estimator , '' @xmath2 , is a minimax estimator for the normal model , and more generally for any distribution with finite covariance matrix.=1 stein ( @xcite ) , considering general estimators of the form @xmath10 , gave an expression for the risk of these estimators based on a key lemma , which has come to be known as stein s lemma . numerous results on shrinkage estimation in the general spherically symmetric case followed based on some generalization of stein s lemma to handle the cross product term @xmath11 $ ] in the expression for the risk of the estimator . a substantial number of papers for the multivariate normal and nonnormal distributions have been written over the decades following stein s monumental results . for an earlier expository development of stein estimation for nonnormal location models see brandwein and strawderman ( @xcite ) . this paper covers the development of stein estimation for spherically symmetric distributions since brandwein and strawderman ( @xcite ) . it is not encyclopedic , but touches on only some of the significant results for the nonnormal case . given an observation , @xmath2 , on a @xmath1-dimensional spherically symmetric multivariate distribution with unknown mean , @xmath0 and whose density is @xmath12 ( for @xmath13 ) , we will consider the problem of estimating @xmath0 subject to the squared error loss function , that is , @xmath14 is a measurable ( vector - valued ) function , and the loss given by @xmath15 where @xmath16 and @xmath17.the risk function of @xmath18 is defined as @xmath19 unless otherwise specified , we will be using the loss defined by ( [ eq11 ] ) . other loss functions such as the loss @xmath20 will be occasionally used , especially when there is also an unknown scale parameter , and minimaxity , as opposed to domination , is the main object of study . we will have relatively little to say about the important case of confidence set loss , or of loss estimation . in section [ sec2 ] we provide some additional intuition as to why the stein estimator of the mean vector @xmath0 makes sense as an approximation to an optimal linear estimator and as an empirical bayes estimator in a general location problem . the discussion indicates that normality need play no role in the intuitive development of stein - type shrinkage estimators . section [ sec3 ] is devoted to finding improved estimators of @xmath0 for spherically symmetric distributions with a known scale parameter using results of brandwein and strawderman ( @xcite ) and berger ( @xcite ) to bound the risk of the improved general estimator @xmath21 . section [ sec4 ] considers estimating the mean vector for a general spherically symmetric distribution in the presence of an unknown scale parameter , and , more particularly , when a residual vector is available to estimate the scale parameter . it extends some of the results from section [ sec3 ] to this case as well as presenting new improved estimators for this problem . the results in this section indicate a remarkable robustness property of stein - type estimators in this setting , namely , that certain of the improved estimators dominate @xmath2 uniformly for all spherically symmetric distributions simultaneously ( subject to risk finiteness ) . in section [ sec5 ] we consider the restricted parameter space problem , particularly the case where @xmath0 is restricted to a polyhedral cane , or more generally a smooth cone . the material in this section is adapted from fourdrinier , strawderman and wells ( @xcite ) . in section [ sec6 ] we consider some of the advancements in bayes estimation of location vectors for both the known and unknown scale cases . we present an intriguing result of maruyama maruyama ( @xcite)which is related to the ( distributional ) robustness of stein estimators in the unknown scale case treated in section [ sec4 ] . section [ sec7 ] contains some concluding remarks .

some emphasis is placed on developing intuition as to why shrinkage should work in location problems whether the underlying population is normal or not . considerable attention is devoted to generalizing the `` stein lemma '' which underlies much of the theoretical development of improved minimax estimation for spherically symmetric distributions . some attention is also given to the problem of estimating a location vector restricted to lie in a polyhedral cone . .

this paper reviews advances in stein - type shrinkage estimation for spherically symmetric distributions . some emphasis is placed on developing intuition as to why shrinkage should work in location problems whether the underlying population is normal or not . considerable attention is devoted to generalizing the `` stein lemma '' which underlies much of the theoretical development of improved minimax estimation for spherically symmetric distributions . a main focus is on distributional robustness results in cases where a residual vector is available to estimate an unknown scale parameter , and , in particular , in finding estimators which are simultaneously generalized bayes and minimax over large classes of spherically symmetric distributions . some attention is also given to the problem of estimating a location vector restricted to lie in a polyhedral cone . .

1211.6823

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lhc is expected to confirm if there is a new particle at 125 gev by the end of this year . the likelihood for a new discovery is rather high . nevertheless , whether this new particle is the sm higgs boson is not an easy question to answer . here the scenario of this 125 gev particle produced by vector - boson fusion , instead of gluon fusion as the dominant production mechanism for the standard model higgs boson , is studied in details . by using the forward dijet tagging technique , one can single out the vector - boson fusion mechanism . we studied a number of popular new physics models that have been employed to interpret the observed particle at 125 gev , including fermiophobic higgs boson , the randall - sundrum radion , inert - higgs - doublet model , two - higgs - doublet model , and the mssm . since the inclusive diphoton channel showed an excess over the sm predictions , we first selected the parameter space of each model that can give an inclusive diphoton rate larger than or equal to the sm rate . then , we calculate the exclusive @xmath22 diphoton production rate in vbf for that parameter space . if the diphoton mode excess seen at lhc-7 can be firmly established by the new lhc-8 data , it will be the utmost task to identify the nature of this particle . perhaps , it is simply the sm higgs boson with some level of statistical fluctuation , but it could also be the rs radion @xcite , fermiophobic higgs boson @xcite , the light cp - even higgs boson of the 2hdm @xcite , the higgs boson of the ihdm @xcite , or one of the cp - even higgs bosons in other extensions of the mssm @xcite , all of which can allow an enhancement to the @xmath8 production rate . on the other hand , the vector - boson fusion , as singled out by the dijet tag , provides useful information in helping to differentiate among various models . it is not hard by browsing through fig . [ ratio ] to conclude the following * if a similar rate is seen in inclusive production but no large excess is seen in the exclusive vbf production it would unlikely be a fermiophobic higgs boson . * if a similar rate or excess is seen in inclusive production but some events are seen in exclusive vbf production rate , it would unlikely be the rs radion . * if moderate excess is seen in both inclusive production and exclusive vbf production , it could be the higgs boson of the ihdm , 2hdm , or the mssm . however , if the excess is over 60% it will pose severe challenge to the mssm . it seems easy to rule out either fermiophobic higgs boson or rs radion , providing that we see no large excess or some events in vbf channel , respectively . however , it is still difficult to distinguish the other models when the inclusive and exclusive rates are similar to or slightly larger than the sm values . if the production rate of the diphoton mode at 125 gev lines up with the sm prediction eventually , it is still premature to conclude this is coming from the sm higgs boson . other alternatives in mssm , nmssm , or other susy models can also be mimicking the sm higgs boson , depending on the parameter space of the new physics model . in any case , once the signals at 125 gev are confirmed further studies including all possible decay modes are to be taken into account in order to discriminate these many alternatives beyond the standard model . vector - boson fusion is the next most important production mechanism that must be taken into account to fully identify the newly discovered particle .

, the alternative vector - boson fusion is more sensitive to electroweak symmetry breaking . using the well known dijet - tagging technique to single out the vector - boson fusion mechanism , we investigate potential of vector - boson fusion to discriminate a number of models suggested to give an enhanced inclusive diphoton production rate .

this review is based on the talk presented at the susy 2012 ( beijing ) . the new particle around 125 gev observed at the large hadron collider ( lhc ) is almost consistent with the standard model higgs boson , except that the diphoton decay mode may be excessive . we summarize a number of possibilities . while at the lhc the dominant production mechanism for the higgs boson of the standard model and some other extensions is via the gluon fusion process , the alternative vector - boson fusion is more sensitive to electroweak symmetry breaking . using the well known dijet - tagging technique to single out the vector - boson fusion mechanism , we investigate potential of vector - boson fusion to discriminate a number of models suggested to give an enhanced inclusive diphoton production rate .

1405.7966

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with detections for about 560 million objects , _ wise _ represents a major step forward in the surveying and understanding of the infrared sky . its combination of up to 1000 times higher sensitivity than previous ir surveys , and a relatively high angular resolution , enables studies of source samples with unprecedented statistical significance . we have computed colour tracks in the _ wise _ photometric system for two families of models : smooth spherical shells and clumpy dust torus models , and decided to study local / galactic populations in this paper , and the extragalactic sky in nikutta et al . ( in preparation ) . the model tracks provide guidance for the observed distribution of sources in _ wise _ cc diagrams , such as illustrated in the left panel in fig . [ fig : compare - to - wise ] . the main results of our computations are shown in the right panel in fig . [ fig : compare - to - wise ] . the model - based colour tracks outline reasonably well the distribution of sources expected to be associated with dust emission ( i.e. all source types except t dwarfs and stars without dusty shell ) . the location of dust - free stars coincides very well with the optically thin point of all dust - shell models irrespective of the dust composition . deviations from the zero - point are caused by _ wise _ filters and being sensitive to the blackbody peaks of the coolest stars , thus producing colours other than those for the rayleigh jeans slope . in the other extreme , at high optical depths , the dusty model tracks of ism dust shells with shallow radial density distributions overlap with those cc areas populated by ultra - luminous infrared galaxies ( ulirgs ) , which are known to be deeply shrouded in dust @xcite . we find that _ wise _ photometry alone is sufficient to reliably classify c - rich and o - rich asymptotic giant branch stars with dusty shells ( section [ sec : agb ] ) . with the large population of agb stars in the _ wise _ catalogue we were able to define magnitude and colour selection criteria that distinguish between the two classes . it is necessary to regard the distribution of _ wise _ colours as a three - dimensional arrangement in colour colour colour space . the traditional two - dimensional orthogonal projections are very helpful , but not sufficient . with the ability to cleanly separate the local populations of c - rich and o - rich agb stars we computed the most detailed map of the c : o - rich star count ratio for the milky way and its satellites ( see section [ sec : co - ratio ] ) . we find a strong spatial gradient away from the galactic plane , with the magellanic clouds showing a c : o ratio about 1000 times higher than the galactic bulge . we also clearly uncover the sagittarius dwarf spheroidal galaxy in the map . we find that the c : o dusty agb star ratio increases with distance from the lmc centre about twice as fast as measured for near - ir selected samples of early agb stars . detailed modelling of these measurements has the potential to shed new light on the formation and evolution of lmc . dusty model tracks for shells with rdws follow the identified agb plumes well . by mapping the previously found colour selection criteria to model parameters , specifically inner dust shell temperature @xmath21 and shell optical depth , we found observational constraints on these model parameters . they seem to indicate slight differences in the physical properties of c - rich and o - rich agb shells ( see section [ sec : agb - analysis ] ) . spherical dusty shell models with flat radial density distributions generate _ wise _ colours compatible with ysos . yso samples selected using _ iras _ and _ wise _ surveys have very little overlap due to vastly different imaging depths : while _ iras _ was sensitive to bright sources with relatively high visual optical depths , _ wise _ detects much fainter ysos with relatively small optical depths ( see section [ sec : yso ] ) . to investigate further how well models describe the _ wise _ colours of ir sources , sufficiently large samples need to be studied object - by - object , with sed fitting for each source over a large wavelength range . the _ spitzer _ sage survey @xcite , for instance , has been previously used for such a task . @xcite matched the ir _ spitzer _ spectra with optical and near - ir data to produce broad - band seds for more than 30000 agb stars in the lmc , and fitted them with _ grams _ models @xcite . thanks to _ wise _ , a similar study can be now undertaken for agb stars in the galaxy . clumpy models of agn dust torus emission , with their more complicated geometry and dust distributions , are much better than simple spherical shells in explaining the general location of qsos and other agns in the _ wise _ cc diagram . the location of the highest clumpy model density aligns almost perfectly with the centre of the circular region identified as ` seyferts ' by @xcite in the left panel of fig . [ fig : compare - to - wise ] . a detailed study of the _ wise_colours of agns will be presented in the companion paper ( ) . [ [ acknowledgements ] ] acknowledgements : + + + + + + + + + + + + + + + + + we are grateful to maria - rosa cioni for illuminating discussions and for making her data available to us . we reproduced fig . 12 from @xcite as part of our fig . [ fig : compare - to - wise ] by permission of the aas and the authors . we thank chao - wei tsai for providing us a high - quality version . we thank both referees for their helpful suggestions which improved the paper . we express our gratitude to xavier koenig for reminding us of the disk / shell dichotomy of yso models ( see section [ sec : yso ] ) , and to james davenport for his insightful post - submission comments on the variability information in the wise database . we are also thankful to patricia arvalo and ron wilhelm for helpful discussions . rn acknowledges support by the alma - conicyt fund , project no . 31110001 , and by fondecyt grant i thanks the hungarian academy of sciences for its support through the distinguished guest professor grant no . i and nhw acknowledge support by nsf grant ast-1008784 to the university of washington . me acknowledges nasa support and the award of an npp senior fellowship from orau , which supported a sabbatical leave at jpl / caltech where much of this work was completed . this publication makes use of data products from the wide - field infrared survey explorer , which is a joint project of the university of california , los angeles , and the jet propulsion laboratory / california institute of technology , funded by the national aeronautics and space administration . funding for sdss - iii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , and the u.s . department of energy office of science . the sdss - iii web site is http://www.sdss3.org/. sdss - iii is managed by the astrophysical research consortium for the participating institutions of the sdss - iii collaboration including the university of arizona , the brazilian participation group , brookhaven national laboratory , carnegie mellon university , university of florida , the french participation group , the german participation group , harvard university , the instituto de astrofisica de canarias , the michigan state / notre dame / jina participation group , johns hopkins university , lawrence berkeley national laboratory , max planck institute for astrophysics , max planck institute for extraterrestrial physics , new mexico state university , new york university , ohio state university , pennsylvania state university , university of portsmouth , princeton university , the spanish participation group , university of tokyo , university of utah , vanderbilt university , university of virginia , university of washington , and yale university . this research has made use of the ned which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . some of the results in this paper have been derived using the healpix / healpy package @xcite . , j. a. , phillips , m. m. , & terlevich , r. 1981 , , 93 , 5 , p. , & demers , s. 2011 , in asp conf . ser . , vol . 445 , why galaxies care about agb stars ii : shining examples and common inhabitants , ed . f. kerschbaum , t. lebzelter , & r. f. wing , 479 , m. r. , et al . 2005 , , 129 , 2562 , a. d. , et al . 2007 , , 655 , 212 , m. l. , et al . 2013 , , 774 , 83 , m .- l. 2009 , , 506 , 1137 , m .- l. , & habing , h. j. 2003 , , ( ch03 ) , 402 , 133 , k. r. , et al . 2007 , , 134 , 2398 , j. j. , et al . 2012 , , 198 , 6 , b. t. 2003 , , 598 , 1017 , a. , & rowan - robinson , m. 1994 , , 266 , 212 , m. p. , van dyk , s. d. , & price , s. d. 2001 , , 122 , 1844 , m. , & ivezi , . 2001 , , 327 , 403 , m. w. , abedigamba , o. p. , & whitelock , p. a. 2010 , , 408 , l76 , l. , et al . 2010 , , 724 , 1030 , k. m. , hivon , e. , banday , a. j. , wandelt , b. d. , hansen , f. k. , reinecke , m. , & bartelmann , m. 2005 , , 622 , 759 , m. 1988 , grain optical properties , technical report , y. , et al . 2008 , , 60 , 435 , . , beers , t. c. , & juri , m. 2012 , , 50 , 251 , . , connolly , a. , vanderplas , j. , & gray , a. 2014 , statistics , data mining and machine learning in astronomy ( princeton university press ) , . , & elitzur , m. 1997 , , 287 , 799 , . , & elitzur , m. 2000 , , 534 , l93 , . , & elitzur , m. 2010 , , 404 , 1415 , . , nenkova , m. , & elitzur , m. 1999 , arxiv : astro - ph/9910475 , . , et al . 2007 , , 134 , 973 , t. , ivezi , . , & knapp , g. r. 2002 , , 337 , 749 , t. h. , et al . 2011 , , 735 , 112 , a. , van loon , j. t. , khosroshahi , h. , & mirtorabi , m. t. 2013 , , 432 , 2824 , e. a. , et al . 2010 , , 710 , 1444 , n. a. , sirocky , m. m. , hao , l. , spoon , h. w. w. , marshall , j. a. , elitzur , m. , & houck , j. r. 2007 , , 654 , l45 , p. , girardi , l. , bressan , a. , groenewegen , m. a. t. , silva , l. , & granato , g. l. 2008 , , 482 , 883 , j. s. , rumpl , w. , & nordsieck , k. h. 1977 , , 217 , 425 , m. , et al . 2006 , , 132 , 2268 , j. , feast , m. , whitelock , p. , olivier , e. , matsunaga , n. , & da costa , g. 2008 , , 385 , 1045 , m. , sirocky , m. m. , ivezi , . , & elitzur , m. 2008a , apj , 685 , 147 , m. , sirocky , m. m. , nikutta , r. , ivezi , . , & elitzur , m. 2008b , , 685 , 160 , g. , et al . 1984 , , 278 , l1 , s. , & weinberg , m. d. 2000 , , 542 , 804 , r. , hunt - 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we develop colour and magnitude criteria that are based only on _ wise _ data to select asymptotic giant branch ( agb ) stars with circumstellar dust shells , and separate them into o - rich and c - rich classes . with these criteria we produce an all - sky map for the count ratio of the two populations . we find that the c : o number ratio for dusty agb stars increases with distance from the lmc centre about twice as fast as measured for near - ir selected samples of early agb stars .

through matches with the sloan digital sky survey ( sdss ) catalogue we identify the location of various families of astronomical objects in _ wise _ colour space . we identify reliable indicators that separate galactic / local from extragalactic sources and concentrate here on the objects in our galaxy and its closest satellites . we develop colour and magnitude criteria that are based only on _ wise _ data to select asymptotic giant branch ( agb ) stars with circumstellar dust shells , and separate them into o - rich and c - rich classes . with these criteria we produce an all - sky map for the count ratio of the two populations . the map reveals differences between the galactic disc , the magellanic clouds and the sgr dwarf spheroidal galaxy , as well as a radial gradient in the large magellanic cloud ( lmc ) disc . we find that the c : o number ratio for dusty agb stars increases with distance from the lmc centre about twice as fast as measured for near - ir selected samples of early agb stars . detailed radiative transfer models show that _ wise _ colours are well explained by the emission of centrally heated dusty shells where the dust has standard properties of interstellar medium ( ism ) grains . the segregation of different classes of objects in _ wise _ colour space arises from differences in properties of the dust shells : those around young stellar objects have uniform density distributions while in evolved stars they have steep radial profiles . [ firstpage ] radiative transfer stars : agb and post - agb galaxy : structure magellanic clouds infrared : general infrared : stars .

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turbulence is an important ingredient for understanding the properties and characteristics of molecular clouds and star - forming regions . turbulent gas motions are highly supersonic as indicated by the superthermal line widths ubiquitously observed throughout molecular clouds ( williams , blitz & mckee 2000 ) . these motions carry enough energy to halt global collapse and act as stabilizing agent for the entire cloud . however , it can be shown that interstellar turbulence decays quite rapidly on time scales of the order of the free - fall time of the system ( mac low et al . 1998 , stone , ostriker & gammie 1998 , padoan & nordlund 1999 ) . to explain the observed long life times , turbulence in molecular clouds must be constantly driven ( gammie & ostriker 1996 , mac low 1999 ) . the interplay between self - gravity on the one hand ( leading to local collapse and star formation ) and turbulent gas motion on the other hand ( trying to prevent this process ) plays a key role in determining the structure of molecular clouds . altogether , understanding the characteristics of compressible , supersonic , and constantly replenished turbulence in self - gravitating media is an important ingredient for an adequate description of molecular clouds dynamics . and vice versa , from analyzing the spatial and dynamical structure of molecular clouds we can gain insight into the phenomenon of turbulence ( for an overview over interstellar turbulence see franco & carraminana 1999 ) . unfortunately , a complete and comprehensive theory of turbulence does not exist . due to the enormous complexity of the problem , progress has been slow since kolmogorov s pioneering work in 1941 , where he derived simple scaling laws for incompressible , stationary , and homogeneous turbulence by postulating a self - similar energy cascade downwards from the driving scale to the dissipation range . most effort has since been put in finding an adequate closure procedure , i.e. in finding a way to express the highest - order correlation in the hierarchy of equations governing turbulent motion ( for an excellent overview see lesieur 1997 ; also boratav , eden & erzan 1997 ) . however , a satisfying description of turbulence has yet to be found . correlation and distribution functions of dynamical variables are frequently deployed for characterizing the kinematical properties of turbulent molecular clouds . besides using 2-point statistics ( e.g. scalo 1984 , kleiner & dickman 1987 , kitamura et al . 1993 , miesch & bally 1994 , larosa , shore & magnani 1999 ) , many studies have hereby concentrated on 1-point statistics , namely on analyzing the probability distribution function ( pdf ) of the ( column ) density and of dynamical observables , e.g. of the centroid velocities of molecular lines and their increments . the density pdf has been used to characterize numerical simulations of the interstellar medium by vzquez - semadeni ( 1994 ) , padoan , nordlund , & jones ( 1997 ) , passot , & vzquez - semadeni ( 1998 ) and scalo et al . velocity pdf s for several star - forming molecular clouds have been determined by miesch & scalo ( 1995 ) and miesch , scalo & bally ( 1998 ) . lis et al . ( 1996 , 1998 ) analyzed snapshots of a numerical simulation of mildly supersonic , decaying turbulence ( without self - gravity ) by porter , pouquet , & woodward ( 1994 ) and applied the method to observations of the @xmath0-ophiuchus cloud . altogether , the observed pdf s exhibit strong non - gaussian features , they are often nearly exponential with possible evidence for power - law tails in the outer parts . this disagrees with the nearly gaussian behavior typically found in experimental measurements and numerical models of incompressible turbulence . the observed centroid velocity _ increment _ pdf s are more strongly peaked and show stronger deviations from gaussianity than numerical models of incompressible turbulence predict . furthermore , the spatial distribution of the largest centroid velocity differences ( determining the tail of the distribution ) appears ` spotty ' across the face of the clouds ; there is no convincing evidence for filamentary structure . miesch et al . ( 1998 ) conclude that turbulence in molecular clouds involves physical processes that are not adequately described by incompressible turbulence or mildly supersonic decay simulations ( see also mac low & ossenkopf 2000 ) . it is the principal goal of this paper to extend previous determinations of pdf s from numerical models into a regime more applicable for interstellar turbulence by ( 1 ) by calculating fully supersonic flows , ( 2 ) by including self - gravity , and ( 3 ) by incorporating a ( simple analytic ) description of turbulent energy input . for comparison with molecular cloud observations , i discuss the dynamical properties of decaying and stationary ( i.e. driven ) , supersonic , isotropic turbulence in self - gravitating isothermal gaseous media . the pdf s for the density , for the line centroid velocity and for their increments are derived as function of time and evolutionary state of the turbulent model . the structure of this paper is as follows : section [ sec : remarks ] introduces and defines the statistical tools applied in the current study . it is followed in sec . [ sec : model ] by a description of the numerical scheme used to compute the time evolution of the turbulent flows . [ sec : init ] shows that already simple variance effects in random gaussian fields are able to introduce strong _ non_-gaussian distortions to the pdf s which makes a clear - cut interpretation difficult . section [ sec : decay - non - grav ] contains the analysis of decaying , initially highly supersonic turbulence without self - gravity . this effect is then added to the simulations presented in sec . [ sec : decay - with - gravity ] . the model most relevant for molecular cloud dynamics is discussed in sec . [ sec : driven - with - gravity ] . it includes a simple driving term to replenish the turbulent cascade . finally , in sec . [ sec : summary ] all results are summarized .

turbulence is essential for understanding the structure and dynamics of molecular clouds and star - forming regions . one - point probability distribution functions ( pdf s ) of dynamical variables have been suggested as appropriate statistical measures and applied to several observed molecular clouds . in addition , random gaussian velocity fields are analyzed to estimate the influence of variance effects . to characterize the flow properties , it appears therefore very difficult to distinguish between different physical processes on the basis of pdf s only , which limits their applicability for adequately characterizing interstellar turbulence . _ ( accepted for publication in the astrophysical journal ) _

turbulence is essential for understanding the structure and dynamics of molecular clouds and star - forming regions . there is a need for adequate tools to describe and characterize the properties of turbulent flows . one - point probability distribution functions ( pdf s ) of dynamical variables have been suggested as appropriate statistical measures and applied to several observed molecular clouds . however , the interpretation of these data requires comparison with numerical simulations . to address this issue , sph simulations of driven and decaying , supersonic , turbulent flows with and without self - gravity are presented . in addition , random gaussian velocity fields are analyzed to estimate the influence of variance effects . to characterize the flow properties , the pdf s of the density , of the line - of - sight velocity centroids , and of the line centroid increments are studied . this is supplemented by a discussion of the dispersion and the kurtosis of the increment pdf s , as well as the spatial distribution of velocity increments for small spatial lags . from the comparison between different models of interstellar turbulence , it follows that the inclusion of self - gravity leads to better agreement with the observed pdf s in molecular clouds . the increment pdf s for small spatial lags become exponential for all considered velocities . however , all the processes considered here lead to non - gaussian signatures , differences are only gradual , and the analyzed pdf s are in addition projection dependent . it appears therefore very difficult to distinguish between different physical processes on the basis of pdf s only , which limits their applicability for adequately characterizing interstellar turbulence . _ ( accepted for publication in the astrophysical journal ) _

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sph simulations of driven and decaying , supersonic , turbulent flows with and without self - gravity have been analyzed in this study . it extends previous investigations of mildly supersonic , decaying , _ non_-self - gravitating turbulence ( lis et al . 1996 , 1998 ) into a regime more relevant molecular clouds , by ( a ) considering highly supersonic flows and by including ( b ) self - gravity and ( c ) a driving source for turbulence . the flow properties are characterized by using the probability distribution functions of the density , of the line - of - sight velocity centroids , and of their increments . furthermore the dispersion and the kurtosis of the increment pdf s are discussed , as well as the spatial distribution of the velocity increments for the smallest spatial lags . \(1 ) to asses the influence of variance effects , simple gaussian velocity fluctuations are studied . the insufficient sampling of random gaussian ensembles leads to distorted pdf s similar to the observed ones . for line profiles this has been shown by dubinski et al . ( 1995 ) . \(2 ) decaying , initially highly supersonic turbulence without self - gravity leads to pdf s which also exhibit deviations from gaussianity . for the trans- and subsonic regime this has been reported by lis et al . ( 1996 , 1998 ) . however , neglecting gravity and thus not allowing for the occurance of collapse motions , these distortions are not very pronounced and can not account well for the observational data ( lis et al . 1998 , miesch et al . 1998 ) . \(3 ) when including gravity into the models of decaying initially supersonic turbulence , the pdf s get into better agreement with the observations . during the early dynamical evolution of the system turbulence carries enough kinetic energy to prevent collapse on all scales . in this phase the properties of the system are similar to those of non - gravitating hydrodynamic supersonic turbulence . however , as turbulent energy decays gravitational collapse sets in . first localized and on small scales , but as the turbulent support continues to diminish collapse motions include increasingly larger spatial scales . the evolution leads to the formation of an embedded cluster of dense protostellar cores ( see also klessen & burkert 2000 ) . as the collapse scale grows , the @xmath0- , @xmath6- , and @xmath9-pdf s get increasingly distorted . in particular , the @xmath9-pdf s for small spatial lags are strongly peaked and exponential over the entire range of measured velocities . this is very similar to what is observed in molecular clouds ( for @xmath0-ophiuchus see lis et al 1998 ; for orion , mon r2 , l1228 , l1551 , and hh83 see miesch et al . 1998 ) . \(4 ) the most realistic model for interstellar turbulence considered here includes a simple ( non - local ) driving scheme . it is used to stabilize the system against collapse on large scales . again non - gaussian pdf s are observed . despite global stability , local collapse is possible and the system again evolves towards the formation of an embedded cluster of accreting protostellar cores . as the adopted driving scheme introduces a bias towards maintaining a gaussian velocity distribution , the properties of the pdf s fall in between the ones of pure hydrodynamic supersonic turbulence and the ones observed in systems where self - gravity dominates after sufficient turbulent decay . this situation may change when considering more realistic driving schemes . \(5 ) a point of caution : the use of @xmath6- and @xmath9-pdf s to unambiguously characterize interstellar turbulence and to identify possible physical driving mechanisms may be limited . _ all _ models considered in the current analysis lead to non - gaussian signatures in the pdf s , differences are only gradual . in molecular clouds the number of physical processes that are expected to give rise to deviations from gaussian statistics is large . simple statistical sampling effects ( sec . [ sec : init ] ) and turbulent intermittency caused by vortex motion ( lis et al . 1996 , 1998 ) , as well as the effect self - gravity ( sec . [ sec : decay - with - gravity ] ) and of shock interaction in highly supersonic flows ( mac low & ossenkopf 2000 ) , _ all _ will lead to non - gaussian signatures in the observed pdf s . also stellar feedback processes , galactic shear and the presence of magnetic fields will influence the interstellar medium and create distortions in the velocity field . this needs to be studied in further detail . in addition , the full 3-dimensional spatial and kinematical information is not accessible in molecular clouds , measured quantities are always projections along the line - of - sight . as the structure of molecular clouds is extremely complex , the properties of the pdf s may vary considerably with the viewing angle . attempts to disentangle the different physical processes influencing interstellar turbulence therefore should no rely on analyzing velocity pdf s alone , they require additional statistical information . i thank a. burkert , f. heitsch , and m .- mac low for many fruitful and stimulating discussions , and the editor s. shore for his comments on the paper and his help with an extremely slow and non - responsive ( anonymous ) referee . adams , f.c . , wiseman , j.j . 1994 , , 435 , 693 balkovsky , e. , falkovich , g. 1998 , , 57 , r1231 balkovsky , e. , falkovich , g. , kolokolov , i. , lebedev , v. 1997 , , 78 , 1452 ballesteros - paredes , j. , vzquez - semadeni , e. , scalo , j. 1999 , , 515 , 286 bate , m.r . , bonnell , i.a , price , n.m . 1995 , , 277 , 362 bate , m.r . , burkert , a. 1997 , , 288 , 1060 benz , w. 1990 , in the numerical modeling of nonlinear stellar pulsations , ed . buchler , kluwer academic publisher , dordrecht bonazzola , s. , perault , m. , puget , j.l , heyvaerts , j. , falgarone , e. , panis , j.f . 1992 , j. fluid . , 245 , 1 boratav , o. , eden , a. , erzan , a. ( eds . ) 1997 , turbulence modeling and vortex dynamics , springer verlag , heidelberg bronstein , i.n . , semendjajew , k.a . 1979 , taschenbuch der mathematik , teubner verlagsgesellschaft , leibzig burkert , a. , klessen , r.s . , bodenheimer , p. 1998 , in the orion complex revisited , eds . m. mccaughrean & a. burkert , asp conference series , in press cao , n. , chen , s. , she , z .- s . 1996 , , 76 , 3711 chertkov , m. , kolokolov , i. , vergassola , m. 1997 , , 56 , 5483 crutcher , r. m. 1999 , , 520 , 706 dubinski , j. , narayan , r. , phillips , t.g . 1995 , , 448 , 226 ebisuzaki , t. , makino , j. , fukushige , t. , taiji , m. , sugimoto , d. , ito , t. , okumura , s.k . 1993 , , 45 , 269 falgarone , e. , lis , d.c . , phillips , t.g . , pouquet , a. , porter , d.h . , woodward , p.r . 1994 , , 436,728 falgarone , e. , panis , j .- f . , heithausen , a. , prault , m. , stutzki , j. , puget , j .- l . , bensch , f. 1998 , , 331 , 669 falgarone , e. , phillips , t.g . 1990 , , 359 , 344 falkovich , g. , lebedev , v. 1997 , , 79 , 4159 forster , d. , nelson , d.r . , stephen , m.j . 1977 , , 16 , 732 franco , j. , carraminana , a. ( eds . ) 1999 , interstellar turbulence , cambridge university press frisch , u. 1995 , turbulence the legacy of a. n.kolmogorov , cambridge university press gammie , c.f . , ostriker , e. e.c . 1996 , , 466 , 814 hockney , r.w . , eastwood , j.w . 1988 , computer simulation using particles , iop publishing ltd . , bristol and philadelphia jahyesh , warhaft , z. 1991 , , 67 , 3503 kleiner , s.c . , dickman , r.l . 1987 , , 312 , 837 klessen , r.s . 1997 , , 292 , 11 klessen , r.s . , burkert , a. , bate , m.r . 1998 , , 501 , l205 klessen , r.s . , burkert , a. 2000 , , 128 in press ( astro - ph/9904090 ) klessen , r.s . , heitsch , f. , mac low , m .- 2000 , , accepted ( astro - ph/9911068 ) kida , s. , murakami , y. 1989 , fluid dyn . res . , 4 , 347 kitamura , y. , sunada , k. , hayashi , m. , hasegawa , t. 1993 , , 413 , 221 kolmogorov , a.n . 1941 , dokl . nauk sssr , 30 , 301 ( reprinted in proc . r. soc . lond . a , 434 , 9 ( 1991 ) ) lamballais , e. , lesieur , m. , mtais , o. 1997 , , 56 , 761 larosa , t.n . , shore , s.n . , magnani , l. 1999 , , 512 , 761 lesieur , m. 1997 , turbulence in fluids , 3 . , kluwer academic publishers , dordrecht lis , d.c . , keene , j. , phillips , t.g . , pety , j. 1998 , , 504 , 889 lis , d.c . , pety , j. , phillips , t.g . , falgarone , e. 1996 , , 463 , 623 machiels , l. , deville , m.o . 1998 , j. comp . phys . , 145 , 256 mac low , m .- 1999 , , 524 , 169 mac low , m .- m . , klessen , r.s . , burkert , a. , smith , m.d . 1998 , , 80 , 2754 mac low , m .- , ossenkopf , v. 2000 , , 353 , 339 miesch , m.s . , bally , j. 1994 , , 429 , 645 miesch , m.s . , scalo , j.m . 1995 , , 450 , l27 miesch , m.s . , scalo , j.m . , bally , j. 1998 , , submitted ( astro - ph/9810427 ) monaghan , j.j . 1992 , , 30 , 543 monaghan , j.j . , gingold , r.a . 1983 , j. comp . phys . , 52 , 135 padoan , p. , nordlund , , jones , b.j.t . 1997 , , 288 , 145 padoan , p. , nordlund , . 1999 , , 526 , 279 passot , t. , vzquez - semadeni , e. 1998 , , 58 , 4501 porter , d.h . , pouquet , a. , woodward , p.r . 1994 , phys . fluids , 6 , 2133 scalo , j.m . 1984 , , 7 , 556 scalo , j.m . , vzquez - semadeni , e. , chappell , d. , passot , t. 1998 , , 504 , 835 she , z .- s . 1991 , fluid dyn . res . , 8 , 143 she , z .- s . , jackson , e. , orszag , s.a . 1991 , proc . lond . a , 434 , 101 steinmetz , m. 1996 , , 278 , 1005 stone , j. m. , ostriker , e. c. , gammie , c. f. : 1998 , , 508 , l99 stutzki , j. , gsten , r. 1990 , , 412 , 233 sugimoto , d. , chikada , y. , makino , j. , ito , t. , ebisuzaki , t. , umemura , m. 1990 , nature , 345 , 33 umemura , m. , fukushige , t. , makino , j. , ebisuzaki , t. , sugimoto , d. , turner , e.l . , loeb , a. 1993 , , 45 , 311 vainshtein , s.i . 1997 , , 56 , 6787 van der marel , r. p. , franx , m. 1993 , , 407 , 525 vzquez - semadeni , e. 1994 , , 423 , 681 vzquez - semadeni , e. , gazol , a. 1995 , , 303 , 204 vincent , a. , meneguzzi , m. 1991 , j. fluid mech . , 225 , 1 vio , r. , fasano , g. , lazzarin , m. , lessi , o. 1994 , , 289 , 640 williams , j.p . , de geus , e.j . , blitz , l. 1994 , , 428 , 693 williams , j. p. , blitz , l. , mckee , c. f. 2000 , in protostars and planets iv , eds . v. mannings , a. boss & s. russell , in press

of driven and decaying , supersonic , turbulent flows with and without self - gravity are presented . the pdf s of the density , of the line - of - sight velocity centroids , and of the line centroid increments are studied . this is supplemented by a discussion of the dispersion and the kurtosis of the increment pdf s , as well as the spatial distribution of velocity increments for small spatial lags . from the comparison between different models of interstellar turbulence the increment pdf s for small spatial lags become exponential for all considered velocities . however , all the processes considered here lead to non - gaussian signatures , differences are only gradual , and the analyzed pdf s are in addition projection dependent .

turbulence is essential for understanding the structure and dynamics of molecular clouds and star - forming regions . there is a need for adequate tools to describe and characterize the properties of turbulent flows . one - point probability distribution functions ( pdf s ) of dynamical variables have been suggested as appropriate statistical measures and applied to several observed molecular clouds . however , the interpretation of these data requires comparison with numerical simulations . to address this issue , sph simulations of driven and decaying , supersonic , turbulent flows with and without self - gravity are presented . in addition , random gaussian velocity fields are analyzed to estimate the influence of variance effects . to characterize the flow properties , the pdf s of the density , of the line - of - sight velocity centroids , and of the line centroid increments are studied . this is supplemented by a discussion of the dispersion and the kurtosis of the increment pdf s , as well as the spatial distribution of velocity increments for small spatial lags . from the comparison between different models of interstellar turbulence , it follows that the inclusion of self - gravity leads to better agreement with the observed pdf s in molecular clouds . the increment pdf s for small spatial lags become exponential for all considered velocities . however , all the processes considered here lead to non - gaussian signatures , differences are only gradual , and the analyzed pdf s are in addition projection dependent . it appears therefore very difficult to distinguish between different physical processes on the basis of pdf s only , which limits their applicability for adequately characterizing interstellar turbulence . _ ( accepted for publication in the astrophysical journal ) _

0909.0940

i

particle packing problems are ancient , dating back to the dawn of civilization . bernal has remarked that `` heaps '' ( particle packings ) were the first things that were ever measured in the form of basketfuls of grain for the purpose of trading or of collection of taxes @xcite . dense packings of hard particles have served as useful models to understand the structure of liquid , glassy and crystal states of matter @xcite , granular media @xcite , and heterogeneous materials @xcite . understanding the symmetries and other mathematical properties of the densest packings in arbitrary dimensions is a problem of long - standing interest in discrete geometry and number theory @xcite . a large collection of nonoverlapping solid objects ( particles ) in @xmath6-dimensional euclidean space @xmath7 is called a packing . the packing density @xmath8 is defined as the fraction of space @xmath7 covered by the particles . a problem that has been a source of fascination to mathematicians and scientists for centuries is the determination of the densest arrangement(s ) of particles that do not tile space and the associated maximal density @xmath9 @xcite . finding the maximal - density packing arrangements is directly relevant to understanding the structure and properties of crystalline equilibrium phases of particle systems as well as their ( zero - temperature ) ground - state structures in low dimensions in which the interactions are characterized by steep repulsions and short - ranged attractions . the preponderance of previous investigations have focused on dense packings of spheres in various dimensions @xcite . for congruent particles in three dimensions , the sphere is the only non - tiling particle for which the densest packing arrangements can be proved @xcite . it is only very recently that attention has turned to finding the maximal - density packing arrangements of nonspherical particles in @xmath0 , including ellipsoids @xcite , tetrahedra @xcite , and superballs @xcite . very little is known about the densest packings of polyhedral particles @xcite . + the platonic solids ( mentioned in plato s timaeus ) are convex polyhedra with faces composed of congruent convex regular polygons . there are exactly five such solids : the tetrahedron ( p1 ) , icosahedron ( p2 ) , dodecahedron ( p3 ) , octahedron ( p4 ) , and cube ( p5 ) ( see fig . [ platonic ] ) @xcite . one major concern in this paper is the determination of the densest packings of each of the platonic solids in three - dimensional euclidean space @xmath0 , except for the cube , which is the only platonic solid that tiles space . it is useful to highlight some basic geometrical properties of the platonic solids that we will employ in subsequent sections of the paper . the dihedral angle @xmath10 is the interior angle between any two face planes and is given by @xmath11 where @xmath12 is the number of sides of each face and @xmath13 is the number of faces meeting at each vertex . thus , @xmath10 is @xmath14 , @xmath15 , @xmath16 , @xmath17 , and @xmath18 , for the tetrahedron , icosahedron , dodecahedron , octahedron , and cube , respectively , where @xmath19 is the golden ratio . thus , since the dihedral angle for the cube is the only one that is a submultiple of @xmath20 , the cube is the only platonic solid that tiles space . we note in passing that in addition to the regular tessellation of space by cubes in the simple cubic lattice arrangement , there are an infinite number of other irregular tessellations of space by cubes @xcite . figure [ random - squares ] shows a portion of a realization of a two - dimensional analog of such an irregular tessellation . every polyhedron has a dual polyhedron with faces and vertices interchanged . the dual of each platonic solid is another platonic solid , and therefore they can be arranged into dual pairs : the tetrahedron is self - dual ( i.e. , its dual is another tetrahedron ) , the icosahedron and dodecahedron form a dual pair , and the octahedron and cube form a dual pair . + an archimedean solid is a highly symmetric , semi - regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices . there are thirteen archimedean solids : truncated tetrahedron ( a1 ) , truncated icosahedron ( a2 ) , snub cube ( a3 ) , snub dodecahedron ( a4 ) , rhombicosidodecahdron ( a5 ) , truncated icosidodecahdron ( a6 ) , truncated cuboctahedron ( a7 ) , icosidodecahedron ( a8 ) , rhombicuboctahedron ( a9 ) , truncated dodecahedron ( a10 ) , cuboctahedron ( a11 ) , truncated cube ( a12 ) and truncated octahedron ( a13 ) ( see fig . [ archimedean ] ) . note that the truncated octahedron is the only archimedean solid that tiles space . another important observation is that the tetrahedron ( p1 ) and the truncated tetrahedron ( a1 ) are the only platonic and archimedean solids , respectively , that are not _ centrally symmetric_. a particle is centrally symmetric if it has a center @xmath21 that bisects every chord through @xmath21 connecting any two boundary points of the particle , i.e. , the center is a point of inversion symmetry . we will see that the central symmetry of the majority of the platonic and archimedean solids ( p2 p5 , a2 a13 ) distinguish their dense packing arrangements from those of the non - centrally symmetric ones ( p1 and a1 ) in a fundamental way . some basic definitions concerning packings are given here . saturated _ packing is one in which there is no space available to add another particle to the packing . a _ lattice _ @xmath22 in @xmath7 is a subgroup consisting of the integer linear combinations of vectors that constitute a basis for @xmath7 @xcite . a _ lattice packing _ @xmath23 is one in which the centroids of the nonoverlapping particles are located at the points of @xmath22 , each oriented in the same direction . the set of lattice packings is a subset of all possible packings in @xmath7 . in a lattice packing , the space @xmath7 can be geometrically divided into identical regions @xmath24 called _ fundamental cells _ , each of which contains just the centroid of one particle . thus , the density of a lattice packing is given by @xmath25 where @xmath26 is the volume of a @xmath6-dimensional particle and @xmath27 is the volume of a fundamental cell . a more general notion than a lattice packing is a periodic packing . a _ periodic _ packing of congruent particles is obtained by placing a fixed nonoverlapping configuration of @xmath28 particles ( where @xmath29 ) with _ arbitrary orientations _ in each fundamental cell of a lattice @xmath22 . thus , the packing is still periodic under translations by @xmath22 , but the @xmath28 particles can occur anywhere in the chosen fundamental cell subject to the nonoverlap condition . the packing density of a periodic packing is given by @xmath30 where @xmath31 is the number density , i.e. , the number of particles per unit volume . the determination of the maximal - density arrangements of non - tiling polyhedral particles is a notoriously difficult problem , especially since such extremal structures will generally be non - bravais - lattice packings . computer simulations that seek the maximal - density packings can be an indispensable tool , especially if they can incorporate collective motions of the particles in order to obtain , in principle , the highest possible densities . however , the challenge presented by polyhedral particles in @xmath0 is the non - smooth ( i.e. , nonanalytic ) nature of the particle shape . in the case of smoothly - shaped particles , such as spheres , ellipsoids and superballs , one can construct analytic overlap potential functions " for the particles @xcite and hence one can employ efficient collision - driven molecular dynamics ( md ) growth packing algorithms that inherently involve collective particle motions @xcite . the fact that analytic overlap potential functions can not be constructed for polyhedral particles prevents us from using event - driven md growth methods to study such systems . in this paper , we devise a novel optimization scheme , called the adaptive shrinking cell ( asc ) , that can be applied to generate dense packings of polyhedra in @xmath0 . we employ it specifically to obtain the densest known packings of tetrahedra , icosahedra , dodecahedra , and octahedra with densities @xmath32 , @xmath2 , @xmath3 , and @xmath4 , respectively . the result for tetrahedra improves upon the density reported in our recent investigation @xcite . unlike the densest tetrahedral packing , which must not be a bravais lattice packing @xcite , the densest packings of the other non - tiling platonic solids that we obtain are their corresponding densest lattice packings @xcite . we also derive a simple upper bound on the maximal density of packings of congruent nonspherical particles , and apply it to platonic solids , archimedean solids , superballs and ellipsoids . we introduce the asphericity " parameter @xmath33 ( ratio of the circumradius to inradius ) to show that when @xmath33 is sufficiently small , the upper bounds are relatively tight and thus close to the corresponding densities of the optimal lattice packings of octahedra , dodecahedra and icosahedra as well as of the majority of the archimedean solids with central symmetry . our simulation results as well as theoretical arguments lead us to conjecture that the densest packings of platonic and archimedean solids with central symmetry are given by their corresponding densest lattice packings . this can be regarded to be the analog of kepler s sphere conjecture for these solids . the truncated tetrahedron is the only non - centrally symmetric archimedean solid , the densest known packing of which is a non - lattice packing with density as high as @xmath5 . our work also suggests that the optimal packings of superballs are their corresponding densest lattice packings . in a recent letter @xcite , we briefly reported the densest known packings of the non - tiling platonic solids obtained using the asc algorithm and proposed the aforementioned conjecture concerning the optimal packings of the platonic and archimedean solids . in this paper , we expand on theoretical and computational details and report additional new results . in particular , we provide comprehensive details about the asc scheme and the simulation results ( sec . ii ) , including a discussion about the various initial configurations we used for the asc algorithm ( sec . moreover , we have improved on the highest tetrahedral packing density reported in ref . @xcite ( i.e. , from @xmath34 to @xmath1 ) , by exploring a broad range of dynamical parameters for the algorithm and initial configurations . certain pair statistics of the densest known packing of tetrahedra ( e.g. , the contact number , the centroidal correlation function and the face - normal correlation function ) are given ( sec . it is noteworthy that the densest tetrahedral packing is a non - bravais structure with a complex periodic cell and possesses _ no long - range order_. the initial configurations for the icosahedral , dodecahedral and octahedral packings are described and the numerical challenges in producing dense packings of such polyhedral particles are discussed ( sec . in addition , a detailed derivation of the upper bound and tables containing the geometrical characteristics of the platonic and archimedean solids as well as their upper bound values are given ( sec . the upper bound is also applied to superballs and ellipsoids ( which was not done in ref . moreover , we provide the major elements of a possible proof of our conjecture ( sec . we also discuss how our conjecture could be generalized to other centrally symmetric polyhedral particles such as prisms and anti - prisms as well as high - dimensional analogs of the platonic solids . our work also naturally leads to another conjecture reported here for the first time , namely , the optimal packing of any convex , congruent polyhedron without central symmetry is generally not a ( bravais ) lattice packing ( sec . furthermore , we discuss the possible applications and generalizations of the asc scheme to predict the crystal structures of polyhedral nanoparticles and to the study of random packings of hard polyhedra . finally , we collect in appendices basic packing characteristics of various optimal lattice and non - lattice packings of polyhedra ( including lattice vectors ) that have been scattered throughout the literature and provide lattice vectors and other characteristics of the densest known packings of tetrahedra ( obtained here ) and truncated tetrahedra .

understanding the nature of dense particle packings is a subject of intense research in the physical , mathematical and biological sciences . the preponderance of previous work has focused on spherical particles , and very little is known about dense polyhedral packings . this novel optimization problem is solved here ( using a variety of multi - particle initial configurations ) to find the dense packings of each of the platonic solids in three - dimensional euclidean space , except for the cube , which is the only platonic solid that tiles space . we find the densest known packings of tetrahedra , icosahedra , dodecahedra , and octahedra with densities , , , and , respectively . it is noteworthy that the densest tetrahedral packing possesses _ no long - range order_. unlike the densest tetrahedral packing , which must not be a bravais lattice packing , the densest packings of the other non - tiling platonic solids that we obtain are their previously known optimal ( bravais ) lattice packings . we also derive a simple upper bound on the maximal density of packings of congruent nonspherical particles , and apply it to platonic solids , archimedean solids , superballs and ellipsoids . provided that what we term the asphericity " ( ratio of the circumradius to inradius ) is sufficiently small , the upper bounds are relatively tight and thus close to the corresponding densities of the optimal lattice packings of the centrally symmetric platonic and archimedean solids . our simulation results , rigorous upper bounds , and other theoretical arguments lead us to the conjecture that the densest packings of platonic and archimedean solids with central symmetry are given by their corresponding densest lattice packings . this can be regarded to be the analog of kepler s sphere conjecture for these solids . the truncated tetrahedron is the only non - centrally symmetric archimedean solid , the densest known packing of which is a non - lattice packing with density at least as high as . we discuss the validity of our conjecture to packings of superballs , prisms and anti - prisms as well as to high - dimensional analogs of the platonic solids . finally , we discuss the possible applications and generalizations of the asc scheme in the predicting the crystal structures of polyhedral nanoparticles and the study of random packings of hard polyhedra .

understanding the nature of dense particle packings is a subject of intense research in the physical , mathematical and biological sciences . the preponderance of previous work has focused on spherical particles , and very little is known about dense polyhedral packings . we formulate the problem of generating dense packings of nonoverlapping , non - tiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem , which we call the adaptive shrinking cell ( asc ) scheme . this novel optimization problem is solved here ( using a variety of multi - particle initial configurations ) to find the dense packings of each of the platonic solids in three - dimensional euclidean space , except for the cube , which is the only platonic solid that tiles space . we find the densest known packings of tetrahedra , icosahedra , dodecahedra , and octahedra with densities , , , and , respectively . it is noteworthy that the densest tetrahedral packing possesses _ no long - range order_. unlike the densest tetrahedral packing , which must not be a bravais lattice packing , the densest packings of the other non - tiling platonic solids that we obtain are their previously known optimal ( bravais ) lattice packings . we also derive a simple upper bound on the maximal density of packings of congruent nonspherical particles , and apply it to platonic solids , archimedean solids , superballs and ellipsoids . provided that what we term the asphericity " ( ratio of the circumradius to inradius ) is sufficiently small , the upper bounds are relatively tight and thus close to the corresponding densities of the optimal lattice packings of the centrally symmetric platonic and archimedean solids . our simulation results , rigorous upper bounds , and other theoretical arguments lead us to the conjecture that the densest packings of platonic and archimedean solids with central symmetry are given by their corresponding densest lattice packings . this can be regarded to be the analog of kepler s sphere conjecture for these solids . the truncated tetrahedron is the only non - centrally symmetric archimedean solid , the densest known packing of which is a non - lattice packing with density at least as high as . we discuss the validity of our conjecture to packings of superballs , prisms and anti - prisms as well as to high - dimensional analogs of the platonic solids . in addition , we conjecture that the optimal packing of any convex , congruent polyhedron without central symmetry generally is not a lattice packing . finally , we discuss the possible applications and generalizations of the asc scheme in the predicting the crystal structures of polyhedral nanoparticles and the study of random packings of hard polyhedra .

0909.0940

c

we have formulated the problem of generating dense packings of nonoverlapping polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem , which we call the adaptive shrinking cell ( asc ) scheme . the procedure allows both a sequential search of the configurational space of the particles and the space of lattices via an adaptive fundamental cell that shrinks on average to obtain dense packings . we have applied the asc to generate the densest known packings of the platonic solids . for tetrahedra , we find a packing with density @xmath116 , which is a periodic ( non - bravais lattice ) packing with a complex basis . unlike the other platonic solids , finding dense packings of tetrahedra with our algorithm requires having good initial configurations . the densest packing was found using 314 particles in a rhombical fundamental cell that is similar to that of the hexagonal close packing . as we stressed in our earlier work @xcite and continue to confirm in this paper , it is possible that denser packings of tetrahedra will involve increasingly larger numbers of particles in the fundamental cell . in fact , the higher density found here is realized by a larger periodic packing ( 314 particles per cell ) than the one reported in ref . @xcite ( 72 particles per cell ) with density @xmath117 . it is apparent the obtained densest known tetrahedral packing is disordered in the sense that it possesses no long - range order , at least on the scale of the simulation box . this packing can be considered to be a disordered `` mixture '' of distorted wagon wheels and individual tetrahedra and it is distinct from the one reported in ref . @xcite in both the arrangement of the wagon wheels and the extent of the distortion of the wagon wheels . although we can not rule out the possibility of the existence of denser packings involving a more ordered arrangement of the wagon wheels and individual tetrahedra , it is reasonable to expect that wagon wheels will be key building blocks in denser packings and should at least be slightly distorted to fill the interparticle gaps in wagon - wheel clusters more efficiently , which necessarily introduces a certain degree of disorder to the packing . if denser packings of tetrahedra must involve larger number of particles without long - range order , than it raises the amazing prospect that the densest packings of tetrahedra might be truly disordered , due to the geometrical frustration associated with the lack of central symmetry of a tetrahedron and that tetrahedra can not tile space . this would be the first example of a maximally dense packing of congruent convex three - dimensional particles without long - range order . however , we can not offer definitive conclusions about this possibility at this stage . it is clear that in future work in the search for denser packings , increasingly larger number of tetrahedra must be considered , which can only be studied using greater computational resources . our simulation results and rigorous upper bounds strongly suggest that the optimal lattice packings of the centrally symmetric platonic solids ( octahedra , dodecahedra and icosahedra ) are indeed the densest packings of these particles , especially since these arise from a variety of initial `` dilute '' multi - particle configurations within the fundamental cell @xcite . it is noteworthy that a different simulation procedure ( an event - driven molecular dynamics growth algorithm with an adaptive fundamental cell ) has recently been used to demonstrate that the densest packings of octahedral - like superballs ( which contains the perfect octahedron ) are likely to be the optimal lattice packings @xcite . moreover , the fact that the optimal lattice packing densities of certain centrally symmetric nonspherical particles , such as the archimedean solids with central symmetry and convex superballs , are relatively close to their upper bounds as well as other theoretical arguments given below suggest that the densest packings of these particles may also be given by their optimal lattice packings . it is crucial to stress that the nonspherical particles in this family do not deviate appreciably from a sphere , i.e. , their corresponding asphericity @xmath33 is always bounded and relatively close to unity , and , moreover , their three principle axes ( directions ) are equivalent . this is in contrast to the ellipsoid , which , although centrally symmetric , generally possesses three principle axes ( directions ) that are inequivalent and its asphericity can increase without limit as the largest aspect ratio grows . these characteristics suggest that the densest ellipsoid arrangements are non - lattice packings , which indeed has been verified @xcite . our simulation results and the ensuing theoretical arguments lead to the following conjecture : conjecture 1 : _ the densest packings of the centrally symmetric platonic solids are given by their corresponding optimal lattice packings . _ we now sketch what could be the major elements of a proof of this conjecture . in the case of each of the platonic solids , face - to - face contacts are favored over vertex - to - face contacts to achieve higher packing densities , since the former allows the particle centroids to get closer to one another . such contacting neighbor configurations around each particle reduce the volume of the corresponding convex hull joining the centroids of the contacting particles , and the fraction of space covered by the particles within this convex hull should be increased ; see fig . [ octagon_pack ] for a two - dimensional illustration . @xmath118{octagon_a.eps } & \includegraphics[height=3.0cm , keepaspectratio]{octagon_b.eps } & \includegraphics[height=3.0cm , keepaspectratio]{octagon_c.eps } & \includegraphics[height=3.0cm , keepaspectratio]{octagon_d.eps } \\ \mbox{\bf ( a ) } & \mbox{\bf ( b ) } & \mbox{\bf ( c ) } & \mbox{\bf ( d ) } \end{array}$ ] to achieve the densest packing , the fraction of space covered by the particles within the convex hull should ideally be maximized and so should the number of face - to - face contacts per particle . of course , this is only a local criterion that may not be consistent with the densest global packing . however , it will be seen that the equivalence of the three principle directions of a centrally symmetric platonic solid is crucial for this local optimization criterion to be consistent with the globally densest packing . it is noteworthy that orienting each of the particles in the packings of centrally symmetric platonic solids enable a larger number of face - to - face contacts and thus allows the maximal fraction of space covered by the particles within the convex hull . for example , a particle with @xmath24 faces , possesses @xmath119 families of axes that go through the centroid of the particle and intersect the centrally - symmetric face pairs such that the particles ( in the same orientation ) with their centroids arranged on these axes form face - to - face contacts . the requirement that the particles have the same orientation is globally consistent with a lattice packing . indeed , in the optimal lattice packings of the centrally symmetric platonic solids , each particle has the maximum number of face - to - face contacts that could be obtained without violating the impenetrability condition . it is highly unlikely that such particles possessing three equivalent principle directions and aligned in the same direction could form a more complicated non - lattice periodic packings with densities that are larger than the optimal lattice packings . such non - lattice packings would arise to take advantage of the rotational degrees of freedom . by requiring particle alignments , only translational degrees of freedom remain and hence optimization over these degrees of freedom would lead to the globally optimal packings , which should be lattice packings . constraining rotational degrees of freedom in this way in a non - lattice packing would at best lead to a local optimum in density . this conclusion is clearly supported by our simulations , which use multiple - particle configurations in the fundamental cell and only produce the optimal lattice packings . in the aforementioned arguments , a key step that is difficult to prove is the observation that alignment of each of the particles maximizes the number of face - to - face contacts and thus the fraction of space covered by the particles within the convex hull joining the centroids of the contacting neighbors around a central polyhedron . a rigorous verification of this step would lead to the consistency of the aforementioned local and global optimization criteria . it is noteworthy that in two dimensions , our local criterion to achieve the optimal packings of centrally symmetric regular polygons ( the two - dimensional counterparts of the centrally symmetric platonic solids ) amounts to the identification of optimal neighbor configurations with the maximal edge - to - edge contacts per particle such that the convex hull joining the centroids of the contacting neighbors is minimal . this statement is rigorously true in two dimensions because it is tantamount to a theorem due to fejes tth @xcite , which states that the densest packing of a centrally symmetric particle in two dimensions can be obtained by circumscribing the particle with the minimal centrally symmetric hexagon , which of course tiles @xmath120 . finding the minimal circumscribing centrally symmetric hexagon is equivalent to finding the minimal area convex hull joining the centroids of the six contacting particles ( the maximal number can be obtained in two dimensions for centrally symmetric particles ) . the fact that local optimality is consistent with the global optimality in two dimensions ( e.g. , a centrally symmetric hexagon can always tessellate the space ) does not hold in three dimensions . although we have presented a three - dimensional generalization of the fejes tth theorem , by replacing the minimal hexagon with the minimal convex - hull volume , as pointed out before , it is extremely difficult to provide a rigorous proof for it . although conjecture 1 applies to the centrally symmetric platonic solids , all of our arguments apply as well to each of the centrally symmetric archimedean solids . it can not be true for the truncated tetrahedron , which is the only non - centrally symmetric archimedean solid . specifically , it immediately follows from the results of ref . that a non - lattice packing of truncated tetrahedra can be constructed based on the `` primitive welsh '' tessellation ( i.e. , by removing the small regular tetrahedra ) that possesses the density @xmath121 , which is appreciably larger than the optimal - lattice - packing density of @xmath122 , and contains two particle centroids per fundamental cell . in fact , given that the truncated tetrahedra can not tile space , the density of the `` primitive welsh '' packing of truncated tetrahedra is so large that it may be the optimal packing of such particles . the lattice vectors of this periodic packing are given in appendix c. since the arguments used to justify conjecture 1 apply equally well to the 12 centrally symmetric archimedean solids , we are led to the following more general conjecture : conjecture 2 : _ the densest packings of the centrally symmetric platonic and archimedean solids are given by their corresponding optimal lattice packings . _ the aforementioned arguments can also be extended to the case of superballs , but here the local principle curvatures at the contacting points should be sufficiently small so as to maximize the fraction of space covered by the particles within the convex hull joining the centroids of the neighbors . the central symmetry and equivalence of the three principle directions of superballs means that dense packings of such objects are favored when the particles are aligned , which again leads to consistency between local and global optimality . the fact that the optimal lattice packing densities of superballs is relatively close to the upper - bound values , at least around the sphere point , as well as results from previous molecular dynamics simulations @xcite also strongly suggest that the densest packings of these particles are given by their corresponding optimal lattice packings . it is noteworthy that under the assumption that conjecture 2 is valid , one has upper bounds that are the complete analog of ( [ lemma ] ) , i.e. , @xmath123 , \label{lemma2}\ ] ] where @xmath124 is the volume of an appropriately chosen centrally symmetric platonic or archimedean solid and @xmath125 is the corresponding optimal density for such a solid , which according to conjecture 2 is the optimal lattice packing . this bound will generally be sharper than bound ( [ lemma ] ) because the reference optimal packing is less symmetric than the sphere . for example , the conjectured bound ( [ lemma2 ] ) will be sharp for slightly deformed platonic and archimedean solids or nonspherical particles derived by smoothing the vertices , edges and faces of polyhedra . @xmath126{cut_square_a.eps } & \includegraphics[height=4.35cm , keepaspectratio]{cut_square_b.eps } \\ \mbox{\bf ( a ) } & \mbox{\bf ( b ) } \end{array}$ ] our work also naturally leads to another conjecture : conjecture 3 : _ the optimal packing of any convex , congruent polyhedron without central symmetry generally is not a ( bravais ) lattice packing . _ in other words , the set of such polyhedra whose optimal packing is not a lattice is overwhelmingly larger than the set whose optimal packing is a lattice . we have seen that because the regular tetrahedron and truncated tetrahedron lack central symmetry , dense packings of such objects favor face - to - face contacts . such orientations immediately eliminate the possibility that lattice packings ( in which particles must have the same orientations ) are optimal . similarly , it is very plausible that dense packings of most convex , congruent polyhedra without central symmetry are facilitated by face - to - face contacts and hence the optimal packings can not be lattices . for example , consider a square with one missing corner , i.e. , an isosceles triangle with a right angle ( see fig . [ cut_square ] ) . at first glance , one might surmise that if the missing piece is sufficiently small , the original lattice packing should still be optimal or nearly optimal ( see fig . [ cut_square]a ) , since lattice packings are optimal for squares . however , no matter how small the missing piece may be , a periodic packing in which the fundamental cell contains two pentagons can be constructed that tile the plane ( see fig . [ cut_square]b ) . this is done by taking advantage of the asymmetry of the particle . thus , we see from this counterintuitive example that if the particle does not possess central symmetry , it is possible to exploit its rotational degrees of freedom to yield a periodic packing with a complex basis that are generally denser than the optimal lattice packing . on the other hand , there are special cases where the lattice will be optimal , such as for the rhombic dodecahedron that has one corner clipped @xcite . however , these special cases are overwhelmed in number by those whose optimal packings are not lattices . if conjecture 3 is valid , it also applies to nonspherical particles derived by smoothing the vertices , edges and faces of polyhedra provided that the particle curvature at face - to - face contacts is sufficiently small . it should not go unnoticed that the densest packings of all of the platonic and archimedean solids reported here as well as the densest known packings of superballs @xcite and ellipsoids @xcite have densities that exceed the optimal sphere packing density @xmath127 . these results are consistent with a conjecture of ulam who proposed , without any justification , that the optimal density for packing congruent spheres is smaller than that for any other convex body @xcite . the sphere is perfectly isotropic with an asphericity @xmath33 of unity , and therefore , as noted earlier , its rotational degrees of freedom are irrelevant in affecting its packing characteristics . on the other hand , each of the aforementioned convex non - spherical particles break the continuous rotational symmetry of the sphere and thus its broken symmetry can be exploited to yield the densest possible packings . however , broken rotational symmetry in and of itself may not be sufficient to satisfy ulam s conjecture if the convex particle has a little or no symmetry . it will also be interesting to determine whether our conjecture can be extended to other polyhedral packings . the infinite families of prisms and antiprisms @xcite provide such a class of packings . prism _ is a polyhedron having bases that are parallel , congruent polygons and sides that are parallelograms . an _ antiprism _ is a polyhedron having bases that are parallel , congruent polygons and sides that are alternating bands of triangles . prisms with an even number of sides and antiprisms are centrally symmetric . although prisms and antiprisms are naturally grouped with the archimedean solids ( i.e. , they are polyhedra in which the same regular polygons appear at each vertex ) , they are generally much less symmetric than either the platonic or archimedean solids . moreover , even the centrally symmetric prisms and antiprisms generally do not possess three equivalent directions . thus , it is less obvious whether bravais lattices would still provide the optimal packings for these solids , except for prisms that tile space ( e.g. , hexagonal prism or rhombical prisms ) . in future work , it would be desirable to test whether our conjecture extends to prisms and antiprisms that possess central symmetry and three equivalent directions using the asc scheme . it is worth noting that in four dimensions , the analogs of the tetrahedron , cube , octahedron , dodecahedron and icosahedron are the four - dimensional regular simplex , hypercube , cross polytope , 120-cell and 600-cell , respectively . all of these four - dimensional polytopes possess central symmetry , except for the simplex @xcite . while the hypercube and cross polytope tile @xmath128 , the optimal packings of simplices are still likely to be non - lattices . since our conjecture for the three - dimensional platonic solids should still apply in four dimensions , the densest packings of the 120-cell and 600-cell could be their corresponding optimal lattice packings . the cross polytopes for @xmath129 no longer tile space , and their optimal packings may still be their densest lattice packings provided that @xmath6 is sufficiently small . however , in sufficiently high dimensions , the densest lattice packings of the centrally symmetric polytopes are probably no longer optimal , since lattice packings in high dimensions are known to possess huge holes " into which additional particles can be inserted , yielding higher packing densities with possibly non - lattice arrangements . indeed , it has recently been argued that disordered sphere packings in very high dimensions could be denser than any ordered packing @xcite . recent progress in particle synthesis methods have enabled the production of a wide spectrum of nanoparticle shapes such as tetrahedra @xcite , cubes @xcite , icosahedra @xcite and prisms @xcite . in such applications , it would be of great interest to predict the corresponding crystal structures , which might possess unusual symmetries and properties . the idea of incorporating collective particle motions due to the adaptive fundamental cell should still make it efficient to search the desired crystal structures formed by those polyhedral nano - building blocks . finally , it is worth noting that the asc algorithm is also suitable to generate random packings of polyhedral particles . crucial dynamical parameters of the system , such as the strain rate can be properly controlled to produce packings with varying degrees of disorder , including the maximally random jammed ones @xcite . we will explore disordered packings in future work .

we formulate the problem of generating dense packings of nonoverlapping , non - tiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem , which we call the adaptive shrinking cell ( asc ) scheme . in addition , we conjecture that the optimal packing of any convex , congruent polyhedron without central symmetry generally is not a lattice packing .

understanding the nature of dense particle packings is a subject of intense research in the physical , mathematical and biological sciences . the preponderance of previous work has focused on spherical particles , and very little is known about dense polyhedral packings . we formulate the problem of generating dense packings of nonoverlapping , non - tiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem , which we call the adaptive shrinking cell ( asc ) scheme . this novel optimization problem is solved here ( using a variety of multi - particle initial configurations ) to find the dense packings of each of the platonic solids in three - dimensional euclidean space , except for the cube , which is the only platonic solid that tiles space . we find the densest known packings of tetrahedra , icosahedra , dodecahedra , and octahedra with densities , , , and , respectively . it is noteworthy that the densest tetrahedral packing possesses _ no long - range order_. unlike the densest tetrahedral packing , which must not be a bravais lattice packing , the densest packings of the other non - tiling platonic solids that we obtain are their previously known optimal ( bravais ) lattice packings . we also derive a simple upper bound on the maximal density of packings of congruent nonspherical particles , and apply it to platonic solids , archimedean solids , superballs and ellipsoids . provided that what we term the asphericity " ( ratio of the circumradius to inradius ) is sufficiently small , the upper bounds are relatively tight and thus close to the corresponding densities of the optimal lattice packings of the centrally symmetric platonic and archimedean solids . our simulation results , rigorous upper bounds , and other theoretical arguments lead us to the conjecture that the densest packings of platonic and archimedean solids with central symmetry are given by their corresponding densest lattice packings . this can be regarded to be the analog of kepler s sphere conjecture for these solids . the truncated tetrahedron is the only non - centrally symmetric archimedean solid , the densest known packing of which is a non - lattice packing with density at least as high as . we discuss the validity of our conjecture to packings of superballs , prisms and anti - prisms as well as to high - dimensional analogs of the platonic solids . in addition , we conjecture that the optimal packing of any convex , congruent polyhedron without central symmetry generally is not a lattice packing . finally , we discuss the possible applications and generalizations of the asc scheme in the predicting the crystal structures of polyhedral nanoparticles and the study of random packings of hard polyhedra .

1212.6664

c

we have characterized the properties of the middle - aged @xmath0-ray and x - ray pulsar j0357 + 3205 ( morla ) and its tail . the x - ray spectrum of the pulsar is consistent with a magnetospheric non - thermal component plus thermal emission from hot spots ; the lack of any detected thermal component from the whole surface makes morla the coldest ns in its age range . + folding the x - ray photons at the expected pulsar period using the lat ephemeris yields marginal evidence for modulation , with 2 peaks , neither of them aligned with the single gamma - ray peak ( see figure [ figp ] ) . we confirmed the presence of a diffuse emission @xmath19 long , the largest tail of x - ray emission associated with any rotation - powered pulsar . such an extended emission can not be explained in terms of the usual bow - shock ram - pressure - dominated pulsar wind nebula . in fact , the following problems arise : + - the existence of the tail is problematic for a pulsar with such a low @xmath153 as morla ; + - no bow shock has been resolved around the pulsar ; + - the lack of any nebular emission around the pulsar , where the particle acceleration is maximum , can not be explained ; + - the nebular spectrum lacks any spatial evolution , a necessary signature of the radiative cooling of the electrons accelerated at the wind termination shock ; + - the very asymmetric brightness profile in the direction perpendicular to the main axis of the tail requires a large ad - hoc inhomogeneity of the ism around the pulsar ; + - fitting the _ xmm - newton _ nebular spectra with a powerlaw , we found the nebular n@xmath21 to be higher than the galactic value and only marginally in agreement with the n@xmath21 of the pulsar . we propose a thermal bremsstrahlung model as an alternative explanation of the tail emission . in this scenario , the emission comes from the shocked ism material heated up to x - ray temperatures . this model gives full account of the peculiar features of the tail : + - the lack of any detectable spatial evolution in the tail spectrum is due to the long bremsstrahlung cool - down time ; + - the peculiar asymmetries of the brightness profile can be interpreted in terms of small changes in the ism density that strongly affect the brehmsstralung emissivity ; + - most of the energy in the pre - shock flow is carried by the ions , while the electron temperature is responsible for the x - ray emission ; the coulomb heating time of the electrons behind the shock is fully in agreement with the lack of any detected nebular emission near the pulsar ; + - the value of n@xmath21 measured in the tail agrees both with the value obtained for the pulsar and the galactic value . + this scenario allows us to estimate some parameters of the pulsar and of the ism around it . for a bremsstrahlung - emitting tail we estimate the pulsar distance to be between 300 and 900 pc . a pulsar velocity of @xmath11900 km s@xmath2 is required , in agreement with the pulsar proper motion for distances of some hundreds parsecs and a high inclination . the mean density of the ism is required to be @xmath10.2 atoms @xmath103 and the temperature of some 10@xmath8 k. this type of hot gas usually presents lower densities , but a denser phase ( possibly detected by @xcite ) is predicted to be the result of the action of massive stellar winds and supernova explosions . however , the low metallicity we obtained from the spectral fit makes the explanation of this gas envelope more diffcult . + a high inclination of the system ( @xmath370@xmath4 ) is predicted in both models . this value provides further support to the bremsstrahlung model , where the cool - down time demands for a longer tail , and adds to the problems of a synchrotron model . for all these reasons , we believe morla s nebula to be the first example of a new `` turtle s tail '' class of thermally - emitting nebulae , ironically associated with fast moving pulsars . + until now we have no clear evidence of other pulsars characterized by a tail emitting via thermal bremsstrahlung , possibly for the requirements of a very fast pulsar and a hot , dense ism . moreover , energetic pulsars can also generate classic synchrotron nebulae , that may outshine a bremsstrahlung component . the recently discovered nebula associated with the source igr j11014 - 6103 , suspected of being a high - velocity pulsar , resembles the tail of morla : further studies of this feature could lead to a second example of a turtle s tail nebula . this work was supported by the contract swift asi - inaf 1 - 004 - 11 - 0 . we warmly thank the apj referee for the useful comments and suggestions as well as the iasf - inaf staff who constructively participated in the discussion during my `` astrosiesta '' presentation . abdo , a.a . 2009 , science , 325 , 848 abdo , a.a . 2009 , science , 325 , 840 abdo , a.a . 2009 , apj , 700 , 597 abdo , a.a . 2010 , apj , 187 , 460 anders , e. & grevesse , n. 1989 , gecoa , 53 , 197 atwood , w.b . et al . 2009 , apj , 697 , 1071 bandiera , r. 2008 , a&a , 490 , 3 becker et al . 2012 , apj , 755 , 141 bland - hawthorn , j. & reynolds , r. 2000 , arxiv : astro - ph/0006058 borkowski , k.j . et al . 2001 , apj , 548 , 820 buccheri , r. et al . 1983 , a&a , 128 , 245 bucciantini , n. , 2002 , a&a 387 , 1066 bucciantini , n. , et al . , 2005 , a&a 443 , 519 chatterjee , s. & cordes , j.m . 2002 , apj , 575 , 407 cheng , k.s . 1986 , apj , 300 , 500 cordes , j.m . 1993 , nature , 362 , 133 de luca , a. & molendi , s. 2004 , a&a , 419 , 837 de luca , a. et al . 2005 , apj , 623 , 1051 de luca , a. et al . 2011 , apj , 733 , 104 de luca , a. et al . , submitted to apj dickey , j.m . et al . 1990 , ara&a , 28 , 215 gaensler , b.m . , et al . , 2004 , apj 616 , 383 gaensler , b.m . & slane , p.o . 2006 , ara&a , 44 , 17 garmire , g.g . 2003 , spie 4851 , 28 goldreich , p. & julian , w.h . , 1969 , apj 157 , 869 harding , a.k . & muslimov , a.g . , 2001 , apj 556 , 987 harding , a.k . & muslimov , a.g . , 2002 , apj 568 , 862 harding , a.k . & muslimov , a.g . , 2004 , cosp , 35 , 562 hui , c. y. , & becker , w. 2006 , a&a , 457 , l33 hui , c.y . & becker , w. 2007 , a&a 467 , 1209 hui , c.y . 2012 , apj , 747 , 74 jacoby , g. h. et al . 1998 , proc . spie , 3355 , 721 jager , o.c . & djannati - 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using a new _ xmm - newton _ observation , we have characterized the x - ray properties of the middle - aged radio - quiet-ray pulsar j0357 + 3205 ( named morla ) and its tail . the x - ray emission from the pulsar is consistent with a magnetospheric non - thermal origin plus a thermal emission from a hot spot ( or hot spots ) . the lack of a thermal component from the whole surface makes morla the coldest neutron star in its age range . the study of the 9-long tail confirmed the lack of extended emission near the pulsar itself . the tail shows a very asymmetric brightness profile and its spectrum lacks any spatial variation . we found the nebular emission to be inconsistent with a classical bow - shock , ram - pressure dominated pulsar wind nebula . we propose thermal bremsstrahlung as an alternative mechanism for morla s tail emission . in this scenario , this can fully explain the peculiar features of the tail , assuming a hot , moderately dense interstellar medium around the pulsar . for a bremsstrahlung - emitting tail , we can estimate the pulsar distance to be between 300 and 900 pc . a pulsar velocity of km s is required - which would make morla the pulsar with the largest velocity - and high inclination angles ( ) are preferred . we propose morla s nebula as the first example of a new `` turtle s tail '' class of thermally - emitting nebulae associated to high velocity pulsars .

using a new _ xmm - newton _ observation , we have characterized the x - ray properties of the middle - aged radio - quiet-ray pulsar j0357 + 3205 ( named morla ) and its tail . the x - ray emission from the pulsar is consistent with a magnetospheric non - thermal origin plus a thermal emission from a hot spot ( or hot spots ) . the lack of a thermal component from the whole surface makes morla the coldest neutron star in its age range . we found marginal evidence for a double - peaked modulation of the x - ray emission . the study of the 9-long tail confirmed the lack of extended emission near the pulsar itself . the tail shows a very asymmetric brightness profile and its spectrum lacks any spatial variation . we found the nebular emission to be inconsistent with a classical bow - shock , ram - pressure dominated pulsar wind nebula . we propose thermal bremsstrahlung as an alternative mechanism for morla s tail emission . in this scenario , the tail emission comes from the shocked interstellar medium ( ism ) material heated up to x - ray temperatures . this can fully explain the peculiar features of the tail , assuming a hot , moderately dense interstellar medium around the pulsar . for a bremsstrahlung - emitting tail , we can estimate the pulsar distance to be between 300 and 900 pc . a pulsar velocity of km s is required - which would make morla the pulsar with the largest velocity - and high inclination angles ( ) are preferred . we propose morla s nebula as the first example of a new `` turtle s tail '' class of thermally - emitting nebulae associated to high velocity pulsars .

astro-ph0607512

c

from our study of 19,464 galaxies in the deep2 galaxy redshift survey , we conclude that the color density relation observed in the local universe is also seen at @xmath1 , with the fraction of red galaxies increasing with local galaxy overdensity at essentially all epochs studied @xmath136 and over all environments probed ( from voids to large groups ) . at all redshifts , however , there still exists a population of red galaxies in underdense environments . in addition , we find that the color density relation evolves with redshift , growing weaker with lookback time such that at @xmath4 the relationship may be nonexistent within the range of environments probed by the deep2 survey ( i.e. , not including massive clusters ) . when viewed in conjunction with the results from studies of the galaxy luminosity function at @xmath137 @xcite , our findings provide direct evidence that the red sequence is built up preferentially in overdense environments ( i.e. , galaxy groups , as deep2 does not sample rich clusters ) , thereby producing the observed increase in the slope of the red fraction versus overdensity relation at later time . these results are in agreement with the general picture painted by studies of the morphology density relation in galaxy clusters at @xmath137 . for example , building upon the work of @xcite , @xcite and @xcite find that the fraction of early type galaxies increases steadily with density in cluster environments out to @xmath9 , with the strength of the correlation weaker at @xmath9 than in local samples . corresponding work by @xcite also finds significant evolution in the morphology density relation within massive clusters at @xmath138 , with the early type fraction observed to steadily decline with increasing redshift . using data from the canada france hawaii telescope legacy survey ( cfhtls ) , @xcite similarly find that over the redshift range @xmath139 both the red fraction and early type fraction increase in high density regions with decreasing redshift . while the fraction of galaxies with early type morphologies in the @xcite sample is constant with @xmath3 in low density environments , they find that the red fraction @xmath140 steadily increases in the `` field '' from @xmath103 to @xmath11 , in constrast to our results which show no evolution in the red fraction in regions of low galaxy density at @xmath123 . the differences between our results and those of @xcite could result from the use of photometric redshifts to determine environments in that work ; as shown by @xcite , photometric redshifts can not cleanly discriminate the environments of galaxies , as even the smallest photometric redshift errors achieved are much larger than galaxy correlation lengths ( @xmath141 comoving mpc versus @xmath142 comoving mpc for @xmath143 ) . our findings also reproduce the general trend found by @xcite based on the vvds survey ; they , too , find that the color density relation weakens with redshift over the range @xmath144 . however , within their study the fraction of galaxies on the red sequence shows no significant dependence on overdensity at @xmath145 . in contrast , we find a highly significant relationship between red fraction and environment at @xmath146 , even for highly differing subsamples ; only at @xmath4 are our results consistent with density independence , as seen in fig.[redfrac_withz ] . when binning the deep2 data in the same redshift ranges as that of @xcite , the differences between the deep2 and vvds results are readily apparent ( see figure [ direct_comp ] of this work and figure 6 of * ? ? given this apparent contradiction for @xmath147 and that the work of @xcite employs the most analogous data set to that presented here , a more detailed examination is required . first of all , because rest frame galaxy colors ( which depend on photometry and coarsely on redshift ) are almost entirely independent of the environment measurements ( which depend upon angular positions and high precision redshifts ) , we consider it unlikely that the highly significant correlation between red fraction and environment , which we find at @xmath9 , is false . it persists in all four samples considered here , which should differ from each other by more than sample b should differ from the vvds volume limited sample . since there are few galaxies in the gap between the red and blue populations , modest differences in the definition of @xmath81 have minimal effect , as well , so this is unlikely to explain any differences . in an effort to conduct a more direct comparison between the vvds and deep2 results , we attempt to replicate as closely as possible those vvds subsamples for which we can establish a volume complete deep2 analogue and apply to them the same red fraction definition as employed by @xcite . while in this paper we generally define the red fraction , @xmath81 , according to a color division in @xmath45 versus @xmath34 color magnitude space , @xcite utilize a luminosity independent selection in @xmath148 . using the cfht / megacam @xmath149 and @xmath150 filter response , quantum efficiency , telescope throughput , and atmospheric extinction estimates , the k correction code ( _ kcorrect _ version v4_1_2 ) of @xcite , and our cfht @xmath35 photometry @xcite , we compute the rest frame @xmath148 color for each galaxy in the deep2 spectroscopic sample . @xcite divide samples according to johnson / cousins @xmath33band absolute magnitude in the ab system , taking @xmath20 ; this is identical to the @xmath34 used throughout this paper ( cf . we are therefore able to place the deep2 galaxies in the same color magnitude space as that of @xcite and define `` red '' according to the vvds definition ( @xmath151 ) . in order to match the vvds samples as closely as possible , we have constructed deep2 samples covering identical redshift regimes ( @xmath152 and @xmath153 ) and absolute magnitude limits ( @xmath154 ) as vvds subsamples studied by @xcite . because of the differences between the deep2 @xmath79-band and vvds @xmath155-band selections , it is possible to replicate only some of the vvds subsamples . for @xmath156 , we can construct volume limited deep2 samples down to @xmath157 , while for @xmath158 we are able to construct a volume limited sample matching the vvds @xmath159 data set , and a very nearly volume limited sample with @xmath160 . figures 7 and 8 of @xcite illustrate the red fraction versus overdensity trends for the corresponding samples drawn from vvds . as shown in figure [ ug_comp ] , the deep2 results for volume limited samples at @xmath161 and @xmath162 are consistent with the vvds results for similarly selected data sets . however , the errors on the vvds trends between red fraction and environment are significantly larger ( @xmath163 those for deep2 ) . to make this figure , we map the data points from figure 7 of @xcite onto the deep2 results by plotting the extreme - overdensity vvds points at the same abcissa values as the extreme - overdensity deep2 points . this is necessary because citetcucciati06 measures environments over much larger scales than we do in deep2 , and density contrasts on larger scales should be smaller . however , locally , at least , the same trends are found using environments measured on smaller and larger scales @xcite . no scaling , however , is applied to the vvds red fraction values , as plotted in figure [ ug_comp ] . the difference in normalization of @xmath164 between deep2 and vvds could be due to k correction errors in either sample , or , conceivably , due to a possible tendency of vvds to fail to obtain high confidence redshifts for red galaxies as often as blue , especially at @xmath135 . from this comparison to the @xcite results , we conclude that the color density relation at @xmath145 , as observed by deep2 , is generally consistent with the vvds measurements . however , due to their larger uncertainties ( likely principally due to their smaller sample size ) , the color density relation found here could not have been detected significantly by @xcite . given that a perfect match between our samples and techniques and those of @xcite is impossible , especially due to the overdensity mapping applied in figure [ ug_comp ] , we also consider other possible reasons for why a trend present in deep2 could be missed within the vvds data set . it is quite possible that fundamental differences in the samples observed could contribute to the differing conclusions at @xmath9 from the deep2 and vvds analyses . in particular , the vvds sample includes a subset of objects to @xmath165 , while deep2 samples down to a limit of @xmath24 . as a consequence , while the surveys have comparable depths for the bluest objects , vvds is deeper for red galaxies at @xmath1 , which have @xmath166@xmath167 . as a result , @xcite include fainter red galaxies in their @xmath81 measurements than we do in our standard samples ( in the volume limited subsamples , the respective depths are indentical , of course ) , and are able to study samples with color independent @xmath34 limits down to @xmath168 ( for @xmath158 ) . as shown in fig . [ ug_comp ] , however , volume limited deep2 samples matching vvds samples in luminosity range do exhibit a significant color density trend where the equivalent vvds samples do not . in addition to the @xcite sample being small ( 6,582 galaxies ) in comparison to our deep2 sample , yielding increased poisson errors , it is also limited to a single @xmath169 field , which increases the uncertainties due to sample ( or `` cosmic '' ) variance compared to our sample . the differences between our results and those of @xcite , however , are likely not attributable to cosmic variance alone . as shown in figure [ cvplot ] , the variation in the @xmath164overdensity relation from field to field within the deep2 survey is small , with each field yielding a color density relation consistent with that of the full sample . cosmic variance mostly changes the overall red fraction in a given field and the relative abundance of the different environments , but not the strength of a trend . in addition to smaller sample sizes , which yield larger errors in @xmath164 , there are other phenomena which could obscure a true correlation between red fraction and overdensity in vvds data preferentially at high redshift . one possibility is that environment errors in the @xcite sample are large compared to their environment bins at @xmath145 . we note that the 5%95% range of measured overdensities increases with @xmath3 in their data set , as seen in fig . 6 of @xcite ; this could reflect increasing errors in their environment measures ( in the deep2 data set , in contrast , the 5%95% range in measured overdensities is nearly independent of redshift ) . another difference is that @xcite use a large smoothing kernel ( @xmath170 mpc ) in measuring environments . estimating overdensities on such large scales can be problematic due to the small number of independent resolution elements across such a small field ( at @xmath12 , @xmath171 corresponds to @xmath172 comoving mpc ) and due to the large percentage of the sample which falls within one smoothing scale length of a survey boundary or edge ( @xmath173 of the vvds field by area at @xmath9 ) . differences between the true relationship connecting color and environment on smaller scales and 5 mpc scales ( as used by * ? ? ? * ) could also account for discrepancies between deep2 and vvds results , but at @xmath174 , at least , correlations between galaxy properties and environment measurements on @xmath175 and @xmath176 mpc scales appear to differ significantly only in noise properties @xcite . finally , another effect that could dilute the measurements of @xcite results from the fact that at @xmath135 the redshift regime where a lack of a color density relation is found in the @xcite data the vvds sample is dominated by lower quality vvds redshifts ( @xmath177 , * ? ? ? a number of tests have found that the @xmath177 redshifts have a nonnegligible error rate ( @xmath178 , o. ilbert , private communication ; c. wolf , private communication ; * ? ? ? * ) , which would cause sources to be included in the @xcite sample at @xmath1 incorrectly , with both erroneous k corrections and erroneous overdensity measurements . this contamination would dilute any true correlation between rest frame color and environment . in this paper , we use only higher confidence deep2 redshifts , which have an overall failure rate below 2% based upon tests with repeated observations @xcite . while the color density results of @xcite differ when compared to the trends found in the full deep2 sample , a comparison of similar samples ( cf . fig . [ ug_comp ] ) illustrates that the deep2 and vvds results are mostly in agreement where they overlap , given the significantly larger errors for the @xcite data set , which are likely due to the smaller vvds sample size . the various sources of error discussed above ( cf . 4.1 ) could also be at play , though the dominant uncertainty appears to be statistical in nature . overall , both studies independently find that the color density relation grows weaker with increasing redshift . although trends at @xmath153 are not significant for any of the vvds samples , at lower redshift @xcite conclude that the color density relation is stronger for brighter galaxies than faint ones . in contrast , we do not observe significant variations in the color density trend for samples differing in @xmath34 . that is , over the absolute magnitude ranges probed in fig . [ ug_comp ] , the slope of the @xmath164overdensity relation exhibits no statistically significant dependence on luminosity in our measurements . the volume limited subsamples in fig . [ ug_comp ] , however , are overlapping rather than independent in luminosity and only probe a limited range of @xmath34 . thus , the lack of significant luminosity dependence to the color density relation within deep2 is not a strong statement . as shown by @xcite , the dependence of mean environment on luminosity and color is effectively separable at @xmath9 , which implies that the dependence of the color density relation on luminosity should not be strong over the luminosity range covered by deep2 . within the context of the larger picture of galaxy evolution , as discussed in 4.2 , a luminosity dependence to the evolution of the color density relation may well exist . comparison of our results and those of clustering studies at @xmath9 ( e.g. , * ? ? ? * ; * ? ? ? * ) to clustering measurements of bright galaxies at @xmath179 ( e.g. , * ? ? ? * ) lead to similar conclusions . as explained by @xcite , such a result can be easily understood as an example of cosmic `` downsizing '' @xcite , where the cessation of star formation occurs first in high luminosity galaxies or high mass halos ( i.e. , high density environments ) . however , the methods used in this paper do not detect this trend within the deep2 data set . a quite striking result from our work is the difference between the evolution of the red fraction in under and overdense environments spanning the redshift range @xmath123 ; while @xmath81 in underdense environments remains roughly constant with @xmath3 in our sample , we find that the red fraction in dense environments decreases with @xmath3 , such that it is roughly equal to the fraction in underdense environments at @xmath98 . studying the properties of group galaxies in deep2 , @xcite find similar evolution in the color density relation from @xmath180 , with the fraction of blue galaxies in groups becoming comparable to that of the field at @xmath15 . given @xmath175 gyr to move from the blue cloud to the red sequence ( e.g. , * ? ? ? * ; * ? ? ? * ) , if the color density relation first arises at @xmath181 , then the physical mechanisms responsible must start to become operative at @xmath182 within a concordance cosmology . this observed evolution in the color density relation and the existence of an epoch at which environment dependent quenching initiates are both consistent with the current theoretical picture in which the conversion of blue galaxies into members of the red sequence occurs in dark matter halos with mass greater than some critical value @xmath183 . as halos pass this mass threshold in such hot flow / cold flow accretion models , the infalling cold gas supply to the central galactic disk is virial shocked and shut off such that the galaxy will quickly burn its remaining fuel and redden ( e.g. , * ? ? ? * ; * ? ? ? * ) . within the models of @xcite and others ( see also * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , low energy agn activity is included to suppress the cooling of shocked gas and the recommencement of star formation . at yet higher redshifts @xmath184 , even in halos above this critical threshold , quenching does not occur since cooling is effectively able to remove the pressure support behind the virial shock @xcite . at later times , the evolution of the halo mass function @xcite in combination with the near redshift independence of the critical mass @xcite leads to a continual increase in the number of halos above the threshold mass . given the correlation between halo mass and environment in simulations ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , this thereby predicts an evolution in the color density relation ( i.e. , becoming stronger ) at @xmath185 . in this picture , the color density or morphology density relation within cluster environments likely persists out to higher redshifts , as cluster galaxies reside in the most massive halos , those first to reach the critical mass at @xmath179 . as deep2 primarily samples the more common , less massive groups , the color density relation is still weak at somewhat later times , @xmath15 . in addition to predicting evolution of the color density relation at @xmath186 , these hot flow / cold flow accretion models also provide an additional mechanism by which to explain the presence of red galaxies residing in underdense regions ( cf . 3.2 ) . while passive evolution or merging of several smaller galaxies to form a fossil group are also viable physical mechanisms by which to create such galaxies , the tail ( at @xmath187 ) of the halo mass function in low density environments naturally leads to the existence of at least some true red sequence galaxies in voids . the measured evolution in the color density relation as presented here should be directly related to measurements of galaxy clustering at high redshift . we predict that the clustering of @xmath5 galaxies at @xmath188 should depend only weakly on color . studies of galaxy clustering by spectral type or by color at high redshift ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) have shown that blue , star forming galaxies at @xmath9 are less strongly clustered than their red counterparts . such clustering work , however , spans a broad redshift range ( extending to redshifts less than unity ) and the galaxy samples utilized are dominated in number by galaxies at @xmath158 , where we still find a significant color density relation . unfortunately , the deep2 sample includes a modest number of galaxies @xmath189 at @xmath190 , with very few on the red sequence ; we therefore lack the statistical power needed to compute correlation strengths for subsamples by galaxy color at such redshifts . at yet higher redshifts @xmath184 there are indications that clustering depends on color . studies of uv selected galaxies and red , near ir bright galaxies have found significant differences in clustering strengths depending on the sample selection , with the latter being more strongly clustered ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? furthermore , within near ir bright samples , the measured correlation length depends significantly on apparent color ( e.g. , @xmath191 or @xmath192 ) , such that blue near ir bright galaxies cluster like uv selected lyman break galaxies ( lbgs ) , while the red near ir bright galaxies exhibit a correlation length larger by a factor of roughly two @xcite . the red , near ir bright samples observed at early epochs , however , are likely the antecedents of the rarest , most massive red galaxies today and are not representative of the progenitors of deep2 galaxies ; their correlation length at @xmath193 already exceeds that of the brightest and reddest deep2 galaxy samples . presumably , if we were to study similarly extreme samples at @xmath15 ( e.g. , galaxies in massive clusters analogous to the candidates studied by * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , we should find a significant color density relation . instead , the progenitors of deep2 galaxies were bluer and/or fainter at @xmath179 and resembled the lbgs more than those red galaxies which are most readily observed at high redshift . thus , our observations of the evolution of the red fraction in low density and high density environments do not contradict the current set of clustering measurements at higher redshift @xmath7 or observations of massive clusters at @xmath1 . like the cluster galaxies , the red , near ir selected , massive galaxies seen at high @xmath3 , given their observed clustering , are likely to reside in very massive halos , which should be the first halos to cross the threshold quenching mass . in fact , estimates of their star formation rates indicate that they are actively forming stars in large quantities @xcite ; hence , they do not appear to generally have been quenched at @xmath179 , though more recent observations of near ir selected galaxies at @xmath179 indicate relatively low star formation activity in at least a portion of the massive galaxy population at high redshift @xcite .

using a sample of 19,464 galaxies drawn from the deep2 galaxy redshift survey , we study the relationship between galaxy color and environment at . the entire redshift regime studied , we find that the color density relation evolves continuously , with red galaxies more strongly favoring overdense regions at low relative to their red sequence counterparts at high redshift . at , the red fraction only weakly correlates with overdensity , implying that any color dependence to the clustering of galaxies at that epoch must be small . our findings add weight to existing evidence that the build up of galaxies on the red sequence has occurred preferentially in overdense environments ( i.e. , galaxy groups ) at . furthermore , we identify the epoch at which typical galaxies began quenching and moved onto the red sequence in significant number .

using a sample of 19,464 galaxies drawn from the deep2 galaxy redshift survey , we study the relationship between galaxy color and environment at . we find that the fraction of galaxies on the red sequence depends strongly on local environment out to , being larger in regions of greater galaxy density . at all epochs probed , we also find a small population of red , morphologically early type galaxies residing in regions of low measured overdensity . the observed correlations between the red fraction and local overdensity are highly significant , with the trend at detected at a greater than level . over the entire redshift regime studied , we find that the color density relation evolves continuously , with red galaxies more strongly favoring overdense regions at low relative to their red sequence counterparts at high redshift . at , the red fraction only weakly correlates with overdensity , implying that any color dependence to the clustering of galaxies at that epoch must be small . our findings add weight to existing evidence that the build up of galaxies on the red sequence has occurred preferentially in overdense environments ( i.e. , galaxy groups ) at . furthermore , we identify the epoch at which typical galaxies began quenching and moved onto the red sequence in significant number . the strength of the observed evolutionary trends at suggests that the correlations observed locally , such as the morphology density and color density relations , are the result of environment driven mechanisms ( i.e. , `` nurture '' ) and do not appear to have been imprinted ( by `` nature '' ) upon the galaxy population during their epoch of formation .