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two different temperature dependencies of the thermal conductivity are observed , for @xmath0 : linear at low magnetic field and quadratic for magnetic field larger than 1 tesla . at the same field value , a plateau appears in the field dependency of the residual term of thermal conductivity .

r

1405.0817

we performed thermal conductivity measurements on a single crystal of the ferromagnetic superconductor ucoge under magnetic field . two different temperature dependencies of the thermal conductivity are observed , for @xmath0 : linear at low magnetic field and quadratic for magnetic field larger than 1 tesla . at the same field value , a plateau appears in the field dependency of the residual term of thermal conductivity . such observations suggest a multigap superconductivity with a line of nodes in the superconducting gap . thermal conductivity , ferromagnetic superconductor , multigap , re - entrance of superconductivity , ucoge . 74.20.rp,74.25.fc,71.27.+a ,

( color online ) lorenz ratio @xmath39 obtained from the thermal conductivity and resistivity data presented in figure [ fig : kappa_rho_hb]a . all the curves extrapolate to 1 at @xmath40k , reflecting the good quality of the measurement . in inset the residual thermal conductivity contribution ( @xmath41 ) is shown ( see text).,scaledwidth=48.0% ] + in figure [ fig : ll0 ] the lorenz ratio ( @xmath42 ) calculated for different values of the magnetic field applied along the @xmath30 crystallographic direction is plotted . for @xmath21 the wiedemann - franz law @xmath43 is obeyed within 5% which reflect the validity of our measurements . the equality indicates that at low temperatures , electrical and thermal currents are transported by the same carriers : the electrons . at finite temperatures two effects can produce a deviation from the unity of @xmath44 . other thermal carrier channels such as phonon or magnon excitations will enhance this ratio . in contrary the ratio will be lower than one if a strong electron electron inelastic scattering , reducing the efficiency of electronic thermal conductivity , dominates @xcite . in a conventional metal , magnons are absent and as few phonons are present at low temperatures , the ratio is reduced below 1 for the lowest temperatures and exceeds 1 in the higer temperatures regime due to the phonons contribution . the depth of the minimum in @xmath44 depends on the mean free path of the quasiparticles . as the sample investigated has a relatively low @xmath45 value the mean free path of the quasiparticles is short and only a weak deviation from 1 is expected for @xmath44 at low temperatures . in figure [ fig : ll0 ] the increase of @xmath44 above 1 from the lowest temperatures indicates the presence of another type of heat carrier than the electrons . as ucoge is ferromagnetic , magnons or uniaxial fluctuations are good candidates @xcite . an analysis of the anisotropy of this contribution with heat current direction re - enforce this hypothesis @xcite . we can obtain the approximate value of this additional thermal conductivity contribution ( @xmath46 ) by assuming the lorenz ratio is 1 for the electronic contribution : @xmath47 with @xmath48 @xmath49 @xmath50 . we found that the magnetic contribution is independent of a magnetic field applied along the @xmath30 crystallographic direction ( inset figure [ fig : ll0 ] ) while it is strongly reduced by a magnetic field applied in the @xmath15 crystallographic direction , as expected for longitudinal spin fluctuations @xcite and in agreement with a previous study using a different technique to extract the magnetic contribution @xcite . in order to further analyze the temperature dependence of thermal conductivity , we subtract the additional contribution obtained previously ( @xmath51 ) and calculated the thermal conductivity one would observe if the compound was not superconducting , hereafter called normal contribution to thermal conductivity ( @xmath52 ) . this is done by extrapolating the normal state resistivity to @xmath21 assuming a fermi liquid dependence ( @xmath53 ) . then we calculated the electronic contribution to thermal conductivity using the wiedemann franz law : @xmath54 . note that this is only possible due to the moderate @xmath45 value of the sample , when practically no deviation from the wiedemann franz law are expected . indeed , for a more general study @xcite , a phenomenological model had to be introduced for the electronic thermal conductivity which prevent any further discussion of the temperature dependence . the ratio of superconducting to `` extrapolated normal state '' thermal conductivity in the superconducting state ( @xmath55 ) is reported in figure [ fig : ks_kn_t ] ( a ) and ( b ) for different magnetic fields applied along the @xmath30 crystallographic direction . such ratio is related to the fraction of superfluid quasiparticles . we can clearly distinguish two different temperatures dependencies : linear for @xmath56 t and quadratic otherwise . panel ( c ) of figure [ fig : ks_kn_t ] emphases the linear and quadratic temperature dependencies with a double logarithmic plot . the temperature dependence of thermal conductivity is related to the type of nodes ( points , lines ) and their opening angle @xcite . the different temperature dependencies indicate two different gap structures depending on the field range . there is no report of a phase transition between two different superconducting phases , neither with temperature nor upon applying a magnetic field , as required in order to modify the symmetry of the superconducting gap and our measurements support a crossover . therefore , we infer a multigap superconducting state and not multiple superconducting states . the low field temperature dependence would then result from the addition of the thermal conductivity of the two bands , while at high fields only the band with the larger superconducting gap would be superconducting . the high magnetic field temperature dependence , @xmath57 , suggests the presence of a line of nodes in the gap of the superconducting band , as expected in analogy to urhge @xcite . note that the observation of two different field ranges is independent of the temperature dependence of the subtracted @xmath46 contribution . a similar evolution of the temperature dependence of thermal conductivity was observed in well known two - band superconductors such as mgb@xmath11 @xcite , cecoin@xmath58 @xcite and nbse@xmath11 @xcite although with different power laws . the small deviation from linearity of @xmath55 at low temperatures ( @xmath59 ) for @xmath60 t is understood in the multigap scenario as corresponding to the characteristic energy of the smaller gap ( figures [ fig : kappa_rho_hb ] ( a ) and [ fig : ks_kn_t ] ) . ( color online ) field dependence of the ratio @xmath61 : ( a ) for @xmath8 ( red squares ) , ( b ) for @xmath0 ( orange circles ) . ( c ) comparison between @xmath62 ( see text ) of ucoge and the single gap superconductor nb ( black squares @xcite ) and the two - band superconductors pros@xmath35sb@xmath63 ( green triangles @xcite ) , mgb@xmath11 @xmath64 ( blue diamonds @xcite ) and mgb@xmath11 @xmath8 ( violet stars @xcite ) . @xmath65 of ucoge is taken as 25 tesla in ( c).,scaledwidth=48.0% ] the idea of a multigap superconductivity is re - enforced by the appearance of a plateau above @xmath66 t in the field evolution of the residual term of thermal conductivity , for @xmath0 ( figure [ fig : ks_kn_h ] ( b ) ) . the experimental resolution might not allow to observe such feature for @xmath8 ( figure [ fig : ks_kn_h ] ( a ) ) . the decoupling between the two gaps might also be weaker in this configuration . if we assume that the residual term for @xmath60 t is due to an inhomogeneous part of the sample never superconducting , we can extend the analysis by comparing ucoge to well established two gaps superconductors , as pros@xmath35sb@xmath63 and mgb@xmath11 ( fig . [ fig : ks_kn_h ] ( c ) ) . here we have assumed two parallel contributions to thermal conductivity @xmath67 , with @xmath68 and @xmath69 for the never superconducting contribution . @xmath69 is assumed to be field independent . independently of this assumption , the three systems : ucoge , pros@xmath35sb@xmath63 and mgb@xmath11 presented in figure [ fig : ks_kn_h ] are characterized by two energy scales corresponding to the values of the two respective gaps . the field dependence of @xmath70 for a single gap superconductor is drastically different to the one found in ucoge as demonstrated with the case of nb . a ferromagnetic system has inherently two bands , for majority and minority electron spins . it is therefore tempting to map the two superconducting gaps to the two ferromagnetic bands . the different strength of superconductivity could then be explained by the proximity to the lifshitz phase transition , previously reported @xcite . the strong increase of density of state would enhance the superconducting coupling . it is however not clear whether such bands could be decoupled enough electronically to induced multigap superconductivity . a classical scenario of the two gaps occurring on different fermi pockets is another possibility .

the spectral energy distribution suggests that pg 1254 + 047 is intrinsically x - ray weak , in addition to being heavily x - ray absorbed . if the x - ray absorber forms in a wind that is radiatively accelerated to the bal velocities , then the wind must be launched from a radius of about @xmath7 cm with a mass loss rate of @xmath8 m@xmath9 yr@xmath10 .

i

astro-ph0108383

we present _ chandra _ observations of the radio - quiet broad absorption line ( bal ) qso pg 1254 + 047 . we find that it is a weak x - ray source , with a total of @xmath0 photons measured in 36 ksec across the observed energy range @xmath1 kev . its x - ray weakness is consistent with the known correlation between @xmath2 and the strength of the uv absorption lines . the spectral energy distribution suggests that pg 1254 + 047 is intrinsically x - ray weak , in addition to being heavily x - ray absorbed . the x - ray absorption column density is @xmath3 @xmath4 for neutral gas , while the intrinsic ( unabsorbed ) emission spectrum has @xmath5 . the data are fit best by including an ionized ( rather than neutral ) absorber , with column density @xmath6 @xmath4 . the degree of ionization is consistent with the uv bals , as is the total column density if the strongest uv lines are saturated . if the x - ray absorber forms in a wind that is radiatively accelerated to the bal velocities , then the wind must be launched from a radius of about @xmath7 cm with a mass loss rate of @xmath8 m@xmath9 yr@xmath10 .

almost all quasi - stellar objects ( qsos ) are x - ray sources . the reprocessing of the x - rays by intervening matter along the line - of - sight to the qso imprints informative features on the resulting spectrum ( e.g. , turner 1991 ) . x - ray absorption studies provide an important tool to determine the physical and chemical state of the gas associated with qsos ( e.g. , netzer 1996 ) . a subclass of qsos that have interesting x - ray properties in terms of continuum strength and absorption are the broad absorption line ( bal ) qsos ( foltz et al . 1990 ; weymann et al . they display broad ( fwhm @xmath11 km s@xmath10 ) absorption lines in the rest - frame ultraviolet ( uv ) , which originate in an outflow of matter from the central engine of the qso . the outflow velocity may reach up to @xmath12 ( foltz et al . determining the relation between the gases producing the x - ray and uv absorption has profound implications for the wind properties , such as geometry , launch radius , acceleration mechanism and mass loss rate ( e.g. , mathur , elvis , & singh 1995 ; murray , chiang , & grossman 1995 ; hamann 1998 ) . balqsos are also usually x - ray faint , especially in soft x - rays ( brandt , laor , & wills 2000 ) . the similarity of balqsos and non - balqsos in other parts of the spectrum suggest that x - ray weakness is due to heavy absorption . the high ionization state inferred from the uv absorption lines indicates that the x - ray absorbers are not generally neutral ; they could be similar to the `` warm '' absorbers measured frequently in seyfert 1 galaxies ( george et al . 1998 ; reynolds 1997 ) . one major obstacle to understanding the relationship between bals and the x - ray absorbers has been that the total column densities derived from the bals ( typically @xmath13 @xmath4 , hamann , korista & morris 1993 ) , are 3 or more orders of magnitude less than those deduced from x - rays ( cf . brandt et al . 2000 ; gallagher et al . 1999 ; green et al . 2001 ) . however , there is now growing evidence that the bals are much more optically thick than previously realized ( hamann 1998 , arav et al . 1999 , wang et al . 1999 ) , and therefore the total column densities in _ outflowing _ bal gas may be as large as the x - ray absorbers . the correlated appearance of uv and x - ray absorption features ( brandt et al . 2000 ) shows clearly that the two absorbers are ( somehow ) physically related . a key question now is whether these features are manifestations of the same gas . in this paper , we discuss chandra x - ray observations of pg 1254 + 047 . this object shows bals ( @xmath14 ) that are blueshifted with respect to the systemic velocity of the qso ( @xmath15 ) . it is also characterized by being an x - ray faint source ( wilkes et al . hamann ( 1998 ) used the relative strengths of the bals in this source to show that 1 ) most of the lines are saturated and , 2 ) the total column density is _ at least _ @xmath16 @xmath4 . those results probably apply generally to balqsos , but pg 1254 + 047 is of particular interest because its bals are `` detached '' from the emission lines appearing at blueshifted velocities from @xmath1715,000 to @xmath1727,000 km s@xmath10 . if there is a high column density x - ray absorber in this source that can be identified with the bal gas , then that x - ray absorber must also be outflowing at minimally @xmath18 km s@xmath10 . such a finding would substantially impact the derived mass loss rates and place severe constraints on models of the wind acceleration ( hamann 1998 ; hamann & brandt 2001 ) . our aim here is to determine the properties of the x - ray spectrum , search for signs of absorption , and define the relationship between the uv and x - ray absorbing gas .

its x - ray weakness is consistent with the known correlation between @xmath2 and the strength of the uv absorption lines . the x - ray absorption column density is @xmath3 @xmath4 for neutral gas , while the intrinsic ( unabsorbed ) emission spectrum has @xmath5 . the data are fit best by including an ionized ( rather than neutral ) absorber , with column density @xmath6 @xmath4 . the degree of ionization is consistent with the uv bals , as is the total column density if the strongest uv lines are saturated .

r

astro-ph0108383

we present _ chandra _ observations of the radio - quiet broad absorption line ( bal ) qso pg 1254 + 047 . we find that it is a weak x - ray source , with a total of @xmath0 photons measured in 36 ksec across the observed energy range @xmath1 kev . its x - ray weakness is consistent with the known correlation between @xmath2 and the strength of the uv absorption lines . the spectral energy distribution suggests that pg 1254 + 047 is intrinsically x - ray weak , in addition to being heavily x - ray absorbed . the x - ray absorption column density is @xmath3 @xmath4 for neutral gas , while the intrinsic ( unabsorbed ) emission spectrum has @xmath5 . the data are fit best by including an ionized ( rather than neutral ) absorber , with column density @xmath6 @xmath4 . the degree of ionization is consistent with the uv bals , as is the total column density if the strongest uv lines are saturated . if the x - ray absorber forms in a wind that is radiatively accelerated to the bal velocities , then the wind must be launched from a radius of about @xmath7 cm with a mass loss rate of @xmath8 m@xmath9 yr@xmath10 .

we want to understand the reason behind the low count rate : is it due to intrinsic absorption , intrinsic x - ray weakness , or both ? given the paucity of photons detected , our approach is that of elimination , starting with the simplest model and increasing the level of complexity only after exhausting all means to satisfactorily fit the data with a given model . throughout the analysis we assume solar abundances . we also use xspec for @xmath25 minimization after binning the spectrum to have at least 10 counts / bin . based on experimentation , we find that @xmath25 analysis leads to outcomes similar to cash statistics . the results of @xmath25 statistics are listed in table 1 . we explain below the models in more detail . _ model a _ : we fit the data with a power law continuum of the form @xmath26 , where @xmath27 is the normalization of the power law at 1 kev , in units of photons @xmath4 s@xmath10 kev@xmath10 , and @xmath28 is the x - ray photon index , absorbed by a galactic column density of @xmath29 @xmath4 ( lockman & savage 1995 ) . both the normalization and the photon index were left as free parameters ( figure 2 ) . the slope was found to be rather flat , @xmath30 , for a qso , where usually @xmath31 in the observed frame of 0.5 - 10 kev ( reeves et al . the flatness of the x - ray slope suggests that there is additional intrinsic absorption . _ model b _ : we adopt a `` normal '' qso continuum , specified by @xmath32 and @xmath33 ( laor et al . 1997 ) , with @xmath34 , where @xmath35 and @xmath36 are the rest - frame specific fluxes at 2500 and 2 kev , respectively . we attenuate this continuum through an intrinsic neutral absorber , with @xmath37 , at @xmath38 . we derive the rest - frame @xmath35 from its b - magnitude , including the appropriate galactic dereddening , @xmath39 ( lockman & savage 1995 ) , and the k - correction ( see green 1996 ) . the choice of @xmath40 then determines the normalization of the power law at the observed energy of 2 kev@xmath41 . in figure 3 , the poor fit at low energies suggests intrinsic absorption , while the bad overall fit indicates that the observed x - ray weakness can not be explained by absorption alone . the bad overall fit indicates that pg 1254 + 047 is both intrinsically x - ray weak and heavily absorbed . the large discrepancy between the data and model is due to the fact that absorption not only decreases the x - ray flux but also deforms the intrinsic spectrum , where the effect is most pronounced at low energies . _ model c _ : to study the possibility of both intrinsic x - ray weakness and absorption , we remove the constraint that @xmath33 and hence allow the normalization of the power law to vary . the fits improve drastically , though not to the extent of giving an acceptable fit ( @xmath42 ) . we show the results in figure 4 . it is evident that the fit does not strongly support neutral absorption due to the large discrepancy between the data and the models at soft energies . also , we know that there is no neutral absorber with the above quoted column density because the uv spectra do not contain low - ionization metal lines ( hamann 1998 ) . _ model d _ : we explore absorption by ionized gas . we hereafter leave the normalization as a free parameter . the amount of absorption depends on the intrinsic total hydrogen column density and the ionization parameter , @xmath43 , defined as the ratio of the density of hydrogen ionizing photons to that of hydrogen particles ( h@xmath44 + h@xmath45 ) . we model the ionized absorber using the photoionization code cloudy ( ferland et al . we generate a grid of qso continua attenuated through ionized absorbers described by a grid of @xmath43 and @xmath46 . the incident continuum is a piecewise powerlaw ( zheng et al . 1996 ; laor et al . 1997 ) , which is similar to that used in hamann ( 1998 ) . the ultimate results are not critically dependent on the shape the continuum , as long as it in general agreement with that of qsos ( hamann 1997 ) . we then use xspec to interpolate on this grid to find the best fitting model of the observed continuum . hamann ( 1998 ) derived the range of @xmath43 and @xmath46 values that are consistent with the measured bals ( his figure 7 ) . larger total @xmath46 must be accompanied by large @xmath43 . for model d we fix @xmath47 to be consistent with both the bal data and the large x - ray column densities derived here . the resulting fit ( figure 5 ) improves considerably with @xmath48 and @xmath49 @xmath4 . the value of @xmath27 corresponds to an intrinsic ( unabsorbed ) @xmath50 , suggesting that pg 1254 + 047 is intrinsically x - ray weak . we comment more on this in the following section . _ model e _ : it is similar to model d , except that we use a steeper powerlaw index of @xmath51 . the final results do not deviate a lot from those of model d. we experimented with this steep spectrum to see if we can evade the requirement of intrinsic x - ray weakness which the previous models suggested ( see discussion below ) . for the models with intrinsic absorption ( b - e ) , we also experimented with putting the x - ray absorber at the redshift of the uv absorption lines instead of at the systemic velocity of the qso . this redshift difference is unresolvable with acis . nonetheless placing the x - ray absorber at @xmath52 leads to lower column densities ( by a factor of less than 2 ) .

we observe an underlying , diffuse population of old stars , following an r@xmath1 distribution , confirming that this system is somewhat relaxed . the lack of tidal features and multiple bulges , combine with the need for an exceptionally massive ( @xmath5 m@xmath3 ) cold gas reservoir , suggest that this star formation is not the result of a merger of gas - rich galaxies .

r

1211.7058

we present _ hubble space telescope wide field camera 3 _ observations of the core of the phoenix cluster ( spt - clj2344 - 4243 ) in five broadband filters spanning rest - frame 10005500 . these observations reveal complex , filamentary blue emission , extending for @xmath040 kpc from the brightest cluster galaxy . we observe an underlying , diffuse population of old stars , following an r@xmath1 distribution , confirming that this system is somewhat relaxed . the spectral energy distribution in the inner part of the galaxy , as well as along the extended filaments , is a smooth continuum and is consistent with that of a star - forming galaxy , suggesting that the extended , filamentary emission is not due to the central agn , either from a large - scale ionized outflow or scattered polarized uv emission , but rather a massive population of young stars . we estimate an extinction - corrected star formation rate of 798 @xmath2 42 m@xmath3 yr@xmath4 , consistent with our earlier work based on low spatial resolution ultraviolet , optical , and infrared imaging . the lack of tidal features and multiple bulges , combine with the need for an exceptionally massive ( @xmath5 m@xmath3 ) cold gas reservoir , suggest that this star formation is not the result of a merger of gas - rich galaxies . instead , we propose that the high x - ray cooling rate of @xmath62700 m@xmath3 yr@xmath4 is the origin of the cold gas reservoir . the combination of such a high cooling rate and the relatively weak radio source in the cluster core suggests that feedback has been unable to halt cooling in this system , leading to this tremendous burst of star formation .

in figure [ fig:3x2 ] we show the newly - acquired far - uv through optical hst images of the core of the phoenix cluster , which provide a detailed picture of this system . these images show significant , extended filamentary emission at all wavelengths from @xmath610005500 , overlaid on a relatively smooth population of older , red stars . the most extended pair of filaments to the north of the bcg are @xmath66@xmath19 ( 40 kpc ) in length , similar to the most extended filaments seen in abell 1795 @xcite , and the perseus cluster @xcite . we measure a total rest - frame far - uv flux density of f@xmath20 = 1.26@xmath2110@xmath22 erg s@xmath4 @xmath23 hz@xmath4 , consistent with the galex - derived flux presented in @xcite . the fact that such complex , filamentary morphology is present in all five filters suggests that the bcg is forming stars at a prodigious rate . in the wavelength range covered , there may be contributing emission from the @xmath241549 ( f225w ) , [ ] ( f625w ) , and [ ] and h@xmath25 ( f814w ) lines . however , the f336w and f475w bands , which have similar surface brightnesses to the other three bands , should be relatively free from emission lines , suggesting that young stars , not ionized gas , is the dominant source of the observed flux in figure [ fig:3x2 ] . in figure [ fig : rgb ] we show a three - color ( f475w , f625w , f814w ) image of the cluster core . this figure shows a clear difference in the stellar populations between the young ( blue ) filaments and the underlying , smoothly - distributed , old ( red ) stars . the peak of the emission in all bands is coincident ( within the positional uncertainties ) with the x - ray point source . to the northwest and southeast of the emission peak are dark lanes , most likely due to obscuration by dust . overall , the color of the filamentary emission appears roughly constant with radius , and is reminiscent of a young , star - forming galaxy . we see no evidence for multiple bulges or tidal features , both of which would indicate that this system is the result of a recent merger of gas - rich galaxies . figure [ fig : sbprof ] shows the multi - band surface brightness profiles of the bcg ( left panel ) , which have been computed along radial cuts at four different angles ( 90@xmath26 , 120@xmath26 , 180@xmath26 , 210@xmath26 ) , chosen to avoid the blue , filamentary emission . the radial surface brightness profile follows an r@xmath1 profile , which is typical of relaxed , early - type galaxies @xcite . such r@xmath1 surface brightness distributions are also common in the final stages ( single - nucleus ) of low - redshift ( @xmath27 ) gas - rich mergers ( ulirgs ; e.g. , * ? ? * ; * ? ? ? however , with a half - light radius of @xmath617 kpc and a stellar mass of @xmath28 m@xmath3 @xcite , this bcg is a factor of @xmath64 larger in size @xcite , a factor of @xmath660 higher in stellar mass @xcite , and resides in an environment @xmath650100 times richer @xcite than normal for @xmath27 ulirgs . projecting these 1-dimensional profiles back onto the sky , we can separate diffuse , giant elliptical emission ( middle panel ) from clumpy , star - forming emission ( right panel ) . the lack of smooth , arcing tidal features and multiple bulges in the residual image ( right panel ) suggests that this complex , extended emission did not originate from a recent merger with one or more gas - rich disk galaxies . all of these factors argue that the phoenix bcg is unlike a traditional ulirg by any definition other than the high total infrared luminosity . in figure [ fig : sed ] we provide the spectral energy distribution ( sed ) in several representative regions around the bcg . the diffuse emission at large and small radii indicate a significant positive age gradient in the diffuse population . at large ( r @xmath640 kpc ) radii , the diffuse emission is qualitatively consistent with a 25 gyr old elliptical galaxy , while at smaller radii ( @xmath620 kpc ) the diffuse stellar populations appear to be much younger ( bluer ) , similar in color to a star - forming spiral galaxy . the extended , morphologically - complex filaments , after subtraction of the diffuse stellar component , show an excess of uv emission at all radii . the sed of the brightest filaments appear remarkably similar to the diffuse component in the central region , suggesting that these stars are being mixed on short timescales . in the faintest , most extended filaments , there is a substantial excess of emission in the f225w and f625w filters , at the location of the redshifted @xmath241549 and [ ] lines , respectively , suggesting that these filaments may also contain warm ( @xmath29k ) , ionized gas a scenario supported by the extended emission lines reported in @xcite . the overall flatness of the sed in the uv - bright regions is exactly what one would expect for a mix of young stars and warm , ionized gas , given the width of the broadband filters . at the peak of the optical emission , coincident with the x - ray source , the sed is qualitatively well matched by a dusty type-2 qso @xcite , which is consistent with our x - ray observations of a highly - reddened hard x - ray point source . the combination of figures [ fig:3x2][fig : sed ] paint a picture of an old , giant elliptical galaxy that is experiencing a resurgence of star formation . below we re - evaluate the sfr in this system and describe various scenarios to explain this star - forming activity , building on the discussion of @xcite .

the spectral energy distribution in the inner part of the galaxy , as well as along the extended filaments , is a smooth continuum and is consistent with that of a star - forming galaxy , suggesting that the extended , filamentary emission is not due to the central agn , either from a large - scale ionized outflow or scattered polarized uv emission , but rather a massive population of young stars . instead , we propose that the high x - ray cooling rate of @xmath62700 m@xmath3 yr@xmath4 is the origin of the cold gas reservoir .

c

1211.7058

we present _ hubble space telescope wide field camera 3 _ observations of the core of the phoenix cluster ( spt - clj2344 - 4243 ) in five broadband filters spanning rest - frame 10005500 . these observations reveal complex , filamentary blue emission , extending for @xmath040 kpc from the brightest cluster galaxy . we observe an underlying , diffuse population of old stars , following an r@xmath1 distribution , confirming that this system is somewhat relaxed . the spectral energy distribution in the inner part of the galaxy , as well as along the extended filaments , is a smooth continuum and is consistent with that of a star - forming galaxy , suggesting that the extended , filamentary emission is not due to the central agn , either from a large - scale ionized outflow or scattered polarized uv emission , but rather a massive population of young stars . we estimate an extinction - corrected star formation rate of 798 @xmath2 42 m@xmath3 yr@xmath4 , consistent with our earlier work based on low spatial resolution ultraviolet , optical , and infrared imaging . the lack of tidal features and multiple bulges , combine with the need for an exceptionally massive ( @xmath5 m@xmath3 ) cold gas reservoir , suggest that this star formation is not the result of a merger of gas - rich galaxies . instead , we propose that the high x - ray cooling rate of @xmath62700 m@xmath3 yr@xmath4 is the origin of the cold gas reservoir . the combination of such a high cooling rate and the relatively weak radio source in the cluster core suggests that feedback has been unable to halt cooling in this system , leading to this tremendous burst of star formation .

the deep , high spatial resolution hst uv and optical imaging presented in 3 have revealed an exceptionally complex system . below we utilize this improved spatial resolution to estimate a new , uv - derived sfr for the bcg in the phoenix cluster , followed by a discussion of three possible origins for the extended , filamentary uv emission . the sfr reported in @xcite , while utilizing an array of multi - wavelength data , necessarily required multiple assumptions to remove agn contamination . with the addition of high - resolution hst uv imaging , we avoid such assumptions , leaving only the ( typical ) assumptions of dust extinctions and star formation laws . @xmath21 0.2@xmath19 bins overlaid in regions with @xmath30 detections in both the f336w and f475w bands . right : smoothed reddening map , derived assuming a flat uv sed in the absence of reddening @xcite . this map allows us to perform _ local _ reddening corrections on the uv images , yielding a more tightly constrained estimate of the extinction - corrected uv luminosity.,scaledwidth=49.0% ] to estimate the reddening , we assume that the reddening - free sed is flat at 15003000 @xcite . since the f225w filter may be contaminated by emission , we use the mean @xmath31 ( rest frame @xmath32 ) flux ratio to derive a reddening correction , assuming @xmath33 for e(b - v ) = 0 . in figure [ fig : ebv ] we show the spatial distribution of the reddening , e(b - v ) , over regions with significant ( @xmath34 ) uv flux . we note that the mean reddening in this map agrees well with the reddening presented in @xcite from balmer line ratios ( e(b - v ) = 0.34 ) . using the _ local _ reddening correction and uncertainty we can accurately correct the uv luminosity , resulting in a more confident estimate of l@xmath35 = 5.7 @xmath2 0.3 @xmath21 10@xmath36 erg s@xmath4 hz@xmath4 and a uv - derived sfr of 798 @xmath2 42 m@xmath3 yr@xmath4 @xcite . given the near - ir - estimated stellar mass of m@xmath37 m@xmath3 @xcite , this high sfr implies that in 100 myr the central galaxy in the phoenix cluster will form 23% of its stellar mass . we note that this estimate is consistent with the agn - subtracted sfr quoted in @xcite of 739 @xmath2 160 m@xmath3 yr@xmath4 and with the empirical , extinction - implicit , method of @xcite , which yields sfr@xmath38 m@xmath3 yr@xmath4 . inspired by the high far - infrared luminosity , coupled with the hard x - ray and radio source , a viable explanation for this system is a dusty agn driving a large - scale outflow . while there is undoubtedly a powerful agn in the core of the phoenix cluster , the new hst data suggest that the substantial uv luminosity can not be fully attributed to a point - like agn . only a small fraction ( @xmath3910% ) of the total uv luminosity originates from a central point source , with the majority originating from extended , filamentary regions . furthermore , the high relative fluxes in the f336w and f475w bands , which should be free from line emission , suggest that the majority of the uv / optical flux in these complex filaments is continuum emission . we also find a general lack of uv / blue emission along the minor axis of the central galaxy , contrary to what is typically observed in wide - angle agn - driven outflows @xcite . thus , we argue that the filamentary uv emission does not result from an outflow . in iras 09104 + 4109 ( e.g. , * ? ? ? * ) , along with other powerful radio galaxies , much of the extended uv continuum is due to scattered , polarized light from a heavily - obscurred qso . however , the uv continuum in iras 09104 + 4109 is @xmath620 times fainter than that presented here for the phoenix cluster @xcite . considering the fact that iras 09104 + 4109 is already an extreme system , it seems unlikely that this additional factor of 20 can be accounted for with the same model . the majority of known ultraluminous infrared galaxies ( ulirgs ) appear to be late - stage mergers of gas - rich galaxies ( @xmath695% ; * ? ? ? * ) , which begs the question : is the extreme star formation in the core of the phoenix cluster fueled by a gas - rich merger ? assuming a relation between molecular gas depletion time and specific star formation rate @xcite , we estimate an h@xmath10 depletion time of 212@xmath2110@xmath40 yr , which is consistent with those measured in two nearby cooling flows : a1068 ( 4@xmath41 yr ; * ? ? ? * ) and a1835 ( 5@xmath41 yr ; * ? ? ? assuming a 1-to-1 correspondence between the total mass of stars formed and the mass of the cold gas reservoir , this timescale implies a molecular gas mass of 1.59.5@xmath42 m@xmath3 , consistent with more recent work by @xcite , yielding 1.05.0@xmath42 m@xmath3 . this cold gas mass is significantly higher than that measured for gas - rich galaxies in the virgo cluster ( e.g. , * ? ? ? further , the process of increasing the cold gas content by compressing atomic gas during a merger would be highly inefficient in the core of the phoenix cluster due to ram pressure stripping of the hi disk during the initial galaxy infall - a process observed in the virgo cluster , which has an icm density @xmath610 times lower than phoenix . our preferred explanation in @xcite was that the star formation in the cluster core is being fueled by gas cooling out of the icm . this remains the most plausible avenue for such a large amount of cold gas to reach the core of the cluster , and is supported by the exceptionally bright x - ray cool core and relatively weak radio source . such an imbalance between cooling and feedback could lead to rapid cooling of the icm , fueling bursts of star formation . following @xcite , we estimate from the x - ray data the mass deposition rate of the cooling flow , combining the x - ray cooling luminosity with the gravitational potential of the cluster in order to correct for gravitational work done as the gas falls towards the cluster center . we obtain an icm cooling rate of m = 2700 @xmath2 700 m@xmath3 yr@xmath4 which is enough to fuel a 798 m@xmath3 yr@xmath4 starburst , assuming the feedback mechanism that prevents star formation in nearby clusters is operating less efficiently in phoenix . in the future , high resolution x - ray spectroscopy of the cool core ( e.g. , * ? ? ? * ) will provide firm estimates of the icm cooling rate down to low temperatures , revealing whether or not this scenario is a plausible fuel source for this massive starburst .

these observations reveal complex , filamentary blue emission , extending for @xmath040 kpc from the brightest cluster galaxy . we estimate an extinction - corrected star formation rate of 798 @xmath2 42 m@xmath3 yr@xmath4 , consistent with our earlier work based on low spatial resolution ultraviolet , optical , and infrared imaging .

i

1211.7058

we present _ hubble space telescope wide field camera 3 _ observations of the core of the phoenix cluster ( spt - clj2344 - 4243 ) in five broadband filters spanning rest - frame 10005500 . these observations reveal complex , filamentary blue emission , extending for @xmath040 kpc from the brightest cluster galaxy . we observe an underlying , diffuse population of old stars , following an r@xmath1 distribution , confirming that this system is somewhat relaxed . the spectral energy distribution in the inner part of the galaxy , as well as along the extended filaments , is a smooth continuum and is consistent with that of a star - forming galaxy , suggesting that the extended , filamentary emission is not due to the central agn , either from a large - scale ionized outflow or scattered polarized uv emission , but rather a massive population of young stars . we estimate an extinction - corrected star formation rate of 798 @xmath2 42 m@xmath3 yr@xmath4 , consistent with our earlier work based on low spatial resolution ultraviolet , optical , and infrared imaging . the lack of tidal features and multiple bulges , combine with the need for an exceptionally massive ( @xmath5 m@xmath3 ) cold gas reservoir , suggest that this star formation is not the result of a merger of gas - rich galaxies . instead , we propose that the high x - ray cooling rate of @xmath62700 m@xmath3 yr@xmath4 is the origin of the cold gas reservoir . the combination of such a high cooling rate and the relatively weak radio source in the cluster core suggests that feedback has been unable to halt cooling in this system , leading to this tremendous burst of star formation .

we report new hst observations of the phoenix cluster ( spt - clj2344 - 4243 ) with wfc3-uvis in five filters covering rest - frame wavelengths 1000 - 5500 . the high spatial resolution of hst is able to separate bright uv emission from the agn and the surrounding diffuse , extended emission , definitively confirming the presence of a starburst in the bcg . the morphology of this central galaxy is complex , with narrow filaments extending for @xmath040 kpc , reminiscent of the nearby perseus and abell 1795 clusters . we argue that the majority of the observed uv emission is due to young stars , on the basis of the complex morphology and flat sed over the wavelength range 10005500 . we confirm the high sfr presented in @xcite , measuring an extinction - corrected , agn - removed uv - derived sfr of 798 @xmath2 42 m@xmath43 yr@xmath4 . we find that merger driven scenarios would require an unreasonably large number of gas rich galaxies to supply the cold gas reservoir required to fuel the starburst , and conclude that the starburst is likely fueled by a massive cooling flow .

we present a combination method based on orignal version of davidson algorithm for extracting few of the lowest eigenvalues and eigenvectors of a sparse symmetric hamiltonian matrix and the simplest version of lanczos technique for obtaining a tridiagonal representation of the hamiltonian to compute the continued fraction expansion of the green s function at a very low temperature .

i

1409.3374

we present a combination method based on orignal version of davidson algorithm for extracting few of the lowest eigenvalues and eigenvectors of a sparse symmetric hamiltonian matrix and the simplest version of lanczos technique for obtaining a tridiagonal representation of the hamiltonian to compute the continued fraction expansion of the green s function at a very low temperature . we compare the davidson@xmath0lanczos method with the full diagonalization on a one - band hubbard model on a bethe lattice of infinite - coordination using dynamical mean field theory .

the infinite lattice coordination limit introduced by metzner and vollhardt@xcite forms the basis for the dynamical mean field theory(dmft)@xcite that maps the hubbard model@xcite onto an anderson impurity model(aim)@xcite . even though the spatial degrees of freedom are completely frozen and the anderson impurity model is much simpler than the original lattice model , it is still a nontrivial many - body problem . in practice , the most difficult step in the dmft iterative procedure is the repeated calculation of the impurity green s function @xmath1 of the impurity problem for any given arbitrary conduction electron effective bath @xmath2 . anderson impurity model can be solved either by numerical methods like exact diagonalization(ed)@xcite , quantum monte carlo(qmc)@xcite , numerical renormalization group(nrg)@xcite or by analytic methods like iterated perturbation theory(ipt)@xcite . most of these methods have limitations confining them to a particular regime , ie high temperature(qmc ) or low temperature(ed , nrg ) . exact diagonalization(ed)@xcite is an important technique for studying quantum many - body systems . green s function at finite temperature can be computed using all the eigenvalues and eigenvectors obtained via full diagonalization . full diagonalization needs an explicit representation of the matrix , requiring lot of memory space . therefore it is limited to small clusters because of large memory required for an exponentially growing hilbert space . moreover , for diagonalizing an @xmath3 matrix , @xmath4 floating point operations(flops ) are required . but if the matrix is sparse and a few eigenvalues and eigenvectors are required then we can resort to iteration methods like the lanczos@xcite method or the davidson@xcite method . green s function at zero temperature can computed by continued fraction expansion using lanczos coefficients . green s function at very low temperature can be computed by the set of equations used by capone et al@xcite . lanczos method is an implementation of the rayleigh ritz procedure@xcite on a krylov subspace@xcite whereas davidson method is on non - krylov subspace . in this paper , we use the orignal version of davidson method and the simplest version of the lanczos algorithm and find that the inclusion of davidson method in evaluation of green s function in low temperature regime can be favourably used to our advantage . the contents of this paper are organised as follows . in section ii . , we describe the orthogonal projection method explaining the lanczos and davidson algorithm . in section iii . , we discuss the computation of green s function at different temperature regimes . section iv . gives a sketch of dmft procedure . in section v. , we show the comparision between the davidson@xmath0lanczos method of computation of green s function and the full ed . finally in section vi . , we discuss the advantages of this combination method .

we present a comparison of the predictions of stellar models with the luminosity of the lower main sequence ( @xmath0 ) using k dwarfs in the hipparcos catalog . a major advantage of our comparison is that distances in our sample are known with good accuracy , while tests that involve open and globular clusters are constrained by potentially inaccurate distances . we compare the data with a range of isochrones from the literature .

i

astro-ph0203118

we present a comparison of the predictions of stellar models with the luminosity of the lower main sequence ( @xmath0 ) using k dwarfs in the hipparcos catalog . the parallaxes of our comparison stars are known to better than 15% and metallicities have been recently determined from photometry . a major advantage of our comparison is that distances in our sample are known with good accuracy , while tests that involve open and globular clusters are constrained by potentially inaccurate distances . we show that the luminosity of the lower main sequence relative to a fiducial ( solar metallicity ) isochrone is a simple function of metallicity : @xmath1 } - 0.04577 $ ] . we compare the data with a range of isochrones from the literature . none of the models fit all the data , although some models do clearly better than others . in particular , metal rich isochrones seem to be difficult to construct . the relationship between luminosity , colour and metallicity for k dwarfs is found to be very tight . we are thus able to derive metallicities for k dwarfs based on their position in the hipparcos colour - magnitude diagram with accuracies better than 0.1 dex . the metallicity - luminosity relation for k dwarfs leads to a new distance indicator with a wide range of possible applications . = -1.0 cm stars - metallicities , isochrones

stellar isochrones are commonly used to predict or interpret the properties of distant stellar systems . two popular uses are to derive ages and metallicities of resolved stellar populations ( such as open and globular clusters ) and to determine the evolutionary state and ages of unresolved systems using the integrated light and synthetic stellar population models ( see e.g. stetson , vandenberg & bolte 1996 ; sarajedini , chaboyer & demarque 1997 ; jimenez , flynn & kotoneva 1998 ; carraro , girardi & chiosi 1999 ; chaboyer , green & liebert 1999 ; liu & chaboyer 2000 ; jimenez 1999 ) . the agreement between stellar theoretical models and the sun is outstanding ( e.g bahcall et al 2001 ) , but comparisons of models to data for other metallicities and masses is still an arduous task . comparisons of this type have been restricted in the past to open and globular clusters ( e.g. westera et al 2002 , cassisi et al 2000 ) , but in both cases distances and luminosities are a source of considerable uncertainty . nevertheless , good agreement has been found between isochrones and data from globular clusters , i.e. isochrones at low metallicity are good . much more difficult to check is the accuracy of metal rich isochrones ( [ fe / h ] @xmath2 ) . our aim in this paper is to make such a comparison for stars on the lower main sequence ( k dwarfs ) , using the accurate distances ( and thus luminosities ) provided by the esa hipparcos mission . the width of the lower main sequence has long been held to be a consequence of the metallicities of the stars ( for a review see e.g. reid , 1999 ) . however , this has been difficult to test without having precise parallaxes and metallicities and furthermore the ability to remove multiple stars . the hipparcos catalogue makes this possible for the first time . in this paper we use hipparcos parallaxes of a sample of 213 nearby k dwarfs ( in the absolute magnitude range @xmath0 , or broadly g8 to k3 ) , for which photometric metallicities are available from kotoneva and flynn ( 2002 ) , to calibrate the luminosity of k dwarfs of a given colour as a function of metallicity and compare these luminosities to isochrones from the literature . the paper is organised as follows . in section 2 we describe the sample . in section 3 we compare different isochrone sets from the literature to stars of similar metallicity in the sample . having found that no isochrone set is able to fit the whole range of metallicities in the data , we construct an empirical calibration of the main sequence luminosity with the metallicity in section 4 . comparing with the original sample of spectroscopically analysed k dwarfs , the relation turns out to be surprisingly precise , and we discuss applications of this calibration in section 5 . we draw our conclusions in section 6 .

we show that the luminosity of the lower main sequence relative to a fiducial ( solar metallicity ) isochrone is a simple function of metallicity : @xmath1 } - 0.04577 $ ] . none of the models fit all the data , although some models do clearly better than others . in particular , metal rich isochrones seem to be difficult to construct . we are thus able to derive metallicities for k dwarfs based on their position in the hipparcos colour - magnitude diagram with accuracies better than 0.1 dex .

c

astro-ph0203118

we present a comparison of the predictions of stellar models with the luminosity of the lower main sequence ( @xmath0 ) using k dwarfs in the hipparcos catalog . the parallaxes of our comparison stars are known to better than 15% and metallicities have been recently determined from photometry . a major advantage of our comparison is that distances in our sample are known with good accuracy , while tests that involve open and globular clusters are constrained by potentially inaccurate distances . we show that the luminosity of the lower main sequence relative to a fiducial ( solar metallicity ) isochrone is a simple function of metallicity : @xmath1 } - 0.04577 $ ] . we compare the data with a range of isochrones from the literature . none of the models fit all the data , although some models do clearly better than others . in particular , metal rich isochrones seem to be difficult to construct . the relationship between luminosity , colour and metallicity for k dwarfs is found to be very tight . we are thus able to derive metallicities for k dwarfs based on their position in the hipparcos colour - magnitude diagram with accuracies better than 0.1 dex . the metallicity - luminosity relation for k dwarfs leads to a new distance indicator with a wide range of possible applications . = -1.0 cm stars - metallicities , isochrones

we have shown that the luminosity of lower main sequence k dwarf stars at a given colour is a simple function of metallicity ( @xmath63 } - 0.04577 $ ] ) . it was possible to show this because of the availability of ( 1 ) accurate hipparcos parallaxes , ( 2 ) a recently developed photometric metallicity index for k dwarfs and ( 3 ) the possibility to identify and remove the multiple stars from the sample . we have tested several sets of isochrones from the literature and we show that none of them fit the data completely , and in particular metal rich isochrones remain difficult to construct . we have adopted the solar isochrone from jimenez , flynn and kotoneva ( 1998 ) as a fiducial line relative to which the luminosity of k dwarfs as a function of a metallicity has been empirically calibrated . the calibration stars are a small sample of k dwarfs with very accurate spectroscopically determined metallicities and hipparcos absolute magnitudes . we find that the relation is very precise and may be used to derive metallicities for k dwarfs based on their position in the colour - magnitude diagram with accuracies better than 0.1 dex . it is also a good distance indicator for k dwarfs if the metallicity can be independently established .

we present a complete next - to - leading order ( nlo ) calculation for the total cross section for inclusive higgs pair production via bottom - quark fusion at the cern large hadron collider ( lhc ) in the minimal supersymmetric standard model ( mssm ) and the minimal supergravity model ( msugra ) .

r

0710.4331

we present a complete next - to - leading order ( nlo ) calculation for the total cross section for inclusive higgs pair production via bottom - quark fusion at the cern large hadron collider ( lhc ) in the minimal supersymmetric standard model ( mssm ) and the minimal supergravity model ( msugra ) . we emphasize the contributions of squark and gluino loops ( sqcd ) and the decoupling properties of our results for heavy squark and gluino masses . the enhanced couplings of the @xmath0 quark to the higgs bosons in supersymmetric models with large @xmath1 yield large nlo sqcd corrections in some regions of parameter space .

in this section , we present the next - to - leading - order inclusive cross sections for the production of a pair of neutral higgs bosons via bottom quark fusion in the mssm and msugra models at the cern lhc . as in our previous paper @xcite , we use the lowest order cteq6l1 parton distribution functions ( pdfs ) @xcite with a factorization scale @xmath104 and the leading - order evolution of the strong coupling @xmath105 with a renormalization scale @xmath106 to calculate the lo cross sections and use the cteq6 m pdfs with the next - to - leading - order evolution of @xmath105 to evaluate the nlo inclusive cross sections . for simplification , we use the same renormalization and factorization scales @xmath107 . we evaluate the bottom quark mass occuring in the @xmath108 yukawa couplings using the @xmath109 mass , @xmath110 , with a two - loop heavy quark running mass with @xmath111 and the nlo evolution of the strong coupling constant , modified to decouple the effects of the top quark@xcite . the higgs couplings are in appendix c @xcite and we compute the higgs boson masses to one - loop accuracy @xcite . = 6.5 in in fig . [ fig : mssm1 ] , we show the lo and nlo cross sections versus the pseudoscalar higgs mass @xmath10 . we assume @xmath112 and compute the @xmath0 squark masses and mixing angles from eqa . [ bsmass ] and [ bsmixing ] . our nlo cross sections include the @xmath25 corrections from the @xmath16 initial state and the @xmath26 corrections from the @xmath113 initial state , along with the sqcd corrections from gluino - sbottom loops . we show our results with @xmath114 ( red ) and @xmath115 ( blue ) at @xmath116 gev . to compare with @xmath117 fusion , we also plot the cross section from the @xmath117 initial state ( dot ) @xcite . we note that the cross sections for higgs pair production in the mssm are significantly larger than in the standard model , due to enhancements at large @xmath1 . the resonant enhancements due to @xmath98 channel scalar exchange are clearly visible in the @xmath118 and @xmath119 curves . at @xmath115 , the cross section for pair of the lightest neutral higgs boson ( @xmath15 ) from @xmath16 fusion is much larger than the cross section from the gluon - gluon initial state , while the rate for pair production of the heavier neutral higgs bosons ( @xmath19 and @xmath20 ) from @xmath16 fusion is highly suppressed relative to the gluon - gluon production . but at @xmath114 , gluon fusion dominates pair of the lightest neutral higgs boson ( @xmath15 ) production and is comparible with @xmath16 production for the heavier neutral higgs bosons ( @xmath19 and @xmath20 ) production . = 3.in figs . [ fig : mssm2 ] and fig . [ fig : mssm3 ] show the nlo cross sections versus @xmath10 with @xmath116 gev and @xmath114 . we present the nlo cross section with only gluon qcd corrections ( dash - dot - dot , green ) , nlo cross section with only gluino - sbottom sqcd corrections ( dot , blue),and the complete nlo cross section with qcd and sqcd corrections together ( dash , red ) . we note : * the nlo sqcd correction to @xmath120 is small . the dominant contribution to the nlo correction to light higgs pair production is from the pure qcd contribution . * for heavy higgs pair and pseudoscalar higgs pair production , the susy qcd corrections become dominant . the pure gluon nlo contribution is much smaller in magnitude than the contribution from sqcd . in fig . [ fig : mssm4 ] , we plot the ratio of the nlo sqcd correction normalized to the born cross section , @xmath121 , with @xmath122 gev , and @xmath115 ( dash - dot - dot , green ) , @xmath123 ( dash , blue ) and @xmath124 ( solid , red ) . in the limit of large squark masses , @xmath125 approaches a common non - zero constant for @xmath19 and @xmath20 production . light higgs pair production , however , decouples for large @xmath10 and large susy masses . this decoupling behaviour is also seen in the decay @xmath126 @xcite and the production process @xmath127@xcite . in fig . [ fig : mssm5 ] , we fix @xmath10 and all squark masses to be @xmath128 gev and plot @xmath125 versus the gluino mass @xmath129 with @xmath130 ( dash - dot - dot , green ) , @xmath123 ( dash , blue ) and @xmath124 ( solid , red ) . this figure does not demonstrate a decoupling behaviour . in this model , supersymmetry is assumed to be broken in a hidden sector consisting of fields that interact with the usual particles and their superpartners only via gravity . supersymmetry breaking is communicated to the visible sector via gravitational interactions . within the msugra framework , it is assumed that at some high scale ( frequently taken to be @xmath131 ) all scalar fields have a common susy breaking mass @xmath132 , all gauginos have a common mass @xmath133 , and all soft susy breaking scalar trilinear couplings have a common value @xmath134 . electroweak symmetry breaking is assumed to occur radiatively . this fixes the magnitude of the superpotential parameter @xmath135 . the soft susy breaking bilinear higgs boson mass parameter can be eliminated in favour of @xmath1 , so that the model is completely specified by the parameter set : @xmath136 all the sparticle masses and couplings required for phenomenological analysis can be obtained via renormalization group evolution between the scale of grand unification and the weak scale . we show the lo ( dot ) and nlo ( solid ) cross sections versus @xmath132 with @xmath137 for @xmath115 in fig . [ fig : msugra1 ] and @xmath114 in fig . [ fig : msugra2 ] . we plot six curves in each frame , three lo cross sections ( dot ) and three nlo cross sections ( solid ) . the nlo curves include both the pure qcd and the sqcd contributions . as shown in the graphs , blue lines are cross sections with @xmath138 gev , @xmath139 , green lines have @xmath138 gev , @xmath140 , and red lines are for @xmath141 gev , @xmath139 . comparing figs . [ fig : msugra1 ] and [ fig : msugra2 ] we see a strong dependence on @xmath1 . * when @xmath115 , flipping the sign of @xmath135 has little effect on either the lo or the nlo cross sections with @xmath138 gev . as @xmath1 increases to 50 , we notice that flipping the sign of @xmath135 has a large effect when @xmath142 gev as shown in fig . [ fig : msugra2 ] . * for large @xmath132 , the cross sections approach a common value , independent of @xmath133 and @xmath135 .

we measured the absolute proper motion of a water maser spot associated with s crt , referred to the quasar j1147@xmath00724 located at an angular separation of 1.23@xmath1 . in observations spanning nearly two years , we have detected the maser spot at the lsr velocity of 34.7kms@xmath2 , for which we measured the annual parallax of 2.33@xmath30.13mas corresponding to a distance of 430@xmath4pc .

r

0808.1151

we present a distance measurement for the semiregular variable s crateris ( s crt ) based on its annual parallax . with the unique dual beam system of the vlbi exploration for radio astrometry ( vera ) telescopes , we measured the absolute proper motion of a water maser spot associated with s crt , referred to the quasar j1147@xmath00724 located at an angular separation of 1.23@xmath1 . in observations spanning nearly two years , we have detected the maser spot at the lsr velocity of 34.7kms@xmath2 , for which we measured the annual parallax of 2.33@xmath30.13mas corresponding to a distance of 430@xmath4pc . this measurement has an accuracy one order of magnitude better than the parallax measurements of hipparcos . the angular distribution and three - dimensional velocity field of maser spots indicate a bipolar outflow with the flow axis along northeast - southwest direction . using the distance and photospheric temperature , we estimate the stellar radius of s crt and compare it with those of mira variables .

in figure [ fig - spectr ] , cross - power spectra of s crt from 2005/019(upper ) and 2006/069(lower ) on the mizusawa iriki baseline are presented . the time variation of the flux densities with the total power spectrum are presented in figure [ lightcurves](b ) with an indication of each lsr velocity . the 34.7kms@xmath2 spot underwent a radio flare(e.g . this flare started in february 2006 and reached a maximum of 371jy in march 31(2006/090 ) , then it decreased to 60jy in july . during the flare , this spot did not show structural change . the cross - power spectrum at the same time showed significantly weaker ( @xmath1830% ) flux density than that of the total power spectrum , indicating that some of the flared emission is resolved on the vera baselines . in figure [ fig - sky ] , we present the positions of maser spot at the lsr velocity of 34.7kms@xmath2 relative to the phase tracking center . throughout the present vlbi observations , this maser spot was bright enough to be detected on all baselines in the phase referencing analyses . the proper motion was clearly modulated by a parallax . based on a least - squares fitting analysis , the parallax was determined to be 2.33@xmath30.13mas which corresponds to a distance of 430@xmath4pc . here , we adopted position errors of each measurement that are obtained as the root sum squares of three error factors , and the details are given in section 4.1 . in the estimation of the parallax , we adopt a very small number of assumptions : the maser spot is moving on a linear trajectory with respect to the star , i.e. , there is no acceleration , and the reference source is fixed on the sky , i.e. , no motions due to core shift or jet features . from the fitting results , the linear proper motions of the reference spot ( @xmath16 , @xmath17 ) were obtained to be ( @xmath16 , @xmath17 ) @xmath13 ( @xmath19masyr@xmath2 , @xmath20masyr@xmath2 ) . this motion is the combination of the proper motion of s crt system and internal motion of the maser spot in the system . considering the offset of the reference spot from the phase tracking center ( @xmath21,@xmath22 ) @xmath13 ( @xmath23mas , @xmath24mas ) , the j2000.0 absolute coordinates of this spot in 2005/292 were obtained to be ( @xmath11,@xmath12 ) @xmath13 ( 11h 52 m 44.96969s , @xmath007@xmath1 35 48.0958 ) . this is the position as referenced to the position of j1147@xmath00742 and in relative offset to the original phase tracking centre . the uncertainty of this position is estimated as @xmath8400@xmath5as based on the errors in our phase referencing analysis ( detailed in section 4.1 ) and icrf position of j1147@xmath00724 . the reference source j1147@xmath00724 exhibited an unresolved structure . the correlated amplitude as a function of ( @xmath25 ) distance is flat and the upper limit of the source size is 0.8mas ( fwhm ) , which is the minor axis of the synthesized beam in the present observation . in addition , we confirmed that the images of j1147@xmath00724 showed no distinctive change during the observations . is indicated with the vertical dashed line in the spectra . the blue - shifted component with respect to the stellar velocity has been brighter than the red - shifted one in the majority of our observations . , width=302 ] in figure [ fig - map ] , we present the angular distribution and three - dimensional velocity field of maser spots in s crt covering a 60mas @xmath9 60mas region . the maser spot with the lsr velocity of 34.7kms@xmath2 is placed at the map origin . at the distance of 430pc , 1mas corresponds to 0.43au , and 1masyr@xmath2 corresponds to a velocity of 2.04kms@xmath2 . the color index in figure [ fig - map ] shows the lsr velocity range from 34.0 to 41.0kms@xmath2 . the blue- and red - shifted components are separated into the northeast and southwest parts of the area . the relative motion of each spot ( @xmath26 , @xmath27 ) with respect to the reference spot are used to determine the average motion ( @xmath28 , @xmath29 ) and , hence we obtained ( @xmath28 , @xmath29 ) @xmath13 ( @xmath01.605masyr@xmath2 , @xmath00.252masyr@xmath2 ) . then , we subtracted ( @xmath28 , @xmath29 ) from ( @xmath26 , @xmath27 ) to obtain the internal motions ( @xmath30 , @xmath31 ) , that are presented with arrows in figure [ fig - map ] . we successfully detected the internal motions of 26 maser spots . the typical transverse speed was obtained to be 2.72masyr@xmath2 , corresponding to 5.56kms@xmath2 , by averaging the internal motions of all 26spots . the parameters of the motions are presented in table [ spot ] in the increasing order of lsr velocity . for the reference spot , we subtracted the internal motion from the proper motion ( @xmath16 , @xmath17 ) and , thus , the proper motion of s crt system was estimated to be ( @xmath32masyr@xmath2 , @xmath33masyr@xmath2 ) . in the new hipparcos catalog @xcite , the absolute proper motion of s crt was ( @xmath34masyr@xmath2 , @xmath35masyr@xmath2 ) , representing good consistency with our result within the errors . ccccccccc i d & @xmath36&@xmath37 & @xmath38 & @xmath39 & @xmath30 & @xmath40 & @xmath31 & @xmath41 + & ( kms@xmath2)&(mas ) & ( mas ) & ( jybeam@xmath2)&(masyr@xmath2 ) & & ( masyr@xmath2 ) & + 1 & 34.10 & @xmath01.25 & 0.34 & 2.3 & & & & + 2 & 34.53 & @xmath01.71 & @xmath02.50 & 2.7 & @xmath00.01 & 0.01 & 4.90 & 2.58 + 3 & 34.55 & 0.76 & @xmath05.39 & 4.4 & 4.15 & 0.55 & @xmath01.19 & 0.06 + 4 & 34.68 & 0.00 & 0.00 & 19.5 & 1.61 & & 0.25 & + 5 & 34.68 & @xmath016.97 & @xmath00.34 & 4.6 & @xmath00.55 & 0.02 & 0.69 & 0.09 + 6 & 34.68 & @xmath02.85 & @xmath00.91 & 8.1 & & & & + 7 & 34.72 & 0.73 & @xmath01.42 & 1.8 & 3.50 & 0.29 & @xmath01.09 & 0.45 + 8 & 34.72 & 1.43 & @xmath02.00 & 1.9 & 2.10 & 0.54 & 0.88 & 0.14 + 9 & 34.74 & 1.64 & @xmath010.71 & 5.8 & & & & + 10 & 34.94 & @xmath01.72 & @xmath03.04 & 1.6 & 0.63 & 0.50 & 3.56 & 0.37 + 11 & 34.95 & 1.45 & @xmath01.86 & 35.4 & 2.08 & 0.89 & 0.58 & 0.06 + 12 & 34.97 & 2.51 & @xmath07.51 & 2.3 & & & & + 13 & 34.97 & 1.11 & @xmath027.05 & 2.5 & & & & + 14 & 35.10 & @xmath00.03 & 0.01 & 8.4 & 1.85 & 0.74 & 0.10 & 0.04 + 15 & 35.10 & @xmath02.89 & @xmath00.92 & 4.9 & & & & + 16 & 35.16 & 3.52 & @xmath02.50 & 3.5 & & & & + 17 & 35.16 & 2.13 & @xmath05.20 & 3.2 & & & & + 18 & 35.18 & 2.38 & @xmath07.37 & 2.1 & & & & + 19 & 35.18 & 1.14 & @xmath027.01 & 2.1 & & & & + 20 & 35.52 & 1.30 & @xmath02.21 & 1.5 & 2.05 & 0.90 & 0.68 & 0.36 + 21 & 35.52 & @xmath017.32 & @xmath00.74 & 1.3 & @xmath00.66 & 0.06 & 0.80 & 0.11 + 22 & 35.54 & @xmath05.04 & @xmath01.04 & 0.9 & & & & + 23 & 36.45 & 3.17 & @xmath010.90 & 1.3 & 3.39 & 0.52 & @xmath00.98 & 0.49 + 24 & 37.89 & @xmath014.77 & @xmath022.00 & 0.8 & @xmath04.37 & 0 & @xmath08.49 & 0 + 25 & 38.32 & @xmath027.32 & @xmath026.17 & 1.3 & & & & + 26 & 38.73 & @xmath027.06 & @xmath028.97 & 1.0 & @xmath02.83 & 0.15 & 0.67 & 0.45 + 27 & 38.73 & @xmath019.16 & @xmath021.19 & 0.9 & @xmath04.70 & 0 & 2.46 & 0 + 28 & 38.74 & @xmath029.53 & @xmath023.72 & 0.9 & & & & + 29 & 38.74 & @xmath011.30 & @xmath027.07 & 1.0 & @xmath00.55 & 0.02 & 0.69 & 0.09 + 30 & 38.91 & @xmath04.01 & @xmath026.46 & 1.1 & @xmath01.60 & 0.43 & @xmath00.65 & 0.29 + 31 & 39.15 & @xmath03.67 & @xmath025.96 & 0.8 & @xmath02.69 & 0.30 & @xmath00.30 & 0.18 + 32 & 39.15 & @xmath019.40 & @xmath021.04 & 2.2 & @xmath02.67 & 0.37 & 0.95 & 0.44 + 33 & 39.57 & @xmath019.87 & @xmath020.95 & 3.4 & @xmath03.26 & 0 & 0.14 & 0 + 34 & 39.57 & @xmath07.18 & @xmath022.73 & 2.2 & & & & + 35 & 39.57 & @xmath019.02 & @xmath018.52 & 2.0 & & & & + 36 & 39.59 & 6.15 & @xmath01.49 & 1.8 & & & & + 37 & 39.61 & @xmath04.73 & @xmath028.23 & 0.7 & 1.49 & 0 & 0.23 & 0 + 38 & 39.74 & @xmath05.14 & @xmath023.02 & 1.0 & & & & + 39 & 40.00 & @xmath018.91 & @xmath018.58 & 1.2 & & & & + 40 & 40.01 & @xmath06.22 & @xmath020.02 & 4.7 & & & & + 41 & 40.03 & @xmath04.81 & @xmath028.14 & 1.0 & 1.59 & 0 & 0.18 & 0 + 42 & 40.03 & @xmath02.29 & @xmath026.22 & 2.0 & & & & + 43 & 40.16 & @xmath09.75 & @xmath030.09 & 1.6 & 0.68 & 0.38 & @xmath00.72 & 0.06 + 44 & 40.42 & @xmath020.47 & @xmath020.21 & 1.1 & @xmath01.49 & 0.23 & @xmath03.01 & 0.51 + 45 & 40.58 & @xmath05.73 & @xmath026.12 & 2.6 & 0.54 & 0.05 & @xmath00.26 & 0.17 + 46 & 41.00 & @xmath05.03 & @xmath031.63 & 1.1 & & & & + 47 & 41.00 & @xmath05.70 & @xmath026.20 & 5.4 & 1.32 & 1.27 & @xmath00.81 & 0.42 +

we present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on spin hall magnetoresistance observed in normal metal / ferromagnetic insulator bilayers ( such as pt / y@xmath0fe@xmath1o@xmath2 ) and normal metal / ferromagnetic metal bilayers ( such as pt / co ) , in which the angle of magnetization influences the magnetoresistance of the normal metal . in the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin hall effect and subsequently the magnetoresistance , while on the ferromagnet side the quantum tunneling effect is detrimental to the interface spin current which also affects the spin accumulation . the influence of generic material properties such as spin diffusion length , layer thickness , interface coupling , and insulating gap can be quantified in a unified manner , and experiments that reveal the quantum feature of the magnetoresistance are suggested .

i

1607.03409

we present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on spin hall magnetoresistance observed in normal metal / ferromagnetic insulator bilayers ( such as pt / y@xmath0fe@xmath1o@xmath2 ) and normal metal / ferromagnetic metal bilayers ( such as pt / co ) , in which the angle of magnetization influences the magnetoresistance of the normal metal . in the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin hall effect and subsequently the magnetoresistance , while on the ferromagnet side the quantum tunneling effect is detrimental to the interface spin current which also affects the spin accumulation . the influence of generic material properties such as spin diffusion length , layer thickness , interface coupling , and insulating gap can be quantified in a unified manner , and experiments that reveal the quantum feature of the magnetoresistance are suggested .

the electrical control of magnetization dynamics has been a central issue in the field of spintronics@xcite , owing to its possible applications in magnetic memory devices with low power consumption . a particularly promising mechanism for the electrical control is to utilize the spin hall effect@xcite ( she ) in a normal metal ( nm ) , such as pt or ta , to convert an electric current into a spin current , and subsequently to magnetization dynamics in an adjacent magnet via mechanisms such as spin - transfer torque@xcite ( stt ) . in reverse , the inverse spin hall effect@xcite ( ishe ) can convert the spin current generated by certain means , for instance spin pumping@xcite , into an electric signal . a particularly intriguing phenomenon that involves both she and ishe is the spin hall magnetoresistance@xcite ( smr ) , in which a charge current in an nm causes a spin accumulation at the edge of the sample due to she , yielding a finite spin current at the interface to a ferromagnet . through ishe , the spin current gives an electromotive force along the original charge current , effectively changing the magnetoresistance of the nm . the two major ingredients that determine smr are the spin diffusion@xcite in the nm and the spin current at the nm / ferromagnet interface . the spin diffusion part has been addressed in detail by chen _ et al . _ for the nm / ferromagnetic insulator ( nm / fmi ) bilayer , such as pt / y@xmath0fe@xmath1o@xmath2 ( pt / yig ) , and fmi / nm / fmi trilayer@xcite . this approach solves the spin diffusion equation in the presence of she and ishe in a self - consistent manner , where the spin current at the nm / fmi interface serves as a boundary condition . however , the interface spin current remains an external parameter for which experimental or numerical input is needed@xcite . on the other hand , a quantum tunneling formalism has emerged recently as an inexpensive tool to calculate the interface spin current from various material properties such as the insulating gap of the fmi and the interface @xmath3 coupling@xcite . the quantum tunneling theory also successfully explains@xcite the reduced spin pumping spin current when an additional oxide layer is inserted between nm and fmi@xcite . it is then of fundamental importance to combine the spin diffusion approach with the quantum tunneling formalism for the interface spin current to give a complete theoretical description of the smr , in particular to quantify how various material properties influence the smr . in this article we provide a minimal formalism that bridges the quantum tunneling formalism to the spin diffusion approach . we focus on the smr in nm / fmi bilayer realized in pt / yig , and the nm / ferromagnetic metal ( nm / fmm ) bilayer realized in pt / co and ta / co@xcite . the spin diffusion in the nm is assumed to be described by the same formalism of chen _ et al._@xcite , whereas the interface spin current is calculated from the quantum tunneling formalism@xcite . in the nm / fmm bilayer , we consider an fmm that has long spin diffusion length and a small thickness , such that the spin diffusion effect is negligible and the spin transport is predominately of quantum origin@xcite . this is presumably adequate for the case of ultrathin co films@xcite , but not for materials with very short spin diffusion length such as permalloy@xcite . within this formalism , the effect of material properties including spin diffusion length of the nm , interface @xmath3 coupling , insulating gap of the fmi , and the thickness of each layer can all be treated on equal footing . in particular , we reveal the signature of quantum interference in smr in nm / fmm bilayer , and discuss the situation in which it can be observed . the structure of the article is arranged in the following manner . in sec . ii , we detail the quantum tunneling formalism for the interface spin current in the nm / fmi bilayer , and how it is adopted into the spin diffusion approach that describes the nm . section iii generalizes this recipe to the nm / fmm bilayer , and discuss the observability of the predicted signature of quantum interference in smr . section iv gives the concluding remark .

maxwell equations including riemannian analogues of the plebaski demiaski metrics . our classification can be viewed as a riemannian analogue of a result in relativity due to r. debever , n. kamran , and r. mclenaghan , and is a natural extension of the classification of selfdual einstein hermitian @xmath0-manifolds , obtained independently by r. bryant and the first and third authors . our main results also classify the latter , providing new examples of explicit extremal khler metrics . for both the einstein maxwell and the extremal ambitoric structures , @xmath3 and @xmath4 are quartic polynomials , but with different conditions on the coefficients . in the sequel to this paper we consider global examples , and use them to resolve the existence problem for extremal khler metrics on toric @xmath0-orbifolds with @xmath5 .

i

1302.6975

we present a local classification of conformally equivalent but oppositely oriented @xmath0-dimensional khler metrics which are toric with respect to a common @xmath1-torus action . in the generic case , these `` ambitoric '' structures have an intriguing local geometry depending on a quadratic polynomial @xmath2 and arbitrary functions @xmath3 and @xmath4 of one variable . we use this description to classify einstein @xmath0-metrics which are hermitian with respect to both orientations , as well a class of solutions to the einstein maxwell equations including riemannian analogues of the plebaski demiaski metrics . our classification can be viewed as a riemannian analogue of a result in relativity due to r. debever , n. kamran , and r. mclenaghan , and is a natural extension of the classification of selfdual einstein hermitian @xmath0-manifolds , obtained independently by r. bryant and the first and third authors . these einstein metrics are precisely the ambitoric structures with vanishing bach tensor , and thus have the property that the associated toric khler metrics are extremal ( in the sense of e. calabi ) . our main results also classify the latter , providing new examples of explicit extremal khler metrics . for both the einstein maxwell and the extremal ambitoric structures , @xmath3 and @xmath4 are quartic polynomials , but with different conditions on the coefficients . in the sequel to this paper we consider global examples , and use them to resolve the existence problem for extremal khler metrics on toric @xmath0-orbifolds with @xmath5 .

riemannian geometry in dimension four is remarkably rich , both intrinsically , and through its interactions with general relativity and complex surface geometry . in relativity , analytic continuations of families of lorentzian metrics and/or their parameters yield riemannian ones @xcite , while concepts and techniques in one area have analogues in the other . in complex geometry , e. calabi s extremal khler metrics @xcite have become a focus of attention as they provide canonical riemannian metrics on polarized complex manifolds , generalizing constant gauss curvature metrics on complex curves . the first nontrivial examples are on complex surfaces . this paper concerns a notion related both to relativity and complex surface geometry . an _ ambikhler structure _ on a real @xmath0-manifold ( or orbifold ) @xmath6 consists of a pair of khler metrics @xmath7 and @xmath8 such that @xmath9 and @xmath10 induce the same conformal structure ( i.e. , @xmath11 for a positive function @xmath12 on @xmath6 ) ; @xmath13 and @xmath14 have opposite orientations ( equivalently the volume elements @xmath15 and @xmath16 on @xmath6 have opposite signs ) . a product of two riemann surfaces is ambikhler . to obtain more interesting examples , we suppose that both khler metrics are toric , with common torus action , which we call `` ambitoric '' . more precisely , we suppose that there is a @xmath1-dimensional subspace @xmath17 of vector fields on @xmath6 , linearly independent on a dense open set , whose elements are hamiltonian and poisson - commuting killing vector fields with respect to both @xmath18 and @xmath19 . is a symplectic form , hamiltonian vector fields @xmath20 and @xmath21 _ poisson - commute _ iff the poisson bracket @xmath22 with respect to @xmath23 is zero . this holds iff @xmath24 . ] the theory of hamiltonian @xmath1-forms in four dimensions @xcite implies that any orthotoric khler metric and certain khler metrics of calabi type are ambitoric . such metrics provide interesting examples of extremal khler surfaces @xcite . here we give a local classification of ambitoric structures in general , and an explicit description of the extremal khler metrics thus unifying and generalizing these works . our examples include riemannian analogues of plebaski demiaski metrics @xcite ; the latter are einstein maxwell spacetimes of petrov type d , which have been extensively studied @xcite , and classified by r. debever , n. kamran and r. g. mclenaghan @xcite . in riemannian geometry , the type d condition means that both half - weyl tensors @xmath25 are degenerate , i.e. , at any point of @xmath6 at least two of the three eigenvalues of @xmath25 coincide ( where @xmath26 and @xmath27 are viewed as symmetric tracefree operators acting on the three - dimensional spaces of selfdual and antiselfdual @xmath1-forms respectively ) . einstein metrics @xmath28 with degenerate half - weyl tensors have been classified when @xmath29 or @xmath30 @xcite otherwise , the riemannian goldberg sachs theorem @xcite and the work of a. derdziski @xcite imply that @xmath28 is ambikhler , with compatible khler metrics @xmath31 ; conversely @xmath32 , where @xmath33 are the scalar curvatures of @xmath34 . from the @xmath35-invariance of the ricci tensor of @xmath28 , it follows that @xmath36 are commuting killing vector fields for @xmath34 , which means that @xmath37 are both extremal khler metrics . a little more work yields the following result . [ thm : ahe - refined ] let @xmath38 be an oriented einstein @xmath0-manifold with degenerate half - weyl tensors @xmath25 . then @xmath28 admits compatible ambitoric extremal metrics @xmath39 near any point in a dense open subset of @xmath6 . conversely , an ambikhler structure is conformally einstein on a dense open subset if and only if its bach tensor vanishes . this suggests classifying such einstein metrics within the broader context of _ extremal ambikhler metrics _ or , equivalently , ambikhler metrics for which the bach tensor is _ diagonal _ , i.e. , both @xmath13 and @xmath14 invariant . we also discuss riemannian metrics of `` plebaski demiaski type '' , for which the tracefree ricci tensor satisfies @xmath40 for some constant @xmath41 . in particular @xmath42 is diagonal . these two curvature generalizations also give rise to ambitoric structures . [ thm : at - rough ] an ambikhler structure @xmath43 , not locally a khler product , nor of calabi type , nor conformal to a @xmath44-selfdual ricci - flat metric , is locally : ambitoric if and only if there is a compatible metric @xmath28 with @xmath42 diagonal ; further , @xmath28 has plebaski demiaski type if and only if it has constant scalar curvature ; extremal and ambitoric if and only if the bach tensor of @xmath41 is diagonal . thus motivated , we study ambitoric structures in general and show that in a neighbourhood of any point , they are either of calabi type ( hence classified by well - known results ) , or `` regular '' . our explicit local classification in the regular case ( theorem [ thm : ambitoric ] ) relies on subtle underlying geometry which we attempt to elucidate , although some features remain mysterious . for practical purposes , however , the classification reduces curvature conditions ( pdes ) on ambitoric structures to systems of functional odes . we explore this in greater detail in section [ s : curvature ] , where we compute the ricci forms and scalar curvatures for an arbitrary regular ambitoric pair @xmath45 of khler metrics . this leads to an explicit classification of the extremal and conformally einstein examples ( theorem [ thm : main ] ) . we also identify the metrics of plebaski demiaski type among ambitoric structures ( theorem [ thm : einstein - maxwell])their relation to killing tensors is discussed in appendix [ killing ] . we summarize the main results from theorems [ thm : ambitoric][thm : einstein - maxwell ] loosely as follows . let @xmath39 be a regular ambitoric structure . then : there is a quadratic polynomial @xmath2 and functions @xmath3 and @xmath4 of one variable such that the ambitoric structure is given by ( and these are regular ambitoric ) ; @xmath46 is an extremal khler metric @xmath47 @xmath48 is an extremal khler metric @xmath47 @xmath3 and @xmath4 are quartic polynomials constrained by three specific linear conditions ; @xmath34 are conformally einstein ( i.e. , bach - flat ) if and only if they are extremal , with an additional quadratic relation on the coefficients of @xmath3 and @xmath4 ; @xmath34 are conformal to a constant scalar curvature metric of plebaski demiaski type if and only if @xmath3 and @xmath4 are quartic polynomials constrained by three specific linear conditions ( different , in general , from the extremality conditions ) . let @xmath38 be an einstein @xmath0-manifold for which the half - weyl tensors @xmath26 and @xmath27 are everywhere degenerate . then on a dense open subset of @xmath6 , the metric @xmath28 is locally homothetic to one of the following : a real space form ; a product of two riemann surfaces with equal constant gauss curvatures ; an einstein metric of the form @xmath49 , where @xmath9 is a bach - flat khler metric with nonvanishing scalar curvature @xmath50 , described in proposition or theorem . in the second part of this work we shall obtain global consequences of these local classification results . in particular , we shall resolve the existence problem for extremal khler metrics on toric @xmath0-orbifolds with @xmath5 . the first author was supported by an nserc discovery grant and is grateful to the institute of mathematics and informatics of the bulgarian academy of sciences where a part of this project was realized . the second author thanks the leverhulme trust and the william gordon seggie brown trust for a fellowship when this project was conceived in 2001 , and to the epsrc for a subsequent advanced research fellowship . the authors are grateful to liana david and the centro georgi , pisa , and to banff international research station for opportunities to meet in 2006 and 2009 , when much of this work was carried out . they thank maciej dunajski , niky kamran , claude lebrun and arman taghavi - chabert for very useful discussions and comments .

we present a new method to introduce phase - space fluctuations in transport theories , corresponding to a full implementation of the boltzmann - langevin equation for fermionic systems . it is based on the procedure originally developed by bauer et al . for transport codes employing the test particle method . in the new procedure , accurate tests are carried out in one and two dimensional idealized systems , and finally results for a full 3d application are shown . we stress the reliability of this method , which can be easily plugged into existing tranport codes using test particles , and its general applicability to systems characterized by instabilities , like for instance multifragmentation processes . fluctuations ; stochastic collision integral ; fermionic systems ; transport theories . + pacs numbers : 24.10.cn ; 24.60.ky , 25.70.pq

i

0802.0377

we present a new method to introduce phase - space fluctuations in transport theories , corresponding to a full implementation of the boltzmann - langevin equation for fermionic systems . it is based on the procedure originally developed by bauer et al . for transport codes employing the test particle method . in the new procedure , the pauli principle is carefully checked , leading to a good reproduction of the correct fluctuations in the `` continuum limit '' ( @xmath0 ) . accurate tests are carried out in one and two dimensional idealized systems , and finally results for a full 3d application are shown . we stress the reliability of this method , which can be easily plugged into existing tranport codes using test particles , and its general applicability to systems characterized by instabilities , like for instance multifragmentation processes . fluctuations ; stochastic collision integral ; fermionic systems ; transport theories . + pacs numbers : 24.10.cn ; 24.60.ky , 25.70.pq

in recent years , the dynamics of heavy ion collisions at intermediate energy has been extensively investigated within the framework of transport theories , such as the nordheim approach , in which the vlasov equation for the one - body phase space density , @xmath1 , is supplemented with a pauli - blocked boltzmann collision term @xcite . the basic ingredients that enter the resulting transport equation , often called boltzmann - uehling - uhlenbeck ( buu ) equation , are the self - consistent mean - field potential and the two - body scattering cross sections . these transport models hence describe the time evolution of the reduced one - body density in phase - space and , consequently , they are suited for the description of one - body observables , such as inclusive particle spectra in nuclear collisions , average collective flows and excitations . however , they can not provide a reliable description of fluctuation phenomena , such as multi - fragmentation processes , i.e. the break - up of excited nuclear systems into many pieces . in fact , neither fluctuations of one - body observables nor many - body correlations can be addressed with this class of mean - field models . hence suitable extensions , including fluctuations of the one - body density , have to be considered . an intense theoretical work on fluctuations in nuclear dynamics has started in the past years , also stimulated by the availability of large amounts of experimental data on fragment formation in intermediate energy heavy ion collisions and the possibility to observe a liquid - gas phase transition @xcite . in order to introduce fluctuations in transport theories , a number of different avenues have been taken , that can be essentially reconducted to two different classes of models . one is the class of molecular dynamics models @xcite while the other kind is represented by stochastic mean - field approaches @xcite . in molecular dynamics models the many - body state is represented by a simple product wave function , with or without antisymmetrization . the single particle wave functions are assumed to have a fixed gaussian shape . in this way , though nucleon wave functions are supposed to be independent ( mean - field approximation ) , the use of localized wave packets induces many - body correlations both in mean - field propagation and hard two body scattering ( collision integral ) , which is treated stochastically . hence this way to introduce many - body correlations and produce a trajectory branching is essentially based on the use of empirical gaussian wave packets . if wave functions were allowed to assume any shape , the method would become identical to standard mean - field descriptions . while the wave function localization appears appropriate to describe final fragmentation channels , where each single particle wave function should be localized within a fragment , the use of fixed shape localized wave packets in the full dynamics could affect the correct description of one - body effects , such as spinodal instabilities and zero sound propagation @xcite . on the other side , in the so - called stochastic mean - field approaches , the stochastic extension of the transport treatment for the one - particle density is obtained by introducing a stochastic term representing the fluctuating part of the collision integral @xcite , in close analogy with the langevin equation for a brownian motion . this can be derived as the next - order correction , in the equation describing the time evolution of @xmath2 , with respect to the standard average collision integral , leading to the boltzmann - langevin ( bl ) equation . thus , the system is still described solely in terms of the reduced one - body density @xmath2 , but this function experiences a stochastic time evolution in response to the random effect of the fluctuating collision term . in this way density fluctuations are introduced , that are amplified when instabilities or bifurcations occur in the dynamics . this procedure is suitable also for addressing multifragmentation phenomena , since fragments can be associated with the regions where the spacial density becomes larger , which finally can be reconstructed by sampling the one - body distribution function . a specific method for solving the boltzmann - langevin equation by direct numerical simulation was introduced in refs.@xcite . in this numerical implementation , the one - particle density @xmath3 is represented on a lattice of grid points in phase space and the collision integral is treated by considering all possible transitions between phase space cells , adding a noise term whose features are related to the average rate of transitions between two specified initial cells and two final cells . the numerical implementation of this method has only been possible in two dimensions ( 2d ) because it requires too large computer resources in 3d . hence several approximate solutions of the bl equations have been formulated , mostly based on the projection of the bl noise only on a given dynamical variable ( such as the local quadrupole tensor of the momentum distribution ) or on @xmath4 space only @xcite . more tractable fluctuating terms , such as a stochastic force added to the mean - field potential , have also been proposed and extensively applied to multifragmentation studies @xcite . however , the implementation of the full structure in phase space of the original bl term can still be considered as an important goal to reach . in fact , this would allow to treat a more general class of phenomena , where the correct description of fluctuations and correlations in @xmath5 space is essential ( such as particle production and fragment velocity correlations for instance ) . moreover , also in the multi - fragmentation mechanism , that is dominated by spacial density fluctuations , a more accurate representation of the full phase space dynamics , including fluctuations , would allow to improve the description of the fragment kinematical properties and correlations . we also stress the general interest of this effort . indeed transport phenomena occur in many physical systems , for which a more precise description of the time evolution of the one - body distribution function , including the effect of many - body correlations , would be important . a first attempt to introduce a fluctuating collision term in a 3d transport approach was made by bauer et al . this method can be implemented relatively easily into standard transport codes that adopt the scattering of pseudo - particles ( or test particles ) as a method of solution of the collision integral and it consists essentially in forcing similar two - body collisions to occur for neighboring test particles , defined according to a given distance in phase space , so that effectively two nucleons are involved in each particular collision event . the distance should reproduce the phase - space shape of the nucleon wave function . in this way the random nature of the two - body scattering , that in the standard codes applies only to test particles and is washed - out when using a huge number of them , is transferred to entire nucleons . however , in the procedure proposed in ref.@xcite the pauli blocking is checked only for the collision of the two original test particles and not for the entire swarm affected , leading to some unpleasant features in the description of fermionic systems . indeed the pauli - blocking violation introduces important inaccuracies in the fluctuations of the one - body density . in the present manuscript we present a new method to reconstruct the phase space nucleon wave function in mean - field approaches , in such a way that the pauli - blocking is checked for the entire cloud of moved particles this will improve the description of the fluctuation variance , approaching the one expected for fermionic systems . we will also pay special attention to the definition of the phase - space metric that would optimize the value of this variance . the paper is organized as follows : we will first recall the main ingredients of the bl theory , in order to connect the formalism with the numerical implementation adopted ( section 2 ) . then we will discuss in more detail the methods that have been proposed so far to solve the boltzmann - langevin equation ( section 3 ) . the new procedure that we follow to build fluctuations is presented in section 4 . several results demonstrating and analyzing in detail the method are discussed from section 5 to 8 . conclusions and perspectives are drawn in section 9 .

we present a sample of 46 galaxy nuclei from 12 nearby ( @xmath0 ) hickson compact groups ( hcgs ) with a complete suite of 124 2mass+_spitzer _ nuclear photometry . this parameter is more powerful for identifying low to moderate - luminosity mid - infrared activity than other measures which include data at rest - frame @xmath2 that may be dominated by stellar photospheric emission . while the hcg galaxies clearly have a bimodal distribution in this parameter space , a comparison sample from the _ spitzer _ nearby galaxy survey ( sings ) matched in @xmath3-band total galaxy luminosity is continuously distributed . comparing these two mid - infrared diagnostics of nuclear activity to optical spectroscopic identifications from the literature reveals some discrepancies , and we discuss the challenges of distinguishing the source of ionizing radiation in these and other lower luminosity systems . we find a significant correlation between the fraction of mid - infrared active galaxies and the total mass in a group , and investigate possible interpretations of these results in light of galaxy evolution in the highly interactive system of a compact group environment .

i

0710.0372

we present a sample of 46 galaxy nuclei from 12 nearby ( @xmath0 ) hickson compact groups ( hcgs ) with a complete suite of 124 2mass+_spitzer _ nuclear photometry . for all objects in the sample , blue emission from stellar photospheres dominates in the near - infrared through the 3.6 irac band . twenty - five of 46 ( 54% ) galaxy nuclei show red , mid - infrared continua characteristic of hot dust powered by ongoing star formation and/or accretion onto a central black hole . we introduce @xmath1 , the spectral index of a power - law fit to the 4.58.0 irac data , and demonstrate that it cleanly separates the mid - infrared active and non - active hcg nuclei . this parameter is more powerful for identifying low to moderate - luminosity mid - infrared activity than other measures which include data at rest - frame @xmath2 that may be dominated by stellar photospheric emission . while the hcg galaxies clearly have a bimodal distribution in this parameter space , a comparison sample from the _ spitzer _ nearby galaxy survey ( sings ) matched in @xmath3-band total galaxy luminosity is continuously distributed . a second diagnostic , the fraction of 24 emission in excess of that expected from quiescent galaxies , @xmath4 , reveals an additional three nuclei to be active at 24 . comparing these two mid - infrared diagnostics of nuclear activity to optical spectroscopic identifications from the literature reveals some discrepancies , and we discuss the challenges of distinguishing the source of ionizing radiation in these and other lower luminosity systems . we find a significant correlation between the fraction of mid - infrared active galaxies and the total mass in a group , and investigate possible interpretations of these results in light of galaxy evolution in the highly interactive system of a compact group environment .

the first galaxies and their environments differed substantially from those locally , often involving multiple interactions as seen in the _ hst _ ultra deep field ( e.g. , * ? ? ? compared to all other nearby environments , present - day compact galaxy groups most closely reproduce the interaction environment of the early universe ( @xmath5 ) when galaxies assembled through hierarchical formation ( e.g. , * ? ? ? * ) , and galaxy groups combined to form proto - clusters ( in dense regions ; e.g. , rudick+06 ) or massive ellipticals ( in the field ; white ) . because of their high space densities ( with comparable surface densities to the centers of rich galaxy clusters ; e.g. , rubin+91 ) and low velocity dispersions ( @xmath6 ) , compact groups of galaxies are ideal environments for studying the mechanisms of interaction - induced star formation and nuclear activity . from optical spectroscopic surveys , hickson compact groups ( hcgs ) are known to host a population of galaxies with emission - line nuclear spectra characteristic of star - formation and/or active galactic nuclei ( agns ) . based on the optical spectroscopic survey of @xcite , the agn fraction in hcgs is found to be @xmath7 , perhaps consistent with the @xmath8 nuclear activity level found for nearby @xmath9 galaxies ( with greater detection sensitivity ; hoetal97a ) and significantly higher than the @xmath10 agn fraction identified optically in cluster galaxies ( with @xmath11 ; dressler85 ) . further , hcg agns ( including low - luminosity agns , hereafter llagns ; hcgs host no known seyfert 1-luminosity agns ) are preferentially found in optically luminous , early - type galaxies with little or no ongoing star formation in the cores of evolved groups . similarly , many galaxies in clusters host llagns in the local universe ( e.g. , * ? ? ? * ) , in particular brightest cluster galaxies @xcite . typically , the most active star - forming galaxies are late - type spirals in the outskirts of groups . @xcite interpreted relative distributions of star - forming and agn - hosting galaxies as indicating a clear evolutionary scenario whereby group cores are mature collapsed systems in which the high galaxy densities led to increased gravitational interactions and hence more rapid exhaustion of gas reservoirs in the past through star formation . ( the radiatively weak agns in the evolved group cores require only a small amount of gas for fueling . ) a similar study by @xcite found that the fraction of emission - line hcg galaxies was comparable to the field , and conversely concluded that the hcg environment does _ not _ trigger either star formation or agn activity . the initial expectation that the interactions evident in the compact group environment would naturally lead to markedly enhanced levels of star formation compared with the field has not been satisfied , and a coherent understanding of the history of gas and cold dust in compact groups has proven elusive . an analysis of the co content in hcg galaxies found them to be similar to those in the field , in loose groups , and in other environments ; a notable exception is the @xmath12 of hcg spirals that are co deficient . this suggests less , not more , star formation in hcgs compared to other environments @xcite . at the same time , the detection of a few hcg elliptical and s0 galaxies in both co and the far - infrared ( unlike typical galaxies of these types ) suggests that tidal interactions are influencing galaxy evolution to some extent . while the far - infrared power is similar to comparison samples , the ratios of 25 to 100 _ iras _ fluxes implies a greater number of intense , nuclear starbursts in hcg galaxies @xcite . clearly , a robust and consistent understanding of the impact of the compact group environment on galaxy properties has not yet emerged . one possible difficulty to date is the predominant use of optical emission - line studies to identify activity both star - forming and accretion - dominated . ground - based studies of bright galaxies can easily obscure low - contrast emission lines through their dilution by a strong stellar contribution ( e.g. , * ? ? ? * ) ; intrinsic absorption can also mask spectroscopic signatures . the clear discrepancy between the @xmath10 agn fraction in galaxy clusters from optical spectroscopic surveys ( e.g. , * ? ? ? * ) compared to the larger fraction ( @xmath13 for luminous galaxies ) revealed by x - ray observations ( e.g. , * ? ? ? * ) is illustrative of this problem . as highlighted by @xcite , mismatched sample selection and detection techniques can create apparent ( and false ) discrepancies in agn fractions between environments . in this paper , we take an alternate approach , focusing on the mid - infrared spectral energy distributions ( seds ) of individual galaxy nuclei to clearly identify the thermal , hot dust continua that signify neutral gas heated by ionizing photons from either young stars or an agn . the clear discrepancy between a blue , quiescent galaxy sed where the mid - infrared is dominated by the raleigh - jeans tail of stellar photospheres and the red , mid - infrared sed of warm to hot dust emission offers promise for reducing the ambiguity of previous compact group studies . * hereafter j07 ) have presented the first results from a cycle 1 _ spitzer _ irac ( 3.68.0 ) and mips ( 24 ) imaging survey of 46 galaxies in 12 nearby hcgs . in brief , this work revealed trends between the evolutionary states of compact groups ( determined from their dynamical and masses ) , and their mid - infrared colors and luminosities . galaxies in relatively gas - rich groups tend to have colors most indicative of star formation and agn activity , and galaxies in gas - poor groups predominantly exhibit a narrow range of mid - infrared colors that are consistent with the light from quiescent stellar populations . the galaxies in this sample of 12 compact groups also occupy infrared color space in a distinctly different way than the population of galaxies in the _ spitzer _ first look survey ( fls ; e.g. , lacy04 ) , notably exhibiting a `` gap '' in their color distribution not found in the fls sample . all of these results suggest that the environment of a compact group is intimately connected to the mid - infrared activity of the member galaxies . we present additional analysis of the nuclei of these galaxies , focusing in particular on developing diagnostics for identifying quantitative measures of mid - infrared activity with the ultimate goal of exploring the nature of mid - infrared emission , i.e. , quiescent , star - forming , and/or accretion - powered . we also explore the connections between mid - infrared nuclear properties and other features of individual galaxies including morphology , optical spectral type , and the host group s evolutionary stage . because of their proximity ( @xmath14 ) , we can spatially extract nuclear photometry for the hcg galaxies to reduce contamination from the extended galaxy that is inevitable in surveys of more distant galaxies . throughout we assume a @xmath15-cdm cosmology with @xmath16 , @xmath17 , and @xmath18mpc@xmath19 ( e.g. , * ? ? ?

for all objects in the sample , blue emission from stellar photospheres dominates in the near - infrared through the 3.6 irac band . a second diagnostic , the fraction of 24 emission in excess of that expected from quiescent galaxies , @xmath4 , reveals an additional three nuclei to be active at 24 .

r

0710.0372

we present a sample of 46 galaxy nuclei from 12 nearby ( @xmath0 ) hickson compact groups ( hcgs ) with a complete suite of 124 2mass+_spitzer _ nuclear photometry . for all objects in the sample , blue emission from stellar photospheres dominates in the near - infrared through the 3.6 irac band . twenty - five of 46 ( 54% ) galaxy nuclei show red , mid - infrared continua characteristic of hot dust powered by ongoing star formation and/or accretion onto a central black hole . we introduce @xmath1 , the spectral index of a power - law fit to the 4.58.0 irac data , and demonstrate that it cleanly separates the mid - infrared active and non - active hcg nuclei . this parameter is more powerful for identifying low to moderate - luminosity mid - infrared activity than other measures which include data at rest - frame @xmath2 that may be dominated by stellar photospheric emission . while the hcg galaxies clearly have a bimodal distribution in this parameter space , a comparison sample from the _ spitzer _ nearby galaxy survey ( sings ) matched in @xmath3-band total galaxy luminosity is continuously distributed . a second diagnostic , the fraction of 24 emission in excess of that expected from quiescent galaxies , @xmath4 , reveals an additional three nuclei to be active at 24 . comparing these two mid - infrared diagnostics of nuclear activity to optical spectroscopic identifications from the literature reveals some discrepancies , and we discuss the challenges of distinguishing the source of ionizing radiation in these and other lower luminosity systems . we find a significant correlation between the fraction of mid - infrared active galaxies and the total mass in a group , and investigate possible interpretations of these results in light of galaxy evolution in the highly interactive system of a compact group environment .

from a visual examination of the near through mid - infrared seds ( fig . 1 ) , the close correspondence of the @xmath3-band through 3.6photometric data points with an elliptical galaxy template indicates that stellar emission dominates in this wavelength regime in every galaxy . to account for this , we normalize a 13 gyr elliptical galaxy template @xcite to the @xmath3 and @xmath37 band flux densities . with this simple normalization , the elliptical galaxy sed predicts the 3.68.0 flux densities for 21 of the 46 ( 46% ) galaxies remarkably well . these include the entire membership of the evolved and x - ray - bright hcgs 42 and 62 . the remaining 25 galaxies ( counting hcg 31ace as 3 galaxies ) , have mid - infrared continua that rise to longer wavelengths . this clear qualitative difference is illustrated quantitatively with the histogram of @xmath1 values shown in figure [ fig : hists]b . no hcg galaxy nuclei inhabit the parameter space between @xmath1 values of @xmath43 and 0.25 ; for the integrated hcg galaxy seds , the distribution is comparable , with none found in the range of @xmath1(gal ) of @xmath43 to 0.12 . this is in stark contrast to the distribution of @xmath1 values of the sings galaxies ( plotted in the same figure ) that shows a significant fraction within the hcg gap . we also point out a noticeable peak near @xmath1@xmath44 for the sings galaxies whereas the hcg galaxies ( and nuclei ) are more evenly distributed from @xmath45 to @xmath46 . the larger number of hcg objects with @xmath1@xmath47 compared to sings galaxies likely reflects the larger number of early types in the former sample . however , morphological differences do not account for all of the discrepancy , as a direct comparison of the spirals in the two samples finds that while 11 of 47 ( 23% ) of the sings spirals have @xmath1 values in the range from 1.3 to 0 , none of the 17 hcg spirals do . a kolmogorov - smirnov analysis confirms the overall differences in the populations , giving only 0.12% and 0.35% probabilities that the sings galaxies are drawn from the same distribution as the hcg nuclei and galaxies , respectively . ( the hcg nuclei and galaxies are consistent with eachother at 22.5% probability . ) hereafter , we will utilize the break in the hcg @xmath1 distribution to distinguish `` mid - infrared active '' ( @xmath1@xmath48 ) from `` mid - infrared quiescent '' ( @xmath1@xmath49 ) nuclei and galaxies . we investigate this difference in more detail by plotting @xmath1 vs. @xmath50 for both the hcg and sings galaxies , coded by galaxy morphology in figure [ fig : alphalum24 ] . it is perhaps most illuminating to compare the sings and hcg spiral galaxies ( @xmath51 symbols in fig . [ fig : alphalum24 ] ) . while the two groups cover a comparable range of @xmath50 , the hcg galaxies are systematically redder in the mid - infrared , i.e. , with more negative values of @xmath1 . within the hcg galaxies , morphology is evidently a strong predictor of @xmath1 , with elliptical and s0 galaxies almost exclusively populating the parameter space of @xmath1@xmath47 . we next consider the utility of measuring @xmath34 , the fraction of @xmath32 attributable to non - stellar ( i.e. , hot dust ) emission . a plot of @xmath34 vs. @xmath52 shows a clear positive correlation in the hcg population , with higher values of @xmath52 corresponding to larger values of @xmath34 , as shown in figure [ fig : fracd]a . this correlation is highly significant according to the non - parametric spearman s @xmath53 test which gives a probability , @xmath54 , of @xmath55 for @xmath56 that these parameters are uncorrelated . while the hcg nuclei known to have optical absorption - line spectra ( filled circles ) all have values of @xmath34@xmath57 consistent with purely stellar emission and @xmath52@xmath58 hz@xmath19 , there is no clear separation in this parameter space between galaxies identified as agns or star - forming . this is perhaps surprising , as one might expect agns to have larger values of @xmath34 than star - forming galaxies because of the typically hotter temperatures of dust emission associated with harder ionizing continua . this is true even for seyfert 2 galaxies that are typically assumed to have intrinsic absorption that blocks the direct line of sight to the accretion disk ( e.g. , * ? ? ? one source of hot dust emission in star - forming galaxies that may contribute significantly at @xmath59 is from dust shells around agb stars , ( e.g. , * ? ? ? the five known low - ionization nuclear emission region ( liner ) galaxies ( open squares ) , which can be powered by either star - formation or accretion ( e.g. , * ? ? ? * ) , also do not lie in a distinct region within this parameter space . the recent mid - infrared spectroscopic survey of @xcite found two distinct liner populations separable by infrared luminosity ; the two populations can be divided at @xmath60@xmath61 ( where @xmath62 is integrated from 81000 ) . in brief , infrared emission lines , continuum shape , and pah features indicate that infrared - luminous liners are more closely linked to starburst galaxies , while infrared - faint liners were identified primarily with agns . however , the presence of high ionization lines such as [ ] seems to indicate that as many as 90% of all liners in their sample contain agns , though accretion power is not energetically dominant in the majority of cases . the two liners in our sample with no evidence for mid - infrared activity , 42a and 62a , are known x - ray sources , and therefore likely do host agns . their low mid - infrared luminosities and weak emission - line signatures in the optical indicate that the agns are not particularly powerful . given that their values of of 4.0@xmath63 and 6.6@xmath63@xmath61 are also the two lowest in the sample , they might be identified with the infrared - faint liners of @xcite . the other three ( 16a , 16d , and 90d ) may therefore be star - formation powered , though this remains ambiguous without mid - infrared spectra . focusing on longer wavelengths , three galaxies show evidence for dust emission at 24 that is not evident when only considering the irac data . in particular , a plot of @xmath40 vs. @xmath4 reveals a clear separation between galaxies at @xmath4@xmath64 , see figure [ fig : fracd]b . with only one exception ( 62d ) , all known hcg absorption - line galaxies have @xmath4@xmath65 and @xmath40@xmath66 . none of the identified star - forming galaxies is in that region , while two liners ( 42a and 62a ) and one optical agn ( 22a ) are . while all of the galaxies identified as mid - infrared - active from their values of @xmath1@xmath67 have @xmath40@xmath68 and @xmath4@xmath69 , an additional three galaxies , the seyfert 2s 16b and 61a and the absorption - line galaxy 62d , appear as 24-excess sources . an examination of their mid - infrared seds ( fig . [ fig : sed ] ) indicates that these galaxies likely include a strong contribution from stellar photospheric emission throughout most of the irac bands , and only at 24 , near a minimum of the elliptical template sed , is there sufficient contrast to see the low - luminosity dust continuum . hereafter , we designate all sources with @xmath4@xmath70 and @xmath40@xmath68 as `` 24-active '' . combining diagnostics of mid - infrared and 24 activity , @xmath40 vs. @xmath1 is shown in figure [ fig : alphas ] , coded by both richness ( as listed in column 9 of table [ tab : groups ] ) and galaxy morphology . in this plot , it is clear again that all nuclei designated as mid - infrared - active are also 24-active , though the converse is not true for three objects . the dashed line represents @xmath1=@xmath40 , and the elliptical galaxy nuclei ( with the exception of 62d ) are all tightly clustered near this line . these objects are also typically in -poor groups . nuclei from each of the most -rich ( type i ) groups , 2 , 16 , 31 , and 61 , have the most negative ( reddest ) @xmath1 values . this implies a connection between the availability of and 24activity from both agns and star formation . however , not all nuclei within an -rich group are 24-active , though the fraction is quite high ranging from 67 to 100% for the four -rich groups ( see table [ tab : groups ] ) . evaluating the relationship between the fraction of 24-active ( @xmath4@xmath70 ) nuclei and group mass as shown in figure [ fig : gas]a , the non - parametric spearman s @xmath53 test gives a probability , @xmath54 , of only @xmath71 for @xmath72 that these parameters are uncorrelated . considering only mid - infrared - active galaxies , the correlation is less significant ( @xmath73 ; @xmath74 ) , though still present . thirty - one of the 46 hcg galaxies have @xmath75 masses ( including 14 upper limits ) calculated from co surveys @xcite . ( of these , 90bd and 31ace were unresolved in the radio images . ) in a plot of @xmath75 vs. @xmath50 , the most mid - infrared luminous nuclei have large amounts of @xmath75 , however , there is quite a large scatter as shown in figure [ fig : gas]b . in fact , not all mid - infrared luminous galaxies have large @xmath75 reservoirs . however , more complete and deeper molecular gas surveys are needed to explore this relationship in further detail . given the proximity of our targets , the _ spitzer _ angular resolution offers a handle on investigating the difference between nuclear and integrated galaxy parameters for identifying potential nuclear activity . this is particularly relevant for survey work , where more distant objects are typically unresolved with _ spitzer_. using the criterion that values of @xmath1@xmath48 indicate mid - infrared activity , the galaxy and nuclear data for the hcg sample are completely consistent ( see figure [ fig : hists]b ) . at longer wavelengths , however , there are some discrepancies . in particular , @xmath4@xmath70 as the discriminant for a 24 excess yields some differences depending on whether the integrated galaxy light or nuclear light is considered . though all galaxies with @xmath4@xmath76 also have @xmath4@xmath77 , four additional galaxies 7b , 42a , 42b , and 90b have 24 excesses in their integrated galaxy light . this is also evident from visual inspection of their seds as plotted in figure [ fig : sed ] . the values of @xmath4 of the integrated galaxy vs. nuclear light are shown in figure [ fig : galnuc ] . the four discrepant galaxies are all early type ( sb0 , e3 , sb0 , and e0 , respectively ) ; the 24 excess is thus evidence of low - level star formation occurring outside of the nuclei in these galaxies . if such objects were at a much greater distance such as typical of large area surveys , the corresponding lack of spatial resolution could therefore lead to inaccuracies in the nuclear classification based on mid - infrared data alone . no activity would be missed , but some objects would be classified as 24- active ( and therefore potentially hosting llagns ) where extranuclear star formation is in fact responsible .

we present a simple theoretical framework to describe the thermal noise of a microscopic mechanical beam in a viscous fluid : we use the sader approach to describe the effect of the surrounding fluid ( added mass and viscous drag ) , and the fluctuation dissipation theorem for each flexural modes of the system to derive a general expression for the power spectrum density of fluctuations . this prediction is compared with an experimental measurement on a commercial atomic force microscopy cantilever in a frequency range covering the two first resonances . a very good agreement is found on the whole spectrum , with no adjustable parameters but the thickness of the cantilever .

c

0811.3429

we present a simple theoretical framework to describe the thermal noise of a microscopic mechanical beam in a viscous fluid : we use the sader approach to describe the effect of the surrounding fluid ( added mass and viscous drag ) , and the fluctuation dissipation theorem for each flexural modes of the system to derive a general expression for the power spectrum density of fluctuations . this prediction is compared with an experimental measurement on a commercial atomic force microscopy cantilever in a frequency range covering the two first resonances . a very good agreement is found on the whole spectrum , with no adjustable parameters but the thickness of the cantilever .

in this paper , we have presented a simple theoretical framework to describe the thermal noise of a mechanical beam in a viscous fluid . under the assumption of an infinitely thin and long cantilever , we used the sader approach to describe the effect of the surrounding fluid ( added mass and viscous drag ) . using the fluctuation dissipation theorem for each flexural modes of the system , we derived a general expression for the power spectrum density of fluctuations as the sum of the contribution of the different modes . this prediction has been compared with an experimental measurement on a commercial afm cantilever in a frequency range covering the 2 first resonances . a very good agreement has been found on the whole spectrum , with no adjustable parameters but the thickness of the cantilever . this analysis can be very useful in the afm area , where the thermal motion of the cantilever is of great practical importance ( as a lower bound to measurable forces or as a mechanical driving on its own ) : it is not limited to a fit of resonances only , but gives an _ a priori _ knowledge of the cantilever noise on the whole frequency spectrum . i thank f. vittoz and f. ropars for technical support , and p. paolino , s. ciliberto , a. petrosyan , j.p . aim and f. bertin for stimulating discussions . this work has been partially supported by contract anr-05-blan-0105 - 01 of the agence nationale de la recherche in france .

we present a simple way of coding and compressing the data on board the planck instruments ( hfi and lfi ) to address the problem of the on board data reduction . this is a critical issue in the planck mission . the total information that can be downloaded to earth is severely limited by the telemetry allocation . this limitation could reduce the amount of diagnostics sent on the stability of the radiometers and , as a consequence , curb the final sensitivity of the cmb anisotropy maps . our proposal to address this problem consists in taking differences of consecutive circles at a given sky pointing . to a good approximation , these differences are independent of the external signal , and are dominated by thermal ( white ) instrumental noise . using simulations and analytical predictions we show that high compression rates , @xmath0 , can be obtained with minor or zero loss of cmb sensitivity . possible effects of digital distortion are also analized . thus , this study constitutes an important step towards a more realistic modeling of the final sensitivity of the cmb temperature anisotropy maps . # 1 # 1([#1 ] ) # 1 # 1 # 1 # 1 # 1 # 1 # 1 # 1 # 1to 0pt#1

i

astro-ph9908289

we present a simple way of coding and compressing the data on board the planck instruments ( hfi and lfi ) to address the problem of the on board data reduction . this is a critical issue in the planck mission . the total information that can be downloaded to earth is severely limited by the telemetry allocation . this limitation could reduce the amount of diagnostics sent on the stability of the radiometers and , as a consequence , curb the final sensitivity of the cmb anisotropy maps . our proposal to address this problem consists in taking differences of consecutive circles at a given sky pointing . to a good approximation , these differences are independent of the external signal , and are dominated by thermal ( white ) instrumental noise . using simulations and analytical predictions we show that high compression rates , @xmath0 , can be obtained with minor or zero loss of cmb sensitivity . possible effects of digital distortion are also analized . the proposed scheme allows for flexibility to optimize the relation with other critical aspects of the mission . thus , this study constitutes an important step towards a more realistic modeling of the final sensitivity of the cmb temperature anisotropy maps . # 1 # 1([#1 ] ) # 1 # 1 # 1 # 1 # 1 # 1 # 1 # 1 # 1to 0pt#1

the planck satellite is designed to measure temperature fluctuations in the cosmic microwave background ( cmb ) with a precision of @xmath1 , and angular resolution of about 5 arcminutes . the payload consists of a 1.5 - 2.0 m gregorian telescope which feeds two instruments : the high frequency instrument ( hfi ) with 56 bolometer arrays operated at @xmath2 and frequencies of @xmath3ghz and the low frequency instrument ( lfi ) with 56 tuned radio receivers arrays operated at @xmath4 ( @xmath5 ) and frequencies of @xmath6 ghz ( see http://astro.estec.esa.nl/sa-general/projects/planck/ for more information ) . data on board planck consist of @xmath7 differential temperature measurements , spanning a range of values we shall call @xmath8 . preliminary studies and telemetry allocation indicate the need for compressing these data by a ratio of @xmath9 . here we will consider under what conditions it might be possible to achieve such a large compression factor . a discretized data set can be represented by a number of bits , @xmath10 , which for linear analogue - to - digital converters ( adc ) is typically given by the maximum range @xmath11 : @xmath12 . if we express the joint probability for a set of n measurements as @xmath13 , we have that the shannon entropy per component of the data set is : h - 1 _ i_1 , , i_n p_i_1 , , i_n _ 2(p_i_1 , , i_n ) . [ h ] shannon s theorem states that @xmath14 is a lower bound to the average length of the code units . we will therefore define the theoretical ( optimal ) compression rate as c_r , opt [ cr ] for a uniform distribution of @xmath7 measurements we have @xmath15 and @xmath16 , which equals the number of bits per data . thus : it is not possible to compress a ( uniformly ) random distribution of measurements . gaztaaga ( 1998 ) , have argued that a _ well calibrated signal _ will be dominated by thermal ( white ) noise in the instrument : @xmath17 and therefore suggested that the digital resolution @xmath18 only needs to be as small as the instrumental rms white noise : @xmath19 . the nominal @xmath20 pixel sensitivity will only be achieved after averaging ( on earth ) . this yields compression rates of @xmath21 . on the other hand maris ( 1999 ) have used the same formalism as gaztanaga but fixing the final dynamical range @xmath8 to some fiducial values , so that the digital resolution is then given by @xmath22 , independently of @xmath23 . again , assuming a well calibrated signal dominated by thermal ( white ) noise , this approach yields smaller compression rates of @xmath24 , as it is obvious from the fact that the digital resolution is larger ( @xmath18 is smaller ) . in both cases , the effect of the cmb signal ( eg dipole ) and other sources ( such as the galaxy ) have been ignored . several questions arise from these studies . what is the optimal value of @xmath18 and what are the penalties ( distortions ) involved when using large values of @xmath18 ? moreover , can the data gathered by the on board instruments be really modeled as a white noise signal ? in other words , are the departures from gaussianity ( due to the galactic , foregrounds , dipole and cmb signals ) important ? this latter question is closely related to the way data will be processed ( and calibrated ) on board , for example : if and how the dipole is going to be used for calibration . these issues together with the final instrument specifications seem to play an important role on the final range of values @xmath8 and , therefore , the possible compression rates . this is somehow unfortunate as compression would then be related in a rather complicated way to the nature of the external signal and also to critical issues of the internal data processing issues . here we shall present a simple way of coding the on board data that will solve the lossless compression problem in a much simpler way . this will be done independently of the internal calibration or the nature of the external signal ( cmb or otherwise ) . we will also address the issue of the digital distortion introduced ( the penalty ) as a function of the final compression ( the prize ) . in section 2 we give a summary of some critical issues related to the on - board data . our coding and compression proposals are presented in 3 , while simulations are dicussed in 4 . we end up with some concluding remarks .

we show that a self - segregated social structure can emerge from this process , i.e. , extreme learning strategies are always favoured while intermediate learning strategies tend to die out . this result may contribute to understanding some levels of organization and cooperative behaviour in ecological and social systems .

i

0804.3485

we present an agent - based model inspired by the evolutionary minority game ( emg ) , albeit strongly adapted to the case of competition for limited resources in ecology . the agents in this game become able , after some time , to predict the _ a priori _ best option as a result of an evolution - driven learning process . we show that a self - segregated social structure can emerge from this process , i.e. , extreme learning strategies are always favoured while intermediate learning strategies tend to die out . this result may contribute to understanding some levels of organization and cooperative behaviour in ecological and social systems . we use the ideas and results reported here to discuss an issue of current interest in ecology : the mistimings in egg laying observed for some species of bird as a consequence of their slower rate of adaptation to climate change in comparison with that shown by their prey . our model supports the hypothesis that habitat - specific constraints could explain why different populations are adapting differently to this situation , in agreement with recent experiments . , and evolutionary learning , climate change , limited resources , predator - prey

minority games ( challet and zhang , 1998 ) , and more recently evolutionary minority games ( emg ) ( johnson et . al . , 1999a ; johnson et . al . , 2000 ; de cara et . al . , 2000 ; johnson et . al . , 2003 ; hod and nakar , 2002 ; hod , 2003 ; sysi - aho et . al . , 2003 ; johnson et . al . , 1999b ; lo et . al . , 2000 ) , have received widespread attention in recent years as a useful model to describe competition for highly limited resources in complex systems , especially in economics . these games are essentially based on a minority rule ( challet and zhang , 1998 ) according to which @xmath0 agents compete repeatedly for some resources by choosing between two options a or b. each agent makes its choice , and those agents belonging to the less ( most ) frequently chosen option are considered the winners ( losers ) , so they are rewarded ( fined ) . so , the idea behind this game is that the agents must always try to be in the minority : few individuals choosing the same option as yourself means less competitors , and so it should be easier to obtain the resource . the decisions taken by the agents are chosen according to a pool of strategies available , and these strategies are based on the @xmath1 previous outcomes in the game , as that information is assumed to be accessible to all of the agents . to give a simple example , a specific strategy in a minority game with @xmath2 has the form @xmath3 this means that if the two previous winning options in the game were ( a , a ) , an agent following strategy @xmath4 will choose option a the next time ; if the last winning options were ( a , b ) , that agent will choose b , and so on . at the beginning of the game several strategies are assigned to each agent , and the agent tends to choose from among them the strategy that gave better results in the past ; however , many different versions of the minority game exist , where the rules that determine the strategies chosen by the agents are different . here , we will skip the minor details on the mechanisms of the minority game , since that is outside the scope of the current work ; an exhaustive compilation of works on minority games can be found in http://www.unifr.ch/econophysics . in the evolutionary version ( emg ) of the game ( johnson et . al . , 1999a ) , all the agents are assigned the same strategies but they can _ i ) _ follow that given strategy with probability @xmath5 or _ ii ) _ do exactly the opposite with probability @xmath6 , where @xmath5 is different for each agent ( the subindex @xmath7 denotes the @xmath7th agent ) . those agents performing the worst ( losing many times ) are forced to change their value of @xmath5 ; so , in the emg there is an implicit learning process based on _ trial and error . _ as a consequence , the system tends towards an optimal distribution of @xmath5 values for which the number of winners is as close to @xmath8 as possible ( note that , by definition , in a minority game the number of winners can not be higher than @xmath8 ) . as reported in ( johnson et . al . , 1999a ) , the most striking result arising from the emg is the natural emergence of segregated behaviour : those agents that behave in an extreme way ( @xmath9 and @xmath10 ) perform better than those with intermediate behaviour , so that the individuals tend to segregate into two groups : those who always follow the given strategy and those who never follow the strategy . from the point of view of complex systems , it has been claimed that this result may help to understand some levels of organization such as crowding ( johnson et . al . , 2000 ; cont and bouchaud , 2000 ) and cooperation ( de cara , 2000 ) , which are common in many social and biological systems . specifically , within the context of the emg some authors have coined the term _ unintentional _ or _ indirect cooperation _ to illustrate the behaviour observed ( quan et . al . , 2003 ; hod and nakar , 2004)_. _ this concept refers to the fact that in the emg many agents tend to behave similarly ( either @xmath9 or @xmath10 ) , but not consciously , but rather because the global winning probability is higher that way . this is different from other games ( for example , the well - known prisoner s dilemma ) where cooperation is a conscious option given to the agents ( nowak et . al . , 2004 ; nowak 2006 ) .

our model supports the hypothesis that habitat - specific constraints could explain why different populations are adapting differently to this situation , in agreement with recent experiments . , and evolutionary learning , climate change , limited resources , predator - prey

c

0804.3485

we present an agent - based model inspired by the evolutionary minority game ( emg ) , albeit strongly adapted to the case of competition for limited resources in ecology . the agents in this game become able , after some time , to predict the _ a priori _ best option as a result of an evolution - driven learning process . we show that a self - segregated social structure can emerge from this process , i.e. , extreme learning strategies are always favoured while intermediate learning strategies tend to die out . this result may contribute to understanding some levels of organization and cooperative behaviour in ecological and social systems . we use the ideas and results reported here to discuss an issue of current interest in ecology : the mistimings in egg laying observed for some species of bird as a consequence of their slower rate of adaptation to climate change in comparison with that shown by their prey . our model supports the hypothesis that habitat - specific constraints could explain why different populations are adapting differently to this situation , in agreement with recent experiments . , and evolutionary learning , climate change , limited resources , predator - prey

we have presented a model that sets the ideas of minority games , which are considerably popular tools for describing competition for resources in economics , into an ecological context . the model presented here shows how social segregation emerges from an evolutionary learning process ( determined by the distribution @xmath27 ) in a group of individuals competing for strongly limited resources . note that if the learning process were not introduced to the model , then the dynamics of the system would be trivial . neither persistent nor wise behaviour on its own is an efficient strategy ; evolutionary learning is the key ingredient here for finding efficient cooperation between both . this idea , together with the robustness shown by our model ( many other implementations with more realistic rules led to similar qualitative results ) seems to suggest that our model could be of interest for understanding social organization in complex evolutionary systems . the results obtained here show that in the situation described by our model intermediate learning strategies can not persist for long times ; the tendency is always towards improvement ( @xmath36 ) , suppression ( @xmath30 ) or the coexistence of both ( segregated distribution ) . it also contradicts the intuitive idea that those individuals with a higher learning capacity must always be favoured by selection . this is a consequence of the strong competition process which is assumed in our elg and in minority games in general : sometimes the _ a priori _ worst option can be the best because many agents tend to choose the _ a priori _ best option and then competition for the latter is higher . finally , we come back to the problem of egg laying in birds described before , which can now be addressed using the ideas about learning and phenotypic plasticity discussed here . in order to provide an analogy with our model , we could imagine that option a means laying early and option b means laying later . those individuals with a higher plasticity very quickly become able to follow some environmental cues in order to predict the right option a or b. however , if the penalty for choosing a wrong option is not high ( because there are some other food resources available , or there are some other environmental constraints on laying ... ) then selection will not favour individuals with higher plasticity . in that case , when the individuals must face sudden environmental changes their capacity to respond will be weak . in those habitats where phenotypic plasticity is strongly rewarded ( i.e. , for @xmath11 small in our model ) , individuals are expected to follow efficient learning strategies , so they will be able to respond better to environmental changes . therefore , the results of our model provide an evolutionary basis to the idea that environmental constraints from each specific habitat could explain why different bird populations are responding differently to climate - driven changes in the behaviour of their prey , as recent experiments have suggested ( gienapp and visser , 2006 ) . however , empirical evidence supporting our ideas about learning and phenotypic plasticity is still lacking . we believe that it would be of major interest if experimentalists were to attempt to check the predictions made by our model in real ecological systems .

one is the lynden - bell entropy maximization analysis that introduced violent relaxation . ( instead of stirling , we utilize a very accurate smooth approximation for @xmath0 . ) the second analysis extends entropy production extremization to self - gravitating systems , also without the use of the stirling approximation . we implicitly assume that all of the phase - space is equally accessible . both thermodynamic approaches lead to the same equilibrium structures .

i

1201.5899

we present an analysis of two thermodynamic techniques for determining equilibria of self - gravitating systems . one is the lynden - bell entropy maximization analysis that introduced violent relaxation . since we do not use the stirling approximation which is invalid at small occupation numbers , our systems have finite mass , unlike lynden - bell s isothermal spheres . ( instead of stirling , we utilize a very accurate smooth approximation for @xmath0 . ) the second analysis extends entropy production extremization to self - gravitating systems , also without the use of the stirling approximation . in addition to the lynden - bell ( lb ) statistical family characterized by the exclusion principle in phase - space , and designed to treat collisionless systems , we also apply the two approaches to the maxwell - boltzmann ( mb ) families , which have no exclusion principle and hence represent collisional systems . we implicitly assume that all of the phase - space is equally accessible . we derive entropy production expressions for both families , and give the extremum conditions for entropy production . surprisingly , our analysis indicates that extremizing entropy production rate results in systems that have maximum entropy , in both lb and mb statistics . in other words , both thermodynamic approaches lead to the same equilibrium structures .

understanding how collisionless systems attain a specific mechanical equilibrium state is fundamentally important to astrophysics . for example , the cold dark matter structures that exist around galaxies are expected to fall into this class of system . individual dark matter constituents ( whatever they may be ) should evolve according to a mean - field gravitational potential , free of the influence of individual encounters . the range of mechanical equilibria available to a collisionless system is defined by the jeans equation , which represents the condition that no portion of the system experiences a net force . unfortunately , the jeans equation admits an infinity of solutions . even if the mass distribution is specified , there is an infinite set of acceptable mechanical equilibria , each involving a different velocity distribution . for spherical systems , these velocity distributions differ in their anisotropy profile that quantifies radial versus tangential motion . however , the question remains , how and/or why does any one collisionless system evolve to its particular mechanical equilibrium end - state , and what are the properties of such a state ? the statistical mechanics description of thermodynamics provides one path to obtaining the description of the final relaxed state . a fully relaxed system is the most statistically likely state of that system , or the one with an entropy maximum . in calculating the most likely state it is implicitly assumed that all states of the system are equally accessible . such an approach was taken by @xcite and applied to self - gravitating collisionless systems , with the hope of explaining the observed light distribution of elliptical galaxies . a collisionless system can be thought of as a fluid in the 6d phase - space of position and velocity . the ` particles ' in lynden - bell s analysis are parcels of phase - space , _ i.e. , _ parcels of this fluid , and so the distribution function ( df ) representing the phase - space density is defined in terms of energy per unit mass , not energy per particle . the analysis resulted in a df similar to the fermi - dirac case , but with a different normalization . @xcite argued that a non - degenerate limit is appropriate for stellar systems , and thus arrived at a df similar to that of the maxwell - boltzmann case ( an exponential ) which resulted in the isothermal sphere representing thermal equilibrium . since the isothermal sphere has an infinite extent and mass , its emergence from the entropy maximization procedure , which demanded a finite mass system , presented a contradiction . this apparent failure of entropy maximization was puzzling , and it was often argued that such systems do not have states of maximum entropy . some effort was made to investigate maximizing entropy with additional constraints beyond mass , energy , and angular momentum @xcite . other routes involving minimum energy states of self - gravitating systems were also developed ( _ e.g. , _ * ? ? ? recently , @xcite ( based on earlier work by * ? ? ? * ) has pointed out that the reason for the system s infinite mass was the use of the stirling approximation , @xmath1 . in contrast to systems usually treated in standard statistical mechanics , self - gravitating systems can apparently have small phase - space occupation numbers @xmath2 , making stirling a poor approximation . specifically , these systems have regions of phase - space or energy - space that are nearly or completely unoccupied , such that @xmath2 will be small . spatially , these regions can correspond to the center of the potential as well as its outer edge . using maxwell - boltzmann statistics and the exact @xmath3 , @xcite has found a distribution function from entropy maximization that is very similar to @xcite models . @xcite have shown that the energy - space occupation function @xmath4 derived using a very accurate smooth approximation to @xmath3 closely resembles the results of collisionless @xmath5-body simulations @xcite . from a statistical point of view , entropy is simply a measurement of the number of states accessible to a particular system . this relationship is most commonly expressed quantitatively as , @xmath6 where @xmath7 is the number of accessible states and @xmath8 is the boltzmann constant which serves to give entropy the correct thermodynamic units . as a result , counting procedures are key to determining specific realizations of entropy . @xcite discusses how there are four counting types that lead to physically relevant situations . bose - einstein statistics follow from counting states for indistinguishable particles that can co - habitate in the same state . when indistinguishable particles are not allowed to share states , fermi - dirac ( fd ) statistics emerge . classical maxwell - boltzmann ( mb ) statistics result from counting states available to distinguishable particles that can share states . completing the symmetry , systems where distinguishable ` particles'actually , parcels of phase - space cannot co - occupy states obey what has become known as lynden - bell ( lb ) statistics ( statistics ` iv ' in lynden - bell s original notation ) . each type of statistics will produce different representations of entropy , but we will focus on the two that deal with classical , or distinguishable particles , namely , lb and mb . we briefly recap the notation used in @xcite before proceeding with our discussion . the six - dimensional position - velocity phase - space ( @xmath9,@xmath10 ) is the usual setting for determining the statistics . imagine phase - space to be divided into a very large number of nearly infinitesimal parcels , called micro - cells , each having volume @xmath11 . each micro - cell can either be occupied or unoccupied by one of the @xmath5 phase - space elements of the system . these elements can be thought of as representing the fine - grained distribution function , which has a constant density value @xmath12 . because collisionless processes imply incompressibility of the fine - grained distribution function , the phase elements can not co - habitate . if phase - space is also partitioned on a coarser level so that some number @xmath13 of micro - cells occupy a macro - cell , then we can discuss a coarse - grained distribution function . the volume of a macro - cell is then @xmath14 and the @xmath15th macro - cell contains @xmath16 phase elements . we assume that while the volume of a macro - cell is much larger than that of a micro - cell , it is still very small compared to the full extent of phase - space occupied by the system . the number of ways of organizing the @xmath16 elements into the @xmath13 micro - cells without co - habitation is , @xmath17 if the elements were allowed to multiply occupy micro - cells , as in mb statistics , this number would be given by @xmath18 . to get the total number of accessible states , the possible ways to distribute the @xmath5 phase elements into @xmath16 chunks must also be included . @xcite derives , @xmath19 in the mb case , the only change is that the factorial ratio in the final product term is replaced by @xmath18 . the lb case disallows two phase - space elements from inhabiting the same phase - space location , so it explicitly takes into account the incompressibility of a collisionless fluid . since we are primarily interested in dark matter halos , lb is the natural case to consider . for completeness , and for the sake of having a comparison , we also treat the mb case , in the appendix . we argue that the lack of an exclusion principle in the mb case is equivalent to allowing collisions between particles . in a collisional system , particles from distant phase - space locations can be scattered into any other phase - space location , thereby increasing the phase - space density at the latter location . in principle , there is no limit to how high the density can get through such scatterings . in practice , the phase - space density probably can not become very high at most locations , but it can be higher than the original fine - grained df . we note that it is common to use mb to represent collisional systems . for example , @xcite argues that it is the correct statistics to use for globular clusters where the relatively small number of stars allows the cluster to relax through two - body interactions . it then makes sense that the energy distribution that the cluster will arrive at will be the same as that in a cloud of gas , which relaxes through collisions between molecules . in the non - degenerate limit , when the micro - cells are very sparsely populated and the density of the coarse - grained distribution function is very dilute compared to that of the fine - grained function , both lb and mb distribution functions , and hence density profiles , will look the same . in this paper we explore two possible approaches to deriving the final equilibrium state of self - gravitating systems , for each of the two types of statistics , lb and mb . in both , we use a very accurate , smooth approximation for @xmath0 valid for arbitrary occupation numbers @xmath20 . however , the price we pay for this improved approximation is the loss of analytic solutions . the first approach assumes that the final state is the maximum entropy state , an assumption that was first used in the context of self - gravitating systems in 1950 s @xcite . the second approach , again in the context of self - gravitating systems , was first taken by @xcite ; it posits that the final state corresponds to the extremum of entropy production rate . we explore extremizing entropy production because it has not been established beyond a doubt that real or computer simulated systems do fully relax to maximum entropy states . it is possible that their steady - state configurations do not correspond to maximum entropy . prior work on thermal non - equilibrium systems , but not in astrophysical contexts , suggests that stationary states like mechanical equilibrium occur when entropy production is extremized ( _ e.g. , _ * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? we investigate their applicability to self - gravitating systems in mechanical equilibrium . the new aspect in the present paper is that we use a very accurate approximation for @xmath0 , unlike our previous paper that assumed the stirling approximation . as @xcite has shown , replacing stirling with an accurate approximation ( i ) results in systems with finite total mass and energy , and ( ii ) significantly changes the structure of the systems . in all , we present four derivations ; entropy maximization for the lb and mb statistics are covered in sections [ lbsmax ] and [ smax ] . extremization of entropy production for lb and mb statistics are carried out in sections [ lbsigma ] and [ sigmax ] , respectively . we develop expressions for the relaxation functions ( see [ recap ] ) , and use these to better understand the evolution of coarse - grained distribution function . we compare our results with analogous versions of entropy production derived using the standard stirling approximation in @xcite . figure [ tblfig ] puts the present paper ( bwii in the figure ) in context . it is a schematic summary of the various statistical mechanical approaches to self - gravitating systems . the possible ways to frame the problem appears at the top of the figure ; one can formulate the problem in either the regular phase - space , or the energy space . below the thick horizontal line we show the two different routes for attaining the final steady - state state : maximizing entropy , and extremizing entropy production . once these choices are made one has to decide whether small occupation number regime will be important or not , and hence whether to use the stirling approximation for @xmath21 , or not . in the latter case , one must then decide whether to use the discrete ( `` discr . '' ) step - like , i.e. exact version of @xmath22 , or to approximate it with some smooth function ( `` cont . '' ) which remains very accurate down to small @xmath20 . note that hw10 and the present paper use different but similar approximations . there is no physical reason to introduce the exclusion principle in the energy state - space , hence the corresponding regions are marked as `` not relevant '' . the bottom entries of some columns in the table contain names of papers where the corresponding options were considered . k66 in parentheses below bwii means that @xcite results are nearly identical to ours . @xmath23 under lb67 means that @xcite final result , the isothermal sphere , had infinite mass . much of the background material for this work may be found in @xcite , and we briefly summarize these previously obtained results in section [ recap ] .

we derive entropy production expressions for both families , and give the extremum conditions for entropy production . surprisingly , our analysis indicates that extremizing entropy production rate results in systems that have maximum entropy , in both lb and mb statistics . in other words ,

i

1201.5899

we present an analysis of two thermodynamic techniques for determining equilibria of self - gravitating systems . one is the lynden - bell entropy maximization analysis that introduced violent relaxation . since we do not use the stirling approximation which is invalid at small occupation numbers , our systems have finite mass , unlike lynden - bell s isothermal spheres . ( instead of stirling , we utilize a very accurate smooth approximation for @xmath0 . ) the second analysis extends entropy production extremization to self - gravitating systems , also without the use of the stirling approximation . in addition to the lynden - bell ( lb ) statistical family characterized by the exclusion principle in phase - space , and designed to treat collisionless systems , we also apply the two approaches to the maxwell - boltzmann ( mb ) families , which have no exclusion principle and hence represent collisional systems . we implicitly assume that all of the phase - space is equally accessible . we derive entropy production expressions for both families , and give the extremum conditions for entropy production . surprisingly , our analysis indicates that extremizing entropy production rate results in systems that have maximum entropy , in both lb and mb statistics . in other words , both thermodynamic approaches lead to the same equilibrium structures .

@xcite have investigated entropy production in self - gravitating systems described by mb and lb and have developed expressions for the entropy production , @xmath24 for both the mb , @xmath25 \ : { \mathrm{d}}{\ensuremath{\boldsymbol{v}}},\ ] ] and lb cases , @xmath26 \ : { \mathrm{d}}{\ensuremath{\boldsymbol{v}}},\ ] ] where constant @xmath27 in equation [ siglb0 ] is @xmath28 . in these expressions , @xmath29 is the coarse - grained distribution function and @xmath30 is the relaxation function and forms the right - hand side of the boltzmann equation , @xmath31 if one were to assume , for a moment , that in the above equation @xmath29 is a fine - grained df , then the right hand side would be zero for collisionless systems . in other words @xmath32 , which means that on fine - grained scales there is no change in , or production of entropy ; in collisionless systems , entropy is fixed throughout evolution . let us be clear , we are not advocating for a specific process as a source for @xmath30 , like collisions in a gas . the relaxation function simply describes the lagrangian time rate of change of the distribution function . returning to our case where @xmath29 represents the coarse - grained df , equation [ boltzeqn ] states that entropy is produced [ and as we argue in @xcite it happens even in systems that have attained macroscopic steady - state ] because on microscopic scales the fine - grained df continues to wind and twist , which when combined with coarse - graining , gives rise to non - zero entropy change . from a different starting point , @xcite develops an expression for the right - hand side of equation [ boltzeqn ] in terms of a `` diffusion current '' that relates to correlations between fluctuations in the fine - grained distribution function . while that work details the makeup of this diffusion current , we simply focus on the broad behavior of the relaxation function . we find extremum entropy production conditions by setting the variation of entropy production , @xmath33 equal to zero . this operation gives expressions for the relaxation function . for the mb case , @xmath34 the lb relaxation function is slightly more complex , @xmath35}-c}.\ ] ] like @xcite , the @xcite work assumes that the large @xmath2 stirling approximation is valid for the systems being investigated . here , we will be deriving relations analogous to equations [ sigmb0 ] , [ siglb0 ] , [ gmb0 ] , and [ glb0 ] , but using a very accurate approximation , after discussing the results of entropy maximization below .

we present an implementation and an experimental evaluation of an algorithm that , given a connected graph g ( represented by adjacency lists ) , estimates in sublinear time , with a relative error @xmath0 , the minimum spanning tree weight of g ( see @xcite for a theoretical exposure of the algorithm ) . since the theoretical performances have already been shown and demonstrated in the above - mentioned paper of chazelle et al . some technical insights are given on the implementation of the algorithm and on the dataset used in the test phase , hence to show how the experiment has been carried out even for reproducibility purposes ; the results are then evaluated empirically and widely discussed , comparing these with the performances of the prim algorithm and the kruskal algorithm , launching several runs on a heterogeneous set of graphs and different theoretical models for them . we assume hereafter that the reader has knowledge about the cited paper as we will just recap the theoretical results . minimum spanning tree , sublinear time algorithms , randomized algorithm , approximation algorithm , minimum spanning tree weight , experimental evaluation 68w20 , 68w25 , 68r10

i

1701.08128

we present an implementation and an experimental evaluation of an algorithm that , given a connected graph g ( represented by adjacency lists ) , estimates in sublinear time , with a relative error @xmath0 , the minimum spanning tree weight of g ( see @xcite for a theoretical exposure of the algorithm ) . since the theoretical performances have already been shown and demonstrated in the above - mentioned paper of chazelle et al . our goal is , exclusively , to experimental evaluate the algorithm and at last to present the results . some technical insights are given on the implementation of the algorithm and on the dataset used in the test phase , hence to show how the experiment has been carried out even for reproducibility purposes ; the results are then evaluated empirically and widely discussed , comparing these with the performances of the prim algorithm and the kruskal algorithm , launching several runs on a heterogeneous set of graphs and different theoretical models for them . we assume hereafter that the reader has knowledge about the cited paper as we will just recap the theoretical results . minimum spanning tree , sublinear time algorithms , randomized algorithm , approximation algorithm , minimum spanning tree weight , experimental evaluation 68w20 , 68w25 , 68r10

we will discuss here some preliminary observations and assumptions . first of all , we observe that we need a set of graphs that satisfies the following points : * they should be finite and should not be multigraphs ; * they should be undirected ; * they should have weighted edges ; * the weights on the edges should be integers ; since the graph is finite , it is enough to show that there exist @xmath1 such that it is the maximum weight on the edges of the graph ; * they might contain self - loops ; * they have to be connected ( the graph has only one connected component ) ; * they should be represented with adjacency lists ; * they should be represented in the same manner ( we need an unvarying file format ) . unfortunately , the graphs and their representations , which can easily be found on the internet , do nt accomplish all of this requirements at the same time , although many standards for the file format are available . given this observation , our choice was to use randomly generated graphs , hence to implement our own graphs generator . this gives us the opportunity to generate a wide set of connected graphs , with tunable parameters , carefully chosen looking forward to the tests ; these parameters include the number of nodes , the number of edges and the edges weight , nonetheless the distribution law for the edges . the edges between the nodes are step - by - step randomly constructed , respecting the connection requirement . the different types of graphs that we use in our experimental evaluation are presented afterwards . after studying the paper we made some assumptions . one of the problem we encountered is that the theoretical algorithm assumes to have as input only graph @xmath2 and to have direct access to the family of graphs @xmath3 is an induced subgraph of @xmath2 such that the maximum weight on his edges is @xmath4 ( e.g. @xmath5 is exactly @xmath2 ) ] ; with `` direct '' we intend that no computation is required to extract @xmath3 , which is not true . in fact , we can show easily that a lower bound for the extraction of all the family is , at least , @xmath6 ( i.e. is linear on the number of edges ) . a nave approach would cost @xmath6 for the extraction of @xmath3 for a given @xmath4 , hence @xmath7 for the whole family ; a better approach could order the edges in @xmath8 and build the family in a single pass on the edges , achieving @xmath9 . having as input only @xmath2 , it would seem that the algorithm is responsible for the extraction of the family , but this is not desirable due to this lower bound that would sabotage the overall performance . finally we decided to consider this cost as a part of the construction of the data structure of the graph , to be done prior to the call of the algorithm .

quantitative comparisons are made of the influence of the jet opening angle on the above parameters of the radio knots , as would be estimated for two widely discussed variants of relativistic nuclear jets , namely , those having uniform bulk speed and those in which the bulk lorentz factor of the flow decreases with distance from the jet axis ( a ` spine sheath ' flow ) .

i

0707.4023

we present analytical modelling of conical relativistic jets , in order to evaluate the role of the jet opening angle on certain key parameters that are inferred from vlbi radio observations of blazar nuclear jets . the key parameters evaluated are the orientation angle ( i.e. , the viewing angle ) of the jet and the apparent speed and doppler factor of the radio knots on parsec scales . quantitative comparisons are made of the influence of the jet opening angle on the above parameters of the radio knots , as would be estimated for two widely discussed variants of relativistic nuclear jets , namely , those having uniform bulk speed and those in which the bulk lorentz factor of the flow decreases with distance from the jet axis ( a ` spine sheath ' flow ) . our analysis shows that for both types of jet velocity distributions the expectation value of the jet orientation angle at first falls dramatically with increases in the ( central ) jet lorentz factor , but it levels off at a fraction of the opening angle for extremely relativistic jets . we also find that the effective values of the apparent speeds and doppler factors of the knots always decline substantially with increasing jet opening angle , but that this effect is strongest for ultra - relativistic jets with uniform bulk speed . we suggest that the paucity of highly superluminal parsec - scale radio components in tev blazars can be understood if their jets are highly relativistic and , being intrinsically weaker , somewhat less well collimated , in comparison to the jets in other blazars . [ firstpage ] blazars : general galaxies : active galaxies : jets galaxies : nuclei galaxies : radio continuum

although very long baseline interferometry ( vlbi ) monitoring of the radio knots in blazar jets has revealed several sources containing knots with apparent speeds @xmath0 in excess of 25@xmath1 ( e.g. , kellermann et al . 2004 ; piner et al . 2006 ) , the typical speeds for blazars known to emit the highest energy @xmath2-ray photons ( tev blazars ) are found to be much more modest , with @xmath3 , and their radio knots are often subluminal ( e.g. , edwards & piner 2002 ; piner & edwards 2004 ) . the glaring contrast with the very large bulk lorentz factors in the parsec - scale blazar jets ( @xmath4 ) , as inferred from tev flux variations ( e.g. , krawczynski , coppi & aharonian 2002 ) , has been highlighted by several authors ( e.g. , giroletti et al . 2004 ; gopal - krishna , dhurde & wiita 2004 ; piner & edwards 2004 , 2005 ; levinson 2006 ) . similar ultra - relativistic bulk lorentz factors have also been inferred from the intraday radio variability of some blazars ( e.g. , rickett , kedziora - chudczer & jauncey 2002 ; macquart & de bruyn 2006 ) and , more directly , from vlbi measurements of the brightness temperatures of several blazar nuclei ( e.g. , horiuchi et al . 2004 ; cf . , kovalev et al . 2005 ) . the large mis - match between the estimates of @xmath5 derived from these different types of observations has led some authors to postulate a dramatic jet deceleration between sub - parsec and parsec scales ( e.g. , georganopoulos & kazanas 2003 ; cf . , piner & edwards 2005 ) . an alternative approach has been to invoke a ` spine sheath ' configuration for the jets such that the fast spine close to the jet axis is surrounded by an appropriately slow moving sheath ( e.g. , baan 1980 ; komissarov 1990 ; laing 1993 ; meier 2003 ; ghisellini , tavecchio & chiaberge 2005 ) . these considerations recently led us to undertake an analytical study which showed that the modest apparent speeds of the knots of blazars , which are mostly unresolved by vlbi , can be reconciled with the extremely relativistic bulk motion inferred for tev , and some other , blazars as noted above , if one considers a modest full opening angle @xmath6@xmath7 for the parsec - scale jets ( gopal - krishna , dhurde & wiita 2004 , hereafter paper i ) . we also showed that the actual viewing angles , @xmath8 , of such _ conical _ jets from the line - of - sight can be substantially larger than those commonly inferred ( e.g. jorstad et al . 2005 ) by combining the flux variability and the vlbi proper motion data ( gopal - krishna , wiita & dhurde 2006 , paper ii ) . direct support for the assumption of _ conical _ parsec - scale jets comes from the vlbi imaging of the nuclear jets in the nearest two radio galaxies , m87 ( biretta , junor & livio 2002 ) and centaurus a ( horiuchi et al . 2006 ) . our focus in this paper is on making a quantitative comparison of the predictions for two widely discussed jet forms ( i.e. , those with uniform @xmath5 and those with velocities decreasing away from the jet axis , the spine sheath types ) , of the extents to which some key parameters of the vlbi radio knots in blazar jets would be influenced by the jet opening angle . the three main jet parameters examined are the apparent speed ( @xmath9 ) of the knot , its doppler factor ( @xmath10 ) and the viewing angle ( @xmath8 ) to the jet axis from our line - of - sight . although discussed specifically for blazar jets , the present results are also relevant for @xmath2-ray burst sources ( grbs ) which too are believed to arise from extremely relativistic jets , with @xmath11 , and with even larger solid angles ( e.g. , mszros 2002 ; liang et al . 2006 , and references therein ) .

our analysis shows that for both types of jet velocity distributions the expectation value of the jet orientation angle at first falls dramatically with increases in the ( central ) jet lorentz factor , but it levels off at a fraction of the opening angle for extremely relativistic jets . we also find that the effective values of the apparent speeds and doppler factors of the knots always decline substantially with increasing jet opening angle , but that this effect is strongest for ultra - relativistic jets with uniform bulk speed .

c

0707.4023

we present analytical modelling of conical relativistic jets , in order to evaluate the role of the jet opening angle on certain key parameters that are inferred from vlbi radio observations of blazar nuclear jets . the key parameters evaluated are the orientation angle ( i.e. , the viewing angle ) of the jet and the apparent speed and doppler factor of the radio knots on parsec scales . quantitative comparisons are made of the influence of the jet opening angle on the above parameters of the radio knots , as would be estimated for two widely discussed variants of relativistic nuclear jets , namely , those having uniform bulk speed and those in which the bulk lorentz factor of the flow decreases with distance from the jet axis ( a ` spine sheath ' flow ) . our analysis shows that for both types of jet velocity distributions the expectation value of the jet orientation angle at first falls dramatically with increases in the ( central ) jet lorentz factor , but it levels off at a fraction of the opening angle for extremely relativistic jets . we also find that the effective values of the apparent speeds and doppler factors of the knots always decline substantially with increasing jet opening angle , but that this effect is strongest for ultra - relativistic jets with uniform bulk speed . we suggest that the paucity of highly superluminal parsec - scale radio components in tev blazars can be understood if their jets are highly relativistic and , being intrinsically weaker , somewhat less well collimated , in comparison to the jets in other blazars . [ firstpage ] blazars : general galaxies : active galaxies : jets galaxies : nuclei galaxies : radio continuum

fig . 2 shows a steep initial decline of @xmath68 with increasing @xmath52 , regardless of the chosen values of @xmath40 or @xmath39 . this decline continues until the regime of ultra - relativistic jets ( @xmath69 ) is reached , whereafter @xmath59 becomes essentially independent of @xmath52 . the near constancy of @xmath68 for extremely relativistic jets is particularly striking for the conical jets having a uniform @xmath5 and at least a moderate opening angle ( @xmath70@xmath7 . further , in this ultra - relativistic regime , the tendency for @xmath71 to increase with @xmath40 is found to accelerate with the increase in the opening angle @xmath40 . interestingly , these trends found for the uniform @xmath5 jets are also shared by both representative forms of spine sheath jets considered here . quantitatively , for @xmath72 , ultra - relativistic jets of all the three forms ( i.e. , @xmath73 and @xmath62 ) , have @xmath59 in the narrow range from @xmath74 to @xmath75 . the corresponding range of @xmath68 for @xmath76 jets is @xmath75 to @xmath77 , for all @xmath5s above @xmath78 . from fig . 2 , it is also evident that in a typical radio flux - limited sample of blazars , a larger opening angle of an ultra - relativistic jet would correspond to a considerably larger @xmath68 ; hence a milder fore - shortening due to projection is typically expected ( see paper ii for an expanded discussion of this last point for uniform velocity jets ) . we now examine the influence of @xmath40 on the _ effective _ apparent speed of a radio knot , c@xmath23 , and its _ effective _ doppler factor , @xmath24 ( eqs . 4 & 5 ) . these are displayed in fig . 3 ( @xmath66 ) and in fig . 4 ( @xmath50 ) for the computed expectation values @xmath68 ( which is a function of @xmath40 , @xmath52 , @xmath34 and @xmath10 and hence varies along each curve , as explained above ) . good analytical fits to simple exponential curves were found to all the computed values of @xmath23 and they are quoted within those figures . exponential functions also gave good fits to all but two of the 18 cases considered for @xmath24 ; in those cases the displayed polynomial fits were found to be substantially better . firstly , it is seen that the decline of @xmath23 with @xmath40 is sharper for the knots associated with jets of higher @xmath5 ( for both uniform and stratified types ) . on the other hand , for well collimated jets ( i.e. , @xmath79 ) , @xmath23 for the uniform @xmath5 case would typically be 1.5 to 2 times higher than for the @xmath80 and between 2 and 4 times higher for the @xmath81 ( the two spine sheath cases ) . thus , the fastest _ spine _ component of the jet flow , which is near the jet axis , would be substantially concealed in the vlbi measurements . it is interesting to note that the much sharper fall of @xmath23 with @xmath40 found for the uniform @xmath5 case ( especially in fig . 2 ) ensures that already for modest jet opening angles , the value for @xmath23 of such jets would drop below the corresponding values for both of the spine sheath models considered here . for @xmath82 this crossover is seen to occur near @xmath83 and @xmath84 , for @xmath85 and @xmath86 , respectively , such that beyond these modest jet opening angles , @xmath23 rapidly approaches mildly relativistic ( or , even sub - relativistic ) values in the case of extremely relativistic jets with uniform @xmath5 . this steep fall of @xmath23 was first pointed out in paper i for the case of uniform @xmath5 jets and we find here a similar , albeit milder , dependence for the stratified ultra - relativistic jets as well ( figs . 3 and 4 ) . it is also worth noting that while for well collimated ultra - relativistic jets @xmath23 is more strongly suppressed ( relative to the uniform @xmath5 case ) when @xmath5 is more peaked towards the axis ( i.e. , @xmath87 ) ; the opposite is found for the jets having a significant opening angle ( @xmath88 to @xmath89 , with the exact cross - over value of @xmath40 depending on @xmath52 and @xmath34 . in summary , provided the conical jet is moderately wide ( @xmath90 ) , the measured apparent speeds of the vlbi knots would typically remain under @xmath91 , even if @xmath52 were extremely large ( @xmath92 ) , _ not only for the uniform @xmath5 jets but even for the stratified jets_. the right columns of figs . 3 and 4 illustrate the @xmath40-dependence of the ` effective doppler factor ' ( @xmath24 ) for the uniform @xmath5 jets and for the two stratified jet forms ; recall that @xmath24 is the cube root ( for the @xmath82 case ) , or square root ( for @xmath50 ) of the flux boosting factor , @xmath47 , averaged over the radio knot ( eq . 4 ) . again , each point of these profiles is meant for the corresponding value of @xmath59 , as discussed above . it is seen that for cases of very good collimation ( @xmath93 ) , the uniform @xmath5 jets would typically have 2 to 4 times larger @xmath24 compared to the stratified jets , implying roughly an order - of - magnitude stronger doppler boost . as expected for stratified jets , a sharper spine sheath contrast ( i.e. , a larger @xmath39 ) leads to a lower @xmath24 . further , as for @xmath23 , a significant reduction in @xmath24 with @xmath40 is the typical expectation for both kinds of jet , the dependence being stronger for extremely relativistic jets , particularly the uniform @xmath5 type ( figs . 3 and 4 ) this leads to a situation where extremely relativistic jets of both uniform and stratified @xmath5 types end up with comparable @xmath24 values , once @xmath40 exceeds about @xmath94 , although the @xmath24 values for the uniform jets do remain larger than those for the stratified jets over the wide parameter space considered here . these still very high values of @xmath24 mean that rapid variability in tev @xmath2-ray emission is to be expected in any of our ultrarelativistic models as the variability timescale is proportional to @xmath95 . significant changes in tev fluxes on sub - hour timescales have been reported for mrk 421 ( e.g. , baejoski et al . 2005 ) . often , vlbi observations reveal different apparent speeds for the radio knots in the same jet . this is usually interpreted by postulating that the knots reflect ` pattern speeds ' which can be substantially different from the underlying speed of the jet ( e.g. , vermeulen & cohen 1994 ; cohen et al . 2007 ) . in our picture , such variations can be readily understood in terms of surface brightness distributions across the different knots being dissimilar . moreover , the observed lack of sources with large apparent speeds but low brightness temperatures ( e.g. , kovalev et al . 2005 ; homan et al . 2006 ) also suggests that the intrinsic pattern speed should be broadly correlated to the jet s bulk speed . as noted in paper i , for the case of fully collimated jets the bulk lorentz factor would have to quickly drop by 1 to 2 orders of magnitude between sub - parsec ( tev ) and parsec ( radio vlbi ) scales in order to reconcile the very large doppler factors inferred from the compactness argument with the marginally superluminal ( even sub - luminal ) motion observed for the vlbi knots ( sect . 1 ) . at present there is no direct observational evidence for such drastic deceleration ( and the concomitant dissipation ) occurring on sub - parsec scales in blazar nuclei . rather , for cygnus a , where sub - pc radio knot motions can be measured from millimetre vlbi and the jets are close to the plane of the sky ( so that small changes in direction would not yield significant apparent speed changes ) the evidence favors modest acceleration , not deceleration , on the sub - pc scale ( bach et al . one aim of our model is to eliminate the need for such a massively rapid deceleration . a key question is : why is the lorentz factor dichotomy so striking only for tev blazars ( e.g. , piner & edwards 2004 ) ? essentially all blazars show two correlated peaks in their spectral energy distributions and are now usually classified by the frequency at which the lower frequency ( synchrotron ) peak is strongest ( e.g. , padovani & giomni 1995 ; sambruna , maraschi & urry 1996 ) . now , according to the popular scheme unifying high energy peaked ( hbl ) and low energy peaked blazars ( lbl ) ( e.g. , sambruna et al . 1996 ; fossati et al . 1998 ) , tev emission , which is an hbl characteristic , would be more common among lower luminosity blazars . this hypothesis has been supported by a recent study , which indicates that the synchrotron peaks for powerful blazars ( the flat - spectrum radio quasars ) all remain below the rather high energy ( @xmath96 1 kev ) which is characteristic of hbls and tev blazars ( padovani 2007 ) . we also recall that extragalactic jets tend to be less well collimated for lower luminosity sources , although this is only well established on the kpc scales where their opening angles can be routinely measured ( e.g. , bridle 1984 ) . opening angles on sub - pc scales can be measured fairly unambiguously only for very nearby sources such as m87 ( biretta et al . 2002 ) and centaurus a ( horiuchi et al . 2006 ) where the jets lie rather close to the plane of the sky ; both of these are indeed relatively weak sources with wide jets . on the scale of nuclear jets blandford ( 1993 ) gives a theoretical argument for this weak / wide correlation . assuming it does hold , then the correlation between hbl properties and intrinsically weaker jets would mean that the jet opening angle should be larger for tev emitting jets . likely consequences of this are : ( a ) the probability of detecting tev blazars would be enhanced , since , even though the tev emission itself is probably beamed very sharply , its effective beaming angle is in fact much larger , and actually more like the jet opening angle ( see , phinney 1985 ; blandford 1993 ; begelman , rees & sikora 1994 ) ; ( b ) the wider jet would mean a bigger reduction in the apparent velocity of the radio knot ( paper i and figs . 3 and 4 ) . we suggest that the combination of these factors is probably responsible for the intriguing preference of tev blazars to display slower motions of their vlbi knots .

we present combinatorial operators for the expansion of the kronecker product of irreducible representations of the symmetric group @xmath0 . this leads to a combinatorial description of the kronecker powers of the irreducible representations indexed with the partition @xmath1 which specializes the concept of oscillating tableaux in young s lattice previously defined by s. sundaram . we call our specialization _ kronecker tableaux_. their combinatorial analysis leads to enumerative results for the multiplicity of any irreducible representation in the kronecker powers of the form @xmath2 .

i

math0503307

we present combinatorial operators for the expansion of the kronecker product of irreducible representations of the symmetric group @xmath0 . these combinatorial operators are defined in the ring of symmetric functions and act on the schur functions basis . this leads to a combinatorial description of the kronecker powers of the irreducible representations indexed with the partition @xmath1 which specializes the concept of oscillating tableaux in young s lattice previously defined by s. sundaram . we call our specialization _ kronecker tableaux_. their combinatorial analysis leads to enumerative results for the multiplicity of any irreducible representation in the kronecker powers of the form @xmath2 .

the subject of the present work is the investigation of the kronecker product , sometimes called inner tensor product , of irreducible representations of the symmetric group @xmath0 . given two linear representations @xmath3 which associate linear operators to permutations @xmath4 , the kronecker product of @xmath5 and @xmath6 , denoted @xmath7 , is the representation of @xmath0 defined by @xmath8 which is the action on the tensor product @xmath9 of vector spaces @xmath10 and @xmath11 by means of the tensor product @xmath12 of the linear operators @xmath13 and @xmath14 . the irreducible representations of @xmath0 are the representations which are indecomposable as direct sums of representations . they are indexed with the partitions @xmath15 of @xmath16 : @xmath17 the kronecker product @xmath18 of two irreducible representations of @xmath0 is in general not an irreducible representation of @xmath0 and the fundamental problem of expanding it as a direct sum of irreducible representations @xmath19 goes back to the foundation of the representation theory . this problem was studied by murnaghan @xcite , littlewood @xcite and more recently by lascoux @xcite , garsia and remmel @xcite , thibon _ et al . _ @xcite , and others ( see @xcite and references therein ) . to obtain the decomposition coefficients @xmath20 , one can use the characters of the corresponding representations . the character of a representation @xmath5 of @xmath0 is the map @xmath21 which sends permutations @xmath22 to the traces of @xmath13 : @xmath23 the fact that the character of the kronecker product @xmath7 of two representations is obtained by multiplying the traces of the linear operators @xmath13 and @xmath14 : @xmath24 is a straightforward consequence of the definition of tensor product of linear operators . hence one can use property ( [ eq1 ] ) of characters and the character table , indexed by integer partitions of @xmath16 ( see table [ tab : char ] for example ) to compute the characters of a kronecker product of two irreducible representations . let us recall that the character values @xmath25 on two permutations @xmath26 in the same conjugacy class @xmath27 are equal . therefore we use the notation @xmath28 for the value of the irreducible character @xmath29 on any element of the conjugacy class @xmath27 . [ ex1 ] _ let table [ tab : char ] be the table of the irreducible characters of @xmath30 . _ c|r|r|r|r|c @xmath31@xmath32 & @xmath33 & @xmath34 & @xmath35 & @xmath36 & @xmath37 ' '' '' + & @xmath38 & @xmath38 & @xmath38 & @xmath38 & @xmath38 ' '' '' + & @xmath39 & @xmath40 & @xmath39 & @xmath38 & @xmath41 ' '' '' + & @xmath40 & @xmath39 & @xmath42 & @xmath40 & @xmath42 ' '' '' + & @xmath38 & @xmath40 & @xmath39 & @xmath39 & @xmath41 ' '' '' + & @xmath39 & @xmath38 & @xmath38 & @xmath39 & @xmath38 ' '' '' the character of the kronecker product @xmath43 of the irreducible representation @xmath44 with itself is obtained by multiplying each element of the row - vector @xmath45 in table [ tab : char ] with itself and we obtain @xmath46 since table [ tab : char ] contains the row - vectors of all possible irreducible characters and that @xmath47 is obviously not one of these rows , it is immediate that the character represented by @xmath47 is not irreducible . but we observe that the identity @xmath48 is true by adding the rows of table [ tab : char ] corresponding to the partitions in the right hand side . @xmath49 more generally , the problem of finding the coefficients @xmath50 has a solution when one accepts to use the character table @xmath51 $ ] of @xmath0 : @xmath52 identity ( [ eq3 ] ) follows from the orthonormality of the characters @xmath29 with respect to the standard scalar product in the group algebra of @xmath0 and from ( [ eq1 ] ) . but since the coefficients @xmath50 are positive integers , we find equation ( [ eq3 ] ) unsatisfactory and the goal of this paper is to contribute to other avenues for computing the coefficients @xmath50 . our presentation is in three steps . first we define operators on the ring of symmetric functions which reproduce tensor product of irreducible representations when they act on schur functions . second we specialize these operators to the tensor powers @xmath2 , for @xmath53 , and we develop a combinatorial model to represent these tensor powers . finally we obtain some enumerative results for the multiplicity of any irreducible representation in the kronecker powers of the form @xmath54 .

we present here two epochs of space vlbi observations at 18 cm of the bl - lac type object mkn 501 . vlbi data at 6 and 18 cm of the bl - lac type object mkn 421 are also presented . # 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in

i

astro-ph9810430

we present here two epochs of space vlbi observations at 18 cm of the bl - lac type object mkn 501 . thanks to the high resolution of these new data we have found that the inner jet is centrally brightened at its beginning but becomes extended and limb brightened at @xmath0 8 mas from the core . moreover a comparison between the two epochs shows the presence of a possible proper motion with apparent velocity = 6.7c . vlbi data at 6 and 18 cm of the bl - lac type object mkn 421 are also presented . observational data have been used to constrain the jet velocity and orientation . # 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in

mkn 501 and mkn 421 are two nearby bl - lac type objects at z = 0.034 and 0.030 , respectively . they are well studied sources in radio , optical and x - ray bands being among the brightest bl - lac objects at all wavelengths . mkn 421 was the first source to be detected at tev energies , followed by mkn 501 . in the radio band , both sources show a kpc scale morphology and a total radio power consistent with the expectation of unified scheme models that bl - lac type sources are fr i galaxies oriented at small angles to the line of sight . we present here new space vlbi observations of mkn 501 and vlbi data of mkn 421 . mkn 501 was observed at 18 cm on august 4th , 1997 and april 8th , 1998 in a space vlbi project using the halca satellite and 12 ground stations . mkn 421 was observed at 6 cm in july 1995 with the vlba and at 18 cm in february 1996 with the global vlbi . the data of both sources were correlated in socorro ( nm - usa ) and reduced with the aips package . a hubble costant of 50 km sec@xmath1 mpc@xmath1 is assumed throughout .

we present master formulas for the divergent part of the one - loop effective action for an arbitrary ( both minimal and nonminimal ) operators of any order in the 4-dimensional curved space . they can be considered as computer algorithms , because the one - loop calculations are then reduced to the simplest algebraic operations .

c

hep-th9605206

we present master formulas for the divergent part of the one - loop effective action for an arbitrary ( both minimal and nonminimal ) operators of any order in the 4-dimensional curved space . they can be considered as computer algorithms , because the one - loop calculations are then reduced to the simplest algebraic operations . some test applications are considered by reduce analitical calculation system . pacs nombers 11.10.gh , 04.62.+v

in this paper we calculate the divergent part of the one - loop effective action for an arbitrary ( minimal and nonminimal ) operators without any restrictions to their form and order in the curved space - time , using thooft - veltman diagram technique @xcite . actually , we made some operations , that encounter in calculating feynman diagrams , namely , integration over a loop momentum , summation of all divergent graphs and obtaining a manifestly covariant result by its weak field limit in the general case . then , in order to calculate the divergent part of the effective action , one should only substitute the explicit expression for second variation of an action . unfortunately , the master formula is very large and can hardly be used for calculations without computers . nevertheless , on the base of the general algorithm we obtained one - loop counterterms for some examples , namely , an arbitrary minimal operator , the vector field operator and the gravity theory in the @xmath106-gauge . our results were in agreement with the ones found earlier . the calculations were made by the tensor package for the reduce analytical calculation system @xcite . for the considered examples the required memory and execution time were the following ( we used ibm-486/dx-2/66/8 mb ) : \1 . calculation of the rr contribution for an arbitrary minimal operator by ( [ rr ] ) took 17 seconds . in this case the required memory was about 500 kb . \2 . for the vector field operator and its square execution time was 174 and 515 seconds respectively . required memory was 2 mb . the calculation of the one - loop counterterms for the gravity theory in the @xmath106-gauge took 170 minutes while the required memory was 8 mb . * acknolegments * we are very grateful to professors d.v.shirkov ( jinr , dubna ) and a.a.slavnov ( steklov mathematical institute ) on the attention to our work , dr . m.yu.kalmykov ( jinr , dubna ) and dr . v.v.zhytnikov ( moskow pedagogical university , moskow ) on the valuable discussions . * appendix *

we present one - dimensional simulation results for the cold atom tunneling experiments by the heidelberg group [ g. zrn _ et al . et al . _ , we use our numerical calculations along with the experimental tunneling rates for the non - interacting system to reparameterize the trapping potential . the reparameterized trapping potentials serve as input for our simulations of two interacting particles . for two interacting ( distinguishable ) atoms on the upper branch , , we compare the time dynamics with that of two identical fermions and discuss the implications of fermionization on the dynamics . for two attractively - interacting atoms on the molecular branch our first set of calculations yields qualitative but not quantitative agreement with the experimentally measured tunneling rates . we obtain quantitative agreement with the experimentally measured tunneling rates if we allow for a weakened radial confinement .

i

1509.00931

we present one - dimensional simulation results for the cold atom tunneling experiments by the heidelberg group [ g. zrn _ et al . _ , phys . rev . lett . * 108 * , 075303 ( 2012 ) and g. zrn _ et al . _ , phys . rev . lett . * 111 * , 175302 ( 2013 ) ] on one or two @xmath0li atoms confined by a potential that consists of an approximately harmonic optical trap plus a linear magnetic field gradient . at the non - interacting particle level , we find that the wkb ( wentzel - kramers - brillouin ) approximation may not be used as a reliable tool to extract the trapping potential parameters from the experimentally measured tunneling data . we use our numerical calculations along with the experimental tunneling rates for the non - interacting system to reparameterize the trapping potential . the reparameterized trapping potentials serve as input for our simulations of two interacting particles . for two interacting ( distinguishable ) atoms on the upper branch , we reproduce the experimentally measured tunneling rates , which vary over several orders of magnitude , fairly well . for infinitely strong interaction strength , we compare the time dynamics with that of two identical fermions and discuss the implications of fermionization on the dynamics . for two attractively - interacting atoms on the molecular branch , we find that single - particle tunneling dominates for weakly - attractive interactions while pair tunneling dominates for strongly - attractive interactions . our first set of calculations yields qualitative but not quantitative agreement with the experimentally measured tunneling rates . we obtain quantitative agreement with the experimentally measured tunneling rates if we allow for a weakened radial confinement .

open quantum systems are at the heart of many physical phenomena from nuclear physics to quantum information theory @xcite . in fact , all `` real '' quantum systems are , to some extent , open systems . interactions with the environment cause decoherence , resulting in non - equilibrium dynamics . it is often simpler to design experiments that probe non - equilibrium physics than it is to design experiments that probe equilibrium physics . conversely , the theoretical toolkit for describing systems in equilibrium is generally much farther developed than that for describing systems in non - equilibrium . ultracold atom systems provide a platform for realizing clean and tunable quantum systems @xcite . over the past few years , much effort has gone into describing non - equilibrium experiments that are accessible , within approximate or exact frameworks , to theory . notable experiments are the equilibration dynamics of one - dimensional bose gases @xcite , the spin dynamics of dipolar molecules in optical lattices with low filling factor @xcite , and the tunneling dynamics of effectively one - dimensional few - fermion systems @xcite . this paper focuses on the latter set of experiments . specifically , the goal of the present work is to describe the tunneling dynamics of few - fermion systems , which are prepared in a well defined quasi - eigenstate ( metastable state ) , into free space . we consider small systems and directly solve the time - dependent schrdinger equation in coordinate space . as we will show , this approach provides a means to quantify the importance of the particle - particle interaction , covering time scales from a fraction of the trap scale to thousands times the trap scale . alternatively , one could adopt a quantum optics perspective and pursue a master equation approach . tunneling is arguably the most quantum phenomenon there is : if the system was behaving classically , tunneling would be absent @xcite . tunneling plays an important role across physics , chemistry and technology . the scanning tunneling microscope @xcite , for example , nicely illustrates how a physics phenomenon , the tunneling of electrons , has been turned into a powerful practical tool ( the imaging of materials ) . the @xmath1-decay , i.e. , the decay of a @xmath2he nucleus from a heavy nucleus , is an example discussed in most undergraduate physics texts ( see , for example , ref . the typical picture is to identify an effective reaction coordinate and to obtain the tunneling rate from a wkb analysis . while powerful , such treatments completely neglect the effect of interactions . interactions also play a crucial role in sorting out under which conditions electrons in light atoms tunnel sequentially or simultaneously @xcite . the two - particle system considered in this work has been realized experimentally and is the possibly simplest scenario that deals with a truly open quantum system ( the atoms can escape to infinity ) in which interactions ( short - range atom - atom interactions ) play a crucial role . as we will show , even for this relatively simple set - up , matching theory and experiment is a non - trivial task . of course , two - particle tunneling has been investigated previously in this and related contexts @xcite . the remainder of this paper is organized as follows . section [ sec_system ] introduces the hamiltonian , the heidelberg experiment and selected simulation details . sections [ sec_molecular ] and [ sec_upper ] discuss the molecular and upper branch tunneling dynamics . for both cases , it is argued that the trapping potential needs to be reparameterized . using the reparameterized trapping potential , numerical simulations for the tunneling dynamics of two distinguishable @xmath0li atoms on the molecular branch and the upper branch are discussed . comparisons with the experimentally measured tunneling rates are presented . finally , sec . [ sec_summary ] summarizes and provides an outlook . simulation details and some technical aspects are relegated to appendices [ app_br][app_flux - anal ] .

we present results concerning resolvent estimates for the linear operator associated with the system of differential equations governing 2 dimensional perturbations of plane couette flow . numerical approximations indicate that norm of the resolvent is proportional to @xmath1 in the whole region of interest .

i

math0208139

we present results concerning resolvent estimates for the linear operator associated with the system of differential equations governing 2 dimensional perturbations of plane couette flow . we prove estimates on the @xmath0 norm of the resolvent of this operator showing this norm to be proportional to the reynolds number @xmath1 for a region of the unstable half plane . for the remaining region , we show that the problem can be reduced to estimating the solution of a homogeneous ordinary differential equation with non - homogeneous boundary conditions . numerical approximations indicate that norm of the resolvent is proportional to @xmath1 in the whole region of interest . [ theorem]lemma @=11 addtoresetequationsection

we consider the initial boundary value problem @xmath2 where @xmath3 \times [ 0 , \infty ) \longrightarrow \mathbb{r}^2 $ ] is the unknown function @xmath4 . @xmath5 is the vector field @xmath6 and the reynolds number @xmath1 is a positive parameter . the forcing @xmath7 is a given @xmath8 function satisfying satisfying @xmath9 and @xmath10 for all @xmath11 \times [ 0 , \infty)$ ] . these equations are the linearization of the equations governing 2 dimensional perturbations @xmath12 of @xmath6 , known as couette flow , which is a steady solution of @xmath13 the pressure term @xmath14 in ( [ eq1.1 ] ) is determined in terms of @xmath15 by the linear elliptic equation @xmath16 we note that @xmath17 depends linearly on @xmath15 , and is determined up to a constant . the estimates derived in this paper are independent of @xmath17 . with @xmath17 given by the above equation , the solution @xmath15 of ( [ eq1.1 ] ) remains divergence free for all @xmath18 . therefore we drop the continuity equation and write the problem as @xmath19 with @xmath15 satisfying the boundary conditions described in ( [ eq1.1 ] ) . note that @xmath20 is a linear operator on @xmath21 , @xmath22\times [ 0 , 1]$ ] . the @xmath0 inner product and norm over @xmath23 are denoted by @xmath24 as motivation , consider a general linear evolution equation @xmath25 formally , after laplace transformation with respect to @xmath26 , the transformed equation is @xmath27 for @xmath28 , where @xmath29 is the laplace transform of @xmath15 . the solution of the transformed equation is given by @xmath30 where @xmath31 is the identity operator , and then we get the solution of ( [ eq1.3 ] ) by applying the inverse laplace transform to @xmath29 . moreover , from ( [ eq1.6 ] ) , @xmath32 we recall the following definition : let @xmath33 be a linear operator in a banach space @xmath34 and @xmath35 the identity operator . the resolvent set @xmath36 of @xmath33 is the set of all complex numbers @xmath37 such that the operator @xmath38 exists , is bounded and has a dense domain in @xmath34 . the linear operator @xmath39 , for @xmath40 , is said to be the resolvent of @xmath33 . the set @xmath41 is the spectrum of @xmath33 . therefore , if the complex number @xmath37 is such that @xmath42 , the formal argument above to express the transformed function @xmath29 in terms of the transformed forcing @xmath43 by ( [ eq1.6 ] ) is valid and we have the estimate ( [ eq1.7 ] ) . according to romanov @xcite , the unstable half plane @xmath44 is contained in the resolvent set of the linear operator @xmath45 defined in ( [ eq1.5 ] ) , for all positive reynolds numbers @xmath1 , and the eigenvalue of @xmath46 with largest real part is at a distance from the imaginary axis proportional to @xmath47 . our aim in this paper is to estimate the resolvent constant @xmath48 . for each @xmath1 , we derive estimates on the @xmath0 norm of the resolvent for the region @xmath49 . for the remaining region , we prove that we can reduce the problem to estimating the norm of the solution of a homogeneous ordinary differential equation with non - homogeneous boundary conditions . this is the main contribution of the paper , since in principle it simplifies the problem either if one wants to prove the estimates analytically or use numerical computations . we perform numerical computations that indicate that the @xmath0 norm of the resolvent is proportional to @xmath1 also for @xmath50 . we note that , according to romanov @xcite , this is the best possible dependence of the resolvent on the reynolds number . this dependence is better than the 3 dimensional case , since results in liefvendahl & kreiss@xcite , reddy & henningson@xcite , trefethen _ et al._@xcite , kreiss _ et al._@xcite , also partly based in computations , indicate the @xmath0 norm of the resolvent to be proportional to @xmath51 . in all the papers above , the computations are performed using different methods than the one used here .

this dependence is a simple linear one , when expressed in terms of appropriate variables , suggesting an exact mathematical law . this is the first known relation between topological and kinematical properties of three - body systems . we have used these results to predict the periods of several sets of as yet undiscovered orbits , but the relation also indicates that the number of periodic three - body orbits with periods shorter than any finite number is countable .

i

1507.08096

we present results of numerical calculations showing a three - body orbit s period s @xmath0 dependence on its topology . this dependence is a simple linear one , when expressed in terms of appropriate variables , suggesting an exact mathematical law . this is the first known relation between topological and kinematical properties of three - body systems . we have used these results to predict the periods of several sets of as yet undiscovered orbits , but the relation also indicates that the number of periodic three - body orbits with periods shorter than any finite number is countable .

there is , at present , no deeper understanding of periodic three - body orbits in newtonian gravity , than the simple change of scale of spatial and temporal coordinates , see sect . 10 of ref . @xcite , that can be compared with kepler s third law for two - body motion , ref . kepler extracted his laws from the astronomical data concerning two - body periodic orbits collected by tycho brahe and his predecessors . unlike a two - body orbit , a periodic three - body orbit is characterized both by its kinematic and geometric properties and by its topology , which can be described algebraically by a word , or an element @xmath1 of free group @xmath2 on two letters @xmath3 ( and their inverses @xmath4 ) , see refs . the algorithm used for `` reading '' of words corresponding to periodic orbits is described in the appendix of ref . . graphically , this amounts to classifying closed curves according to their `` topologies '' in a plane with two punctures . the closed curves are stereographic projections of periodic orbits from the shape - sphere , with three punctures - for a detailed explanation , see refs . @xcite , and for graphic illustrations , see the web - site @xcite - onto a plane with two punctures , the puncture at the `` north pole '' having been projected to infinity . that procedure leads to the aforementioned free group @xmath2 on two letters @xmath5 , where ( for definiteness ) a denotes a clockwise `` full turn '' around the right - hand - side puncture , and b denotes the counter - clockwise full turn around the other puncture in the plane / sphere . in this way the topology of an orbit can be transformed into an algebraic object that can be further manipulated . but , even within this particular method of assigning a sequence of symbols to a topology there remains an ambiguity , regarding the question which puncture should be taken as the `` north pole '' of the stereographic projection , see appendix [ ss : ambiguity ] . the length of the word generally depends on this choice , see appendix [ s : alternative_word ] . we resolve this ambiguity by using the ( common ) symmetry axis of all presently known collisionless zero - angular - momentum periodic orbits to define the `` north pole '' , which we call the `` natural '' , or `` symmetric '' choice , because it leads to equal numbers @xmath6 of small letters @xmath7 and @xmath8 , as well as equal numbers @xmath9 of capital letters @xmath10 , or @xmath11 . these relations need not hold with a different choice of `` north pole '' , however , e.g. with cyclically permuted punctures , generally @xmath12 and @xmath13 , see appendix [ s : alternative_word ] . moreover , the above - described procedure , is not the only way of assigning a sequence of symbols to a topology , for an alternative , together with our results expressed in these alternative terms , see appendix [ s : alternative ] . to date there is no collection of astronomical data regarding periodic orbits of three bodies comparable to brahe s collection of two - body orbits . therefore , if one wishes to study general properties of the three - body system one must resort to numerical studies . to this end , in this letter we use the world s total ( published ) data set containing 46 distinct collisionless periodic orbits , refs . @xcite , to extract the following ( wholly unexpected ) linear dependence of the ( generalized ) kepler s third law for the ratio @xmath14 of `` rescaled '' periods ( i.e. periods evaluated at one common energy @xmath15 ) of three - body orbits , @xmath16 on their topologies @xmath17 , specifically on ( one half of ) the number of all letters @xmath18 , see fig . [ fig : period ] . here @xmath19 is the number of small letters @xmath7 , or @xmath8 , and @xmath20 is the number of capital letters @xmath10 , or @xmath11 contained in the latter @xmath17 , and @xmath21 if the free - group word describing the figure-8 orbit , ref . we have divided the total number of letters @xmath22 into two parts because orbits fall into different classes with distinct values of @xmath19 and @xmath20 , see table [ tab : sd13 ] . of presently known ( zero - angular - momentum ) three - body orbits divided by the period of the figure-8 orbit @xmath23 , versus one half of the length of word @xmath22 , i.e. , one half of the number of all letters in the free - group word @xmath17 describing the orbit , @xmath24 , where @xmath19 is the number of small letters @xmath7 , or @xmath8 , and @xmath20 is the number of capital letters @xmath10 , or @xmath11 in the letter @xmath17 . four ( linear , quadratic , cubic and quartic ) fits are shown as solid lines of different colors , yet they overlap so much that the difference can be seen only at @xmath25 . ] the worst - case disagreement of this linear dependence with the data is about 10% , though generally it is ( much ) better , occasionally reaching the limits ( six significant decimal places ) of our numerical precision . in this letter we point out four more accurate ( than 10 % ) , yet still approximate sub - sequences of orbits , and one possibly exact regularity . for clarity s sake , we show in fig . [ fig : period_nonsatellites ] the corresponding graph for non - satellite orbits , only . note that the range of the abscissa in fig . [ fig : period_nonsatellites ] only reaches the value @xmath26 . of 16 presently known non - satellite zero - angular - momentum three - body orbits divided by the period of the figure-8 orbit @xmath23 versus one half of the length of word @xmath22 , i.e. , one half of the number of all letters in the free - group word @xmath17 describing the orbit , @xmath24 , where @xmath19 is the number of small letters @xmath7 , or @xmath8 , and @xmath20 is the number of capital letters @xmath10 , or @xmath11 in the letter @xmath17 . four ( linear , quadratic , cubic and quartic ) fits are shown as solid lines of different colors . ] at this point a few words must be said about the statistical significance of results presented in fig . [ fig : period ] , or equivalently about @xmath27 , the number of distinct periodic orbits of `` length '' @xmath22 : 1 ) at small length values one can explicitly count the mathematically allowed orbits and show that many have already been found , see appendix [ ss : conjugacy ] . 2 ) as one increases the number of letters @xmath22 , the number of topologically distinct orbits @xmath27 grows rapidly , see appendix [ ss : conjugacy ] , and the number of presently discovered ( and displayed here ) orbits pales in comparison with that number . the number @xmath27 is not necessarily the same one as the number of physically possible orbits - moore has shown by explicit examples how mathematically allowed orbits disappear as the exponent in the potential is reduced from @xmath28 to @xmath29 in newtonian gravity , ref . @xcite the large number of still possibly undetected orbits makes the observed linearity of the graph , fig . [ fig : period ] , at higher values of @xmath22 all the more impressive : note that 24 , out of grand total of 46 orbits taken from refs . @xcite , extend up to @xmath26 . these 24 orbits include 10 ( non - choreographic ) figure - eight satellites from ref . @xcite . among these 24 there are 16 non - satellite orbits that are shown separately in fig . [ fig : period_nonsatellites ] . the remaining 22 ( of 46 ) orbits are the new ( @xmath30=5 , 7 , 14 , 17 , 22 , 26 , 35 , 41 figure - eight satellite ) choreographies , ref . @xcite , that extend up to @xmath31 and thus test the proposed linear dependence(s ) farther into the previously unexplored region . we emphasize that three of these new choreographic orbits are not satellites of the figure - eight . the most precise regularity explains two previously noticed , but unexplained identities : a ) the identity of periods ( to 16 decimal places , in ref . @xcite ) ; and b ) the identity of actions ( to seven significant digits , in ref . @xcite ) , of two distinct orbits with the same topology , _ viz . _ of moore s and simo s figure-8 solutions , evaluated at equal energies . the same phenomenon was observed among seven independent @xmath32 figure - eight satellites reported in ref . @xcite , and the two butterfly orbits in ref . moreover , the ratio of periods of two different-@xmath30 satellites equals the ratio of the corresponding @xmath30 s , to high precision . an extension of this rule to arbitrary @xmath30 predicts the periods , and actions of new , as yet undiscovered three - body orbits and helps one to identify and classify newly discovered orbits , as in ref . the four less precise linear regularities also predict new families of orbits , with somewhat lower precision . before we proceed to present the evidence and state the regularities in their algebraic forms , we must first define what we mean by kepler s third law in a three - body system ? kepler s first law , which states that a periodic two - body trajectory must be an ellipse , manifestly holds only in the two - body case ; his second law , which asserts conservation of angular momentum , holds for any number of bodies , but generally does not have a simple geometrical interpretation as in the two - body case . his third law , which relates the square of the orbital period @xmath0 of a planet to the cube of the semi - major axis @xmath33 of its orbit , i.e. , @xmath34 , also has a proper three - body generalization , despite its appearance . as only lagrange s three - body orbits are elliptical , we must address the question what corresponds to the semi - major axis @xmath33 in kepler s third law for arbitrary periodic three - body orbits ? the answer to this question can be found by remembering the virial theorem , ref . @xcite , for the newtonian potential and then by using the hyper - spherical three - body variables , ref . @xcite . as the `` overall size '' of a three - body system is determined by a time - average ( to be specified below ) over one period of the hyper - radius @xmath35 ; and the virial theorem relates the time - average of the potential energy @xmath36 to the ( constant ) total energy @xmath15 , so it is the harmonic mean ( over one period ) of the hyper - radius @xmath37 , defined as @xmath38 , that corresponds to the semi - major axis @xmath33 in the three - body case , see footnote . , where @xmath39 is the energy of the system and @xmath40 is a constant ( equal to the integral of the orbit over the shape sphere ) that depends on the particular orbit : every periodic three - body orbit passes through a different sequence of shapes ( including lagrange s elliptic ones , in which @xmath41 ) during one period , so each orbit has a different value of the constant @xmath40 , but the validity of the scaling law @xmath42 should be immediately clear . this amounts to the well known fact that kepler s third law follows from the spatio - temporal ( mechanical ) scaling laws , which , in turn , follow from the homogeneity of the newtonian gravity s ( two - body ) potential , ref . the scaling laws are @xmath43 , @xmath44 , and consequently @xmath45 . the ( total ) energy scales as @xmath46 , the period @xmath0 as @xmath47 and angular momentum as @xmath48 . ] thus , we ( may ) replace the `` mean size '' @xmath37 of the three - body system in kepler s third law @xmath49 with the inverse absolute value of energy @xmath50 , i.e. , @xmath51 , or equivalently @xmath52 . in the newtonian two - body potential @xcite . ] the constant on the right - hand - side of this equation is not `` universal '' in the three - body case , as it is in the two - body case : it may depend on both the family of the three - body orbit and its angular momentum @xmath53 , see refs . the angular momentum @xmath53 transforms differently under scale transformations than the period @xmath0 , which is the reason why only the vanishing angular momentum @xmath54 is a `` fixed point '' under scaling . for this reason , we confine ourselves here to three - body orbits with zero angular momentum , and , for simplicity s sake , to equal masses .

we present solutions to the accretion disk structure equations in which advective cooling is accounted for in a self - consistent way . these solutions are quite different from those solutions obtained earlier by other authors , where advective cooling was not treated self - consistently .

m

astro-ph9601008

we present solutions to the accretion disk structure equations in which advective cooling is accounted for in a self - consistent way . it is shown that for high rates of accretion , above a critical value , when without advection there are no solutions extending continuously from large to small radii , there exist global solutions with _ self - consistent _ advective cooling . these solutions are quite different from those solutions obtained earlier by other authors , where advective cooling was not treated self - consistently .

in describing accretion disks when advective cooling is important , one can use the following model : we assume that advective cooling is added in a _ self - consistent _ way to other ( local ) cooling mechanisms in a keplerian , geometrically thin disk . we neglect the radial momentum equation and suggest that the disk thickness is everywhere small . this simplification is not too serious because neglecting these factors leads to quantitative corrections only , while neglecting advection cooling leads to qualitatively different solutions . this was discussed in detail by abramowicz et al ( 1995 ) and chen et al ( 1995 ) . their treatment of advective cooling was not _ self - consistent _ , however , as their advection parameter , @xmath11 , was assumed to be constant throughout the disk as well as being independent of the accretion rate . thus we assume that the disk is geometrically thin and the rotational velocity is keplerian under the pseudo - newtonian potential proposed by paczyski and wiita ( 1980 ) , @xmath12 . we normalize the accretion rate as @xmath13 , where @xmath14 . the non - relativistic disk structure equations without advection , in the case of the newtonian potential , together with the method of their solutions have been described earlier ( see artemova et al 1996 ) . here we will outline the main difference related to the use of the potential of paczyski and wiita and to the inclusion of the advective cooling process in the energy balance . paczyski and bisnovatyi - kogan ( 1981 ) were the first to describe a method to account for the advective cooling in the disk accretion problem . the angular velocity for the paczyski and wiita potential is @xmath15^{1/2}$ ] . recall that conservation of angular momentum for a steady - state accretion in the @xmath16-disk model can be written as @xmath17 where the factor , @xmath18 , accounts for the boundary condition at the inner edge of the disk , @xmath19 . neglecting advection we have @xmath20 . the half thickness of the disk is denoted by @xmath21 , and @xmath22 is the total pressure in the equatorial plane of the disk . the viscous heating rate per unit area , @xmath23 , is given by the formula ( see e.g. bisnovatyi - kogan , 1989 ; frank , king & raine , 1992 ) @xmath24 the advection cooling rate can be written in the form ( see chen and taam 1993 ) : @xmath25 where @xmath26 is the temperature , @xmath27 is the specific entropy , and @xmath28 is a factor which characterizes the advective cooling . this factor can be written in the form : @xmath29 , \label{eq : g3}\ ] ] where , @xmath30 is the energy per unit mass of the gas , @xmath31 is the matter density and @xmath32 . the energy equation has the form @xmath33 , where @xmath34 is the rate of all local cooling processes ( see artemova et al 1996 ) . all other equations are the same as in artemova et al ( 1996 ) . the principal difference here is that now the energy balance is described by a differential equation rather than an algebraic one . the boundary conditions for this system are the following : at large , @xmath35 , the solution must coincide with the solution obtained without advection , and at the inner disk boundary we should not require that @xmath36 , but rather we treat @xmath37 as an eigenvalue of the problem and allow it to be less than @xmath38 . we solved this system of equations by the method of subsequent iterations , with fixed @xmath39 and @xmath16 , and varying @xmath37 to obtain a _ self - consistent _ solution . we did this in two steps : started one calculation from large radii and another at the inner edge of the disk and adjusting @xmath37 until the solutions matched near @xmath40 .

2dflens is the first wide - area spectroscopic survey specifically targeting the area mapped by deep - imaging gravitational lensing fields , in this case the kilo - degree survey . , we describe the motivation , target selection , spectroscopic observations , and clustering analysis of 2dflens .

i

1608.02668

we present the 2-degree field lensing survey ( 2dflens ) , a new galaxy redshift survey performed at the anglo - australian telescope . 2dflens is the first wide - area spectroscopic survey specifically targeting the area mapped by deep - imaging gravitational lensing fields , in this case the kilo - degree survey . 2dflens obtained @xmath0 redshifts in the range @xmath1 over an area of @xmath2 deg@xmath3 , and is designed to extend the datasets available for testing gravitational physics and promote the development of relevant algorithms for joint imaging and spectroscopic analysis . the redshift sample consists first of @xmath4 luminous red galaxies ( lrgs ) , which enable analyses of galaxy - galaxy lensing , redshift - space distortion , and the overlapping source redshift distribution by cross - correlation . an additional @xmath5 redshifts form a magnitude - limited ( @xmath6 ) nearly - complete sub - sample , allowing direct source classification and photometric - redshift calibration . in this paper , we describe the motivation , target selection , spectroscopic observations , and clustering analysis of 2dflens . we use power spectrum multipole measurements to fit the redshift - space distortion parameter of the lrg sample in two redshift ranges @xmath7 and @xmath8 as @xmath9 and @xmath10 , respectively . these values are consistent with those obtained from lrgs in the baryon oscillation spectroscopic survey . 2dflens data products will be released via our website http://2dflens.swin.edu.au . surveys , large - scale structure of universe , cosmology : observations

a wide set of cosmological observations suggests that the dynamics of the universe are currently dominated by some form of ` dark energy ' , which in standard friedmann - robertson - walker ( frw ) models is propelling an acceleration in late - time cosmic expansion . however , the physical nature of dark energy is not yet understood , and its effects are subject to intense observational scrutiny . efforts in this area to date have focused on mapping out the cosmic expansion history using baryon acoustic oscillations ( baos ) as a standard ruler ( e.g. beutler et al . 2011 , blake et al . 2011b , anderson et al . 2014 , kazin et al . 2014 , delubac et al . 2015 , aubourg et al . 2015 , alam et al . 2016 ) and type ia supernovae as standard candles ( e.g. conley et al . 2011 , suzuki et al . 2012 , betoule et al . these probes have yielded important constraints on the ` homogeneous expanding universe ' , including @xmath11 distance measurements and a @xmath12 determination of the value of the equation - of - state of dark energy , @xmath13 . however , measurements of the laws of gravity that describe the ` clumpy universe ' are currently less advanced , and only a combination of complementary observations of expansion and gravitational growth will discriminate between the different possible physical manifestations of dark energy . efforts have focused on establishing whether the laws of general relativity ( gr ) , well - tested on solar - system scales , are a good description of gravity on cosmological scales 14 orders of magnitude larger . there are two particularly important observable signatures of gravitational physics that can be used for this purpose , and these two methods gain considerable leverage when combined . the first observable is the peculiar motions of galaxies as they fall toward overdense regions as non - relativistic test particles . these motions produce correlated doppler shifts in galaxy redshifts that create an overall clustering anisotropy as a function of the angle to the line - of - sight , known as redshift - space distortion ( rsd ) . this pattern has been measured by a number of galaxy redshift surveys ( e.g. blake et al . 2011a , beutler et al . 2012 , de la torre et al . 2013 , samushia et al . 2014 , beutler et al . 2014 , marin et al . 2016 , alam et al . 2016 ) and has permitted the growth rate of cosmic structure to be measured with @xmath14 accuracy at some epochs . the second gravitational probe is the patterns of weak lensing imprinted by the deflections of light rays from distant galaxies as they travel through the intervening large - scale structure as relativistic test particles . this signal may be measured using correlations in the apparent shapes of background galaxies in deep imaging surveys ( e.g. heymans et al . 2012 , huff et al . 2014 , kuijken et al . 2015 , becker et al . 2016 , hildebrandt et al . whilst the cosmological parameter constraints possible from gravitational lensing statistics are still improving , the measurement offers several key advantages such as its insensitivity to galaxy bias . velocities and lensing are complementary because only their combination allows general deviations to the einstein field equations to be constrained ( zhang et al . 2007 , song et al . modern theories of gravity may be classified by the manner in which they warp or perturb the spacetime metric ( and the way this warping is generated by matter ) . in general two types of perturbations are possible : spacelike and timelike . in gr these perturbations are equal and opposite , but in ` modified gravity ' scenarios a difference is predicted . examples of such frameworks include generalizing the ` action ' of gr as a function of the ricci curvature , such as in @xmath15 gravity models ( sotiriou & faraoni 2010 ) , or embedding ordinary 3 + 1 dimensional space into a higher - dimensional manifold such as ` cascading gravity ' ( de rham et al . 2008 ) or ` galileon gravity ' ( chow & khoury 2009 ) . these scenarios make different observable predictions . joint cosmological fits to weak gravitational lensing and galaxy redshift - space distortion statistics can be performed using datasets without sky overlap ( e.g. simpson et al . however , the availablity of overlapping imaging and spectroscopic surveys yields several scientific benefits . first , since the same density fluctuations source both the lensing and galaxy velocity signals , the partially - shared sample variance reduces the uncertainty in the gravity fits ( mcdonald & seljak 2009 ) , and the addition of the shape - density correlation statistics ( ` galaxy - galaxy lensing ' ) enables new measurements to be constructed such as the ` gravitational slip ' ( zhang et al . 2007 ) . a series of authors ( gaztanaga et al . 2012 ; cai & bernstein 2012 ; de putter , dore & das 2014 ; kirk et al . 2015 ; eriksen & gaztanaga 2015 ) have predicted statistical improvements resulting from overlapping surveys , although the degree of this improvement depends on assumptions and survey configuration ( font - ribera et al . 2014 ) . perhaps more importantly , the actual benefit of overlapping surveys exceeds statistical forecasts because weak lensing measurements are limited by a number of sources of systematic error which may be mitigated using same - sky spectroscopic - redshift observations . one of the most significant systematic errors is the calibration of the source photometric redshifts which are required for cosmic shear tomography ( ma , hu & huterer 2006 ) . overlapping spectroscopic surveys are a powerful means of performing this calibration ( newman et al . 2015 ) , using approaches including both observation of complete spectroscopic sub - samples and analysis of cross - correlation statistics ( mcquinn & white 2013 , de putter , dore & das 2014 ) . conversely , the gravitational lensing imprint allows independent calibration of the galaxy bias parameters that are a key systematic limitation to redshift - space distortion analysis ( e.g. buddendiek et al . finally , overlapping imaging and spectroscopy enables a wide range of other science including studies of galaxy clusters , strong lensing systems and galaxy evolution . the first wide - area overlapping spectroscopic and cosmic shear surveys only recently became available and currently span a shared area of @xmath16 deg@xmath3 , consisting of an overlap between two lensing imaging surveys the canada - france - hawaii telescope legacy survey ( cfhtls ; gwyn 2012 , heymans et al . 2012 ) and the 2nd red sequence cluster survey ( rcs2 ; gilbank et al . 2011 , hildebrandt et al . 2016a ) and two spectroscopic redshift surveys the wigglez dark energy survey ( drinkwater et al . 2010 ) and the baryon oscillation spectroscopic survey ( boss ; dawson et al . this overlap has permitted a number of studies including a new consistency test of gr via a measurement of gravitational slip at @xmath17 ( blake et al . 2016 ) , joint constraints on halo occupation distribution and cosmological parameters ( more et al . 2015 ) , tests of imaging photometric redshift performance via cross - correlation ( choi et al . 2016 ) and new measurements of small - scale galaxy bias parameters ( buddendiek et al . 2016 ) . wide - area overlap between spectroscopic and imaging surveys requires significant further extension to realize its full scientific potential . two of the deep imaging surveys currently being performed to measure gravitational lensing the 1500 deg@xmath3 kilo - degree survey ( kids ; kuijken et al . 2015 ) at the european southern observatory vlt survey telescope ( vst ) , and the 5000 deg@xmath3 dark energy survey ( des ; becker et al . 2016 ) at the blanco telescope are located largely in the southern hemisphere , whereas the largest existing wide - area spectroscopic surveys have been carried out by the sloan telescope in the northern hemisphere . with this in mind , we have created the 2-degree field lensing survey ( 2dflens ) , a new southern - hemisphere spectroscopic redshift survey using the anglo - australian telescope ( aat ) . the 2df - aaomega multi - fibre spectroscopic system at the aat has conducted a series of such projects including the 2-degree field galaxy redshift survey ( 2dfgrs ; colless et al . 2001 ) , the wigglez dark energy survey ( drinkwater et al . 2010 ) , the galaxy and mass assembly survey ( gama ; driver et al . 2011 ) , and ozdes ( yuan et al . 2015 ) . this paper describes the design , performance and initial clustering analysis of 2dflens . key initial scientific analyses , some in conjunction with kids , are presented by five associate papers ( joudaki et al . 2016b , johnson et al . 2016 , amon et al . 2016 , wolf et al . 2016 , janssens et al . section [ secdesign ] motivates the survey design : the choice of fields and targets . section [ sectarsel ] describes the process of selecting targets from input photometric imaging catalogues , and section [ secspecobs ] discusses the spectroscopic observing campaign including aat data reduction and galaxy redshift determination . section [ secselfunc ] describes the calculation of the selection function of the spectroscopic observations , which forms the basis of the ensuing galaxy clustering measurements . section [ secmock ] outlines the construction of the survey mock catalogues which are used to estimate the covariance matrix of the clustering statistics , whose measurement is discussed in section [ secclus ] . we summarize in section [ secconc ] .

we present the 2-degree field lensing survey ( 2dflens ) , a new galaxy redshift survey performed at the anglo - australian telescope . the redshift sample consists first of @xmath4 luminous red galaxies ( lrgs ) , which enable analyses of galaxy - galaxy lensing , redshift - space distortion , and the overlapping source redshift distribution by cross - correlation . an additional @xmath5 redshifts form a magnitude - limited ( @xmath6 ) nearly - complete sub - sample , allowing direct source classification and photometric - redshift calibration . in this paper these values are consistent with those obtained from lrgs in the baryon oscillation spectroscopic survey . 2dflens data products will be released via our website http://2dflens.swin.edu.au

i

1608.02668

we present the 2-degree field lensing survey ( 2dflens ) , a new galaxy redshift survey performed at the anglo - australian telescope . 2dflens is the first wide - area spectroscopic survey specifically targeting the area mapped by deep - imaging gravitational lensing fields , in this case the kilo - degree survey . 2dflens obtained @xmath0 redshifts in the range @xmath1 over an area of @xmath2 deg@xmath3 , and is designed to extend the datasets available for testing gravitational physics and promote the development of relevant algorithms for joint imaging and spectroscopic analysis . the redshift sample consists first of @xmath4 luminous red galaxies ( lrgs ) , which enable analyses of galaxy - galaxy lensing , redshift - space distortion , and the overlapping source redshift distribution by cross - correlation . an additional @xmath5 redshifts form a magnitude - limited ( @xmath6 ) nearly - complete sub - sample , allowing direct source classification and photometric - redshift calibration . in this paper , we describe the motivation , target selection , spectroscopic observations , and clustering analysis of 2dflens . we use power spectrum multipole measurements to fit the redshift - space distortion parameter of the lrg sample in two redshift ranges @xmath7 and @xmath8 as @xmath9 and @xmath10 , respectively . these values are consistent with those obtained from lrgs in the baryon oscillation spectroscopic survey . 2dflens data products will be released via our website http://2dflens.swin.edu.au . surveys , large - scale structure of universe , cosmology : observations

in this paper we have introduced the 2-degree field lensing survey ( 2dflens ) , a new galaxy redshift survey performed at the anglo - australian telescope which extends the spectroscopic - redshift coverage of gravitational lensing surveys in the southern sky , with a particular focus on the overlapping kilo - degree survey ( kids ) . 2dflens contains @xmath0 objects with good - quality redshifts , including @xmath4 luminous red galaxies and @xmath5 objects which form a magnitude - limited nearly - complete sub - sample . the lrgs may be utilized for analysis of galaxy - galaxy lensing , redshift - space distortion and determination of the imaging source redshift distribution by cross - correlation , and the magnitude - limited sample may be employed for direct source classification and photometric - redshift calibration . in this paper we have presented the survey selection function and clustering measurements for the lrg sample and corresponding mock catalogues . we fitted redshift - space distortion models to the clustering multipoles , finding rsd parameters @xmath9 and @xmath195 for redshift ranges @xmath7 and @xmath196 , respectively . these values are consistent with those obtained from lrgs in the baryon oscillation spectroscopic survey , and ( when combined with the best - fitting galaxy bias factors ) , consistent with the predictions of the standard @xmath77cdm cosmological model . five associate science papers are currently in preparation : * _ johnson et al . ( 2016 ) _ present a new quadratic - estimation method for constraining the source redshift distribution of an imaging survey via cross - correlations with a spectroscopic redshift survey , with an application to kids and 2dflens data . * _ joudaki et al . ( 2016b ) _ perform self - consistent cosmological model fits to overlapping cosmic shear , galaxy - galaxy lensing and redshift - space distortion data from kids and 2dflens . * _ amon et al . ( 2016 ) _ determine new measurements of the gravitational slip statistic , @xmath38 , to large scales , using data from kids and 2dflens . * _ wolf et al . ( 2016 ) _ use the magnitude - limited sample of 2dflens redshifts to compare various techniques for direct photometric - redshift calibration based on kernel - density estimation , machine learning with neural networks , and template fits . * _ janssens et al . ( 2016 ) _ analyze the ` red - nugget ' spare - fibre sample to place new constraints on the redshift evolution of compact early - type galaxies . 2dflens data products will be released with the publication of these papers via our website http://2dflens.swin.edu.au .

we present the @xmath0smic @xmath1yman-@xmath2 @xmath3ransfer code ( @xmath4 ) , a massively parallel monte - carlo radiative transfer code , to simulate lyman-@xmath2 ( ly@xmath2 ) resonant scattering through neutral hydrogen as a probe of the first galaxies . we explore the interaction of centrally produced ly@xmath2 radiation with the host galactic environment . ly@xmath2 photons emitted from the luminous starburst region escape with characteristic features in the line profile depending on the density distribution , ionization structure , and bulk velocity fields . for example , anisotropic ionization exhibits a tall peak close to line centre with a skewed tail that drops off gradually . idealized models of first galaxies explore the effect of mass , anisotropic hii regions , and radiation pressure driven winds on ly@xmath2 observables . finally , we discuss the emergent spectra and surface brightness profiles of these objects in the context of high-@xmath6 observations . the first galaxies will likely be observed through the red damping wing of the ly@xmath2 line . observations will be biased toward galaxies with an intrinsic red peak located far from line centre that reside in extensive hii super bubbles , which allows hubble flow to sufficiently redshift photons away from line centre and facilitate transmission through the intergalactic medium . even with gravitational lensing to boost the luminosity this preliminary work indicates that ly@xmath2 emission from stellar clusters within haloes of @xmath7 is generally too faint to be detected by the _ james webb space telescope _ ( _ jwst _ ) . [ firstpage ] lyman-@xmath2 emission radiative transfer resonant scattering line : profiles cosmology : theory galaxies : formation galaxies : high - redshift

i

1409.4480

we present the @xmath0smic @xmath1yman-@xmath2 @xmath3ransfer code ( @xmath4 ) , a massively parallel monte - carlo radiative transfer code , to simulate lyman-@xmath2 ( ly@xmath2 ) resonant scattering through neutral hydrogen as a probe of the first galaxies . we explore the interaction of centrally produced ly@xmath2 radiation with the host galactic environment . ly@xmath2 photons emitted from the luminous starburst region escape with characteristic features in the line profile depending on the density distribution , ionization structure , and bulk velocity fields . for example , anisotropic ionization exhibits a tall peak close to line centre with a skewed tail that drops off gradually . idealized models of first galaxies explore the effect of mass , anisotropic hii regions , and radiation pressure driven winds on ly@xmath2 observables . we employ mesh refinement to resolve critical structures . we also post - process an _ ab initio _ cosmological simulation and examine images captured at various distances within the 1 mpc@xmath5 comoving volume . finally , we discuss the emergent spectra and surface brightness profiles of these objects in the context of high-@xmath6 observations . the first galaxies will likely be observed through the red damping wing of the ly@xmath2 line . observations will be biased toward galaxies with an intrinsic red peak located far from line centre that reside in extensive hii super bubbles , which allows hubble flow to sufficiently redshift photons away from line centre and facilitate transmission through the intergalactic medium . even with gravitational lensing to boost the luminosity this preliminary work indicates that ly@xmath2 emission from stellar clusters within haloes of @xmath7 is generally too faint to be detected by the _ james webb space telescope _ ( _ jwst _ ) . [ firstpage ] lyman-@xmath2 emission radiative transfer resonant scattering line : profiles cosmology : theory galaxies : formation galaxies : high - redshift

observations of lyman-@xmath2 ( ly@xmath2 ) sources are a powerful probe of the high - redshift universe ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? in particular , the prominence of the ly@xmath2 line at @xmath8 allows for spectroscopic confirmation of redshift measurements of individual distant galaxies . ly@xmath2 sources are also a compelling probe of the cosmic dark ages leading up to reionization see @xcite for a perspective on high-@xmath6 observations . historically , @xcite determined that galaxies from the first billion years after the big bang would be powerful emitters of ly@xmath2 photons , though observations of these sources eluded us for longer than expected . however , robust detections are becoming more regular , especially if the stellar mass is comparable to the milky way or the star formation rate ( sfr ) is elevated ( e.g. sfr @xmath9 ; * ? ? ? * ) . within the earliest galaxies hard uv radiation from massive stars is reprocessed into ly@xmath2 photons ; however , because neutral hydrogen ( hi ) is opaque to the ly@xmath2 line , many of these photons may be resonantly trapped , and consequently suffer significant dust absorption . despite these effects , observations have determined that the ly@xmath2 escape fraction , @xmath10 , actually increases at higher redshifts @xcite . at some point , although the photons are no longer destroyed by dust , they are scattered out of the line of sight and some fraction of the ly@xmath2 emission is lost to the background as their sources become spatially extended ly@xmath2 haloes @xcite . various mechanisms have been explored to explain the unusually high @xmath10 of high-@xmath6 galaxies . in all likelihood this is a result of the complicated resonant line transfer , galactic structure , and peculiar dust properties . for example , multiple scatterings that facilitate excursions to the wings of the frequency profile ; large - scale flows that induce doppler shifts ; and the geometry of dense , dusty clouds within a clumpy interstellar medium that provide pathways for escape ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in this work , we push these questions to the very first galaxies ( for a review see * ? ? ? assessing the observability of such early ly@xmath2 sources is nontrivial . indeed , going to higher redshifts introduces physical effects that compete in either strengthening or attenuating the ly@xmath2 signal @xcite . on one hand , the intergalactic medium ( igm ) becomes increasingly neutral at higher @xmath6 , resulting in a more difficult escape for ly@xmath2 photons @xcite . on the other hand , the same igm also becomes increasingly devoid of dust @xcite . furthermore , population iii ( so - called pop iii ) stellar sources are predicted to have been more efficient ionizers , boosting the ly@xmath2 luminosity @xcite . the fact remains that high - redshift ly@xmath2 sources are being observed out to @xmath11 . still , many details regarding the epoch of reionization ( eor ) , or the inhomogeneous phase transition around @xmath12 , are uncertain and may greatly affect interpretations of ly@xmath2 transfer through the igm @xcite . some of the most effective methods for identifying high - redshift objects involve the ly@xmath2 line . in particular , lyman - break galaxies ( lbgs ) are generally massive galaxies for which neutral hydrogen produces a sharp drop in the spectra due to absorption @xcite . lyman-@xmath2 emitters ( laes ) are young , less - massive galaxies with active star formation and strong ly@xmath2 emission @xcite . it is an important frontier to push ly@xmath2 selection methods towards the highest possible redshifts . for galaxies at @xmath13 the neutral fraction of the intervening igm increases enough for their spectra to yield complete absorption of photons blueward of the ly@xmath2 line . this is the well - known `` gunn - peterson trough '' @xcite which is characteristic of lbgs . however , these massive , evolved galaxies become increasingly rare at high redshifts . the lae luminosity function also declines as redshift increases , and the observed trend is robustly established for @xmath14 ( e.g. * ? ? ? * ; * ? ? ? * ) and expected to continue beyond @xmath15 @xcite . because a strong detection of the highly - redshifted ly@xmath2 line requires the emitter to be young and relatively dust free conditions which are naturally expected for the first galaxies laes are likely their typical manifestation . high - redshift ly@xmath2 candidates must be followed up by spectroscopy in order to guard against false positives from foreground contaminants . fortunately , moderate- to high-@xmath6 surveys are underway that will dramatically increase the sample size of ly@xmath2 galaxies and better characterize their statistical properties . for example , the hobby - eberly telescope dark energy experiment ( hetdex ) is a large integral - field spectroscopic survey expected to detect a million laes @xcite . currently , there are several candidates at @xmath16 ( e.g. * ? ? ? * ) , with the highest spectroscopically - confirmed source announced at @xmath17 by @xcite . other records have been found using gamma - ray bursts ( grbs ) , active galactic nuclei ( agn ) , or ( sub-)mm observations of redshifted thermal dust emission @xcite . however , it is unclear how these other selection methods relate to ly@xmath2 predictions . such connections may complement ly@xmath2 observations , even if the phenomena originate from the luminous deaths of individual massive stars ( i.e. grbs ) or are not associated with a ` normal ' activity of the first galaxies ( e.g. agn or high amounts of dust ) . ly@xmath2 radiative transfer within the first galaxies is a timely problem because next - generation facilities will provide high resolution data by the end of the decade . the _ james webb space telescope _ ( _ jwst _ ; * ? ? ? * ) and large - aperture ground - based observatories ) , thirty meter telescope ( tmt ; http://www.tmt.org/[www.tmt.org ] ) , and the european extremely large telescope ( e - elt ; http://www.eso.org/sci/facilities/eelt/[www.eso.org/sci/facilities/eelt ] ) . ] offer the prime avenue for observing ly@xmath2 emission at the high-@xmath6 frontier and will significantly contribute to our understanding of the ionization history at the end of the dark ages @xcite . however , significant progress has also been made on a number of complementary probes of the high-@xmath6 universe . several 21-cm array experiments ) , the murchison wide - field array ( mwa ; http://www.mwatelescope.org/[www.mwatelescope.org ] ) , the precision array to probe the epoch of reionization ( paper ; http://eor.berkeley.edu/[eor.berkeley.edu ] ) , and ultimately the square kilometer array ( ska ; http://www.skatelescope.org/[www.skatelescope.org ] ) . ] are coming online to map the distribution of hi over the course of reionization . the ly@xmath2 and 21-cm lines are related through the wouthuysen - field mechanism for which ly@xmath2 scatterings pump electrons into the excited hyperfine state , thereby coupling the spin and kinetic temperatures @xcite . finally , an ideal complementary ly@xmath2 probe is encoded in the cosmic infrared background ( cib ) because the integrated radiation from all background stars and galaxies has been redshifted to ir wavelengths @xcite . the ly@xmath2 contribution is seen through the correlation of sources across characteristic length scales ( for a review see * ? ? ? a number of authors have studied ly@xmath2 radiative transfer within different contexts . we have greatly benefited from and hope to add to the body of work in this area . a partial list of references include : @xcite . the state of the art is to apply post - processing radiative transfer to realistic hydrodynamical simulations , which is justified for many large scale systems . we use this method in conjunction with semi - analytic models to ascertain the feedback of ly@xmath2 radiation on the galactic assembly process . our focus on the very first galaxies , in their proper cosmological context , is different from previous research that has targeted more massive systems at redshifts close to , or after , reionization ( e.g. * ? ? ? such systems require a statistical description of ly@xmath2 transmission through the igm as described by @xcite and @xcite . photons that scatter out of the line of sight due to the neutral fraction of the igm are effectively lost to the background . therefore , the observability of ly@xmath2 emitters will provide independent constraints on reionization @xcite . measurements of the ly@xmath2 flux from first galaxies depend heavily on the observed line of sight in addition to the properties of the host system and igm . therefore , rather than solving a potentially intractable transfer equation with complex angular dependence we take advantage of monte - carlo radiative transfer techniques to accurately build emergent spectral energy distributions ( seds ) . in order to perform ly@xmath2 simulations we have developed a new massively parallel code called @xmath4 the @xmath0smic @xmath1yman-@xmath2 @xmath3ransfer code . in section [ subsec : rs ] , the basic physics of ly@xmath2 transport is presented . in section [ sec : methodology ] , we discuss the general methodology behind @xmath4 and provide further algorithmic details in section [ sec : schemes ] . in section [ sec : tests ] , the code is tested against both static and dynamic setups . in section [ sec : toy ] , we construct idealized analytical models to explore how fundamental parameters , including halo mass , virialization redshift , bulk velocity , and ionization structure , affect ly@xmath2 transport in the first galaxies . these well - motivated models help test our methods and sensitivity . section [ sec : sim ] describes our implementation of the _ ab initio _ cosmological simulation of @xcite as post - processing conditions for @xmath4 . in section [ sec : results ] we analyze and discuss the emergent line of sight flux distributions and surface brightness profiles for both the idealized analytic cases and the cosmological simulation . finally , in section [ sec : conc ] we reflect on the implications of this study with regard to future ly@xmath2 observations with the _ jwst_.

most of these masers are associated with the interaction between the supernova remnant sgraeast and the interstellar medium , but a few masers are associated with the circumnuclear disk ( cnd ) . the monitoring program covered five epochs and a timescale of 20 - 195 days , during which no masers disappeared and no new masers appeared . the masers associated with the northeastern interaction region between the supernova remnant and the @xmath0 ^-1 kms@xmath1 molecular cloud show the highest level of variability . this can be explained with the @xmath0 ^-1 kms@xmath1 molecular cloud being located behind the supernova remnant and with a region of high oh absorbing column density along the line of sight . possibly the supernova remnant provides additional turbulence to the gas in this region , through which the maser emission must travel . the masers in the southern interaction region are located on the outermost edge of sgraeast which line of sight is not covered by either absorbing oh gas or a supernova remnant , in agreement with the much lower variability level observed . similarly , the masers associated with the cnd show little variability , consistent with them arising through collisions between relatively large clumps of gas in the cnd and no significant amount of turbulent gas along the line of sight .

c

1107.4341

we present the first variability study of the 1720 mhz oh masers located in the galactic center . most of these masers are associated with the interaction between the supernova remnant sgraeast and the interstellar medium , but a few masers are associated with the circumnuclear disk ( cnd ) . the monitoring program covered five epochs and a timescale of 20 - 195 days , during which no masers disappeared and no new masers appeared . all masers have previously been detected in a single epoch observation about one year prior to the start of the monitoring experiment , implying relatively stable conditions for the 1720 mhz oh masers . no extreme variability was detected . the masers associated with the northeastern interaction region between the supernova remnant and the @xmath0 ^-1 kms@xmath1 molecular cloud show the highest level of variability . this can be explained with the @xmath0 ^-1 kms@xmath1 molecular cloud being located behind the supernova remnant and with a region of high oh absorbing column density along the line of sight . possibly the supernova remnant provides additional turbulence to the gas in this region , through which the maser emission must travel . the masers in the southern interaction region are located on the outermost edge of sgraeast which line of sight is not covered by either absorbing oh gas or a supernova remnant , in agreement with the much lower variability level observed . similarly , the masers associated with the cnd show little variability , consistent with them arising through collisions between relatively large clumps of gas in the cnd and no significant amount of turbulent gas along the line of sight .

during the 195 days over which our study took place the most significant result is that the northeastern masers associated with the snr / ism interaction show a higher degree of variability than the rest of the masers . over the observed timescale no masers disappeared , and no new masers appeared . compared to our observations in 2005 ( paperi ) one new maser appeared ( or more precisely , this time fulfilled our detection criteria ) . the two `` archival '' masers , included for completeness in paperi , remain undetected . this indicates a quite stable environment for both snr / ism and cnd masers during our monitoring campaign . in this section we first discuss how variability can be introduced by both external and intrinsic ( sect . [ intr ] ) sources . thereafter , we explore the nature of the variability of the snr ( sect . [ snrvar ] ) and cnd ( sect . [ cndvar ] ) masers respectively . observational errors such as a systematic incorrect value in the derived value of our flux calibrator in one of our epochs , pointing errors , etc . , will have a predictable signature in the individual measurements . we have carefully looked for these in both our target and calibrator data and conclude that none of them contribute to the overall results . flux variations can also be produced by interstellar scintillation @xcite . this causes variations on timescales of a few minutes . such short timescales are not considered in our study since in data averaged over a minute only a couple of masers would be bright enough to be reliably detected . assuming that the variability of the maser intensity is not due to observational effects , variability studies can be used to probe the maser environment . changes in maser peak velocity could indicate acceleration , such as observed in outflows @xcite . in stellar masers , periodic maser variations may be related to periodicity found in the central object , in turn affecting the pumping conditions and/or the maser path length . sio masers in the evolved mira variables are examples of how the maser luminosity is a result of the phase of the central star ( e.g. * ? ? ? another example can be found in star forming regions ( sfrs ) , where 22 ghz water masers are well - known to exhibit maser variability . the variability of these masers are characterized by large ( sometimes several orders of magnitude ) amplitude variations , and often with velocity drifts of a few ^-1 kms@xmath1per year @xcite . this occurs on timescales from a few hours to years . water masers associated with sfrs are excited behind shocks , presumably caused by outflows or jets driven by the young stellar object ( yso ) , and much of the variation can be attributed to changes in the luminosity of the yso , in turn affecting the pumping rate via changes in the outflows and jets @xcite . oh masers associated with sfrs are predominantly observed in the radiatively pumped 1665 and 1667 mhz lines ( sometimes accompanied by masers in the 1612 and 1720mhz transitions ) , and variability of those masers have been investigated by multiple groups @xcite . the long term variability ( weeks to months ) can be attributed to changes in the number density of inverted oh molecules , or path length changes . in contrast , the short term variability is assumed to be related to sudden changes in the pumping mechanism , reflecting fluctuations in the host star luminosity . for oh masers in snrs , the situation has been unknown . the 1720 mhz oh transition was for a long time the only transition observed near snrs @xcite , although recent observations have shown sgra to harbor 36.2 and 44.1 ghz methanol masers @xcite . the 1720 mhz oh masers are usually assumed to originate in the post - shock region where the expanding snr collides with the surrounding medium . no dedicated variability studies of 1720 mhz oh masers have been published to date , and we therefore know little about the stability of the maser environment in these sources . here we have a shocked environment and since this is a large scale phenomena it must arise in the maser generating column density , or from the subsequent propagation of emission through the interstellar medium . the northeastern snr masers clearly are variable on the timescales of weeks to months . these masers are the result of the snr sgraeast ramming into the @xmath0 ^-1 kms@xmath1 cloud and we expect the post - shock medium to display density variations due to turbulence in those regions , given that a shock has recently passed . assuming that the masers can be considered as a series of velocity coherent regions of gas , bulk gas flow and turbulent motion in the source will move parts of the maser column in and out of velocity coherence along the line of sight . as a result , the maser will exhibit intensity variations . for the northeastern masers this can not be the only source of the variability though , since much higher levels of variability are observed than toward other regions of sgraeast . it is not clear whether it is the maser generating column density itself or the medium in front of the masers that is causing the variability . however , the @xmath0 ^-1 kms@xmath1 cloud is thought to be located behind sgraeast ( e.g. , * ? ? ? * paperi ) and thus between the observer and the masers . when observing this group of masers we therefore probably look through a longer path length of turbulent gas than toward other regions of sgraeast . this is supported by oh absorption observations showing this region harbors a much higher absorbing oh column density than the southern and northwestern interaction regions ( paperi , karlsson et al . it is possible that the supernova covering the northeastern region contributes to the turbulence of this column density . in contrast , the southern masers are occurring in a region where the two snr sgraeast and g359.02@xmath100.09 are colliding . here there is no clear evidence of large columns of gas in front of the masers , and no supernova crossing the line of sight . the cnd masers exhibit much less variability than the northeastern snr masers , with no maser displaying variability with a @xmath14 . if the northeastern snr / ism maser variability is due to passage of the maser through a screen of hot turbulent gas , the ( non-)variability of the cnd masers is consistent with cnd located _ in front of _ sgraeast ( paperi ) . since variability could give insight into the maser environment , we consider whether the low variability is consistent with the presumed pumping and amplification conditions in the cnd . here the pumping can not be due to a snr / ism shock , but the cnd masers are thought to be pumped by collisions between clumps in the cnd ( paperi ) . the number of clumps within the line of sight are probably only a few since once a clump has moved out of the line of sight , a maser is likely to disappear completely . assuming an inclination of 65@xmath29 @xcite and thus a rotational velocity of approximately 160 ^-1 kms@xmath1 of the maser emitting clouds in the cnd , the motion in the plane of the sky over the 195 days is minimal ; only @xmath30 pc ( approximately 8 au ) . this is much smaller than the high density cloud core sizes of @xmath31 pc that are estimated by molecular line observations @xcite . similarly , assuming typical relative clump velocities of 20 - 30 ^-1 kms@xmath1 in the sky - plane and 0.1 pc in size , a clump will pass by a compact maser in @xmath323900 years . for a clump size of 1 au the corresponding time is 2 months . if clump collisions and motions are involved in determining the path lengths for the cnd masers , given the low variability levels observed the clumps must be much larger than 1 au in size . more likely they are only a fraction of the size of the dense molecular clumps observed in hcn , perhaps corresponding to a high density region of the clump . for such clump sizes little variability can be expected due to path length changes . a factor that could contribute to a more stable maser gain in the cnd region is the pumping conditions . as measured in molecular line emission , hcn and hco@xmath33 line intensity is stronger in the cnd than in regions associated with , for example , the @xmath0 ^-1 kms@xmath1 cloud @xcite , implying higher densities . a higher density would result in a higher collision rate , thus keeping the pumping at a higher rate eventually resulting in more stable maser intensities . note that @xcite show that densities @xmath34 @xmath35 are needed for clump - clump collisions to produce 1720mhz pumping , which is slightly higher than the c - shock post - region density of @xmath36 @xmath35 for the snr masers @xcite . what the exact pumping conditions and the pumping rate really are is difficult to calculate , and depends on the ortho - para @xmath37 ratio in the region . both @xcite and @xcite have found that collisions with para - h@xmath5 can strongly suppress the 1720 mhz inversion . ortho- and para - h@xmath5 are thought to be formed on grains with a ratio of 3:1 . at low temperatures ( @xmath38 k ) proton exchange reaction convert ortho - h@xmath5 into para - h@xmath5 , making the para - h@xmath5 being the dominant species . as the temperature increases , there is less of a difference , but still with para - h@xmath5 dominating @xcite . however , to create the 1720 mhz maser only a small amount of ortho - h@xmath5 is required , since the collision rate for ortho - h@xmath5 usually is larger by a factor of 2 - 3 than the para rates @xcite . the equilibrium ratio for ortho - para h@xmath5 is @xmath39 , which is equal to 1 for a temperature @xmath40k , implying the temperature should be cooler than this value . this is consistent with a high density environment in the cnd where the gas temperature is thermalized with the dust temperatures of 20 - 80k @xcite , although molecular studies of the cnd imply excitation temperatures anywhere between 50 - 200k @xcite . @xcite use nh@xmath41(2,2)/nh@xmath41)(1,1 ) ratios to derive rotational gas temperatures between 20 - 70 k , mostly in the outer regions of the cnd . perhaps , next to path - length geometry ( paperi ) , this is a reason that 1720 mhz masers are not seen all across the cnd ; if temperatures are too high the 1720 mhz emission will be suppressed .

we present the orbital solutions for four ob spectroscopic binaries , mt145 , gsc 03161 - 00815 , 2mass j20294666 + 4105083 , and schulte 73 , and the partial orbital solution to the b spectroscopic binary , mt372 , as part of an ongoing study to determine the distribution of orbital parameters for massive binaries in the cygnus ob2 association . emerging evidence also shows that the distribution of @xmath11 is flat and consistent with `` pik s law '' .

i

0903.1265

we present the orbital solutions for four ob spectroscopic binaries , mt145 , gsc 03161 - 00815 , 2mass j20294666 + 4105083 , and schulte 73 , and the partial orbital solution to the b spectroscopic binary , mt372 , as part of an ongoing study to determine the distribution of orbital parameters for massive binaries in the cygnus ob2 association . mt145 is a new , single - lined , moderately eccentric ( @xmath0 ) spectroscopic binary with period of @xmath1 days . gsc 03161 - 00815 is a slightly eccentric ( @xmath2 ) , eclipsing , interacting and double - lined spectroscopic binary with a period of @xmath3 days . 2mass j20294666 + 4105083 is a moderately eccentric ( @xmath4 ) double - lined spectroscopic binary with a period of @xmath5 days . schulte 73 is a slightly eccentric ( @xmath6 ) , double - lined spectroscopic binary with a period of @xmath7 days and the first `` twin '' in our survey with a mass ratio of @xmath8 . mt372 is a single - lined , eclipsing system with a period of @xmath9 days and low eccentricity ( @xmath10 ) . of the now 18 known ob binaries in cyg ob2 , 14 have periods and mass ratios . emerging evidence also shows that the distribution of @xmath11 is flat and consistent with `` pik s law '' .

in this work , the third part of our ongoing survey to determine the distribution of binary orbital parameters in the cyg ob2 association , we presented three new binary systems ( mt145 , schulte 73 , & mt372 ) and confirmed the binary status of one massive binary candidate ( a45 ) . we also provided the first spectroscopic orbital solution to the eclipsing binary , a36 and a partial solution to the eclipsing , single - lined system , mt372 . while mt145 , schulte 73 , a45 , and mt372 are likely members of the cluster based on their systemic velocities ( deviating by only @xmath120.615 from the cluster mean of @xmath73 obtained in paper i and well within the association s radial velocity dispersion ) the status of a36 , with a systemic velocity of @xmath110 , remains uncertain . the system could be a runaway binary or a background object ( though both do not seem very probable ) . however , if we do include a36 , the current total for ob binaries in cyg ob2 is now 18 . of these 18 , 14 have period and mass ratio estimates . in addition , with six partial spectroscopic solutions , eight full spectroscopic solutions , three partial photometric solutions , and four full photometric solutions , cyg ob2 is on a track to become the cluster with the highest number of ob binary solutions . at seven it currently ties ngc 6231 @xcite for the highest number of full o - star binary solutions . the locations of all 18 systems are shown in figure [ binaries ] . no evidence of grouping is apparent . table [ binaries ] lists several key parameters for all 18 systems , including the star designation , photometric and/or spectroscopic binary type ( _ type _ ) , spectral classifications ( _ s.c . _ ) , period ( _ p _ ) , mass ratio when available ( _ q _ ) , and literature references ( _ ref _ ) . with the exception of schulte 9 ( @xmath111 years ) , periods for all systems are less than 25.2 days , with a mean of 9.6 days . eleven systems have a period less than 5 days . the 17 systems with periods less than 25.2 days also appear to obey pik s law @xcite , which states that the distribution of @xmath11 is flat . to avoid histogram binning selection effects , we choose to show the normalized cumulative distribution of the logarithm of the periods ( open diamonds ) in figure [ oepik ] . the flat relation of pik s law translates to a linear relation in a cumulative distribution . for comparison purposes , we also include the normalized cumulative distributions of o binaries in ngc 6231 ( * ? ? ? * solid triangles ) and the 54 ob binaries from the 9th spectroscopic binary catalog ( * ? ? ? * asterisks ) . all 3 cumulative distributions contain systems with periods less than 25.2 days and were normalized at a period of 8.9 days . to test the linearity of the cyg ob2 distribution , we computed its linear pearson correlation coefficient . the distribution yields a coefficient of @xmath112 ( where @xmath113 is a perfectly linear relation ) . the linearity is illustrated by the best fit line ( solid line ) in figure [ oepik ] . the dashed line in the figure represents a perfect pik distribution ( i.e. , a perfectly flat distribution within the range of periods in cyg ob2 ) . a two sided kolmogorov - smirnov ( @xmath114 ) test between the pik and cyg ob2 distributions gives a 38% probability that both were drawn from the same parent distribution . @xmath114 tests between cyg ob2 and ngc 6231 on the one hand and cyg ob2 and the 9th spectroscopic binary catalog ( @xmath115 days ) on the other , yield 91% and 62% probabilities of being drawn from the same parent distribution , respectively . interestingly , the cumulative distributions of cyg ob2 and ngc 6231 have a high correlation and are very similar in appearance , including an upturn near @xmath116 . one wonders if this upturn is a true deviation from a linear relation ( i.e. , a preference for periods around 5 days ) , just a coincidence related to small number statistics , or observational bias . though the latter case is a possible explanation for the upturn in ngc 6231 , we do not believe this is the case with cyg ob2 because several of the systems with periods around 5 days come from other programs with different observational cadences ( e.g. , mt421 and b17 ) . figure [ pvse ] displays the relation between the orbital periods and eccentricities for eight of the systems in cyg ob2 ( open diamonds ) , six of the systems in ngc 6231 ( solid triangles ) and 66 of the systems in the 9th spectroscopic binary catalog ( asterisks ) . the eccentricities in cyg ob2 range from circular to moderately eccentric ( 0.291 ) , while the total distribution in figure [ pvse ] has an eccentricity range of zero to @xmath120.75 for periods ranging from @xmath120.5 days to 100 days . systems with periods less than a few days tend toward more circular orbits , while systems with larger periods ( @xmath117 days ) display a full range of eccentricities . this agrees with previous studies such as @xcite . there is a paucity of highly eccentric systems longer than 30 days . this likely stems from an incompleteness of the surveys at longer periods and is not a true trend . the cyg ob2 star , a45 , falls on the high - eccentricity side of the shorter period systems with an eccentricity of 0.273 and a period of 2.884 days . it does not appear to be particularly close to the majority of ob stars in the cluster center ( see figure [ binaries ] ) , and so dynamical interaction with a massive neighbor does not seem a likely source of its higher eccentricity ( unless it is a runaway system ) . it is possible that further observations of this system will constrain the eccentricity to a slightly more circular orbit , but its position in the figure is hardly removed from the rest , and therefore , its moderately elliptical orbit is not extraordinary . the remainder of cyg ob2 stars fall well within the remaining distribution . with the exception of mt421 and mt429 , all the cyg ob2 systems have early - type companions and mass ratios widely ranging from @xmath118 ( mt258 ) to @xmath8 ( schulte 73 ) . one may see this as an indication that the companions are not randomly drawn from a @xcite or similar field star initial mass function ( imf ) . however , given that the current sample encompasses a number of systems that are double - lined spectroscopic binaries ( i.e. , they are easier to detect ) this assessment may be premature and biased . only time will tell , as we have a number of single - lined spectroscopic binary candidates still to investigate and a spectral database that has not been completely tapped . we continue to analyze these candidates with the long term goal of providing accurate distributions for binary orbital parameters of massive stars with an assumed shared formation history . we thank the time allocation committees of the lick , keck , wiyn , and wiro observatories for granting us observing time and making this project possible . we are also grateful for support from the national science foundation through research experience for undergraduates ( reu ) program grant ast 03 - 53760 and through grant ast 03 - 07778 , and the support of the wyoming nasa space grant consortium through grant nng05g165h . we would also like to graciously thank , in no particular order , christopher rodgers , emily may , megan bagley , michael dipompeo , michael alexander , jessie runnoe , and sabrina cales for their generous help in observing at wiro through good skies and bad , and jerry bucher and james weger for their ample help and upkeep of wiro facilities . bonnell , i. a. , bate , m. r. , & zinnecker , h. 1998 , mnras , 298 , 93 comern , f. , et al . 2002 , a&a , 389 , 874 comern , f. , & pasquali , a. 2007 , a&a , 467 , 23 conti , p. s , leep , e. m. 1974 , apj , 193 , 113 contreras , m. e. , rodriguez , l. f. , tapia , m. , cardini , d. , emanuele , a. , badiali , m. , & persi , p. 1997 , apj , 488 , 153 de becker 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latham , d. w. , torres , g. 1999 , aspc , 185 , 354 stroud , v. e. , clark , j.s . , negueruela , i. , roche , p. , & norton , a.j . 2009 , a&a , submitted walborn , n. r. 1973 , apj , 180 , l35 walborn , n. r. , & fitzpatrick , e. l. 1990 , pasp , 102 , 379 walborn , n. r. , & howarth , i. d. 2000 , pasp , 112 , 1446 williams , et al . 2008 , apj , 682 , 492 wilson , o. c. 1948 , pasp , 60 , 385 wilson , o. c. , & abt , a. 1951 , apj , 144 , 477 wozniak , p. r. , et al . 2004 , aj , 127 , 2436 , northern sky variability survey : public data release 1999 jul 45 & keck / hires & 38906270 in 35 orders & 31.6 & 0.1 & 2,451,3632,451,364 + 1999 jul 2123 & lick / hamilton & 36507675 in 81 orders & 31.6 & 0.1 & 2,451,3812,451,383 + 1999 aug 2123 & lick / hamilton & 36507675 in 81 orders & 31.6 & 0.1 & 2,451,4112,451,413 + 1999 oct 1415 & keck / hires & 37005250 in 29 orders & 31.6 & 0.1 & 2,451,4662,451,467 + 2000 jul 1011 & lick / hamilton & 36507675 in 81 orders & 31.6 & 0.1 & 2,451,7362,451,737 + 2000 sep 1819 & keck / hires & 37005250 in 29 orders & 31.6 & 0.1 & 2,451,8052,451,806 + 2001 aug 24 & wiyn / hydra & 38004490 in order 2 & 1200 & 0.9 & 2,452,146 + 2001 sep 89 & wiyn / hydra & 38004490 in order 2 & 1200 & 0.9 & 2,452,1612,452,162 + 2004 nov 2830 & wiyn / hydra & 38004490 in order 2 & 1200 & 0.9 & 2,453,3382,453,340 + 2005 jul 1821 & wiro / wiro - spec & 38004490 in order 1 & 2400 & 2.5 & 2,453,5702,453,573 + 2005 jul 1820,22 & wiro / wiro - spec & 38004490 in order 1 & 2400 & 2.5 & 2,453,6322,453,635 + 2005 oct 13 & wiro / longslit & 40506050 in order 2 & 600 & 2.5 & 2,453,657 + 2006 jun 1620 & wiro / longslit & 39005900 in order 2 & 600 & 2.5 & 2,453,9032,453,907 + 2006 jul 1516,20 & wiro / longslit & 39005900 in order 2 & 600 & 2.5 & 2,453,9322,453,935 + 2006 sep 811 & wiyn / hydra & 38004490 in order 2 & 1200 & 0.9 & 2,453,9872,453,990 + 2006 oct 7 & wiro / longslit & 39005900 in order 2 & 600 & 2.5 & 2,454,016 + 2007 jun 2830 & wiro / longslit & 39005900 in order 2 & 600 & 2.5 & 2,454,2802,454,282 + 2007 jul 46 & wiyn / hydra & 38204510 in order 2 & 1200 & 0.9 & 2,454,2852,454,287 + 2007 aug 28sep 4 & wiro / longslit & 55506850 in order 1 & 1800 & 1.5 & 2,454,3412,454,348 + 2007 oct 23,25,2729,31 & wiro / longslit & 55506850 in order 1 & 1800 & 1.5 & 2,454,3972,454,405 + 2007 nov 1,35 & wiro / longslit & 55506850 in order 1 & 1800 & 1.5 & 2,454,4062,454,410 + 2008 jun 1015 & wiyn / hydra & 38204510 in order 2 & 1200 & 0.9 & 2,454,6282,454,633 + 2008 jun 2330 & wiro / longslit & 52106680 in order 1 & 1800 & 1.5 & 2,454,6412,454,648 + 2008 jul 21,2227 & wiro / longslit & 52506740 in order 1 & 1800 & 1.5 & 2,454,6692,454,675 + 2008 aug 1722 & wiro / longslit & 52506740 in order 1 & 1800 & 1.5 & 2,454,6962,454,701 + 2008 sep 12,1316,19 & wiro / longslit & 52506740 in order 1 & 1800 & 1.5 & 2,454,7222,454,729 + 2008 oct 1418 & wiro / longslit & 52506740 in order 1 & 1800 & 1.5 & 2,454,7542,454,758 + lrrrrr @xmath119 ( days ) & 25.140 ( 0.008 ) & 4.674 ( 0.004 ) & 2.884 ( 0.001 ) & 17.28 ( 0.03 ) & 2.228 ( fixed ) + @xmath120 & 0.291 ( 0.009 ) & 0.10 ( 0.01 ) & 0.273 ( 0.002 ) & 0.169 ( 0.009 ) & 0.0 ( fixed ) + @xmath23 ( deg ) & 158.3 ( 0.6 ) & 359.2 ( 0.7 ) & 188.8 ( 0.1 ) & 7.3 ( 0.8 ) & 344 ( 146 ) + @xmath24 ( ) & -19.3 ( 0.4 ) & -47 ( 2 ) & 5 ( 1 ) & -11 ( 2 ) & 3 ( 7 ) + @xmath25 ( hjd-2,400,000 ) & 51789.08 ( 0.04 ) & 54693.836 ( 0.009 ) & 54728.209 ( 0.001 ) & 54700.89 ( 0.03 ) & 54755 ( 9 ) + @xmath121 ( ) & 48.9 ( 0.7 ) & 169 ( 9 ) & 126.1 ( 0.3 ) & 117 ( 2 ) & 75 ( 20 ) + @xmath122 ( ) & & 243 ( 2 ) & 273 ( 17 ) & 117.9 ( 0.8 ) & + @xmath90 ( ) & 22.6 ( 0.5 ) & @xmath12319.8 ( 0.9 ) & @xmath12312 ( 1 ) & @xmath12311.2 ( 0.2 ) & 17.5 + @xmath92 ( ) & 6.0 ( 0.1)13.8 ( 0.6 ) & @xmath12313.8 ( 0.9 ) & @xmath1235.3 ( 0.5 ) & @xmath12311.1 ( 0.2 ) & @xmath1210.0 + @xmath124 ( ) & 0.267 ( 0.012 ) & 6.9 ( 0.2 ) & 0.534 ( 0.004 ) & 2.8 ( 0.1 ) & 0.099 ( 0.080 ) + @xmath125 ( ) & & 2.3 ( 0.4 ) & 5 ( 1 ) & 2.81 ( 0.06 ) & + s. c.@xmath30 & o9iii & b0ib & b0.5v & o8iii & b0v + s. c.@xmath31 & mid b & b0iii & b2v ? b3v ? & o8iii & b2?v + @xmath48sin @xmath33 ( ) & 23.2 ( 0.3 ) & 15.6 ( 0.8 ) & 6.91 ( 0.02 ) & 39.4 ( 0.5 ) & 3.4 ( 0.9 ) + @xmath95sin @xmath33 ( ) & & 22.345 ( 0.003 ) & 14.96 ( 0.01 ) & 39.675 ( 0.004 ) & + @xmath126 ( ) & 8.9 & 29.3 & 25 & 5.1 & 14.9 + @xmath127 ( ) & & 10.0 & 47 & 6.7 & + ccrrr 51,381.50 .......................... & 0.788 & 1.7 & 10.3 & 1.8 + 51,383.50 .......................... & 0.867 & -24.7 & 15.1 & -1.0 + 51,467.90 .......................... & 0.225 & -21.5 & 4.4 & 9.2 + 51,736.50 .......................... & 0.909 & -33.5 & 11.3 & 7.8 + 51,737.50 .......................... & 0.948 & -56.4 & 13.7 & 3.5 + 51,805.76 .......................... & 0.664 & 22.8 & 3.2 & 7.9 + 52,146.70 .......................... & 0.225 & -23.6 & 3.6 & 6.9 + 52,161.81 .......................... & 0.826 & -7.4 & 4.1 & 2.4 + 52,162.67 .......................... & 0.860 & -17.8 & 3.8 & 3.3 + 53,338.63 .......................... & 0.637 & 14.0 & 4.4 & -1.9 + 53,340.59 .......................... & 0.715 & 10.7 & 4.2 & -0.4 + 53,570.50 .......................... & 0.860 & -40.0 & 8.3 & -18.9 + 53,572.50 .......................... & 0.940 & -66.4 & 10.0 & -10.3 + 53,632.50 .......................... & 0.327 & -10.5 & 11.5 & -2.7 + 53,633.50 .......................... & 0.367 & -10.6 & 6.7 & -9.3 + 53,636.50 .......................... & 0.486 & 11.5 & 5.2 & -0.3 + 53,657.50 .......................... & 0.321 & -0.8 & 6.8 & 8.0 + 53,903.75 .......................... & 0.116 & -71.7 & 8.4 & -7.1 + 53,903.76 .......................... & 0.117 & -74.7 & 9.1 & -10.3 + 53,904.72 .......................... & 0.155 & -33.1 & 7.8 & 18.8 + 53,904.73 .......................... & 0.155 & -41.0 & 7.6 & 10.7 + 53,904.90 .......................... & 0.162 & -65.6 & 7.7 & -16.1 + 53,905.77 .......................... & 0.197 & -49.4 & 6.8 & -10.6 + 53,905.90 .......................... & 0.202 & -48.1 & 7.3 & -11.0 + 53,906.74 .......................... & 0.235 & -19.3 & 8.5 & 8.6 + 53,906.89 .......................... & 0.241 & -42.2 & 10.6 & -15.8 + 53,907.78 .......................... & 0.277 & -20.5 & 10.2 & -2.7 + 53,907.88 .......................... & 0.280 & -28.4 & 7.1 & -11.4 + 53,932.75 .......................... & 0.270 & -17.0 & 7.9 & 2.5 + 53,932.85 .......................... & 0.274 & 2.5 & 8.8 & 20.9 + 53,932.86 .......................... & 0.274 & 6.4 & 10.3 & 24.8 + 53,935.89 .......................... & 0.395 & -14.7 & 12.8 & -17.3 + 53,987.70 .......................... & 0.456 & 1.8 & 4.6 & -7.6 + 53,988.75 .......................... & 0.497 & 9.9 & 4.4 & -2.8 + 53,989.66 .......................... & 0.534 & 13.7 & 4.7 & -1.0 + 53,990.86 .......................... & 0.581 & 17.3 & 4.3 & 1.1 + 54,280.83 .......................... & 0.116 & -61.7 & 7.0 & 3.0 + 54,280.87 .......................... & 0.117 & -56.5 & 6.6 & 7.8 + 54,281.70 .......................... & 0.150 & -60.2 & 8.5 & -6.7 + 54,281.78 .......................... & 0.153 & -50.9 & 7.8 & 1.4 + 54,281.85 .......................... & 0.156 & -51.5 & 7.0 & -0.0 + 54,282.70 .......................... & 0.190 & -44.8 & 7.9 & -4.1 + 54,282.77 .......................... & 0.193 & -45.6 & 6.0 & -5.7 + 54,282.83 .......................... & 0.195 & -45.9 & 6.9 & -6.8 + 54,285.93 .......................... & 0.318 & -6.0 & 4.3 & 3.3 + 54,286.66 .......................... & 0.348 & -7.6 & 5.2 & -3.4 + 54,287.73 .......................... & 0.390 & 5.3 & 4.3 & 3.2 + 54,397.71 .......................... & 0.765 & 5.0 & 16.7 & 0.7 + 54,399.69 .......................... & 0.843 & -22.0 & 15.3 & -6.9 + 54,401.67 .......................... & 0.922 & -47.9 & 16.0 & -0.3 + 54,402.71 .......................... & 0.964 & -54.1 & 14.6 & 12.3 + 54,754.62 .......................... & 0.949 & 75.4 & 7.4 & 9.8 + 54,755.60 .......................... & 0.388 & -36.6 & 6.3 & 1.7 + 54,756.60 .......................... & 0.840 & 16.0 & 3.0 & -8.9 + 54,757.59 .......................... & 0.283 & 6.9 & 3.9 & -1.9 + 54,758.72 .......................... & 0.788 & 6.9 & 3.4 & 6.3 + lcrrrr ptabularcr ptabularcr ptabularcr 54,403.61 .......................... & 0.910 & -163.4 ( 5.6 ) & 27.7 & 167.5 ( 4.9 ) & 4.2 + 54,403.70 .......................... & 0.928 & -174.9 ( 5.0 ) & 30.9 & 184.7 ( 4.3 ) & 1.0 + 54,405.71 .......................... & 0.357 & 103.4 ( 5.3 ) & 47.6 & -194.2 ( 3.5 ) & 3.1 + 54,406.63 .......................... & 0.555 & 105.4 ( 3.7 ) & 5.6 & -261.1 ( 3.4 ) & -5.3 + 54,406.76 .......................... & 0.582 & 108.6 ( 3.7 ) & 16.2 & -244.5 ( 3.7 ) & 0.2 + 54,409.73 .......................... & 0.218 & -23.6 ( 5.5 ) & 45.3 & -23.0 ( 3.7 ) & -3.3 + 54,410.67 .......................... & 0.419 & 98.4 ( 3.7 ) & 10.5 & -243.8 ( 3.4 ) & -1.8 + 54,628.88 .......................... & 0.103 & -163.3 ( 2.6 ) & 24.6 & 147.2 ( 2.5 ) & -5.3 + 54,633.74 .......................... & 0.143 & -150.6 ( 3.1 ) & -0.8 & 108.1 ( 3.3 ) & 11.0 + 54,669.84 .......................... & 0.867 & -116.5 ( 6.2 ) & 34.0 & 113.4 ( 4.1 ) & 7.4 + 54,672.78 .......................... & 0.495 & 100.3 ( 3.8 ) & -4.4 & -280.6 ( 3.7 ) & -16.1 + 54,673.88 .......................... & 0.730 & -37.7 ( 12.9 ) & -33.6 & -92.2 ( 7.1 ) & 11.6 + 54,696.69 .......................... & 0.610 & 109.0 ( 14.4 ) & 27.6 & -236.8 ( 3.5 ) & -8.4 + 54,696.96 .......................... & 0.669 & 125.2 ( 4.3 ) & 79.0 & -155.7 ( 3.9 ) & 21.1 + 54,697.66 .......................... & 0.818 & -129.9 ( 5.9 ) & -32.7 & 23.1 ( 3.4 ) & -6.8 + 54,697.96 .......................... & 0.882 & -163.1 ( 4.3 ) & 2.4 & 129.6 ( 3.7 ) & 2.4 + 54,698.75 .......................... & 0.052 & -198.2 ( 4.4 ) & 24.4 & 200.8 ( 7.1 ) & -2.9 + 54,700.87 .......................... & 0.505 & 103.7 ( 3.7 ) & -1.3 & -254.3 ( 3.4 ) & 10.3 + 54,701.90 .......................... & 0.724 & 1.7 ( 3.6 ) & 0.8 & -114.0 ( 3.8 ) & -2.9 + 54,403.66 ........................... & 0.447 & 106.3 ( 14.89 ) & -6.7 & -257.5 ( 5.33 ) & -28.2 + 54,403.74 ........................... & 0.476 & 127.4 ( 12.48 ) & 14.6 & -225.1 ( 6.17 ) & 3.9 + 54,405.72 ........................... & 0.161 & 7.9 ( 5.40 ) & 3.8 & -33.0 ( 25.14 ) & -39.6 + 54,405.74 ........................... & 0.169 & -56.9 ( 6.78 ) & -67.9 & -12.9 ( 16.19 ) & -4.5 + 54,406.64 ........................... & 0.483 & 87.3 ( 15.39 ) & -25.3 & -200.5 ( 8.72 ) & 28.0 + 54,406.65 ........................... & 0.486 & 87.3 ( 20.36 ) & -25.1 & -165.5 ( 11.95 ) & 62.6 + 54,406.77 ........................... & 0.527 & 135.4 ( 13.52 ) & 26.4 & -171.1 ( 7.89 ) & 49.6 + 54,409.74 ........................... & 0.557 & 126.6 ( 9.00 ) & 21.8 & -226.0 ( 5.93 ) & -14.5 + 54,410.68 ........................... & 0.882 & -84.1 ( 14.51 ) & -9.6 & 233.8 ( 6.10 ) & 57.1 + 54,641.84 ........................... & 0.046 & -126.0 ( 5.87 ) & -14.6 & 226.6 ( 6.80 ) & -30.0 + 54,647.81 ........................... & 0.116 & -28.5 ( 8.80 ) & 11.4 & 4.0 ( 8.07 ) & -97.9 + 54,672.90 ........................... & 0.817 & 9.7 ( 15.16 ) & 26.3 & 8.3 ( 19.51 ) & -43.0 + 54,724.70 ........................... & 0.784 & -17.0 ( 17.09 ) & -26.4 & 4.0 ( 23.56 ) & 9.0 + 54,724.78 ........................... & 0.810 & 23.8 ( 7.31 ) & 34.1 & -1.4 ( 23.90 ) & -39.0 + 54,725.72 ........................... & 0.135 & -17.0 ( 10.74 ) & 3.9 & 6.8 ( 8.43 ) & -53.8 + 54,726.72 ........................... & 0.483 & 115.3 ( 10.66 ) & 2.7 & -250.6 ( 7.71 ) & -22.2 + 54,726.79 ........................... & 0.508 & 111.6 ( 13.80 ) & 0.6 & -228.2 ( 6.83 ) & -3.2 + 54,729.70 ........................... & 0.517 & 139.9 ( 11.19 ) & 29.8 & -234.4 ( 6.08 ) & -11.2 + 54,747.59 ........................... & 0.721 & 21.5 ( 5.86 ) & -27.6 & -4.1 ( 6.10 ) & 87.0 + 54,748.60 ........................... & 0.071 & -76.2 ( 6.34 ) & 11.4 & 285.4 ( 26.42 ) & 80.1 + 54,754.77 ........................... & 0.212 & -15.6 ( 10.59 ) & -59.0 & 3.2 ( 44.57 ) & 81.7 + 52,161.65 .......................... & 0.071 & -133.5 ( 2.0 ) & -1.9 & 110.7 ( 2.0 ) & 1.5 + 54,628.75 .......................... & 0.825 & -118.3 ( 2.9 ) & -43.6 & 86.5 ( 2.5 ) & 31.3 + 54,628.88 .......................... & 0.833 & -112.4 ( 3.6 ) & -31.8 & 89.1 ( 2.1 ) & 27.9 + 54,629.87 .......................... & 0.890 & -157.5 ( 3.1 ) & -34.0 & 88.6 ( 2.1 ) & -15.3 + 54,630.74 .......................... & 0.941 & -156.9 ( 2.9 ) & -4.9 & 121.3 ( 2.1 ) & -10.5 + 54,630.85 .......................... & 0.947 & -166.7 ( 2.5 ) & -12.3 & 122.3 ( 2.1 ) & -11.9 + 54,633.86 .......................... & 0.121 & -115.2 ( 2.4 ) & -22.0 & 95.6 ( 2.1 ) & 25.5 + 54,696.75 .......................... & 0.760 & -31.4 ( 6.8 ) & -5.4 & 0.5 ( 2.0 ) & -5.7 + 54,696.96 .......................... & 0.772 & -13.4 ( 2.9 ) & 21.2 & 16.1 ( 3.8 ) & 1.1 + 54,697.77 .......................... & 0.819 & -67.9 ( 5.3 ) & 1.9 & 46.8 ( 1.8 ) & -3.5 + 54,697.85 .......................... & 0.824 & -81.4 ( 3.0 ) & -8.0 & 60.9 ( 2.0 ) & 6.9 + 54,697.92 .......................... & 0.828 & -70.8 ( 2.9 ) & 5.9 & 69.9 ( 2.4 ) & 12.7 + 54,698.71 .......................... & 0.874 & -122.4 ( 1.9 ) & -10.5 & 88.7 ( 1.8 ) & -3.7 + 54,698.91 .......................... & 0.885 & -125.2 ( 3.1 ) & -5.0 & 107.1 ( 2.8 ) & 6.5 + 54,699.72 .......................... & 0.932 & -148.7 ( 1.4 ) & -0.6 & 127.3 ( 1.4 ) & -0.8 + 54,699.93 .......................... & 0.944 & -142.4 ( 1.7 ) & 10.9 & 138.2 ( 1.6 ) & 5.1 + 54,700.72 .......................... & 0.990 & -150.0 ( 2.1 ) & 11.8 & 131.3 ( 1.6 ) & -9.5 + 54,701.73 .......................... & 0.048 & -155.0 ( 1.8 ) & -9.8 & 126.9 ( 1.5 ) & 3.7 + 54,701.94 .......................... & 0.061 & -142.0 ( 2.7 ) & -3.8 & 124.4 ( 2.2 ) & 8.4 + 54,724.69 .......................... & 0.377 & 66.8 ( 3.3 ) & 6.6 & -91.7 ( 2.8 ) & -8.2 + 54,724.81 .......................... & 0.384 & 73.1 ( 1.8 ) & 11.2 & -88.7 ( 1.4 ) & -3.6 + 54,725.69 .......................... & 0.435 & 69.4 ( 1.5 ) & -1.0 & -93.3 ( 1.4 ) & -0.1 + 54,725.80 .......................... & 0.441 & 70.8 ( 1.6 ) & -0.2 & -93.3 ( 1.5 ) & 0.4 + 54,726.70 .......................... & 0.493 & 69.0 ( 1.7 ) & -3.0 & -90.4 ( 1.6 ) & 3.9 + 54,726.82 .......................... & 0.500 & 67.5 ( 1.6 ) & -4.2 & -87.9 ( 1.5 ) & 5.9 + 54,729.66 .......................... & 0.664 & 27.0 ( 2.0 ) & -2.4 & -52.7 ( 1.9 ) & -2.8 + 54,729.84 .......................... & 0.675 & 22.2 ( 2.1 ) & -2.2 & -52.9 ( 2.1 ) & -8.1 + lccccl mt059 & sb1 & o8v & b & 4.8527 ( 0.0002 ) & 0.220.67 & 1 + mt145 & sb1 & o9iii & mid b & 25.140 ( 0.008 ) & 0.260.63 & 2 + mt252 & sb2 & b2iii & b1v & 1819 & 0.8 ( 0.2 ) & 1 + mt258 & sb1 & o8v & b & 14.660 ( 0.002 ) & 0.180.89 & 1 + mt372 & ea?/sb1 & b0v & b2?v & 2.228 ( fixed ) & @xmath120.6 & 2,3 + mt421 & ea & o9v & b9v a0v & 4.161 & @xmath120.160.19 & 4 + mt429 & ea & b0v & ? ? & 2.9788 & & 4 + mt696 & sb2/ew / ke & o9.5v & early b & 1.46 & & 5 + mt720 & sb2 & early b & early b & @xmath128 5 & & 1 + mt771 & sb2 & o7v & o9v & 1.5 : & 0.8 ( 0.1 ) & 1 + schulte 3 & sb2/ea ? & o6iv ? & o9iii & 4.7464 ( 0.0002 ) & 0.44 ( 0.08 ) & 1,6 + schulte 5 & eb & o7ianfp & ofpe / wn9 ( & b0v ? ) & 6.6 & 0.28 ( 0.02 ) & 7,8,9,10,11,12 + schulte 8a & sb2 & o5.5i & o6 ? & 21.908 & 0.86 ( 0.04 ) & 13,14 + schulte 9 & sb2 & o5 ? & o67 ? & 2.355 yr & & 15 + schulte 73 & sb2 & o8iii & o8iii & 17.28 ( 0.03 ) & 0.99 ( 0.02 ) & 2 + a36 & sb2/ea & b0ib & b0iii & 4.674 ( 0.004 ) & 0.70 ( 0.06 ) & 2,16,17 + a45 & sb2 & b0.5v & b2v ? b3v ? & 2.884 ( 0.001 ) & 0.46 ( 0.02 ) & 2,17 + b17 & sb2 & o7 ? & o9 ? & 4.0217 ( 0.0004 ) & @xmath121 ? & 18,19 +

with respect to the magnitude of the gravitational lens system at its discovery , in 1986 , um673 was 0.3 magnitude brighter . we also present @xmath0 magnitudes and @xmath1 colours of seven field stars situated in the vicinity of the lens , based on a 3.5-month monitoring during the year 2000 .

i

astro-ph0107312

we present the results of a photometric ccd monitoring of the gravitational lens system um673 , that took place from 1995 to 2000 . in total , the doubly - imaged quasar was observed in the @xmath0-band during 29 photometric nights , using optical telescopes with dimensions in the range 0.6 m to 1.3 m . we detected a significant variability in the total light of the um673 system , that is , in the light of the two qso images plus the lensing galaxy . with respect to the magnitude of the gravitational lens system at its discovery , in 1986 , um673 was 0.3 magnitude brighter . furthermore , our december 1996 measurements show that between november 1995 and october 1997 the system became even brighter , reaching a magnitude difference of 0.5 magnitude with respect to its discovery value . we also present @xmath0 magnitudes and @xmath1 colours of seven field stars situated in the vicinity of the lens , based on a 3.5-month monitoring during the year 2000 .

@xcite presented um673 ( @xmath2 ) as a `` new case of gravitational lensing '' . the two lensed images originate from a quasar at a redshift @xmath3 , while the lensing galaxy is much closer to the milky way ( @xmath4 ) . the angular separation between component @xmath5 and @xmath6 was found to be @xmath7 , while the magnitude of the qso images and the lens galaxy , at the time of discovery , was @xmath8 , @xmath9 and @xmath10 magnitude , resulting in a total magnitude @xmath11 , with a standard deviation of the order of 0.2 magnitude . they concluded that um673 appeared to be one of the most luminous quasars , due to the amplification of image @xmath5 by gravitational lensing . a spectroscopic study of this gravitational lens was published by @xcite , in order to investigate the size of the corresponding @xmath12 clouds . since they found that the equivalent widths of the @xmath12 lines in the spectra of @xmath5 and @xmath6 are well correlated , they concluded that both light beams actually cross the same clouds . data from this paper were used by @xcite to test their model for the minihalo of the @xmath12 forest for the case of um673 . @xcite observed um673 from 1987 to 1993 . the observations were performed in the @xmath6-band , to eliminate any possible contamination originating from the deflecting galaxy . they mainly derived the magnitude difference of the two qso components , because the observing conditions were of modest quality for most of the nights . the photometric zero point was computed for the nights of 1988 october 31 , 1988 december 17 and 1991 october 27 . the respective joint @xmath6 magnitude of the two qso components ( no contribution from the galaxy in the @xmath6-band ) was 168 , 169 and 167 . their results led to the conclusion that the quasar was not showing any significant variability , but the accuracy of the relative photometry was of the order of 0.05 to 0.2 magnitude . the mean @xmath6-band magnitude difference was @xmath13 . in a later report based on an eso key - program for photometric monitoring of gravitational lenses , @xcite confirmed the above conclusions . during a 2-days workshop held in hambourg , @xcite presented some _ preliminary _ results from the 1988 - 1994 monitoring of the lens . the relative photometry of component @xmath5 , with respect to a reference magnitude @xmath14 , was indicating variations of the order of 0.2 magnitude ! unfortunately , nothing more was ever published , and therefore no additional information concerning the reduction method used or the reference magnitude could be found . in a recently published paper concerning @xmath15 observations of gravitational lenses , @xcite reported on observations of um673 performed in november 1994 . the @xmath0 magnitude of the components @xmath5 , @xmath6 , and the galaxy was @xmath16 and @xmath17 respectively , resulting in an integrated magnitude of @xmath18 . the error on the total magnitude is of the order of @xmath19 . the sloan digital sky survey ( @xmath20 ) also observed um673 . having their own photometric system under preparation @xcite , they presented their measurements in a preliminary red filter , designated as @xmath21 ( see section [ comparison with the literature ] ) . observations in the @xmath21 filter were performed in 1995 november 24 and 1996 december 12 . for the first period , @xcite reported @xmath22 , while for the second period @xcite reported @xmath23 . we report in this paper about a photometric monitoring through the years 1995 - 2000 , with conclusions to significant variations in the total light of the gravitational lens system . we also present @xmath0 magnitudes and @xmath1 colours of seven field stars , situated in the neighborhood of um673 . these results , based on data which were accumulated during a period of 3.5 months , consist in a preliminary tool for directly checking the photometric variability of the quasar .

we present the results of a photometric ccd monitoring of the gravitational lens system um673 , that took place from 1995 to 2000 . in total , the doubly - imaged quasar was observed in the @xmath0-band during 29 photometric nights , using optical telescopes with dimensions in the range 0.6 m to 1.3 m . furthermore , our december 1996 measurements show that between november 1995 and october 1997 the system became even brighter , reaching a magnitude difference of 0.5 magnitude with respect to its discovery value .

c

astro-ph0107312

we present the results of a photometric ccd monitoring of the gravitational lens system um673 , that took place from 1995 to 2000 . in total , the doubly - imaged quasar was observed in the @xmath0-band during 29 photometric nights , using optical telescopes with dimensions in the range 0.6 m to 1.3 m . we detected a significant variability in the total light of the um673 system , that is , in the light of the two qso images plus the lensing galaxy . with respect to the magnitude of the gravitational lens system at its discovery , in 1986 , um673 was 0.3 magnitude brighter . furthermore , our december 1996 measurements show that between november 1995 and october 1997 the system became even brighter , reaching a magnitude difference of 0.5 magnitude with respect to its discovery value . we also present @xmath0 magnitudes and @xmath1 colours of seven field stars situated in the vicinity of the lens , based on a 3.5-month monitoring during the year 2000 .

we have been monitoring the gravitational lens um673 through the years 1995 - 2000 . to measure the total light of the lens ( component @xmath5 + component @xmath6 + lensing galaxy ) we constrained ourselves to aperture photometry . the numerous observations obtained during each run ( several hours per night ) , allowed us to reach a photometric precision of a few hundredths of a magnitude . the photometric calibration was performed with the help of several photometric standard stars . although the observations were performed using several configurations , all measurements agree with the conclusion that the qso has undergone a long term variability , that corresponds to a brightening in the total light of the system of @xmath58 0.3 magnitude in respect to its discovery value , in 1987 . from the agreement between the 1995 and 1997 measurements we see that this variability had its peak ( additional 02 brightening ) in 1996 . the @xmath0 magnitude of um673 we derived was 16.30@xmath590.02 in november 1995 , 16.08@xmath590.01 in december 1996 , 16.30@xmath590.01 in october 1997 , 16.23@xmath590.05 in october 1998 and 16.34@xmath590.01 for the last quarter of 2000 ( fig . [ variability ] ) . thanks to the optimized configuration of the skinakas observatory , we managed to have @xmath33 and @xmath0 measurements of seven field stars in the vicinity of um673 during the period september - december 2000 . although more observations are needed for a better knowledge about the stability of these stars over a longer time - basis , the photometric reduction showed no significant variability at the level 002 - 003 . the measurements obtained after 1996 seem to form a plateau at around @xmath60 , indicating that since 1997 the quasar seems to be in a less variable , or even quiet , state . nevertheless , we propose a systematic monitoring of um673 at a rate of a few images at fixed time intervals . with the help of the reference stars , differential photometry would directly show any new variability in the system . we also suggest new measurements with instruments allowing analysis of the spectra of the components for comparison with earlier ones , and photometric observations to derive the fluxes of the two qso components . we thank dr . a. erikson ( dlr , berlin ) for his introduction to the 0.6 m bochum telescope and for his help to convert our ccd data to fits format , and a. kougentakis for his excellent assistance during the observations at skinakas observatory . t.n . would like to thank n. shatsky , visiting astronomer at rob , for the helpful discussions . + the authors would like to acknowledge prof . j. surdej , for his useful comments . finally , it is a pleasure to thank the referee , dr . r. schild , for his constructive suggestions . + this research ( d.s . ) was mainly carried out in the framework of the projects `` service centres and research networks '' , and `` ples dattraction interuniversitaires '' p4/05 , both initiated and financed by the belgian federal scientific services ( dwtc / sstc ) . t.n . acknowledges support from the project `` chercheurs supplmentaires aux etablissements scientifiques federaux '' . acknowledges support from a p.en.e.d . " program of the general secretariat of research and technology of greece , and the royal observatory of belgium for financing his visit in brussels . + skinakas observatory is a collaborative project of the university of crete , the foundation for research and technology - hellas and the max - planck - institut fr extraterrestrische physik . daulie , g. , hainaut , o. , hutsmkers , d. , magain , p. , remy , m. , smette , a. , surdej , j. & van drom , e. 1993 , in 31st lige international astrophysical colloquium , gravitational lenses in the universe , ed . surdej , j. , fraipont - caro , d. , gosset , e. , et al . , ( lige : univ . of lige press ) , 181 rrrrr 1995 nov 03/09 - 10 & 0.6 m bochum & th 7882 & r & 180 + 1996 dec 09 - 19 & 0.6 m bochum & th 7882 & r & 300 + 1997 oct 22 - 26 & 0.9 m dutch & tektronix tk512cb & r & 1200 + 1998 oct 29 & 1.2 m kryonerion & class i si502 & r & 120 + 2000 aug 23 & 1.0 m ogs & thomson & r & 120 + 2000 sep 03/11/18 & 1.3 m skinakas & tektronix si003b & r & 240 + 2000 nov 02 - 03/23 & 1.3 m skinakas & tektronix si003b & r & 240 + 2000 dec 14 - 15 & 1.3 m skinakas & tektronix si003b & r & 240 + rrr 1995 nov 03 & 16.27 @xmath38 0.06 & + 1995 nov 09 & 16.31 @xmath38 0.06 & 16.30 @xmath38 0.02 + 1995 nov 10 & 16.32 @xmath38 0.06 & + 1996 dec 09 & 16.11 @xmath38 0.05 & + 1996 dec 10 & 16.12 @xmath38 0.05 & + 1996 dec 11 & 16.10 @xmath38 0.05 & + 1996 dec 12 & 16.09 @xmath38 0.05 & + 1996 dec 13 & 16.05 @xmath38 0.05 & + 1996 dec 14 & 16.07 @xmath38 0.05 & 16.08 @xmath38 0.01 + 1996 dec 15 & 16.08 @xmath38 0.05 & + 1996 dec 16 & 16.11 @xmath38 0.05 & + 1996 dec 17 & 16.07 @xmath38 0.05 & + 1996 dec 18 & 16.08 @xmath38 0.05 & + 1996 dec 19 & 16.04 @xmath38 0.05 & + 1997 oct 22 & 16.29 @xmath38 0.02 & + 1997 oct 23 & 16.30 @xmath38 0.02 & + 1997 oct 24 & 16.30 @xmath38 0.02 & 16.30 @xmath38 0.01 + 1997 oct 25 & 16.30 @xmath38 0.02 & + 1997 oct 26 & 16.29 @xmath38 0.02 & + 1998 oct 29 & 16.23 @xmath38 0.05 & 16.23 @xmath38 0.05 + 2000 aug 23 & 16.30 @xmath38 0.02 & + 2000 sep 03 & 16.34 @xmath38 0.02 & + 2000 sep 11 & 16.35 @xmath38 0.02 & + 2000 sep 18 & 16.31 @xmath38 0.03 & + 2000 nov 02 & 16.35 @xmath38 0.02 & 16.34 @xmath38 0.01 + 2000 nov 03 & 16.34 @xmath38 0.02 & + 2000 nov 23 & 16.35 @xmath38 0.02 & + 2000 dec 14 & 16.34 @xmath38 0.02 & + 2000 dec 15 & 16.35 @xmath38 0.02 & + rrrr 1 & 01 45 12.05 @xmath6109 47 49 & 15.92 @xmath38 0.02 & 0.51 @xmath38 0.03 + 2 & 01 45 07.15 @xmath6109 49 01 & 16.61 @xmath38 0.02 & 0.94 @xmath38 0.03 + 3 & 01 45 08.73 @xmath6109 43 13 & 17.12 @xmath38 0.02 & 0.33 @xmath38 0.03 + 4 & 01 45 03.43 @xmath6109 44 18 & 17.37 @xmath38 0.02 & 0.84 @xmath38 0.04 + 5 & 01 44 57.90 @xmath6109 44 09 & 17.42 @xmath38 0.02 & 0.84 @xmath38 0.04 + 6 & 01 44 56.26 @xmath6109 44 15 & 17.80 @xmath38 0.02 & 0.42 @xmath38 0.04 + 7 & 01 44 56.63 @xmath6109 43 02 & 16.75 @xmath38 0.03 & 0.38 @xmath38 0.04 +

we present two - dimensional febry - perot observations of emission - line distribution and kinematics in nearly spiral galaxies . the latter , in turn , could help build a pseudo - bulge . in the second paper in this series , we will apply the kinematic analysis tools to a sample of 9 late - type spiral galaxies observed with the fantomm fabry - perot spectrometer at the canada - france - hawaii telescope .

i

0706.0407

we present two - dimensional febry - perot observations of emission - line distribution and kinematics in nearly spiral galaxies . we have developed and demonstrated the utility of a number of analysis tools which have general applicability , but which we have , so far , applied to only one galaxy ( m 74 , fathi et al . 2007 ) . in this galaxy , we have found kinematic signatures of radial motions caused by an m=2 perturbation . such a perturbation may well be responsible for the inflow of material forming the nuclear ring and the inner rapidly rotating disc - like structure . the latter , in turn , could help build a pseudo - bulge . in the second paper in this series , we will apply the kinematic analysis tools to a sample of 9 late - type spiral galaxies observed with the fantomm fabry - perot spectrometer at the canada - france - hawaii telescope .

in studying galactic dynamics , kinematic measurements over two spatial dimensions provide the necessary wealth of information . currently used methods for achieving such observations , have either limited angular resolution ( radio or submillimeter astronomy ) or cover a relatively small field of view ( integral field units ) . we use fabry - perot interferometry , which combined the high spatial sampling with large field of view , an ideal combination for studying extended objects such as galaxies . we aim to study a sample of 9 late - type spiral galaxies ( ngc 3049 , ngc 4294 , ngc 4519 , ngc 4654 , ngc 5371 , ngc 5921 , ngc 5964 , ngc 7479 , ngc 7741 ) , all observed with the fantomm fabry - perot interferometer ( hernandez et al . 2003 ) at the 3.6 meter canada - france - hawaii telescope . the observations yiel the ideal combination of the spatial coverage and resolution by covering a field of @xmath0 with angular resolution of 048/pixel . fantomm is optimized for targeting the 6562.8 h@xmath1 emission - line , which we use to study the dynamics of the star - forming gas .

we have developed and demonstrated the utility of a number of analysis tools which have general applicability , but which we have , so far , applied to only one galaxy ( m 74 , fathi et al . 2007 ) . in this galaxy , we have found kinematic signatures of radial motions caused by an m=2 perturbation . such a perturbation may well be responsible for the inflow of material forming the nuclear ring and the inner rapidly rotating disc - like structure .

m

0706.0407

we present two - dimensional febry - perot observations of emission - line distribution and kinematics in nearly spiral galaxies . we have developed and demonstrated the utility of a number of analysis tools which have general applicability , but which we have , so far , applied to only one galaxy ( m 74 , fathi et al . 2007 ) . in this galaxy , we have found kinematic signatures of radial motions caused by an m=2 perturbation . such a perturbation may well be responsible for the inflow of material forming the nuclear ring and the inner rapidly rotating disc - like structure . the latter , in turn , could help build a pseudo - bulge . in the second paper in this series , we will apply the kinematic analysis tools to a sample of 9 late - type spiral galaxies observed with the fantomm fabry - perot spectrometer at the canada - france - hawaii telescope .

the data are reduced homogenously , both following the standard data reduction packages and the improved idl - based reduction package developed by daigle et al . ( 2006 ) . in fig . [ fig : n4519 ] , we illustrate the derived maps for one example in our sample of 9 galaxies ( ngc 4519 ) . the velocity fields are used to analyze the rotational components by means of tilted - ring and harmonic decomposition techniques ( e.g. , fathi et al . 2005 ) . the rotation curve is in turn used to derive the angular frequencies and the effects of gravitational perturbations on the evolution of structures in the disk . in conjunction with hii region catalogues , we are then able to extract and quantify the kinematic effects of individual hii regions , and to separate these from the role of the gravitational perturbations on the observed velocity fields . moreover , by averaging the velocity dispersion maps along elliptic annuli , we are able to derive the h@xmath1-emitting gas velocity dispersion profiles to study the effect of feedback and disk heating mechanisms as a function of galactocentric radius . the data analysis methods have been applied on the nearby late - type spiral galaxy , m 74 , and the utility of the codes are presented in detail in fathi et al .

we find that the decay of the density fluctuations can be well described by compressed , thus faster than exponential , correlation functions which can be modeled by the well - known kohlrausch - williams - watts function with a shape exponent @xmath2 larger than one . these features seem to be universal in metallic glasses and suggest a non diffusive nature of the dynamics . this universality is supported by the possibility of describing the fast increase of the structural relaxation time with waiting time using a unique model function , independently of the microscopic details of the system . \\

c

1301.6610

we present x - ray photon correlation spectroscopy measurements of the atomic dynamics in a zr@xmath0ni@xmath1 metallic glass , well below its glass transition temperature . we find that the decay of the density fluctuations can be well described by compressed , thus faster than exponential , correlation functions which can be modeled by the well - known kohlrausch - williams - watts function with a shape exponent @xmath2 larger than one . this parameter is furthermore found to be independent of both waiting time and wave - vector , leading to the possibility to rescale all the correlation functions to a single master curve . the dynamics in the glassy state is additionally characterized by different aging regimes which persist in the deep glassy state . these features seem to be universal in metallic glasses and suggest a non diffusive nature of the dynamics . this universality is supported by the possibility of describing the fast increase of the structural relaxation time with waiting time using a unique model function , independently of the microscopic details of the system . \\

in conclusion , we have studied the physical aging in a zr@xmath0ni@xmath1 metallic glass , by following the temporal evolution of the structural relaxation process at the interatomic length scale . we find that the decay of the density fluctuations can be well described by compressed , thus faster than exponential correlation functions , suggesting a peculiar origin for the atomic dynamics @xcite . this behavior seems to be universal in metallic glasses @xcite , and can not be explained by the well - known theories for glasses dynamics , which predict a stretched exponential shape of the correlation functions , even in the glassy state @xcite . model systems such as hard spheres and lennard - jones are unable to reproduce these intriguing dynamic effects @xcite . in these model systems , indeed , the dynamics appears to be always characterized by a broad spectrum of relaxations . conversely , very similar results have been previously reported for out of equilibrium soft materials , suggesting a universal microscopic dynamics for these very different systems @xcite . in these systems , the compressed behavior arises from ballistic - like motion due to the presence of internal stresses in the out of equilibrium state @xcite . it would be interesting to check whether this is also the case for metallic glasses however , a @xmath8 dependence study would require a much stronger signal than the one achievable even at a third generation synchrotron source as the one used for the present study . notwithstanding , indication of the presence of distinct processes of atomic motion in metallic glasses have been reported for different zr - based metallic glass - formers studied with nuclear magnetic resonance @xcite . in these systems the diffusive , collective motion is found to be accompanied by hopping which becomes dominant in the glassy state , and could then be related to the observed compressed relaxation process in our glass . + albeit we could not get information on the @xmath8 dependence of the relaxation time due to the impossibility of measuring simultaneously different @xmath8s , we have investigated the nature of the dynamics at different wave - vectors and sample ages . we find that the shape of the correlation functions does not show any dependence neither on the sample age nor on the wave - vector , at least for @xmath8s around the maximum of the static structure factor of the system , which is at @xmath30 @xmath29 . these findings allow then to rescale all the correlation curves on the top of each other and define a time - waiting time - wave - vector superposition principle in the fast aging regime . + the value of @xmath2 seems to depend on the details of the system , being larger in zr - based systems than in the previously reported mg@xmath9cu@xmath10y@xmath11 @xcite . as both these glasses were obtained with the same thermal protocol , we speculate that the observed difference could be related to a larger atomic mobility in the first system and to the consequent presence of larger internal stresses . despite this small difference , the comparison between the two metallic glasses suggests the existence of a universal dynamical behavior , also indicated by the scaling of the fast aging regime for the relaxation time to a single curve , independently of the microscopic details of the systems . additional theoretical and experimental works is clearly required to elucidate this remarkable dynamical behavior of metallic glasses . + + we acknowledge f. zontone , h. vitoux , k. lhoste , l. claustre for technical support during the xpcs experiments and e. pineda an p. bruna for providing the samples .

we propose a new theory to explain the formation of spiral arms and of all types of outer rings in barred galaxies . we have extended and applied the technique used in celestial mechanics to compute transfer orbits . thus , our theory is based on the chaotic orbital motion driven by the invariant manifolds associated to the periodic orbits around the hyperbolic equilibrium points . in particular , spiral arms and outer rings are related to the presence of heteroclinic or homoclinic orbits . thus , @xmath0 rings are associated to the presence of heteroclinic orbits , while @xmath1 rings are associated to the presence of homoclinic orbits . spiral arms and @xmath2 rings , however , appear when there exist neither heteroclinic nor homoclinic orbits . we examine the parameter space of three realistic , yet simple , barred galaxy models and discuss the formation of the different morphologies according to the properties of the galaxy model .

i

0712.4391

we propose a new theory to explain the formation of spiral arms and of all types of outer rings in barred galaxies . we have extended and applied the technique used in celestial mechanics to compute transfer orbits . thus , our theory is based on the chaotic orbital motion driven by the invariant manifolds associated to the periodic orbits around the hyperbolic equilibrium points . in particular , spiral arms and outer rings are related to the presence of heteroclinic or homoclinic orbits . thus , @xmath0 rings are associated to the presence of heteroclinic orbits , while @xmath1 rings are associated to the presence of homoclinic orbits . spiral arms and @xmath2 rings , however , appear when there exist neither heteroclinic nor homoclinic orbits . we examine the parameter space of three realistic , yet simple , barred galaxy models and discuss the formation of the different morphologies according to the properties of the galaxy model . the different morphologies arise from differences in the dynamical parameters of the galaxy .

bars are very common features in disk galaxies . according to eskridge _ et al . _ [ ] in the near infrared @xmath3 of the galaxies are strongly barred and @xmath4 are weakly barred . a large fraction of barred galaxies show either spiral arms emanating from the ends of the bar or spirals that end up forming outer rings ( elmegreen & elmegreen [ ] ; sandage & bedke [ ] ) . spiral arms are believed to be density waves ( lindblad [ ] ) . toomre [ ] , finds that the spiral arms are density waves that propagate outwards towards the principal lindblad resonances , where they damp . so other mechanisms for replenishment are needed ( see for example lindblad [ ] ; toomre [ ] ; toomre & toomre [ ] ; sanders & huntley [ ] ; athanassoula [ ] for more details ) . rings have been studied by schwarz [ ] . the author studies the response of a gaseous disk galaxy to a bar - like perturbation . he relates the rings with the position of the principal lindblad resonances . there are different types of outer rings and they can be classified according to the relative orientation of the principal axes of the inner and outer rings ( buta [ ] ) . if the two axes are perpendicular , the outer ring has an eight - shape and it is called @xmath0 ring . if they are parallel , it is called @xmath2 ring . there are galaxies where both types of rings are present , in which case the outer ring is simply called @xmath1 ring . our approach is from the dynamical systems point of view . we first note that both spiral arms and ( inner and outer ) rings emanate from , or are linked to , the ends of the bar , where the unstable equilibrium points of a rotating system are located . we also note that , so far , no common theory for the formation of both features has been presented . we therefore study in detail the neighbourhood of the unstable points and we find that spiral arms and rings are flux tubes driven by the invariant manifolds associated to the periodic orbits around the unstable equilibrium points . this paper is organised as follows . in sec . [ sec : model ] , we give the characteristics of each component of the model and the potential used to describe it . in sec . [ sec : dyn ] , we give the equations of motion and we study the neighbourhood of the equilibrium points . in particular , we give definitions of the lyapunov periodic orbits , the invariant manifolds associated to them , and of the homoclinic and heteroclinic orbits . in sec . [ sec : res ] , we present our results and in sec . [ sec : sum ] , we briefly summarise .

we reanalyse the cell theory of lennard - jones and devonshire and find that in addition to the critical point originally reported for the @xmath0 potential ( and widely quoted in standard textbooks ) , the model exhibits a further critical point . we show that the latter is actually a more appropriate candidate for liquid - gas criticality than the original critical point . epsf

c

cond-mat0111240

we reanalyse the cell theory of lennard - jones and devonshire and find that in addition to the critical point originally reported for the @xmath0 potential ( and widely quoted in standard textbooks ) , the model exhibits a further critical point . we show that the latter is actually a more appropriate candidate for liquid - gas criticality than the original critical point . epsf

we have shown that the original ljd cell theory critical point for the @xmath26-@xmath27 potential @xcite terminates a line of pseudo solid - liquid coexistence , rather than a liquid - gas transition as originally postulated . moreover , we find that the model exhibits a further first order transition , which we believe is a more appropriate candidate for the liquid - vapour line than that suggested by ljd . it seems likely that ljd overlooked the transition we have found because at the time of their study , numerical integration was extremely labour intensive , rendering it difficult to attain the rather low densities at which the gas - like phase appears . presumably also , the proximity of their critical point temperature to the `` real '' lj critical point ( estimated at the time from experimental data for argon ) , made it tempting to make the identification they did . in hindsight this agreement can only be regarded as coincidental ; one would expect a crude mean field theory such as the cell model to considerably _ overestimate _ the critical temperature due to the neglect of fluctuations . the new critical point reported here does indeed do so . of course a critical point between a solid - like and liquid - like states ( as found by ljd ) is an artifact of the cell structure of the model , which imposes long ranged orientational and translational order on the liquid where none exists in reality . the inability of cell theory to accurately represent disordered phases has long been appreciated and several attempts have been made to ameliorate this and other shortcomings of the approach . these include zero- and multiple - occupancy of cells ( `` hole '' theories ) @xcite ; calculations of interactions with second- and higher nearest neighbours ( see eg . ref . @xcite ) ; use of numerical integration to give more accurate cell shapes and free volumes @xcite ; and differing methods for calculating the cell potential ( see eg . however , none of these extensions fully address the underlying lattice approximation which renders suspect any cell theory equation of state for a liquid - by definition , a disordered state without a lattice . even hole theories will only be able to represent a liquid of appreciable density as a highly defective crystal . finally we briefly point out implications of our findings for other recent work on cell theory . in ref . @xcite a modified cell theory is introduced with the specific intention of engineering a freezing transition . this authors state that no such transition exists in the ljd cell theory , in the apparent belief that the critical point of the bare model is liquid - gas in character . in other recent work ( which in fact motivated the present study ) , a cell model has been employed to study the phenomenon of the second critical point which is observed in pure fluids interacting via so - called core - softened potentials @xcite . in such systems liquid - liquid phase separation occurs in addition to liquid - gas coexistence . clearly in view of our finding , that even the basic cell theory for the @xmath26-@xmath27 potential exhibits two critical points , the results of such studies should be interpreted with caution . we intend to report in depth on this matter in a future communication . lennard - jones , j.e . , devonshire , a.f . london * a163 * , 53 ( 1937 ) ; ibid * a165 * , 1 ( 1938 ) . kirkwood , j.g . , j. chem . phys . * 18 * , 380 ( 1950 ) . barker , j.a . , lattice theories of the liquid state , pergamon press ( 1963 ) . hill , t.l . , _ statistical mechanics - principles and selected applications _ , mcgraw - hill ( 1956 ) chapter 8 . fowler r.h . , and guggenheim , e.a . _ statistical thermodynamics for students of physics and chemistry _ , cambridge university press ( 1949 ) . burshtein , a.i . ; _ introduction to thermodynamics and kinetic theory of matter _ , wiley ( new york ) ( 1996 ) . modarress , h. , ahmadnia , e. , and mansoori , g.a . ; j. chem . phys . * 111 * , 10236 ( 1999 ) ; pourgheysar , p. , mansoori , g.a . and h. , ahmadnia , e. ; j. chem . phys . * 105 * , 9580 ( 1996 ) . sadr - lahijany , m.r . , scala , a. , buldyrec , s.v . , stanley , h.e . ; phys . * 81 * , 4895 ( 1998 ) . press , w.h . , teukolsky , s.a . , vetterling , w.t . , flannery , b.p . , _ numerical recipes in c _ , cambridge university press ( 1992 ) . potoff , j.j . , and panagiotopoulos , a.z . , j. chem . phys . * 109 * 10914 ( 1998 ) , and references therein .

we report heating - compensated interlayer tunneling spectroscopy ( its ) performed on stacks of overdoped bi@xmath0sr@xmath0cacu@xmath0o@xmath1 intrinsic junctions , where most of bias - induced heating in the its was eliminated . the onset temperature of the pseudogap ( pg ) , revealed in the hump structure of the electronic excitation spectra , reached nearly room temperature for our overdoped intrinsic junctions , which represented the genuine pg onset . at a temperature below but close to @xmath2 , both the superconducting coherence peak and the pseudogap hump coexisted , implying that the two gaps are of separate origins . the hump voltage increased below @xmath2 , following the superconducting gap voltage , which led to a conclusion that the hump structure below @xmath2 in our its arose from the combined contribution of the quasiparticle spectral weights of two different characters ; one of the superconducting state and another of the pg state near the antinodal region .

i

0803.2457

we report heating - compensated interlayer tunneling spectroscopy ( its ) performed on stacks of overdoped bi@xmath0sr@xmath0cacu@xmath0o@xmath1 intrinsic junctions , where most of bias - induced heating in the its was eliminated . the onset temperature of the pseudogap ( pg ) , revealed in the hump structure of the electronic excitation spectra , reached nearly room temperature for our overdoped intrinsic junctions , which represented the genuine pg onset . at a temperature below but close to @xmath2 , both the superconducting coherence peak and the pseudogap hump coexisted , implying that the two gaps are of separate origins . the hump voltage increased below @xmath2 , following the superconducting gap voltage , which led to a conclusion that the hump structure below @xmath2 in our its arose from the combined contribution of the quasiparticle spectral weights of two different characters ; one of the superconducting state and another of the pg state near the antinodal region .

conventional superconductors in their superconducting state are characterized by opening of the superconducting gap ( sg ) in the electronic density of states ( dos ) . superconductivity appears when electrons bind into cooper pairs and condense with long - range order below the superconducting transition temperature @xmath2 . cuprate superconductors , however , as one of the most intriguing characteristics in their normal state , show the unusual emergence of the pseudogap ( pg ) in the electronic excitation spectrum even above @xmath2 , which persists up to a temperature @xmath3 , the pg onset temperature . it has been widely accepted that understanding the pg origin and the relation between the pg and the sg may lead to a key to finding the basic mechanism of high - temperature superconductivity,@xcite which is not fully resolved up to the present . there are two schools of thought as to understanding the pg in the cuprate physics : one - gap and two - gap ones . one - gap school regards the pg as the precursor of the sg , where thermal fluctuations destroy long - range order while maintaining gap - like features in the excitation spectra in a certain high - temperature range ( @xmath4 ) of the normal state . thus , the pg in question is believed to bring about the partial depletion of the dos at the normal - state fermi surface@xcite , resulting in the fermi arcs.@xcite the other school interprets the pg , especially in the underdoped regime , in terms of two gaps ; a small sg revealed in the nodal regions and a large gap of different origin in the antinodal regions . in the two - gap model , the fermi arcs are believed to emerge due to long - range order that , however , is not associated with the superconducting order . above @xmath2 the sg may vanish , leaving the other long - range order connected to the fermi arcs , fermi surface nestings@xcite or fermi surface pockets@xcite . recent raman and angle - resolved - photoemission - spectroscopy ( arpes ) measurements show the consequences of opening of two gaps in underdoped single - layer hgba@xmath0cuo@xmath5 superconductors and bilayer bi@xmath0sr@xmath0ca@xmath6y@xmath7cu@xmath0o@xmath8 superconductors , respectively.@xcite the surface tunneling studies on the pg behavior suggest that the pg can evolve into the sg in the norm of one gap.@xcite in interlayer tunneling measurements on densely stacked intrinsic josephson junctions ( ijjs)@xcite formed in the layered cuprates , however , it has been proposed that the sg vanishes at @xmath2 and the pg may exist both below and above @xmath2 . this experimental observation from ijjs is claimed to provide the norm of two gaps , where the sg and the pg are considered to be of different origins.@xcite the interlayer tunneling reveals the intrinsic bulk tunneling properties between cuo@xmath0 superconducting layers , which can be an advantage of this scheme compared to other surface - sensitive spectroscopic methods . recently , however , it has been suggested that the experimental observations of the ijjs could be affected by the self - heating generated in a high - bias region , which was caused by the poor thermal conductivity of bi@xmath0sr@xmath0cacu@xmath0o@xmath8 ( bi-2212 ) and other materials involved in the tunneling measurements.@xcite the zero - bias tunneling process in the @xmath9 axis is very sensitive to the electronic dos at the normal - state fermi surface . in particular , the zero - bias tunneling resistance @xmath10 in the bi-2212 is weighted by the tunneling of quasiparticles in the antinodal region of the fermi surface.@xcite thus , @xmath10 is expected to increase rapidly as the pg opens and the corresponding dos is partially depleted at the fermi surface . in this point of view , the onset temperature of the pg opening can be defined as the characteristic temperature @xmath11 , at which @xmath10 deviates from the @xmath12-linear temperature dependence in @xmath10 vs @xmath12 curves.@xcite recently , kawakami _ et al._,@xcite based on the temperature dependence of @xmath10 , have shown that both the electron- and the hole - doped cuprates have common spin - singlet correlations in forming the pg , both of which thus close in high magnetic fields . the closing fields of the pg and the sg , however , show much different temperature dependencies from each other , which indicates that the two gaps are of separate origins . difference in origins of the two gaps is in line with the coexistence of the superconducting state and the pg state observed by the interlayer tunneling spectroscopy ( its ) in hole - doped bi-2212 ijjs , which is represented by the sharp peak and the broad hump structure below @xmath2.@xcite relating the hump structure in the high - energy windows of the its to the formation of the pg was controversial up to the present , however , again because of possible self - heating in a high - bias region,@xcite although there have been many efforts to reduce the self - heating effect in the its , by adopting schemes such as reducing the junction area , reducing the number of stacked junctions , and adopting pulsed biasing.@xcite in this study , for an overdoped bi-2212 sample fabricated on an as - grown single crystal , we discriminate the pg onset temperature , defined by the appearance of the hump structure ( @xmath13 ) in the its while lowering temperature , from that obtained by the @xmath10 vs @xmath12 behavior ( @xmath11 ) . to obtain the interlayer tunneling characteristics that are essentially free from self - heating artifact , we adopted the recently developed technique of heating - compensated its , where a large portion of the bias - induced self - heating was removed.@xcite in contrast to @xmath11@xmath14 190 k , the hump structure persisted up to temperatures much higher than commonly perceived . we then numerically illustrate that , with significant self - heating , @xmath13 would reduce down to @xmath11 , which confirms the previous reports by others in the heating - dominated case.@xcite we thus suggest that the @xmath13 represents the genuine onset of the pg . as in earlier works@xcite , with decreasing temperature below @xmath2 , the hump voltages in our heating - free its increases , along with the increase of the superconducting gap size . it turns out that this unusual temperature variation of the hump voltage below @xmath2 results from the combined tunneling contribution of the quasiprticles associated with both the sg and the pg in the electronic state . since the antinodal tunneling is weighted , the behavior of this pg obtained in the its of our overdoped bi-2212 should be related to the electronic structure of the antinodal region in the first brillouin zone of the cuo@xmath0 layers .

the flares were simulated by calculating the atmospheric response to a beam of non - thermal electrons injected at the apex of a one - dimensional closed coronal loop , and include heating from thermal soft x - ray , extreme ultraviolet and ultraviolet ( xeuv ) emission . the equations of radiative transfer and statistical equilibrium were treated in non - lte and solved for numerous transitions of hydrogen , helium , and ca ii allowing the calculation of detailed line profiles and continuum emission . the dynamics are characterized by a long gentle phase of near balance between flare heating and radiative cooling , followed by an explosive phase with beam heating dominating over cooling and characterized by strong hydrodynamic waves . for a strong flare ( @xmath0x - class ) , the gentle phase is much shorter , and we speculate that for even stronger flares the gentle phase may be essentially non - existent . during the explosive phase , synthetic profiles for lines formed in the upper chromosphere and transition region show blue shifts corresponding to a plasma velocity of @xmath0120 km s@xmath1 , and lines formed in the lower chromosphere show red shifts of @xmath040 km s@xmath1 .

m

astro-ph0507335

we report on radiative hydrodynamic simulations of moderate and strong solar flares . the flares were simulated by calculating the atmospheric response to a beam of non - thermal electrons injected at the apex of a one - dimensional closed coronal loop , and include heating from thermal soft x - ray , extreme ultraviolet and ultraviolet ( xeuv ) emission . the equations of radiative transfer and statistical equilibrium were treated in non - lte and solved for numerous transitions of hydrogen , helium , and ca ii allowing the calculation of detailed line profiles and continuum emission . this work improves upon previous simulations by incorporating more realistic non - thermal electron beam models and includes a more rigorous model of thermal xeuv heating . we find xeuv backwarming contributes less than 10% of the heating , even in strong flares . the simulations show elevated coronal and transition region densities resulting in dramatic increases in line and continuum emission in both the uv and optical regions . the optical continuum reaches a peak increase of several percent which is consistent with enhancements observed in solar white light flares . for a moderate flare ( @xmath0m - class ) , the dynamics are characterized by a long gentle phase of near balance between flare heating and radiative cooling , followed by an explosive phase with beam heating dominating over cooling and characterized by strong hydrodynamic waves . for a strong flare ( @xmath0x - class ) , the gentle phase is much shorter , and we speculate that for even stronger flares the gentle phase may be essentially non - existent . during the explosive phase , synthetic profiles for lines formed in the upper chromosphere and transition region show blue shifts corresponding to a plasma velocity of @xmath0120 km s@xmath1 , and lines formed in the lower chromosphere show red shifts of @xmath040 km s@xmath1 .

the basic method of solution is described in detail in ah99 and @xcite . here we briefly outline the procedure . the equations of hydrodynamics , population conservation and radiative transfer are solved simultaneously on a one - dimensional adaptive grid @xcite using the radyn code of @xcite . the code has been modified to include the effects of flare heating from a non - thermal electron beam , heating from high temperature soft x - ray , extreme ultraviolet and ultraviolet emission ( hereafter , we refer to these collectively as xeuv emission ) and optically thin cooling resulting from bremsstrahlung and collisionally excited metal transitions . hydrodynamic effects due to gravity , thermal conduction and compressional viscosity are included as described in ah99 . we have additionally modified the code to include the double power - law electron beam energy distributions recently observed in solar flares with the rhessi satellite @xcite . we incorporate the effects of xeuv heating from a large number of high temperature lines using results from the chianti @xcite and atomdb databases @xcite . we obtain the non - lte solution to the population equations for a six level with continuum hydrogen atom , nine level with continuum helium atom and six level with continuum ca ii atom using the technique of @xcite . the bound - bound and bound - free transitions which are calculated in detail are listed in tables [ table : bb ] & [ table : bf ] . all lines are calculated assuming complete redistribution , but for the lyman transitions the effects of partial redistribution are approximated by truncating the line profiles at 10 doppler widths . other transitions are included as background opacity in lte . the opacities are computed from the uppsala package of @xcite . we include optically thin radiative cooling from bremsstrahlung and coronal metal transitions using emissivities from the atomdb database . the equations are solved on an adaptive grid using 191 grid points in depth , 5 in angle and up to 100 in frequency for each transition . we have found it necessary to employ an adaptive grid in order to resolve large shocks which propagate through the atmosphere . a magnetic flux tube is typically modeled as a semi - circular loop with footpoints embedded in the photosphere and apex in the corona . by symmetry we need only consider one leg of the loop which we take to be a cylinder of constant cross section . in this approximation the atmospheric height , @xmath2 , is the only spatial degree of freedom . we use the pf2 model of ah99 as the preflare atmosphere . the pf2 atmosphere was generated by adding a transition region and corona to the model atmosphere of @xcite . to resolve the steep gradients present in the transition region pf2 required 191 grid points . constant non - radiative quiescent heating was applied to grid zones with photospheric column mass ( i.e. column mass greater than 7.6 g @xmath3 ) to balance the energy losses in the photosphere . the upper boundary was set at @xmath4 km and held at @xmath5 k. with these boundary conditions and no external sources of heating , the atmosphere was allowed to relax to a state of hydrodynamic equilibrium . in the standard flare reconnection model , electrons located near the loop apex are accelerated to high energies and travel downward through the atmosphere depositing energy and producing hard x - ray bremsstrahlung radiation . for the simulations presented here , we assume that the electron beam is the primary source of flare heating in the lower solar atmosphere . recently , @xcite analyzed hard x - ray spectra observed with rhessi to obtain the injected electron energy spectrum at 20 s intervals throughout the 23 july 2002 x - class solar flare . the injected electrons are found to have a double power law energy distribution of the form @xmath6 where @xmath7 is the electron energy flux that enters the magnetic loop ; @xmath8 is the cutoff energy below which the x - ray emission is assumed to be thermal ; and @xmath9 is the break energy where the distribution shifts from spectral index @xmath10 to @xmath11 . using equation [ eqn : dpl ] we calculated the energy deposition rate as a function of column depth using the method of @xcite which assumes that the energetic particles are slowed and deposit their heat through coulomb interactions . to account for the changing partial ionization of hydrogen we have adopted the treatment of @xcite . the resulting heating rate as a function of column depth is , @xmath12 + \right . \nonumber \\ \left . \left ( \frac{n^*(n)}{n^*_c } \right)^{-\frac{\delta_u}{2 } } \left ( \frac{e_b}{e_c } \right)^{\delta_u-\delta_l } b_{x_b } \left ( \frac{\delta_u}{2},\frac{1}{3 } \right ) \right\}\end{aligned}\ ] ] where @xmath13 , @xmath14 , @xmath15 is the hydrogen ionization fraction , @xmath16 and @xmath17 are the coulomb logarithms defined in @xcite , and @xmath18 is the cosine of the pitch angle of the beam ; @xmath19 in our simulations . the quantity @xmath20 is the incomplete beta function for @xmath21 where @xmath22 is the maximum column depth penetration of a beam with cutoff energy @xmath8 . @xmath23 is defined similarly for @xmath9 . @xmath24 is the equivalent column depth in a fully ionized plasma defined by @xmath25 and @xmath26 is the cutoff depth in a fully ionized plasma . the parameters @xmath10 , @xmath11 , @xmath7 , @xmath8 and @xmath9 are obtained by fitting the hard x - ray spectra observed during a flare to models for thick target bremsstrahlung as described in @xcite . in a future paper , we will use the time - dependent beam parameters they have obtained to simulate the 23 july 2002 solar flare . in this paper , we take @xmath10 , @xmath11 , @xmath8 , and @xmath9 to be constant with values of 3.0 , 4.0 , 37 kev and 105 kev , respectively , corresponding to the peak of the 23 july 2002 flare . figure [ fig : qe ] shows the initial energy deposition rate of the electron beam and compares it with the initial deposition rate from ah99 . ah99 used a single power law electron energy spectrum with a spectral index , @xmath27 , and a cutoff energy , @xmath28 kev . the lower spectral indices and the higher energy cutoff we employ result in energy deposition that extends deeper in the atmosphere and has a broader spatial extent . non - thermal electrons affect the atmosphere not only by energy deposition but also through direct collisional ionization . we estimate collisional ionization due to non - thermal electrons using the technique of @xcite . they find the non - thermal collisional ionization rate from the ground state to be @xmath29 where @xmath30 is the hydrogen number density and @xmath31 is the beam energy deposition rate due to collisions with neutral hydrogen and is related to the total energy deposition rate defined in equation [ eqn : qe ] by @xmath32 . they also find that ionizations from the ground state dominate , so we neglect non - thermal collisional ionizations from excited states . mass motions during flares raise the density in the transition region and corona which can greatly increase the emissivity of xeuv photons from these regions . the outward directed photons we detect as elevated emission , while the downward directed photons cause `` backwarming '' : heating of the lower atmosphere due to increased photoionizations . we have used the atomdb database to determine the thermal volume monochromatic emissivity as a function of wavelength and temperature . we include emissivities calculated for approximately 34,000 transitions at 37 temperature points ranging from @xmath4 k to @xmath33 k. the transitions have been gathered into 14 wavelength bins ranging from 1 @xmath34 to 2500 @xmath34 . table [ table : xbins ] lists the range and emissivity - weighted central wavelengths of each bin . when calculating these emissivities , we have taken care not to include transitions that are already solved in detail in radyn ( cf . table [ table : bb ] ) . since the xeuv emission produced in low - temperature , optically - thick layers is negligible , we assume that all such emission originates from the higher temperature , optically - thin layers . the xeuv flux incident on a layer with optical depth @xmath35 is given by , @xmath36 where @xmath37 is the source function , given by the ratio of the emissivity to the linear extinction coefficient . for layers close to the layer under consideration ( @xmath38 , where @xmath39 is the separation between layers and @xmath40 is the loop cross - sectional diameter ) , @xmath41 in the above integral is @xmath42 , the second exponential integral . however , in order to avoid overestimating the emission from distant layers ( @xmath43 ) we follow @xcite ; and ah99 in treating the distant layers as point sources . in that case @xmath41 is given by , @xmath44 where @xmath45 is defined in equation 10 of ah99 . the xeuv photons heat the lower atmosphere through photoionization . the average scale height of our model atmosphere is greater than the thermalization depth scale of @xcite , so we assume that the energy of the photoionized electrons is transformed entirely to heat in each atmospheric layer . the volumetric heating rate is given by , @xmath46 d\nu\;,\ ] ] where @xmath47 is the number density for ion @xmath48 , @xmath49 is the ionization potential , @xmath50 is the photoionization cross section , and the sum is over approximately 150 ions . the cross sections and number densities were obtained from the chianti database . our method for calculating the xeuv heating is similar to the soft x - ray heating of ah99 , but differs in the extent of the atomic transitions included . ah99 considered emission only between 1 and 250 divided into seven bins , while we include 14 bins in the range 1 to 2500 , i.e. including substantial euv and uv heating . for example , c iii @xmath51977 , which was not included in ah99 , is a significant contributor in our backwarming calculations . figure [ fig : compxray ] compares our xeuv heating rate with that of ah99 at a comparable time late in a moderate flare . our xeuv heating rate is approximately 10 times larger than the rate in ah99 .

we report the discovery of two damped ly@xmath0 absorption - line systems ( dlas ) near redshift @xmath1 along a single quasar sightline ( q1727 + 5302 ) with neutral hydrogen column densities of @xmath2 and @xmath3 atoms @xmath4 . their sightline velocity difference of 13,000 km s@xmath5 corresponds to a proper separation of 106@xmath6 mpc if interpreted as the hubble flow ( @xmath7 , @xmath8 ) . consequently , this rare configuration of four high-@xmath15 absorbers with a total sightline velocity extent of 30,600 km s@xmath5 may represent a large filament - like structure stretching over a proper distance of 241@xmath6 mpc along our sightline , and a region in space capable of harboring excessive amounts of neutral gas . future studies of this region of the sky are encouraged .

i

astro-ph0404609

we report the discovery of two damped ly@xmath0 absorption - line systems ( dlas ) near redshift @xmath1 along a single quasar sightline ( q1727 + 5302 ) with neutral hydrogen column densities of @xmath2 and @xmath3 atoms @xmath4 . their sightline velocity difference of 13,000 km s@xmath5 corresponds to a proper separation of 106@xmath6 mpc if interpreted as the hubble flow ( @xmath7 , @xmath8 ) . the random probability of such an occurrence is significantly less than 3% . follow - up spectroscopy reveals neutral gas - phase zn abundances of [ zn / h ] = @xmath9 ( 26.5% solar ) and @xmath10 ( 4.7% solar ) , respectively . the corresponding cr abundances are [ cr / h ] = @xmath11 ( 5.5% solar ) and @xmath12 ( 1.7% solar ) , respectively , which is evidence for depletion onto grains . follow - up ir images show the two most likely dla galaxy candidates to have impact parameters of @xmath13 kpc and @xmath14 kpc if near @xmath1 . they are significantly underluminous relative to the galaxy population at @xmath1 . to investigate the possibility of additional high-@xmath15 absorbers we have searched the sdss database for @xmath16 quasars within 30 arcmin of the original sightline . five were found , and two show strong - absorption near @xmath1 , consistent with classical dla absorption @xmath17% of the time , but almost always @xmath18 atoms @xmath4 . consequently , this rare configuration of four high-@xmath15 absorbers with a total sightline velocity extent of 30,600 km s@xmath5 may represent a large filament - like structure stretching over a proper distance of 241@xmath6 mpc along our sightline , and a region in space capable of harboring excessive amounts of neutral gas . future studies of this region of the sky are encouraged .

intervening damped ly@xmath0 absorption - line systems ( dlas ) in quasar spectra are very rare , with an incidence of @xmath19 per unit redshift at @xmath1 ( rao , turnshek , & nestor 2004 , hereafter rtn2004 ) . consequently , unless dlas are correlated , the appearance of two dlas along any single quasar sightline ( `` double - damped '' ) represents a very unlikely event . as such , the discovery of any double - damped absorption warrants a closer investigation . here we report the discovery of double - damped absorption near @xmath1 in the sloan digital sky survey ( sdss ) quasar q1727 + 5302 during our most recent _ hubble space telescope _ uv spectroscopic survey for dlas ( rtn2004 ) . the purpose of the present paper is to report initial results pertaining to this discovery , and thereby encourage future studies of this region of the sky . the velocity separation of the absorption is 13,000 km s@xmath5 , which corresponds to a proper radial distance of @xmath20 mpc if interpreted as due to the hubble flow . , @xmath8 , and @xmath21 km s@xmath5 mpc@xmath5 ( @xmath22 ) . ] we speculate that this configuration may represent a neutral hydrogen gas filament with a large cosmological extent along our sightline . in fact , the comoving size of this putative filament would be larger than anything previously reported . as discussed in earlier contributions ( e.g. , rao & turnshek 2000 , hereafter rt2000 , and references therein ) , dlas are excellent tracers of the bulk of the neutral hydrogen gas in the universe , and the aim of our most recent dla uv survey has been to improve our knowledge of the incidence and cosmological mass density of dlas at redshifts @xmath23 . the new sample which led to the discovery of the double - damped absorption was derived from the sdss early data release ( edr ) ( schneider et al . we applied a strong - rest equivalent width ( rew ) selection criterion ( rt2000 ) to optical spectra in order to identify candidate dla absorption lines ( @xmath24 atoms @xmath4 ) , and then we obtained hst stis uv spectra to confirm or refute their presence . the current overall success rate for identifying dlas with this method is @xmath17% . since the @xmath252796,2803 absorption lines are saturated , the rew of the absorption is most closely tied to kinematic spread , not column density . recently , nestor et al . ( 2003 ) have discussed evidence for a correlation between kinematic spread and metallicity . the paper is organized as follows . in 2 we present the hst discovery spectrum for the double - damped absorption , a follow - up mmt spectrum used to determine neutral - gas - phase metal abundances , and irtf imaging data used to search for galaxies associated with the double - damped absorbers along the quasar sightline . in 3 we summarize evidence that exists for strong absorption systems near @xmath1 in other sdss quasars in the same region of the sky . a brief summary and discussion of the results is presented in 4 .

exact analytical expressions of the localized modes are found in both one dimensional and two - dimensional geometry with self - focusing and self - defocusing kerr nonlinearity . this result has been verified by the direct numerical simulation of the governing equation . the transverse power flow density associated with these localized modes has also been examined .

i

1304.2105

we report the existence and properties of localized modes described by nonlinear schrdinger equation with complex @xmath0-symmetric rosen - morse potential well . exact analytical expressions of the localized modes are found in both one dimensional and two - dimensional geometry with self - focusing and self - defocusing kerr nonlinearity . linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters although corresponding linear schrdinger eigenvalue problem possesses unbroken @xmath0-symmetry . this result has been verified by the direct numerical simulation of the governing equation . the transverse power flow density associated with these localized modes has also been examined .

recently , there has been considerable amount of attention to theoretical and experimental investigation of light propagation in parity - time ( @xmath0 ) symmetric optical media @xcite . the interest in study of such @xmath0-symmetric optical materials has its roots in quantum mechanics : the paraxial equation of diffraction is mathematically equivalent to that of quantum schrdinger equation . quantum mechanics requires that the spectrum of every physical observable should be real , which of course are satisfied by hermitian operators . however , bender and boettcher @xcite pointed out that some non - hermitian hamiltonians with @xmath0-symmetry can also exhibit an entirely real spectrum and may constitute unitary quantum systems without violating any of the axioms of quantum mechanics . moreover , it has been shown that for a @xmath0-symmetric complex hamiltonian , there may exist a threshold above which its eigenvalues are not real but become complex , and the system undergoes a phase transition because of spontaneous @xmath0-symmetry breaking . in general the action of the parity @xmath1 and time @xmath2 operators is defined as @xmath3 , @xmath4 and @xmath3 , @xmath5 , @xmath6 , respectively . a hamiltonian with a complex @xmath0-symmetric potential requires that the real part of the potential must be even function of position and the imaginary part should be odd @xcite . in optics such complex @xmath0-symmetric structure can be designed through a judicious designs that involve both optical gain / loss regions and the process of index guiding @xcite . in such settings , complex refractive index distribution @xmath7 plays the role of an optical potential so that the index guiding @xmath8 and the gain / loss profile @xmath9 satisfy @xmath10 and @xmath11 , respectively . unusual exotic phenomena like @xmath0 phase transition , band merging , double refraction , non - reciprocity @xcite , and unidirectional invisibility @xcite etc have been reported to exist in linear @xmath0-symmetric complex optical media . spontaneous @xmath0-symmetry breaking has been experimentally observed in active or passive @xmath0 dimers @xcite and periodic lattices @xcite . these findings , in turn , have stimulated considerable research activity in the non - linear @xmath0-symmetric systems as well . in the nonlinear domain , a novel class of one and two dimensional localized modes were found to exist below and above the phase transition point @xcite and the interplay between the kerr nonlinearity and the @xmath0 threshold was investigated @xcite . subsequently , nonlinear modes are studied in complex @xmath0-symmetric periodic @xcite , gaussian @xcite , bessel @xcite , scarf - ii @xcite , and harmonic @xcite potentials , as well as in a harmonic trap with a rapidly decaying @xmath0-symmetric imaginary component @xcite . stable localized modes in a @xmath0-symmetric slab waveguide with distributed gain and loss are found in @xcite . existence of optical solitons in @xmath0-symmetric nonlinear couplers with gain / loss @xcite , gap solitons in @xmath0-symmetric optical lattices @xcite and optical defect modes in @xmath0-symmetric potentials @xcite are also reported . stable 1d and 2d bright spatial solitons are found to exist in defocusing kerr media with @xmath0-symmetric scarf ii potentials @xcite . also , it has been found that the gray solitons in @xmath0-symmetric potentials can be stable @xcite . however the existence of nonlinear localized modes in yet another important potential e.g. complex @xmath0-symmetric rosen - morse well has not been reported so far . the complex rosen - morse potential well is characterized by the same real component as the complex scarf - ii potential , however , its imaginary component is different . in fact , in contrast with the real component , the imaginary potential component does nt vanish asymptotically , rather it tends to a finite value . this is the reason why the phenomenon of spontaneous breakdown of @xmath0-symmetry is elusive in such system @xcite . nevertheless , the bound state energy eigenvalues of @xmath0-symmetric rosen - morse potential well undergoes a shift from negative to positive domain for certain range of parameters which controls the strength of the potential . in this paper , we investigate the propagation of nonlinear beam in a single @xmath0 waveguide cell which is characterized by the nonlinear schrdinger equation with complex rosen - morse potential well . specifically , the existence of the spatial localized modes have been reported in both one - dimensional and two - dimensional settings with self - focusing and self - defocusing kerr nonlinearity . we have shown , with the help of linear stability analysis of the one - dimensional localized modes , that though the spontaneous breakdown of @xmath0-symmetry does not occur in complex rosen - morse well the localized modes corresponding to nonlinear schrdinger equation are always unstable . this linear instability has been verified by direct numerical simulation of the governing equation . the transverse power flow density associated with these nonlinear localized modes has also been examined .

we report the existence and properties of localized modes described by nonlinear schrdinger equation with complex @xmath0-symmetric rosen - morse potential well . linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters although corresponding linear schrdinger eigenvalue problem possesses unbroken @xmath0-symmetry .

i

1304.2105

we report the existence and properties of localized modes described by nonlinear schrdinger equation with complex @xmath0-symmetric rosen - morse potential well . exact analytical expressions of the localized modes are found in both one dimensional and two - dimensional geometry with self - focusing and self - defocusing kerr nonlinearity . linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters although corresponding linear schrdinger eigenvalue problem possesses unbroken @xmath0-symmetry . this result has been verified by the direct numerical simulation of the governing equation . the transverse power flow density associated with these localized modes has also been examined .

to summarize , we have investigated the existence and properties of nonlinear localized modes in a single @xmath0 waveguide cell characterized by the nonlinear schrdinger equation with complex rosen - morse potential well . the closed form expressions for the localized modes in such one- and two - dimensional self - focusing and self - defocusing kerr nonlinear media are obtained . the transverse power flow density is shown to remain positive for some parameter values which indicates that power flow is in a single direction , mainly from gain towards loss regions . however , linear stability analysis of the one - dimensional solitons reveals that these solitons are unstable over the whole range of the potential parameter in spite of the fact that corresponding linear schrdinger eigenvalue problem possesses unbroken @xmath0-symmetry . the main reason behind such instability is that unlike the real part , the imaginary part of the complex rosen - morse potential well does not vanish asymptotically . therefore any small fluctuation in the field intensity is amplified ( or absorbed ) which leads to the instability . the results presented here definitely encourage one to search for the stable localized modes ( if any ) of the nonlinear schrdinger equation with the @xmath0-symmetric rosen - morse potential well in the presence of higher - order / competing or other nonlinearities .

we report the recent results from the computer simulations of a fermion - gauge - scalar model with dynamical chiral - symmetry breaking and chiral transition induced by the scalar field . this model might be considered to be a possible alternative to the higgs mechanism of mass generation .

i

hep-lat9411072

we report the recent results from the computer simulations of a fermion - gauge - scalar model with dynamical chiral - symmetry breaking and chiral transition induced by the scalar field . this model might be considered to be a possible alternative to the higgs mechanism of mass generation . a new scheme is developed for detecting the chiral transition . our results show with higher precision than the earlier works that the chiral transition line joins the higgs phase transition line , separating the higgs and nambu ( chiral - symmetry breaking ) phases . the end point of the higgs transition with divergent correlation lengths is therefore suitable for an investigation of the continuum limit .

some strongly coupled lattice fermion - gauge models with a charged scalar field , which break chiral symmetry dynamically , might be considered to be a possible alternative to the higgs mechanism for mass generation , as discussed in @xcite . let us concentrate on a prototype with @xmath0 gauge group , a scalar of fixed modulus and one staggered fermion ( corresponding to 4 flavors ) , where both the scalar and fermion have charge one . the action has been described in @xcite with three bare parameters @xmath1 . the dynamical mass generation is meaningful only in the chiral limit @xmath2 . we consider here the phase transition line * net * between two phases @xcite : \(1 ) dynamical mass generation ( nambu ) phase , below the * net * line , where chiral symmetry is spontaneously broken ( @xmath3 ) due to the strong gauge fluctuations so that the fermion mass @xmath4 is dynamically generated ; \(2 ) higgs phase , above the * nets * line , where the higgs mechanism is operative , but @xmath5 . the scalar field induces a second order chiral phase transition * ne * line which opens the possibility for approaching the continuum . whether such a model can replace the higgs mechanism depends crucially on the existence and renormalizability of the continuum limit . to search for such a continuum theory and grasp its nature , we need to make precise determination of the second order phase transition point with divergent correlation lengths . for such a purpose , we have done extensive simulations using hybrid monte carlo ( hmc ) algorithm and developed some new methods for locating the * ne * line .

we report the results from an _ asca _ observation of the high - luminosity , radio - loud quasar pks 0637@xmath0752 ( redshift 0.654 ) , covering the 0.815 kev band in the quasar - frame . we find the source to have a luminosity @xmath1 in the 210 kev band , a factor of @xmath2 lower than during a previous _ ginga _ observation . the continuum appears to be well modeled by a simple power - law with @xmath3 , with no evidence for absorption by material intrinsic to the quasar , or fe - k emission ( with an equivalent width @xmath4 ev at 90% confidence ) . however we do find evidence for a narrow emission line at an energy @xmath5 kev and equivalent width @xmath6 ev ( both in the quasar frame ) . line emission at these energies has not been observed in any other active galaxy or quasar to date .

c

astro-ph9807349

we report the results from an _ asca _ observation of the high - luminosity , radio - loud quasar pks 0637@xmath0752 ( redshift 0.654 ) , covering the 0.815 kev band in the quasar - frame . we find the source to have a luminosity @xmath1 in the 210 kev band , a factor of @xmath2 lower than during a previous _ ginga _ observation . the continuum appears to be well modeled by a simple power - law with @xmath3 , with no evidence for absorption by material intrinsic to the quasar , or fe - k emission ( with an equivalent width @xmath4 ev at 90% confidence ) . however we do find evidence for a narrow emission line at an energy @xmath5 kev and equivalent width @xmath6 ev ( both in the quasar frame ) . line emission at these energies has not been observed in any other active galaxy or quasar to date . we reject the possibility that this line is the result of instrumental artifacts , and briefly explore possible identifications . _ accepted july 1998 for publication in astrophysical journal letters _

we have reported the results of a new x - ray observation of pks 0637@xmath0752 with _ asca_. although the luminosity had diminished by a factor of @xmath2 compared to previous _ ginga _ observations ( six and eight years earlier ) , the _ asca _ data are the most sensitive to date in the 0.510 kev band ( @xmath60 kev in the quasar frame ) . however , the _ asca _ luminosity is consistent with an _ exosat _ observation made twelve years earlier . it is possible that the larger field of view of _ ginga _ was confused with another source which may have contributed to the higher luminosity so the apparent variability should be treated with caution . we find the continuum to be well modeled by a simple power - law with @xmath3 and galactic absorption . we find no evidence for fe - k emission although the data allow a line with moderate equivalent width ( 90% confidence quasar - frame upper limits in the range 4182 ev , corresponding to line intrinsic widths in the range 00.5 kev respectively ) . our most important result from the _ asca _ observation is the discovery of a narrow emission line at an energy @xmath5 kev . we have presented strong evidence that this is not an instrumental artefact and is likely to be associated with pks 0637@xmath0752 itself . with conservative assumptions for systematic errors , we find the line center to lie in the range 1.481.72 kev and to have an ew of @xmath6 ev in the quasar frame . line emission in this energy band has not been observed in any other agn to date , and its identification is not at all obvious . the allowed range of energies encompasses transitions from mgxi xii , fexxii xxvi and nixix xxviii ( assuming no bulk motion ) . highly ionized gas is commonly seen in absorption in low luminosity seyfert 1 galaxies ( e.g. reynolds 1997 ; george _ et al . _ 1998 ) and in emission in some seyfert 1 ( below ) and many seyfert 2 galaxies ( e.g. turner _ et al . . however theoretical models of both optically - thick and optically - thin gas predict the stronger lines elsewhere in the spectrum , particularly due to a blend of o , ne and fe lines @xmath61 kev ( e.g. see zycki _ _ 1994 ; kallman _ et al . _ 1996 ; netzer 1996 , and references therein ) . indeed the presence of emission lines at such energies was suggested in _ einstein _ sss observations ( e.g. turner _ et al . _ 1991 ) and have been detected in the _ asca _ spectra of ngc 4151 ( figure 1 in yaqoob _ 1995 ) , pg 1244 + 026 ( blend at @xmath45 kev , fiore _ 1998 ) , and ton s 180 ( blend at @xmath62 kev , turner , george , nandra 1998 ) . the detection of ovii(0.57 kev ) emission has been claimed in the case the _ asca _ data from ngc 3783 ( george , turner , netzer 1995 ) , mkn 290 ( turner _ et al . _ 1996 ) , and ic 4329a ( cappi _ et al . _ 1996 ) , although uncertainties in the calibration @xmath63 kev make their reality less compelling . however , none of these lines are consistent with the observational result for pks 0637@xmath0752 without an assumption of bulk in / outflow . the emission feature closest in energy to that reported in pks 0637@xmath0752 and which has also been observed in _ asca _ data from both seyfert 2 galaxies ( turner _ et al . _ 1997 ) and starburst galaxies ( e.g. ptak _ et al . _ 1997 ) is the sixiii(1.841.86 kev ) blend . however , the identification of the line observed in pks 0637@xmath0752 with such emission not only requires an anomalous si abundance relative to o , ne , s and fe , but redshifting of the new emission - line energy by @xmath640.30 ( i.e. the line - emitting matter must be _ in_falling at velocities @xmath65 ) with respect to the optical emission line gas which has @xmath9 ( hunstead _ et al . future observations of this intriguing x - ray emission - line feature at high spectral resolution with _ axaf _ , _ xmm _ and _ astro - e _ , will clearly help to shed light on its identity and origin . the authors thank the _ asca _ mission operations team at isas , japan , and all the instrument teams for their dedication and hard work in making these _ asca _ observations possible . this research made use of the heasarc archives at the laboratory for high energy astrophysics , nasa / gsfc . lccc @xmath41 & @xmath66 & @xmath67 & @xmath67 @xmath11 ( @xmath68 ) & @xmath69 & @xmath70 & @xmath71 @xmath47 ( kev ) & & @xmath72 & 0.01 ( fixed ) @xmath46 ( kev ) & & @xmath73 & @xmath74 @xmath48 & & @xmath75 & @xmath76 ew ( ev ) & & @xmath77 & @xmath78 @xmath40 & 568.5 & 553.8 & 553.9 degrees of freedom & 530 & 527 & 528 cappi , m. , mihara , t. , matsuoka , m. , hayashida , k. , weaver , k.a . , & otani , c. 1996 , , 458 , 149 comastri , a. , setti , g. , zamorani , g. , elvis , m. , giommi , p. , wilkes , b. , & mcdowell , j. 1992 , , 384 , 62 dickey , j.m . , & lockman , f.j . 1990 , ann . rev dotani , t. , _ et al . _ 1997 , _ ascanews _ , 5 , 14 eracleous , m. , & halpern , j. 1998 , , in press elvis , m. , & fabbiano , g. 1984 , , 280 , 91 fiore , f. , _ et al . _ 1998 , , 298 , 103 fukazawa , y. , ishida , m. , & ebisawa , k. 1997 , _ ascanews _ , 5 , 3 george , i.m . , turner , t.j . , & netzer , h. 1995 , , 438 , l67 george , i.m . , turner , t.j . , netzer , h. , nandra , k. , mushotzky , r.f . , & yaqoob , t. 1998 , , 114 , 73 grandi , p. , _ et al . _ 1997 , , 325 , l17 hunstead , r.w . , murdoch , h.s . , & shobbrook , r.r . 1978 , , 185 , 149 kallamn , t.r . , liedahl , d. , osterheld , a. , goldstein , w. , & kahn , s. 1996 , , 465 , 994 lawson , a.j . , turner , m.j.l . , williams , o.r . , stewart , g.c . , & saxton , r.d . 1992 , , 259 , 743 lawson , a.j . , & turner , m.j.l . 1997 , , 288 , 920 nandra , k. , mushotzky , r.f . , george , i.m . , turner , t.j . , & yaqoob , t. 1997a , , 488 , 91 nandra , k. , george , i.m . , mushotzky , r.f . , turner , t.j . , & yaqoob , t. 1997b , , 476 , 70 nandra , k. , george , i.m . , mushotzky , r.f . , turner , t.j . , & yaqoob , t. 1998 , in preparation netzer , h. 1996 , , 473 , 781 orr , a. , molendi , s. , fiore , f. , grandi , p. , parmar , a.n . , & owens , a. 1997 , , 324 , l77 ptak , a. , serlemitsos , p. , yaqoob , t. , mushotzky , r.f . , & tsuru , t. 1997 , , 113 , 1286 reeves , j.n . , turner , m.j.l . , ohashi , t. , & kii , t. 1997 , , 292 , 468 reynolds , c.s . 1997 , , 286 , 513 saxton , r.d . , turner , m.j.l . , williams , o.r . , stewart , g.c . , ohashi , t. , & kii , t. 1993 , , 262 , 635 tanaka , y , inoue , h. , & holt , s.s . 1994 , , 46 , l37 turner , t.j . , george , i.m . , nandra , k. 1991 , , in press turner , t.j . , weaver , k.a . , mushotzky , r.f . , holt , s.s . , & madejski , g.m . 1991 , , 381 , 85 turner , t.j . , george , i.m . , kallman , t. , yaqoob , t. , & zycki , p.t . 1996 , , 472 , 571 turner , t.j . , george , i.m . , nandra , k. , & mushotzky , r.f . 1997 , , 113 , 23 wilkes , b.j . , & elvis , m. 1987 , , 323 , 243 williams , o.r . , _ _ 1992 , , 259 , 743 yaqoob , t. , edelson , r. , weaver , k. a. , warwick , r. s. , mushotzky , r. f. , serlemitsos , p. j. , & holt , s. s. 1995 , apj , 453 , l81 yaqoob , t. 1998 , , 500 , 893 zamorani , g. , _ et al . _ 1981 , , 245 , 357 zamorani , g. , giommi , p. , maccacaro , t. , & tanabaum , h. 1984 , , 278 , 28 zycki , p.t . , krolik , j.h . , zdziarski , a.a . , & kallman , t.r . 1994 , , 437 , 597

a proportion of these sources show relatively low [ oiii]@xmath7/h@xmath0 line ratios , which are similar to those of narrow line seyfert 1 galaxies suggesting small mass black holes which are rapidly growing . in the subsample of our survey with both [ oiii]@xmath7 and hard x - ray coverage , at least @xmath8% show an excess of [ oiii]@xmath7 emission , by a factor of 510@xmath9 , relative to the hard x - ray luminosity compared to the correlation between these two properties seen in seyferts and qsos locally . from our spectral diagnostics , we propose that the strong [ oiii]@xmath7 emission in these galaxies arises from shocks in dense gaseous regions in this vigorously star - forming population .

r

astro-ph0607580

we report the results of a systematic near - infrared spectroscopic survey using the subaru , vlt and keck telescopes of a sample of high redshift ultra - luminous infrared galaxies ( ulirgs ) mainly composed of submillimeter - selected galaxies . our observations span the restframe optical range containing nebular emission lines such as h@xmath0 , [ oiii]@xmath1 , and [ oii]@xmath2 , which are essential for making robust diagnostics of the physical properties of these ulirgs . using the h@xmath3/h@xmath0 emission line ratios , we derive internal extinction estimates for these galaxies similar to those of local ulirgs : @xmath4 . correcting the h@xmath3 estimates of the star formation rate for dust extinction using the balmer decrement , results in rates which are consistent with those estimated from the far - infrared luminosity . the majority ( @xmath5% ) of our sample show spectral features characteristic of agn ( although we note this partially reflects an observational bias in our sample ) , with @xmath6% exhibiting broad balmer emission lines . a proportion of these sources show relatively low [ oiii]@xmath7/h@xmath0 line ratios , which are similar to those of narrow line seyfert 1 galaxies suggesting small mass black holes which are rapidly growing . in the subsample of our survey with both [ oiii]@xmath7 and hard x - ray coverage , at least @xmath8% show an excess of [ oiii]@xmath7 emission , by a factor of 510@xmath9 , relative to the hard x - ray luminosity compared to the correlation between these two properties seen in seyferts and qsos locally . from our spectral diagnostics , we propose that the strong [ oiii]@xmath7 emission in these galaxies arises from shocks in dense gaseous regions in this vigorously star - forming population . we caution that due to sensitivity and resolution limits , our sample is biased to strong line emitters and hence our results do not yet provide a complete view of the physical properties of the whole high - redshift ulirg population .

we show all of our spectra in figure 1 . we identified emission lines in 20 spectra out of 22 targets which were observed . most of the smgs show weak h@xmath0 emission , but many show strong ( and sometimes broad and distorted ) profiles in [ oiii]@xmath1 . some of our spectra show additional emission lines of [ neiii ] , [ nev]and [ oi]@xmath33 , which are common in agn . five of the smgs from our sample ( smmj09431 + 4700 ( h6 ) , smmj123549.44 + 621536.8 , smmj123716.01 + 620323.3 , smmj163639.01 + 405635.9 , and smmj163650.43 + 405734.5 ) display spatially extended structures ( @xmath341.0 ) in either [ oiii]@xmath7 and/or h@xmath3 emission line ( figure 2 , see smail et al . 2003 ; swinbank et al . 2005 for evidence of the spatial extension in smmj163650.43 + 405734.5 ) . several of our observations are particularly noteworthy and we discuss them here . this galaxy is identified as a submillimeter source associated with a spiral galaxy at @xmath36 , which shows features typical of a seyfert 1 ( smail et al . 1997 , 2002 ; soucail et al . the strong and featureless continuum , together with the spatially compact emission line flux indicates agn activity ; an interpretation which is further supported by the detection of this source in hard x - rays by bautz et al . ( 2000 ) . our spectrum shows at least two peaks in the h@xmath3 emission line with fwhm@xmath37400kmsec@xmath17 , consistent with these lines arising from independent components within the system . if we force fit a single gaussian profile to the h@xmath3 emission , we determine fwhm@xmath38kmsec@xmath17 , which if it arises from an agn is narrower than typical seyfert 1 galaxies , although broader than seyfert 2 galaxies ( @xmath39kmsec@xmath17 ) . this source is also detected by co observation by greve et al . ( 2005 ) with a double peaked profile with a fwhm of @xmath40kmsec@xmath17and a separation between the two peaks of @xmath41kmsec@xmath17 , consistent within the errors with our measurements from h@xmath3 . we therefore choose to interpret the double - peaked h@xmath3 line as evidence for a merger or interaction in this system , with any agn - produced broad component undetected in our spectrum . this source was discovered by cowie , barger & kneib ( 2002 ) , and has been identified with two distinct @xmath11jy radio counterparts : h6 and h7 ( ledlow et al . these are lensed sources , lying behind a massive cluster abell851 at @xmath42 although the amplification is modest : @xmath43 . the redshift for h6 was measured by ledlow et al . ( 2002 ) as @xmath44 from ly@xmath3 , h7 was not observed . the restframe ultraviolet properties of h6 suggest it hosts an agn with spectral features similar to a narrow - line seyfert 1 ( ledlow et al . we placed the nirspec slit across both radio components and detected [ oiii]@xmath7emission from both sources at redshifts of @xmath45 and @xmath46 for h6 and h7 , respectively . we also detected narrow ( fwhm@xmath47 kmsec@xmath17 ) h@xmath0 emission from h6 . the [ oiii]@xmath7 emission from h6 is spatially extended(@xmath48 or 14.5kpc ; figure 2 ) , but has no significant velocity gradient across @xmath49kpc in projection . no hard x - ray emission was detected with the upper limits on f@xmath50 as @xmath5110@xmath52 erg sec@xmath17 @xmath53 ( ledlow et al . co line emission is also detected by neri et al . ( 2003 ) and tacconi et al . ( 2006 ) based on our restframe optical redshift , originating from h7 at @xmath54 . millimeter continuum emission has been seen from h6 , but assuming the gas reservoir is at the redshift we find from [ oiii]@xmath7 , the gas mass of the agn - dominated component , h6 , is a factor of a few lower than that of h7 . this source has apparent double - peaked , narrow ( @xmath55kmsec@xmath17 ) emission lines in [ oii]@xmath2 and [ oiii]@xmath1 , with the two components spatially offset by @xmath56 . the one dimensional spectra also shows signs of broad h@xmath0emission at @xmath57 with a fwhm of @xmath58 kmsec@xmath17 . both the [ oiii]@xmath7 and the [ oii]@xmath2 emissions are spatially extended with faint wings on scales of approximately 1@xmath25 ( @xmath49kpc ) , see figure 2 . there may also be a very weak , broad multiplet of feii@xmath59 ( figure 1 ) , potentially indicating the presence of the narrow line seyfert 1 ( nls1 ) type agn component ( osterbrock & pogge 1985 ; goodrich 1989 ) . this is consistent with the results of alexander et al . ( 2005b ) , which indicated the presence of a heavily obscured agn with n@xmath60@xmath53 based on their x - ray spectral analysis . the spatial extension in the bright core of the [ oiii]@xmath7 likely indicates merging components or rotation along the slit , while the extended wings may reflect `` superwind '' activity . this source is very bright in the optical ( @xmath61 ) with a redshift of @xmath62 and it was classified as a qso by chapman et al . ( 2005 ) based on the broad rest uv emission lines and comparable luminosities in rest optical and far - infrared wavelength , which exceed 10@xmath63 erg sec@xmath17 . the source has also been detected in hard x - rays by alexander et al . ( 2005b ) . our spectrum shows several hydrogen balmer lines such as h@xmath0 , h@xmath64 and h@xmath65 with broad fwhm@xmath66 ( @xmath672700kmsec@xmath17 ) and the [ oiii]@xmath1 doublet with fwhm@xmath66 of @xmath67kmsec@xmath17 . we also detected the [ neiii ] and several feii lines at 34@xmath68 significance . the restframe optical spectrum is dominated by continuum emission without stellar absorption features , suggesting a large contribution from the agn component to the total rest - frame optical flux . the [ oiii]@xmath7 emission lines are wide fwhm@xmath69kmsec@xmath17 and spatially extended ( @xmath70 ; 12kpc ) indicating dynamically active gas motion ( figure 2 ) . the estimated hydrogen column density from the x - ray spectral analysis is relatively low ( n@xmath71@xmath53 ) , which implies the agn does not suffer from large extinction . it should be noted that the redshift based on the restframe - uv emission lines is @xmath72 , which is blueshifted by @xmath73kmsec@xmath17 from the redshift indicated by the restframe optical nebular emission line . this velocity offset may arise due to broad ly@xmath3 emission which may be affected by dust extinction and resonance scattering . this source is another example of a nls1 type agn . it lies at @xmath74 and our spectrum displays broad h@xmath0 emission , with fwhm@xmath75kmsec@xmath17 and a low [ oiii]@xmath7/h@xmath0 ratio ( @xmath76 ) . this source has ly@xmath3 [ civ ] and heii emission lines in the rest uv spectrum and was classified as a qso by chapman et al . the rest - frame optical emission is dominated by very strong continuum emission without stellar absorption lines , supporting the presence of a luminous agn component . unfortunately , there is no coverage of h@xmath3 emission for this object and so we could not constrain the internal extinction . the [ nev ] line ( which is a very clean indicator of agn activity ; osterbrock 1989 ) is detected . furthermore , this source was detected by the x - ray imaging by mushotzky et al . ( 2000 ) , confirming the presence of a luminous agn in the source . this source is a good example of a heavily extincted starburst in an smg and was recently discussed by swinbank et al . this @xmath77 galaxy has weak h@xmath0 emission line with h@xmath3/h@xmath0@xmath78 . the h@xmath3 and [ oiii]@xmath7 emission lines are spatially extended ( @xmath79 or 10 kpc)(figure 2 ) . there is only an upper limit on its x - ray emission , f@xmath80ergsec@xmath17@xmath53 from manners et al.(2003 ) , which does not strongly constrain the presence of a luminous agn given the possibility of substantial absorption ( e.g. alexander et al . the possible detection of [ oi]@xmath33 emission line may hint at the presence of an agn , although the line ratios of [ oi]@xmath33/h@xmath3@xmath81 and [ oiii]@xmath7/h@xmath0@xmath82 can be explained by a relatively highly ionized starburst nebulae ( osterbrock et al . 1989 ) . this heavily obscured agn at @xmath83 ) was found in the mambo survey of greve et al . ( 2004 ) ( and is also called n21200.18 ) and was detected in x - ray imaging with _ chandra _ ( manners et al . it has broad , fwhm@xmath842500kmsec@xmath17 , emission lines of ly@xmath3 , [ civ ] and h@xmath3 in the rest - frame uv and optical wavelengths , with a high [ oi]@xmath33/h@xmath3 ratio ( @xmath85 ) ( willott et al . 2003 ; swinbank et al . 2006 ) which is typical of agn ( osterbrock 1989 ) . our data also show asymmetric h@xmath0 and [ oiii]@xmath86 emission line profiles , which exhibit `` blue wings '' in their profiles . such profiles have been interpreted as evidence for wind activity from the agn , although contribution from other components is possible ( swinbank et al . 2006 ) . our isaac spectrum shows strong , narrow h@xmath3 h@xmath0 [ oiii]@xmath1 and [ nii ] emission lines at a redshift of @xmath87 ( fwhm@xmath88 of h@xmath0 is @xmath89kmsec@xmath17 ) . to investigate the restframe optical properties , we retrieved an archival @xmath90-band image taken with subaru telescope s prime focus camera ( suprime - cam ) using smoka . the image shows an elongated structure , @xmath91 , towards the north - west and the spectrum was taken with the slit aligned along the major axis of this source . we identify two separate h@xmath3 emission lines with a velocity offset of @xmath92kmsec@xmath17and a spatial offset @xmath93@xmath94 ( @xmath95kpc ) . these suggest the system is a merger . the h@xmath3 and h@xmath0 emission lines do not show asymmetric profiles or detectable broad line components . since many of our individual spectra have modest signal - to - noise , we have also constructed several composite spectra to investigate the general properties of subsets of the smg population . we create the composite spectra by deredshifting each spectrum based on redshifts measured from the [ oiii]@xmath7 lines , subtracting continuum emission using a first order spline fit and averaging all of the spectra with 3-@xmath68 clipping after normalizing by [ oiii]@xmath7flux . we smoothed the higher resolution spectra taken at keck and vlt to match the low resolution subaru spectra before stacking . either stacking the spectra with weights based on their individual signal - to - noise ratio or an unweighted stack does not alter any of the conclusions below . we derive a composite spectrum for those sources which show qso signatures ( `` qso '' ; i.e. , classified as qso ) and for those galaxies that individually show signs of an agn in their optical spectra ( `` opt - agn '' ; i.e. , those classified as agn in the column of `` class '' under `` opt '' category in table 2 ) . the former is made from only three individual spectra , while the latter comes from nine spectra . the resulting composite spectra are shown in figure 3 . we do not make a composite of starburst ( `` sb '' ) sources since there are only two sources in our sample classified as `` sb '' or intermediate ( `` int '' ) from their restframe optical spectra . the details of the classification will be discussed in 4.1 . the emission lines of h@xmath0 and [ oiii]@xmath1 lines are clearly seen in both the composite spectra . in addition in the `` qso '' spectrum , many strong lines are visible , including [ neiii]@xmath96 and several feii lines at @xmath97 , 5167 and 52005360 , although the [ oii]@xmath2 line is only marginally detected . by fitting a gaussian to the h@xmath0 and [ oiii]@xmath1 emission lines , we measure the fwhm@xmath88 of h@xmath0as @xmath98kmsec@xmath17 after correction for the instrumental resolution . this is @xmath99kmsec@xmath17 lower than the average fwhm of qsos at @xmath1002.1 ( jarvis & mclure 2006 ) . the [ oiii]@xmath7/h@xmath0 ratio is @xmath101 . all these spectral features are typical of type 1 agns studied locally . on the other hand in the composite `` opt - agn '' spectrum , a gaussian profile fit to the h@xmath0 emission line yields fwhm@xmath88 of @xmath102kmsec@xmath17 ( it should be noted that the h@xmath0 line fit is not improved by including a narrow line component due to the low spectral resolution of our spectra ) and [ oiii]@xmath7/h@xmath0ratio of @xmath103 , in addition the [ oii]@xmath2 line is well - detected . the h@xmath0 line , which is broader than typical type 2 agns , and relatively low [ oiii]@xmath7/h@xmath0 line ratio , is similar to that of local nls1 ( although by definition these should have [ oiii]@xmath7/h@xmath0/@xmath1043.0 ) . the feii emission lines , which are one of the characteristic features seen in local nls1 s , are marginally detected with @xmath105 features seen around 5200 in the spectrum , and we can see some marginal detections in individual spectra ( smmj123549.44 + 621536.8 , smmj123635.59 + 621424.1 , smmj163650.43 + 405734.5 , and smmj163706.51 + 405313.8 ) , all of which have broad h@xmath0 emission of fwhm@xmath106kmsec@xmath17(figure 1 ) . the resultant spectrum is consistent with a scenario where the restframe optical spectra classified as `` agn '' in the uv in reality comprise two types : one has relatively broad , @xmath107kmsec@xmath17 , fwhm for the h@xmath0 lines and the other has narrow h@xmath0 lines with a relatively high [ oiii]@xmath7/h@xmath0 ratio , typical of type 2 agns . there are clearly differences in the extinction of the circumnuclear region of these two types of objects implied by the difference in luminosity and spectroscopic properties of the restframe - uv emission , although there is no systematic difference in the h@xmath3/h@xmath0 ratio we measure for them .

, we derive internal extinction estimates for these galaxies similar to those of local ulirgs : @xmath4 . correcting the h@xmath3 estimates of the star formation rate for dust extinction using the balmer decrement , results in rates which are consistent with those estimated from the far - infrared luminosity .

c

astro-ph0607580

we report the results of a systematic near - infrared spectroscopic survey using the subaru , vlt and keck telescopes of a sample of high redshift ultra - luminous infrared galaxies ( ulirgs ) mainly composed of submillimeter - selected galaxies . our observations span the restframe optical range containing nebular emission lines such as h@xmath0 , [ oiii]@xmath1 , and [ oii]@xmath2 , which are essential for making robust diagnostics of the physical properties of these ulirgs . using the h@xmath3/h@xmath0 emission line ratios , we derive internal extinction estimates for these galaxies similar to those of local ulirgs : @xmath4 . correcting the h@xmath3 estimates of the star formation rate for dust extinction using the balmer decrement , results in rates which are consistent with those estimated from the far - infrared luminosity . the majority ( @xmath5% ) of our sample show spectral features characteristic of agn ( although we note this partially reflects an observational bias in our sample ) , with @xmath6% exhibiting broad balmer emission lines . a proportion of these sources show relatively low [ oiii]@xmath7/h@xmath0 line ratios , which are similar to those of narrow line seyfert 1 galaxies suggesting small mass black holes which are rapidly growing . in the subsample of our survey with both [ oiii]@xmath7 and hard x - ray coverage , at least @xmath8% show an excess of [ oiii]@xmath7 emission , by a factor of 510@xmath9 , relative to the hard x - ray luminosity compared to the correlation between these two properties seen in seyferts and qsos locally . from our spectral diagnostics , we propose that the strong [ oiii]@xmath7 emission in these galaxies arises from shocks in dense gaseous regions in this vigorously star - forming population . we caution that due to sensitivity and resolution limits , our sample is biased to strong line emitters and hence our results do not yet provide a complete view of the physical properties of the whole high - redshift ulirg population .

using near - infrared spectroscopy we have observed the redshifted h@xmath0 the [ oiii]@xmath1 and [ oii]@xmath2 emission lines in a sample of 22 ultra - luminous infrared galaxies at high redshifts . twenty of the sources in our sample are submillimeter galaxies at @xmath1633.5 . combining our observations with previous studies of the h@xmath3 and the [ nii ] emission from these galaxies and also with observations of their hard x - ray and far - infrared emission , we have placed constraints on the physical properties of this population . we conclude the following : 1 . a majority of our sample ( 14/22 ) have spectra which are classified as `` agn '' or `` qso '' based on several restframe optical spectroscopic diagnostics . specifically , for those sources with detections of the four emission lines necessary to construct a bpt diagram , 8/9 are classified as `` agn '' . it should be noted that there is no confirmed pure starburst galaxy in our sample , although several sources show intermediate spectral properties . this is likely to be caused by our sample selection , which is biased towards galaxies with bright near - infrared magnitudes and also to those exhibiting strong line emission . thus we caution that our results should not be taken as representative of the whole smg population . 2 . using the h@xmath3/h@xmath0 flux ratio we are able to estimate the internal extinction in our smgs . we measure a median extinction of @xmath164 , which is similar to the extinction measured in local ulirgs . this value is also consistent with the estimates from the sed fitting in the restframe uv / optical which are derived under the assumption of a dominant dust - reddened young starburst ( smail et al . we compare the sfrs derived from the dust - extinction - corrected h@xmath3 luminosities with those derived from the far - infrared luminosities , and find reasonable consistency between these for most of the smgs in our sample . the fact that the corrected h@xmath3-derived sfrs correspond closely to those estimated from the far - infrared suggests that star - formation is the major contributor to the far - infrared luminosities in smgs . at least 11/19 of the smgs in our sample show a clear excess in the ratio of their [ oiii]@xmath7 to x - ray luminosities relative to values for local agns . the five sources with the highest [ oiii]@xmath7/h@xmath0 ratios ( @xmath137 ) , which are classified as `` agn '' from our spectral diagnostics , show this [ oiii]@xmath7 excess . one possible explanation for the [ oiii]@xmath7 excess is that it is produced by `` compton - thick '' agns . however , this is inconsistent with the column density measurements ( n@xmath165 ) from fitting of the x - ray spectra for the sources in cdfn and we argue that this is unlikely in most smgs . instead , we suggest that the most plausible cause of the [ oiii]@xmath7 excess is shock - induced emission arising from vigorous star formation ( `` super - wind '' activity ) . this scenario is supported in several galaxies by spatially extended and/or distorted / multiple [ oiii]@xmath7 emission line profiles . furthermore , using limits on the electron temperatures from [ oiii ] and [ nii ] emission line ratios , we can explain the excess [ oiii]@xmath7 emission as arising from shocks in dense regions within these systems . the balmer line widths in 9/22 sample galaxies exhibit broad emission components with relatively small fwhms ( @xmath1663700kmsec@xmath17 ) . three of them are classified as `` qso '' , but have smaller h@xmath0 fwhm ( 21002600kmsec@xmath17 ) than are typical for qsos . they also have lower [ oiii]@xmath7/h@xmath0 ratios and relatively strong feii emission , both of which are characteristics of local narrow line seyfert 1s . among the other six sources , only one shows a low [ oiii]@xmath7/h@xmath0 ratio , and four show high [ oiii]@xmath7/h@xmath0 ratios ( larger than seen in nls1 s ) . however , the high [ oiii]@xmath7/h@xmath0 ratios may arise from [ oiii]@xmath7 excesses due to shock excitation and hence removing this contribution would yield lower ratios more consistent with nls1 classification . several of these sources also have tentative evidence for feii emission , again characteristic of nls1s . thus , once account is taken of the potential contribution from shocks to the excess [ oiii]@xmath7 emission , there appears to be close similarities between smgs and nls1s . the spectral classification of smgs as nls1s may then indicate ( as has been claimed for local nls1s ) that smgs have small mass black holes which are rapidly growing at high accretion rates ( alexander et al . 2005ab ; borys et al . deeper spectroscopic observations are essential to search for any obscured broad balmer lines which might indicate larger smbh masses and confirm the presence of feii lines which are common in the nls1s . summarising our results : we conclude that our sample of smgs contains a population of vigorously star - forming galaxies with high sfrs and strong extinction . the activity in these systems is driving shocks through the dense gas reservoirs they contain and some of this material is being expelled from the galaxies . in addition , many of our sources show evidence for low - mass , but rapidly growing , super - massive black holes . these results confirm the critical place of the submillimeter - bright phase in defining the properties of massive galaxies forming at high redshifts . we are grateful to michael balogh , bob nichol , chris miller and dave alexander for their providing invaluable information and discussions . tt and ks are also thank to all staffs of subaru telescope , especially to dr . kentaro aoki and dr . takuya fujiyoshi for the supports on our subaru / ohs observation . we also thank to the anonymous referee for the various comments and suggestions to improve our manuscript . irs acknowledges support from the royal society . jeg acknowledges support from a pparc postgraduate studentship . ams acknowledges a pparc fellowship . alexander , d.m . 2003 , 126 , 539 alexander , d. , smail , i. , bauer , f. , chapman , s.c . , blain , a.w . , ivison , r. 2005a , 434 , 738 . alexander , d. , smail , i. , bauer , f. , chapman , s.c . , blain , a.w . , ivison , r. 2005b , 632 , 736 alonso - 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hawthorn , j. 2005 , 43 , 769 wandel , a. 2002 , 565 , 762 waskett , t.j.,eales , s.a . , gear , w.k . , mccracken , h.j . , brodwin , m. , nandra , k. , laird , e.s . , & lilly , s. 2004 , 350 , 785 willott , c. et al . 2003 , 339 , 397 yan , l. , chary , r. , armus , l. , teplitz , h. , helou , g. , frayer , d. , fadda , d. , surace , j. & choi , p. 2005 , 628 , 604 and 2@xmath167 significance respectively . the upper axis gives the restframe wavelength scale at the source redshift . the shaded regions are areas effected by strong sky emission or absorption . [ fig1 ] ] lrrrrrl & & & & & & + + & & & & & & + smmj123549.44 + 621536.8 & 7200 & apr 6 2004 & j&h & 6.8@xmath168 & 12.0@xmath1691.4 & + smmj123606.85 + 621021.4 & 7200 & feb 15 2005 & j&h & 8.7@xmath170 & 7.4@xmath1691.4 & + smmj123622.65 + 621629.7 & 7200 & apr 7 2004 & j&h & 9.0@xmath171 & 11.0@xmath1691.4 & + smmj123635.59 + 621424.1 & 7200 & feb 16 2005 & j&h & 7.5@xmath172 & 25.0@xmath1691.4 & + smmj123716.01 + 620323.3 & 4000 & feb 16 2005 & j&h & 6.3@xmath173 & 74.0@xmath1691.4 & + smmj123721.87 + 621035.3 & 7200 & jun 24 2004 & j&h & 0.43@xmath174 & 21.0@xmath1691.4 & + smmj131215.27 + 423900.9 & 600 & feb 16 2005 & j&h & 13.9@xmath175 & 190.0@xmath16923.0 & + smmj131222.35 + 423814.1 & 2000 & jun 25 2004 & j&h & 12.7@xmath176 & 120.0@xmath16920.0 & + smmj163639.01 + 405635.9 & 7200 & jun 24 2004 & j&h & 5.5@xmath177 & @xmath10422.0 & + smmj163650.43 + 405734.5 & 7000 & may 18 2003 & j&h & 50.5@xmath178 & @xmath10422.0 & smail et al . ( 2003 ) + mmj163655 + 4059 & 3600 & apr 7 2004 & j&h & 10.9@xmath179 & 150.0@xmath16921.0 & + smmj163706.51 + 405313.8 & 7200 & apr 6 2004 & j&h & 7.2@xmath180 & @xmath10422.0 & + smmj221733.02 + 000906.0 & 3000 & jun 24 2004 & j&h & 1.9@xmath181 & @xmath10428.0 & + smmj221733.79 + 001402.1 & 7200 & jun 25 2004 & j&h & 4.9@xmath182 & @xmath10428.0 & + & & & & & & + + & & & & & & + smmj02399 - 0134 & 4500 & nov 24,25 2004 & j & 6.5@xmath183 & 32.0@xmath1695.0 & + & 2400 & nov 25 2004 & z & & & + smmj030227.73 + 000653.5 & 6000 & nov 23 2004 & j & 5.8@xmath184 & 60.0@xmath16910.0 & + rgj030257.94 + 001016.3 & 4500 & nov 23 2004 & h & 7.7@xmath185 & 60.0@xmath16910.0 & + smmj105702.50 - 033602.6 & 4500 & nov 23 2004 & h & 5.0@xmath173 & @xmath10410.0 & + smmj221737.39 + 001025.1 & 9000 & nov 23,24 2004 & k & 21.0@xmath186 & @xmath10428.0 & + & 6000 & nov 25 2004 & h & & & + & & & & & & + + & & & & & & + smmj09431 + 4700(h6 ) & 2400 & apr 8 2004 & k & 15.0@xmath187 & @xmath10413.0 & + smmj09431 + 4700(h7 ) & 2400 & apr 8 2004 & k & 15.0@xmath187 & @xmath10413.0 & + smmj131201.17 + 424208.1 & 2400 & apr 8 2004 & k & 20.2@xmath188 & 52.8@xmath16940.0 & + & & & & & & + + & & & & & & + smmj04431 + 0210 & & & & 3.5@xmath172 & & frayer et al . ( 2003 ) + smmj14011 + 0252(j1 ) & & & & 6.8@xmath176 & @xmath10444.0 & motohara et al.(2005 ) + smmj163658.19 + 410523.8 & & & & 10.9@xmath179 & @xmath10422.0 & simpson et al.(2004 ) + lrrrrrrcccrl object & @xmath189 & h@xmath3 flux & h@xmath0 flux & [ o iii]@xmath190 flux & [ o iii]@xmath191 flux & [ o ii]@xmath192 flux & & rest fwhm@xmath193 & comment + & & & uv & h@xmath194 & opt & km@xmath195sec@xmath17 & + smmj02399 - 0134 & 1.061 & 75.8@xmath169 15.0 & @xmath10411.0 & @xmath10411.0 & @xmath10411.0 & & agn & agn & & 1530@xmath169500 + smmj030227.73 + 000653.5 & 1.408 & 15.2@xmath169 2.0 & 1.9@xmath169 1.1 & 10.7@xmath169 3.2 & 7.2@xmath169 2.6 & & sb & agn & agn & @xmath104100 & + rgj030258.94 + 001016.3 & 2.239 & 1.8@xmath169 0.5 & @xmath1040.3 & 9.2@xmath169 2.1 & 0.85@xmath169 0.30 & & int & agn & agn & & + smmj09431 + 4700(h6 ) & 3.350 & & 0.3@xmath169 0.2 & 1.7@xmath169 0.3 & 0.7@xmath169 0.4 & & sb & & sb ? & 350@xmath16950 & extended [ oiii]@xmath7 + smmj09431 + 4700(h7 ) & 3.347 & & @xmath1040.15 & 0.5@xmath169 0.1 & @xmath1040.15 & & & & & & + smmj105702.50 - 033602.6 & 2.423 & 0.6@xmath169 0.2 & @xmath1040.19 & @xmath1040.19 & @xmath1040.19 & & & sb & & & van dokkum et al . ( 2004 ) ; miss the slit ? + smmj123549.44 + 621536.8 & 2.195 & 15.0@xmath169 1.0 & 1.6@xmath169 1.0 & 6.4@xmath169 1.3 & 1.9@xmath169 0.8 & 2.9@xmath169 0.8 & sb & int & agn & 2150@xmath169500 & [ oiii]@xmath7 double peaks and extended + smmj123606.85 + 621021.4 & 2.505 & 2.0@xmath169 0.3 & @xmath1040.043 & @xmath1040.043 & @xmath1040.043 & @xmath1040.043 & sb & int & & & slit on companion object ? + smmj123622.65 + 621629.7 & 2.462 & 3.4@xmath169 0.6 & @xmath1040.8 & @xmath1040.8 & @xmath1040.8 & 2.1@xmath169 0.5 & sb & sb & & & + smmj123635.59 + 621424.1 & 2.005 & 11.1@xmath169 1.2 & & 2.0@xmath169 0.6 & 2.4@xmath169 0.5 & & agn & agn & agn ? & & + smmj123716.01 + 620323.3 & 2.053 & & 28.1@xmath169 3.2 & 19.5@xmath169 2.4 & 9.7@xmath169 2.2 & & qso & & agn & 2130@xmath169500 & multiple peaks and extended [ oiii]@xmath7 + smmj123721.87 + 621035.3 & 0.979 & 6.2@xmath169 1.1 & & & & & & sb & & & + smmj131201.17 + 424208.1 & 3.408 & & 0.18@xmath1690.15 & 0.79@xmath1690.19 & 0.27@xmath1690.19 & & agn & & agn ? & & + smmj131215.27 + 423900.9 & 2.555 & 11.8@xmath169 1.0 & 3.1@xmath169 2.6 & 5.6@xmath169 2.2 & 2.2@xmath169 1.6 & @xmath1040.23 & qso & & agn & 2540@xmath169500 & + smmj131222.35 + 423814.1 & 2.560 & & 12.1@xmath169 4.5 & 5.5@xmath169 2.5 & 2.6@xmath169 2.5 & 2.0@xmath169 1.5 & qso & & agn & 2580@xmath1691000 & + smmj163639.01 + 405635.9 & 1.485 & 7.3@xmath169 0.7 & 0.7@xmath169 0.5 & 2.5@xmath169 0.5 & 1.1@xmath169 0.4 & & sb & sb & int & @xmath1041400 & extended h@xmath3 + smmj163650.43 + 405734.5 & 2.380 & 14.2@xmath169 1.5 & 2.3@xmath169 0.6 & 27.0@xmath169 2.1 & 6.8@xmath169 1.3 & 14.0@xmath169 0.8 & int & agn & agn & 3720@xmath169500 & reevaluated after smail et al . ( 2003 ) + mmj163655 + 4059 & 2.605 & 18.4@xmath169 2.4 & 2.7@xmath169 1.0 & 47.1@xmath169 1.6 & 15.7@xmath169 1.6 & 3.6@xmath169 0.9 & agn & agn & agn & 2410@xmath169600 & blue wings in h@xmath0 and [ oiii]@xmath86 + smmj163706.51 + 405313.8 & 2.373 & 7.4@xmath169 1.4 & 0.6@xmath169 0.3 & 5.7@xmath169 0.6 & 1.9@xmath169 0.6 & 1.0@xmath169 0.3 & agn & agn & agn & 1590@xmath169500 & + smmj221733.02 + 000906.0 & 0.926 & 9.6@xmath169 1.2 & & & & & & sb & & & + smmj221733.79 + 001402.1 & 2.551 & 8.5@xmath169 3.5 & 1.2@xmath169 0.6 & 1.2@xmath169 0.2 & @xmath1040.5 & 0.7@xmath169 0.3 & sb & sb & agn ? & 1860@xmath169600 & + smmj221737.39 + 001025.1 & 2.610 & 20.7@xmath169 6.0 & 0.6 @xmath1690.4 & 6.0@xmath169 0.4 & 1.2@xmath169 0.4 & & sb & agn & agn & 290@xmath16950 & + & & & & & & & & & + smmj04431 + 0210 & 2.510 & 1.6@xmath169 0.1 & @xmath1040.3 & 0.4@xmath169 0.1 & & & & agn ? & agn & & frayer et al . ( 2003 ) + smmj14011 + 0252(j1 ) & 2.565 & 1.3@xmath169 0.4 & 0.3@xmath169 0.1 & @xmath1040.2 & @xmath1040.2&0.4@xmath1690.1 & sb & sb & sb & & motohara et al . ( 2005 ) + smmj163658.19 + 410523.8 & 2.448 & 1.9@xmath169 0.4 & 0.2@xmath169 0.1 & 0.4@xmath169 0.1 & 0.3@xmath169 0.1 & 0.4@xmath169 0.2 & sb & sb & agn & & simpson et al . ( 2004 ) + & & & & & & & + composite(all ) & & & 1.0 & 0.7@xmath196 & 0.4@xmath196 & 0.3@xmath197 & & & & 3100@xmath169500 & + composite(qso ) & & & 1.0 & 0.36@xmath198 & 0.19@xmath199 & @xmath1040.12 & & & & 3200@xmath1691000 & + composite(opt - agn ) & & & 1.0 & 3.2@xmath200 & 1.2@xmath201 & 1.2@xmath202 & & & & 1730@xmath169500 & +

we report the results of broadband ( 0.952.46 ) near - infrared spectroscopic observations of the cassiopeia a supernova remnant . using a clump - finding algorithm in two - dimensional dispersed images , we identify 63 ` knots ' from eight slit positions and derive their spectroscopic properties .

i

1703.03551

we report the results of broadband ( 0.952.46 ) near - infrared spectroscopic observations of the cassiopeia a supernova remnant . using a clump - finding algorithm in two - dimensional dispersed images , we identify 63 ` knots ' from eight slit positions and derive their spectroscopic properties . all of the knots emit [ ] lines together with other ionic forbidden lines of heavy elements , and some of them also emit h and he lines . we identify 46 emission line features in total from the 63 knots and measure their fluxes and radial velocities . the results of our analyses of the emission line features based on principal component analysis show that the knots can be classified into three groups : ( 1 ) he - rich , ( 2 ) s - rich , and ( 3 ) fe - rich knots . the he - rich knots have relatively small , @xmath0 , line - of - sight speeds and radiate strong he i and [ ] lines resembling closely optical quasi - stationary flocculi of circumstellar medium , while the s - rich knots show strong lines from o - burning material with large radial velocities up to @xmath1 indicating that they are supernova ejecta material known as fast - moving knots . the fe - rich knots also have large radial velocities but show no lines from o - burning material . we discuss the origin of the fe - rich knots and conclude that _ they are most likely `` pure '' fe ejecta synthesized in the innermost region during the supernova explosion . _ the comparison of [ ] images with other waveband images shows that these dense fe ejecta are mainly distributed along the southwestern shell just outside the unshocked @xmath2ti in the interior , supporting the presence of unshocked fe associated with @xmath2ti .

a massive star builds up onion - like layers of different chemical elements synthesized by hydrostatic nuclear burning processes during its lifetime . at the end of its evolution , the innermost fe core collapses into a neutron star , which triggers a core - collapse supernova ( sn ) explosion . the detailed process of the explosion is complicated and poorly understood , but a consensus from theoretical studies suggests that the explosion should be asymmetric and turbulent , especially near the core ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) . multi - dimensional numerical simulations have shown that the explosion also leads to extensive mixing and inversion among the stratified layers by hydrodynamic instabilities ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? a distinct method to explore the explosion dynamics of sne , therefore , would be to investigate the detailed chemical and kinematic properties of sn ejecta material in nearby young galactic supernova remnants ( snrs ) where the imprints of explosion remain . cassiopeia a ( hereafter cas a ) , at the age of @xmath3 years @xcite , is one of the best studied young galactic snrs . its sn explosion was classified as type iib based on the optical spectra of light echoes @xcite , which implies that the progenitor was probably a star of @xmath4@xmath5 that had lost a significant portion , but not all , of its h - rich envelope before the explosion . over the past several decades , cas a has been extensively studied in almost all wavebands from radio to gamma - rays . the complex spatial distribution of _ shocked _ sn ejecta , such as the x - ray - emitting fe - rich ejecta plumes beyond the si - rich material and o / s - rich optical knots outlying the bright ejecta shell ( e.g. , * ? ? ? * ; * ? ? ? * ) , indicates an explosion resulting in an inversion of the chemical layers . furthermore , the inhomogeneous distribution of _ unshocked _ sn ejecta radiating si and ti emission lines @xcite implies that the explosion was turbulent near the progenitor core . in the visible waveband , many bright optical knots are presented in and around cas a. they have been classified into two major groups based on their proper motions and line - of - sight velocities : ( 1 ) fast - moving knots ( fmks ) and ( 2 ) quasi - stationary flocculi ( qsfs ) . the fmks show large proper motions and high radial velocities , corresponding to expansion velocities of up to @xmath6 ( e.g. , * ? ? ? * ; * ? ? ? they have spectral features strongly enhanced in o and other heavy elements ( e.g. , s and ar ) that are mostly synthesized from the nuclear burning process in a deep stellar layer , while showing no detectable h or he emission lines ( e.g. , * ? ? ? * ; * ? ? ? based on their high expansion velocities and chemical composition , they have been regarded as dense material ejected from the disrupted layer of the progenitor after the sn explosion . the dynamical and chemical properties of the qsfs are very different from those of the fmks . the qsfs have considerably slower velocities ( @xmath7 ) , and so their typical expansion age is @xmath8 years @xcite , which is much larger than the age of the remnant . they are bright in [ ] and h@xmath9 emission , with a handful of other h and he emission lines , in optical spectra ( e.g. , * ? ? ? * ; * ? ? ? considering these properties , qsfs are believed to be dense circumstellar medium ( csm ) blown out from the progenitor prior to the sn explosion . in addition , some intermediate optical knots , that is , the so called fast - moving flocculi ( fmfs ) or nitrogen knots ( nks ) , were reported by @xcite . while their spectra , which show strong [ ] 6548 , 6583 accompanied by weak h@xmath9 without any lines of o and s , are analogous to those of qsfs @xcite , their proper motions are larger than @xmath10 , corresponding to @xmath11 @xcite . most of them have been found outside of the bright main ejecta shell . therefore , these outlying n - rich knots have been interpreted as being fragments of the progenitor s photosphere expelled by the sn blast wave at the time of explosion . the dynamical and chemical properties of these different types of optical knots have provided important clues to unveiling the snr s origin and evolution . for example , the expansion center and age were determined from the proper motions of the fmks ( e.g. , * ? ? ? * ; * ? ? ? * and references therein ) , and the three - dimensional ( 3d ) structure of the ejecta knots reconstructed from spectral mapping observations has shown that the sn ejecta is expanding spherically but is systematically receding at a speed of @xmath12 at a distance of 3.4 kpc @xcite . the dense , slow - moving qsfs indicate that the progenitor had undergone significant and inhomogeneous mass loss during the red supergiant phase @xcite . although this velocity - based classification is an efficient way to classify the knots as sn ejecta and csm , which have distinctive expansion velocities , i.e. , a few @xmath13 vs. a few @xmath14 , it encounters limitations when characterizing the sn ejecta material from the different nucleosynthetic layers . according to previous numerical simulations for core - collapse sn explosions , the radial velocity profiles of heavy elements in sn ejecta are almost identical @xcite . several models in @xcite predict the velocity separation of up to @xmath15 between different heavy elements . their velocity profiles , however , are very broad ( a few @xmath13 ) , so that their distributions largely overlap . these numerical simulations may imply that sn material from different nucleosynthetic layers is barely distinguishable in velocity space . in order to comprehend the explosion dynamics , therefore , a more systematic classification of sn ejecta based on their chemical composition is needed . in this paper , we report the results of broad near - infrared ( nir ) spectroscopic observations toward the main ejecta shell of cas a , focusing on classification of the emission knots based on their _ spectrochemical _ properties . the nir study of cas a has been relatively limited in the literature , although there are many bright forbidden lines of various elements in the nir waveband , some of which may arise from the deep nucleosynthetic layers . as far as we are aware , the only nir spectroscopic study covering the entire _ jhk _ bandpass was conducted by @xcite , who obtained low - resolution ( @xmath16 ) spectra of five fmks and three qsfs that were previously known . they showed that the spectra of the fmks are dominated by [ ] 1.029 , 1.032 , 1.034 , 1.037 ( hereafter [ ] 1.03 multiplets ) and [ ] 1.188 , as well as two high - ionization si lines , [ ] 1.963 and [ ] 1.430 , while those of the qsfs show strong he i 1.083 accompanied by h emission lines . a dozen bright [ ] lines are also detected in both fmks and qsfs . our spectra confirm these features . here we present the spectrochemical classification of knots and discuss their characteristics . the organization of the paper is as follows . in section [ sec - obs ] , we outline our spectroscopic observations and data reduction procedures . an explanation of how we identified individual knots from two - dimensional ( 2d ) dispersed images and derived their spectral properties is given in section [ sec - ide ] . in sections [ sec - pca ] and [ sec - dis ] , we carry out a classification of the knots using principal component analysis ( pca ) and discuss the origin of knots in different classes . finally , the paper is summarized in section [ sec - sum ] .

the results of our analyses of the emission line features based on principal component analysis show that the knots can be classified into three groups : ( 1 ) he - rich , ( 2 ) s - rich , and ( 3 ) fe - rich knots . we discuss the origin of the fe - rich knots and conclude that _ they are most likely `` pure '' fe ejecta synthesized in the innermost region during the supernova explosion . _ the comparison of [ ] images with other waveband images shows that these dense fe ejecta are mainly distributed along the southwestern shell just outside the unshocked @xmath2ti in the interior , supporting the presence of unshocked fe associated with @xmath2ti .

i

1703.03551

we report the results of broadband ( 0.952.46 ) near - infrared spectroscopic observations of the cassiopeia a supernova remnant . using a clump - finding algorithm in two - dimensional dispersed images , we identify 63 ` knots ' from eight slit positions and derive their spectroscopic properties . all of the knots emit [ ] lines together with other ionic forbidden lines of heavy elements , and some of them also emit h and he lines . we identify 46 emission line features in total from the 63 knots and measure their fluxes and radial velocities . the results of our analyses of the emission line features based on principal component analysis show that the knots can be classified into three groups : ( 1 ) he - rich , ( 2 ) s - rich , and ( 3 ) fe - rich knots . the he - rich knots have relatively small , @xmath0 , line - of - sight speeds and radiate strong he i and [ ] lines resembling closely optical quasi - stationary flocculi of circumstellar medium , while the s - rich knots show strong lines from o - burning material with large radial velocities up to @xmath1 indicating that they are supernova ejecta material known as fast - moving knots . the fe - rich knots also have large radial velocities but show no lines from o - burning material . we discuss the origin of the fe - rich knots and conclude that _ they are most likely `` pure '' fe ejecta synthesized in the innermost region during the supernova explosion . _ the comparison of [ ] images with other waveband images shows that these dense fe ejecta are mainly distributed along the southwestern shell just outside the unshocked @xmath2ti in the interior , supporting the presence of unshocked fe associated with @xmath2ti .

we have carried out nir spectroscopic observations toward the main ejecta shell of the young snr cas a. in total , 63 individual knots were identified from eight slit positions by using a clump - finding algorithm . each of these knots has distinct kinematical and spectral properties . within the _ jhk _ spectral range ( 0.942.46 ) , we found 46 emission line features including a dozen bright [ ] lines , forbidden lines of other metallic species , and h and he lines . we employed the pca method to classify the knots based on their relative line fluxes into three distinctive groups : he - rich knots of pre - supernova circumstellar wind material , plus s - rich and fe - rich knots of sn ejecta material . the he - rich and s - rich knots correspond to qsfs and fmks studied in the visible waveband , while fe - rich knots , showing in general only [ ] emission lines , are likely ` pure ' dense fe ejecta from the innermost layer of the progenitor . we summarize our main results as follows . the pca showed that the nir spectral lines can be grouped into three groups : ( 1 ) group 1 , composed of h i and he i lines together with [ ] lines , ( 2 ) group 2 , composed of forbidden lines of si , p , and s , and ( 3 ) group 3 , composed of forbidden fe lines . the lines in the first two pcs are strongly correlated with each other , while the correlation is rather weak among the forbidden fe lines in group 3 . these three spectral groups of the emission lines are almost independent in 3d pc space ( figure [ fig - atr ] ) . the distribution of the knots in the pc planes matches well with the above spectral groups , and we classified the knots into three groups : ( 1 ) he - rich , ( 2 ) s - rich , and ( 3 ) fe - rich knots . the knots belonging to these three groups are well separated from each other in f([]-1.03)/f([]-1.644 ) vs. f(he i-1.083)/f([]-1.644 ) plane ( figure [ fig - fluxratio ] ) , so that one may use these line ratios to classify the knots in cas a. it would be interesting to determine whether this classification methodology applies for other core - collapse snrs . \3 . the he - rich knots show bright emission lines of he i 1.083 and [ ] together with [ ] and h i lines . their line - of - sight speeds are small ( @xmath42 ) . from these chemical and kinematical characteristics , we conclude that the he - rich knots are dense csm swept up by the sn blast wave . these knots correspond to the previously known qsfs . the s - rich knots show strong forbidden lines of s together with [ ] and [ ] , and their line - of - sight speeds reach a few 1000 @xmath78 . these chemical and kinematical properties indicate that the s - rich knots are dense sn ejecta material mostly originating from the o - burning layers and swept up by a reverse shock . these knots correspond to the fmks detected in previous optical studies . the fe - rich knots only show strong [ ] and [ ] lines , and no or weak he i 1.083 lines . like the s - rich knots , they have large line - of - sight speeds ( up to @xmath63 ) and broad line widths ( 1035 ) , but they do not show the lines from si , p , and s. some fe - rich knots show he i 1.083 but their fluxes compared to the [ ] lines are much weaker than those of the he - rich knots . these spectroscopic properties suggest that the fe - rich knots are most likely `` pure '' dense fe ejecta from the innermost layer of the sn . the comparison of [ ] 1.644 images with the _ hst _ acs / wfc f850lp and f775w and _ nustar _ @xmath2ti images reveals that these fe ejecta are mainly distributed in the sw main ejecta shell , just outside the unshocked @xmath2ti in the interior . this supports that there could be a large amount of unshocked `` pure '' fe ejecta associated with @xmath2ti . together with the diffuse , x - ray - emitting `` pure '' fe ejecta detected by _ chandra _ , our result implies that the fe ejecta synthesized in the innermost region develop large - scale non - uniformity during the sn explosion and are expelled asymmetrically . this seems to be consistent with the low - mode , convection - driven sn explosion model . we wish to thank the anonymous referee for the very useful comments and suggestions which helped us improve the quality of the paper . we thank brian grefenstette and fiona harrison for providing the _ nustar _ data . we also want to thank john raymond and sung - chul yoon for helpful discussions . the interactive 3d figures were made by using asymptote which is a descriptive vector graphics language . this research was supported by basic science research program through the national research foundation of korea(nrf ) funded by the ministry of science , ict and future planning ( 2014r1a2a2a01002811 ) . cccrccr 2008 jun 29 & 1 & 23:23:28.54 + 58:50:32.2 & 0.0 & both & 50.50 & 300 @xmath79 4 + & 8 & 23:23:18.13 + 58:50:14.4 & 13.4 & ab & 51.00 & 300 @xmath79 5 + & 2 & 23:23:37.60 + 58:49:59.7 & 288.7 & ab & 50.25 & 300 @xmath79 4 + & st & 23:48:53.97 + 59:58:44.3 & 0.0 & ab & 30.00 & 30 @xmath79 6 + 2008 aug 08 & 3 & 23:23:41.11 + 58:48:45.2 & 36.1 & ab & 45.25 & 300 @xmath79 6 + & 4 & 23:23:24.77 + 58:47:12.2 & 12.0 & ab & 46.25 & 300 @xmath79 6 + & 5 & 23:23:18.50 + 58:47:25.1 & 307.3 & os & 30.00 & 300 @xmath79 1 + & 6 & 23:23:18.33 + 58:47:23.5 & 307.3 & os & 30.00 & 300 @xmath79 1 + & 7 & 23:23:13.57 + 58:47:49.2 & 5.2 & ab & 45.25 & 300 @xmath79 6 + & st & 23:48:53.97 + 59:58:44.3 & 0.0 & ab & 30.00 & 30 @xmath79 8 + cc|c|rcrrr 1 & 1 & 23:23:28.54 + 58:50:47.6 & 8.75 & s & 8.0 ( 0.5 ) & @xmath80 ( 2 ) & 589 ( 8) + 1 & 2 & 23:23:28.54 + 58:50:34.1 & 3.25 & s & 10.6 ( 0.7 ) & @xmath81 ( 2 ) & 165 ( 4 ) + 1 & 3 & 23:23:28.54 + 58:50:33.8 & 5.00 & he & 5.8 ( 0.1 ) & @xmath82 ( 2 ) & 793 ( 5 ) + 1 & 4 & 23:23:28.54 + 58:50:32.3 & 5.50 & s & 3.3 ( 2.0 ) & @xmath83 ( 17 ) & 96 ( 13 ) + 1 & 5 & 23:23:28.54 + 58:50:31.1 & 5.75 & s & 4.9 ( 0.2 ) & @xmath84 ( 2 ) & 383 ( 3 ) + 1 & 6 & 23:23:28.54 + 58:50:27.6 & 3.00 & s & 3.3 ( 0.5 ) & @xmath85 ( 3 ) & 132 ( 4 ) + 1 & 7 & 23:23:28.54 + 58:50:26.6 & 5.75 & fe & 9.8 ( 0.4 ) & @xmath86 ( 2 ) & 561 ( 10 ) + 1 & 8 & 23:23:28.54 + 58:50:25.8 & 3.00 & s & 3.4 ( 0.4 ) & @xmath87 ( 2 ) & 198 ( 5 ) + 2 & 1 & 23:23:35.19 + 58:50:06.0 & 4.50 & fe & 5.5 ( 0.9 ) & @xmath88 ( 6 ) & 204 ( 10 ) + 2 & 2 & 23:23:35.10 + 58:50:06.3 & 5.75 & s & 9.3 ( 3.6 ) & @xmath89 ( 14 ) & 75 ( 10 ) + 2 & 3 & 23:23:35.83 + 58:50:04.3 & 8.00 & s & 4.2 ( 1.7 ) & @xmath90 ( 20 ) & 140 ( 12 ) + 2 & 4 & 23:23:38.21 + 58:49:58.1 & 9.25 & s & 7.0 ( 0.5 ) & @xmath91 ( 3 ) & 480 ( 10 ) + 2 & 5 & 23:23:38.21 + 58:49:58.1 & 6.50 & s & 11.0 ( 1.0 ) & @xmath92 ( 3 ) & 339 ( 12 ) + 2 & 6 & 23:23:38.70 + 58:49:56.8 & 3.75 & s & 9.2 ( 1.7 ) & @xmath93 ( 2 ) & 164 ( 7 ) + 3 & 1 & 23:23:41.64 + 58:48:50.9 & 6.75 & s & 8.2 ( 0.3 ) & @xmath94 ( 3 ) & 460 ( 6 ) + 3 & 2 & 23:23:41.28 + 58:48:47.0 & 5.00 & s & 7.6 ( 0.3 ) & @xmath95 ( 3 ) & 310 ( 4 ) + 3 & 3 & 23:23:40.92 + 58:48:43.2 & 7.25 & s & 7.3 ( 0.1 ) & @xmath96 ( 2 ) & 972 ( 4 ) + 3 & 4 & 23:23:40.52 + 58:48:38.9 & 6.50 & s & 7.2 ( 0.3 ) & @xmath97 ( 4 ) & 434 ( 8) + 3 & 5 & 23:23:40.16 + 58:48:35.1 & 5.75 & s & 6.2 ( 1.2 ) & @xmath98 ( 7 ) & 121 ( 7 ) + 4 & 1 & 23:23:24.90 + 58:47:16.8 & 5.25 & fe & 15.4 ( 1.4 ) & @xmath99 ( 5 ) & 240 ( 6 ) + 4 & 2 & 23:23:24.82 + 58:47:13.9 & 3.75 & s & 10.6 ( 0.6 ) & @xmath100 ( 4 ) & 289 ( 4 ) + 4 & 3 & 23:23:24.77 + 58:47:12.2 & 5.75 & fe & 7.5 ( 0.4 ) & @xmath101 ( 3 ) & 298 ( 5 ) + 4 & 4 & 23:23:24.73 + 58:47:10.7 & 6.25 & s & 9.9 ( 0.3 ) & @xmath102 ( 3 ) & 606 ( 5 ) + 4 & 5 & 23:23:24.73 + 58:47:10.7 & 4.00 & fe & 6.6 ( 0.4 ) & @xmath103 ( 4 ) & 236 ( 4 ) + 4 & 6 & 23:23:24.72 + 58:47:10.2 & 5.75 & s & 10.3 ( 0.3 ) & @xmath104 ( 3 ) & 577 ( 6 ) + 5 & 1 & 23:23:17.21 + 58:47:32.7 & 5.25 & s & 11.5 ( 0.8 ) & @xmath105 ( 3 ) & 313 ( 7 ) + 5 & 2 & 23:23:17.28 + 58:47:32.3 & 5.25 & s & 8.8 ( 0.5 ) & @xmath106 ( 3 ) & 561 ( 10 ) + 5 & 3 & 23:23:17.34 + 58:47:32.0 & 4.50 & fe & 8.7 ( 0.9 ) & @xmath107 ( 4 ) & 286 ( 8) + 5 & 4a & 23:23:17.26 + 58:47:32.4 & 6.25 & s & 8.3 ( 0.3 ) & @xmath108 ( 3 ) & 537 ( 7 ) + 5 & 4b & 23:23:17.34 + 58:47:32.0 & 6.25 & he & 8.3 ( 0.1 ) & @xmath108 ( 3 ) & 2149 ( 7 ) + 5 & 5 & 23:23:17.62 + 58:47:30.3 & 5.25 & s & 9.3 ( 0.5 ) & @xmath109 ( 3 ) & 456 ( 6 ) + 5 & 6 & 23:23:17.88 + 58:47:28.8 & 4.75 & s & 8.8 ( 0.8 ) & @xmath110 ( 4 ) & 273 ( 8) + 5 & 7 & 23:23:18.00 + 58:47:28.0 & 3.75 & s & 7.2 ( 0.6 ) & @xmath111 ( 3 ) & 215 ( 5 ) + 5 & 8 & 23:23:18.72 + 58:47:23.8 & 5.00 & s & 10.8 ( 0.5 ) & @xmath112 ( 3 ) & 492 ( 9 ) + 5 & 9 & 23:23:19.41 + 58:47:19.7 & 1.75 & s & 11.9 ( 1.8 ) & @xmath113 ( 8) & 99 ( 5 ) + 5 & 10 & 23:23:19.49 + 58:47:19.3 & 9.75 & fe & 7.9 ( 0.0 ) & @xmath114 ( 3 ) & 4959 ( 8) + 6 & 1 & 23:23:17.02 + 58:47:31.3 & 3.50 & s & 6.6 ( 0.9 ) & @xmath115 ( 6 ) & 245 ( 8) + 6 & 2 & 23:23:17.07 + 58:47:31.0 & 3.25 & s & 9.0 ( 0.7 ) & @xmath116 ( 4 ) & 340 ( 7 ) + 6 & 3 & 23:23:16.94 + 58:47:31.7 & 4.25 & s & 10.2 ( 0.3 ) & @xmath117 ( 3 ) & 667 ( 7 ) + 6 & 4a & 23:23:17.22 + 58:47:30.0 & 2.75 & he & 10.0 ( 2.1 ) & @xmath118 ( 6 ) & 58 ( 6 ) + 6 & 4b & 23:23:17.30 + 58:47:29.6 & 2.75 & s & 10.4 ( 3.6 ) & @xmath118 ( 6 ) & 34 ( 6 ) + 6 & 5 & 23:23:17.22 + 58:47:30.0 & 3.00 & s & 7.4 ( 0.8 ) & @xmath119 ( 5 ) & 272 ( 6 ) + 6 & 6 & 23:23:17.53 + 58:47:28.2 & 6.25 & s & 10.4 ( 0.4 ) & @xmath120 ( 3 ) & 714 ( 8) + 6 & 7 & 23:23:17.99 + 58:47:25.5 & 4.50 & s & 7.8 ( 0.3 ) & @xmath121 ( 3 ) & 623 ( 8) + 6 & 8 & 23:23:18.47 + 58:47:22.6 & 2.75 & s & 9.3 ( 0.7 ) & @xmath122 ( 4 ) & 171 ( 5 ) + 6 & 9 & 23:23:18.75 + 58:47:21.0 & 2.75 & fe & 8.3 ( 0.5 ) & @xmath123 ( 4 ) & 258 ( 5 ) + 6 & 10 & 23:23:19.04 + 58:47:19.3 & 3.50 & fe & 7.3 ( 0.4 ) & @xmath124 ( 3 ) & 283 ( 5 ) + 6 & 11 & 23:23:19.29 + 58:47:17.8 & 6.50 & fe & 6.9 ( 0.2 ) & @xmath125 ( 3 ) & 676 ( 7 ) + 6 & 12 & 23:23:19.52 + 58:47:16.4 & 4.25 & fe & 9.9 ( 1.7 ) & @xmath126 ( 6 ) & 92 ( 6 ) + 7 & 1 & 23:23:13.66 + 58:47:56.4 & 3.25 & s & 10.2 ( 0.7 ) & @xmath127 ( 3 ) & 161 ( 3 ) + 7 & 2 & 23:23:13.62 + 58:47:53.2 & 5.50 & he & 8.4 ( 0.2 ) & @xmath128 ( 3 ) & 424 ( 6 ) + 7 & 3 & 23:23:13.51 + 58:47:44.2 & 4.00 & he & 8.5 ( 0.2 ) & @xmath129 ( 2 ) & 647 ( 9 ) + 7 & 4 & 23:23:13.49 + 58:47:42.0 & 2.75 & he & 8.5 ( 0.3 ) & @xmath130 ( 3 ) & 480 ( 10 ) + 7 & 5 & 23:23:13.46 + 58:47:39.7 & 3.25 & he & 9.1 ( 0.2 ) & @xmath131 ( 3 ) & 516 ( 7 ) + 8 & 1 & 23:23:18.56 + 58:50:28.1 & 3.25 & s & 8.1 ( 0.9 ) & @xmath132 ( 3 ) & 180 ( 7 ) + 8 & 2 & 23:23:18.43 + 58:50:24.0 & 6.00 & s & 7.6 ( 0.5 ) & @xmath133 ( 3 ) & 369 ( 9 ) + 8 & 3 & 23:23:18.22 + 58:50:17.1 & 6.25 & s & 7.3 ( 0.4 ) & @xmath134 ( 2 ) & 443 ( 9 ) + 8 & 4 & 23:23:18.07 + 58:50:12.3 & 5.25 & s & 9.2 ( 0.4 ) & @xmath135 ( 3 ) & 364 ( 6 ) + 8 & 5 & 23:23:17.93 + 58:50:07.7 & 4.50 & s & 10.8 ( 1.6 ) & @xmath136 ( 6 ) & 170 ( 8) + 8 & 6 & 23:23:17.88 + 58:50:06.2 & 4.00 & s & 13.6 ( 1.7 ) & @xmath137 ( 3 ) & 139 ( 5 ) + 8 & 7 & 23:23:17.76 + 58:50:02.3 & 4.75 & s & 9.4 ( 0.7 ) & @xmath138 ( 4 ) & 378 ( 10 ) + 8 & 8 & 23:23:17.76 + 58:50:02.1 & 4.00 & s & 6.8 ( 0.8 ) & @xmath139 ( 5 ) & 239 ( 12 ) + 8 & 9 & 23:23:17.67 + 58:49:59.1 & 4.00 & s & 8.1 ( 0.6 ) & @xmath140 ( 3 ) & 294 ( 6 ) + cc|lr|rr|r 1 & 1 & [ s iii ] @xmath141 - @xmath142 & 0.95311 & 7.2 ( 0.2 ) & 9233 ( 261 ) & + 1 & 1 & [ c i ] @xmath143 - @xmath142 & 0.98241 & @xmath144 ( @xmath144 ) & @xmath144 ( 15 ) & + 1 & 1 & [ c i ] @xmath141 - @xmath142 & 0.98503 & @xmath144 ( @xmath144 ) & @xmath144 ( 15 ) & + 1 & 1 & [ s ii ] @xmath145 - @xmath146 & 1.02867 & 8.4 ( 0.1 ) & 2317 ( 18 ) & line - fix + 1 & 1 & [ s ii ] @xmath147 - @xmath146 & 1.03205 & 8.4 ( - ) & 3182 ( - ) & line - fix + 1 & 1 & [ s ii ] @xmath145 - @xmath148 & 1.03364 & 8.4 ( - ) & 2185 ( 13 ) & line - fix + 1 & 1 & [ s ii ] @xmath147 - @xmath148 & 1.03705 & 8.4 ( - ) & 1058 ( - ) & line - fix + 1 & 1 & [ n i ] @xmath147 - @xmath149 & 1.03979 & @xmath144 ( @xmath144 ) & @xmath144 ( 12 ) & + 1 & 1 & [ n i ] @xmath145 - @xmath149 & 1.04074 & @xmath144 ( @xmath144 ) & @xmath144 ( 14 ) & + 1 & 1 & [ s i ] @xmath141 - @xmath142 & 1.08212 & 9.9 ( 0.5 ) & 207 ( 15 ) & + 1 & 1 & he i @xmath150 - @xmath151 & 1.08302 & @xmath144 ( @xmath144 ) & @xmath144 ( 11 ) & + 1 & 1 & h i pa@xmath57 & 1.09381 & @xmath144 ( @xmath144 ) & @xmath144 ( 9 ) & + 1 & 1 & [ s i ] @xmath143 - @xmath142 & 1.13059 & @xmath144 ( @xmath144 ) & @xmath144 ( 13 ) & + 1 & 1 & [ p ii ] @xmath143 - @xmath142 & 1.14682 & 7.8 ( 0.7 ) & 293 ( 48 ) & oh - cont + 1 & 1 & [ p ii ] @xmath141 - @xmath142 & 1.18828 & 9.8 ( 0.1 ) & 736 ( 15 ) & + 1 & 1 & [ fe ii ] @xmath152 - @xmath153 & 1.24854 & @xmath144 ( @xmath144 ) & @xmath144 ( 7 ) & + 1 & 1 & [ fe ii ] @xmath154 - @xmath155 & 1.25214 & @xmath144 ( @xmath144 ) & @xmath144 ( 8 ) & + 1 & 1 & [ fe ii ] @xmath156 - @xmath33 & 1.25668 & 10.2 ( 0.3 ) & 388 ( 15 ) & + 1 & 1 & [ fe ii ] @xmath157 - @xmath155 & 1.27035 & @xmath144 ( @xmath144 ) & @xmath144 ( 18 ) & + 1 & 1 & [ fe ii ] @xmath154 - @xmath158 & 1.27878 & 4.0 ( 0.6 ) & 30 ( 6 ) & + 1 & 1 & h i pa@xmath56 & 1.28181 & @xmath144 ( @xmath144 ) & @xmath144 ( 12 ) & + 1 & 1 & [ fe ii ] @xmath159 - @xmath153 & 1.29427 & 9.3 ( 1.0 ) & 133 ( 22 ) & oh - cont + 1 & 1 & [ fe ii ] @xmath157 - @xmath158 & 1.29777 & @xmath144 ( @xmath144 ) & @xmath144 ( 12 ) & + 1 & 1 & [ fe ii ] @xmath152 - @xmath33 & 1.32055 & 17.5 ( 2.6 ) & 92 ( 18 ) & + 1 & 1 & [ fe ii ] @xmath154 - @xmath153 & 1.32778 & 12.3 ( 2.1 ) & 67 ( 15 ) & + 1 & 1 & [ fe ii ] @xmath160 - @xmath153 & 1.53347 & 8.7 ( 0.9 ) & 95 ( 12 ) & oh - cont + 1 & 1 & [ fe ii ] @xmath161 - @xmath158 & 1.59947 & 9.8 ( 1.1 ) & 76 ( 11 ) & oh - cont + 1 & 1 & [ si i ] @xmath143 - @xmath142 & 1.60683 & @xmath144 ( @xmath144 ) & @xmath144 ( 5 ) & + 1 & 1 & [ fe ii ] @xmath160 - @xmath33 & 1.64355 & 13.7 ( 0.1 ) & 589 ( 8 ) & + 1 & 1 & [ si i ] @xmath141 - @xmath142 & 1.64545 & @xmath144 ( @xmath144 ) & @xmath144 ( 7 ) & + 1 & 1 & [ fe ii ] @xmath162 - @xmath155 & 1.66377 & 14.0 ( 1.5 ) & 73 ( 11 ) & oh - cont + 1 & 1 & [ fe ii ] @xmath161 - @xmath153 & 1.67688 & 15.4 ( 0.5 ) & 146 ( 8 ) & + 1 & 1 & [ fe ii ] @xmath162 - @xmath158 & 1.71113 & @xmath144 ( @xmath144 ) & @xmath144 ( 9 ) & + 1 & 1 & [ fe ii ] @xmath163 - @xmath155 & 1.74494 & @xmath144 ( @xmath144 ) & @xmath144 ( 5 ) & + 1 & 1 & [ fe ii ] @xmath163 - @xmath158 & 1.79710 & @xmath144 ( @xmath144 ) & @xmath144 ( 62 ) & + 1 & 1 & [ fe ii ] @xmath162 - @xmath153 & 1.80002 & @xmath144 ( @xmath144 ) & @xmath144 ( 240 ) & + 1 & 1 & [ fe ii ] @xmath161 - @xmath33 & 1.80939 & @xmath144 ( @xmath144 ) & @xmath144 ( 689 ) & + 1 & 1 & [ si vi ] @xmath146 - @xmath148 & 1.96287 & 16.4 ( 0.6 ) & 501 ( 27 ) & + 1 & 1 & [ fe ii ] @xmath164 - @xmath165 & 2.04601 & @xmath144 ( @xmath144 ) & @xmath144 ( 20 ) & + 1 & 1 & he i @xmath166 - @xmath167 & 2.05813 & @xmath144 ( @xmath144 ) & @xmath144 ( 12 ) & + 1 & 1 & [ fe ii ] @xmath168 - @xmath165 & 2.13277 & @xmath144 ( @xmath144 ) & @xmath144 ( 9 ) & + 1 & 1 & [ fe iii ] @xmath169 - @xmath170 & 2.14511 & @xmath144 ( @xmath144 ) & @xmath144 ( 10 ) & + 1 & 1 & h i br@xmath57 & 2.16553 & @xmath144 ( @xmath144 ) & @xmath144 ( 11 ) & + 1 & 1 & [ fe iii ] @xmath171 - @xmath172 & 2.21779 & @xmath144 ( @xmath144 ) & @xmath144 ( 13 ) & + 1 & 1 & [ fe ii ] @xmath173 - @xmath174 & 2.22379 & @xmath144 ( @xmath144 ) & @xmath144 ( 10 ) & + 1 & 1 & [ fe iii ] @xmath169 - @xmath175 & 2.24209 & @xmath144 ( @xmath144 ) & @xmath144 ( 13 ) & + ccrr 1 & 9.8 & 42.7 & 42.7 + 2 & 5.1 & 22.2 & 64.9 + 3 & 4.7 & 20.4 & 85.3 + 4 & 1.1 & 4.7 & 90.0 + 5 & 1.0 & 4.2 & 94.2 + 6 & 0.4 & 1.8 & 96.0 + 7 & 0.3 & 1.3 & 97.4 + 8 & 0.2 & 0.7 & 98.1 + 9 & 0.1 & 0.5 & 98.6 + 10 & 0.1 & 0.4 & 98.9 +

we review a recent asymptotic weak noise approach to the kardar - parisi - zhang equation for the kinetic growth of an interface in higher dimensions . the weak noise approach provides a many body picture of a growing interface in terms of a network of localized growth modes . scaling in 1d

i

0802.1285

we review a recent asymptotic weak noise approach to the kardar - parisi - zhang equation for the kinetic growth of an interface in higher dimensions . the weak noise approach provides a many body picture of a growing interface in terms of a network of localized growth modes . scaling in 1d is associated with a gapless domain wall mode . the method also provides an independent argument for the existence of an upper critical dimension .

in this paper we have presented a short review of a recently developed asymptotic weak noise approach to the kardar - parisi - zhang equation . the scheme provides a many body description of a growing interface in terms of a dynamical network of growth modes . the growth modes are the elementary building blocks and their propagation accounts for the kinetic growth . kinetic transitions are determined by an associated dynamical action , replacing the customary free energy landscape . superimposed on the network is a gas of diffusive modes . in 1d the dispersion laws delimit the universality classes : in the kpz case the gapless domain wall modes yield @xmath43 , the diffusive modes being subdominant ; in the ew case the domain walls are absent and the gapless diffusive modes yield @xmath47 . in higher d the scaling results based on the weak noise method are still subject to scrutiny . finally , we mention that the weak noise method has also been applied to the noise - driven ginzburg - landau equation , a finite - time - singularity model , and dna bubble dynamics @xcite . 99 a. -l . barabasi and h. e. stanley , _ fractal concepts in surface growth _ ( cambridge university press , 1995 ) ; j. krug and h. spohn , _ solids far from equilibrium ; kinetic roughening of growing surfaces : fractal concepts in surface growth _ ( cambridge university press , 1992 ) ; j. krug , adv . 46 * , 139 ( 1997 ) m. kardar , g. parisi and y. c. zhang , phys . lett . * 56 * , 889 ( 1986 ) ; e. medina , t. hwa , m. kardar and y. c. zhang , phys . a * 39 * , 3053 ( 1989 ) t. halpin - healy and y. c. zhang , phys . 254 * , 215 ( 1995 ) d. forster , d. r. nelson and m. j. stephen , phys . * 36 * , 867 ( 1976 ) ; phys . a bf 16 , 732 ( 1977 ) m. kardar and y. c. zhang , phys . 58 * , 2087 ( 1987 ) ; m. kardar , nucl . b bf 290 , 582 ( 1987 ) h. c. fogedby , phys . lett . * 94*,195702 ( 2005 ) ; phys . e * 73 * , 031104 ( 2006 ) ; phys . e * 68 * , 026132 ( 2003 ) ; phys . e59 , 5065 ( 1999 ) ; phys . e57 , 49431 ( 1998 ) ; phys . 80 , 1126 ( 1998 ) l. onsager and s. machlup , phys . rev . * 91 * , 1505 ( 1953 ) , ibid 1512 ; p c. martin , e. d. siggia and h. a. rose , phys . rev . a * 8 * , 423 ( 1973 ) ; r. baussch , h. k. janssen and h. wagner , z. phys . b * 24 * , 113 ( 1976 ) d. a. huse , c. l. henley and d. s. fisher , phys . lett . * 55 * , 2924 ( 1985 ) ; e. frey and u. c. tuber , phys . e * 50 * , 1024 ( 1994 ) ; e. frey , u. c. tuber and t. hwa , phys . e * 53 * , 4424 ( 1996 ) ; k. j. wiese , j. stat . phys . * 93 * , 143 ( 1998 ) ; f. colaiori and m. a. moore , phys . lett . * 86 * , 3946 ( 2001 ) ; m. lssig , phys . rev . lett . * 80 * , 2366 ( 1998 ) ; nucl . b * 448 * , 559 ( 1995 ) ; m. lssig and h. kinzelbach , phys . lett . * 78 * , 903 ( 1997 ) ; p. le doussal and k.j . wiese , phys . e * 72 * , 035101 ( 2005 ) h. c. fogedby , j. hertz and a. svane , europhys . lett . * 62 * , 795 ( 2003 ) ; h. c. fogedby and v. poutkaradze , phys . e * 66 * , 021103 ( 2002 ) ; hans c. fogedby and ralf metzler , phys . lett . * 98 * , 070601 ( 2007 ) .

we review the physics of charged impurities in the vicinity of graphene . the long - range nature of coulomb impurities affects both the nature of the ground state density profile as well as graphene s transport properties . we discuss the screening of a single coulomb impurity and the ensemble averaged density profile of graphene in the presence of many randomly distributed impurities . finally , we discuss graphene s transport properties due to scattering off charged impurities both at low and high carrier density .

i

0812.1795

we review the physics of charged impurities in the vicinity of graphene . the long - range nature of coulomb impurities affects both the nature of the ground state density profile as well as graphene s transport properties . we discuss the screening of a single coulomb impurity and the ensemble averaged density profile of graphene in the presence of many randomly distributed impurities . finally , we discuss graphene s transport properties due to scattering off charged impurities both at low and high carrier density .

graphene is a two dimensional sheet of carbon whose atoms arrange in a honeycomb lattice with nearest neighbor atoms forming strong sp@xmath0 bonds . the electronic properties of this material are mostly determined by the @xmath1 orbitals with each carbon atom contributing one electron to a bloch band whose low energy properties are adequately described by a dirac - weyl effective hamiltonian . while the study of dirac fermions has emerged in several contexts in theoretical condensed matter physics , its experimental realization about three years ago , in the form of gated graphene devices , @xcite where the carrier density can be tuned continuously from electron - like carriers for positive bias to hole - like carriers for negative gate voltage , has prompted a prolific theoretical and experimental effort to understand the properties of this novel material . most of excitement surrounding graphene stems from one of the following peculiar properties : ( i ) electrons and holes in graphene have a gapless linear dispersion relation in contrast to the parabolic dispersion of other more conventional electron gases ; ( ii ) the carriers in graphene are chiral a property that has striking consequences such as the `` half - integer '' quantum hall effect @xcite ; and ( iii ) carriers in graphene live at an exposed almost perfect @xmath2d surface that is amenable to surface probes @xcite and surface manipulation . @xcite in addition , we note that there is the potential of mass producing graphene through epitaxial growth methods , @xcite and that graphene has remarkable mechanical properties @xcite which only further enhance the interest . in this perspective , we look at one important aspect of graphene which is the influence of disorder on its ground state and transport properties . we demonstrate that for graphene , charged ( i.e. coulomb ) impurities behave qualitatively different from neutral impurities @xcite and dominate graphene s transport properties at low carrier density . the importance of the coulomb nature of graphene impurities was first highlighted by ando , @xcite where by calculating the intraband contribution to the polarizability and absorbing the interband ( i.e. electron - hole ) contribution into a redefinition of the dielectric constant @xcite he showed that charged impurities could explain the conductivity being linear - in - density as was seen in experiments . @xcite similar conclusions were obtained by nomura and macdonald @xcite using a complete screening " model ( i.e. @xmath3 ) , cheianov and falko using a numerical thomas - fermi approximation @xcite and in ref . using the full random - phase - approximation ( rpa ) . analytic expressions for the rpa polarizability function calculated first in ref . and then in refs . revealed that for momentum transferred on the fermi circle ( i.e. @xmath4 ) the graphene dielectric function calculated using the rpa was identical to the much simpler thomas - fermi approximation at @xmath5 ( see fig . [ fig : dielectric_function ] ) . this then made it possible to calculate the rpa - boltzmann conductivity analytically , @xcite and the dependence of graphene s conductivity on the fine - structure constant @xmath6 was recently verified experimentally . @xcite the importance of coulomb scattering in explaining the observed graphene transport properties soon prompted an interest in investigating the properties of a single charged impurity embedded in graphene . katsnelson @xcite studied this problem using a fermi - thomas approximation , followed by studies in refs . who were mostly interested in effects beyond the rpa such as determining the critical impurity charge for which the coulomb impurity forms bound states and the screening properties of graphene in the supercritical regime . = 0.9 it was understood by refs . that as one approached the dirac point , one would soon encounter a situation where the gate voltage induced carrier density would be smaller than the fluctuation of carrier density induced by the charged impurities thereby breaking the graphene landscape into puddles of electrons and holes . solving numerically for the conductivity using a finite - sized kubo formalism for a limited range of impurity concentrations , ref . concluded that the coulomb disorder model gave a _ universal _ minimum conductivity whose value did not depend on the charged impurity concentration , but that was larger than that expected for clean dirac fermions , @xcite while ref . argued that this would give rise to a _ non - universal _ minimum conductivity whose value depended on the concentration of charged impurities . ref . developed a mean field approach to understand the properties of graphene at the dirac point by calculating an effective carrier density self - consistently . this theory made quantitative predictions about the dependence of the minimum conductivity and rms carrier density on the charged impurity concentration and substrate dielectric constant , and in particular argued that cleaner graphene samples would have larger minimum conductivity . ref . then studied the ground state properties of graphene by minimizing an energy functional comprising kinetic energy , hartree , exchange @xcite and correlation @xcite contributions in the presence of coulomb disorder . this work made quantitative predictions about properties of the carrier density distribution , both at and away from the dirac point , and enabled ref . to develop an effective medium theory to calculate the graphene s conductivity through these inhomogeneous puddles , capturing quantitatively the minimum conductivity plateau that is seen in experiments . @xcite we mention that underlying the existence of this minimum conductivity plateau is the high transmission of graphene p - n junctions , which has been the subject of theoretical @xcite and experimental study . @xcite for the purposes of this paper we do not discuss quantum interference effects ( see ref . and references therein ) or the strongly interacting regime ( see ref . and references therein ) . the remainder of this paper is structured as follows . in section [ sec : single ] we discuss the problem of the screening of a single coulomb impurity in the sub - critical regime as a useful toy model to understand the many impurity problem that we address in section [ sec : ground ] where we study the case of many coulomb impurities that are uncorrelated and distributed uniformly in order to study the ground state properties of graphene . in section [ sec : boltzmann ] , we review the high - density boltzmann transport theory , and discuss the effective medium theory ( emt ) in section [ sec : emt ] . in sections [ sec : expts ] , [ sec : mincond ] , and [ sec : recent ] we briefly review the experimental situation , discuss graphene minimum conductivity , and recent theoretical work not covered in this review . we then conclude in section [ sec : conclusion ] .

we review the theory and phenomenology of the axial u(1 ) problem with emphasis on the role of gluonic degrees of freedom in the low - energy @xmath0 and @xmath1 reactions . 150 mm 239 mm -11 mm 6 mm 0 cm [ cols= " < " , ] 12 mm * gluonic effects in @xmath2-nucleon interactions * + * steven d. bass * + _ ect * , strada delle tabarelle 286 , i-38050 villazzano , trento , italy _ 10 mm

i

hep-ph0108187

we review the theory and phenomenology of the axial u(1 ) problem with emphasis on the role of gluonic degrees of freedom in the low - energy @xmath0 and @xmath1 reactions . 150 mm 239 mm -11 mm 6 mm 0 cm [ cols= " < " , ] 12 mm * gluonic effects in @xmath2-nucleon interactions * + * steven d. bass * + _ ect * , strada delle tabarelle 286 , i-38050 villazzano , trento , italy _ 10 mm

@xmath3 and @xmath2 physics together with polarised deep inelastic scattering provide complementary windows on the role of gluons in dynamical chiral symmetry breaking . gluonic degrees of freedom play an important role in the physics of the flavour - singlet @xmath4 channel @xcite through the qcd axial anomaly @xcite . the most famous example is the @xmath5 problem : the masses of the @xmath3 and @xmath2 mesons are much greater than the values they would have if these mesons were pure goldstone bosons associated with spontaneously broken chiral symmetry @xcite . this extra mass is induced by non - perturbative gluon dynamics @xcite and the axial anomaly @xcite . for the first time since the discovery of qcd ( and the u(1 ) problem ) precise data are emerging on processes involving @xmath2 production and decays . there is presently a vigorous experimental programme to study the @xmath0 and @xmath1 reactions close to threshold in low - energy proton - nucleon collisions at celsius @xcite and cosy @xcite . new data on @xmath2 photoproduction , @xmath6 , are expected soon from jefferson laboratory @xcite following earlier measurements at elsa @xcite . the light - mass `` exotic '' meson states with quantum numbers @xmath7 observed at bnl @xcite and cern @xcite in @xmath8 and @xmath9 scattering were discovered in decays to @xmath10 and @xmath11 suggesting a possible connection with axial u(1 ) dynamics . further `` exotic '' studies are proposed in photoproduction experiments at jefferson laboratory . at higher energies anomalously large branching ratios have been observed by cleo for @xmath12-meson decays to an @xmath2 plus additional hadrons @xcite and for the @xmath13 @xcite process . the @xmath12 decay measurements have recently been confirmed in new , more precise , data from babar @xcite and belle @xcite . the lep data on @xmath2 production in hadronic jets is about 40% short of the predictions of the string fragmentation models employed in the jetset and ariadne monte - carlos without an additional @xmath2 `` suppression factor '' @xcite . first measurements of @xmath14 decays have been performed at cleo @xcite . the new wasa 4@xmath15 detector @xcite at celsius will enable precision studies of @xmath3 and @xmath2 decays . data expected in the next few years provides an exciting new opportunity to study axial u(1 ) dynamics and to investigate the role of gluonic degrees of freedom in @xmath3 and @xmath2 physics . in this lecture we focus primarily on @xmath2 production in proton - proton collisions together with a brief review of the axial u(1 ) problem in qcd . the role of gluonic degrees of freedom and ozi violation in the @xmath2nucleon system has been investigated through the flavour - singlet goldberger - treiman relation @xcite , the low - energy @xmath1 reaction @xcite and @xmath2 photoproduction @xcite . the flavour - singlet goldberger - treiman relation connects the flavour - singlet axial - charge @xmath16 measured in polarised deep inelastic scattering with the @xmath2nucleon coupling constant @xmath17 . working in the chiral limit it reads @xmath18 where @xmath17 is the @xmath2nucleon coupling constant and @xmath19 is an ozi violating coupling which measures the one particle irreducible coupling of the topological charge density @xmath20 to the nucleon . in eq.(1 ) @xmath21 is the nucleon mass and @xmath22 ( @xmath23gev ) renormalises @xcite the flavour - singlet decay constant . the coupling constant @xmath19 is , in part , related @xcite to the amount of spin carried by polarised gluons in a polarised proton . the large mass of the @xmath2 and the small value of @xmath16 @xmath24 extracted from deep inelastic scattering @xcite ( about a @xmath25 ozi suppression ) point to substantial violations of the ozi rule in the flavour - singlet @xmath26 channel @xcite . a large positive @xmath27 is one possible explanation of the small value of @xmath28 . it is important to look for other observables which are sensitive to @xmath19 . ozi violation in the @xmath2nucleon system is a probe of the role of gluons in dynamical chiral symmetry breaking in low - energy qcd . working with the @xmath5extended chiral lagrangian for low - energy qcd @xcite see section 3 below one finds a gluon - induced contact interaction in the @xmath1 reaction close to threshold @xcite : @xmath29 here @xmath30 is the gluonic contribution to the mass of the singlet 0@xmath31 boson and @xmath32 is a second ozi violating coupling which also features in @xmath33 scattering . the physical interpretation of the contact term ( 3 ) is a `` short distance '' ( @xmath34fm ) interaction where glue is excited in the interaction region of the proton - proton collision and then evolves to become an @xmath2 in the final state . this gluonic contribution to the cross - section for @xmath1 is extra to the contributions associated with meson exchange models @xcite . there is no reason , a priori , to expect it to be small . what is the phenomenology of this gluonic interaction ? since glue is flavour - blind the contact interaction ( 3 ) has the same size in both the @xmath1 and @xmath35 reactions . celsius @xcite have measured the ratio @xmath36 for quasifree @xmath3 production from a deuteron target up to 100 mev above threshold . they observed that @xmath37 is approximately energy - independent @xmath38 over the whole energy range see fig.1 . the value of this ratio signifies a strong isovector exchange contribution to the @xmath3 production mechanism @xcite . this experiment should be repeated for @xmath2 production . the cross - section for @xmath1 close to threshold has been measured at cosy @xcite . following the suggestion in @xcite a new cosy-11 , uppsala university collaboration @xcite has been initiated to carry out the @xmath35 measurement . the more important that the gluon - induced process ( 3 ) is in the @xmath1 reaction the more one would expect @xmath39 to approach unity near threshold after we correct for the final state interaction between the two outgoing nucleons . ( after we turn on the quark masses , the small @xmath40 mixing angle @xmath41 degrees means that the gluonic effect ( 3 ) should be considerably bigger in @xmath2 production than @xmath3 production . ) @xmath2 phenomenology is characterised by large ozi violations . it is natural to expect large gluonic effects in the @xmath1 process . in section 2 we give a brief introduction to the u(1 ) problem . section 3 introduces the chiral lagrangian approach and section 4 makes contact with the experimental data from celsius and cosy .

we illustrate the usefulness of this analysis approach by demonstrating fiber - based ellipsometry , where the polarization state of the probe light is unknown , and , yet , the ellipsometric angles of the investigated sample ( @xmath0 and @xmath1 ) are obtained with an accuracy comparable to that of conventional ellipsometry instruments by measuring changes to the generalized polarization state .

r

1110.3995

we show that , under the right conditions , one can make highly accurate polarization - based measurements without knowing the absolute polarization state of the probing light field . it is shown that light , passed through a randomly varying birefringent material has a well - defined orbit on the poincare sphere , which we term a generalized polarization state , that is preserved . changes to the generalized polarization state can then be used in place of the absolute polarization states that make up the generalized state , to measure the change in polarization due to a sample under investigation . we illustrate the usefulness of this analysis approach by demonstrating fiber - based ellipsometry , where the polarization state of the probe light is unknown , and , yet , the ellipsometric angles of the investigated sample ( @xmath0 and @xmath1 ) are obtained with an accuracy comparable to that of conventional ellipsometry instruments by measuring changes to the generalized polarization state .

the measured polarization states of the output of the pm fiber are plotted in fig . [ polarization - sphere - exp](a ) as zero - dimensional points on the two - dimensional surface of the poincare sphere , where all data are , unless it is specifically stated otherwise , normalized so that the total intensity is unity . the notable feature is that despite the wide variation in temperature , the polarization states are not observed to fall randomly on the two - dimensional poincare surface . instead , a single , one - dimensional orbit is traced out , which is shown more clearly by taking a cross section through the sphere to obtain a projection of the orbit in a stokes vector plane ( fig . [ polarization - sphere - exp](b ) ) . the analysis of the orientation of this orbit is key to performing polarization - based measurements without precise knowledge of the polarization of the probing light field . + to show that this polarization orbit can be used as a generalized , higher dimensional polarization state and be used to make polarization - based measurements , we show how the two ellipsometric parameters , @xmath0 and @xmath1 can be calculated from changes to the polarization orbit . we begin by considering light exiting a fiber in a set of polarization states denoted by @xmath4 where the subscript and superscript denote the polarization coordinate systems of the sample ( @xmath5 ) and the fiber ( @xmath6 ) . an isotropic reflecting surface transforms the polarization state of incident light according to the following mueller matrix in the sample coordinate system @xcite @xmath7 \label{iso refle surf}\ ] ] where @xmath8 and @xmath9 and @xmath10 are intensity reflectivities for the @xmath11 and @xmath12 polarized light respectively . the initial states become @xmath13 in other words , the ellipsometric information of the sample is carried in a global transformation from @xmath4 to @xmath14 the matrix @xmath15 is a direct sum of the matrices of its two block diagonal subspaces . the ( desired ) values of @xmath16 and @xmath17 can , thus , be obtained separately . the set of polarization states of the light field incident on , and reflected by the sample are given by @xmath18 , & \mathcal{r}_{xy } = \left[\begin{array}{c } r_{1}\\ r_{2}\\ r_{3}\\ r_{4 } \end{array}\right ] \end{array}\ ] ] substituting equations [ eq : stokes ] into equation [ eq : transform ] gives @xmath19 dividing eqs . [ eq : rforpsi1 ] by [ eq : rforpsi2 ] and rearranging gives : @xmath20 where @xmath21 and @xmath22 . @xmath1 is obtained by requiring consistency between equations [ eq : rfordelta1 ] and [ eq : rfordelta2 ] . note that equations [ eq : rfordelta1 ] and [ eq : rfordelta2 ] have the form of a scaling factor and a rotation , which , when applied to an ellipse , reduces its area and changes the orientation of its major axis in stokes space . in practice , since the polarization orbit , when projected in the plane of the 3rd and 4th stokes vectors , is an ellipse , @xmath1 is the angle difference between the orientations of the ellipses given by @xmath4 and @xmath23 . it is important to note that our analysis assumes that all states are measured in the @xmath6 coordinate system . slight changes of alignment between the coordinate system of the fiber and the sample introduces an extra rotation to the polarization state that depends on the misalignment angle , @xmath24 . in that case , it can be shown that the systematic error added to @xmath0 and @xmath1 is of the order of @xmath25 . provided that the physical alignment of the pm - fiber is held sufficiently constant , the uncertainty in @xmath1 and @xmath0 should be comparable to that of conventional ellipsometry . to demonstrate the applicability of this analysis , we performed fiber - based ellipsometry on three multilayer bragg reflecting samples @xcite , two of which have been coated with amorphous hydrogenated carbon @xcite . spectroscopic ellipsometry ( wollam m2000 ) revealed that the carbon layers on these samples are 0.3 , and 0.8 nm thick , while the third , supposedly uncoated sample , has @xmath260.1 nm naturally occurring carbon layer with a different composition to that of the first two samples . both conventional and fiber - based ellipsometry measurements were performed at an angle of incidence of 66@xmath3 . the raw ellipsometric data from the fiber - based ellipsometer , using the experimental procedure described described above , is shown in fig . [ carbon samples](a ) . the measured orbits have been projected onto the plane of the third and fourth stokes vector components ( the inset shows the three dimensional representation of the data ) . as illustrated by the zoomed in section , shown in fig . [ carbon samples](b ) , the data for each sample are systematically modified by the sub - nanometer layers of carbon to generate three different ellipses . the data for each sample show very little deviation from the fitted ellipse . + using the analysis described above , we obtain the @xmath0 and @xmath1 values presented in tab . [ psi and delta values ] . these values agree well with those obtained from a conventional ellipsometer . the small systematic difference between the values from the two instruments is due to a small difference in the angle of incidence between the two measurements ( the accuracy of the angle of incidence is @xmath270.5@xmath3 ) . .@xmath0 and @xmath1 values for fiber - based ellipsometric measurements ( columns 2 and 3 ) and conventional ellipsometer measurements ( columns 4 and 5 ) on carbon - coated mlms [ cols="^,^,^,^,^",options="header " , ] [ psi and delta values ]

it is shown that light , passed through a randomly varying birefringent material has a well - defined orbit on the poincare sphere , which we term a generalized polarization state , that is preserved . changes to the generalized polarization state can then be used in place of the absolute polarization states that make up the generalized state , to measure the change in polarization due to a sample under investigation .

c

1110.3995

we show that , under the right conditions , one can make highly accurate polarization - based measurements without knowing the absolute polarization state of the probing light field . it is shown that light , passed through a randomly varying birefringent material has a well - defined orbit on the poincare sphere , which we term a generalized polarization state , that is preserved . changes to the generalized polarization state can then be used in place of the absolute polarization states that make up the generalized state , to measure the change in polarization due to a sample under investigation . we illustrate the usefulness of this analysis approach by demonstrating fiber - based ellipsometry , where the polarization state of the probe light is unknown , and , yet , the ellipsometric angles of the investigated sample ( @xmath0 and @xmath1 ) are obtained with an accuracy comparable to that of conventional ellipsometry instruments by measuring changes to the generalized polarization state .

to understand why pm fibers that are subject to varying temperature and strain , produce a polarization orbit , a numerical model of a non - ideal pm fiber was developed . in simple terms , the fiber is a strongly birefringent material with a time and space - dependent beat length , and some degree of polarization mode cross - talk . in this model , the orientation of the axes of birefringence and the refractive index difference between the two axes changes as a function of position along the fiber and time . to analyze the effect of such a fiber , we break the fiber up into ideal segments , @xmath28 . mathematically , this corresponds to rotating the coordinate system of the fiber for light entering a fiber segment and then reversing the rotation upon exiting . the phase delay experienced by the light field then depends on its orientation relative to the rotated coordinate system . this introduces a polarization change that is purely due to the relative phase delay of the components of the electric field along the local axes of birefringence . the transfer matrix of the entire fiber is then given by a series of matrix multiplications @xcite : @xmath29 @xmath30 and @xmath31 are rotations due to an angular ( @xmath32 ) misalignment of the axes of birefringence of two neighboring ideal segments , while @xmath33 is the matrix transfer function due to the phase delay . the phase delay is expressed as a function of the beat length , @xmath34 , normalized to the segment length . both @xmath34 and @xmath35 are time dependent in a constrained but random manner . in these simulations , the maximum limits of @xmath32 and changes to @xmath36 were given by the yield strength of glass the strain required to introduce these variations should not break the fiber . to allow direct comparison between the model results and experimental results , the average variation in @xmath32 was determined by specifying a maximum polarization cross - talk per unit length . as the phase change varies as a function of position and time in the fiber , the output polarization states form a simple , circular orbit in stokes space . the effect of cross - talk is to introduce deviations from a simple orbit in stokes space , instead , a more complicated , but repeating , orbit is obtained . numerically evaluating equation [ fiber cross talk ] under conditions that the maximum total cross talk is 20 db , which is the maximum specified cross - talk for our fiber , shows ( see fig . [ model - results ] ) that , even in the presence of a small amount of cross - talk , the polarization orbit can still be approximated by a simple orbit ( the elongation of the red markers in fig . [ model - results ] indicate the deviation from a simple orbit ) . importantly , these simulations indicate that , as long as we can quantify the polarization orbit of an optical component , then it will be possible to use light exiting that component for polarization - based measurements . it should be noted there is the ( slim ) possibility that the polarization change induced by the sample is a rotation in the plane of the polarization orbit . in this case , the sample is undetectable . this problem can be avoided by making measurements at more than one angle of incidence . for a total polarization mode cross talk of 20 db . time - dependent temperature changes cause changes to the local degree and orientation of the fiber s birefringence . the resulting output is an orbit on the poincare sphere.,width=226 ] in conclusion , we have demonstrated that sensitive polarization - based measurements are possible even when the polarization state of the probing light field has been passed through an optical element with an unpredictably fluctuating birefringence . this is possible because , for a fixed input polarization , the environmentally induced fluctuations in the output polarization after propagation through an optical element or material still lie in a single orbit of the poincare sphere , creating what we have termed a generalized , higher dimensional polarization state . polarization - based measurements can then be made by analyzing changes to the higher dimensional state , rather than the individual polarization states that make up the higher dimensional state . to illustrate this , we demonstrated a fiber - based ellipsometer , capable of detecting carbon layers with a thickness of 0.3 nm .

we show that for a large class of contact @xmath0-manifolds the groups of vassiliev invariants of legendrian and of framed knots are canonically isomorphic . as a corollary , we obtain that the group of finite order arnold s @xmath1-type invariants of wave fronts on a surface @xmath2 is isomorphic to the group of vassiliev invariants of framed knots in the spherical cotangent bundle @xmath3 of @xmath2 . on the other hand we construct the first examples of contact manifolds for which vassiliev invariants of legendrian knots can distinguish legendrian knots that realize isotopic framed knots and are homotopic as legendrian immersions .

i

math0005002

we show that for a large class of contact @xmath0-manifolds the groups of vassiliev invariants of legendrian and of framed knots are canonically isomorphic . as a corollary , we obtain that the group of finite order arnold s @xmath1-type invariants of wave fronts on a surface @xmath2 is isomorphic to the group of vassiliev invariants of framed knots in the spherical cotangent bundle @xmath3 of @xmath2 . on the other hand we construct the first examples of contact manifolds for which vassiliev invariants of legendrian knots can distinguish legendrian knots that realize isotopic framed knots and are homotopic as legendrian immersions .

in this section we describe the main results of the paper . ( in case any of the terminology appears to be new to the reader , the corresponding definitions are given in the next section . ) if a contact structure on a @xmath0-manifold is cooriented , then every legendrian knot ( i.e. a knot that is everywhere tangent to the contact distribution ) has a natural framing ( a continuous normal vector field ) . hence when studying legendrian knots in such contact manifolds the main question is to distinguish those of them that realize isotopic framed knots . similarly if the contact structure is parallelized , then every transverse knot ( i.e. a knot that is everywhere transverse to the contact distribution ) also has a natural framing , and when studying transverse knots in such contact manifolds again the main question is to distinguish those of them that realize isotopic framed knots . vassiliev invariants proved to be an extremely useful tool in the study of framed knots , and the conjecture is that they are sufficient to distinguish all the isotopy classes of framed knots . vassiliev invariants can also be easily defined in the categories of legendrian and of transverse knots . in this paper we study the relationship between the groups of vassiliev invariants of these three categories of knots , and explore when these invariants can be used to distinguish legendrian knots that realize isotopic framed knots . consider a contact manifold @xmath4 with a cooriented contact structure . fix an abelian group @xmath5 , a connected component @xmath6 of the space of framed immersions of @xmath7 into @xmath4 , and a connected component @xmath8 of the space of legendrian immersions of @xmath7 into @xmath4 . we study the relation between the groups of @xmath5-valued vassiliev invariants of framed knots from @xmath6 and of @xmath5-valued vassiliev invariants of legendrian knots from @xmath9 . the main results obtained in this paper are described below . [ first ] the groups of @xmath5-valued vassiliev invariants of legendrian knots from @xmath9 and of framed knots from @xmath6 are canonically isomorphic , provided that the euler class of the contact bundle vanishes on every @xmath10 realizable by a mapping @xmath11 . ( see theorem [ isomorphismobtained ] and proposition [ interpretationconditionii ] . ) using theorem [ first ] we show that : the groups of @xmath5-valued vassiliev invariants of legendrian knots from @xmath9 and of framed knots from @xmath6 are canonically isomorphic , provided that one of the following conditions holds : 1 : : the contact structure is tight ; 2 : : the euler class of the contact bundle is in the torsion of @xmath12 ( in particular if the euler class is zero ) . 3 : : the contact manifold is closed and admits a metric of negative sectional curvature . ( see sections [ homologysphere ] and [ negativecurvature ] and theorem [ tight ] . ) as a corollary , we get that for any surface @xmath2 the group of finite order arnold s @xmath1-type invariants of wave fronts on @xmath2 is isomorphic to the group of vassiliev invariants of framed knots in the spherical cotangent bundle @xmath3 of @xmath2 . previously the isomorphism of the groups of vassiliev invariants of legendrian and of framed knots was known only in the case where @xmath13 and @xmath4 is the standard contact @xmath14 ( result of d. fuchs and s. tabachnikov @xcite ) or the standard contact solid - torus ( result of j. hill @xcite ) . the proofs of these isomorphisms were based on the fact that for the @xmath15-valued vassiliev invariants of framed knots in these manifolds there exists a universal vassiliev invariant also known as the kontsevich integral . ( currently the existence of the kontsevich integral is known only for a total space of an @xmath16-bundle over a compact oriented surface with boundary , see the paper @xcite of andersen , mattes , and reshetikhin . ) thus the approach used in @xcite and @xcite to show the isomorphism of the groups of vassiliev invariants is not applicable for almost all contact @xmath0-manifolds and abelian groups @xmath5 and our results appear to be a strong generalization of the results of fuchs , tabachnikov and hill . we also construct the first examples where vassiliev invariants can be used to distinguish legendrian knots that realize isotopic framed knots and are homotopic as legendrian immersions . these are also the first examples where the groups of vassiliev invariants of legendrian and of framed knots from the corresponding components of the spaces of legendrian and of framed immersions are not canonically isomorphic . the manifold @xmath17 admits infinitely many cooriented contact structures for which there exist legendrian knots that can be distinguished by @xmath18-valued vassiliev invariants even though they realize isotopic framed knots and are homotopic as legendrian immersions . ( see theorem [ example1 ] and theorem [ example2 ] in which the similar result is proved for any orientable total space of an @xmath7-bundle over a nonorientable surface of a sufficiently high genus . ) for transverse knots we obtain the following result ( see theorem [ isomorphismobtainedtransverse ] ) : let @xmath19 be a contact manifold with a parallelized contact structure , then the groups of @xmath5-valued vassiliev invariants of transverse and of framed knots ( from the corresponding components of the spaces of transverse and of framed immersions ) are canonically isomorphic .

we show that in a large class of supersymmetric models with spontaneously broken @xmath0 symmetry , neutron antineutron oscillations occur at an observable level even though the scale of @xmath0 breaking is very high , @xmath1 gev , as suggested by gauge coupling unification and neutrino masses .

i

hep-ph0108089

we show that in a large class of supersymmetric models with spontaneously broken @xmath0 symmetry , neutron antineutron oscillations occur at an observable level even though the scale of @xmath0 breaking is very high , @xmath1 gev , as suggested by gauge coupling unification and neutrino masses . we illustrate this phenomenon in the context of a recently proposed class of seesaw models that solves the strong cp problem and the susy phase problem using parity symmetry . we obtain an _ upper _ limit on @xmath2 oscillation time in these models , @xmath3 sec . this suggests that a modest improvement in the current limit on @xmath4 of @xmath5 sec will either lead to the discovery of @xmath2 oscillations , or will considerably restrict the allowed parameter space of an interesting class of neutrino mass models . epsf.tex ( # 1 width # 2)=#2

it is widely believed that the most natural and appealing explanation of the recent neutrino oscillation results is provided by the seesaw mechanism @xcite incorporated into extensions of the standard model that include a local @xmath0 symmetry . the simplest models with local @xmath0 symmetry are the left - right symmetric models @xcite based on the gauge group @xmath6 . these models have the additional virtue that they explain the origin of parity violation in weak interactions as a consequence of spontaneous symmetry breaking in very much the same way as one explains the strength of the weak interaction in the standard model . stability of the higgs sector under radiative corrections calls for weak scale supersymmetry as in the minimal supersymmetric standard model ( mssm ) . it has recently been shown that if the mssm is embedded into a left right symmetric framework at a high scale @xmath7 gev , as suggested by neutrino oscillation data and by gauge coupling unification , it helps solve some important problems faced by the mssm , viz . , the susy cp problem @xcite , the strong cp problem @xcite and the @xmath8 problem . supersymmetric models with such a high scale embedding are therefore attractive candidates for physics beyond the standard model . it was noted many years ago @xcite that the electric charge formula of the left right symmetric models , @xmath9 , allows one to conclude from pure group theoretic arguments that parity symmetry breaking implies a breakdown of @xmath0 symmetry as well with the constraint that @xmath10 . this simple relation is profoundly revealing . it says that the neutrinos must be majorana particles since the lepton number breaking terms in the theory must obey @xmath11 selection rule . this conclusion follows directly if higgs triplets are used to break @xmath12 symmetry since @xmath13 for triplets , it also holds when higgs doublets are used for this purpose , since gauge invariance requires the presence of two such doublets in the mass term for the neutrinos . secondly , for purely hadronic baryon number violating processes , baryon number must change by at least two units , @xmath14 . this means that models based on left right symmetric gauge structure can lead to the process where a neutron transforms itself into an antineutron ( @xmath2 oscillation@xcite ) , while they may forbid the decay of the proton , which is a @xmath15 process . while the above group theory argument predicts the existence of @xmath2 oscillation in left right symmetric models , its strength will depend on the details of the model . using simple dimensional analysis it is easy to find that the lowest dimensional operators that contributes to @xmath2 oscillation are six quark operators , a typical one being @xmath16 . this operator has dimension 9 and therefore the coupling strength scales as @xmath17 , where @xmath18 is the scale of new physics . it is natural to identify @xmath18 with the scale of @xmath0 ( or parity ) breaking . the current lower limit on @xmath2 oscillation time , @xmath19 sec @xcite , sec @xcite . ] implies an upper limit @xmath20 gev@xmath21 . for @xmath2 oscillations to be observable then , the scale @xmath18 should be rather low , @xmath22 gev . one class of models where @xmath23 transition manifests itself through higgs boson exchange has been discussed in ref . there it was shown that if the @xmath6 model is embedded into the @xmath24 gauge group , then @xmath2 oscillations can arise at an observable level if the @xmath25 breaking scale is in the 100 tev range . in these models , @xmath2 oscillation amplitude is intimately tied to an understanding of small neutrino masses via the seesaw mechanism as well as the breaking of quark lepton degeneracy implied by @xmath25 symmetry . the same higgs field that breaks @xmath25 and generates heavy majorana masses for the right handed neutrinos also mediate @xmath2 oscillations here . with the scale of @xmath25 breaking in the 100 tev range , these models would appear to be incompatible with gauge coupling unification . furthermore , such a low scale of parity breaking would not yield naturally neutrino masses in the range suggested by current experiments . if we raise the scale of parity/@xmath25 breaking to values above @xmath26 gev , so that small neutrino masses in the right range are generated naturally , then @xmath2 transition amplitude becomes unobservably small in these models . oscillation was noted in the context of a susy @xmath27 model in ref . these models possess accidental symmetries that lead to light ( @xmath28 gev ) diquark higgs bosons even though the scale of parity violation is high . as a result , the @xmath2 oscillation operator can have observable strength . unification of gauge couplings is however difficult to achieve in these models . ] does the above arguments mean that @xmath2 oscillations are beyond experimental reach based on current neutrino oscillation phenomenology ? in this letter we will show that this is not the case in a class of attractive seesaw models with local @xmath0 symmetry . we will see that in these models a new class of @xmath29 operators is induced as a consequence of parity breaking . these operators lead to observable @xmath2 oscillation despite the scale @xmath30 of parity breaking being close to the conventional gut scale of @xmath31 gev . in fact , @xmath32 increases with @xmath30 and therefore one has the inverse phenomenon that increasing @xmath30 leads to stronger @xmath2 oscillation amplitude . interestingly , the scale @xmath30 implied by neutrino masses is such that @xmath2 oscillation should be accessible experimentally with a modest improvement in the current limit . we obtain an _ upper _ limit of @xmath33 sec in this class of models . this prediction becomes sharper in a concrete model where flavor symmetries reduce considerably the uncertainties in the estimate of @xmath4 . we emphasize that our upper limit is derived in the context of conventional seesaw models of neutrino mass without using any special ingredients to enhance @xmath2 oscillation amplitude . this should provide new impetus for an improved experimental search for @xmath2 oscillations .

we study a two - component model for gelation consisting of @xmath0-functional monomers ( the gel ) and inert particles ( the solvent ) . after equilibration as a simple liquid , the gel particles are gradually crosslinked to each other until the desired number of crosslinks has been attained . at a critical crosslink density the largest gel cluster percolates and an amorphous solid forms . as the crosslink density @xmath1 approaches its critical value @xmath2 , the shear viscosity diverges : @xmath3 with @xmath4 a nonuniversal concentration - dependent exponent .

i

cond-mat0207304

we study a two - component model for gelation consisting of @xmath0-functional monomers ( the gel ) and inert particles ( the solvent ) . after equilibration as a simple liquid , the gel particles are gradually crosslinked to each other until the desired number of crosslinks has been attained . at a critical crosslink density the largest gel cluster percolates and an amorphous solid forms . this percolation process is different from ordinary lattice or continuum percolation of a single species in the sense that the critical exponents are new . as the crosslink density @xmath1 approaches its critical value @xmath2 , the shear viscosity diverges : @xmath3 with @xmath4 a nonuniversal concentration - dependent exponent .

it is generally accepted that percolation is an essential aspect of gelation or vulcanization it is doubtful that even in a highly entangled melt of long polymers a nonzero value of the static shear modulus could exist in the absence of an infinite connected network . however , percolation has usually been studied in rather special limits . site and bond percolation of a single species on regular lattices are very well characterized and off - lattice percolation seems to present no new features @xcite , at least insofar as critical behavior is concerned . more closely related to real gels are the so - called correlated percolation models where the distribution of crosslinks is drawn from a boltzmann distribution appropriate for a nearest neighbor lattice gas @xcite . except at special points in the phase diagram these models are also in the universality class of the simple percolation problem . in our previous work on transport properties near the gel point @xcite , we have also used a simple one - species percolation process to produce the incipient gel . we found that the shear viscosity diverges as the percolation concentration @xmath2 is approached according to @xmath5 with @xmath6 . this value of the exponent @xmath4 is in excellent agreement with a prediction of de gennes based on a superconductor - normal conductor analogy @xcite and with recent analytical work on a rouse model @xcite . it is also reasonably close to some experimental results for @xmath4 @xcite but quite different from that produced by another set of experiments @xmath7 @xcite . thus it seems reasonable to ask if different versions of the crosslinking process might produce significantly different cluster size distributions from percolation and , consequently , different rheological properties . gelation often occurs in the presence of a solvent and over some period of time rather than instantaneously , as in the usual percolation models . to simulate this feature , we have considered a two - species model consisting of a fraction @xmath8 of @xmath0-functional particles that are eligible to bond irreversibly to others of the same kind . the remaining particles are inert and function as a background liquid through which the gel particles and clusters diffuse . crosslinking occurs in stages : the equations of motion of all the particles are integrated forward for a fixed number of time steps between crosslinking attempts and this process is continued until the desired number of crosslinks is attained . at a critical concentration of crosslinks , @xmath2 , ( in the thermodynamic limit ) the largest cluster percolates and an amorphous solid forms . for this process one can calculate the usual static or geometrical quantities used to characterize percolating systems , _ e.g. _ , the fraction of particles on the ` infinite cluster ' , @xmath9 , the mean mass of finite clusters , @xmath10 , the fraction of samples percolating @xmath11 , the cluster size distribution @xmath12 where @xmath13 is the mass of a cluster and the radius of gyration @xmath14 where @xmath15 is the fractal dimension of the clusters . for simple percolation processes , @xmath16 , @xmath17 and these two exponents determine the others through scaling relations @xcite . here we find , at least for small @xmath8 , that the cluster size distribution , even at @xmath2 , is not well described by a simple power law . however , the other static quantities listed above do display power law behavior near @xmath2 and a standard finite - size scaling analysis provides a very good collapse of our data . moreover , the hyperscaling relation @xmath18 , where @xmath19 is the dimensionality and @xmath20 the correlation length exponent , is satisfied . this suggests that this percolation transition is fundamentally describable in terms of a fixed point with two ( at least ) relevant scaling fields . as the percolation point is approached from below , the shear viscosity diverges according to @xmath3 . in contrast to our previous work on a model without solvent , we find values of @xmath4 in the range @xmath21 as compared with @xmath6 . these results suggest that the critical behavior of transport coefficients of systems close to the gel point is nonuniversal . the structure of this article is as follows . in section [ sec : model ] we describe the present model and simulation procedures in more detail . the geometric properties of the system are discussed in section [ sec : percolation ] and the data on the shear viscosity are presented in section [ sec : visco ] . we conclude with a brief summary and discussion in section [ sec : discu ] .

we identify the critical solution in spherically symmetric collapse , find evidence for its universality , and study the approach to this critical solution in the absence of spherical symmetry . for the cases that we consider , aspherical deviations from the spherically symmetric critical solution decay in damped oscillations in a manner that is consistent with the behavior found by gundlach in perturbative calculations . our simulations are performed with an unconstrained evolution code , implemented in spherical polar coordinates , and adopting moving - puncture " coordinates .

c

1509.08730

we study critical phenomena in the gravitational collapse of a radiation fluid . we perform numerical simulations in both spherical symmetry and axisymmetry , and observe critical scaling in both supercritical evolutions , which lead to the formation of a black hole , and subcritical evolutions , in which case the fluid disperses to infinity and leaves behind flat space . we identify the critical solution in spherically symmetric collapse , find evidence for its universality , and study the approach to this critical solution in the absence of spherical symmetry . for the cases that we consider , aspherical deviations from the spherically symmetric critical solution decay in damped oscillations in a manner that is consistent with the behavior found by gundlach in perturbative calculations . our simulations are performed with an unconstrained evolution code , implemented in spherical polar coordinates , and adopting moving - puncture " coordinates .

we perform numerical simulations of radiation fluids close to the onset of black - hole formation and study critical phenomena for spherically symmetric as well as aspherical initial data . we find critical scaling for both subcritical and supercritical evolutions , and for both spherical and aspherical data . we also identify the critical solution in spherical evolutions , find evidence for its universality , and demonstrate how , in aspherical evolutions , near - critical data perform a damped oscillation around the spherical critical solution at least in the cases we consider . our results are consistent with those of gundlach @xcite , who used perturbation techniques to show that all aspherical perturbations of the critical solution decay in damped oscillations ( see also @xcite , as well as @xcite for similar calculations for scalar fields . ) matching our numerical results to damped oscillations of the form ( [ mg ] ) we find damping coefficients and frequencies that are within about 10% of those reported in @xcite . however , our results also do not rule out the existence of a growing nonspherical mode as reported by choptuik _ et.al . _ @xcite , since those modes may only appear for larger deviations from sphericity , closer to the critical point , or perhaps they may appear only for some matter models , but not for others . it is also possible that the grid resolutions adopted in this paper are not sufficient to detect this mode . we plan to further pursue this issue in future studies . in addition to studying critical phenomena in the aspherical collapse of radiation fluids , this paper serves as a demonstration that an unconstrained evolution code , using `` moving - puncture '' coordinates , is suitable for the study of critical collapse , at least for some matter models ( see also @xcite for recent discussions of this issue . ) it is a pleasure to thank steve liebling and frans pretorius for helpful conversations , and chuck evans both for conversations and for sharing numerical data from @xcite . we would also like to thank carsten gundlach for pointing us to reference @xcite , and for several very useful comments . twb would like to thank the max - planck - institut fr astrophysik in garching ( germany ) for its hospitality . this work was supported in part by nsf grant phy-1402780 to bowdoin college , and by the max - planck - institut fr astrophysik .

we study lower bounds on information dissemination in adversarial dynamic networks . the tokens need to be broadcast to all nodes through a synchronous network in which the topology can change arbitrarily from round to round provided that some connectivity requirements are satisfied . if the network is guaranteed to be connected in every round and each node can broadcast a single token per round to its neighbors , there is a simple token dissemination algorithm that manages to deliver all @xmath0 tokens to all the nodes in @xmath2 rounds . we show that for any randomized token - forwarding algorithm , @xmath6 rounds are necessary . if nodes can only send a single token per round , but we are guaranteed that the network graph is @xmath7-vertex connected in every round , we show a lower bound of @xmath8 , which almost matches the currently best @xmath9 upper bound . further , if the network is @xmath10-interval connected , a notion that captures connection stability over time , we prove that @xmath11 rounds are needed . the best known upper bound in this case manages to solve the problem in @xmath12 rounds . finally , we show that even if each node only needs to obtain a @xmath13-fraction of all the tokens for some @xmath14 $ ] , @xmath15 are still required .

i

1208.6051

we study lower bounds on information dissemination in adversarial dynamic networks . initially , @xmath0 pieces of information ( henceforth called tokens ) are distributed among @xmath1 nodes . the tokens need to be broadcast to all nodes through a synchronous network in which the topology can change arbitrarily from round to round provided that some connectivity requirements are satisfied . if the network is guaranteed to be connected in every round and each node can broadcast a single token per round to its neighbors , there is a simple token dissemination algorithm that manages to deliver all @xmath0 tokens to all the nodes in @xmath2 rounds . interestingly , in a recent paper , dutta et al . proved an almost matching @xmath3 lower bound for deterministic token - forwarding algorithms that are not allowed to combine , split , or change tokens in any way . in the present paper , we extend this bound in different ways . if nodes are allowed to forward @xmath4 tokens instead of only one token in every round , a straight - forward extension of the @xmath2 algorithm disseminates all @xmath0 tokens in time @xmath5 . we show that for any randomized token - forwarding algorithm , @xmath6 rounds are necessary . if nodes can only send a single token per round , but we are guaranteed that the network graph is @xmath7-vertex connected in every round , we show a lower bound of @xmath8 , which almost matches the currently best @xmath9 upper bound . further , if the network is @xmath10-interval connected , a notion that captures connection stability over time , we prove that @xmath11 rounds are needed . the best known upper bound in this case manages to solve the problem in @xmath12 rounds . finally , we show that even if each node only needs to obtain a @xmath13-fraction of all the tokens for some @xmath14 $ ] , @xmath15 are still required .

the growing abundance of ( mobile ) computation and communication devices creates a rich potential for novel distributed systems and applications . unlike classical networks , often the resulting networks and applications are characterized by a high level of churn and , especially in the case of mobile devices , a potentially constantly changing topology . traditionally , changes in a network have been studied as faults or as exceptional events that have to be tolerated and possibly repaired . however , particularly in mobile applications , dynamic networks are a typical case and distributed algorithms have to properly work even under the assumption that the topology is constantly changing . consequently , in the last few years , there has been an increasing interest in distributed algorithms that run in dynamic systems . specifically , a number of recent papers investigate the complexity of solving fundamental distributed computations and information dissemination tasks in dynamic networks , e.g. , @xcite . particularly important in the context of this paper is the synchronous , adversarial dynamic network model defined in @xcite . while the network consists of a fixed set of participants @xmath16 , the topology can change arbitrarily from round to round , subject to the restriction that the network of each round needs to be connected or satisfy some stronger connectivity requirement . we study lower bounds on the problem of disseminating a bunch of tokens ( messages ) to all the nodes in a dynamic network as defined in @xcite . initially @xmath0 tokens are placed at some nodes in the network . time is divided into synchronous rounds , the network graph of every round is connected , and in every round , each node can broadcast one token to all its neighbors . if in addition , all nodes know the size of the network @xmath1 , we can use the following basic protocol to broadcast all @xmath0 tokens to all the nodes . the tokens are broadcast one after the other such that for each token during @xmath17 rounds , every node that knows about the token forwards it . because in each round , there has to be an edge between the nodes knowing the token and the nodes not knowing it , at least one new node receives the token in every round and thus , after @xmath17 rounds , all nodes know the token . assuming that only one token can be broadcast in a single message , the algorithm requires @xmath18 rounds to disseminate all @xmath0 tokens to all the nodes . even though the described approach seems almost trivial , as long as we do not consider protocols based on network coding , @xmath2 is the best upper bound known . in @xcite , token - forwarding algorithm _ is defined as an algorithm that needs to forward tokens as they are and is not allowed to combine or change tokens in any way . note that the algorithm above is a token - forwarding algorithm . in a recent paper , dutta et al . show that for deterministic token - forwarding algorithms , the described simple strategy indeed can not be significantly improved by showing a lower bound of @xmath19 rounds @xcite . their lower bound is based on the following observation . assume that initially , every node receives every token for free with probability @xmath20 ( independently for all nodes and tokens ) . now , with high probability , whatever tokens the nodes decide to broadcast in the next round , the adversary can always find a graph in which new tokens are learned across at most @xmath21 edges . hence , in each round , at most @xmath21 tokens are learned . because also after randomly assigning tokens with probability @xmath20 , overall still roughly @xmath22 tokens are missing , the lower bound follows . we extend the lower bound from @xcite in various natural directions . specifically , we make the contributions listed in the following . all our lower bounds hold for deterministic algorithms and for randomized algorithms assuming a strongly adaptive adversary ( cf.section [ sec : model ] ) . our results are also summarized in which is discussed in section [ sec : related ] . [ [ multiple - tokens - per - round ] ] multiple tokens per round : + + + + + + + + + + + + + + + + + + + + + + + + + + assume that instead of forwarding a single token per round , each node is allowed to forward up to @xmath23 tokens in each round . in the simple token - forwarding algorithm that we described above , we can then forward a block of @xmath24 tokens to every node in @xmath17 rounds and we therefore get an @xmath25 round upper bound . we show that every ( randomized ) token - forwarding algorithm needs at least @xmath26 rounds . [ [ interval - connectivity ] ] interval connectivity : + + + + + + + + + + + + + + + + + + + + + + it is natural to assume that a dynamic network can not change arbitrarily from round to round and that some paths remain stable for a while . this is formally captured by the notion of interval connectivity as defined in @xcite . a network is called @xmath10-interval connected for an integer parameter @xmath27 if for any @xmath10 consecutive rounds , there is a stable connected subgraph . it is shown in @xcite that in a @xmath10-interval connected dynamic network , @xmath0-token dissemination can be solved in @xmath28 rounds . in this paper , we show that every ( randomized ) token - forwarding algorithm needs at least @xmath29 rounds . [ [ vertex - connectivity ] ] vertex connectivity : + + + + + + + + + + + + + + + + + + + + if instead of merely requiring that the network is connected in every round , we assume that the network is @xmath7-vertex connected in every round for some @xmath30 , we can also obtain a speed - up . because in a @xmath7-vertex connected graph , every vertex cut has size at least @xmath7 , if in a round all nodes that know a token @xmath31 broadcast it , at least @xmath7 new nodes are reached . the basic token - forwarding algorithm thus leads to an @xmath32 upper bound . we prove this upper bound tight up to a small factor by showing an @xmath33 lower bound . [ [ delta - partial - token - dissemination ] ] @xmath13-partial token dissemination : + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + finally we consider the basic model , but relax the requirement on the problem by requiring that every node needs to obtain only a @xmath13-fraction of all the @xmath0 tokens for some parameter @xmath34 $ ] . we show that even then , at least @xmath35 rounds are needed . this also has implications for algorithms that use forward error correcting codes ( fec ) to forward coded packets instead of tokens . we show that such algorithms still need at least @xmath36 rounds until every node has received enough coded packets to decode all @xmath0 tokens .

this bound is saturated by formulas constructed from a single majority - like gates . we show that these gates can be used to compute any boolean function reliably below the noise bound . random boolean formulas , @xmath0-noise , reliable computation .

c

1206.4851

we study noisy computation in randomly generated k - ary boolean formulas . we establish bounds on the noise level above which the results of computation by random formulas are not reliable . this bound is saturated by formulas constructed from a single majority - like gates . we show that these gates can be used to compute any boolean function reliably below the noise bound . random boolean formulas , @xmath0-noise , reliable computation .

the paper extends previous work @xcite on the reliability of computation in boolean formulas and generation of random boolean functions @xcite , by investigating the properties of formulas constructed by a random growth process whereby computing elements , primarily @xmath3-ary balanced gates , are subject to @xmath0-noise . we show that the noisy growth process is ergodic above the noise bound @xmath19 and hence the formulas generated by it are unreliable . we also show that formulas constructed from majority - like gates , which saturate this bound , can be used for computing any boolean function when @xmath75 . our earlier work , which uses methods of non - equilibrium statistical physics , suggests that the same noise bound also applies to the noisy feed - forward @xcite and recurrent boolean networks @xcite . the current analysis is restricted to reliable computation in a growth process that uses only _ balanced _ gates and produces ( without noise ) only _ one _ boolean function ; but we envisage that it can be extended to study more general scenarios of non - balanced gates and a richer distributions of boolean functions @xcite .

we study partially and totally associative ternary algebras of first and second kind . assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle . we find the sufficient and necessary condition for a ternary multiplication to induce a structure of associative binary algebra in each fiber of this vector bundle . we construct ternary algebras of cubic matrices and find four different totally associative ternary multiplications of second kind of cubic matrices . it is proved that these are the only totally associative ternary multiplications of second kind in the case of cubic matrices . we describe a ternary analog of lie algebra of cubic matrices of second order which is based on a notion of @xmath0-commutator and find all commutation relations of generators of this algebra . 17a40 , 20n10 .

i

0901.2506

we study partially and totally associative ternary algebras of first and second kind . assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle . we find the sufficient and necessary condition for a ternary multiplication to induce a structure of associative binary algebra in each fiber of this vector bundle . given two modules over the algebras with involutions we construct a ternary algebra which is used as a building block for a lie algebra . we construct ternary algebras of cubic matrices and find four different totally associative ternary multiplications of second kind of cubic matrices . it is proved that these are the only totally associative ternary multiplications of second kind in the case of cubic matrices . we describe a ternary analog of lie algebra of cubic matrices of second order which is based on a notion of @xmath0-commutator and find all commutation relations of generators of this algebra . 17a40 , 20n10 . [ firstpage ]

a ternary algebra or triple system is a vector space @xmath1 endowed with a ternary law of composition @xmath2 which is a linear mapping with respect to each its argument , and we will call this mapping a ternary multiplication or triple product of a ternary algebra @xmath1 . hence a ternary algebra is an algebra which closes under a suitable triple product . obviously any binary algebra which closes under double product can be considered as a ternary algebra if one defines the ternary multiplication as twice successively applied binary one , and in this case the ternary multiplication is generated by a binary one . however there are ternary multiplications which can not be obtained as twice successively applied binary multiplication . for instance , pure imaginary numbers or elements of grading one of a superalgebra closes under triple product . a well known example of a ternary matrix algebra is the vector space @xmath3 of @xmath4 matrices endowed with the ternary multiplication @xmath5 , where @xmath6 and @xmath7 is transpose of the matrix @xmath8 . since lie algebras play a fundamental role in physics , particular attention was given to ternary algebras when they were shown to be building blocks of ordinary lie algebras . given ternary algebra one can construct a lie algebra by using the method proposed by kantor in @xcite . this method was extended to super lie algebras in @xcite and later was applied by the same authors in @xcite to construct a gauge field theory by introducing fundamental fields associated with the elements of a ternary algebra . a skew - symmetric bilinear form is an important component in the large class of algebraic structures such as lie algebras , grassmann algebras and clifford algebras . for example , the lie brackets @xmath9:{\frak l}\times{\frak l}\to { \frak l}$ ] of a lie algebra @xmath10 is the skew - symmetric bilinear form , and the multiplication @xmath11 of a grassmann algebra @xmath12 restricted to the subspace of odd elements is the skew - symmetric bilinear form . a skew - symmetry of a bilinear form can be interpreted by means of the faithful representation of the symmetric group @xmath13 , where @xmath14 is the identity permutation , as follows : a bilinear form @xmath15 is skew - symmetric if @xmath16 . making use of this interpretation we can construct a ternary analog of a skew - symmetric bilinear form replacing @xmath17 by @xmath18 with its faithful representation by cubic roots of unity @xmath19 , i.e. @xmath20 , where @xmath14 is the identity permutation and @xmath21 are the cyclic permutations , as follows : a trilinear form @xmath22 is called @xmath0-skew - symmetric if for any elements @xmath23 of a vector space @xmath1 it satisfies @xmath24 the notion of a @xmath0-skew - symmetric form can be assumed as a basis for a ternary analog of grassmann , clifford and lie algebras . these ternary structures were developed in @xcite and applied to construct a ternary analog of supersymmetry algebra in @xcite . in this paper we study algebras with ternary law of composition . in section 2 we consider partially and totally associative ternary algebras of first and second kind . we show that a triple product of a ternary algebra induces three binary multiplications and find the sufficient and necessary condition a triple product of a ternary algebra must satisfy in order to induce the associative binary algebra . assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle . the sufficient and necessary condition a ternary multiplication must satisfy in order to induce a structure of associative binary algebra in each fiber is given in terms of the vector bundle over a ternary algebra . the relations for different kinds of partial and total associativity of a ternary algebra and induced by it binary algebras are found in the terms of the structure constants of a ternary algebra . it should be pointed out that the cohomologies of a ternary algebra of associative type are studied in @xcite . in section 3 we consider an algebraic structure consisting of two bimodules over unital associative algebras with involution and construct a ternary algebra by means of this algebraic structure . choosing different modules , unital associative algebras and homomorphisms we show that this structure allows to construct a large class of ternary algebras including a ternary algebra of rectangular matrices and ternary algebras of sections of a vector bundle over a smooth finite dimensional manifold . we end the section 3 by constructing the binary lie algebra of matrices whose entries are the elements of bimodules and unital associative algebras . it should be mentioned that there are @xmath25-ary generalizations of lie algebra which include the concepts such as @xmath25-ary algebra of lie type enclosing @xmath25-ary nambu algebra , @xmath25-ary nambu - lie algebra . the concept of @xmath25-ary hom - algebra structure generalizing previously mentioned @xmath25-ary generalizations of lie algebra is introduced and studied in @xcite . a good and detailed survey on the theory of ternary algebras can be found in @xcite . it is well known that a large class of associative algebras can be constructed by means of square matrices and their multiplication . though the rectangular matrices can be successfully used to construct a ternary algebra we think that probably more appropriate objects to construct ternary algebras are the cubic matrices . our aim in section 4 is to construct ternary algebras of cubic matrices and to study their structures . we find four different totally associative ternary multiplications of second kind of cubic matrices and prove that these are the only totally associative ternary multiplications of second kind in the case of cubic matrices . it is worth mentioning that our search for associative ternary multiplications of cubic matrices has shown that there is no totally associative ternary multiplication of first kind in the case of cubic matrices . i section 5 we describe the ternary analog of lie algebra of cubic matrices of second order by finding all commutation relations of generators of this algebra with respect to @xmath0-commutator .

we study terahertz radiation induced ratchet currents in low dimensional semiconductor structures with a superimposed one - dimensional lateral periodic potential . microscopically , the photocurrent generation is based on the combined action of the lateral periodic potential , verified by transport measurements , and the in - plane modulated pumping caused by the lateral superlattice . we show that a substantial part of the total current is caused by the polarization - independent seebeck ratchet effect . in addition , polarization - dependent photocurrents occur , which we interpret in terms of their underlying microscopical mechanisms . as a result , the class of ratchet systems needs to be extended by linear and circular ratchets , sensitive to linear and circular polarizations of the driving electro - magnetic force .

i

1101.5051

we study terahertz radiation induced ratchet currents in low dimensional semiconductor structures with a superimposed one - dimensional lateral periodic potential . the periodic potential is produced by etching a grating into the sample surface or depositing metal stripes periodically on the sample top . microscopically , the photocurrent generation is based on the combined action of the lateral periodic potential , verified by transport measurements , and the in - plane modulated pumping caused by the lateral superlattice . we show that a substantial part of the total current is caused by the polarization - independent seebeck ratchet effect . in addition , polarization - dependent photocurrents occur , which we interpret in terms of their underlying microscopical mechanisms . as a result , the class of ratchet systems needs to be extended by linear and circular ratchets , sensitive to linear and circular polarizations of the driving electro - magnetic force .

nonequilibrium spatially - periodic noncentrosymmetric systems are able to transport particles in the absence of an average macroscopic force . the directed transport in such systems , generally known as ratchet effect , has a long history and is relevant for different fields of physics . @xcite if this effect is induced by electro - magnetic radiation , it is usually referred to as photogalvanic ( or sometimes photovoltaic ) effect , particularly if breaking of spatial inversion symmetry is related to the microscopic structure of the system . @xcite blanter and bttiker @xcite have shown that one of the possible realizations of a ratchet is a superlattice ( sl ) irradiated by light through a mask of the same period but phase shifted with respect to the sl yielding a directed current due to local electron gas heating . recently , we have reported an experimental realization of this idea with some modifications . @xcite the photocurrent has been observed in semiconductor heterostructures with a one - dimensional lateral periodic potential induced by etching a noncentrosymmetric grating into the sample cap layer . hence , the in - plane modulation of the pump radiation appears not via a mask with periodic structures but due to near - field effects of terahertz ( thz ) radiation propagating through the grating . this photothermal effect , called also seebeck ratchet effect , @xcite is polarization independent and can be generated even at normal incidence of light . here , we report on the observation and study of radiation induced ratchet effects sensitive to the plane of polarization of linearly polarized light and , in the case of circularly polarized light , to the photon helicity . the theoretical analysis has enabled us to propose microscopic mechanisms of the observed circular and linear ratchet effects , and to demonstrate that they are related to the combined action of an out - of - phase periodic potential and an in - plane modulated pumping of the two - dimensional electron system ( 2des ) . the investigation of these ratchet effects has also been performed on a new set of laterally structured samples with a better controlled asymmetry . the paper is organized as follows . in the next section , we present the theory of ratchet effects stemming from the combined action of the lateral periodic potential and the in - plane pumping by the thz field modulated by the near - field diffraction . we formulate the model in terms of the classical boltzmann equation for the electron distribution function , show the position of this model with respect to other electronic ratchets , and propose a model picture to interpret the observed photocurrents . the symmetry analysis in sect . [ symmetry_analysis ] is followed by solving the kinetic equation ( sec . [ expansion ] ) and deriving equations for the seebeck ratchet current ( sec . [ seebeck ] ) and polarization - dependent photocurrents ( sec . [ polarization ] ) . in sec . [ samples ] , we describe details of the sample preparation and give a short overview of the experimental technique . the experimental results are presented and discussed in sec . [ results ] . section [ summary ] summarizes the study . m , 0.6 @xmath0 m and 0.3 @xmath0 m , respectively . ]

we study the dynamics of a local load sharing fiber bundle model in two dimensions , under an external load ( which increases with time at a fixed slow rate ) applied at a single point . due to the local load sharing nature , the redistributed load remains localized along the boundary of the broken patch .

i

1305.7124

we study the dynamics of a local load sharing fiber bundle model in two dimensions , under an external load ( which increases with time at a fixed slow rate ) applied at a single point . due to the local load sharing nature , the redistributed load remains localized along the boundary of the broken patch . the system then goes to a self - organized state with a stationary average value of load per fiber along the ( increasing ) boundary of the broken patch ( damaged region ) and a scale free distribution of avalanche sizes and other related quantities are observed . in particular , when the load redistribution is only among nearest surviving fiber(s ) , the numerical estimates of the exponent values are comparable with those of the manna model . when the load redistribution is uniform along the patch boundary , the model shows a simple mean - field limit of this self - organizing critical behaviour , for which we give analytical estimates of the saturation load per fiber values and avalanche size distribution exponent . these are in good agreement with numerical simulation results .

the fiber bundle model , since its introduction @xcite , has been studied widely as a prototypical model of failure dynamics @xcite . this discrete element model , involving disorder and non - linear dynamics ( due to thresholds ) , also enables engineers to apply it to analyse the breaking properties of real materials ( e.g , , fiber reinforced composites @xcite ) and its simplicity and occasional analytic tractability @xcite has attracted statistical physicists , specifically for its intriguing dynamical critical behaviors @xcite . there are mainly two extreme versions of this model . both the versions consider a bunch of fibers ( hooke springs ) hanging from a rigid ceiling and a platform is connected to the ends of these fibers and a load hangs from that platform . each fiber has a given limit or load - carrying threshold ( usually taken randomly from some distribution function ) , beyond which it fails . completely different behaviors are observed when the elastic property of the lower platform changes . two extreme cases arise when the platform is either absolutely rigid ( global load sharing case ) or absolutely soft ( though inextensible ; local load sharing case ) . when a fiber breaks in the former case , its extra load is equally shared by all other remaining fibers , due to rigidity of the lower platform . in the latter case , however , due to local deformation of the platform , the load of the broken fiber is only to be carried by nearest surviving neighbours ( stress concentration occurs around the failure or breaking ) . while in the global load sharing version the load at which the system completely fails scales with system size linearly , for the local load sharing case the increase is only sub - linear ( in fact @xmath0 ; @xmath1 being system size @xcite ) . the implication being , the critical load per fiber @xmath2 at which the system fails , becomes finite for the global load sharing case and goes to zero in the large system size limit for the local load sharing case . therefore the observations like divergence of relaxation time , proper scale free size distribution of avalanches , if any , are not seen in the local load sharing case ; unlike in the global load sharing version , where these can be analyzed in detail @xcite . ] .,width=264 ] however , the situation can be quite different if one makes the initial applied load localized ( at an arbitrarily chosen central site ; see fig . [ setup ] ) in a local load sharing fiber bundle model in greater than one dimension ( for one dimension the damage interface can not increase ) . let this load be increased at a slow but constant rate . initially no load is present on any fiber except for the one at the central site . as the applied load increases beyond the failure threshold of this central fiber , it breaks and the load carried by it is redistributed among its nearest neighbours and so on . here we study two versions of the model . in model i : in general , whenever a fiber breaks , the load carried by that fiber is redistributed equally among its nearest surviving neighbour(s ) . in this way , the fibers which are newly exposed to the load , say , after an avalanche , have a relatively low load compared to the ones which are accumulating load shares from the earlier failures and are still surviving . as we shall see later , this helps in maintaining a compact structure of the cluster or patch of the broken fibers . this local force redistribution is justified from the point of view that the newly exposed fibers are presumably further away from the point of loading and therefore have to carry a smaller fraction of the load at the original central site . the fibers on the perimeter of the failed or damaged region , which together are carrying the entire load , increase in number with time . hence the load per fiber decreases during an ongoing avalanche , which is assumed to be a much faster process compared to the external load increase . however , as the load on the bundle increases at a constant ( but slow ) rate , the load per fiber along the boundary will tend to increase . eventually , a dynamically stable state will occur when the load per fiber will fluctuate around a stable value and the system has reached a self - organized state . in this dynamical state , failure of fibers in the process of avalanches is seen to have a scale free size distribution , suggesting the state to be a self - organized critical one . we study this model numerically to estimate the avalanche size and other exponent values . these values are close to those found for stochastic sandpile model or manna model , within our numerical accuracies . we then study a simpler version of this model , model ii , in which the load of a broken fiber is equally shared by all the surviving fibers that have atleast one broken neighbour , i.e. it is equally distributed along the boundary of the broken or damaged patch . due to the fact that local fluctuations are ignored in the process of load redistribution , this version is analytically tractable using a mean - field like approach and the numerical results compare well . as can be seen from fig . [ config1 ] , this version of the fiber bundle model ensures an advancing interfacial ( mode - i ) fracture . this topic is widely studied over decades both theoretically and experimentally ( see @xcite for a recent review ) . particularly , in the plexiglas experiment @xcite two plates were taken and disorder was introduced by sandblasting and then were joined together , making a transparent block with an easy plane . interfacial ( mode - i ) fracture was then studied with it . a similar situation with this model would arise if one of the plates ( or softer surface ) could be pulled from the middle . the advantage of the present situation for experiment and in particular for simulations is that one is free from the need of introducing a cut - off scale by hand as dissipation comes naturally in this model with the increase of effective system size with dynamics . this is a more desireable situation since artificial dissipation scales often cause problems in estimating the exponent values , which had to avoided by measuring a different quantity instead @xcite . below we first present the numerical results for the nearest neighbour load sharing model ( model i ) and then go over to the simpler version of uniform load sharing along boundary ( model ii ) , giving the analytical estimates for the later and comparing them with numerical results .

we study the evolution of spectra of waves that are generated in the convection zone and propagate upward into the photosphere , where we compare the simulated acoustic spectra with the spectrum observed in an fe i line . although there is no pronounced 3 min component in the spectra generated in the convection zone , there are dominant 3 min features in the theoretical spectra , in agreement with the observed spectrum . we interpret the occurrence of the 3 min features as the response of the solar atmosphere to the acoustic waves which shifts high frequency wave energy to low frequencies .

i

astro-ph9704067

we study the evolution of spectra of waves that are generated in the convection zone and propagate upward into the photosphere , where we compare the simulated acoustic spectra with the spectrum observed in an fe i line . although there is no pronounced 3 min component in the spectra generated in the convection zone , there are dominant 3 min features in the theoretical spectra , in agreement with the observed spectrum . we interpret the occurrence of the 3 min features as the response of the solar atmosphere to the acoustic waves which shifts high frequency wave energy to low frequencies . we also find qualitative agreement for the acoustic power between the wave simulations and the observations .

in the present series of papers we investigate the response of the solar atmosphere to acoustic wave excitations . in paper i ( sutmann & ulmschneider 1995a ) we studied the excitation and propagation of small - amplitude ( linear ) adiabatic waves , and in paper ii ( sutmann & ulmschneider 1995b ) , the excitation of large - amplitude adiabatic waves which form shocks . similar numerical and analytical work was carried out by kalkofen et al . these studies show that , for monochromatic or pulse excitation , the solar atmosphere responds with oscillations in an added band of frequencies generally above @xmath0 mhz ( period @xmath1 min ) and that , depending on the type of excitation , these 3 min oscillations usually decay after some time . because both the monochromatic and pulse excitation happen to an atmosphere considered to be initially at rest , these 3 min oscillations could be seen as decaying transients . yet paper i also showed that even with very small amplitude ( linear ) excitations , for the stochastic wave case , the generated 3 min type oscillations did not decay as in a switch - on effect , but were perpetually regenerated due to the stochastic nature of the excitation ( cf . 14 of paper i ) . in paper ii , in addition to monochromatic or pulse excitations , perturbations by four different types ( gaussian , box , exponential and stochastic ) of acoustic wave spectra were studied . it was found that these perturbations led to 3 min oscillations which over the time span of the calculations ( @xmath2 s ) did not decay . below we will refer to the 3 min oscillations near the acoustic cutoff as `` resonance oscillations '' . the 3 min oscillations are also a prominent observational signal in the outer solar atmosphere . in the quiet solar atmosphere they are seen in the interior of supergranulation cells : in the ca ii h and k lines , in h@xmath3 and in the ca ii infrared triplet lines as well as in other , lower - lying photospheric and chromospheric lines . for detailed reviews and discussions of the 3 min oscillations see deubner ( 1991 ) , fleck & schmitz ( 1991 ) , rutten & uitenbroek ( 1991 ) , rossi et al . ( 1992 ) , carlsson & stein ( 1994 ) , rutten ( 1995 , 1996 ) , steffens et al . ( 1995 ) and al ( 1996 ) . the analytical work of paper i will be extended to include the excitation of linear , adiabatic waves by a pulse and by acoustic spectra ( sutmann et al . 1997 ; paper iii ) . for similar analytical work see schmitz & fleck ( 1995 ) . recently ( theurer et al . 1997 ; paper iv ) we investigated the excitation of the solar atmosphere by large - amplitude , non - adiabatic acoustic spectra . in paper ii the excitations with acoustic spectra could not be carried out over extended times because due to shock formation and shock heating the adiabatic waves generate secular changes of the atmospheric structure with temperatures which perpetually rise with time . the non - adiabatic treatment in paper iv avoids this problem . here the excitation leads to a dynamical equilibrium between shock heating and radiative cooling , which results in a time - independent mean atmosphere , where the wave excitation could now be carried out up to arbitrarily large times . as already suspected in paper ii these calculations showed that the 3 min type resonance oscillations near the acoustic cutoff now remain a permanent , non - decaying feature of the wave spectrum and that these 3 min `` resonances '' became more and more prominent with height . it was found that regardless of the initial shape of the acoustic wave spectrum ( gaussian or stochastic ) , introduced at @xmath4 km into the atmosphere , the resulting spectrum at a height of @xmath5 km consisted almost exclusively of components in the 3 min band . moreover , after about 500 s the spectra at a given height no longer showed any time dependence . in an attempt to simulate the observed 3 min oscillations , in particular , those observed in the k@xmath6 bright points in the interior of supergranulation cells , carlsson & stein ( 1994 , 1995 ) excited the oscillations using the observed velocity variation of a low - lying fe i line ( lites et al . they obtained good agreement of observed and simulated h line profiles as well as of the time delay between the oscillations at the fe line and the h line . similar work by cheng & yi ( 1996 ) but employing a different numerical code has recently been carried out . they introduced high - frequency acoustic wave power in addition to the observed spectrum and found that high - frequency waves did not contribute to the 3 min band at chromospheric heights , concluding that the pronounced power in the 3 min band must already be present at the site of generation of the waves . this claim has to be viewed with some caution since their code , which is different from that of carlsson & stein , does not have an adaptive mesh capability and thus does not allow the treatment of shocks and hence the limiting shock strength behaviour and the merging of shocks , that is , of effects we find critical for the generation of power near the acoustic cutoff from high - frequency waves . however , the question remains open whether the 3 min oscillations are introduced into the acoustic spectrum at the height where the waves are generated , or added later by the atmosphere . in recent years it has become clear that the acoustic energy generation in the convection zones of late - type stars is strongly tied to the kolmogorov turbulent energy spectrum , which is now well supported for the solar convection zone by numerical simulations ( cattaneo et al . 1991 ) as well as by high - resolution observations ( muller 1989 , nesis et al . for a discussion see musielak et al . ( 1994 ) . on the basis of this turbulent energy spectrum , the wave generation calculations using the lighthill - stein theory of sound generation produce acoustic spectra that are smooth and have a single broad peak in the 1 min band , i.e. , most of the acoustic power is found at frequencies much higher than the 3 min band ( figs . 3 and 4 ) . this is due to the property of the kolmogorov turbulent cascade in its inertial range ( discussed below ) of extending to frequencies of at least 100 hz under adiabatic conditions when viscosity limits the cascade , or to frequencies of at least 300 mhz when radiative exchange between adjacent bubbles limits the cascade . thus one must reconcile the theory showing the generation of a high - frequency wave spectrum without a noticeable 3 min feature with the observations which show a low - frequency spectrum dominated by the 3 min band . the aim of the present work is to find an answer to this problem . a possible answer is suggested by the results of the previous papers of this series and by the work of kalkofen et al . ( 1994 ) showing that 3 min oscillations can be the response of the atmosphere to wave excitations . we will argue that the 3 min component is a feature that is added by the atmosphere to the acoustic spectrum by shifting power from high frequencies to low frequencies during the propagation of the waves from the convection zone to the photosphere . in our previous work we found two ways by which such a shift is accomplished . 14 of paper i shows that already for a wave excitation with very small amplitude , resulting from an acoustic spectrum with a stochastically changing wave period , one obtains 3 min type resonance oscillations which continuously get regenerated . the second way , as shown in paper iv , is that acoustic wave spectra with larger amplitudes lead to shock formation and shock merging , which generates resonance oscillations . in both cases the stochastic nature of the acoustic wave spectrum leads to oscillations which persist in time . note that in our computations it is necessary to distinguish between the quiet interior of supergranulation cells and the k@xmath6 bright points that are embedded in it . the work reported here concerns mainly the oscillations in the quiet background of the cell interior and not those in the k@xmath6 bright points ( cf . kalkofen 1996 ) , where the periods tend to be somewhat longer than those found in this investigation . in order to test the hypothesis of the transfer of power from high to low frequencies we have made a number of simplifications , such as assuming adiabatic conditions for the atmospheric wave calculations and neglecting effects of the earth s atmosphere as well as instrumental effects when comparing our results with the observations . these simplifications will be removed in subsequent work . section 2 outlines the numerical methods , sect . 3 presents the results and sect . 4 gives the conclusions .

we also clarify the topological structure of the imaginary part in lovelock gravity . these include cylindrical slabs spanning the exterior of a stationary black hole spacetime , `` maximal diamonds '' in various symmetric spacetimes , as well as local near - horizon regions . in the first setup ,

c

1305.2207

we study the imaginary part of the lorentzian gravitational action for bounded regions , as described in arxiv:1301.7041 . by comparing to a euclidean calculation , we explain the agreement between the formula for this imaginary part and the formula for black hole entropy . we also clarify the topological structure of the imaginary part in lovelock gravity . we then evaluate the action s imaginary part for some special regions . these include cylindrical slabs spanning the exterior of a stationary black hole spacetime , `` maximal diamonds '' in various symmetric spacetimes , as well as local near - horizon regions . in the first setup , the black hole s entropy and conserved charges contribute to the action s imaginary and real parts , respectively . in the other two setups , the imaginary part coincides with the relevant entropy .

in this paper , we expanded the study of the imaginary part of the lorentzian gravitational action . the surprising results of the brute - force calculations in @xcite were explained more abstractly , through a relation with euclidean geometries . we also turned around the discussion in @xcite concerning the reality of the hamiltonian , using it to _ explain _ the dependence of @xmath4 in lovelock gravity on only the intrinsic metric of the flip surfaces . we then evaluated @xmath4 for three classes of physically interesting regions . for spacelike - bounded regions describing time evolution outside a stationary black hole ( section [ sec : gh ] ) , we found that the black hole s entropy and conserved charges enter @xmath4 and @xmath7 , respectively . we also found that the `` transition probability '' @xmath217 is inversely proportional to the number of microstates @xmath9 implied by the black hole s entropy . it would be interesting to see if this can be fleshed out into a more detailed physical picture . for null - bounded `` maximal diamonds '' in various symmetric spacetimes , we found that @xmath4 coincides with the entropy that is usually associated to each spacetime . this is an intriguing pattern that calls for a deeper understanding . in particular , it can be taken to support the notion @xcite that null boundaries are best suited for the study of quantum gravity . standard de - sitter space poses an exception to the @xmath200 pattern , which is resolved if one considers the `` elliptical '' de - sitter space ds@xmath5 instead . if one takes @xmath4 seriously as a window into quantum gravity , this may serve as yet another argument favoring ds@xmath5 over ds as the more appropriate spacetime asymptotics . finally , we discussed regions composed of small 1 + 1d diamonds times codimension-2 surfaces @xmath40 . for all such regions , @xmath4 evaluates to the entropy as calculated from @xmath40 . we proposed a physical interpretation for this calculation in two setups : a near - bifurcation - surface region in a stationary black hole spacetime and a near - event - horizon region for a non - stationary black hole . in the future , it would be interesting to try and relate @xmath4 to the concept of entanglement entropy , both in ads / cft @xcite and more generally in quantum field theory . on a more fundamental note , one would like to address the conceptual issues that arise from the non - unitarity of amplitudes @xmath6 for complex @xmath0 . this may serve as a concrete starting point on the broader mystery of the physical content of quantum gravity in finite regions .

however , there exist only few exact results ensuring the existence of itinerant ferromagnetism @xcite . among them , the most renowned is nagaoka s theorem @xcite , which assert that the saturated ferromagnetic state is the unique ground state when one hole is doped on the half - filled hubbard model with infinite @xmath0 coulomb repulsion . , we further characterize this kinetic antiferromagnetism and we describe its microscopic origin , analyzing generic kinetically frustrated electronic models for which , in the limit of infinite coulomb repulsion and one hole doped away half - filling , the nagaoka s theorem is not valid . in particular , we find in both cases that the ground state has antiferromagnetic order : @xmath2 nel order for the triangular lattice and the usual @xmath5 nel order for the square lattice . _ static magnetic structure factor . @xmath29 exhibits two sharp maxima at the momenta @xmath30 and @xmath31 corresponding to a three - sublattice @xmath2 nel order . as note that as we are working in the extremely correlated limit , where the exchange interaction driven by _ virtual _ kinetic processes vanishes , @xmath33 , the magnetic order can only have its origin in the hole motion . on the other hand , as the triangular heisenberg model has the same @xmath2 nel order in its ground state @xcite , for finite @xmath0 ( @xmath34 ) and low doping , there is a synergy between _ real _ and _ virtual _ kinetic processes , that leads to the strengthening of the @xmath2 nel order respect to the half - filled case @xcite . for negative @xmath11 ( not shown in the figure ) if we relax the infinite @xmath0 condition , the kinetic exchange interactions would favor a collinear antiferromagnetic order , characterized by the magnetic wave vector @xmath38 or @xmath39 , so there will be a competition between _ real _ and _ virtual _ kinetic processes , resulting in magnetic incommensuration and phase separation @xcite . in agreement with nagaoka s theorem , for @xmath40 the ground state is the saturated ferromagnet . for ( a ) @xmath3 triangular hubbard ( triangles ) and heisenberg ( circles ) models , without magnetic field ( open symbols ) and with a magnetic field @xmath22 applied to one sublattice ( solid symbols ) ; ( b ) @xmath3 square hubbard model with first- and second - neighbor hopping terms ( @xmath41 ) , without magnetic field ( open squares ) and with a magnetic field @xmath42 applied to one sublattice ( solid squares ) . dashed lines : classical local magnetization . insets : intensity plot @xmath29 for the ( a ) triangular and ( b ) square models . [ fig1](a ) , @xmath46 for finite size clusters does not take _ exactly _ the classical value . fig . [ fig1](b ) shows @xmath46 for the hubbard model on the square lattice , with ( solid squares ) and without ( open squares ) an applied uniform magnetic field in one sublattice . we remark that , at the mean field level , the 120@xmath89 nel ( @xmath5 nel ) state is degenerate with the ferromagnetic one in the triangular case with @xmath85 ( square lattice with @xmath90 ) . p. fazekas , _ electron correlation and magnetism _ ( world scientific , singapore , 1999 ) . y. nagaoka , phys matter * 5 * , l135 ( 1993 ) . to compare similar results between the mean field @xmath46 computed for the two dimensional triangular lattice , and dmrg computations done in clusters with @xmath17 legs , we use the prescription given in ref .

r

1312.6672

we study the infinite @xmath0 hubbard model with one hole doped away half - filling , in triangular and square lattices with frustrated hoppings that invalidate nagaoka s theorem , by means of the density matrix renormalization group . we find that these kinetically frustrated models have antiferromagnetic ground states with classical local magnetization in the thermodynamic limit . we identify the mechanism of this kinetic antiferromagnetism with the release of the kinetic energy frustration as the hole moves in the established antiferromagnetic background . this release can occurs in two different ways : by a non - trivial spin - berry phase acquired by the hole or by the effective vanishing of the hopping amplitude along the frustrating loops . itinerant magnetism has proved to be an elusive subject in condensed matter physics , since itinerant and localized aspects of electrons need to be taken into account on equal footing . the single - band hubbard model , originally proposed to describe metallic ferromagnetism @xcite , has also been associated with antiferromagnetism of kinetic exchange origin close to half - filling . while _ virtual _ kinetic processes favor antiferromagnetism , it is a rule of thumb to link _ real _ kinetic processes with ferromagnetism @xcite . however , there exist only few exact results ensuring the existence of itinerant ferromagnetism @xcite . among them , the most renowned is nagaoka s theorem @xcite , which assert that the saturated ferromagnetic state is the unique ground state when one hole is doped on the half - filled hubbard model with infinite @xmath0 coulomb repulsion . furthermore , a connectivity condition must be fulfilled for the validity of nagaoka s theorem : the sign of the hopping amplitudes around the smallest closed loop of the lattice must be positive , otherwise the hole kinetic energy will be frustrated and the saturated ferromagnetic state will no longer be the ground state . kinetic energy frustration is a quantum mechanical phenomenon without classical analog , easily understood in certain tight - binding models where an electron can not gain the full kinetic energy @xmath1 due to quantum interferences @xcite . this kind of frustration has been considerably less studied than the magnetic one , although recent works indicate that its effects may lead to rich physics , such as , robust superconductivity in strongly repulsive fermionic system @xcite and spontaneous time - reversal symmetry breakings @xcite , among others @xcite . in a seminal work , haerter and shastry @xcite have found a @xmath2 antiferromagnetic nel order as the ground state of the @xmath3 triangular lattice hubbard model when the hole motion is frustrated ( @xmath4 ) , uncovering a new mechanism for itinerant magnetism . in this letter , we further characterize this kinetic antiferromagnetism and we describe its microscopic origin , analyzing generic kinetically frustrated electronic models for which , in the limit of infinite coulomb repulsion and one hole doped away half - filling , the nagaoka s theorem is not valid . in particular , we study the ground state of two hubbard models : one on the triangular lattice with a positive hopping term , and the other on the square lattice with positive second - neighbor hopping term . using the density matrix renormalization group ( dmrg ) @xcite , we find in both cases that the ground state has antiferromagnetic order : @xmath2 nel order for the triangular lattice and the usual @xmath5 nel order for the square lattice . surprisingly , we find that the local staggered magnetization becomes classical ( saturated ) in the thermodynamic limit . this result can be thought as the almost - perfect antiferromagnetic counterpart of the nagaoka ferromagnetism ; the difference is that , as the local staggered magnetization does not commute with the @xmath6 invariant hubbard hamiltonian , classical antiferromagnetic states can not be the exact eigenvectors for finite lattices . based on a simple slave - fermion mean field @xcite , we propose a mechanism responsible for the kinetic antiferromagnetism : if the hole were moving on a ferromagnetic background on these lattices , its kinetic energy would be frustrated . however , when moving in certain antiferromagnetic background , the hole can release its kinetic energy frustration by , depending on the system , acquiring a non - trivial spin berry phase or having zero hopping amplitude along frustrating loops . as the coulomb repulsion is infinite , no exchange interaction exist , being the stabilization of antiferromagnetism of pure kinetic origin . _ hubbard model and dmrg . _ we study the hubbard model , @xmath7 where we use the usual notation , and @xmath8 denotes pairs of neighbor sites connected by the hopping parameters @xmath9 . from the outset , we take @xmath10 we study the hubbard model on two lattices with frustrated kinetic hole energy : the triangular lattice with positive @xmath11 and the square lattice with nearest @xmath12- and positive next - nearest neighbor @xmath13 hopping terms . in the latter case , we choose @xmath14 as a generic point with kinetic frustration . we take @xmath15 as the energy unit . to solve the hubbard model we apply dmrg on ladders of dimension @xmath16 ( see fig . 1 in @xcite ) , with up to @xmath17 legs and @xmath18 rungs . we choose clusters that are compatible with the antiferromagnetic orders found in this work . this means that we take an even number of legs , @xmath19 , for both lattices , and an even ( multiple of 3 ) @xmath20 for the square ( triangular ) lattice . we consider cylindrical boundary conditions with periodic wrapping in the rung direction , and open boundary conditions along the legs . comparing results obtained with clusters of different number of legs , we find that the clusters with @xmath17 give a correct description of the two - dimensional systems . a similar conclusion has been reached previously on square ladders @xcite . we have kept the truncation error less than @xmath21 , assuring that errors of the dmrg are smaller than symbol sizes in each figure . we have also consider the inclusion of a weak pinning magnetic field ( @xmath22 ) acting only on a single site , at the lower left - hand end of the clusters @xcite , or on one magnetic sublattice . in previous works @xcite , the purpose of the small magnetic field has been to pin possible magnetic order , in order to reduce the computational efforts by computing the average value of the local spin instead of correlation functions , optimizing the truncation error . in our work , the inclusion of the weak magnetic field will allow us to highlight the classical character of the ground states . _ static magnetic structure factor . _ to detect the existence of magnetic order , we compute the static magnetic structure factor with dmrg for both lattices , @xmath23 where @xmath24 is the number of sites in the cluster , and @xmath25 run over all sites . in the inset of fig . [ fig1](a ) we show an intensity plot of @xmath26 for a triangular cluster with @xmath17 legs and @xmath27 sites . for positive @xmath28 @xmath29 exhibits two sharp maxima at the momenta @xmath30 and @xmath31 corresponding to a three - sublattice @xmath2 nel order . as these peaks diverge with increasing cluster size , the ground state exhibits a long - range order @xmath2 magnetic pattern . this result has been obtained previously by haerter and shastry@xcite , diagonalizing an effective spin hamiltonian on smaller clusters , up to @xmath32 sites . note that as we are working in the extremely correlated limit , where the exchange interaction driven by _ virtual _ kinetic processes vanishes , @xmath33 , the magnetic order can only have its origin in the hole motion . on the other hand , as the triangular heisenberg model has the same @xmath2 nel order in its ground state @xcite , for finite @xmath0 ( @xmath34 ) and low doping , there is a synergy between _ real _ and _ virtual _ kinetic processes , that leads to the strengthening of the @xmath2 nel order respect to the half - filled case @xcite . for negative @xmath11 ( not shown in the figure ) the magnetic structure factor has a sharp peak at @xmath35 , while it vanishes for all other momenta . this result correspond to a fully polarized ferromagnetic ground state , as predicted by the nagaoka s theorem . in the inset of fig . [ fig1](b ) we show the magnetic structure factor for the @xmath3 hubbard model on square clusters with @xmath17 legs and @xmath36 sites , for @xmath14 . here , there is a marked peak for the magnetic wave vector @xmath37 , corresponding to the usual two - sublattice nel order . if we relax the infinite @xmath0 condition , the kinetic exchange interactions would favor a collinear antiferromagnetic order , characterized by the magnetic wave vector @xmath38 or @xmath39 , so there will be a competition between _ real _ and _ virtual _ kinetic processes , resulting in magnetic incommensuration and phase separation @xcite . in agreement with nagaoka s theorem , for @xmath40 the ground state is the saturated ferromagnet . for ( a ) @xmath3 triangular hubbard ( triangles ) and heisenberg ( circles ) models , without magnetic field ( open symbols ) and with a magnetic field @xmath22 applied to one sublattice ( solid symbols ) ; ( b ) @xmath3 square hubbard model with first- and second - neighbor hopping terms ( @xmath41 ) , without magnetic field ( open squares ) and with a magnetic field @xmath42 applied to one sublattice ( solid squares ) . dashed lines : classical local magnetization . insets : intensity plot @xmath29 for the ( a ) triangular and ( b ) square models . darker color indicates larger magnetic structure factor . @xmath43 and @xmath5 for the triangular and square lattice , respectively.,scaledwidth=46.0% ] _ local magnetization . _ once computed the magnetic structure factor , we can get the order parameter for the antiferromagnetic order , the local staggered magnetization @xmath44 @xcite , where @xmath45 denotes the magnetic sublattices . the cluster - size dependence of @xmath46 for the @xmath3 triangular hubbard model is shown in fig . [ fig1](a ) ( open triangles ) , along with the local magnetization of the triangular heisenberg model ( open circles ) for comparison . the dashed line indicates the classical local magnetization , @xmath47 corrected by the presence of the hole uniformly distributed ( as is confirmed by the dmrg calculations ) . surprisingly , @xmath46 is very close to the classical value , even for small clusters , and it reaches this value in the thermodynamic limit ( @xmath48 ) . on the other hand , in the heisenberg case , strong zero - point quantum fluctuations lead to a drastic reduction of @xmath46 @xcite , and due to the quasi - one dimensional character of the clusters , @xmath46 extrapolates to 0 @xcite . one possible reason for the classical character of the magnetic order is that the effective spin model , obtained after integrating the hole degree of freedom , contains effective long - range interactions ( see eq . 3 in ref @xcite ) that may favor the classical ordering , like in the lieb - mattis model @xcite . as we can see in fig . [ fig1](a ) , @xmath46 for finite size clusters does not take _ exactly _ the classical value . the hubbard hamiltonian is @xmath6 spin rotational invariant and it does not commute with the antiferromagnetic order parameter ; consequently , its ground state can not break this symmetry for finite systems . instead , it is expected that the finite size ground state is a singlet , and that , only in the thermodynamic limit , there can be a spontaneous @xmath6 symmetry breaking driven by the collapse of many low lying states onto the ground state @xcite . the existence of a tower of states for the @xmath3 triangular hubbard model has been confirmed in ref . @xcite . we argue that the small departure of the order parameter from the classical value is related with the singlet character of the finite size ground state , and not with zero - point quantum fluctuations that reduce the order parameter like in quantum antiferromagnets . pictorially , the finite size ground state can be thought as a linear combination of several classical antiferromagnetic states lying in different planes . to strengthen this picture , we apply a small uniform pinning magnetic field , @xmath49 in one sublattice only ( if we apply the magnetic field in only one site , the difference is quantitatively small , of only a few percent ) . fig . [ fig1](a ) shows @xmath46 for the hubbard model with the magnetic field applied ( solid triangles ) and the same for the triangular heisenberg model ( solid circles ) . it can be seen that in the hubbard model now @xmath46 becomes classical , because the magnetic field select one of the classical orders that compose the finite - size ground state . on the other hand , the magnetic field increases @xmath46 of the heisenberg model , but there remains strong zero - point quantum fluctuations . fig . [ fig1](b ) shows @xmath46 for the hubbard model on the square lattice , with ( solid squares ) and without ( open squares ) an applied uniform magnetic field in one sublattice . the same behavior as in the triangular case is found : the local magnetization is close to the classical values when @xmath50 , being enough to apply a small @xmath22 to pin one classical magnetic ground state . _ energy scale._for the triangular lattice , the extrapolated ground state energy is @xmath51 , in agreement with the value obtained in @xcite ( @xmath52 ) , while for the square lattice the extrapolated value is @xmath53 . in order to quantify the energy scale of the kinetic antiferromagnetism , we match the effect of the hole motion to an effective nearest - neighbor antiferromagnetic heisenberg interaction , @xmath54@xcite , resulting @xmath55 , this is the energy difference _ per site _ between the fully - polarized ferromagnetic state and the antiferromagnetic ground states . we have found that @xmath56 ( @xmath57 ) for the triangular ( square ) lattice , for large @xmath58 _ release of the kinetic frustration . _ now we trace back the origin of the kinetic antiferromagnetism by means of a comprehensive mean field approximation . to this end , we use the slave - fermion schwinger - boson representation of the projected electronic degree of freedom in the @xmath59 model , the strong - coupling limit of the hubbard model . here , we give a brief description of the mean field approach ( see supplemental material for the details @xcite ) . in this representation , the projected electronic operator is written as @xmath60 a composition of a schwinger boson @xmath61 , that account for the spin degrees of freedom , and a spinless slave fermion @xmath62 , that describes the charge sector . this representation is replaced in the @xmath59 hamiltonian , resulting @xmath63 where we have defined the @xmath6 invariant operator @xmath64 related with ferromagnetic correlations between sites @xmath65 and @xmath66 @xcite , while @xmath67 describes the hole hopping amplitude . @xmath68 is a bosonic term that represents the spin fluctuations due to the heisenberg term , and it vanishes when @xmath69 @xcite . after a mean field decoupling , we get @xmath70 where the hole kinetic energy dispersion takes the form @xmath71 ( @xmath72 are the relative position vectors of the sites connected by @xmath73 ) . in the one hole case , the ground state energy of the system corresponds to the bottom of @xmath74 . this energy dispersion is tight - binding like , with the hopping terms @xmath73 renormalized by the ferromagnetic mean - field parameter @xmath75 @xmath76 . the presence of the @xmath77 s parameters has two consequences : _ i _ ) on one hand , the hopping terms are renormalized as in the double - exchange mechanism @xcite , @xmath78 where @xmath79 is the angle between the spins separated by vector @xmath80 ; if the spins are antiparallel @xmath81 vanishes ; _ ii _ ) on the other hand , the renormalization can give rise to a non - trivial spin berry phase for non - collinear orders , encoded in the @xmath82 s signs and associated with the solid angle subtended by the spins on a closed loop @xcite . when the system is kinetically frustrated , these two features of the hopping renormalizations act releasing the hole kinetic energy frustration as the hole moves through certain antiferromagnetic patterns . now we describe how this release works in the triangular and square lattice cases . _ triangular lattice : _ for the ferromagnetic state all @xmath83 parameters are equal to @xmath84 , consequently the hole motion is frustrated for @xmath85 . on the other hand , in a @xmath2 nel order the parameters @xmath86 become negative and the others remain positive since @xmath87 @xcite . these negative @xmath77 s turn upside down the hole dispersion , releasing the kinetic frustration of the hole motion . notice that the flux of the @xmath77 s parameters in a closed loop is the solid angle subtended by the magnetic order , and consequently it is associated with the spin - berry phase detected by the hole ( see supplemental material for details @xcite ) . _ square lattice : _ in this case , when @xmath88 the hole motion in a ferromagnetic state is frustrated . however , in the @xmath5 nel order the vanishing of the effective first - neighbor hopping terms , due to their antiparallel spins @xcite , removes the frustrating loops , releasing the kinetic frustration . we remark that , at the mean field level , the 120@xmath89 nel ( @xmath5 nel ) state is degenerate with the ferromagnetic one in the triangular case with @xmath85 ( square lattice with @xmath90 ) . the reason for this degeneracy is that , although the hole motion through the antiferromagnetic states is not frustrated , there is a hole dispersion bandwidth reduction due to the hopping renormalizations @xcite . so , strictly speaking , the mean field numerics does not show the stabilization of the kinetic antiferromagnetism over the nagaoka s state . however , after considering the combined effects of quantum interference and strong - correlation physics beyond the mean field approximation ( like our dmrg predictions ) , the actual kinetic antiferromagnetism emerges . despite the mean field discrepancy , we strongly emphasize that the mean field approach allows to find one of the main ingredient of the kinetic antiferromagnetism , that is , the release of the kinetic frustration . using the insight we gained from the mean field approach , we can predict the appearence of this novel kinetic antiferromagnetism phenomenon in other kinetically frustrated systems , like the anisotropic triangular lattice and the @xmath91 square lattice with @xmath92 preliminary dmrg results show the ubiquity of kinetic antiferromagnetism in these systems ( see supplemmental material @xcite ) . furthermore , we remark that the kinetic antiferromagnetism mechanism is completely different to the exchange one , and in general the ground state selected by this itinerant mechanism does not have to be necessarily the classical ground state of the related heisenberg model . in this context , in particular , the @xmath3 kagom hubbard model with one hole doped and @xmath93 may be a promising candidate for the search of unconventional kinetic antiferromagnetism physics @xcite . finally , if we lift the condition of infinite @xmath94 it is possible to study the synergy between _ real _ and _ virtual _ kinetic processes , in order to highlight the crossover from the heisenberg regime , governed by the exchange interactions , to the kinetic antiferromagnetic one , governed by the kinetic energy . in fig . [ fig2 ] we show the local magnetization of the ground state @xmath2 nel order of the triangular @xmath59 model predicted by the mean field approach and dmrg @xcite , as a function of @xmath95 for doping @xmath96 . there is fairly good qualitative agreement between both methods , and for larger values of @xmath95 the order parameter is close to the heisenberg value calculated within each approach , @xmath97 @xcite and @xmath98 @xcite , while @xmath46 increases with decreasing @xmath95 , until it reaches the classical value for @xmath99 in both methods . of the triangular @xmath59 model as a function of @xmath95 for doping @xmath100 the solid line corresponds to the mean field @xmath46 , the open circles to the dmrg results , the dashed line is to aid the eye . the arrows indicate the @xmath33 and heisenberg @xmath46 limits.,scaledwidth=46.0% ] _ conclusions . _ using the density matrix renormalization group , we find that classical antiferromagnetic ground states can be realized in extremely correlated electronic systems with frustrated kinetic energy . in particular , we study the @xmath3 hubbard model , with one hole doped away half filling , on the positive @xmath11 triangular lattice , and on the square lattice with positive second neighbor hoppings . we also propose a mechanism responsible for this kinetic antiferromagnetism , that is , the release of the kinetic energy frustration driven by , depending on the system , the spin - berry phase acquired by the hole while moving around an antiferromagnetic background , or the vanishing of the effective hopping amplitude along the frustrating loops . this new mechanism for itinerant antiferromagnetism is quite ubiquitous for one hole doped away half filling in kinetically frustrated lattices @xcite , being also relevant in more general situations , like finite @xmath0 regime and low doping cases , as the mean - field results seem to indicate @xcite . it is worth noticing that recent experiments @xcite were able to generate gauge fields which induce frustrated motion of ultracold bosons in triangular optical lattices , opening up the possibility to observe related kinetic antiferromagnetism phenomena . we acknowledge useful discussions with c. d. batista and d. j. garca . this work was partially supported by pip conicet grants 0160 and 0392 . 99 m. c. gutzwiller , phys . rev . lett . * 10 * , 159 ( 1963 ) ; 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p.w . anderson and h. hasegawa , phys . rev . * 100 * , 675 ( 1955 ) . a. eckardt , p. hauke , p. soltan - panahi , c. becker , k. sengstock , and m. lewenstein , europhys . lett . * 89 * , 10010 ( 2010 ) ; j. struck , c. lschlger , r.l . targat , p. soltan - panahi , a. eckardt , m. lewenstein , p. windpassinger , and k. sengstock , science * 333 * , 996 ( 2011 ) . c. j. gazza and h. a. ceccatto , j. phys . : condens . matter * 5 * , l135 ( 1993 ) . to compare similar results between the mean field @xmath46 computed for the two dimensional triangular lattice , and dmrg computations done in clusters with @xmath17 legs , we use the prescription given in ref . @xcite , about choosing the optimal cluster shapes . in the case of 6 legs , this cluster is the @xmath103 ladder .

nel , ferromagnetic , and the collinear stripe order , for @xmath33 and @xmath4 in the triangular lattice.,width=264 ] for @xmath33 , the @xmath150 factors vanish identically , consequently hamiltonian ( [ tjk ] ) is already diagonal and there is no need of a bogoliubov transformation . instead , it is imperative to condense the schwinger bosons , in order to satisfy the averaged constraint ( [ const ] ) . considering bose condensation at different momenta @xmath151 , we can calculate the energy of magnetic phases ( if the phases are locally stable , that is , they satisfy the self - consistent mean - field equations ) characterized by different magnetic wave vectors @xmath148 s . in particular , for the triangular lattice and @xmath85 , we evaluate the energy of the ferromagnetic phase ( @xmath152 ) , the @xmath2 nel order ( @xmath153 ) , and a collinear stripe order ( @xmath154 ) , that is favorable for intermediate doping and @xmath95 @xcite . in fig . [ enertpos ] we show the energy _ per site _ of the three phases as a function of hole doping , calculated for a large cluster ( @xmath155 sites ) that represents the thermodynamic limit . it can be seen that , at the mean - field level , the ferromagnetic phase is the ground state for all the doping range considered , although the 120@xmath89 nel order has a very close energy for doping @xmath156 . the collinear stripe phase always has a much larger energy , and so it is not stabilized by the kinetic energy alone . it should be stressed that after an exhaustive search for solutions of the mean - field equations for finite doping , we have always found that the ferromagnetic phase is the ground state . in the case of only one hole doped away half - filling , we will show in the next section that the ferromagnetic phase is degenerate with the @xmath2 nel order . the energy of both phases is @xmath157 ; while this is the exact ferromagnetic phase energy , it is clearly rather above the exact 120@xmath89 nel phase energy found by our dmrg calculations and exact diagonalization @xcite . it is worthy to note that , once @xmath158 , the 120@xmath89 nel state is strongly favored over the ferromagnetic one @xcite , because the exchange interaction select the 120@xmath89 magnetic pattern in the triangular lattice @xcite . for @xmath159 , it can be seen in fig . [ enertneg ] that the ferromagnetic phase is also the ground state for all doping , but now its energy is well separated from the energies of the other phases considered ( 120@xmath89 nel phase and a representative spiral phase , with magnetic wave vector @xmath160 ) . for negative @xmath11 nagaoka s theorem is valid , and it is believed that ferromagnetism is very stable for further doping @xcite . nel , ferromagnetic , and spiral @xmath160 phases , for @xmath33 and @xmath161 in the triangular lattice.,width=264 ] so , for @xmath85 and @xmath162 the mean - field approximation does not capture that @xmath2 nel order is the unique ground state , as it is degenerate with the ferromagnetic phase . this failure has to do with the mean - field character of the approach , in which we approximate the actual many - body problem by one - body terms . from previous experience @xcite , we expect that the inclusion of gaussian fluctuations above the mean - field solutions will put the slave - fermion predictions in consonance with our dmrg and exact diagonalization @xcite results , lowering the 120@xmath89 nel energy while leaving unchanged the already exact ferromagnetic energy . for the @xmath59 model on the square lattice with first and second neighbor hoppings , with @xmath112 and @xmath163 , we obtained analogous results to the triangular lattice . for @xmath40 , the ferromagnetic phase is clearly the ground state , in accordance with the nagaoka s theorem . for @xmath164 although the ferromagnetic phase is the ground state for all doping considered ( @xmath165 ) , its energy is very close to the energy of the usual @xmath166 nel state , being both states degenerate for one hole doped away half - filling . again , this result does not agree with the dmrg prediction of a unique antiferromagnetic ground state . although the mean - field theory fails to obtain the correct antiferromagnetic ground states for @xmath33 , in the next section we argue that it is a very helpful approach to elucidate the physical mechanism behind the phenomenon of kinetic antiferromagnetism .

dense 1-armed spiral is characterized by its fixed tip . for dense multi - armed spirals , when the initial distance between tips is less than a critical value , the arms collide , connect and disconnect continuously as the spirals rotate . the continuous reconstruction between the front and the back drives the tips to corotate along a rough circle and to meander zigzaggedly . the rotation frequency of tip , the frequency of zigzagged displacement , the frequency of spiral , the oscillation frequency of media , and the number of arms satisfy certain relations as long as the control parameters of the model are fixed .

r

1305.2585

we study the interaction of both dense and sparse multi - armed spirals in bistable media modeled by equations of fitzhugh - nagumo type . dense 1-armed spiral is characterized by its fixed tip . for dense multi - armed spirals , when the initial distance between tips is less than a critical value , the arms collide , connect and disconnect continuously as the spirals rotate . the continuous reconstruction between the front and the back drives the tips to corotate along a rough circle and to meander zigzaggedly . the rotation frequency of tip , the frequency of zigzagged displacement , the frequency of spiral , the oscillation frequency of media , and the number of arms satisfy certain relations as long as the control parameters of the model are fixed . when the initial distance between tips is larger than the critical value , the behaviors of individual arms within either dense or sparse multi - armed spirals are identical to that of corresponding 1-armed spirals .

@xmath12@xmath34 ; ( b ) positive phase sparse spiral ( ppss ) , @xmath4@xmath12@xmath35 ; ( c ) negative phase sparse spiral ( npss ) , @xmath4@xmath12@xmath28 ; ( e)-(g ) corresponding tip paths . ( d ) and ( h ) indicate the initial conditions for generating 1-armed and 2-armed spirals . the thick ( thin ) lines in ( d ) and ( h ) represent the contour lines @xmath1=@xmath13 ( @xmath2=@xmath13 ) , and the dashed circle indicates the initial circle on which the initial tips located . domain size:@xmath36@xmath32@xmath36 space units.,width=302,height=151 ] we first show the evolution of the 1-armed spiral with increasing @xmath4 as shown in figs . 1(a)-(c ) . in order to obtain 1-armed spiral we use the initial condition as indicated in fig . when @xmath4@xmath18@xmath37 the observed spiral is dense as shown in fig . 1(a ) , in which the order parameter @xmath14@xmath12@xmath13 and does not depend on epsilon according to its definition . the tip of the dense spiral keeps a fixed point as shown in fig . when @xmath4@xmath38@xmath37 the observed spiral is sparse as shown in fig . 1(b ) and 1(c ) . the order parameter @xmath13@xmath18@xmath14@xmath18@xmath39 and increases with epsilon . the tip of the sparse spiral follows a circle . the radius of this circle increases with @xmath4 . the trajectories of the tips in this case are shown in figs . 1(f ) and 1(g ) , respectively . the transition between dense spiral and sparse spiral proves to be a subcritical bifurcation @xcite . our emphasis is on the interaction between the arms within a multi - armed dense spiral ( @xmath4@xmath18@xmath37 ) . the tips of multi - armed dense spirals can corotate along a rough circle or fix at their individual points , which depends on their initial separations . figure 2 shows the multi - armed dense spirals with different number of arms generated from different initial circles when @xmath4@xmath12@xmath34 . the horizontal axis represents the radius of the initial circle as indicated in fig . 1(h ) , which shows the initial separation of the tips . the vertical axis represents the number of the initial tips spaced equally on the initial circle . it can be seen that when the distance between initiated tips is larger enough , the arms will rotate independently as shown on the right of the dashed line in fig . 2 . in this case , the number of the arms within the final spiral is equal to that of the initial arms . when the distance between initiated tips is small , the strong interaction between the arms leads to the instability of the multi - armed spiral . some of the arms become unstable and run outside of the domain in the stationary state . the rest of the arms then begin to corotate with each other as is indicated on the left of the dashed line in fig . 2 . the number of the arms within the final spiral is less than that of the initial arms . so , the dashed line in fig . 2 divides these spirals into two groups . it means that there exists a critical radius of the initial circle below which the arms begin to interact strongly with each other . figure 3 gives the dependence of this critical radius @xmath40 on the parameter @xmath4 . it is clear that the critical radius increases with @xmath4 . moreover , for the same @xmath4 , the more the initial arms are , the larger the critical radius is . this is because that , for the spiral with more arms , it becomes easier to interact . , the radius @xmath41 of the stationary circle on the parameter @xmath4 . solid lines ( dashed lines ) represent the radius @xmath40 ( @xmath41 ) . circle dotted line @xmath42 represents the radius of the tip trajectory of 1-armed spiral . the patterned rectangle region near the bifurcation point @xmath4@xmath12@xmath37 shows very complex interaction between the arms . the digits in figure indicate the numbers of the arms . when the radius of the initial circle is less than the critical radius , i.e. , @xmath20@xmath18@xmath40 , strong interaction between arms results in the corotation of tips along one zigzagged circle with radius @xmath41 . when @xmath20@xmath19@xmath40 the arms of multi - armed spirals will rotate independently like 1-armed spirals.,width=264,height=188 ] , @xmath43 , and @xmath44 space . ( c ) and ( d ) plot them in @xmath45 , @xmath43 space . the initial separation of the tips for 2-armed spiral ( 3-armed spiral ) is @xmath20@xmath12@xmath46 ( @xmath20@xmath12@xmath47 ) . smaller ( larger ) separation between the initial tips exhibits repulsive ( attractive ) interaction . inset in ( c ) represents the zigzagged meandering of one tip.,width=264,height=226 ] the strong interaction of multi - armed dense spirals can be studied by following the tip trajectories . 1(a ) and fig . 2 show dense 1-armed spiral and multi - armed spiral at @xmath4@xmath12@xmath34 , respectively . for 1-armed dense spiral [ fig . 1(a ) ] the tip is stable as indicated by the fixed point in fig . for multi - armed dense spirals located on the left of the dashed line in fig . 2 , the tips follow a rough circle and corotate with each other due to their interaction . figure 4 gives two examples which show the rough profiles of the tip trajectories for 2-armed and 3-armed dense spirals , respectively . 4(a ) and 4(c ) show the space - time plots of the two tips within 2-armed spiral , in which the two tips are initiated on an initial circle with smaller radius @xmath20@xmath12@xmath46 . it is clear that the two tips repel each other at first , and then corotate with each other along a circular stationary trajectory with radius @xmath48@xmath12@xmath49 . however , if the tips are initiated on an initial circle with larger radius ( @xmath20@xmath19@xmath48 , but @xmath20@xmath18@xmath40 ) , they firstly attract each other and then corotate along the circular stationary trajectory with the same radius @xmath48@xmath12@xmath49 . figs . 4(b ) and 4(d ) show the attractive interaction for 3-armed spiral , in which the three tips are initiated on an initial circle with larger radius @xmath20@xmath12@xmath47 . the three tips finally corotate along a circle with radius of @xmath50@xmath12@xmath51 . similarly , if @xmath20@xmath18@xmath50 , the tips exhibit repulsive interaction , and also follow the circular stationary trajectory with radius @xmath50@xmath12@xmath51 . here , we should note that the radius @xmath50@xmath19@xmath48 . this is because that the core region of 3-armed spiral is larger than that of 2-armed spiral due to their repulsive interaction . @xmath52@xmath53 on @xmath20 in 2-armed spiral . here , @xmath54 represents the average distance between the two tips in final state . @xmath53 is the wavelength of dense spiral . @xmath40 indicates the critical radius of initial circle . straight lines show the linear fitting . when @xmath20@xmath18@xmath40 the strong interaction between the arms results in the tip corotation along a circular stationary trajectory . in this case , @xmath54@xmath12@xmath53 , which illustrates that the average distance between tips equals to the wavelength of dense spiral.,width=264,height=188 ] we have conducted more numerical simulations for various number of initial arms and obtained the dependence of the radius @xmath41 of the stationary circle on parameter @xmath4 as indicated by the dashed lines in fig . 3 . from fig . 2 and fig . 3 we can draw a conclusion that , as long as the radius @xmath20 of the initial circle is less than @xmath40 ( solid lines in fig . 3 ) , i.e. , @xmath20@xmath18@xmath40 , the arms will interact strongly as shown on the left of the dashed line in fig . 2 . the tips can corotate with each other along a circular stationary trajectory with radius of @xmath41 ( dashed lines in fig . the average distance @xmath54 between tips in the final state equals to the wavelength @xmath53 of dense spiral as shown in fig . 5 . otherwise , when @xmath20@xmath19@xmath40 , the arms will rotate independently like 1-armed dense spiral as shown on the right of the dashed line in fig . the tips are fixed and separated well . therefore , the multi - armed spirals on the right of the dashed line in fig . 2 can be seen as coexistence of several 1-armed dense spirals . the average distance @xmath54 between tips in the final state increases linearly with the radius @xmath20 of the initial circle as shown in fig . 5 , which follows approximately that , @xmath55 the interaction condition in bistable media is different from that in excitable media . vasiev @xmath56 @xmath57 have shown that multi - armed spirals in excitable media can corotate when their tips are less than one wavelength apart @xcite . however , in our case , only when @xmath20@xmath18@xmath40 , multi - armed spirals can corotate , and meanwhile the tips will keep one wavelength apart as they corotate . ) and the back ( @xmath58 ) in 2-armed dense spiral during one cycle . thick ( thin ) lines in ( d)-(f ) , ( j)-(l ) represent the corresponding contours of @xmath1 ( @xmath2 ) . points of intersection between the thick and the thin lines indicate the two tips of 2-armed spiral , which is labeled by @xmath59 and @xmath60 , respectively . the two arms ( up state ) in ( d ) , ( e ) and ( l ) are labeled by @xmath61 and @xmath62 , respectively . the two arms ( down state ) in ( f ) , ( j ) and ( k ) are labeled by @xmath63 and @xmath64 , respectively . time in ( a)-(c ) , ( g)-(i ) is @xmath44@xmath12@xmath13 , @xmath65 , @xmath28 , @xmath66 , @xmath67 , @xmath68 , respectively.,width=264,height=377 ] the strong interaction of dense multi - armed spiral results in arm - switching with tips . figure 6 shows the evolution of a corotating 2-armed spiral during one cycle . firstly , we set the combination of the tips and the arms in figs . 6(a ) and 6(d ) to @xmath59@xmath69@xmath61 and @xmath60@xmath69@xmath62 . the two tips and the two arms separate well . during the development the two arms undergo collision [ figs . 6(b ) and 6(e ) ] , connection [ figs . 6(c ) , 6(f ) , 6(g ) , 6(j ) ] , and disconnection [ figs . 6(h ) and 6(k ) ] . after one cycle , the combination of the tips and the arms turns into @xmath59@xmath69@xmath62 , @xmath60@xmath69@xmath61 , and the arms switch to the other tip as shown in figs . 6(i ) and 6(l ) . this arm - switching will happen in the same way every one cycle . the interaction of multi - armed spirals and the mechanism of arm - switching can be studied by analyzing the interaction between the front and the back , because the arm of bistable spiral is enclosed by a couple of bloch interfaces ( a front and a back ) . in fig . 6(e ) , the arm @xmath61 ( up state ) is enclosed by the front @xmath70 and the back @xmath71 , and so does the other arm @xmath62 . we should notice that when @xmath4@xmath12@xmath34 , for dense 1-armed spiral [ fig . 1(a ) ] , the order parameter @xmath14@xmath12@xmath13 ( @xmath16@xmath12@xmath17 ) . for dense 2-armed spiral [ as figs . 6(a ) and 6(b ) ] , it can be regarded as superposition of two sparse 1-armed spirals ( arms @xmath61 and @xmath62 , ppss ) with individual order parameter @xmath72@xmath12@xmath73 , and the global order parameter keeps @xmath14@xmath12@xmath13 . because the parameter @xmath4@xmath12@xmath34 the two sparse 1-armed spirals ( arms @xmath61 and @xmath62 , @xmath72@xmath12@xmath73 ) tend to expand respectively to dense 1-armed spirals with @xmath72@xmath12@xmath13 . during their expansion the cores begin to collide and connect together [ figs . 6(b ) , 6(c ) , 6(g ) ] , the front and the back will reconstruct . the back @xmath74 and the front @xmath70 enclose and form a new arm @xmath64 ( down state ) , the back @xmath71 and the front @xmath75 enclose and form the other new arm @xmath63 ( down state ) as shown in figs . 6(f ) and 6(j ) . now , the dense 2-armed spiral can also be regarded as superposition of two sparse 1-armed spirals ( arms @xmath63 and @xmath64 , npss ) . similarly , the arms @xmath63 and @xmath64 will expand respectively as the rotation is going on , and the front and the back will reconstruct again . the front of one arm disconnects with the forward back of another arm , and reconnects with the backward back of itself [ figs . 6(i ) and 6(l ) ] . now , the combination of the tips and the arms in figs . 6(i ) and 6(l ) is @xmath59@xmath69@xmath62 , @xmath60@xmath69@xmath61 , and the arms exchange their tips . so , the arm - switching observed in dense multi - arms spiral originates from the reconstruction of the front and the back . it is easy to deduce that undergoing one cycle again the arms will exchange their tips once more . the combination of the tips and the arms will become @xmath59@xmath69@xmath61 and @xmath60@xmath69@xmath62 like it was two cycles ago . in a word , the front and the back reconstruct twice in one cycle , which results in the arms - switching once . this mechanism of reconstruction happens also in other multi - armed dense spirals . of one tip in @xmath45 direction . ( b):parameter @xmath76 . ( c):oscillation intensity of one point far from the spiral center . ( d):distance @xmath54 between two neighboring tips . the parameter @xmath4@xmath12@xmath77 , domain size @xmath78@xmath32@xmath78 space units , space step @xmath79@xmath12@xmath30 space units , time step @xmath29@xmath12@xmath80 time units.,width=264,height=226 ] according to the eikonal equation , @xmath81@xmath12@xmath82 , the curvature @xmath83 of spiral affects the speed @xmath81 of the bloch front and back . during the continuous reconstruction of front and back , the curvature of spiral near the tip changes remarkably as shown in fig . 6(e ) and 6(k ) . the changes in the curvatures of the front and the back result in the speed difference between them , which will drive the tip to zigzag along a rough circle ( zigzagged meandering ) . the rotation direction of tip is determined by the chirality of spiral . 7(a ) shows the time sequence of zigzagged displacement @xmath45 of one tip in @xmath45 direction for dense 3-armed spiral . it can be seen that the zigzagged displacement is tiny ( about 0.36 space unit ) , which is far less than the average diameter of the circular stationary tip trajectory ( about 14.28 space unit ) . in order to confirm if there exists petal meandering ( like that in excitable media ) in the present case , we use the domain size @xmath84@xmath32@xmath84 space units and smaller space step @xmath79@xmath12@xmath85 space units . the numerical simulations with higher spatial resolution show only the zigzagged meandering of spiral . the zigzagged meandering of dense multi - armed spirals in bistable media is different from the petal meandering of spirals in excitable media . this is because the fact that the origins of meandering spirals in bistable and excitable media are different . the zigzagged meandering of multi - armed dense spiral in bistable media results from the interaction of the arms , i.e. , the continuous reconstruction between the front and the back . the petal meandering of spiral in excitable media results from a secondary hopf bifurcation @xcite . in order to illustrate the periodical interaction between the arms , we define a parameter , @xmath86 where , @xmath87 represents the variable @xmath1 at the @xmath88 grid point in two dimensional space . it can represent the frequency of dense multi - armed spiral . 7(b ) shows the periodical change of this parameter @xmath76 for 3-armed spiral . when @xmath76@xmath12@xmath13 , the up state and the down state are entirely symmetrical . we also measure the time sequence of one point far from the spiral center as shown in fig . its frequency is far more than the rotation frequency of the tips [ fig . the distance @xmath54 between two neighboring tips changes periodically as shown in fig . obviously , there exist certain modulations of these time sequences in fig . 7 . in order to clarify these modulations , it is necessary to analyze their corresponding fourier spectra . the zigzagged meandering of multi - armed dense spiral is characterized by several frequencies , the rotation frequency @xmath89 of tip , the frequency @xmath70 of spiral , the oscillation frequency @xmath75 of media , the frequency @xmath90 of zigzagged displacement , and the number @xmath91 of arms . because the tips meander clockwise , the oscillating frequency @xmath75 of one point far from the spiral center is larger than the frequency @xmath70 of spiral . the frequency @xmath75 is closely connected with the number @xmath91 of arms . obviously , the more arms one spiral has , the larger the frequency @xmath75 is . the rotation frequency @xmath89 of tips also increases with the number @xmath91 of arms . these imply that the quantities @xmath89 , @xmath70 , @xmath75 , and @xmath91 satisfy the following relation of eq . ( 5 ) : @xmath92 the applicability of eq . ( 5 ) is explored in fig . 8 which shows the fourier spectra of the corresponding time sequences of 3-armed dense spiral in fig . the rotation frequency of tip is @xmath89@xmath12@xmath93 as indicated in fig . the frequency of spiral is @xmath70@xmath12@xmath94 as indicated in fig . 8(b ) , which is far more than the rotation frequency @xmath89 of tip . the oscillating frequency @xmath75 of one point far from the spiral center is @xmath75@xmath12@xmath95 as shown in fig . these frequencies satisfy the relations of eq . ( 5 ) . because the front and the back reconstruct twice during one cycle as illustrated in fig . 6 , it results in the frequency doubling @xmath96 in the power spectra of distance @xmath54 between two neighboring tips [ as indicated in fig . 8(d ) ] . meanwhile , because the tips are meandering clockwise , the frequency @xmath90 of zigzagged displacement of tip is the sum of the frequency doubling @xmath96 and the rotation frequency @xmath89 of tip : @xmath97 in fig . 8(a ) , it reads @xmath90@xmath12@xmath98 . in addition , the lower frequency @xmath99@xmath12@xmath100 in fig . 8(d ) is always four times the rotation frequency @xmath89 of tip : @xmath101 which should result from the boundary constraint of the square domain to the tips . these relations also hold for other multi - armed dense spirals in our extended simulations , and are not limited to the case of 3-armed dense spiral as shown in figs . 7 and 8 . because the frequency of spiral is determined by the control parameters of the model , the frequency @xmath70 of spiral is almost invariant for multi - armed spirals with different numbers of arms as long as the parameter @xmath4 keeps constant . the other frequencies , @xmath89 , @xmath75 , @xmath99 , and @xmath90 , increase with the number @xmath91 of arms . the parameters @xmath4 , @xmath5 , and @xmath3 control the nonequilibrium ising - bloch bifurcation which plays important role on pattern formation in bistable media @xcite . in the bloch region , the speeds @xmath102 of the bloch interfaces ( front and back ) are determined by the following implicit relation @xcite : @xmath103^{2}/\delta,\end{aligned}\ ] ] here , @xmath104@xmath12@xmath39@xmath105@xmath106 . it shows that decreasing @xmath3 or increasing @xmath5 is equivalent to increasing @xmath4 . in this paper , we use @xmath4 as the main control parameter given that @xmath5@xmath12@xmath22 and @xmath3@xmath12@xmath25 . in our extended simulations , similar interactions of multi - armed spirals have been observed when changing the parameter @xmath5 and @xmath3 in the parameter ranges : @xmath107@xmath18@xmath5@xmath18@xmath108 and @xmath109@xmath18@xmath3@xmath18@xmath110 . however , the parameter @xmath5 could not be set to a large value in the numerical simulation because the absolute values @xmath111 of the two stationary and uniform stable states of system will increase with the parameter @xmath5 . the more the absolute values @xmath111 are , the steeper the interfaces ( front and back ) connected the two stable states become , that will require numerical simulations of smaller space step and demanding computational intensity . extended numerical simulations have also shown our analyses are applicable for general interaction mechanism between multi - armed spirals in bistable media . now , we focus on the interaction of multi - armed sparse spirals [ fig . 9 ] , i.e. @xmath4@xmath38@xmath37 , which is somewhat different from the case of multi - armed dense spirals . in fig . 3 , the circle dotted line @xmath42 represents the radius of the tip trajectory of 1-armed spiral . when @xmath4@xmath38@xmath28 the dashed lines @xmath41 coincide with the circle dotted line @xmath42 . this means that the rigid rotation of an individual arm within multi - armed sparse spiral [ fig . 9 ] is identical to that of 1-armed sparse spiral [ figs . 1(b ) , 1(c ) , 1(f ) , 1(g ) ] . the tips travel along their individual trajectories , i.e. , not always along a rough circle . this is very different from the case of multi - armed dense spirals as illustrated by fig . 4 . in that case , the tips of multi - armed dense spirals corotate and meander zigzaggedly along a rough circle . it shows that the interaction between the arms of dense multi - armed spiral is stronger than that of sparse multi - armed spiral . in addition , when @xmath20@xmath18@xmath40 , the tips only exhibit attractive interaction [ figs . 9(a ) and 9(c ) ] . when @xmath20@xmath19@xmath40 , the tips will develop independently as shown by figs . 9(b ) and 9(d ) , which is similar to the case of dense multi - armed spiral . ( a ) and ( c ) show the attractive process of the two tips . ( b ) and ( d ) show the independent rotation of each tip.,width=264,height=226 ]

we study the interaction of both dense and sparse multi - armed spirals in bistable media modeled by equations of fitzhugh - nagumo type . when the initial distance between tips is larger than the critical value , the behaviors of individual arms within either dense or sparse multi - armed spirals are identical to that of corresponding 1-armed spirals .

c

1305.2585

we study the interaction of both dense and sparse multi - armed spirals in bistable media modeled by equations of fitzhugh - nagumo type . dense 1-armed spiral is characterized by its fixed tip . for dense multi - armed spirals , when the initial distance between tips is less than a critical value , the arms collide , connect and disconnect continuously as the spirals rotate . the continuous reconstruction between the front and the back drives the tips to corotate along a rough circle and to meander zigzaggedly . the rotation frequency of tip , the frequency of zigzagged displacement , the frequency of spiral , the oscillation frequency of media , and the number of arms satisfy certain relations as long as the control parameters of the model are fixed . when the initial distance between tips is larger than the critical value , the behaviors of individual arms within either dense or sparse multi - armed spirals are identical to that of corresponding 1-armed spirals .

in this work , we have studied the interaction of multi - armed spirals in bistable media . in order to illustrate this interaction , we first give the evolution of 1-armed spiral as shown in fig . multi - armed spirals can be obtained by constructing appropriate initial conditions . for dense multi - armed spirals , when @xmath20@xmath18@xmath40 , strong interaction between arms results in the corotation of tips along a zigzagged circle . the tips will keep one wavelength apart as they corotate , which is very different from the case of multi - armed spiral in excitable media . during the spiral rotating , the arms collide , connect and disconnect continuously , which drives the tips to meander zigzaggedly . in one cycle , the front and the back reconstruct twice , the arms switch with the tips once . for dense multi - armed spirals , the rotation frequency @xmath89 of tip , the frequency @xmath70 of spiral , the oscillation frequency @xmath75 of media , the frequency @xmath90 of zigzagged displacement , and the number @xmath91 of arms satisfy the general relations of eqs . ( 5)-(7 ) . when @xmath20@xmath19@xmath40 , the arms in multi - armed dense spirals will rotate independently just like 1-armed dense spiral . for sparse multi - armed spirals , the rigid rotation of an individual arm within multi - armed sparse spiral is identical to that of 1-armed sparse spiral . when @xmath20@xmath18@xmath40 , the tips exhibit only attractive interaction and could rotate along several circles , which is different from the case of dense multi - armed spirals . it should be mentioned that our numerical results are robust against little deviations of the initial conditions used , which makes it reliable to perform correlative studies experimentally . the presented results reveal the general mechanism of interaction of multi - armed spirals in bistable media , and are not limited to the specific cases illustrated by figs . ( 4)-(9 ) . near the bifurcation point @xmath112@xmath12@xmath37 ( the patterned rectangle region in fig . 3 ) , the dynamics of multi - armed spirals will become very complex . in order to investigate this region , higher spatial - temporal resolution ( i.e. , large domain size , small space and time steps ) are fairly necessary . this will need numerical simulations of demanding computational intensity . as is well known pattern formations in bistable media are related to the initial conditions besides the control parameters . in our work , we generated the multi - armed spirals by designing appropriate initial conditions and then studied their interactions . many real chemical experiments , such as the ferroin- , ru(bpy)@xmath113- , and cerium - catalyzed belousov - zhabotinsky and/or iodate - sulfite reactions , are sensitive to visible and/or ultraviolet light @xcite . therefore , light illumination has been widely used to excite desired initial conditions . for example , a couple of spirals can be generated by shadowing a small part of the propagating wave front with a mask . multi - armed spirals with corotation and independent rotation have been observed experimentally by steinbock @xcite and krinsky @xcite in excitable media . light - sensitive catalyst even makes it possible to study the image processing and the effective computational procedure for finding paths in labyrinth based on reaction - diffusion mechanisms @xcite . at present , bistable patterns , such as the 1-armed spirals , the labyrinthine , and the breathing spots , have been studied well in iodate - sulfite reactions experimentally @xcite and in fitzhugh - nagumo model theoretically @xcite . we believe this work provide information to understand the interaction of multi - armed spiral , and hope that our results about the interaction of multi - armed spirals in bistable media can be verified in one of these light - sensitive reactions . for example , multi - armed spiral should be observed by illuminating the ferrocyanide - iodate - sulfite medium with ultraviolet light if employing our suggested initial conditions .

we study the inviscid multilayer saint - venant ( or shallow - water ) system in the limit of small density contrast . we show that , under reasonable hyperbolicity conditions on the flow and a smallness assumption on the initial surface deformation , the system is well - posed on a large time interval , despite the singular limit . by studying the asymptotic limit , we provide a rigorous justification of the widely used rigid - lid and boussinesq approximations for multilayered shallow water flows . the asymptotic behaviour is similar to that of the incompressible limit for euler equations , in the sense that there exists a small initial layer in time for ill - prepared initial data , accounting for rapidly propagating `` acoustic '' waves ( here , the so - called barotropic mode ) which interact only weakly with the `` incompressible '' component ( here , baroclinic ) .

i

1507.02215

we study the inviscid multilayer saint - venant ( or shallow - water ) system in the limit of small density contrast . we show that , under reasonable hyperbolicity conditions on the flow and a smallness assumption on the initial surface deformation , the system is well - posed on a large time interval , despite the singular limit . by studying the asymptotic limit , we provide a rigorous justification of the widely used rigid - lid and boussinesq approximations for multilayered shallow water flows . the asymptotic behaviour is similar to that of the incompressible limit for euler equations , in the sense that there exists a small initial layer in time for ill - prepared initial data , accounting for rapidly propagating `` acoustic '' waves ( here , the so - called barotropic mode ) which interact only weakly with the `` incompressible '' component ( here , baroclinic ) .

this work dedicated to the study of the so - called multilayer saint - venant system , which arises as an approximate model for the propagation of waves in the ocean or atmosphere , when density stratification can not be neglected . we will refer to as _ free surface system _ the following first - order , quasilinear system of @xmath0 coupled evolution equations : @xmath1 here , the unknowns @xmath2 and @xmath3 represent respectively the deformation of the @xmath4 interface and the layer - averaged horizontal velocity in the @xmath4 layer , at time @xmath5 and horizontal position @xmath6 where @xmath7 ; see figure [ f.sketchofthedomain ] . if @xmath8 , then we denote @xmath9 and @xmath10 . we denote by @xmath11 the mass density of the homogeneous fluid in the @xmath4 layer , whereas @xmath12 is the gravitational acceleration . finally , @xmath13 is the depth of the @xmath4 layer . by convention , we set @xmath14 ( above the upper free surface is vacuum ) , and @xmath15 ( the bottom is flat ) . we restrict ourselves to the setting of stable stratification , namely @xmath16 we may rescale the variables so as to replace the factor @xmath17 more precisely , we use the following nondimensionalization : @xmath18 where @xmath19 is a characteristic horizontal length ( say the wavelength of the flow ) , @xmath20 is a characteristic vertical length ( say the typical depth of one layer at rest ) , and @xmath21 is a velocity . such that @xmath22 , then @xmath23 measures the typical velocity of propagation of the baroclinic modes ; see appendix [ s.spectral ] . ] although @xmath24 does not appear in our system , it plays a very important role as the saint - venant system may be seen as the first - order asymptotic model obtained from the full multilayer water - wave system in the limit @xmath25 ; see @xcite in the one - layer case and @xcite in the bilayer ( albeit irrotational ) setting . it may also be formally obtained using the hydrostatic and columnar motion assumptions ; see @xcite . in this work , we ask + * qn : * _ what is the behaviour of the solutions to in the limit @xmath26 ? _ the first observation is that the velocity evolution equations become singular , as @xmath27 since @xmath28 by convention , so that even the existence of solutions on a non - trivial time interval is far from straightforward . at the linear level , it is known @xcite ( see also appendix [ s.spectral ] ) that the flow may be decomposed into @xmath29 modes , propagating as linear wave equations with distinct velocities . in our setting , the first mode , _ i.e. _ the barotropic mode , propagates much faster than the other , baroclinic modes , in the sense that the former is typically of size @xmath30 while the latter are uniformly bounded when @xmath31 ; hence the singularity . while such a decomposition is exact only in the linear setting , we show in this work that the flow behaves in a similar way in the weak density contrast limit even when strong nonlinearities are present , provided that the initial surface deformation is small , the depth of each layer remains positive and shear velocities are not too large . roughly speaking , we show that one may then approximate the flow as the superposition of rapidly propagating acoustic waves and a non - singular `` slow '' mode with non - trivial dynamics . let us be more precise . asymptotically , the fast mode describes the propagation of the free surface , @xmath32 , and total volume flux , namely @xmath33 where @xmath34 and @xmath35 is the orthogonal projection onto irrotational vector fields . one has at first order , in dimension @xmath8 and provided that @xmath32 and @xmath36 are initially balanced so that @xmath37 , the linear acoustic system @xmath38 the slow component contains all the baroclinic modes which interact strongly one with each other in the nonlinear setting . we show that it is asymptotically described by the _ rigid - lid model _ , which is obtained from the free - surface system by setting @xmath39 in the mass conservation equations , and replacing @xmath40 with @xmath41 in the velocity evolution equations ( see @xcite ) . in addition , we apply the so - called _ boussinesq approximation _ ( see _ e.g. _ @xcite ) to the limit system , that is we set @xmath42 in the velocity evolution equations while @xmath43 remains fixed and non - trivial . this yields @xmath44 with the same notation as before , except @xmath45 and @xmath46 . in particular , the first equation is not an evolution equation but a constraint ( conservation of total mass ) , namely @xmath47 physically speaking , @xmath48 is ( up to a constant ) the pressure at the flat , rigid lid . from a mathematical viewpoint , @xmath49 is the lagrange multiplier associated with the above divergence - free constraint . it may be reconstructed from the knowledge of @xmath50 by solving the poisson equation @xmath51 we thus offer a rigorous justification ( the formal justification is generally attributed to armi @xcite ) of the widely used rigid - lid and boussinesq approximations for free surface multilayer shallow - water flows with a small density contrast . before stating our main results , let us recall for convenience the system of equations at stake : @xmath52 where @xmath53 with convention @xmath54 and @xmath55 . in the following , we fix parameters @xmath56 ; and denote @xmath57 we can then reconstruct @xmath58 with @xmath59 ( @xmath60 ) and @xmath61 where @xmath62 is the only parameter allowed to vary , and by assumption @xmath63 it is also convenient to denote ( notice the @xmath64 prefactor ; see remark [ r.small-surface ] below ) @xmath65 so that the control of @xmath66 in sobolev space @xmath67 ( see appendix [ s.notations ] for notations ) yields , when @xmath8 , @xmath68 let us now state the main results of this work . [ t.wp ] let @xmath69 and @xmath70 be such that @xmath71 where @xmath72 , and we recall the convention @xmath54 . one can set @xmath73 such that if @xmath74 satisfies additionally @xmath75 then there exists @xmath76 and a unique @xmath77 strong solution to and @xmath78 , and satisfying , with @xmath79 and @xmath80 for any @xmath81 . moreover , one has @xmath82 uniformly with respect to @xmath83 . [ t.convergence ] let @xmath8 , @xmath69 , and @xmath84 as above . then there exists @xmath76 with @xmath85 and , for @xmath62 sufficiently small , * @xmath86 a unique strong solution to and @xmath78 ; * @xmath87 a unique strong solution to with initial data @xmath88 where @xmath89 is the total depth , @xmath90 with convention @xmath91 and @xmath35 the orthogonal projection onto irrotational vector fields . * @xmath92 a unique strong solution to with @xmath93 moreover , one has for any @xmath94 , @xmath95 where @xmath96 . [ r.small-surface ] as mentioned in the introduction , our hypotheses contain a smallness assumption on the initial deformation of the surface , namely @xmath97 . this assumptions is natural so as to balance the contributions in the ( preserved in time ) energy : @xmath98 without this assumption , the flow possesses a strongly nonlinear barotropic component , and energy methods yield a well - posedness theory over a small time - domain , @xmath81 , @xmath99 ; see proposition [ p.wp-naive ] and remark [ r.naive ] , below . on this timescale , the baroclinic component do not evolve , so that all the dynamics is described by the barotropic component ( asymptotically as @xmath100 ) . the requirement @xmath83 does not lose in generality in theorem [ t.wp ] : the case of non - small @xmath62 follows from the standard well - posedness theory of quasilinear systems , as proved by monjarret in @xcite and stated in proposition [ p.wp-naive ] , below . our proof does not rely on , but rather provides , the existence and uniqueness of strong solutions of the limit ( rigid - lid ) system . in that respect , one may see the free - surface system as a penalized model for relaxing the rigid - lid constraint . sharper well - posedness results for the rigid - lid system in the two - layer case and without the boussinesq approximation are provided in @xcite . theorem [ t.convergence ] is restricted to @xmath8 because we use dispersive decay estimates on rapidly propagating acoustic waves in order to control nonlinear coupling effects between the fast and slow modes . in the case of dimension @xmath101 , and provided that the initial data is sufficiently localized in space , we justified in @xcite a similar mode decomposition of the flow , by making use of the different spatial support of each mode after small time . proposition 4.4 therein , together with proposition [ p.energy-estimate-hs ] in the present work , offer a convergence between the exact and the approximate solution with rate @xmath102 . the same convergence rate holds in the case of dimension @xmath8 and well - prepared initial data , in the sense of proposition [ p.well-prepared initial data ] . in the following , for the sake of simplicity , we limit our study to the case of dimension @xmath8 , although we find it more telling to keep the notation @xmath103 . the proof of theorem [ t.wp ] is easily adapted to the case of dimension @xmath101 . one could add , without any additional difficulty , a uniformly bounded and order - zero term to the system , so as to take into account for instance the coriolis force , atmospheric pressure variations , or bottom topography . notice however that these terms should be of size @xmath102 in the evolution equation for @xmath32 ; in particular , only small topography may be dealt with using directly our strategy . similarly , except in the one - layer case where the the component due to coriolis effect is an anti - symmetric perturbation of a symmetric system , one can not allow a rapid rotation such as in the quasi - geostrophic regime , which would correspond here to @xmath104 where @xmath105 is the rossby number ; see @xcite . our results are valid for arbitrary @xmath29 , but not uniformly . in particular , we can not control the dependence of @xmath106 as @xmath29 grows . thus our strategy can not be adapted to study the system in the limit @xmath107 , corresponding to the physically relevant situation of continuous stratification . a similar shortcoming was already noticed and discussed by ripa in @xcite . a well - posedness result on system is stated and proved in @xcite . it follows from a standard analysis on quasilinear systems since a symbolic symmetrizer may be exhibited ( see section [ s.wp-naive ] below ) . however , due to the presence of singular components in the system , the _ a priori _ maximal time of existence of the solutions may be bounded from below only as @xmath108 using this method . such a result is unsuitable for our purpose as the time interval shrinks to zero in the considered limit , and is inconsistent with oceanographic observations of large amplitude internal waves propagating over long distances ; see _ e.g. _ @xcite and references therein . in order to go beyond this analysis and provide a time of existence of solutions uniformly bounded from below with respect to @xmath62 small , we need to take advantage of some additional structural properties of the system . this structure is put to light by a suitable change of variable , which we describe below . let us introduce the shear velocities , @xmath109 , and the total horizontal momentum , @xmath110 , as follows : @xmath111 so that , conversely , for any @xmath112 , @xmath113 one may rewrite system using the new variables as follows : @xmath114 where @xmath115 , and @xmath116 are meant as the expressions in terms of @xmath117 given in . the above change of variables may be seen as an approximate normal form allowing to decouple the slow and fast components of the flow . indeed , since @xmath118 one sees immediately that the singular terms appear only as linear components on the evolution equations for @xmath119 and @xmath110 or more precisely @xmath33 and involve only @xmath119 and @xmath33 . in other words , the leading - order terms form a system of rapidly propagating acoustic waves in @xmath120 : @xmath121 the remainder contains quasilinear components depending on both the fast ( @xmath122 ) and slow ( @xmath123 ) variables , so we need to consider the full system of equations in order to obtain the desired uniform energy estimates . let us now , for the sake of simplicity , restrict our discussion to the case of dimension @xmath101 . from the above , we may rewrite the system as @xmath124\partial_x{{\sf v}}=\partial_t{{\sf v}}+ \frac1{\varrho}{{\sf l}}\partial_x{{\sf v}}+ { { \sf c}}[{{\sf v}}]\partial_x{{\sf v}}=0\ ] ] where @xmath125 , so that @xmath126 represents the above acoustic wave system for the fast variables , while @xmath127 ; and @xmath128 $ ] contains lower - order ( in terms of @xmath62 ) and coupling terms . we shall make use of the fact that one can construct a `` good '' symmetrizer of the system under the form , namely we exhibit real , positive - definite matrices @xmath129 $ ] such that @xmath129=({{\sf t}}[{{\sf v}}])^\top$ ] and @xmath129{{\sf b}}[{{\sf v}}]=({{\sf t}}[{{\sf v}}]{{\sf b}}[{{\sf v}}])^\top$ ] , and satisfying the decomposition @xmath130={{\sf t}}_{(0)}+{{\sf t}}_{(1)}[{({{\sf id}}-{\sf \pi}_{\rm f})}{{\sf v}}]{({{\sf id}}-{\sf \pi}_{\rm f})}+{\mathcal{o}}({\varrho}),\ ] ] where @xmath131 is the orthogonal projection onto @xmath132 , the slow variables . indeed , one obtains an energy estimate by taking the @xmath133 inner - product of the equation with @xmath129{{\sf v}}$ ] , which only requires to estimate @xmath134{{\sf b}}[{{\sf v } } ] ) } _ { l^\infty}+\norm { \partial_t ( { { \sf t}}[{{\sf v } } ] ) } _ { l^\infty}.\ ] ] using that @xmath135 and @xmath136 are constant operators and that @xmath137\partial_x{{\sf v}}={\mathcal{o}}(1)$ ] , we see that the above are estimated uniformly with respect to @xmath62 small ; thus we have a uniform control of the @xmath133 norm . the corresponding @xmath138 estimate with @xmath69 does not bring additional difficulties , using that @xmath135 commutes with the fourier multiplier @xmath139 . there remains to understand why such symmetrizer exists for our system . one could check , after tedious calculations , that the explicit one provided by monjarret in @xcite ( after applying the congruent transformation associated with the change of variables ) satisfies the necessary hypotheses , but we offer in appendix [ s.spectral ] an alternative and more robust construction . we show that , provided that @xmath140 satisfies , , then @xmath141 $ ] has @xmath142 real and distinct eigenvalues . two of them are asymptotically equivalent to @xmath143 as @xmath100 while the other ones are uniformly bounded with respect to @xmath62 small . the spectral projection corresponding to the former converge towards the projections onto the eigenspaces corresponding the two non - trivial eigenvalues of @xmath135 . using the scale separation between the eigenvalues , one shows that the spectral projections corresponding to the latter are uniformly bounded , and that they converge as @xmath144 towards independent , rank - one projections onto subspaces of @xmath132 . our symmetrizer is then , classically , @xmath130{\stackrel{\rm def}{=}}\sum_{j=1}^{2n } ( { { \sf p}}_j[{{\sf v}}])^\top { { \sf p}}_j[{{\sf v}}]\ ] ] where @xmath145 $ ] is the spectral projection onto the @xmath146 eigenspace of @xmath147 $ ] . that @xmath129 $ ] enjoys the desired properties follows , using standard perturbation theory @xcite , from the fact that @xmath135 is constant , @xmath148 and the strong scale separation between @xmath149 and uniformly bounded eigenvalues . an additional difficulty arises in the situation of horizontal dimension @xmath8 , due to the fact that the symmetrizer of the system which is constructed from the symmetrizer in dimension @xmath101 and a rotational invariance property is only a symbolic symmetrizer , as opposed to symmetrizers in the sense of friedrichs . thus we rely on para - differential calculus , but extra care must be given to `` lower order terms '' in the sense of regularity , which may effectively hurt our energy estimates if they are not uniformly bounded with respect to @xmath62 . as a matter of fact , we use that one can construct an explicit operator ( defined as a fourier multiplier ) which symmetrizes the linear , singular contributions of the system , and use para - differential calculus only on the next order components in terms of @xmath62 . given the uniform ( with respect to @xmath62 small ) energy estimates , the large time well - posedness ( theorem [ t.wp ] ) follows from the standard theory for quasilinear hyperbolic systems . the convergence results ( theorem [ t.convergence ] as well as additional assertions in section [ s.convergence ] ) proceed from rather standard techniques in the study of singular systems ; see references below . in @xcite , the author studied the so - called inviscid bilayer saint - venant ( or shallow water ) system in the limit of small density contrast . the change of variables allowing for uniform energy estimates was exhibited therein , and convergence towards a solution of the rigid - lid limit , as well as a second - order approximation , was deduced in the case of well - prepared initial data . this work is therefore an extension of these results to the situation of ( horizontal ) dimension @xmath8 , ill - prepared initial data as well as arbitrary number of layers . as already noticed in the aforementioned work , our problem has many similarities with the ( two - dimensional ) incompressible limit for euler equations , as studied initially in @xcite . as a matter of fact , if we consider only one layer of fluid , then our problem corresponds exactly to a special case of the isentropic incompressible limit , and we recover the results of ukai @xcite and asano @xcite . we will not detail the very rich history of results concerning this problem ( we let the reader to @xcite for comprehensive reviews ) but rather aim at pointing out similarities and differences of our situation . let us first recall the two - dimensional isentropic euler equations for inviscid , barotropic fluids : @xmath150 where @xmath151 is a given pressure law , @xmath152 is the density , @xmath153 the velocity , and @xmath154 the dimensionless mach number . as claimed above , one recognizes exactly in the one layer setting ( @xmath155 ) , by setting @xmath156 , and identifying @xmath157 of course , the difficulty in our case is that , as one considers additional layers of fluids , these equations are coupled with additional equations on additional unknowns , so as to produce a full quasilinear system . since these additional equations are non - singular with respect to the small parameter , it is tempting to compare our situation with the incompressible limit for the non - isentropic euler equations , where is coupled with an additional evolution equation for the entropy , @xmath158 : @xmath159 and @xmath160 . our situation , however , is quite different . this can be seen from the fact that , contrarily to the non - isentropic euler equations , the linearized system is balanced , in the sense that a small perturbation of the `` slow '' component of the reference state induces only a small deviation for the solution . in other words , using the notation of the above discussion , the symmetrizer of the non - isentropic euler equations does not satisfy @xmath129={{\sf t}}_{(0)}+{{\sf t}}_{(1)}[{({{\sf id}}-{\sf \pi}_{\rm f})}{{\sf v}}]{({{\sf id}}-{\sf \pi}_{\rm f})}+{\mathcal{o}}({\varrho})$ ] but only @xmath129={{\sf t}}_{(0)}+{{\sf t}}_{(1)}[{({{\sf id}}-{\sf \pi}_{\rm f})}{{\sf v}}]+{\mathcal{o}}({\varrho})$ ] ; see discussion in @xcite . this additional property in our situation allows in particular to straightforwardly deduce @xmath138 energy estimates from the corresponding @xmath133 energy estimate ; and to obtain the strong convergence result of theorem [ t.convergence ] simply from dispersive estimates on the `` acoustic '' component of the flow , as originally carried out by ukai @xcite and asano @xcite in the isentropic case . in order to deal with this situation , mtivier and schochet @xcite ( see also @xcite ) rely on the fact that their system enjoys a diagonal block structure and that the symmetrizer commutes exactly with the singular operator , denoted @xmath161 in the above discussion . roughly speaking , this means that we may control the compressible and isentropic component of the flow independently of the acoustic component by simply projecting onto @xmath132 . since such assumptions are only approximately satisfied in our situation , our system is rather related to the `` @xmath62-balanced '' ( and not `` @xmath62-diagonal '' ) systems studied by klainerman and majda @xcite , although we do not restrict ourselves to well - prepared initial data . in this spirit , our proofs rely as little as possible on explicit calculations , thus we expect that the general strategy may be successfully applied to other situations and other frameworks , such as the ones presented in @xcite . this is why we use mostly in the following the terminology of `` fast _ vs _ slow '' mode / component instead of `` barotropic _ vs _ baroclinic '' which is more relevant to our initial oceanographic motivation ( see @xcite ) ; or `` acoustic _ vs _ incompressible '' associated with euler equations . in section [ s.wp-naive ] , we recall that our quasilinear system admits an explicit ( symbolic ) symmetrizer , which yields immediately a well - posedness theory for , for any fixed @xmath162 . in section [ s.normal-form ] , we exhibit the structural properties enjoyed by our system , after the change of variables , , and which allow the uniform ( with respect to @xmath62 small ) energy estimates provided in section [ s.energy-estimates-l2 ] ( proposition [ p.energy-estimate-l2 ] ) and section [ s.energy-estimates-hs ] ( proposition [ p.energy-estimate-hs ] ) . we deduce in section [ s.wp ] the large - time well - posedness result of theorem [ t.wp ] . additionally , we show in proposition [ p.well-prepared initial data ] that an assumption of well - prepared initial data is propagated by the flow for positive times . section [ s.convergence ] is dedicated to convergence results . we first state in proposition [ p.weak-convergence ] a weak convergence result for the solutions of the free - surface system as @xmath100 . as in the incompressible limit for euler equations , the convergence can not be strong uniformly in time , due to the rapidly propagating fast mode . however , we show in proposition [ p.convergence-wp ] that this small initial layer in time vanishes in the case of well - prepared initial data , and then characterize the defect for general initial data in section [ s.convergence-strong ] , yielding theorem [ t.convergence ] . appendix [ s.notations ] contains a description of some notations used throughout the text , as well as a short review of standard results concerning product and commutator estimates in sobolev spaces ( section [ s.product ] ) and bony s paradifferential calculus ( section [ s.para ] ) . finally , appendix [ s.spectral ] is dedicated to some results on the eigenstructure of our system , which are used in section [ s.normal-form ] .

we study the predictability of emergent phenomena in complex systems . using nearest neighbor , one - dimensional cellular automata ( ca ) as an example , we show how to construct local coarse - grained descriptions of ca in all classes of wolfram s classification . we thus show that because in practice one only seeks coarse - grained information , complex physical systems can be predictable and even decidable at some level of description . we show that because of this large - scale simplicity , the probability of finding a coarse - grained description of ca approaches unity as one goes to increasingly coarser scales .

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nlin0508033

we study the predictability of emergent phenomena in complex systems . using nearest neighbor , one - dimensional cellular automata ( ca ) as an example , we show how to construct local coarse - grained descriptions of ca in all classes of wolfram s classification . the resulting coarse - grained ca that we construct are capable of emulating the large - scale behavior of the original systems without accounting for small - scale details . several ca that can be coarse - grained by this construction are known to be universal turing machines ; they can emulate any ca or other computing devices and are therefore undecidable . we thus show that because in practice one only seeks coarse - grained information , complex physical systems can be predictable and even decidable at some level of description . the renormalization group flows that we construct induce a hierarchy of ca rules . this hierarchy agrees well with apparent rule complexity and is therefore a good candidate for a complexity measure and a classification method . finally we argue that the large scale dynamics of ca can be very simple , at least when measured by the kolmogorov complexity of the large scale update rule , and moreover exhibits a novel scaling law . we show that because of this large - scale simplicity , the probability of finding a coarse - grained description of ca approaches unity as one goes to increasingly coarser scales . we interpret this large scale simplicity as a pattern formation mechanism in which large scale patterns are forced upon the system by the simplicity of the rules that govern the large scale dynamics .

the scope of the growing field of complexity science `` ( or complex systems '' ) includes a broad variety of problems belonging to different scientific areas . examples for complex systems `` can be found in physics , biology , computer science , ecology , economy , sociology and other fields . a recurring theme in most of what is classified as complex systems '' is that of _ emergence_. emergent properties are those which arise spontaneously from the collective dynamics of a large assemblage of interacting parts . a basic question one asks in this context is how to derive and predict the emergent properties from the behavior of the individual parts . in other words , the central issue is how to extract large - scale , global properties from the underlying or microscopic degrees of freedom . in the physical sciences , there are many examples of emergent phenomena where it is indeed possible to relate the microscopic and macroscopic worlds . physical systems are typically described in terms of equations of motion of a huge number of microscopic degrees of freedom ( e.g. atoms ) . the microscopic dynamics is often erratic and complex , yet in many cases it gives rise to patterns with characteristic length and time scales much larger than the microscopic ones ( e.g. the pressure and temperature of a gas ) . these large scale patterns often posses the interesting , physically relevant properties of the system and one would like to model them or simulate their behavior . an important problem in physics is therefore to understand and predict the emergence of large scale behavior in a system , starting from its microscopic description . this problem is a fundamental one because most physical systems contain too many parts to be simulated directly and would become intractable without a large reduction in the number of degrees of freedom . a useful way to address this issue is to construct coarse - grained models , which treat the dynamics of the large scale patterns . the derivation of coarse - grained models from the microscopic dynamics is far from trivial . in most cases it is done in a phenomenological manner by introducing various ( often uncontrolled ) approximations . the problem of predicting emergent properties is most severe in systems which are modelled or described by _ undecidable _ mathematical algorithms@xcite . for such systems there exists no computationally efficient way of predicting their long time evolution . in order to know the system s state after ( e.g. ) one million time steps one must evolve the system a million time steps or perform a computation of equivalent complexity . wolfram has termed such systems _ computationally irreducible _ and suggested that their existence in nature is at the root of our apparent inability to model and understand complex systems @xcite . it is tempting to conclude from this that the enterprise of physics itself is doomed from the outset ; rather than attempting to construct solvable mathematical models of physical processes , computational models should be built , explored and empirically analyzed . this argument , however , assumes that infinite precision is required for the prediction of future evolution . as we mentioned above , usually coarse - grained or even statistical information is sufficient . an interesting question that arises is therefore : is it possible to derive coarse - grained models of undecidable systems and can these coarse - grained models be decidable and predictable ? in this work we address the emergence of large scale patterns in complex systems and the associated predictability problems by studying cellular - automata ( ca ) . ca are spatially and temporally discrete dynamical systems composed of a lattice of cells . they were originally introduced by von neumann and ulam @xcite in the 1940 s as a possible way of simulating self - reproduction in biological systems . since then , ca have attracted a great deal of interest in physics @xcite because they capture two basic ingredients of many physical systems : 1 ) they evolve according to a local uniform rule . 2 ) ca can exhibit rich behavior even with very simple update rules . for similar and other reasons , ca have also attracted attention in computer science @xcite , biology @xcite , material science @xcite and many other fields . for a review on the literature on ca see refs . . the simple construction of ca makes them accessible to computational theoretic research methods . using these methods it is sometimes possible to quantify the complexity of ca rules according to the types of computations they are capable of performing . this together with the fact that ca are caricatures of physical systems has led many authors to use them as a conceptual vehicle for studying complexity and pattern formation . in this work we adopt this approach and study the predictability of emergent patterns in complex systems by attempting to systematically coarse - grain ca . a brief preliminary report of our project can be found in ref . . there is no unique way to define coarse - graining , but here we will mean that our information about the ca is locally coarse - grained in the sense of being stroboscopic in time , but that nearby cells are grouped into a supercell according to some specified rule ( as is frequently done in statistical physics ) . below we shall frequently drop the qualifier `` local '' whenever there is no cause for confusion . a system which can be coarse - grained is _ compact - able _ since it is possible to calculate its future time evolution ( or some coarse aspects of it ) using a more compact algorithm than its native description . note that our use of the term compact - able refers to the phase space reduction associated with coarse - graining , and is agnostic as to whether or not the coarse - grained system is decidable or undecidable . accordingly , we define _ predictable _ to mean that a system is decidable or has a decidable coarse - graining . thus , it is possible to calculate the future time evolution of a predictable system ( or some coarse aspects of it ) using an algorithm which is more compact than both the native and coarse - grained descriptions . our work is organized as follows . in section [ ca_intro ] we give an introduction to ca and their use in the study of complexity . in section [ cg_procedure ] we present a procedure for coarse - graining ca . section [ cg_results ] shows and discusses the results of applying our procedure to one dimensional ca . most of the ca that we attempt to coarse - grain are wolfram s 256 elementary rules for nearest - neighbor ca . we will also consider a few other rules of special interest . in section [ kolmogorov_complexity ] we consider whether the coarse - grain - ability of many ca that we found in the elementary rule family is a common property of ca . using computational theoretic arguments we argue that the large scale behavior of local processes must be very simple . almost all ca can therefore be coarse - grained if we go to a large enough scale . our results are summarized and discussed in [ conclusions ] .

the renormalization group flows that we construct induce a hierarchy of ca rules . finally we argue that the large scale dynamics of ca can be very simple , at least when measured by the kolmogorov complexity of the large scale update rule , and moreover exhibits a novel scaling law . we interpret this large scale simplicity as a pattern formation mechanism in which large scale patterns are forced upon the system by the simplicity of the rules that govern the large scale dynamics .

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nlin0508033

we study the predictability of emergent phenomena in complex systems . using nearest neighbor , one - dimensional cellular automata ( ca ) as an example , we show how to construct local coarse - grained descriptions of ca in all classes of wolfram s classification . the resulting coarse - grained ca that we construct are capable of emulating the large - scale behavior of the original systems without accounting for small - scale details . several ca that can be coarse - grained by this construction are known to be universal turing machines ; they can emulate any ca or other computing devices and are therefore undecidable . we thus show that because in practice one only seeks coarse - grained information , complex physical systems can be predictable and even decidable at some level of description . the renormalization group flows that we construct induce a hierarchy of ca rules . this hierarchy agrees well with apparent rule complexity and is therefore a good candidate for a complexity measure and a classification method . finally we argue that the large scale dynamics of ca can be very simple , at least when measured by the kolmogorov complexity of the large scale update rule , and moreover exhibits a novel scaling law . we show that because of this large - scale simplicity , the probability of finding a coarse - grained description of ca approaches unity as one goes to increasingly coarser scales . we interpret this large scale simplicity as a pattern formation mechanism in which large scale patterns are forced upon the system by the simplicity of the rules that govern the large scale dynamics .

in this work we studied emergent phenomena in complex systems and the associated predictability problems by attempting to coarse - grain ca . we found that many elementary ca can be coarse - grained in space and time and that in some cases complex , undecidable ca can be coarse - grained to decidable and predictable ca . we conclude from this fact that undecidability and computational irreducibility are not good measures for physical complexity . physical complexity , as opposed to computational complexity should address the interesting , physically relevant , coarse - grained degrees of freedom . these coarse - grained degrees of freedom maybe simple and predictable even when the microscopic behavior is very complex . the above definition of physical complexity brings about the question of the objectivity of macroscopic descriptions @xcite . is our choice of a coarse - grained description ( and its consequent complexity ) subjective or is it dictated by the system ? our results are in accordance with shalizi and moore @xcite : it is both . in many cases we discovered that a particular ca can undergo different coarse - graining transitions using different projection operators . in these cases the system dictates a set of valid projection operators and we are restricted to choose our coarse - grained description from this set . we do however have some freedom to manifest our subjective interest . the coarse - graining transitions that we found induce a hierarchy on the family of elementary ca ( see fig . [ mapfigure ] ) . moreover , it seems that rule complexity never increases with coarse - graining transitions . the coarse - graining hierarchy therefore provides a partial complexity order of ca where complex rules are found at the top of the hierarchy and simple rules are at the bottom . the order is partial because we can not relate rules which are not connected by coarse - graining transitions . this coarse - graining hierarchy can be used as a new classification scheme of ca . unlike wolfram s , classification this scheme is not a topological one since the basis of our suggested classification is not the ca trajectories . nor is this scheme parametric , such as langton s @xmath10 parameter scheme . our scheme reflects similarities in the algebraic properties of ca rules . it simply says that if some coarse - grained aspects of rule @xmath18 can be captured by the detailed dynamics of rule @xmath19 then rule @xmath18 is at least as complex as rule @xmath19 . rule @xmath18 maybe more complex because in some cases it can do more than its projection . note that our hierarchy may subdivide wolfram s classes . for example rule 128 is higher on the hierarchy than rule 0 . these two rules belong to class 1 but rule 128 can be coarse - grained to rule 0 and it is clear that an opposite transition can not exist . it will be interesting to find out if class 3 and 4 can also be subdivided . in the last part of this work we tried to understand why is it possible to find so many coarse - graining transitions between ca . at first blush , it seems that coarse - graining transitions should be rare because finding valid projection operators is an over constrained problem . this was our initial intuition when we first attempted to coarse - grain ca . to our surprise we found that many ca can undergo coarse - graining transitions . a more careful investigation of the above question suggests that finding valid projection operators is possible because of the structure of the rules which govern the large scale dynamics . these large scale rules are update functions for supercells , whose tables can be computed directly from the single cell update function . they thus contain the same amount of information as the single cell rule . their size however grows with the supercell size and therefore they have vanishing kolmogorov complexities . in other words , the large scale update functions are highly structured objects . they contain many regularities which can be used for finding valid projection operators . we did not give a formal proof for this statement but provided a strong experimental evidence . in our experiments we discovered that the probability to find a valid projection is a universal function of the kolmogorov complexity of the supercell update rule . this universal probability function varies from zero at large kolmogorov complexity ( small supercells ) to one at small kolmogorov complexity ( large supercells ) . it is therefore very likely that we find many coarse - graining transitions when we go to large enough scales . our interpretation of the above results is that of emergence . when we go to large enough scales we are likely to find dynamically identifiable large scale patterns . these patterns are emergent ( or self organized ) because they do not explicitly exist in the original single cell rules . the large scale patterns are forced upon the system by the lack of information . namely , the system ( the update rule , not the cell lattice ) does not contain enough information to be complex at large scales . finding a projection operator is one specific type of an over constrained problem . motivated by our results we looked into other types of over constrained problems . the satisfyability@xcite problem ( k - sat ) is a generalized ( np complete ) form of constraint satisfaction system . we generated random 3-sat instances with different number of variables deep in the un - sat region of parameter space . the generated instances however were not completely random and were generated by generating functions . the generating functions controlled the instance s kolmogorov complexity , in the same way that we used in section [ proj_prob_with_bounded_k ] . we found@xcite that the probability for these instances to be satisfiable obeys the same universal probability function of eq . ( [ rproj_fit ] ) . it will be interesting to understand the origin of this universality and its implications . in this work , we have restricted ourselves to deal with ca because it is relatively easy to look for valid projection operators for them . a greater ( and more practical ) challenge will now be to try and coarse - grain more sophisticated dynamical systems such as probabilistic ca , coupled maps and partial differential equations . these types of systems are among the main work horses of scientific modelling , and being able to coarse - grain them will be very useful , and is a topic of current research , e.g. in material science@xcite . it will be interesting to see if one can derive an emergence length scale for those systems like the one we found for garden of eden " sequences in ca ( section [ gardensofeden ] ) . such an emergence length scale can assist in finding valid projection operators by narrowing the search to a particular scale . ng wishes to thank stephen wolfram for numerous useful discussions and his encouragement of this research project . ni wishes to thank david mukamel for his help and advice . this work was partially supported by the national science foundation through grant nsf - dmr-99 - 70690 ( ng ) and by the national aeronautics and space administration through grant nag8 - 1657 .

we focus on i ) the localization volume of a mode which defines the number of interacting partner modes , ii ) the overlap integrals which determine the interaction strength , iii ) the average spacing between eigenvalues of interacting modes , which sets a scale for the nonlinearity strength , and iv ) resonance probabilities of interacting modes . our results are discussed in the light of recent studies on spreading of wave packets in disordered nonlinear systems , and are related to the quantum many body problem in a random chain .

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1005.4820

we study the properties of mode - mode interactions for waves propagating in nonlinear disordered one - dimensional systems . we focus on i ) the localization volume of a mode which defines the number of interacting partner modes , ii ) the overlap integrals which determine the interaction strength , iii ) the average spacing between eigenvalues of interacting modes , which sets a scale for the nonlinearity strength , and iv ) resonance probabilities of interacting modes . our results are discussed in the light of recent studies on spreading of wave packets in disordered nonlinear systems , and are related to the quantum many body problem in a random chain .

in the absence of nonlinearity ( or many - body interactions in quantum systems ) all eigenstates in one - dimensional random lattices with disorder are spatially localized . this is anderson localization @xcite , which has been discovered fifty years ago in disordered crystals as a localization of electronic wavefunction . it can be interpreted as an interference effect between multiple scatterings of the electron on random defects of the potential . recent experiments on the observation of anderson localization were performed with light propagation in spatially random optical media @xcite , with noninteracting bose - einstein condensates expanding in random optical potentials @xcite , and with wave localization in a microwave cavity filled with randomly distributed scatterers @xcite . in many situations nonlinear terms in the wave equations ( respectively , many body interaction terms in quantum systems ) have to be included . thus , a fundamental question which has attracted the attention of many researchers is what happens to an initial excitation of arbitrary shape in a nonlinear disordered lattice . nonlinearity renormalizes excitation frequencies , thereby inducing interaction between nms . numerical studies show that wave packets spread subdiffusively and anderson localization is destroyed @xcite . in the regime of strong nonlinearity , far from where it can be treated perturbatively , new localization effects of selftrapping occur @xcite . a theoretical explanation of the subdiffusive spreading was offered in refs . it is based on the fact that the considered models are in general nonintegrable . therefore deterministic chaos will lead to an incoherent spreading . estimates of the excitation transfer rate across the packet tail are obtained by calculating probabilities of mode - mode resonances inside the packet . some predictions of this approach include the effect of different degrees of nonlinearity and were successfully tested in @xcite . in this work we study the statistical properties of mode - mode interactions . we focus on i ) the localization volume of a mode which defines the number of interacting partner modes , ii ) the overlap integrals which determine the interaction strength , iii ) the average spacing between eigenvalues of interacting modes which sets a scale for the nonlinearity strength , and iv ) resonance probabilities of interacting modes . we discuss the results in the light of recent studies @xcite on spreading of wave packets in disordered nonlinear systems , and relate our findings to the quantum two interacting particle problem in a random chain . versus normalized eigenvalue for w=0.5 , 1 , 2 , 4 ( from top to bottom ) . inset : zoom for w=0.5 around the bandwidth center . ]

we study the shadows of the fully non - linear , asymptotically flat einstein - dilaton - gauss - bonnet ( edgb ) black holes ( bhs ) , for both static and rotating solutions . we find that , in all cases , these shadows are _ smaller _ than for _ comparable _ kerr bhs , @xmath0 with the same total mass and angular momentum . in order to compare both cases we provide quantitative shadow parameters , observing in particular that the differences in the shadows mean radii are never larger than the percent level . we speculate that this is due to the fact that the komar energy interior to the light rings ( or more precisely , the surfaces of constant radial coordinate that intersect the light rings in the equatorial plane ) is always smaller than the adm mass , and consequently the corresponding shadows are smaller than those of comparable kerr bhs .

i

1701.00079

we study the shadows of the fully non - linear , asymptotically flat einstein - dilaton - gauss - bonnet ( edgb ) black holes ( bhs ) , for both static and rotating solutions . we find that , in all cases , these shadows are _ smaller _ than for _ comparable _ kerr bhs , @xmath0 with the same total mass and angular momentum . in order to compare both cases we provide quantitative shadow parameters , observing in particular that the differences in the shadows mean radii are never larger than the percent level . therefore , generically , edgb bhs @xmath1 be excluded by ( near future ) shadow observations alone . on the theoretical side , we find no clear signature of some exotic features of edgb bhs on the corresponding shadows , such as the regions of negative ( komar , say ) energy density outside the horizon . we speculate that this is due to the fact that the komar energy interior to the light rings ( or more precisely , the surfaces of constant radial coordinate that intersect the light rings in the equatorial plane ) is always smaller than the adm mass , and consequently the corresponding shadows are smaller than those of comparable kerr bhs . the analysis herein provides a clear example that it is the light ring impact parameter , rather than its size " , that determines a bh shadow .

ultraviolet theoretical inconsistencies of einstein s general relativity , such as its non - renormalizability @xcite and the existence of singularities , have since long motivated the suggestion that higher curvature corrections should be taken into account , in an improved theory of gravity ( see @xmath2 @xcite ) . inclusion of a finite set of such higher curvature corrections , however , generically leads to runaway modes ( ostrogradsky instabilities @xcite ) in the classical theory and a breakdown of unitarity due to ghosts , in the quantum theory . these undesirable properties can be simply diagnosed , at the level of the classic field equations , by the presence of third order time ( and consequently also space , by covariance ) derivatives . a natural way around this problem is to require a self - consistent model , obtained as a truncation of the higher curvature expansion , to yield a set of field equations without such higher order derivatives . lovelock @xcite first established , for vacuum gravity , what are the allowed curvature combinations so that the field equations have no higher than second order time derivatives . it turns out that , in a lagrangian , these combinations are simply the euler densities , particular scalar polynomial combinations of the curvature tensors of order @xmath3 . since the @xmath4 euler density is a topological invariant in spacetime dimension @xmath5 and yields a non - dynamical contribution to the action in dimensions @xmath6 , an immediate corollary is that , in @xmath7 vacuum gravity , the most general lovelock theory is a combination of the 0@xmath8 and 1@xmath9 euler density , or in other words , general relativity with a cosmological constant . the 2@xmath10 euler density , known as the gauss - bonnet ( gb ) combination , is a topological invariant in @xmath7 and does not contribute to the dynamical equations of motion if included in the action . there is , however , a simple and natural way to make the gb combination dynamical in a @xmath7 theory : couple it to a dynamical scalar field . this is actually a model that emerges naturally in string theory @xcite ( see also @xcite for a discussion on this point ) , where the scalar field is the dilaton , and can be considered as a simple effective model to investigate the consequences of higher curvature corrections in @xmath7 gravity . the corresponding model takes the name of einstein - dilaton - gauss - bonnet ( edgb ) theory and is described by the action in section [ section_model ] below . black holes ( bhs ) in edgb theory were first shown to exist , in spherical symmetry , by kanti et al . @xcite , wherein they were obtained numerically . these solutions , which moreover are perturbatively stable along their main branch @xcite , are asymptotically flat , regular on and outside an event horizon , and describe a horizon surrounded by a non - trivial dilaton profile . they circumvent some well - known no ( real ) scalar hair theorems , namely those by bekenstein @xcite ( see @xcite for a recent review ) , due to the non minimal coupling of the dilaton to the geometry and the fact that if one associates some _ effective matter _ with the gb term , then this represents _ exotic matter _ , violating the typical energy conditions . one manifestation of this _ effective exotic matter _ is that the bh solutions have regions of negative energy density outside the horizon . another manifestation is that there is a minimal mass for bhs , determined by the gb coupling . we remark that the scalar hair of this bhs has no - independent conserved charge , thus being called _ secondary_. see , @xmath2 @xcite for further discussions of these spherically symmetric solutions and some charged generalizations . rotating bhs in edgb theory were found , fully non - linearly in @xcite ( see also @xcite for perturbative studies ) . a minimal mass depending on the gb coupling still exists for these rotating solutions and , as a novel physical feature , some ( small ) violations of the kerr bound in terms of adm quantities are observed . again , regions with negative energy density exist outside the horizon . in this paper , we shall investigate how the dgb term impacts on one particular observable feature of a bh : its shadow @xcite . bh shadows can be roughly described as the silhouette produced by the bh when placed in front of a bright background . they are determined by the bh absorption cross section for light at high frequencies . over the last few years there has been a renewed theoretical interest in this old concept , first discussed for the kerr bh by bardeen @xcite , due to observational attempts to measure the bh shadow of the supermassive bhs in our galactic center as well as that in the centre of m87 @xcite . in particular , in @xcite , the shadows of a type of hairy bhs that connect continuously to kerr , within general relativity and with matter obeying all energy conditions , called kerr bhs with scalar hair @xcite , have been studied . it has been pointed out that , generically , these shadows are smaller than those of a comparable kerr bh , @xmath0 a vacuum rotating bh with the same total mass and angular momentum . a possible interpretation of this qualitative behaviour is the following : the total mass ( and angular momentum ) of the hairy bhs is now partly stored in the scalar field outside the horizon ; in particular the existence of some energy outside the region of unstable spherical photon orbits , also referred to as photon region ( see section [ subsection_ligh - rings ] ) , implies that less energy exists inside this region and hence the light rings should be smaller ( within an appropriate measure ) as compared to their vacuum counterparts and consequently so should be the shadows . the above interpretation raises an interesting question in relation to the bhs in edgb theory . since these have negative energy densities outside the horizon , how do these regions of _ effective exotic matter _ impact on their shadows ? in particular could there be a negative energy contribution outside the photon region that is sufficiently large to increase the shadow size with respect to a vacuum counterpart ? we remark that for other non - vacuum solutions with physical matter , @xmath0 obeying all energy conditions , the size of the shadow typically decreases with respect to the size of a comparable vacuum kerr bh see @xmath2 @xcite for electrically charged bhs . however , larger shadows have also been observed , @xmath2 , in extended chern - simons gravity @xcite or brane world bhs @xcite which possess _ effective exotic matter _ , similarly to edgb . nevertheless , we shall see that for edgb the shadows are always smaller with respect to the vacuum case , with the maximal deviation being of the order of only a few percent . for some work on bh shadows in different models see @xcite , and in particular @xcite for perturbative edgb bhs . this paper is organized as follows . in section [ section_model ] we describe the edgb model and present its field equations . an overview of the known bh solutions in this model , both static and stationary , is also provided there , together with the corresponding domain of existence and limiting cases . then , in section [ section_shadows ] we present the shadows for a representative sample of solutions and interpret the patterns obtained . we close with a discussion in section [ section_discussion ] .

therefore , generically , edgb bhs @xmath1 be excluded by ( near future ) shadow observations alone . on the theoretical side , we find no clear signature of some exotic features of edgb bhs on the corresponding shadows , such as the regions of negative ( komar , say ) energy density outside the horizon . the analysis herein provides a clear example that it is the light ring impact parameter , rather than its size " , that determines a bh shadow .

c

1701.00079

we study the shadows of the fully non - linear , asymptotically flat einstein - dilaton - gauss - bonnet ( edgb ) black holes ( bhs ) , for both static and rotating solutions . we find that , in all cases , these shadows are _ smaller _ than for _ comparable _ kerr bhs , @xmath0 with the same total mass and angular momentum . in order to compare both cases we provide quantitative shadow parameters , observing in particular that the differences in the shadows mean radii are never larger than the percent level . therefore , generically , edgb bhs @xmath1 be excluded by ( near future ) shadow observations alone . on the theoretical side , we find no clear signature of some exotic features of edgb bhs on the corresponding shadows , such as the regions of negative ( komar , say ) energy density outside the horizon . we speculate that this is due to the fact that the komar energy interior to the light rings ( or more precisely , the surfaces of constant radial coordinate that intersect the light rings in the equatorial plane ) is always smaller than the adm mass , and consequently the corresponding shadows are smaller than those of comparable kerr bhs . the analysis herein provides a clear example that it is the light ring impact parameter , rather than its size " , that determines a bh shadow .

the shadow of a edgb bh is always smaller than the comparable kerr one . however , the deviations observed are always smaller ( in modulus ) than a few percent ( @xmath127 ) . since such differences are below the expected resolution of planned observations @xcite , it is unlikely that in the near future any shadow measurement can exclude or restrict edgb models . + since edgb theory possesses unusual features such as _ effective exotic matter _ , it might come as a surprise that there are no significant effects at the level of the shadow . however , this _ effective exotic matter _ is concentrated close to the horizon , such that there is no negative energy contribution outside the photon region that could significantly affect the shadow s size . at the same time any near - horizon odd effects are concealed from a remote observer by the shadow . + it may come as another surprise , that the light ring size in @xmath36 units can be used as an invariant measure for the light ring size . ] of edgb bhs can , for instance , change by as much as @xmath128 , when considering the static case with @xmath124 , and this effect will increase with further decreasing @xmath16 . the natural question is then : why are the deviations in the shadow size not larger ? for the sake of the argument consider the static case , where it becomes clear that the critical ingredient for the shadow radius is the impact parameter @xmath95 , and not the light ring size . naturally , there is a strong correlation between both concepts , but at the end of the day what matters is the value of the impact parameter . we would like to point out that this observation is often not clear enough in the literature : a large variation of the light ring size does not have to lead to equally large variations of the shadow radius .

we study the system that two atoms simultaneously interact with a single - mode thermal field via different couplings and different spontaneous emission rates when two - photon process is involved . it is found that we indeed can employ the different couplings to produce the atom - atom thermal entanglement in two - photon process . the different atomic spontaneous emission rates are also utilizable in generating thermal entanglement . we also investigate the effect of the cavity leakage . to the initial atomic state @xmath0a slight leakage can relieve the restriction of interaction time and we can obtain a large and steady entanglement . pacs number : 03.67.-a , 03.67.-hz , 42.50.-p

i

quant-ph0509146

we study the system that two atoms simultaneously interact with a single - mode thermal field via different couplings and different spontaneous emission rates when two - photon process is involved . it is found that we indeed can employ the different couplings to produce the atom - atom thermal entanglement in two - photon process . the different atomic spontaneous emission rates are also utilizable in generating thermal entanglement . we also investigate the effect of the cavity leakage . to the initial atomic state @xmath0a slight leakage can relieve the restriction of interaction time and we can obtain a large and steady entanglement . pacs number : 03.67.-a , 03.67.-hz , 42.50.-p

entanglement plays an important role in respect that it is a valuable resource in quantum information processing such as quantum teleportation1 , quantum computation@xcite and quantum cryptography@xcite , _ etc_. several schemes have been proposed to prepare purified and distilled entangled state both theoretically and experimentally@xcite . although the interaction between a quantum system and its surroundings can result in inevitable decoherence of the quantum system , people have recognized that we can employ the interaction to generate entanglement@xcite . the two - atom entangled states are widely studied in cavity qed6,7,8,9,10 . in cavity qed , the dissipation in the model of atoms interacting with magnetic field generally includes two aspects : the cavity leakage through which the intra - cavity magnetic field can exchange information with its environmental noise , the atomic spontaneous emission that is induced by vacuum fluctuation effect . in the sense of using the impact of environmental noise , the noise - assisted entanglement schemes have been put forward by many authors@xcite . plenio and co - work have developed schemes that involves continuous monitoring of photons leaking out of the cavity to entangle atoms one of which is initially exicted@xcite . in ref . [ 10 ] , the author studied the interaction of a thermal field with a two - qubit system that initially prepared in separable states . they demonstrated that entanglement of atom - atom can arise depending on initial preparation of the atoms . also in ref . [ 11 ] , the entanglemet of atom - atom can be generated through interaction of atoms with cavity mode coupled to a white noise . their entanglement can be maximized for intermediate value of noise intensity and initial value of spontaneous rate . in these studies , the couplings of atoms to field are confined to be equal . in fact , the coupling rate @xmath1 between atomic internal levels and the cavity mode depends on the atom s position @xmath2 @xcite . the atoms can not be localized precisely even by employing cooling technology and trapping potential schemes . so , it is practically necessary to address the question : how will the entanglement be when two atoms differently couple to a single model field ? in ref.@xcite , our gruop had shown that different couplings can really assist the induce of entanglement in one - photon process . on the other hand , the atomic spontaneous emission rate is also related to atoms s position@xcite . in real experimental scenario , the atoms s position @xmath2 not only dominates the atom s coupling strength to the field , but also determines the amount of atomic spontaneous emission rate . it has already been reported that the resonant cavity which was made of two spherical niobioum mirrors can enhance or suppress single atomic spontaneous emission by adjusting atom position @xmath3 ( the distance from median plane of cavity)@xcite . but theoretically , atomic spontaneous emissions have been assumed to be equal or even been ignored , and the spontaneous emission has been disliked because of its impact on the entanglement@xcite . up to now we have not found the study that two atoms spontaneous emission rates are not the same . addition to that , the two - photon process is a kind of important one which may show different properties from the case of one photon in quantum information processing , for example , it has been found that the atom - atom entanglement induced by thermal field in two - photon process is larger than that in one - photon process@xcite . in this paper , considering the two - photon process , we aim to study the two atoms simultaneously interacting with a single - mode cavity field with different couplings and different spontaneous emission rates . we find that in two - photon process we indeed can employ the different couplings to produce the the atom - atom thermal entanglement . if the atoms spontaneously emit inevitably , the different spontaneous emission rates is utilizable in generating thermal entanglement . we also investigate the effect of the cavity leakage . to the initial atomic state @xmath4 , the cavity dissipation should be supressed as possible as we can , but to the initial atomic state @xmath0we can keep a slight leakage to relieve the restriction of interaction time so that we can obtain a large and steady entanglement .

we include the effects of confinement by expanding this degree of freedom in harmonic oscillator states . we then study the properties of the resulting multi - channel system . we study the adiabatic curves as a function of @xmath0 , the ratio of the dipolar and confinement length scales .

c

1003.3637

we study two body dipolar scattering with one dimension of confinement . we include the effects of confinement by expanding this degree of freedom in harmonic oscillator states . we then study the properties of the resulting multi - channel system . we study the adiabatic curves as a function of @xmath0 , the ratio of the dipolar and confinement length scales . there is no dipolar barrier for this system when @xmath1 . we also study the wkb tunneling probability as a function of @xmath0 and scattering energy . this can be used to estimate the character of the scattering .

in this paper we have studied quasi 2 dimensional dipolar scattering . we included the effects of confinement by expanding this degree of freedom in harmonic oscillator states , and studied the properties of the resulting multi - channel system . we examined the adiabatic curves as a function of @xmath17 , and found there is a dipolar barrier only when @xmath83 . we used the lowest adiabatic curve to obtain the wkb tunneling probability of this system . we found fits of @xmath65 in the threshold and semi - classical scattering regime . when the system is tunneling dominated these will be good estimates of how likely particles are to make it to the short range . this might also be related to the width of resonances in the system . [ character ] offers a quick means to estimate whether an effective barrier will be produced by a molecular system in an optical lattice . the physical implications of this work are simple , try to maximize @xmath84 . @xmath17 must exceed 0.34 for there to be a dipolar barrier , and should be much larger to significantly inhibit the particles from reaching the short range . if one desires to have a gas in the threshold regime , one must also keep @xmath85 less than 1 . this will leads to an optimal value of @xmath3 , which is set by the external electric field . to give a physical example , set @xmath86nk and @xmath87khz . then for lics , @xmath17 can exceed 100 . however the cost of this would be to make @xmath88 minuscule , less than 1nk , and this would lead to semi - classical scattering . to maintain the thresholds scattering one would have set the field to @xmath89 where @xmath90 is the rotational constant of @xmath91 molecule and @xmath92 is the bare dipole moment . at this field @xmath93 and @xmath94 , which is in the threshold regime and produces @xmath95 . an important physical example is rbk @xcite , for this system if the field is @xmath96 , the field will produce @xmath97 , @xmath98 and @xmath99 . to further decrease @xmath65 lowering the scattering energy might be more feasible than producing a tighter trap . this system will have threshold dipolar scattering and will help suppress the chemical reactions @xcite . there are several important future directions of this research . for example how does the scattering behave when @xmath100 and there are many open confinement thresholds ? how are the resonances in this quasi 2d systems related to the threshold resonances in 3d dipolar systems ? to address this question a short range interaction must be included . this will also open up many avenues for further and more complete studies of these collisions . the author gratefully acknowledges support from the australian research council and partial support from nsf through itamp at harvard university and smithsonian astrophysical observatory . the author thanks s. rittenhouse and e. kuznetsova for discussions . 99 k .- k . et al . _ , science * 322 * 231 , ( 2008 ) . for a recent review see : l. d. carr _ et al . _ new j. phys . * 11 * , 055049 ( 2009 ) . _ , arxiv:1001.2809 . c. ticknor , phys . , * 100 * 133202 ( 2008 ) ; phys . rev . a * 76 * , 052703 ( 2007 ) . v. roudnev and m. cavagnero , phys . a , * 79 * 014701 ( 2009 ) ; j. phys . b , * 42 * , 044017 ( 2009 ) . j. l. bohn , m. cavagnero , and c. ticknor , new j. phys . * 11 * 055039 ( 2009 ) . h. r. sadeghpour , _ et al . _ , j. phys . b * 33 * , r93 ( 2000 ) . e. r. hudson , _ et al . a * 73 * , 063404 ( 2006 ) . s. ospelkaus , _ et al . _ , arxiv:0912.3854 . r. v. krems , physical chemistry chemical physics * 10 * , 4079 ( 2008 ) . z. hadzibabic , _ et al . _ , nature ( london ) * 441 * , 1118 ( 2006 ) p. clade , c. ryu , a. ramanathan , k. helmerson , and w. d. phillips , phys . rev * 102 * , 170401 ( 2009 ) . h. p. bchler , _ et al . _ , phys . rev . lett . * 98 * , 060404 ( 2007 ) . p. rabl and p. zoller , phys . a * 76 * , 042308 ( 2007 ) . d. s. petrov and g. v. shlyapnikov , phys . a , * 64 * , 012706 ( 2001 ) ; d. s. petrov , m. holzmann , and g. v. shlyapnikov , phys . lett . * 84 * , 2551 ( 2000 ) . et al . _ , phys . rev . * 100 * , 073202 ( 2008 ) ; z. li and r. v. krems , phys . a * 79 * , 050701(r ) ( 2009 ) . s. sinha and l. santos , phys . lett . * 99 * , 140406 ( 2007 ) . gu and s. w. quian , phys . lett . a * 136 * , 6 ( 1989 ) . c. ticknor , phys . rev . a. * 80 * 052702 ( 2009 ) . c. h. greene , phys . a * 36 * 4236 ( 1987 ) ; b. e. granger and d. blume phys . rev . lett . * 92 * 133202 ( 2004 ) . m. aymar , c. h. greene , and e. luc - koenig rev . * 68 * 1015 ( 1996 ) ; b. gao , phys . a * 78 * , 012702 ( 2008 ) .

the particle - hole symmetry of majorana states would normally lead to a vanishing seebeck coefficient , i.e. , a vanishing open - circuit voltage resulting from a temperature gradient . we discuss how coupling to a quantum dot with a gate - controlled energy level breaks particle - hole symmetry in a tunable manner . the resulting gate - dependent seebeck coefficient provides a new way to evidence the existence of majorana states , which can be combined with conventional tunnel spectroscopy in the same setup .

c

1310.3645

we theoretically investigate the possibility to use thermolectric measurements to detect majorana bound states and to investigate their coupling to a dissipative environment . the particle - hole symmetry of majorana states would normally lead to a vanishing seebeck coefficient , i.e. , a vanishing open - circuit voltage resulting from a temperature gradient . we discuss how coupling to a quantum dot with a gate - controlled energy level breaks particle - hole symmetry in a tunable manner . the resulting gate - dependent seebeck coefficient provides a new way to evidence the existence of majorana states , which can be combined with conventional tunnel spectroscopy in the same setup . furthermore , the thermoelectric properties rely on the ability of the quantum dot - majorana system to sense the temperature of the bulk superconductor and can be used to extract information about the dissipative decay of majorana states , which is crucial for quantum information applications .

in this work , we have theoretically investigated the thermoelectric properties of a n - qd - mbs junction . the qd level breaks particle - hole symmetry , which is otherwise perfect for a mbs , and leads to a finite seebeck effect . the seebeck coefficient is calculated as a function of the qd level position and is shown to be different for the qd - mbs system than for other origins of sharp conductance resonances . thermoelectric measurements can therefore provide evidence of mbs complementary to standard conductance measurements , where both experiments can be done in the same setup . a further advantage of thermoelectric measurements is that , unlike the conductance , the seebeck coefficient remains large even for very weak tunnel coupling to the mbs . in addition , we have shown that the seebeck coefficient is sensitive to the nature and strength of the coupling of the qd - mbs system to its dissipative environment . for example , the result is markedly different when dissipation is dominated by subgap states in the sc compared to when it is dominated by quasiparticle poisoning . if quasiparticle poisoning dominates dissipation , the associated rate could be estimated from the shape and amplitude of @xmath121 , even without coupling between the two end mbs . i am grateful to heiner linke , hongqi xu , and karsten flensberg for discussions and feedback on the manuscript . financial support from the swedish research council ( vr ) is gratefully acknowledged .

we use a sample of 7 starburst galaxies at intermediate redshifts ( @xmath0 and @xmath1 ) with observations ranging from the observed ultraviolet to 1.4 ghz , to compare the star formation rate ( sfr ) estimators which are used in the different wavelength regimes . galaxies with very different levels of dust extinction as measured with sfr@xmath3/sfr(@xmath4,uncorrected for extinction ) present a similar attenuation a[h@xmath2 ] , as if the balmer lines probed a different region of the galaxy than the one responsible for the bulk of the ir luminosity for large sfrs . we extend this result up to @xmath1 . finally , one of the studied objects is a luminous compact galaxy ( lcg ) that may be suffering similar dust - enshrouded star formation episodes .

c

astro-ph0210344

we use a sample of 7 starburst galaxies at intermediate redshifts ( @xmath0 and @xmath1 ) with observations ranging from the observed ultraviolet to 1.4 ghz , to compare the star formation rate ( sfr ) estimators which are used in the different wavelength regimes . we find that _ extinction corrected _ h@xmath2 underestimates the sfr , and the degree of this underestimation increases with the infrared luminosity of the galaxies . galaxies with very different levels of dust extinction as measured with sfr@xmath3/sfr(@xmath4,uncorrected for extinction ) present a similar attenuation a[h@xmath2 ] , as if the balmer lines probed a different region of the galaxy than the one responsible for the bulk of the ir luminosity for large sfrs . in addition , sfr estimates derived from [ o ii]@xmath63727 match very well those inferred from h@xmath2 after applying the metallicity correction derived from local galaxies . sfrs estimated from the uv luminosities show a dichotomic behavior , similar to that previously reported by other authors in galaxies at @xmath7 . here we extend this result up to @xmath1 . finally , one of the studied objects is a luminous compact galaxy ( lcg ) that may be suffering similar dust - enshrouded star formation episodes . these results highlight the relevance of quantifying the actual @xmath8 of lcgs , as well as that of a much larger and generic sample of luminous infrared galaxies , which will be possible after the launch of sirtf .

in this work we have compared several star formation rate estimators using a small but diverse sample of galaxies at two intermediate redshifts ( @xmath0 and @xmath1 ) . by selecting the sample galaxies on the basis of their isocam-15 @xmath12 m mid - infrared luminosities , we have sampled sfrs ranging from 2 to 160 m@xmath166 . their morphological types include spiral , compact and merging emission - line galaxies . it is important to highlight that the redshift segregation of the sample is also accompanied by a segregation in total far - infrared luminosity , with the farthest galaxies being the most luminous . this fact leads to an ambiguity between luminosity and distance that must be kept in mind when interpreting the results . the observed spectral range includes the most prominent optical emission lines , from [ o ii]@xmath63727 to [ s ii]@xmath396716,6731 . the availability of h@xmath15 and h@xmath2 allows the determination of color excesses in the nebular gas and correcting the emission - line fluxes for extinction . the diagnostic diagrams generated from the corrected emission - line ratios confirm the star - forming nature of the galaxies , as it was already suggested by evidence from their total far - infrared luminosity , observations in the x - ray domain , and the absence of broad emission lines . in addition , the overall characteristics of the selected galaxies , in particular their metallicity and structural properties , also match those of star forming galaxies , both local and at intermediate redshifts . the good agreement between hst and ground - based photometry , in one hand , and the spectrophotometric calibration of the spectra , on the other , allows us to be confident on the reliability of the estimated aperture corrections , the final optical emission - line luminosities , and thus the sfrs from them obtained . our results have shown the following . \(i ) there is a general good agreement in the comparison between the five available sfr indicators ( from uv , [ o ii ] , h@xmath2 , ir and radio luminosities ) for the @xmath0 ( l@xmath167 l@xmath62 ) galaxies , whereas the situation is not the same in the case of the @xmath1 ( l@xmath168 l@xmath62 ) subsample , being the discrepancies different depending on the considered sfr estimator . focusing in the @xmath1 galaxies , the sfrs derived from uv , [ o ii ] and ir luminosities are , respectively , lower , similar and higher , than the values obtained from h@xmath2 . the paradoxical behavior of sfr@xmath150 versus sfr@xmath157 is still subject of debate , and among the possible explanations for the observed discrepancies are temporal variations in the star formation history and luminosity dependent attenuations of the uv emission . from the observational perspective , we confirm the findings of @xcite and extend their result up to @xmath1 . \(ii ) the correction for metallicity of the [ o ii]/h@xmath2 ratio ( using the relation found in local galaxies ) greatly improves the concordance between the sfrs derived from the extinction corrected luminosities of both emission lines . the correction does in fact work for the galaxies in our sample in the two redshift ( or luminosity ) bins . \(iii ) the fit given in eq . ( [ sfrratio_lir ] ) , and shown in fig . [ figure_psfr ] , indicates that _ extinction corrected _ sfr@xmath157 estimates in luminous infrared galaxies at intermediate redshifts miss an increasing fraction of the total sfr , and that the degree of underestimation increases with @xmath8 . this result confirms the finding by @xcite who used an averaged extinction correction of @xmath169 derived from @xmath170 colors . in this work we quantify more rigorously this effect by employing line fluxes corrected for extinction making use of color excesses computed from the balmer decrement . thus , there is here an observational evidence that the balmer emission lines , h@xmath2 and h@xmath15 , do not probe the same region of a galaxy than the one which is responsible for the strong ir luminosity in the case of luminous ir galaxies . this is even more remarquable in fig . [ figure_sfr_amag ] where galaxies with very different sfrs share the same a[h@xmath2 ] . the spatial resolution in the mir is not sufficient to confirm this statement at these redshifts , but the case of the antennae galaxy ngc 4038/4039 @xcite offers a perfect example of such behavior in the local universe . a possible explanation for this effect is that a fraction of the star formation in these galaxies is embedded in dense and opaque dust clouds and that this fraction increases with the total star formation . as already expected , galaxy encounters ( hd2 - 264.1 and hd2 - 264.2 ) and mergers ( gss073_1810 ) are the likely causes for triggering star formation episodes . whether a quantitative estimation of the hidden star formation is definitely inaccessible to rest - frame optical spectroscopic studies , and in particular to the use of the measured h@xmath2 extinction , seems unclear , and deserves further research work . some kind of evolution in galaxies with @xmath159 l@xmath62 at @xmath171 can not be discarded , since , as we have shown in fig . [ figure_psfr ] , an important fraction of local galaxies with those luminosities does not show such a large underestimation of the sfr when using h@xmath2 fluxes instead of far - infrared luminosities . however the scarcity of the galaxy samples strongly demands additional observational work in order to settle this point . the inclusion of two apparently compact galaxies in our sample has allowed us to analyze the relation between the different sfr estimators applied to this kind of object relative to what is measured for spiral - like galaxies . in particular , one of these two objects qualifies as a luminous compact galaxy , with similar properties to those of the lcgs at intermediate redshifts studied by @xcite . surprisingly , this object may be suffering similar dust - enshrouded star formation processes as galaxies with a very different morphological aspect , like the bona fide spiral gss084_4521 or even the antenae - like colliding system gss073_1810 . the confirmation of this still speculative result , which has important implications concerning the accurate estimation of the cosmic sfr density at intermediate redshifts , will be possible after the launch of sirtf . valuable discussions with jaime zamorano , pablo prez - gonzlez and ranga - ram chary are gratefully acknowledged . we thank herv aussel for facilitating us the deconvolved iscocam flux for hd2 - 264.1 and hector flores for providing us with his revised isocam fluxes for the gss galaxies . we are grateful to the staff of the w. m. keck observatory for their help during the observations . this research has made use of the simbad database , operated at cds , strasbourg , france . support for this work has been provided by nsf grants ast 95 - 29028 and ast 00 - 71198 . n.c . acknowledges financial support from a ucm fundacin del amo fellowship , a short contract at ucsc , and from the spanish programa nacional de astronoma y astrofsica under grant aya2000 - 977 . d.e . wishes to thank the american astronomical society for its support through the chretien international research grant and joel primack and david koo for supporting his research through nasa grants nag5 - 8218 and nag5 - 3507 . acknowledges support provided by the national science foundation through grant gf-1002 - 99 and from the association of universities for research in astronomy , inc . , under nsf cooperative agreement ast 96 - 13615 , and cnpq / brazil , for financial support through grant 200510/99 - 1 . j.g.acknowledges financial support from the spanish programa nacional de astronoma y astrofsica under grant aya2000 - 1790 . aragn - salamanca , a. , et al . 2002 , , submitted aussel , h. , cesarsky , c. j. , elbaz , d. , and starck , j. l. 1999 , , 342 , 313 balzano , v. a. 1983 , , 268 , 602 bell , e. f. , and kennicutt , r. c. 2001 , , 548 , 681 bertin , e. , and arnouts , s. 1996 , , 117 , 393 blain , a. w. , smail , i. , ivison , r. j. , and kneib , j. 1999 , , 302 , 632 bouchet , p. , lequeux , j. , maurice , e. , prvot , l. , and prvot - burnichon , m. l. 1985 , , 149 , 330 brandt , w. n. , et al . 2001 , , 122 , 1 brunner , r. j. , connolly , a. j. , and szalay , a. s. 1999 , , 516 , 563 buat , v. , boselli , a. , gavazzi , g. , bonfanti , c. 2002 , , 383 , 801 calzetti , d. , kinney , a. l. , and storchi - 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264.1 & 12 36 49.76 & 62 13 13.1 & 0.475 & 0.012 & 4 ( 0.75 ) & 1200 + hd2 - 264.2 & 12 36 49.38 & 62 13 11.2 & 0.477 & 0.012 & 4 ( 0.75 ) & 1200 + hd4 - 656.1 & 12 36 42.91 & 62 12 16.3 & 0.454 & 0.012 & 4 ( 1.25 ) & 900 + hd4 - 795.111 & 12 36 41.95 & 62 12 05.4 & 0.433 & 0.012 & 4 ( 1.25 ) & 900 + gss073_1810 & 14 17 42.64 & 52 28 45.3 & 0.831 & 0.007 & 1 ( 1.18 ) , 5 ( 0.76 ) & 3000 , 2400 + gss084_4515 & 14 17 40.43 & 52 27 19.4 & 0.812 & 0.008 & 3 ( 1.00 ) , 5 ( 0.76 ) & 3600 , 2400 + gss084_4521 & 14 17 40.55 & 52 27 13.6 & 0.754 & 0.008 & 2 ( 1.00 ) , 5 ( 0.76 ) & 3000 , 2400 l@c@c@c@c@c@c@c@c@c@c@ @xmath172 & @xmath173 & @xmath174 & @xmath175 & @xmath176 & @xmath177 & @xmath178 & @xmath179 & @xmath180 & @xmath181 & @xmath182 + @xmath183 & @xmath184 & @xmath185 & @xmath186 & @xmath187[r]{$>$}0.63 & ( 1 ) \\\mbox{---}\end{array } $ ] & @xmath188 & @xmath189 & @xmath190 & @xmath191 & @xmath192 & @xmath193 + @xmath194 & @xmath195 & @xmath196 & @xmath197 & @xmath198 & @xmath191 & @xmath199 & @xmath200 & @xmath201 & @xmath202 & @xmath203 + @xmath204 & @xmath205 & @xmath206 & @xmath207 & @xmath208 & @xmath191 & @xmath209 & @xmath210 & @xmath211 & @xmath212 & @xmath213 + @xmath214 & @xmath215 & @xmath216 & @xmath191 & @xmath191 & @xmath217 & @xmath218 & @xmath219 & @xmath220 & @xmath221 & @xmath222 + @xmath223 & @xmath224 & @xmath225 & @xmath191 & @xmath191 & @xmath226 & @xmath227 & @xmath228 & @xmath229 & @xmath230 & @xmath231 + @xmath232 & @xmath233 & @xmath234 & @xmath235 & @xmath236 & @xmath237 & @xmath238 & @xmath239 & @xmath240 & @xmath241 & @xmath242 + @xmath243 & @xmath244 & @xmath245 & @xmath246 & @xmath191 & @xmath247 & @xmath248 & @xmath249 & @xmath250 & @xmath251 & @xmath252 + lcccc hd2 - 264.1 & @xmath253 & @xmath254 & @xmath254 & @xmath255 + hd2 - 264.2 & @xmath256 & @xmath257 & @xmath258 & @xmath259 + & & & & + & & & & + hd4 - 656.1 & @xmath260 & @xmath261 & @xmath262 & @xmath263 + hd4 - 795.111 & @xmath264 & @xmath265 & @xmath266 & @xmath267 + & & & & + & & & & + gss073_1810 & @xmath268 & @xmath269 & @xmath270 & @xmath271 + & & & & + & & & & + gss084_4515 & @xmath272 & @xmath273 & @xmath274 & @xmath275 + gss084_4521 & @xmath276 & @xmath253 & @xmath277 & @xmath278 + lccccc hd2 - 264.1 & @xmath279 & @xmath280 & @xmath281 & @xmath282 & @xmath283 + hd2 - 264.2 & @xmath284 & @xmath285 & @xmath286 & @xmath287 & @xmath288 + hd4 - 656.1 & @xmath289 & @xmath290 & @xmath291 & @xmath292 & @xmath293 + hd4 - 795.111 & @xmath294 & @xmath295 & @xmath296 & @xmath297 & @xmath298 + lccccccc gss073_1810 & @xmath299 & @xmath300 & @xmath301 & @xmath302 & @xmath303 & @xmath304 & @xmath305 + gss084_4515 & @xmath306 & @xmath307 & @xmath308 & @xmath309 & @xmath310 & @xmath311 & + gss084_4521 & @xmath312 & @xmath313 & @xmath314 & @xmath315 & @xmath316 & @xmath302 & + lcc hd2 - 264.1 & @xmath317 & @xmath318 + hd2 - 264.2 & @xmath319 & @xmath320 + hd4 - 656.1 & @xmath321 & @xmath320 + hd4 - 795.111 & @xmath322 & @xmath320 + gss073_1810 & @xmath323 & @xmath324 + gss084_4515 & @xmath325 & @xmath326 + gss084_4521 & @xmath327 & @xmath328 + lc@@xmath329cc@@xmath329cc@@xmath329ccc hd2 - 264.1 & @xmath330 & @xmath331 & @xmath332 & @xmath333 & @xmath334 & @xmath335 & @xmath336 & @xmath337 + hd2 - 264.2 & @xmath338 & @xmath339 & @xmath340 & @xmath341 & @xmath342 & @xmath343 & @xmath344 & @xmath345 + hd4 - 656.1 & @xmath346 & @xmath347 & @xmath348 & @xmath349 & @xmath350 & @xmath351 & @xmath352 & @xmath353 + hd4 - 795.111 & @xmath354 & @xmath355 & @xmath356 & @xmath357 & @xmath358 & @xmath359 & @xmath360 & @xmath361 + gss073_1810a & & & @xmath362 & @xmath363 & @xmath364 & @xmath365 & & + gss073_1810b & & & @xmath366 & @xmath367 & @xmath368 & @xmath369 & & + gss073_1810 & @xmath370 & @xmath371 & @xmath372 & @xmath373 & @xmath374 & @xmath375 & @xmath376 & @xmath377 + gss084_4515 & @xmath378 & @xmath379 & @xmath380 & @xmath381 & @xmath382 & @xmath383 & @xmath384 & @xmath385 + gss084_4521 & @xmath386 & @xmath387 & @xmath388 & @xmath389 & @xmath390 & @xmath391 & @xmath392 & @xmath393 + lccccccc hd2 - 264.1 & @xmath394 & @xmath395 & @xmath396 & @xmath397 & @xmath398 & @xmath399 & @xmath400 + hd2 - 264.2 & @xmath401 & @xmath402 & @xmath403 & @xmath404 & @xmath405 & @xmath406 & @xmath407 + hd4 - 656.1 & @xmath408 & @xmath409 & @xmath410 & @xmath411 & @xmath412 & @xmath413 & @xmath414 + hd4 - 795.111 & @xmath415 & @xmath416 & @xmath417 & @xmath418 & @xmath419 & @xmath420 & @xmath421 + gss073_1810a & & @xmath422 & @xmath423 & @xmath424 & & & + gss073_1810b & & @xmath425 & @xmath426 & @xmath399 & & & + gss084_4515 & @xmath427 & @xmath428 & @xmath429 & @xmath430 & @xmath431 & @xmath432 & @xmath433 + gss084_4521 & @xmath434 & @xmath435 & @xmath436 & @xmath437 & @xmath438 & @xmath439 & @xmath440 lcccc hd2 - 264.1 & @xmath4019.7 & @xmath441 & @xmath442 & @xmath443 + hd2 - 264.2 & @xmath4019.4 & @xmath444 & @xmath445 & @xmath446 + hd4 - 656.1 & @xmath4020.6 & @xmath447 & @xmath448 & @xmath449 + hd4 - 795.111 & @xmath4020.1 & @xmath450 & @xmath451 & @xmath452 + gss073_1810a & @xmath4021.3 & @xmath453 & & + gss073_1810b & @xmath4021.4 & @xmath454 & & + gss073_1810 & @xmath4022.1 & & & @xmath455 + gss084_4515 & @xmath4020.1 & @xmath456 & & @xmath457 + gss084_4521 & @xmath4021.7 & @xmath458 & & @xmath457

we allow dependent marginal observations as they occur when common random numbers are used for the simulation of the systems . we also use a generalized scheme for the target of the ranking and selection that allows to bound the error probabilities with a bonferroni approach . * keywords : * sequential ranking and selection , common random numbers , bayesian statistics , multiple testing , missing data

i

1410.6782

we want to select the best systems out of a given set of systems ( or rank them ) with respect to their expected performance . the systems allow random observations only and we assume that the joint observation of the systems has a multivariate normal distribution with unknown mean and covariance . we allow dependent marginal observations as they occur when common random numbers are used for the simulation of the systems . in particular , we focus on positively dependent observations as they might be expected in heuristic optimization where ` systems ' are different solutions to an optimization problem with common random inputs . in each iteration , we allocate a fixed budget of simulation runs to the solutions . we use a bayesian setup and allocate the simulation effort according to the posterior covariances of the solutions until the ranking and selection decision is correct with a given high probability . here , the complex posterior distributions are approximated only but we give extensive empirical evidence that the observed error probabilities are well below the given bounds in most cases . we also use a generalized scheme for the target of the ranking and selection that allows to bound the error probabilities with a bonferroni approach . our test results show that our procedure uses less simulations than comparable procedures from literature even in most of the cases where the observations are not positively correlated . * keywords : * sequential ranking and selection , common random numbers , bayesian statistics , multiple testing , missing data

we consider ranking and selection of systems based on the average performance of the alternatives . the particular set - up used here is motivated by problems from optimization under uncertainty . often in operations research as well as in technical applications the performance of solutions depends on some random influence like market conditions , material quality , or simply measurement errors . we shall call such random influences a random _ scenario_. usually , the aim is then to find a solution with minimal expected costs taken over all scenarios . we assume here that we can describe the random scenario mathematically by a random variable @xmath0 with a distribution @xmath1 . let @xmath2 denote the cost of solution @xmath3 if it has been applied to random scenario @xmath4 then the average costs are given by the expectation @xmath5 . except for particularly simple cases , we will not be able to calculate this expression analytically . instead , we have to estimate @xmath5 based on a sample @xmath6 where @xmath7 are observations of the random variable @xmath8 , usually produced by a stochastic simulation model on a computer . with estimated costs , optimization can be performed by heuristic search methods like genetic algorithms or ant algorithms . typically , these methods take a relatively small set @xmath9 of solutions ( a ` population ' ) and try to improve the quality of @xmath10 iteratively . the improvement step usually includes a _ selection _ of the best or at least the most promising solutions from @xmath10 with respect to their expected costs @xmath11 . as @xmath12 can only be estimated , this selection will return sub - optimal solutions with a certain error probability . often , this probability can be made arbitrarily small by increasing the sample size @xmath13 , i.e. the number of simulations . the aim of this paper is to find selection mechanisms for good solutions suitable for heuristic optimization that have error probabilities below a given bound and use few simulations only . most heuristic optimization procedures do not need the exact values of @xmath14 in order to perform a reasonable selection , instead it is sufficient to find the correct _ ranking _ @xmath15 or even only part of it . as it has been noted before ( see e.g. @xcite ) it is much easier ( needs less simulations ) to estimate the correct ranking than to estimate the correct values . methods of ranking and selection are therefore widely used in heuristic optimization under uncertainty , see e.g. @xcite for an overview . in this paper we have a fixed set @xmath16 of solutions , the observed cost values are assumed to be normally distributed with unknown mean and unknown covariance matrix . we use a bayesian approach and estimate the ranks of the solutions in each iteration based on the present posterior means . roughly , the steps of our procedure to rank and select the solutions can be summarized as follows : 1 . initialization : observe all solutions for a fixed number @xmath17 of scenarios ( = simulations ) . 2 . determine the ranking and selection based on the posterior means given these observations . calculate a lower bound lb(pcs ) for the _ probability of correct selection _ pcs 4 . while lb(pcs ) @xmath18 do 1 . allocate a fixed _ budget _ of additional simulations to the solutions , 2 . recalculate the posterior means , the ranking and selection and lb(pcs ) based on the extended set of observations . 5 . return the last ranking and selection . input parameters are the allowed error probability @xmath19 , the simulation budget @xmath20 and the initial sample size @xmath17 . this is the standard framework of a ( bayesian ) computing budget allocation ( cba ) algorithm , see e.g. in @xcite . our contributions concern the following points which we label for further reference : depend : : we allow for _ dependent observations _ , i.e. we apply the solutions to common random scenarios ( common random numbers , crn ) observing @xmath21 , a vector of possibly dependent , normally distributed values . target : : we use a very _ general concept of a target _ for ranking and selection that includes targets as median or span of means and still allows to bound the probability of a correct selection in a simple bonferroni fashion . alloc : : most importantly , we introduce a new _ heuristic allocation scheme _ for additional simulations based on the posterior distribution of the means and the covariance matrix . this scheme reuses terms that have been evaluated to calculate the lb(pcs ) in the iteration before and therefore requires little additional effort . in the experiments described below , our algorithm needed less simulations to guarantee lb(pcs)@xmath22 than competitors from literature . let us discuss these issues in more detail . * depend * : classical ranking and selection ( r&s ) procedures evaluate the alternatives based on random scenarios drawn _ independently _ for each alternative , see e.g. @xcite . only a few authors ( see e.g. @xcite ) use _ dependent _ samples based on common random numbers ( crn ) for simulation . it is well known , that if the observations are _ positively correlated _ , it is more efficient to use common random numbers ( crn ) , i.e. to compare the solutions on the same scenario ( see e.g. @xcite ) . positive correlation in our case roughly means that if a solution @xmath23 has , for a scenario @xmath24 costs @xmath2 that are above average , then costs @xmath25 will tend to be over average for all the other solutions @xmath26 also . in other words , if some scenario @xmath27 is relatively difficult ( costly ) for solution @xmath28 then @xmath29 will tend to be difficult for all solutions . similarly , a scenario that has small costs ( below average ) for one solution will tend to be an easy scenario for all solutions creating smaller costs for all of them . as this is the behaviour we would expect from a set of solutions at least after some iterations of improvement , it seems to be justified to expect positive correlation and to use crn specific r&s procedures for heuristic optimization . the numerical results below show that if the cost are positively correlated huge savings in simulation effort are indeed possible and if there is no positive correlation our approach is not worse than other procedures . * target * : we fix a set @xmath30 of ranks and try to select ( only ) those solutions that have these ranks with respect to the posterior means ( and sort them if necessary ) . e.g. if we have @xmath31 then we want to select the @xmath32 best solutions ( with minimal means ) . we describe the sets of possible correct selections in a way that uses a minimal set of pairwise comparisons of solutions , see @xcite for a similar approach . this allows to give a bonferroni type of lower bound to the posterior probability of correct selection that involve only one - dimensional @xmath33-distributions . the important and difficult part of this calculation is the determination of the posterior distributions in the presence of incomplete observations due to the possibly unequal allocation of the budget . * alloc * : the expressions forming the bonferroni lower bound for the pcs may be used to identify pairs of solutions for which the comparison has a large error probability and which need more data for a clear r&s decision . this results in a simple allocation rule that is simpler to calculate and turned out to be more efficient in our experiments than greedy ocba allocation rules as they are often used in literature ( see e.g. @xcite ) . this paper is based on the doctoral thesis of one of the authors ( @xcite ) . it is organized along the three issues outlined above as follows . * depend * : in the first section we give the exact mathematical description of the sampling process and describe our bayesian model . details of the rather involved calculation of the posterior distribution with missing data are summarized in an appendix . * target * : the second section generalizes the concept of ranking and selection of solutions to the case of partial selections . * alloc * : in section 3 we introduce several schemes for allocating the simulation budget to solutions based on the posterior distributions . a precise definition of our complete ranking and selection algorithm is given in section 4 . we report on extensive empirical tests with this algorithm in section 5 where we compare it to a greedy type of ocba algorithm and to the standard @xmath34 procedure of @xcite . some conclusions are given in the final section .

the result presented in this paper have practical application in astrophysics . _ few body sys . ( 2014 ) doi : 10.1007/s00601 - 014 - 0922 - 3 * keywords * : restricted four - body problem ; potential from a circular cluster of material points ; stability ; oblateness

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1411.1160

within the framework of restricted four - body problem , we study the motion of an infinitesimal mass by assuming that the primaries of the system are radiating - oblate spheroids surrounded by a circular cluster of material points . in our model , we assume that the two masses of the primaries @xmath0 and @xmath1 are equal to @xmath2 and the mass @xmath3 is @xmath4 . by using numerical approach , we have obtained the equilibrium points and examined their linear stability . the effect of potential created by the circular cluster and oblateness coefficients for the more massive primary and the less massive primary , on the existence and linear stability of the libration point have been critically examine via numerical computation . the stability of these points examined shows that the collinear and the non - collinear equilibrium points are unstable . the result presented in this paper have practical application in astrophysics . = 0.20 in * * -1.2cm0.5 cm effect of oblateness , radiation and a circular cluster of material points on the stability of equilibrium points in the restricted four - body problem _ applied theoretical physics division , department of physics , federal university lafia , p. m. b. 146 , lafia , nigeria . _ few body sys . ( 2014 ) doi : 10.1007/s00601 - 014 - 0922 - 3 * keywords * : restricted four - body problem ; potential from a circular cluster of material points ; stability ; oblateness

in recent years , there has been a growing interest in studying three - body problem with the aim of approximating the behavior of real celestial systems ( @xcite and refs . therein ) . the results from the study have been found useful in the theory of dynamical systems and in astronomy . the simplest form of the three - body problem is restricted three - body problem ( r3bp ) . it describe the motion of an infinitesimal mass moving under the gravitational influence of two massive bodies called the primaries which moves in circular orbits around their center of mass on account of their mutual attraction and the infinitesimal mass not influencing the motion of the primaries . the classical restricted three - body problem possesses five equilibrium points . the first three points @xmath5 , denotes the collinear points while the last two points ( @xmath6 and @xmath7 ) denotes the triangular points . the earth - moon system together with an artificial satellite constitute such problem @xcite . now , with an interest in four - body problem . couple r3bp is one of the examples of restricted four - body problem ( r4bp ) . the smaller body is called as the infinitesimal mas while the remaining massive bodies are called as the primaries . very recently , batagiannis and papadakis @xcite studied the families of simple symmetric and non - symmetric periodic orbits in the restricted four body problem . few among other interesting works are kumari and kushvah @xcite , papadouris and papadakis @xcite , alvarez and vidal @xcite . the purpose for studying r4bp includes their application in general behavior of the synchronous orbit in presence of moon and the sun . in this paper , our aim is to study the motion of an infinitesimal mass by assuming that the primaries of the system are radiating - oblate spheroids surrounded by a circular cluster of material points . by using numerical computation procedure via wolfram mathematica v10 , we locate the libration points and examine their linear stability under the effect of oblateness and gravitational potential from a circular cluster of material points .

within the framework of restricted four - body problem , we study the motion of an infinitesimal mass by assuming that the primaries of the system are radiating - oblate spheroids surrounded by a circular cluster of material points . in our model , we assume that the two masses of the primaries @xmath0 and @xmath1 are equal to @xmath2 and the mass @xmath3 is @xmath4 . by using numerical approach , we have obtained the equilibrium points and examined their linear stability . the effect of potential created by the circular cluster and oblateness coefficients for the more massive primary and the less massive primary , on the existence and linear stability of the libration point have been critically examine via numerical computation . the stability of these points examined shows that the collinear and the non - collinear equilibrium points are unstable . = 0.20 in * * -1.2cm0.5 cm effect of oblateness , radiation and a circular cluster of material points on the stability of equilibrium points in the restricted four - body problem _ applied theoretical physics division , department of physics , federal university lafia , p. m. b. 146 , lafia , nigeria .

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1411.1160

within the framework of restricted four - body problem , we study the motion of an infinitesimal mass by assuming that the primaries of the system are radiating - oblate spheroids surrounded by a circular cluster of material points . in our model , we assume that the two masses of the primaries @xmath0 and @xmath1 are equal to @xmath2 and the mass @xmath3 is @xmath4 . by using numerical approach , we have obtained the equilibrium points and examined their linear stability . the effect of potential created by the circular cluster and oblateness coefficients for the more massive primary and the less massive primary , on the existence and linear stability of the libration point have been critically examine via numerical computation . the stability of these points examined shows that the collinear and the non - collinear equilibrium points are unstable . the result presented in this paper have practical application in astrophysics . = 0.20 in * * -1.2cm0.5 cm effect of oblateness , radiation and a circular cluster of material points on the stability of equilibrium points in the restricted four - body problem _ applied theoretical physics division , department of physics , federal university lafia , p. m. b. 146 , lafia , nigeria . _ few body sys . ( 2014 ) doi : 10.1007/s00601 - 014 - 0922 - 3 * keywords * : restricted four - body problem ; potential from a circular cluster of material points ; stability ; oblateness

in this research , we examined the motion of an infinitesimal mass by assuming that the primaries of the system are radiating - oblate spheroids surrounded by a circular cluster of material points , within the framework of restricted four - body problem . in our model we assume that the two masses of the primaries @xmath0 and @xmath1 are equal to @xmath2 and the mass @xmath3 is @xmath4 . we have obtained the equilibrium points via numerical computation . in table [ tab1 ] we obtained the two collinear points @xmath109 and @xmath110 on the x - axis . firstly , we fixed @xmath111 at 0.0015 in the absent of gravitational potential with @xmath112 and then varies @xmath113 as 0.0000:0.0030:0.0090 . we found that the equilibrium point shifted from left to right . this is also observed in the presence of gravitational potential with @xmath114 . however , when we fixed @xmath113 at 0.0015 and then varies @xmath111 , we found that collinear point @xmath115 shifted from left to right whereas that of @xmath110 shifted from right to left . this is observed in the two cases we considered , i.e. @xmath116 and @xmath117 . in table [ tab2 ] , we present the non - collinear points for the two cases @xmath116 and @xmath117 . it is shown that @xmath118 . we found that our results are in excellent agreement with kumari and kushvah @xcite when @xmath116 also with the ones obtained by papadouris and papadakis @xcite when @xmath119 . we also examined the linear stability of these point and found then to be unstable . an extension to the effect of potential created by the circular cluster and oblateness coefficients for the more massive primary and the less massive primary , on the existence and linear stability of the libration point have also been presented . 99 j. singh and j. j. taura , astrophys space sci * 350 * ( 2014 ) 127 . j. singh and j. j. taura , astrophys space sci * 351 * ( 2014 ) 499 . a. n. baltagiannis and k. e. papadakis , astrophys space sci * 336 * ( 2011 ) 357 . r. kummari and b. s. kushvah , astrophys . space sci . * 349 * ( 2014 ) 693 . j. p. papadouris and k. e. papadakis , astrophys . space sci . * 344 * ( 2013 ) 21 . m. alvarez and c. vidal , math . eng , doi:10.1155/2009/181360 . v. v. radzievskii , astron . j. * 27 * ( 1950 ) 250 . m. miyamoto , r. nagai , publ . astron 27 , 533 ( 1975 ) i. d. peter , j. j. lissauer , planetary science . cambridge university press , new york ( 2001 )

= 0.55 cm we present the exact @xmath0 correction to the process @xmath1 , @xmath2 , for isr@xmath3fsr at and beyond lep2 energies . we compute the size of the respective sub - leading corrections of @xmath4 to the @xmath5 cross section , where @xmath6 is the respective big logarithm in the renormalization group sense so that it is identifiable as @xmath7 when @xmath8 is the squared @xmath9 cms energy . this correction is an important contribution to the differential distributions as they are realized in the mc which allows the very demanding precisions just cited to be achieved . specifically , the exact results for the @xmath0 corrections to @xmath8-channel annihilation hard bremsstrahlung processes under study here were also considered in refs . @xcite . concerning ref . @xcite , the entire result was given only for the case in which the photon angle variables are all integrated out ; here , we give the fully differential results . with regard to ref . thus , by comparing with the two calculations in refs . @xcite as we do here , we get a measure of the size of the mass corrections as well as cross checks on both our differential and our integrated results . @xcite . the appendix contains technical details about the scalar integrals .

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hep-ph0109279

= 0.55 cm we present the exact @xmath0 correction to the process @xmath1 , @xmath2 , for isr@xmath3fsr at and beyond lep2 energies . we give explicit formulas for the completely differential cross section . as an important application , we compute the size of the respective sub - leading corrections of @xmath4 to the @xmath5 cross section , where @xmath6 is the respective big logarithm in the renormalization group sense so that it is identifiable as @xmath7 when @xmath8 is the squared @xmath9 cms energy . comparisons are made with the available literature . we show explicitly that our results have the correct infrared limit , as a cross - check . some comments are made about the implementation of our results in the framework of the monte carlo event generator mc . = 0.6 cm currently , the final lep2 data analysis is in its beginning stages , and the desired total precision tags on the important lep2 physics processes @xmath10 , @xmath2 , are already called out in the lep2 mc workshop in ref . @xcite . it has been demonstrated in ref . @xcite that the monte carlo ( mc ) event generator program @xmath11 @xcite , hereafter referred to as mc , and the semi - analytical program zfitter @xcite realize these precisions ( @xmath12 ) in most channels for inclusive cross sections and that for the fully differential distributions , the mc again meets most of the requirements for the lep2 final data analysis . in this paper , we present exact results on the @xmath0 correction to the single hard bremsstrahlung processes @xmath13 , @xmath2 . this correction is an important contribution to the differential distributions as they are realized in the mc which allows the very demanding precisions just cited to be achieved . specifically , the exact results for the @xmath0 corrections to @xmath8-channel annihilation hard bremsstrahlung processes under study here were also considered in refs . @xcite . we differ from these results as follows . concerning ref . @xcite , the entire result was given only for the case in which the photon angle variables are all integrated out ; here , we give the fully differential results . with regard to ref . @xcite , the completely differential results were given as well but the mass corrections were omitted . in our work , the masses of the electrons and positrons and the masses of the final state fermion and anti - fermion are exactly taken into account in contrast to the literature . thus , by comparing with the two calculations in refs . @xcite as we do here , we get a measure of the size of the mass corrections as well as cross checks on both our differential and our integrated results . our work is organized as follows . in section [ preliminaries ] , we set our notational conventions . in section [ exact - virtual ] , we present our exact amplitudes for the @xmath0 virtual corrections to initial - state and final - state real radiation . in section [ cross - section ] , we derive the differential cross - sections corresponding to these amplitudes in a form useful for comparisons . in section [ comparisons ] , we compare these results with those in refs . @xcite while illustrating our results as they are used in the mc in ref . @xcite . section [ conclusions ] contains our summary remarks . the appendix contains technical details about the scalar integrals .

in this section we calculate the exact virtual correction to @xmath34 , @xmath2 . we proceed in analogy with our results on the virtual correction for the @xmath31-channel dominated low angle bhabha scattering process with a single hard bremsstrahlung in ref . @xcite . specifically , we express the exact amplitude for one real and one virtual photon emitted from the electron lines in the process using the gps conventions @xcite . in ref . @xcite , the corresponding @xmath31 channel result was obtained for electron line emission . here , from the latter result , we first obtain the respective initial - state @xmath8 channel result by crossing the outgoing electron line with the incoming positron line , and replacing the respective final state by @xmath35 , while adding also @xmath36 boson exchange . the results are translated into gps conventions . then , in subsection [ form - factors ] , we provide the detailed form factors appearing in the initial state amplitudes . the corresponding final state amplitudes are presented in subsections [ final - state ] and [ finalstate - formfactors ] . in this subsection , we define notation and set up the exact contribution for one real photon and one virtual photon emitted from the electron lines in the process . the amplitude for real plus virtual photon emission from the initial state may be written @xmath37 where the real photon emission amplitude is @xmath38 , and the factors @xmath39 contain spinor dependence . they will be specified in the next section . in gps conventions , the amplitude @xmath38 for the initial state radiation of a single photon is given by @xmath40 & = & { eq_e\over 2kp_1 } { \hbox{$\overline{v}$}}(p_2,\lambda_2 ) { \hbox{${\rm\bf m}_1$}}({\hbox{$\not\hbox{\kern-2.3pt $ p$}$}}_1 + m - { \hbox{$\not{k}$ } } ) { \hbox{$\not{\epsilon}$}}_\sigma^\star u(p_1,\lambda_1 ) \nonumber\\ & + & { eq_e\over 2kp_2 } { \hbox{$\overline{v}$}}(p_2,\lambda_2 ) { \hbox{$\not{\epsilon}$}}_\sigma^\star ( -{\hbox{$\not\hbox{\kern-2.3pt $ p$}$}}_2 + m + { \hbox{$\not{k}$ } } ) { \hbox{${\rm\bf m}_1$}}u(p_1,\lambda_1)\ , \end{aligned}\ ] ] where @xmath41 is the annihilation scattering spinor matrix . the form factors may be obtained from the corresponding @xmath31-channel result in ref . @xcite for electron line emission . specifically , the @xmath8 channel result can be obtained by crossing the outgoing electron line with the incoming positron line , and replacing the final state by @xmath35 . we also include the effects of @xmath36 exchange in the @xmath8 channel . our previous calculations of @xmath31-channel bremsstrahlung@xcite used the chinese magic conventions@xcite for the photon polarizations . the gps version of the magic photon polarization vector is related to the chinese magic conventions@xcite by @xmath42 the purpose of this change is to recover the more standard convention of defining photon polarization in terms of incoming states . the choice of magic polarization vector affects the amplitude ( [ iniamp ] ) only through the definition of @xmath38 . the remaining factors may thus be obtained directly by crossing from our previous @xmath31-channel results . the magic choice of auxiliary vector for initial state radiation is @xmath43}$ ] , with the definition @xmath44 } & = & \left\ { \begin{array}{ll } q_0\\ q_1\\ q_2 \end{array } \right\}\quad\hbox{if}\quad\left\ { \begin{array}{ll } \mu_1 = \mu_2\\ \mu_0 = \mu_1 = -\mu_2\\ \mu_0 = \mu_2 = -\mu_1 \end{array } \right . .\end{aligned}\ ] ] using the magic polarization vector in ( [ iniamp ] ) and neglecting fermion masses gives @xmath45 where the photon-@xmath36 propagator is @xmath46 and @xmath47 } , { h\left[{0\atop \sigma } { p_3\atop \lambda_3 } { p_4\atop \lambda_4}\right]}\right ) .\ ] ] we now turn to calculating the form factors and spinor factors . it remains to describe the form factors and spinor factors needed to compute @xmath48 . the spinor factors @xmath49 are given by @xmath50 \label{i2 } i_2 & = & { \sqrt{2}\sigma s_{-\lambda_1}(p_1,k ) s_{\lambda_1}(p_2,k ) s_{-\lambda_3}(p_4,k ) s_{\lambda_3}(p_3,k ) \over s_{-\sigma}(p_1,p_2 ) s_{-\sigma}(p_4,p_3 ) i_0 } \end{aligned}\ ] ] where the spinor product is @xmath51 . the factors @xmath49 are crossed versions of in ref . @xcite . we will begin by writing the dominant term @xmath52 . expressions can be found in ref . @xcite for all of the scalar integrals needed for the form factors , which were previously calculated using the ff package @xcite , which implements the methods of ref . the integrals in ref . @xcite are not quite adequate , because of the possibility that @xmath53 . however , it was possible to analytically continue when necessary , and to reproduce the numerical results of the ff package . thus , an expression for the form factors in terms of logarithms and dilogarithms is now available . details on the @xmath8 channel version of the scalar integrals used in ref . @xcite may be found in the appendix . for @xmath54 , using @xmath55 , @xmath56 with @xmath57 , the infrared yfs factor @xmath58 and @xmath59 the second expression is preferred for calculating @xmath60 when @xmath61 may be small . for @xmath62 , @xmath63 and @xmath64 are interchanged in ( [ f0 ] ) . the coefficients of the spinor terms in ( [ iniamp ] ) are , for @xmath65 , @xmath66 and @xmath67 the coefficients @xmath68 are @xmath8-channel versions of @xmath69 in ref . @xcite . for @xmath62 , @xmath63 and @xmath64 are interchanged in ( [ f1 ] ) and ( [ f2 ] ) . the leading log limit is obtained by finding which terms give rise to the leading powers of the ` big logarithm ' @xmath6 when the above expressions are integrated over @xmath63 and @xmath64 . these come from collinear terms where @xmath63 or @xmath64 go to zero . in the collinear limits , when averaged over the azimuthal angle , only the @xmath52 terms remain to order @xmath70 and @xmath6 , _ i.e. _ , to order nll . using the identities @xmath71 the nll limit of the form factor @xmath52 is found to be @xmath72 without mass corrections . mass corrections we have calculated primarily without any approximations , however , in the following we shall present them in the approximation @xmath73 . in particular , in this approximation , we checked by explicit calculation that the result which we obtain for the mass corrections in fact agrees with that implied by the prescription in ref . this prescription is valid for the spin - averaged differential distribution in the limit @xmath73 , but since mass terms are located in the separate ( helicity conservation violating ) spin amplitudes , it is not difficult to `` undo '' the spin summation . the technique of ref . @xcite was originally applied to tree level photon emissions . following the appendix b of ref . @xcite we can apply it also to our case of emission of one virtual and one real photon . taking advantage of the freedom , which we have for presenting mass terms in the @xmath73 approximation , the introduction of the mass correction leads to a replacement of @xmath52 by @xmath74 , where @xmath75 \right\}\end{aligned}\ ] ] with yfs infrared factor @xmath76 mass corrections first appear at order nll , and to this order , @xmath77 only the ll part of @xmath52 contributes to the mass correction , to order nll . the result ( [ mass - ini ] ) gives the complete effect of the mass corrections for the isr neglecting the terms that are suppressed by higher powers of @xmath78 as usual . the amplitudes for final state radiation can be obtained by crossing the incoming electron with the outgoing @xmath18 , and the incoming positron with the outgoing @xmath17 . thus , @xmath79 , @xmath80 , @xmath81 , and @xmath82 in the results of the previous sections . the final state radiation ( fsr ) amplitude can be written in analogy with the isr result ( [ iniamp ] ) , @xmath83 the form factors @xmath84 and the spinor factors @xmath85 are final - state analogs of those in the previous section , and will be defined in the next subsection . the amplitude @xmath86 for the final state radiation of a single photon can be obtained from the initial state amplitude @xmath38 by crossing . crossing leads to spinors with negative energy . a consistent choice of branches gives @xmath87 then we obtain @xmath88 & = & { eq_f \over 2kp_4 } { \hbox{$\overline{u}$}}(p_3,\lambda_3 ) { \hbox{$\overline{\rm\bf m}_1$}}({\hbox{$\not\hbox{\kern-2.3pt $ p$}$}}_4 - m + { \hbox{$\not{k}$ } } ) { \hbox{$\not{\epsilon}$}}_\sigma^\star v(p_4,\lambda_4 ) \nonumber\\ & - & { eq_f \over 2kp_3 } { \hbox{$\overline{u}$}}(p_3,\lambda_3 ) { \hbox{$\not{\epsilon}$}}_\sigma^\star ( { \hbox{$\not\hbox{\kern-2.3pt $ p$}$}}_3 + m + { \hbox{$\not{k}$ } } ) { \hbox{$\overline{\rm\bf m}_1$}}v(p_4,\lambda_4),\end{aligned}\ ] ] where @xmath89 the magic polarization vector for final state radiation is @xmath90}$ ] . using this in ( [ fsramp ] ) gives , in the massless limit , @xmath91 with propagator ( [ prop ] ) and @xmath92 given again by ( [ i0 ] ) . the spinor factors @xmath93 appearing in @xmath94 are given by @xmath95 as before , let . we can obtain the form factor @xmath96 for by substituting @xmath97 in ( [ f0 ] ) , and for by interchanging @xmath98 and @xmath99 in ( [ rsub ] ) . ( since , we have . ) then , for @xmath100,@xmath101 with @xmath102 the expression ( [ rbar ] ) is obtained from ( [ ra2 ] ) using the dilogarithm identity @xmath103 the imaginary parts in ( [ fbar0 ] ) were obtained by assuming the @xmath104 terms in ( [ f0 ] ) came from a small positive imaginary part on @xmath8 or @xmath105 . for @xmath106 , @xmath107 instead : @xmath98 and @xmath99 are interchanged . the coefficients of the spinor terms in ( [ finamp ] ) are , for @xmath100 , @xmath108 @xmath109 for @xmath106 , @xmath98 and @xmath99 are interchanged in ( [ fbar1 ] ) and ( [ fbar2 ] ) . the nll limit is obtained as in the initial state radiation case , except that now the collinear limits are when @xmath98 or @xmath99 become small . only the form factor @xmath96 survives to order nll , and using the identities @xmath110 we find @xmath111 without mass corrections . spin - averaged mass corrections can be obtained from the initial state case ( [ mass - ini ] ) by crossing . the result is that @xmath112 , where @xmath113 where @xmath114 again , mass corrections first appear at order @xmath115 , and to this order , @xmath116 the result ( [ mass - fin ] ) gives the complete effect of fsr mass corrections neglecting terms suppressed by higher powers of @xmath117 as usual .

@xmath0 her is a nearby quadruple system with a g - subgiant primary and several low mass companions arranged in a 2@xmath1 architecture . while the bc components have been well characterized , the ab component has been detected astrometrically and with direct imaging but there has been some confusion over its nature , in particular whether the companion is stellar or substellar . using near - infrared spectroscopy we are able to estimate the spectral type of the companion as a m4@xmath21v star . we combined the astrometry with archival radial velocity measurements to compute an orbit of the system . from the combined orbit ,

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1604.06494

@xmath0 her is a nearby quadruple system with a g - subgiant primary and several low mass companions arranged in a 2@xmath1 architecture . while the bc components have been well characterized , the ab component has been detected astrometrically and with direct imaging but there has been some confusion over its nature , in particular whether the companion is stellar or substellar . using near - infrared spectroscopy we are able to estimate the spectral type of the companion as a m4@xmath21v star . in addition , we have measured the astrometry of the system for over a decade . we combined the astrometry with archival radial velocity measurements to compute an orbit of the system . from the combined orbit , we are able to compute the mass sum of the system . using the estimated mass of the primary , we estimate the mass of the secondary as 0.32 m@xmath3 , which agrees with the estimated spectral type . our computed orbit is preliminary due to the incomplete orbital phase coverage , but it should be sufficient to predict ephemerides over the next decade .

( hd 161797 = hip 86974 = wds 17465 + 2743 ) is the third closest quadruple star system to the sun @xcite at a distance of 8.3 pc @xcite . the system consists of the g5iv primary @xcite surrounded by several m dwarfs . the closest companion is the ab component , which has long been known from astrometric variations of the primary @xcite and from radial velocity ( rv ) variations @xcite . the companion was first imaged by @xcite with the adaptive optics ( ao ) system on the 2.5 m telescope at mt . wilson observatory . there is also the bc pair , which is separated from the primary by 35 and is a pair of m dwarfs in a 43.127@xmath20.013 yr period @xcite . both @xcite and @xcite concluded that the pair was physically bound to @xmath0 her due to common proper motion . there is also a wider d component with a separation of several hundred arcseconds , which is also an m dwarf . @xcite concluded that this is not a physical companion because the proper motion differs dramatically from that of the primary . while binary stars are common , 50%@xmath24% of f6-g2 stars have companions @xcite , quadruples are much less common . quadruples come in two major catagories , 3@xmath41 systems , where a fourth star orbits a triple system in a wide orbit and , 2 + 2 systems , which consist of two binaries orbiting a common center of mass . her is the latter type , which is the more common type @xcite . @xcite found that 10% of nearby solar - type stellar binaries were actually 2 + 2 quadruples and this is likely linked to stellar system formation processes . the @xmath0 her system is one of the best - studied 2 + 2 quadrupole systems ; therefore it serves as an archetype for understanding stellar system formation . improving the characterization of this system is the motivation for this analysis . the primary star in the system exhibits solar - like oscillations @xcite and these have been used to measure the mass of the primary @xcite using asteroseimology ( see section [ orbit_analysis ] ) . a mass determination from an orbital analysis will serve as a useful crosscheck between these two techniques and can be used to improve the theoretical modeling of observed oscillation frequencies @xcite . the nature of the @xmath0 her ab companion has been discussed for over 20 years . most indications are that it is an m - dwarf , but there are persistent possibilities that it is substellar . @xcite used a monte carlo technique to compute probability density functions of the mass of the close companion to @xmath0 her a based on limited rv data and hypothetical , future , single measurements of the angular separation . the study concluded that if the separation was 14 then the companion would have a probable mass on the boundary between substellar and stellar . the angular separation measurements of @xcite fell at the boundary between the two regimes . from the computed @xmath5-band magnitude of the companion , they determined that the companion had to be redder than an m5v and could be substellar as @xcite suggested . @xcite also observed the companion in the near - infrared with the mt . wilson ao system . they were able to measure the photometry of the companion in @xmath6 and @xmath7 filters . using the _ ri _ photometry from @xcite and their _ hk _ photometry and model atmospheres they conclude that the mass should be @xmath80.13 @xmath9 ( equivalent to an m5v ; @xcite ) . they note that the _ ri _ photometry is anomalously bright compared to the model , though the near - infrared photometry agreed with the models to within the error bars . they concluded that the companion is stellar . @xcite observed the system with the mmt in the mid - infrared and estimated the spectral class of the companion to be m4@xmath21 . combining their results with that of @xcite , they computed the ( _ k_-_m _ ) color and noted that it was too red for an m4v star , but was similar to an early t - dwarf . with the possibility that the companion was a brown dwarf , we set out to resolve the prior conflicting color information and determine its spectral type with near - infrared spectroscopy . we also collected multi - epoch astrometry to compute an resolved orbit for the system , allowing for the estimation of the individual masses of the objects .

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ many np - hard winner determination problems admit polynomial - time algorithms when restricting inputs to be single - peaked . commonly , such algorithms employ dynamic programming along the underlying axis . we introduce a new technique : carefully chosen integer linear programming ( ip ) formulations for certain voting problems admit an lp relaxation which is totally unimodular if preferences are single - peaked , and which thus admits an integral optimal solution . this technique gives fast algorithms for finding optimal committees under the pav and chamberlin courant voting rules under single - peaked preferences , as well as for certain owa - based rules . under single - crossing preferences , an advantage of this technique is that no special - purpose algorithm needs to be used to exploit structure in the input preferences : any standard ip solver will terminate in the first iteration if the input is single - peaked , and will continue to work otherwise .

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_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ many np - hard winner determination problems admit polynomial - time algorithms when restricting inputs to be single - peaked . commonly , such algorithms employ dynamic programming along the underlying axis . we introduce a new technique : carefully chosen integer linear programming ( ip ) formulations for certain voting problems admit an lp relaxation which is totally unimodular if preferences are single - peaked , and which thus admits an integral optimal solution . this technique gives fast algorithms for finding optimal committees under the pav and chamberlin courant voting rules under single - peaked preferences , as well as for certain owa - based rules . under single - crossing preferences , young scores can also be calculated . an advantage of this technique is that no special - purpose algorithm needs to be used to exploit structure in the input preferences : any standard ip solver will terminate in the first iteration if the input is single - peaked , and will continue to work otherwise . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ = 1 @topnum0 @botnum0

in a departure from classical voting theory , a growing literature from computational social choice has recently studied _ multi - winner _ voting rules : given diverse preferences of a collection of agents , instead of identifying a single best alternative , we are aiming for a ( fixed - size ) _ set _ of alternatives that jointly are able to represent the preferences of the agents best . such procedures are useful in a wide variety of circumstances : obvious examples include the election of a parliament , or of a committee representing the interests of members of an organisation . other applications can be found in group recommendation systems , or for making decisions about which products or services to offer : which courses should be offered at a university ? which movies should be presented on an airline entertainment system ? several attractive rules for such tasks have been designed by researchers in political science ( e.g. , @xcite @xcite , @xcite @xcite ) and more recently by computer scientists @xcite . many of these rules are defined in terms of some objective function : a winning committee is a set of @xmath0 candidates that maximises this objective . unsurprisingly , then , the winner determination problems of such rules are typically np - hard @xcite . to tackle the complexity of these problems , approximation algorithms @xcite and fixed - parameter tractability approaches @xcite have been developed for these problems , and integer programming formulations have also been designed for them @xcite . another approach to efficiently solving these winner determination problems seeks to exploit underlying structure in the preferences reported by the agents @xcite . a particularly popular _ preference restriction _ in this space is the notion of _ single - peaked preferences _ , due to @xcite and @xcite . under this model , the alternative space has a one - dimensional structure : alternatives are ordered on a left - to - right _ axis _ ; and agents preferences are monotonically decreasing as we move further away from their _ peak _ ( most - preferred alternative ) . in particular , we can expect preferences to be structured this way when voting over the value of a numerical quantity ( such as a tax rate ) . while single - peaked preferences were first employed to escape impossibility results in social choice theory @xcite , it also yields positive algorithmic results : notably , @xcite showed that chamberlin courant s committee selection rule can be computed efficiently when preferences are single - peaked . these results can be extended to other multi - winner voting rules @xcite , and to other preference restriction such as single - crossing preferences , or single - peakedness on trees @xcite . the algorithms mentioned all directly exploit the underlying structure of the preferences . for example , the algorithm due to betzler et al . proceeds by dynamic programming along the single - peaked axis . thus , to use this algorithm , we first need a procedure to uncover this axis . fortunately , efficient recognition algorithms for the mentioned domains are known ; in particular , a suitable axis can be found in linear time @xcite . thus , the approach to tractability via preference restrictions would look roughly like shown in : given input preferences , apply recognition algorithms for several preference restrictions , and if any of these tests succeed , use a special - purpose algorithm that performs well when preferences have the uncovered structure . if none of the tests succeed , fall back to some ( superpolynomial ) general - purpose solver , such as an integer programming solver . but there is something awkward about linking together this cacophony of algorithms : given the amazing progress in solver technology in recent decades ( such as witnessed in sat competitions or in commercial ip solvers ) , it might well be faster in practice to skip these intermediate steps and go straight to cplex . ( this objection becomes stronger once implementation effort is factored in . ) further , modern ip solvers are often able to exploit underlying structure automatically : experimentally , solving times on single - peaked instances are much faster than on random instances . while such an experimental result is nice , performance guarantees are better . could it be that , on certain single - peaked instances , an ip solver performs exponentially worse than special - purpose algorithms ? the answer is no . this paper shows that integer programming solvers will _ provably _ terminate in polynomial time when solving certain voting problems on single - peaked inputs . in more detail , for several voting rules ( including chamberlin courant and proportional approval voting ) , we will design ip formulations which are solved optimally by their lp relaxation when the preference input happens to be single - peaked . since all standard ip solvers first solve the lp relaxation , they will terminate with the correct answer in their first iteration . if the instance is not single - peaked , the ip solver might enter further iterations while solving importantly , our formulations are correct whether or not the input is single - peaked . moreover , this approach to achieving polynomial time efficiency does not require separately running a recognition algorithm ! the ip solver need not know an underlying axis , or even whether the input is single - peaked at all ; the lp relaxation will just ` magically ' have an integral solution . our proofs rely on establishing that the constraint matrices become totally unimodular in the single - peaked case . previous applications of this technique include certain tractable cases of the winner determination problems of combinatorial auctions ( see @xcite @xcite ) . our method also allows us to show that a conjecture due to @xcite is false . they consider structure in _ dichotomous preferences _ based on approval ballots , where agents only submit a binary yes / no decision for every candidate . in particular , they consider an analogue of single - peakedness in this setting ( which they call _ candidate interval _ or _ ci _ ) , which requires there to be an ordering ( axis ) of the candidates such that , for every voter , their set of approved candidates forms an interval of the axis . they then analyse an axiomatically particularly attractive multi - winner rule for the approval setting , known as proportional approval voting ( pav ) . while @xcite showed that pav is efficiently computable for a certain subclass of their ci concept , and obtained fpt results for ci preferences , they conjectured that pav remains np - hard for ci preferences in general . this conjecture appears to be largely based on the difficulty of solving this problem using dynamic programming approaches that typically work in single - peaked settings . our method , on the other hand , allows us to find a polynomial - time algorithm for this case , via ip solving . we then combine the approaches for chamberlin courant and pav to give a similar polynomial time result for so - called owa - based multi - winner rules in the case that preferences are single - peaked . we further give an ip formulation that computes young s voting rule efficiently for single-_crossing _ preferences , and close by briefly sketching applications of our method to some further rules and settings .

_ herschel_/pacs observations of 29 local ( ultra-)luminous infrared galaxies , including both starburst and agn - dominated sources as diagnosed in the mid - infrared / optical , show that the equivalent width of the absorbing oh 65 @xmath0 m @xmath1 @xmath2 line ( @xmath3 ) with lower level energy @xmath4 k , is anticorrelated with the [ c ii]158 @xmath0 m line to far - infrared luminosity ratio , and correlated with the far - infrared luminosity per unit gas mass and with the 60-to-100 @xmath0 m far - infrared color . while all sources are in the active @xmath5 / mode as derived from previous co line studies , the oh65 absorption shows a bimodal distribution with a discontinuity at @xmath6 /. in the most buried sources , oh65 probes material partially responsible for the silicate @xmath7 @xmath0 m absorption . combined with observations of the oh 71 @xmath0 m @xmath8 @xmath9 doublet ( @xmath10 k ) ,

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_ herschel_/pacs observations of 29 local ( ultra-)luminous infrared galaxies , including both starburst and agn - dominated sources as diagnosed in the mid - infrared / optical , show that the equivalent width of the absorbing oh 65 @xmath0 m @xmath1 @xmath2 line ( @xmath3 ) with lower level energy @xmath4 k , is anticorrelated with the [ c ii]158 @xmath0 m line to far - infrared luminosity ratio , and correlated with the far - infrared luminosity per unit gas mass and with the 60-to-100 @xmath0 m far - infrared color . while all sources are in the active @xmath5 / mode as derived from previous co line studies , the oh65 absorption shows a bimodal distribution with a discontinuity at @xmath6 /. in the most buried sources , oh65 probes material partially responsible for the silicate @xmath7 @xmath0 m absorption . combined with observations of the oh 71 @xmath0 m @xmath8 @xmath9 doublet ( @xmath10 k ) , radiative transfer models characterized by the equivalent dust temperature , , and the continuum optical depth at 100 @xmath0 m , @xmath11 , indicate that strong [ c ii]158 @xmath0 m deficits are associated with far - ir thick ( @xmath12 , @xmath13 @xmath14 ) , warm ( @xmath15 k ) structures where the oh 65 @xmath0 m absorption is produced , most likely in circumnuclear disks / tori / cocoons . with their high @xmath16 ratios and columns , the presence of these structures is expected to give rise to strong [ c ii ] deficits . @xmath3 probes the fraction of infrared luminosity arising from these compact / warm environments , which is @xmath17% in sources with high @xmath3 . sources with high @xmath3 have surface densities of both @xmath18 and @xmath19 higher than inferred from the half - light ( co or uv / optical ) radius , tracing coherent structures that represent the most buried / active stage of ( circum)nuclear starburst - agn co - evolution .

from the first spectroscopic observations of ( ultra)luminous infrared galaxies ( ( u)lirgs ) in the far - infrared ( far - ir ) domain with the infrared space observatory ( iso ) , evidence was found that the strength of fine - structure lines ( from both ions and atoms ) in emission are generally anticorrelated with the depth and excitation of the molecular lines observed in absorption @xcite . the most commonly observed line , the fine - structure [ c ii]157.7 @xmath0 m transition ( hereafter [ c ii ] ) , tends to exhibit a strong deficit with respect to the far - ir luminosity in ulirgs relative to less luminous systems @xcite . in normal galaxies , the [ c ii]/fir luminosity ratio remains nearly constant ( @xmath20% ) , while it decreases in galaxies with warmer far - ir colors @xcite . on the other hand , studies of individual templates ( arp 220 and mrk 231 ) indicated that high far - ir radiation densities associated with the nuclear regions of galaxies with [ c ii ] deficits , are required to account for the observed high - lying molecular absorption ( * ? ? ? * ; * ? ? ? * hereafter g - a08 ) . the launch of the _ herschel _ space observatory @xcite has dramatically improved the sensitivity of these measurements . observations with the pacs spectrometer @xcite soon revealed that the observed deficit of [ c ii ] relative to the far - ir emission applies to all far - ir fine - structure lines ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * hereafter g - c11 ) . g - c11 also showed that the deficits are better correlated with @xmath21 than with @xmath22 , while pacs observations of three ( u)lirgs with strong line deficits , ngc 4418 , arp 220 , and mrk 231 , showed deep absorption in high - lying molecular lines ( * ? ? ? * ; * ? ? ? * hereafter g - a12 and g - a14 ) . ngc 4418 is a case in point , as it shows the highest [ c ii ] deficit , a moderate @xmath23 but a high @xmath24 /(g - c11 ) , and the highest - lying absorption among all galaxies with full fir spectra ( g - a12 ) . to explore the connection between intense far - ir fields and both the highly excited molecular gas and the [ c ii ] deficit , we investigate the relationship between the oh @xmath25 transition at @xmath26 @xmath0 m ( hereafter oh65 ) with @xmath4 k , and the [ c ii ] line , @xmath21 , the @xmath7 @xmath0 m silicate absorption , and the far - ir colors , also using measurements of the oh @xmath27 transition at @xmath28 @xmath0 m ( hereafter oh71 , @xmath10 k ) in galaxies for which it is available . oh is a versatile molecule with high abundances in active regions including photodissociated regions ( pdrs ) , cosmic - ray dominated regions ( crdrs ) , and x - ray dominated regions ( xdrs ) ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and traces powerful galactic - scale molecular outflows in some sources ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * hereafter v13 ; g - a14 ) mostly associated with large agn luminosity fractions and luminosities . in extragalactic sources , the oh65 doublet ( when detected ) is absorption - dominated , indicating that the excitation of the lower @xmath29 level is governed by radiative ( rather than collisional ) processes followed by oh65 absorption is not dominant owing to the high @xmath30einstein coefficient of the 84 @xmath0 m ( @xmath31 ) transition ; efficient oh65 absorption involves a high radiation density such that it will also dominate the excitation of @xmath29 under reasonable physical condictions . ] . the oh65 pumping thus involves successive absorptions in the 119 , 84 , and finally in the 65 @xmath0 m doublet with high @xmath30einstein coefficients ( @xmath32 , @xmath33 , and @xmath34 s@xmath35 , see the energy level diagram of oh in g - a14 ) , thus ensuring an excellent probe of strong far - ir fields . 65 @xmath0 m @xmath36 continuum - normalized spectra in all galaxies in the sample , with the velocity plotted relative to the rest - frame wavelength of the blue component of the doublet ( @xmath37 line at @xmath38 @xmath0 m ) . the spectra are grouped according to the values of the equivalent width measured between @xmath39 and @xmath40 around the blue component ( indicated by the solid vertical lines and listed in table [ tbl-2 ] ) . the dotted vertical lines indicate the positions of the two components of the doublet . the green , red , and blue spectra are vertically shifted for clarity . ] 71 @xmath0 m @xmath41 continuum - normalized spectra in all 15 galaxies for which it is available , with the velocity plotted relative to the rest - frame wavelength of the blue component of the doublet at @xmath42 @xmath0 m . the dotted vertical lines indicate the positions of the two @xmath43-components of the doublet , which are blended into a single spectral feature . the spectra are grouped according to the values of the equivalent width measured between @xmath39 and @xmath44 ( indicated by the vertical solid lines and listed in table [ tbl-2 ] ) . the red and blue spectra are vertically shifted for clarity . the position of the @xmath45 line ( @xmath46 k ) is indicated . ] and @xmath40 around the blue component of the doublet , and ( b ) the [ c ii]158 @xmath0 m line to fir ratio , as a function of the the far - ir to co ( 1 - 0 ) luminosity ratio in our galaxy sample . symbol colors and shapes have the same meaning as in fig . [ correl ] . ]

sources with high @xmath3 have surface densities of both @xmath18 and @xmath19 higher than inferred from the half - light ( co or uv / optical ) radius , tracing coherent structures that represent the most buried / active stage of ( circum)nuclear starburst - agn co - evolution .

c

1412.4694

_ herschel_/pacs observations of 29 local ( ultra-)luminous infrared galaxies , including both starburst and agn - dominated sources as diagnosed in the mid - infrared / optical , show that the equivalent width of the absorbing oh 65 @xmath0 m @xmath1 @xmath2 line ( @xmath3 ) with lower level energy @xmath4 k , is anticorrelated with the [ c ii]158 @xmath0 m line to far - infrared luminosity ratio , and correlated with the far - infrared luminosity per unit gas mass and with the 60-to-100 @xmath0 m far - infrared color . while all sources are in the active @xmath5 / mode as derived from previous co line studies , the oh65 absorption shows a bimodal distribution with a discontinuity at @xmath6 /. in the most buried sources , oh65 probes material partially responsible for the silicate @xmath7 @xmath0 m absorption . combined with observations of the oh 71 @xmath0 m @xmath8 @xmath9 doublet ( @xmath10 k ) , radiative transfer models characterized by the equivalent dust temperature , , and the continuum optical depth at 100 @xmath0 m , @xmath11 , indicate that strong [ c ii]158 @xmath0 m deficits are associated with far - ir thick ( @xmath12 , @xmath13 @xmath14 ) , warm ( @xmath15 k ) structures where the oh 65 @xmath0 m absorption is produced , most likely in circumnuclear disks / tori / cocoons . with their high @xmath16 ratios and columns , the presence of these structures is expected to give rise to strong [ c ii ] deficits . @xmath3 probes the fraction of infrared luminosity arising from these compact / warm environments , which is @xmath17% in sources with high @xmath3 . sources with high @xmath3 have surface densities of both @xmath18 and @xmath19 higher than inferred from the half - light ( co or uv / optical ) radius , tracing coherent structures that represent the most buried / active stage of ( circum)nuclear starburst - agn co - evolution .

absorption in high - lying transitions of molecules with high dipolar moment and level spacing ( i.e. mostly light hydrides ) , represented by oh65 and oh71 , has been shown here to be strong in most local ulirgs ( @xmath531% ) and in several lirgs . despite the high columns inferred in galaxies with high @xmath68 , their low [ c ii]/fir and low @xmath532 suggest that both are associated with a `` deficit '' in @xmath19 relative to the far - ir continuum emission , accompanied by additional effects such as significant optical depth in the [ c ii ] line and high excitation of co. high columns and but low @xmath533 are indicative of high radiation densities and small volumes , with the high columns of gas and dust confined to small regions ( an upper limit of which is the observed luminosity ) with its calculated value , @xmath534 , where @xmath535 stands for the projected surface and @xmath536 is the continuum optical depth at frequency @xmath537 along the corresponding line of sight . for reference , the effective radius is @xmath538 pc for @xmath539 ( @xmath540 ) , @xmath541 k , and @xmath512 , which is a lower limit to the physical size in some galaxies owing to clumpiness . the diagnostics in fig . [ correl ] and model results in fig . [ models ] are nevertheless independent of sizes and adopted distances.[foot : size ] ] around the bright , buried illuminating source(s ) ( nearly ) dominating the galaxy output . the relationship between the model parameterization used here and that in terms of the dominant exciting source ( agn or starburst ) , volume and column densities , and ionization parameter ( * ? ? ? * ; * ? ? ? * g - c11 ) , as well as the origin of the deficit in fine - structure lines other than [ c ii ] , will be explored in future work . the inferred column densities associated with @xmath494 , @xmath13 , are higher than those derived from the silicate strength at @xmath7 @xmath0 m . models by @xcite indicate that the observed @xmath542 can be explained with @xmath543 ( @xmath544 ) . since the oh65 regions / structure will block all the inner mid - ir emission passing through it , the observed mid - ir emission and associated silicate absorption are biased toward relatively unabsorbed mid - ir emitting regions . likewise , several sources in the sample show mid - ir agn signatures as [ ne v ] emission ( iras 05189 - 2524 and mrk 273 ; * ? ? ? * v09 ) or an optical broad line region ( e.g. mrk 231 ) , and our direct view of this emission indicates tiny absorbing columns in comparison with those inferred from oh65 . if the oh65 absorption is generated in a circumnuclear disk / torus / cocoon , either the combination of scale height / inclination , and/or clumpiness are required to account for the apparent decrease of extinction with decreasing wavelength . in sources with high contrast in mid - to - far infrared extinction , either extreme clumpiness or important inclination effects are necessarily involved . in other sources , extinction of the mid - ir emission by the oh65 structure is consistent with their low @xmath299 ratio . though these structures are variably clumpy , the oh65 bimodality ( fig . [ distrib]b - c ) suggests that they are coherent and quickly formed , and provide an effective way to obscure the signposts of agns at shorter wavelengths in some sources . in the direction of the warm , optically thick regions / structure where the oh65 absorption is produced , the surface density of both @xmath18 and h@xmath545 mass are significantly higher than the average values previously estimated for the areas within the half - light radius ( from co or optical / uv ) . the grey parallelogram in fig . [ fig4]b indicates the location of the @xmath506 component for the ten sources where both oh65 and oh71 are detected : @xmath546 pc@xmath547 ( @xmath548 ) and @xmath549 kpc@xmath547 ( @xmath504 k ) . the latter high fluxes are consistent with previous estimates using sizes derived from radio emission and strengthen the role of radiation pressure support ( * ? ? ? * ; * ? ? ? * see their fig . 3 ) . for starburst - dominated sources and using a @xcite imf , the corresponding sfrs are @xmath550 yr@xmath35 kpc@xmath547 . for hot _ sub_components in some sources like the @xmath551 component of ngc 4418 , @xmath552 kpc@xmath547 and @xmath553 ( @xmath554 ) on spatial scales of @xmath56 pc ( g - a12 , * ? * ; * ? ? ? * ; * ? ? ? * ) . the solid , dashed , and dotted black lines in fig . [ fig4]b are extrapolations of the fits found in previous studies for subsamples of ( u)lirgs / mergers / smgs . a pure sf scenario involves the shadowing of @xmath555 ( for @xmath556 ) star - forming regions , each with @xmath557 mag and @xmath558 , on spatial scales of @xmath559 pc ; on spatial scales of a few parsecs , there is apparently no analog star - forming region close to the galactic center . as measured with _ @xcite , consistent with its moderate effective @xmath560 k , @xmath561 kpc@xmath547 , and @xmath562 / for a gas - to - dust ratio by mass of 100 @xcite . oh65 is not detected towards sgr a@xmath563 and its circumnuclear disk @xcite , and is detected in emission towards the orion bar pdr indicating collisional excitation in warm and dense gas @xcite . ] the implied gas consumption timescales are @xmath564 myr for @xmath565 k , comparable to those estimated for extreme sources exhibiting powerful oh outflows driven by buried agns @xcite . on the other hand , 21 sources in our sample were analyzed in the oh 119 @xmath0 m transition by v13 , and 12 ( 9 with @xmath293 ) were found to have @xmath566 ( the velocity below which 84% of the absorption takes place ) , most likely indicative of significant agn feedback . the oh65-(u)lirg phase may thus represent the starburst - agn co - evolution phase in its shortlived most buried / active stage . pacs has been developed by a consortium of institutes led by mpe ( germany ) and including uvie ( austria ) ; ku leuven , csl , imec ( belgium ) ; cea , lam ( france ) ; mpia ( germany ) ; inafifsi / oaa / oap / oat , lens , sissa ( italy ) ; iac ( spain ) . this development has been supported by the funding agencies bmvit ( austria ) , esa - prodex ( belgium ) , cea / cnes ( france ) , dlr ( germany ) , asi / inaf ( italy ) , and cicyt / mcyt ( spain ) . e.g - a is a research associate at the harvard - smithsonian cfa , and thanks the spanish ministerio de economa y competitividad for support under projects aya2010 - 21697-c05 - 0 and fis2012 - 39162-c06 - 01 . e.g - a and h.a.s . acknowledge partial support from nhsc / jpl rsa 1455432 ; h.a.s acknowledges nasa grant nnx14aj61 g . basic research in ir astronomy at nrl is funded by the us - onr ; j.f . acknowledges support from nhsc / jpl subcontracts 139807 and 1456609 . s.v . and m.m . acknowledge partial support from nhsc / jpl rsa 1427277 and 1454738 . this research has made use of nasa s astrophysics data system and of gildas ( http://www.iram.fr/iramfr/gildas ) . aalto , s. , radford , s. j. e. , scoville , n. z. , & sargent , a. i. 1997 , , 475 , l107 abel , n. p. , dudley , c. , fischer , j. , satyapal , s. , & van hoof , p. a. m. 2009 , , 701 , 1147 armus , l. , charmandaris , v. , bernard - salas , j. , et al . 2007 , , 656 , 148 brauher , j. r. , dale , d. a. , & helou , g. 2008 , , 178 , 280 burlon , d. , ajello , m. , greiner , j. , comastri , a. , merloni , a. , & gehrels , n. , 728 , 58 casoli , f. , willaime , m .- c . , viallefond , f. , & gerin , m. 1999 , a&a , 346 , 663 chabrier , g. 2003 , , 586 , l133 chung , a. , narayanan , g. , yun , m. s. , heyer , m. , & erickson , n. r. 2009 , aj , 138 , 858 costagliola , f. , aalto , s. , sakamoto , k. , martn , s. , beswick , r. , muller , s. , & klckner , h .- r . 2013 , a&a , 556 , a66 daddi , e. , elbaz , d. , walter , f. , et al . 2010 , , 714 , l118 daz - santos , t. , armus , l. , charmandaris , v. , et al . 2013 , , 774 , 68 daz - santos , t. , armus , l. , charmandaris , v. , et al . 2014 , , in press ( arxiv:1405.3983 ) downes , d. , solomon , p. m. , & radford , s. j. e. 1993 , , 414 , l13 etxaluze , m. , goicoechea , j. r. , cernicharo , j. , polehampton , e. t. , noriega - crespo , a. , molinari , s. , swinyard , b. m. , wu , r. , & bally , j. 2013 , a&a , 556 , a137 farrah , d. ; 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are first derived up to the eighth order by direct decompositions of exponential propagators and further collected using an advanced composition scheme to obtain the algorithms of higher orders . rev . e * 62 * , 8746 ( 2000 ) ] , where high - order algorithms are introduced by standard iterations of a force - gradient integrator of order four , the present method allows to reduce the total number of expensive force and its gradient evaluations to a minimum . at the same time the algorithms are tested in molecular dynamics and celestial mechanics simulations . the results corresponding to sixth- and eighth - order - based composition schemes are also presented up to the sixteenth order . for

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cond-mat0111055

a consequent approach is proposed to construct symplectic force - gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations . within this approach the basic algorithms are first derived up to the eighth order by direct decompositions of exponential propagators and further collected using an advanced composition scheme to obtain the algorithms of higher orders . contrary to the scheme by chin and kidwell [ phys . rev . e * 62 * , 8746 ( 2000 ) ] , where high - order algorithms are introduced by standard iterations of a force - gradient integrator of order four , the present method allows to reduce the total number of expensive force and its gradient evaluations to a minimum . at the same time , the precision of the integration increases significantly , especially with increasing the order of the generated schemes . the algorithms are tested in molecular dynamics and celestial mechanics simulations . it is shown , in particular , that the efficiency of the new fourth - order - based algorithms is better approximately in factors 5 to 1000 for orders 4 to 12 , respectively . the results corresponding to sixth- and eighth - order - based composition schemes are also presented up to the sixteenth order . for orders 14 and 16 , such highly precise schemes , at considerably smaller computational costs , allow to reduce unphysical deviations in the total energy up in @xmath0 times with respect to those of the standard fourth - order - based iteration approach . pacs numbers : 02.60.cb ; 05.10.-a ; 95.10.ce ; 95.75.pq 2

understanding the dynamic phenomena in classical and quantum many - body systems is of importance for the most of areas of physics and chemistry . the development of efficient algorithms for solving the equations of motion in such systems should therefore impact a lot of fields of fundamental research . during the last decade a considerable activity @xcite has been directed on the construction of symplectic time - reversible algorithms that employ decompositions of the evolution operators into analytically solvable parts . the decomposition algorithms exactly preserve all poincar invariants and , thus , are ideal for long - time integration in molecular dynamics @xcite and astrophysical @xcite simulations . the reason is that for these algorithms the errors in energy conservation appear to be bounded even for relatively large values of the size of the time step . this is in a sharp contrast to traditional runge - kutta and predictor - corrector schemes , where the numerical uncertainties increase linearly with increasing the integration time @xcite . the main attention in previous investigations has been devoted to derive different - order decomposition algorithms involving only force evaluations during the time propagation . for instance , the widely used velocity- and position - verlet algorithms @xcite relate , in the general classification , to a three - stages decomposition scheme of the second order with one force evaluation per step . the fourth - order algorithm by forest and ruth @xcite corresponds to a scheme with three such force recalculations and consists of seven single - exponential stages . sixth - order schemes are reproduced @xcite beginning from fifteen stages and seven evaluations of force for each body in the system per given time step . with further increasing the order of force decomposition schemes , the number of stages and thus the number of the corresponding non - linear equations ( which are necessary to solve numerically to obtain the required time coefficients for single - exponential propagations ) increases drastically . in addition , such equations become too cumbersome and all these , taking into account the capabilities of modern supercomputers , led to the impossibility of representing the direct decomposition algorithms of order eighth and higher in an explicit form @xcite . in order to simplify this problem , it was proposed to derive higher - order integrators by composing schemes of lower ( actually second ) orders . the resulting second - order - based composition algorithms have been explicitly obtained up to the tenth order @xcite . relatively recently @xcite , a deeper analysis of the operator factorization process has shown that the class of analytically integrable decomposition integrators can be extended including additionally a higher - order commutator into the single - exponential propagations . as a consequence , a set of new so - called force - gradient algorithms of the fourth order has been introduced . a distinguishable feature of these algorithms is the possibility to generate solutions using only positive values for time coefficients during each substage of the integration . this is contrary to the original decomposition approach , where beyond second order ( as has been rigorously proved by suzuki @xcite ) any scheme expressed in terms of only force evaluation must produce some negative time coefficients . we mention that applying negative time propagations is impossible , in principle , in such important fields as non - equilibrium statistical mechanics , quantum statistics , stochastic dynamics , etc . , because one can not simulate diffusion or stochastic processes backward in time nor sample configurations with negative temperatures . in the case of stochastic dynamics simulations it has been demonstrated explicitly @xcite that using fourth - order force - gradient algorithms leads to much superior propagation over standard verlet - based schemes of the second order in that it allows much larger time steps with no loss of precision . a similar pattern was observed in classical dynamics simulations comparing the usual fourth - order algorithm by forest and ruth with its force - gradient counterparts @xcite . quite recently , chin and kidwell @xcite has considered a question of how to iterate the force - gradient algorithms to higher order . the iteration was based on creutz s and gocksch s approach @xcite according to which an algorithm of order @xmath1 can be obtained by triplet construction of a self - adjoint ( i.e. time - reversible ) scheme of order @xmath2 . then starting from a fourth - order integrator , it has been shown in actual celestial mechanics simulations that for orders 6 , 8 , 10 , and 12 , the numerical errors corresponding to the force - gradient - based schemes are significantly smaller than those of the schemes basing on iterations of usual non - gradient algorithms . the resulting efficiency of the integration has also increased considerably despite an increased computational efforts spent on the calculations of force gradients . the same has been seen in the case of quantum mechanics simulations when solving the time - dependent schrdinger equation @xcite . it is worth emphasizing , however , that the iteration scheme by chin and kidwell is far to be optimal for deriving high - order integrators belonging to the force - gradient class . the reason is that the number of total force and its gradient evaluations increases too rapidly with increasing @xmath2 . remembering that such evaluations constitute the most time - consuming part of the calculations , this may restrict the region of applicability of force - gradient algorithms to relative low orders only . note that high - order computations are especially desirable in problems of astrophysical interest , because than one can observe over a system during very long times . they may also be useful in highly precise molecular dynamics and quantum mechanics simulations to identify or confirm very subtle effects . in the present paper we propose a general approach to construction of symplectic force - gradient algorithms of arbitrary orders . the approach considers the splitting and composing of the evolution operators on the basic level , taking into account the explicit structure of truncation terms at each given order in the time step . this has allowed us to obtain exclusively precise and economical algorithms with using significantly smaller number of single - exponential propagations than that appearing within standard decomposition and iteration schemes . the paper is organized as follows . the equations of motion for classical and quantum systems are presented in section ii.a . the integration of these equations by direct decompositions and their force - gradient generalization are described in section ii.b . explicit expressions for basic force - gradient algorithms of orders 2 , 4 , 6 , and 8 are also given there . the higher - order integration basing on advanced compositions of lower - order schemes is considered in section ii.c . the composition constants for fourth- , sixth- , and eighth - order - based schemes are calculated and written down in the same section up to the overall order 16 . sections iii.a and iii.b are devoted to applications of obtained force - gradient algorithms to molecular dynamics and celestial mechanics simulations , respectively . a comparative analysis of the new algorithms with existing integrators is made there as well . the final discussion and concluding remarks are highlighted at the end in section iv .

a distinct sub - class of anomalous velocity emission features has emerged from recent high quality surveys of the local group environment , namely the compact high velocity clouds ( chvcs ) . comparison of volume and column densities has allowed the first distance estimates to be made ( 600@xmath1300 kpc ) . # 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in

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astro-ph0002320

a distinct sub - class of anomalous velocity emission features has emerged from recent high quality surveys of the local group environment , namely the compact high velocity clouds ( chvcs ) . a program of high - resolution imaging with the westerbork array and the arecibo telescope has begun to provide many insights into the nature of these objects . elongated core components with a velocity gradient consistent with rotation ( v@xmath0 15 ) are seen in many objects . comparison of volume and column densities has allowed the first distance estimates to be made ( 600@xmath1300 kpc ) . the objects appear to be strongly dark - matter dominated with dark - to - gas mass ratios of 3050 implied if the typical distance is 700 kpc . # 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in

the nature of anomalous velocity discovered during @xmath221 cm surveys of the galaxy has been the subject of much debate in the past three decades . there appear to be at least four reasonably distinct classes of this gas , namely : ( 1 ) localized outflows and subsequent inflows associated with massive star formation which are commonly referred to as a `` galactic fountain '' ( shapiro & field , 1976 ; bregman , 1980 ) . ( 2 ) the stream of tidal debris from the interaction of the galaxy with the magellanic clouds is another major source of anomalous velocity . recent imaging ( putman & gibson , 1999 ) has begun to reveal the true extent of this debris system , and allow it to be distinguished from other components . ( 3 ) the extended hvc complexes ( named a , c , h , m , ) which span ten s of degrees on the sky and have recently been determined to have both nearby distances of about 10 kpc ( van woerden et al . 1999 ) and rather low ( @xmath30.1 solar ) metal abundance ( wakker et al . 1999 ) . these diffuse structures appear to be currently merging with the galaxy and each account for some 10@xmath4 m@xmath5 of fresh gas . and finally ( 4 ) the system of compact high velocity clouds ( chvcs ) cataloged by braun & burton ( 1999 ) . the chvcs form a distinct class of compact , high - contrast emission features at anomalous velocity , which can be readily distinguished from the more diffuse components in the recent high quality surveys ; the leiden / dwingeloo survey in the north ( hartmann & burton 1997 ) and the parkes multibeam survey in the south ( see putman & gibson 1999 ) . their average angular size is only 1 degree fwhm and the total velocity width 30 fwhm . the 65 confirmed members of the chvc class share a well - defined kinematic pattern . a global search for the reference frame that minimizes the line - of - sight velocity dispersion of the system , returns the local group standard of rest with high confidence . in this system the velocity dispersion of the population is only 70 , although it is in - falling toward the local group barycenter at about 100 . these properties suggest that the objects are : ( 1 ) associated with the local group rather than the galaxy as such , ( 2 ) that they are likely to reside at quite substantial distances and ( 3 ) have as yet had little tidal interaction with the more massive local group members .

a fundamental limit to the stability of a single - ion optical frequency standard is set by quantum noise in the measurement of the internal state of the ion . a servo algorithm is presented that stabilizes a laser frequency to the single - ion signal and that eliminates errors due to laser frequency drift . numerical simulations of the servo characteristics are compared to experimental data from a frequency comparison of two single - ion standards based on a transition at 688 thz in @xmath0yb@xmath1 . experimentally , an instability @xmath2 is obtained in the frequency difference between both standards .

i

physics0511168

a fundamental limit to the stability of a single - ion optical frequency standard is set by quantum noise in the measurement of the internal state of the ion . we discuss how the interrogation sequence and the processing of the atomic resonance signal can be optimized in order to obtain the highest possible stability under realistic experimental conditions . a servo algorithm is presented that stabilizes a laser frequency to the single - ion signal and that eliminates errors due to laser frequency drift . numerical simulations of the servo characteristics are compared to experimental data from a frequency comparison of two single - ion standards based on a transition at 688 thz in @xmath0yb@xmath1 . experimentally , an instability @xmath2 is obtained in the frequency difference between both standards .

optical atomic frequency standards based on single trapped and laser - cooled ions have made important progress and may soon reach and surpass the level of accuracy that is achievable with cesium atomic clocks in the microwave region today @xcite . an ion trap provides a very well - controllable environment and allows one to work at the conceptually simplest level : with one single atom . it is this simplicity that provides the basis for the high accuracy that can be obtained in spectroscopic measurements on these systems . in atomic frequency standards the frequency of an oscillator producing an electromagnetic wave is stabilized to an atomic reference transition . the error signal for the frequency lock is derived by modulating the oscillator frequency around the atomic resonance and by measuring the resulting modulation of the frequency - dependent excitation probability @xmath3 to the upper atomic level . if only a single ion is used , a difficulty arises from the weakness of this signal and the consequently limited signal - to - noise ratio . the ion is probed repeatedly by pulses of the radiation . the state of the ion after an excitation attempt can be determined by applying laser radiation to induce resonance fluorescence on a transition that shares the lower state with the reference transition . this scheme was proposed by dehmelt and is sometimes called electron shelving @xcite . let us denote the two levels that are connected by the reference transition as @xmath4 and @xmath5 and assume that the ion is initially in the lower state @xmath4 . after an excitation attempt the ion generally will be in a superposition state @xmath6 and the measurement with the electron shelving scheme is equivalent to determining the eigenvalue @xmath7 of the projection operator @xmath8 . if no fluorescence is observed ( the probability for this outcome being @xmath9 ) the previous excitation attempt is regarded successful ( @xmath10 ) , whereas the observation of fluorescence indicates that the excited state was not populated ( @xmath11 ) . in one measurement cycle only one binary unit of spectroscopic information is obtained . under conditions where the average excitation probability @xmath3 is @xmath12 , the result of a sequence of cycles is a random sequence of zeros and ones and the uncertainty in a prediction on the outcome of the next cycle is always maximal . these population fluctuations and their relevance in atomic frequency standards were first discussed by itano et al . , who named the phenomenon quantum projection noise ( qpn ) @xcite . a simple calculation shows that the variance of the projection operator is given by @xcite @xmath13 if the signal - to - noise ratio of a state measurement with a single atom is estimated as @xmath14 , it can be seen that for @xmath15 , @xmath16 only . the stability and the accuracy of an atomic frequency standard are ultimately determined by the signal - to - noise ratio , by the linewidth @xmath17 and by the fluctuations of the center frequency @xmath18 of the atomic resonance @xcite . the instability that is obtained after an averaging time @xmath19 is conveniently expressed by the allan deviation @xmath20 which can be written as @xmath21 this expression describes the case of a standard that is operated in interrogation cycles of duration @xmath22 . @xmath23 denotes the signal - to - noise ratio that is obtained in one cycle and @xmath24 is a numerical constant of order unity . the instability decreases inversely proportional to the square root of the number of cycles , giving rise to @xmath25 . parameters that are obtainable with present single - ion optical frequency standards @xcite are of the order of magnitude @xmath26 and @xmath27 s. there are prospects to reach an accuracy in the range of @xmath28 @xcite , but from equation ( 2 ) it can be seen that with @xmath29 , an averaging time of about @xmath30 s or roughly 10 days would be required to complete a single frequency measurement at this accuracy . for the practical use of such a standard it will therefore be of high importance to find the interrogation conditions and servo techniques which minimize @xmath31 , i.e. which make the most efficient use of the single - ion signal in order to provide a stable reference frequency . in this paper we present a theoretical and experimental study of the stability of a single - ion frequency standard under conditions where qpn is the dominant noise source . because qpn presents a fundamental noise limit if only a single ion is probed , it defines the target below which technical noise due to the short - term frequency instability of the probe laser should be reduced . in the first part of the paper we present results of numerical calculations that allow one to find optimized excitation parameters for the case that the linewidth of the laser is smaller than the natural linewidth of the atomic reference transition . the choice of this regime is motivated by the fact that most optical frequency standards presently use reference transitions with natural linewidths in the range of a few hertz to a few hundred hertz @xcite , whereas the most advanced laser sources already have subhertz linewidths @xcite . with the practically unlimited interaction time for the trapped ion , this situation is in contrast to atomic microwave frequency standards where the natural linewidth is usually much smaller than the linewidth of the interrogation oscillator and where the resolution is limited by the finite interaction time . we compare the instability that is obtainable by excitation with a single laser pulse ( rabi excitation ) and with two pulses ( ramsey excitation ) . the influence of a non - zero laser linewidth and of cycle dead time that is needed for the preparation of the ion and for state detection is discussed . while a final optimization will also have to take the specific frequency noise properties of the probe laser into account , these general results are meant to provide initial guidance in the selection of suitable experimental parameters . during the preparation of the manuscript two related studies were published @xcite and we will comment on the relation to that work at the end of section ( 3 ) . in the second part of the paper we present a servo algorithm that can be used to stabilize the laser frequency to the single - ion signal . we investigate the dynamic behaviour of the servo system and the resulting stability of the frequency standard by numerical monte carlo simulations . possible servo errors due to laser frequency drift are also considered . results from the simulations are compared to data from experiments with two yb@xmath1 frequency standards that implement this servo algorithm . previously , brief descriptions of frequency stabilizations to a single ion were given in @xcite and a more detailed discussion including analytical expressions for the expected instability was presented by bernard et al .

a microscopic approach has been employed to study the kaon productions in heavy ion collisions . the results have been compared with available experimental data . we obtain a non - monotonic horn like structure for @xmath1 when plotted with @xmath0 with the assumption of an initial partonic phase beyond a certain threshold in @xmath2 . experimental values of @xmath3 are also reproduced within the ambit of the same formalism .

i

1006.2972

a microscopic approach has been employed to study the kaon productions in heavy ion collisions . the momentum integrated boltzmann equation has been used to study the evolution of strangeness in the system formed in heavy ion collision at relativistic energies . the kaon productions have been calculated for different centre of mass energies ( @xmath0 ) ranging from ags to rhic . the results have been compared with available experimental data . we obtain a non - monotonic horn like structure for @xmath1 when plotted with @xmath0 with the assumption of an initial partonic phase beyond a certain threshold in @xmath2 . however , a monotonic rise of @xmath1 is observed when a hadronic initial state is assumed for all @xmath0 . experimental values of @xmath3 are also reproduced within the ambit of the same formalism . results from scenarios where the strange quarks and hadrons are formed in equilibrium and evolves with and without secondary productions have also been presented . .

the lattice simulation of quantum chromodynamic equation of state ( eos ) predicts that the properties of nuclear matter at extreme densities and/or temperatures are governed by the partonic degrees of freedom @xcite . a series of experiments have been performed @xcite and planned @xcite to produce such a partonic state of matter , called quark gluon plasma ( qgp ) by colliding nuclei at ultra - relativistic energies . rigorous experimental and theoretical efforts are on to create and detect such a novel state of matter @xcite . various signals have been proposed for the detection of qgp - the pros and cons of these signals are matter of intense debate . the study of the ratio , @xmath4 is one such currently debated issue . @xmath5 is measured experimentally @xcite as a function of centre of mass energy ( @xmath2 ) . it is observed that the @xmath5 increases with @xmath2 and then decreases beyond a certain value of @xmath2 giving rise to a horn like structure , whereas the ratio , @xmath6 increases faster at lower @xmath2 and tend to saturate at higher @xmath2 . explanation of this structure has ignited intense theoretical activities @xcite . several authors have attempted to reproduce the @xmath1 ratio using different approaches . while the authors in @xcite use a hadronic kinetic model , in ref . @xcite high mass unknown hadronic resonances have been introduced through hagedorn formula to describe the data . in ref . @xcite a transition from a baryon dominated system at low energy to a meson dominated system at higher energy has been assumed to reproduce the ratio @xmath1 . the release of color degrees of freedom is assumed in @xcite beyond a threshold in @xmath0 ( resulting in large pion productions ) or the production of larger number of pions than kaons from higher mass resonance decays has also been employed @xcite to explain the data . in the present work we employ a microscopic model for the productions and evolution of strange quarks and hadrons depending on the collision energy . here we examine whether the @xmath1 experimental data can differentiate between the following two initial conditions or two scenarios - after the collisions the system is formed in : ( i ) the hadronic phase for all @xmath0 or ( ii ) the partonic phase beyond a certain threshold in @xmath0 . other possibilities like formation of strangeness in complete thermal equilibrium and evolution in space time ( iii ) without and ( iv ) with secondary productions of quarks and hadrons have been considered . ( v ) results for an ideal case of zero strangeness in the initial state has also been presented . in the context of strangeness enhancement as signal of qgp formation , similar approach _ i.e. _ the assumption of an initial state where non - strange sectors are in equilibrium but the strange degrees of freedom are out of equilibrium ( having density much below their equilibrium values ) were considered in the 1980 s . the strangeness production in a deconfined ( partonic ) phase is enhanced compared to the their production in the confined ( hadronic ) phase primarily because even the lightest strange hadrons , the kaons are much heavier than the strange quarks . moreover , the strange quark has more degrees of freedom ( six ) in a deconfined matter compared to kaons . therefore , the strangeness production during the space time evolution of the system for partonic initial state will be enhanced compared to the hadronic initial state , hence the enhanced production of strangeness could be an efficient signal for deconfinement @xcite . in contrast to these studies gazdzicki and gorenstein @xcite within the ambit of statistical model considered the strangeness production where both the strange and non - strange degrees of freedom are in thermal equilibrium and the production of strangeness during the expansion stage is ignored . in the present work we would like to compare the results on kaon to pion ratio from these two contrasting scenarios . we assume that the non - strange quarks and hadrons are in complete thermal ( both kinetic and chemical ) equilibrium and the strange quarks and strange hadrons are away from chemical equilibrium . therefore , the evolution of the strange sector of the system is governed by the interactions between the equilibrium and non - equilibrium degrees of freedom . the momentum integrated boltzmann equation provides a possible framework for such studies . similar approach has been used to study the sequential freeze - out of elementary particles in the early universe @xcite . for the strangeness productions in the partonic phase we consider the processes of gluon fusion and light quarks annihilation . for the production of @xmath7 and @xmath8 an exhaustive set of reactions involving thermal baryons and mesons have been considered . the time evolution of the densities are governed by the boltzmann equation . the paper is organized as follows . in the next section the rate of strangeness productions in the partonic and hadronic phases are discussed . the space time evolution of the system is presented in section iii . results are presented in section iv and finally section v is devoted to summary and conclusion .

the kaon productions have been calculated for different centre of mass energies ( @xmath0 ) ranging from ags to rhic . however , a monotonic rise of @xmath1 is observed when a hadronic initial state is assumed for all @xmath0 . results from scenarios where the strange quarks and hadrons are formed in equilibrium and evolves with and without secondary productions have also been presented . .

i

1006.2972

a microscopic approach has been employed to study the kaon productions in heavy ion collisions . the momentum integrated boltzmann equation has been used to study the evolution of strangeness in the system formed in heavy ion collision at relativistic energies . the kaon productions have been calculated for different centre of mass energies ( @xmath0 ) ranging from ags to rhic . the results have been compared with available experimental data . we obtain a non - monotonic horn like structure for @xmath1 when plotted with @xmath0 with the assumption of an initial partonic phase beyond a certain threshold in @xmath2 . however , a monotonic rise of @xmath1 is observed when a hadronic initial state is assumed for all @xmath0 . experimental values of @xmath3 are also reproduced within the ambit of the same formalism . results from scenarios where the strange quarks and hadrons are formed in equilibrium and evolves with and without secondary productions have also been presented . .

the evolution of the strangeness in the system formed in nuclear collisions at relativistic energies have been studied within the framework of momentum integrated boltzmann equation . the boltzmann equation has been used to study the evolution of @xmath9 and @xmath10 in the partonic phase and @xmath8 and @xmath7 in the hadronic phase . the calculation has been done for different centre of mass energies ranging from ags to rhic . we get a non - monotonic variation of @xmath1 with @xmath2 when an initial partonic phase is assumed for @xmath158 gev and beyond . a monotonic rise of @xmath1 is observed when a pure hadronic scenario is assumed for all centre of mass energies . the @xmath3 data is unable to differentiate between the two initial conditions mentioned before . some comments on the values of the initial parameter are in order at this point . we have seen that a @xmath159 variation in the initial temperature does not change the results drastically . we have assumed that the initial density of strange quarks or kaons depending on the scenario ( i ) or ( ii ) is about @xmath100 away from the corresponding equilibrium density . results from a scenario where strange quarks or kaons are formed in complete equilibrium and the production is ignored during the evolution then the data is well reproduced ( scenario iii ) . if the the strangeness is produced in equilibrium and the production is included during the expansion stage then the data is overestimated . however , if the system is formed with zero strangeness then the theoretical results underestimate the data substantially . this indicate that the production of strangeness during the expansion of the system is small but not entirely negligible . the deficiency assumed in scenario ii is compensated by the production during evolution . i. arsene _ ( brahms collaboration ) , nucl . a * 757 * , 1 ( 2005 ) ; b. b. back _ et al . _ ( phobos collaboration ) , nucl . phys . a * 757 * , 28 ( 2005 ) ; j. adams _ et al . _ ( star collaboration ) , nucl . phys . a * 757 * , 102 ( 2005 ) ; k. adcox _ ( phenix collaboration ) , nucl . phys . a * 757 * , 184,(2005 ) . c. w. fabjan ( for the alice collaboration ) , j. phys . g * 35 * , 104038 ( 2008 ) ; d. denterria ( for the cms collaboration ) , j. phys.g * 35 * , 104039 ( 2008 ) ; n. grau ( for the atlas collaboration ) , j. phys.g * 35 * , 104040 ( 2008 ) . j. alam , s. chattopadhyay , t. nayak , b. sinha and y . p. viyogi ( eds ) , j. phys . * 35 * ( 2008 ) ( proc . quark matter 2008 ) ; p. stankus , d. silvermyr , s. sorensen and v. greene ( eds . ) , nucl . a * 830 * ( proc . quark matter ) ( 2009 ) .

iterative methods ( such as the jacobi method ) tend to damp out high - frequency components of the error fast , but converges poorly due to slow reduction of low - frequency components . the idea is to use a set of differently coarsed grids to reduce both the short- and long - period errors .

m

astro-ph0611112

a new iterative method for non - lte multilevel polarized radiative transfer in hydrogen lines is presented . iterative methods ( such as the jacobi method ) tend to damp out high - frequency components of the error fast , but converges poorly due to slow reduction of low - frequency components . the idea is to use a set of differently coarsed grids to reduce both the short- and long - period errors . this leads to the so - called multigrid ( mg ) methods . for the grid of @xmath0 spatial points , the number of iterations required to solve a non - lte transfer problem is of the order of @xmath1 this fact could be of great importance for problems with fine structure and for multi - dimensional models . the efficiency of the so - called standard mg iteration in comparison to jacobi iteration is shown . the formalism of density matrix is applied to the demonstrative example of 1d , semi - infinite , non - magnetic , 3-principal level hydrogen atmospheric model . the effect of depolarizing collisions with thermal electrons is taken into account as well as general treatment of overlapping profiles .

most of the existing non - lte solvers use the methods based on @xmath22-operator splitting similar to the one of @xcite . depending on organization , these schemes are numerically equivalent to the jacobi or gauss - seidel smoothing procedures ( for details , see * ? ? ? * ; * ? ? ? these smoothing procedures do reduce high frequencies of the solution fast , but poor convergence is achieved for low frequencies . ( with `` high frequencies '' we mean those which are comparable to the spatial frequency of grid points approximating the continuous scale . ) the principles of mg schemes are based on the idea of using coarse grids to reduce the low frequencies , and fine grids to smooth their high - frequency components . it can be showed that such a process may lead to the optimal cpu time demands of @xmath1 , @xmath0 being the number of points per decade of optical scale . for comparison , the jacobi and gauss - seidel methods scales approximately as @xmath23 . we have applied the non - linear version of the _ standard multigrid _ scheme based on the coarse grid correction ( cgc ) technique ( for details , see * ? ? ? * ; * ? ? ? cgc is the process of correction of the fine - grid approximation of the solution using the solutions on the coarse grids . schematically , it can be described in the following way : the defect ( or residuum ) of the fine - grid approximation is computed by several calls of the sweeping procedure ( jacobi , etc . ) ; then both defect and the initial guess of the solution are restricted to the coarse grid , and a new solution on the coarse grid is obtained using these data . this coarse - grid solution is interpolated to the fine grid , and the density - matrix components are corrected . this process can be repeated recursively for every grid in order of increasing grid steps . this recursive process leads to the so - called v , w , or more complicated diagrams , depending on the way in which the recursion is implemented @xcite . in our code we use the parabolic short - characteristics technique of @xcite , and as a smoothing algorithm we use the jacobi iteration , similar to the one of @xcite , with modifications to include the effects of line overlapping .

we consider the process of line formation in clumpy stochastic media accounting for fluctuating velocity and density fields ( mesoturbulence ) . this approach generalizes our previous reverse monte carlo and entropy - regularized minimization methods which were applied to velocity fluctuations only . hi , cii , siii , civ , siiv , and ovi lines , exhibiting complex profiles , were fitted simultaneously .

i

astro-ph0003078

a new method , based on the simulated annealing algorithm and aimed at the inverse problem in the analysis of intergalactic ( interstellar ) complex spectra of hydrogen and metal lines , is presented . we consider the process of line formation in clumpy stochastic media accounting for fluctuating velocity and density fields ( mesoturbulence ) . this approach generalizes our previous reverse monte carlo and entropy - regularized minimization methods which were applied to velocity fluctuations only . the method allows one to estimate , from an observed system of spectral lines , both the physical parameters of the absorbing gas and appropriate structures of the velocity and density distributions along the line of sight . the validity of the computational procedure is demonstrated using a series of synthetic spectra that emulate the up - to - date best quality data . hi , cii , siii , civ , siiv , and ovi lines , exhibiting complex profiles , were fitted simultaneously . the adopted physical parameters have been recovered with a sufficiently high accuracy . the results obtained encourage the application of the proposed procedure to the analysis of real observational data . = 0.2 cm

qso absorption line spectroscopy being a major activity at many observatories for the last two decades is now developing into a powerful tool for extragalactic research thanks to the new generation of large telescopes . the steady improvement in sensitivity and resolution of spectroscopic instrumentation opens new fields in the study of qso absorption systems . it is now becoming possible to investigate the intensity fluctuations within the line profiles and thus to estimate hydrodynamic characteristics of the absorbing gas . the majority of the narrow qso absorption lines represents intervening systems and allows us to probe the properties of diffuse matter at very high redshifts . resolved profiles of hydrogen lines and especially lines of heavier elements ( ` metals ' ) show a diversity of shapes and structures . up to now , their analysis is based on the assumption that the observed complexity is caused by individual ` clouds ' randomly distributed along the line of sight with slightly different radial velocities . it is also a basic assumption that the hydrodynamic ( ` bulk ' or ` turbulent ' ) velocity distribution inside each cloud is gaussian and completely uncorrelated ( _ microturbulence _ ) . this model implies that each subcomponent of the complex profile being resolved should have a symmetrical profile and its shape should not alter with higher spectral resolution . observations show , however , that the complexity of the line profiles increases with higher resolution , a tendency expected for correlated bulk motions which have , in general , non - gaussian distributions along a given line of sight ( levshakov & kegel 1997 ; levshakov , kegel & mazets 1997 ; levshakov , kegel & takahara 1999 ; papers i , ii , and iii hereafter , respectively ) . it follows that the microturbulent approximation is not appropriate in this case because it does not account for all the relevant physical processes involved in the radiative transfer . moreover , being applied to real data , the microturbulent analysis leads to a loss of valuable information contained in the observations and may even yield unphysical results ( levshakov & kegel 1999 ; levshakov , takahara & agafonova 1999 ; lta hereafter ) . the need for more sophisticated procedures of data analysis becomes therefore obvious . in recent years , it has been shown that accounting for the correlations in the velocity field ( _ mesoturbulence _ ) may change the interpretation of the line measurements substantially ( papers i and ii ) . a mesoturbulent approach has been already successfully applied to the study of the deuterium and hydrogen absorption in q 19371009 ( levshakov , kegel & takahara 1998a ) , q 1718 + 4807 ( levshakov , kegel & takahara 1998b ) , and q 1009 + 2956 ( levshakov , tytler & burles 2000 ) . for all three qsos about the same value for the d / h ratio was derived in contrast to the previously announced microturbulent results . our first inversion codes , the reverse monte carlo ( paper iii ) , and the entropy - regularized minimization ( lta ) , have been developed for a model of a stochastic velocity field neglecting any density fluctuations . they have been applied to the analysis of the hi and di lines and/or to the metal absorption lines with similar profiles when species trace the same volume elements independently on the density fluctuations . in the present paper , we extend this study to the inverse problem for a model of compressible turbulence when one observes non - similar profiles of different atoms and/or ions from the same absorption - line system . as in our previous papers , we use the term ` turbulence ' in a wider sense as compared with hydrodynamic turbulence to label the unknown nature of the line broadening mechanism . in this regard we consider any kind of bulk motions ( infall , outflows , tidal flows etc . ) of more or less stochastic nature leading to fluctuating velocity and density ( temperature ) fields as continuous random functions of the space coordinate along a given line of sight within the intervening absorbing region . two noteworthy works have been recently carried out aiming at the recovery of the physical intergalactic structure from the lyman-@xmath0 forest lines . nusser & haehnelt ( 1999a , b ) developed an inverse procedure based on the relation between density and velocity fourier coefficients . the quality of their recovery is , however , restricted by the assumption that the lyman-@xmath0 forest structure traces mainly the matter density distribution and that the amplitude of the peculiar velocities is rather small to affect the local absorption coefficient significantly . this assumption is questionable since there is no simple way to distinguish _ observationally _ whether the density or the velocity fluctuations are the main source of the ` line - like ' structure observed in the lyman-@xmath0 forest ( levshakov & kegel 1998 ) . moreover , recent studies of nearby large - scale motions in the universe indicate that the hubble flow is considerably perturbed . peculiar velocities in the range from 300 to 500 km s@xmath1 have been found in a sample of galaxies complete out to a distance of 60 mpc ( e.g. , watkins 1997 ; gramann 1998 ; giovanelli et al . 1998 ) , a fact which should be taken into account in the inverse procedures . the method described in the present paper is quite flexible and equally accounts for the density and velocity fluctuations . it is based on a stochastic optimization approach similar to that developed in paper iii . we estimate simultaneously the physical parameters _ and _ appropriate realizations of the density @xmath2 and velocity @xmath3 distributions along the line of sight to reproduce hydrogen and metal lines from a given absorption system . in this regard , the more spectra of different elements are incorporated in the analysis the higher accuracy of the estimation can be obtained . in @xmath4 our model and the underlying basic assumptions are specified . the inversion code is described in @xmath5 . the validity of the method is tested in @xmath6 using simulated sets of noisy line profiles ( hi , cii , siii , civ , siiv , and ovi ) . finally , the main conclusions are outlined in @xmath7 .

a new method , based on the simulated annealing algorithm and aimed at the inverse problem in the analysis of intergalactic ( interstellar ) complex spectra of hydrogen and metal lines , is presented . the method allows one to estimate , from an observed system of spectral lines , both the physical parameters of the absorbing gas and appropriate structures of the velocity and density distributions along the line of sight . the results obtained encourage the application of the proposed procedure to the analysis of real observational data .

c

astro-ph0003078

a new method , based on the simulated annealing algorithm and aimed at the inverse problem in the analysis of intergalactic ( interstellar ) complex spectra of hydrogen and metal lines , is presented . we consider the process of line formation in clumpy stochastic media accounting for fluctuating velocity and density fields ( mesoturbulence ) . this approach generalizes our previous reverse monte carlo and entropy - regularized minimization methods which were applied to velocity fluctuations only . the method allows one to estimate , from an observed system of spectral lines , both the physical parameters of the absorbing gas and appropriate structures of the velocity and density distributions along the line of sight . the validity of the computational procedure is demonstrated using a series of synthetic spectra that emulate the up - to - date best quality data . hi , cii , siii , civ , siiv , and ovi lines , exhibiting complex profiles , were fitted simultaneously . the adopted physical parameters have been recovered with a sufficiently high accuracy . the results obtained encourage the application of the proposed procedure to the analysis of real observational data . = 0.2 cm

we have developed a new method to solve the inverse problem in the analysis of intergalactic ( interstellar ) hydrogen and metal lines arising from clumpy stochastic media . in the method , the random velocity and density configurations along the line of sight are approximated by markovian processes . the global optimization method based upon simulated annealing is then used to fit theoretical line profiles to a set of ` observational ' data . the proposed procedure allows us to estimate the physical parameters of the absorbing gas such as column densities , metal abundances , mean ( density - weighted ) kinetic temperatures for each ion , and mean ionization parameter together with the hydrodynamic characteristics the radial velocity dispersion and the dispersion of the density fluctuations . the computational scheme has been tested on a variety of synthetic spectra that emulate modern observational data : the absorption lines of hi , cii , siii , civ , siiv , and ovi which are usually observed in the lyman limit systems ( @xmath227 @xmath84 ) . the ionization structure of the absorbing region was calculated using the standard photoionization model of donahue & shull ( 1991 ) with a background ionizing spectrum given by mathews & ferland ( 1987 ) . the inversion procedure proved to be very effective and robust allowing us to recover the physical parameters with reasonable accuracy albeit the structure of the random velocity and density fields can not be restored with a pixel - to - pixel conformity . however , the integral characteristics of these random fields , namely , the density - weighted velocity distribution , can be estimated quite precisely . thus we can conclude that our procedure provides reliable results and can be applied to the analysis of real data . note that while performing the inversion of absorption lines , one has to take into account the following . all our computational tests have been carried out under the assumption that the spectrum of the ionizing radiation is known , i.e. we used the same mathews & ferland spectrum to generate ` observational ' data and to fit them with our theoretical profiles . in reality , the characteristics of the ionizing radiation are not known exactly . therefore in real applications several types of the background photoionizing spectra should be tried . the problem how the computational results are affected by different types of the background ionizing radiation will be studied in detail elsewhere . the proposed method has been successfully applied to the analysis of qso high resolution spectral data with possible deuterium absorption at @xmath228 towards apm 08279 + 5255 ( levshakov , agafonova & kegel 2000 ) . it has been demonstrated that the blue - side asymmetry of the hydrogen ly@xmath0 line can be explained quite naturally by an asymmetric configuration of the velocity field only . the results obtained revealed a considerably lower neutral hydrogen column density as compared with the vpf measurements performed by molaro et al . in contrast to molaro et al . , we have managed to fit simultaneously all absorption lines observed in this system . these results can be considered as encouraging and favor the application of the developed computational procedure to the analysis of other high quality observational data . the authors are grateful to ellison et al . for providing the spectra of quasar apm 08279 + 5525 . sal and iia gratefully acknowledge the hospitality of the university of frankfurt / main and the european southern observatory ( garching ) where this work was performed . this work was supported by the deutsche forschungsgemeinschaft and by the rfbr grant no . 00 - 02 - 16007 .