Datasets:

Hendrik-a

/

dancer-data

like 0

astro-ph0506750

r

equations ( 4 - 6 ) are used to estimate the stellar mass for the various scalings . for each scaling , a grid of 10 choices of the scaling constant are made : @xmath48 to 1.0 in steps of 0.1 relative to maximum disk , and for @xmath37 and @xmath38 values ranging from 0.2 to 2.0 in steps of 0.2 . the maximum disk scaling obviously can not exceed unity , while for the other scalings there is no reason not to consider values larger than one . for example , @xmath49 would simply imply an imf heavier than assumed in the nominal population model which has been adopted . however , these values should not exceed maximum disk , and are not allowed to do so . if the choice of @xmath37 or @xmath38 exceeds the maximum disk value for a particular galaxy , the maximum disk value is used instead . half of the sample has saturated at maximum by @xmath50 , so larger values are not considered . the btf ( logarithm of equation 1 ) is fit . ] to the data in table 1 for each set of choices for @xmath1 . every galaxy carries equal weight in the fits . since the data have been selected to be of high quality , the residual uncertainties are likely to be dominated by systematic effects ( such as the precise distance to each galaxy ) rather than factors internal to the data , though these obviously matter as well . in any case , the choice of mass - to - light ratio completely dominates the results . lccccc @xmath51 & + 1.0 & 2.52 & 0.37 & 3.48 & 0.17 & 0.239 + + @xmath31 & + 0.0 & 4.67 & 0.48 & 2.28 & 0.48 & 0.313 + + @xmath36 & + 0.1 & 3.24 & 0.37 & 3.09 & 0.37 & 0.244 + 0.2 & 2.76 & 0.35 & 3.38 & 0.35 & 0.230 + 0.3 & 2.50 & 0.35 & 3.55 & 0.35 & 0.224 + 0.4 & 2.34 & 0.34 & 3.67 & 0.34 & 0.222 + 0.5 & 2.23 & 0.34 & 3.75 & 0.34 & 0.220 + 0.6 & 2.15 & 0.34 & 3.81 & 0.34 & 0.220 + 0.7 & 2.09 & 0.34 & 3.87 & 0.34 & 0.220 + 0.8 & 2.05 & 0.34 & 3.91 & 0.34 & 0.220 + 0.9 & 2.01 & 0.34 & 3.94 & 0.34 & 0.220 + 1.0 & 1.98 & 0.34 & 3.97 & 0.34 & 0.221 + + @xmath37 & + 0.2 & 3.81 & 0.33 & 2.81 & 0.15 & 0.204 + 0.4 & 3.44 & 0.30 & 3.04 & 0.14 & 0.186 + 0.6 & 3.23 & 0.29 & 3.19 & 0.14 & 0.183 + 0.8 & 3.08 & 0.29 & 3.29 & 0.13 & 0.183 + 1.0 & 2.98 & 0.29 & 3.37 & 0.13 & 0.186 + 1.2 & 2.87 & 0.28 & 3.44 & 0.13 & 0.188 + 1.4 & 2.75 & 0.27 & 3.52 & 0.13 & 0.191 + 1.6 & 2.65 & 0.27 & 3.58 & 0.13 & 0.194 + 1.8 & 2.54 & 0.26 & 3.64 & 0.12 & 0.197 + 2.0 & 2.46 & 0.26 & 3.69 & 0.12 & 0.200 + + @xmath38 & + 0.2 & 3.05 & 0.25 & 3.18 & 0.25 & 0.165 + 0.4 & 2.46 & 0.20 & 3.53 & 0.20 & 0.129 + 0.6 & 2.11 & 0.17 & 3.74 & 0.17 & 0.112 + 0.8 & 1.87 & 0.16 & 3.89 & 0.16 & 0.103 + 1.0 & 1.70 & 0.15 & 4.00 & 0.15 & 0.098 + 1.2 & 1.60 & 0.15 & 4.07 & 0.15 & 0.100 + 1.4 & 1.58 & 0.16 & 4.10 & 0.16 & 0.107 + 1.6 & 1.60 & 0.18 & 4.10 & 0.18 & 0.118 + 1.8 & 1.61 & 0.20 & 4.10 & 0.20 & 0.129 + 2.0 & 1.64 & 0.22 & 4.10 & 0.22 & 0.140 + the results of fitting the btf are given in table 2 . the intercept @xmath52 and slope @xmath24 are recorded , together with the formal uncertainties in each ( @xmath53 and @xmath54 ) . also given is the scatter of the data about each relation , @xmath55 . for reference , the input data , in the form of the normal luminosity - based tully - fisher relation is given . it has a scatter @xmath56 , which is equivalent to 0.6 mag . ( base ten logarithms are used throughout ) . note also that the limit @xmath57 is equivalent to the gas - only relation , so is given only once . the results summarized in table 2 are illustrated in figs . 3 and 4 . as the assumed mass - to - light ratio increases , the slope @xmath24 gradually increases while the zero point @xmath23 decreases to compensate . the lowest mass galaxies in table 1 are dominated by gaseous rather than stellar mass , so the btf tends to pivot about them . this can be seen by eye in fig . 2 , where the low end of the relation hardly budges while the more massive , star dominated galaxies move up and down with @xmath1 . these low mass , gas - rich galaxies provide a critical anchor point for the absolute calibration of the btf since their location in this diagram is insensitive to the choice of @xmath1 . the scatter @xmath55 about each fit is shown in fig . the maximum disk scaling has scatter comparable to the scatter in the input luminosities . the use of color information with population synthesis models provides a small increment of improvement in the scatter , as it should if the models succeed in improving the estimate of @xmath1 over a constant value for all objects . as stellar mass is rendered unimportant for very small @xmath36 and @xmath37 the scatter starts to increase . the limit of zero stellar mass , with gas only , obviously makes for an inadequate btf , as one would expect . irrespective of the physics underlying the btf , we expect that the prescription for @xmath1 that comes closest to the correct value will minimize the scatter about it . there may be some intrinsic scatter , but if we can get @xmath1 right , there should be no scatter left due to it . the @xmath35 prescription gives less scatter than either @xmath33 or @xmath34 . there is clear variation in the scatter with @xmath38 , with a well defined minimum at @xmath58 . the same mass - to - light ratio chosen to minimize the residuals from the local mdacc also minimizes the scatter in the global btf . this was already apparent in fig . 6 of mcgaugh ( 2004 ) , and is quantitatively confirmed here . it is rare in extragalactic astronomy that we find a correlation as strong as the btf ( @xmath59 for @xmath58 ) . indeed , the btf is so sharply defined that it has a kurtosis of 1.5 . it is difficult to avoid the conclusion that the choice @xmath58 does effectively give the correct @xmath1 . this provides an absolute calibration of the btf : @xmath60 with @xmath5 in @xmath61 and @xmath15 in @xmath16 . indeed , the scatter in this btf relation is so small that it could be used to estimate @xmath1 with nearly as great accuracy as the full mdacc , but with considerably less information . to apply the latter , we require a well resolved rotation curve and hi surface density map , and detailed surface photometry . the btf requires only global quantities : @xmath29 , @xmath31 from a single dish 21 cm observation , and an estimate of @xmath15 ( preferably from a rotation curve which is sufficiently resolved to perceive the flat part , though @xmath62 would be an adequate substitute , with some penalty in accuracy . ) this btf is consistent with the relation first reported by mcgaugh et al . the slope is identical , but the normalization is somewhat larger . this change is not particularly significant ( @xmath63 ) . it is largely due to the improvement in data quality and the use of @xmath15 rather than @xmath64 . the line - width @xmath11 is systematically larger than @xmath65 , which is more closely approximated by @xmath66 ( broeils 1992 ; verheijen 1997 ) . thus we should expect some increase in @xmath23 simply from the change of circular velocity measures . indeed , it is reassuring that the relation found here is so closely consistent with the previous version . mcgaugh et al . ( 2000 ) chose @xmath1 by a different method , taking a constant value for all galaxies motivated by population models . more importantly , the data are largely independent : the btf of mcgaugh et al . ( 2000 ) included 110 galaxies from bothun et al . ( 1985 ) , 14 from matthews , van driel , & gallagher ( 1998 ) , and 65 from eder & schombert ( 2000 ) that are completely distinct from and independent of the data in table 1 . the agreement of such diverse and independent data sets provides strong confirmation of the basic empirical result . the btf is by far the strongest correlation present in the data , but it is not the only one . there are a few others worth noting . some of these are shown in fig . many others are not shown to avoid redundancy : anything that is correlated with disk mass is also correlated with @xmath15 through the btf . correlation coefficients for the quantities appearing in fig . 5 are given in table 3 . one interesting quantity that can be constructed from the data in table 1 is the fraction of the total observed baryonic mass in the form of stars : @xmath67 . the variation of @xmath68 with disk mass basically shows the turn - away of the stellar mass tf from the btf as one goes from star to gas domination . there is lots of scatter in the @xmath68-@xmath5 diagram which is not reflected in the btf . this reiterates that what matters is mass , not the form it is in . lcccc @xmath15 & 0.99 & 0.78 & 0.77 & 0.53 + @xmath5 & & 0.76 & 0.76 & 0.53 + @xmath68 & & & 0.84 & 0.54 + @xmath1 & & & & 0.64 + together with the mass - to - light ratio and color , @xmath68 is an indicator of the evolutionary state of a galaxy ( mcgaugh & de blok 1997 , 1998a ; schombert , mcgaugh , & eder 2001 ) . as evolution proceeds and a galaxy converts its initial gas into stars , the stellar fraction increases . as old stars accumulate , the mean color reddens , and the mass - to - light ratio increases . one therefor expects these quantities to be related . the evolutionary quantities @xmath68 , @xmath1 , and color do indeed correlate as expected . not only does the mass - to - light ratio increase as the stellar population reddens , so too does @xmath1 climb as @xmath68 increases . indeed , the @xmath1-@xmath68 correlation is the next strongest in table 3 after the btf . in this sample , the evolutionary quantities are correlated with baryonic mass . they are also correlated with @xmath15 , as shown previously by sanders ( 1996 ) . this must follow , given the btf . indeed , figures constructed with @xmath15 instead of @xmath5 look so similar that they are difficult to distinguish . one curious feature of the correlations with disk mass is that all of the evolutionary indicators suggest that more massive disks are typically more evolved . this is opposite what one might naively expect from a hierarchical galaxy formation picture . in such a scenario , small galaxies form first so should have evolved the most . that the opposite is true seems more consistent with monolithic or even top - down galaxy formation . similar results have been found recently at high redshift ( e.g. , juneau et al . 2005 ; treu et al . 2005 ) , where the tendency for massive galaxies to be the most evolved is called `` downsizing . '' if galaxies do form hierarchically , the observed trend suggests that the mechanisms which regulate a galaxy s post - formation evolution dominate over the formation epoch in determining its present evolutionary status . this would appear to be a continuous function of mass , given the continuity in fig . 5 . it does not appear to be as simple as a single epoch of reionization suppressing galaxy formation at a characteristic mass scale . one word of caution is that while these data span a broad range of galaxy properties , they do not constitute a complete volume limited sample . the details of these correlations may well change as other data are added . nevertheless , it seems unlikely that the trend apparent in this figure could be reversed : massive galaxies still in the early stages of evolution seem to be very rare . it is extremely difficult to obtain a sample extending to very low mass which is complete in any meaningful sense . since an hi map is a prerequisite for membership in this sample , it seems likely that there are some low mass , high @xmath68 galaxies which are not represented here . so while there are some clear correlations with disk mass _ in this sample _ , there is no guarantee that precisely these correlations will hold for all galaxies . there is more hope that correlations between the evolutionary parameters @xmath68 , @xmath1 , and @xmath20 will hold , if only because they make so much sense . these cautions do not apply to the btf . there is no hint of deviation from it : the residuals are small and uncorrelated with any measured parameter . there is no reason to suspect that any rotating galaxy deviates from the btf even those that should deviate do not ( mcgaugh & de blok 1998a ; verheijen 2001 ) . the btf appears to be a fundamental relation . the remarkable consistency of the mdacc mass - to - light ratios with stellar population synthesis models has been noted previously ( sanders 1996 ; mcgaugh & de blok 1998b ; sanders & mcgaugh 2002 ; mcgaugh 2004 ) . i have added more color information to the data in table 1 than has previously been available , and this point remains true . indeed , there are now enough data that we can perform a fit in the same manner as done for population synthesis models . following the format of bell & de jong ( 2001 ) , the data are fit to a relation of the form @xmath69 portinari et al . ( 2004 ) note that while their @xmath18-band model @xmath1 are linearly correlated for @xmath70 , they show a break at this point . @xmath1 turns down to lower values for bluer colors than predicted by extrapolation of the line fit to redder colors . i therefor consider two fits to the data : one covering data of all colors , and the other restricted to @xmath70 the relations from the stellar population synthesis models of bell et al . ( 2003 ) and portinari et al . ( 2004 ) are compared with the fits to the data in table 4 . the relation of bell et al . ( 2003 ) is that used to estimate @xmath34 ( equation 7 ) . note the close agreement between the two models : these are virtually indistinguishable in fig . the zero points @xmath71 of the models are dominated by the choice of imf , which is fortuitously close ( kroupa & weidner 2003 ) . lccl bell et al . & @xmath72 & 1.737 & scaled salpeter imf + portinari et al . & @xmath73 & 1.69 & kroupa imf + fit to the data & @xmath74 & 1.83 & @xmath70 + fit to the data & @xmath75 & 2.31 & all colors + there is close agreement between the parameters @xmath71 and @xmath76 fit to the data and those predicted by the models . the mdacc mass - to - light ratios , determined by dynamical methods completely independent of the population models , show precisely the same trends . a slight offset in normalization is apparent , but its formal significance is low . it is tempting to interpret this offset as the molecular gas which has been subsumed into @xmath35 . if the mass of gas in the molecular phase is typically 10% to 20% of that in stars , the offset between models and data would be reconciled . the break at @xmath77 in the models of portinari et al . ( 2004 ) is apparent in the data . fig . 5 shows ( as the dashed line ) the model slope for bluer colors ( from their fig . 28 ) , normalized to match the fit to the data at the break point . this is entirely consistent with the downward trend in the data . the scatter in @xmath1 is also as expected , being larger in @xmath18 than in @xmath12 ( sanders & mcgaugh 2002 ; mcgaugh 2004 ) . this is true also above and below the break point at @xmath78 . below this point , one expects a tremendous amount of scatter from the rapid evolution of young populations . here the scatter is enormous : @xmath79 . above this color , one expects variation in @xmath1 to settle down , as the effects of individual star formation events are moderated by the accumulation of mass from previous generations . for these redder colors , the scatter is @xmath80 . in sum , the @xmath58 mass - to - light ratios are optimal not only in terms of minimizing the scatter in the btf and the mdacc ( from which they come ) , but also in terms of our expectations for stellar populations . indeed , it is hard to imagine better agreement with independent population models to which no fit has been made . moreover , the scatter in the dynamical relations is so small for these high quality data that @xmath1 estimated from the btf itself ( equation 7 ) are nearly indistinguishable from @xmath35 from the mdacc . either empirical method can be employed with unprecedented precision . the value of the slope @xmath24 of the btf is somewhat controversial , being of considerable physical importance . the nominal expectation of cdm is that @xmath81 ( navarro & steinmetz 2000a , b ) , and courteau et al . ( 2003 ) argue that this is consistent with their @xmath10-band data . the @xmath10-band is a good but not perfect indicator of mass , and the hst calibrated distances of sakai et al . ( 2000 ) give an @xmath10-band slope of 4 . this emphasizes the need for a good estimate of @xmath5 and not just @xmath29 . mcgaugh et al . ( 2000 ) found @xmath4 from data and @xmath1 estimates independent of those used here . the key aspect of that study was the large number of very gas rich , low rotation velocity galaxies which tied down the low mass end of the btf . verheijen ( 2001 ) obtained the same result . bell & de jong ( 2001 ) generated stellar population models in an attempt to improve the estimate of @xmath1 . applied to the data of verheijen , they found a btf with @xmath82 . i have , in effect , repeated this analysis with more data and updated models , and find very much the same result : for @xmath83 , @xmath84 ( table 2 ) . it is interesting that while the models and data are in good agreement ( 4.2 ) , use of @xmath34 gives somewhat shallower @xmath24 than @xmath35 or @xmath33(fig . this is attributable in part to the slight difference in normalization ( @xmath71 in table 4 ) . this can not be the entire reason for the difference , as increasing @xmath37 to 2 only increases @xmath24 to 3.7 . the shortcoming of @xmath34 estimated from a single color is that galaxies become beads on a string in the @xmath1-@xmath85 diagram : all the data collapse to fall on the dotted line in fig 5 . the inability to estimate deviations from the mean relation and thereby include a realistic estimate of the scatter seems to result in a bias - band @xmath1-color relation , which became flatter between bell & de jong ( 2001 ) and bell et al . ( 2003 ) . ] in the determination of the slope . relative to the population predicted @xmath34 , @xmath35 is skewed to high values for red colors and to low values for blue colors . one expects such a skew relative to a single straight line fit ( portinari et al . 2004 ) ; it causes a systematic difference in the slope in spite of the close agreement seen in fig . 5 and table 4 . the critical issue for constraining the slope is the dynamic range of the data . as a further test of the slope of the btf , i have sought out galaxies that extend the relation to lower rotation velocities . the slowest rotator in table 1 has @xmath86 . i have searched the literature for galaxies with slower rotation velocities that are of adequate quality to make a useful comparison . there are many slow rotators already in the sample of mcgaugh et al . ( 2000 ) , but there the rotation velocity estimate was based on a line - width ( eder & schombert 2000 ) . here i require that there be a resolved measurement adequate for estimating @xmath15 . table 5 contains the objects found that met these criteria . many of these are due to the recent excellent work of begum & changular ( 2003 , 2004a , b ) which extends down to objects approaching the globular cluster mass scale . in table 5 i give the data necessary for the btf from the data given in each reference cited there . i have estimated @xmath15 myself from the published data . in addition to the best estimate , i give a generous range of uncertainty . in many of these cases , there is a substantial correction for asymptotic drift . the lower limit of @xmath15 takes the lower end of the published errors ignoring the asymptotic drift correction . the upper limit takes the upper end of the experimental errors and includes the correction . this procedure results in a very broad error estimate : the uncertainties listed in table 5 are much larger than @xmath63 . lcccc eso215g?009 & @xmath87 & 23 & 714 & 1 + ugc 11583 & @xmath88 & 119 & 36 & 2,3 + ngc 3741 & @xmath89 & 25 & 224 & 4 + wlm & @xmath90 & 31 & 65 & 5 + kk98 251 & @xmath91 & 12 & 98 & 3 + gr 8 & @xmath92 & 5 & 14 & 6 + cam b & @xmath93 & 3.5 & 6.6 & 7 + ddo 210 & @xmath94 & 0.9 & 3.6 & 8 + for the stellar and gas mass , i take the value given by the original authors . @xmath30 has often been estimated using the models of bell & de jong ( 2001 ) , so these correspond roughly to @xmath95 estimates . rather than an uncertainty , i consider the full range of possible stellar masses , from zero to maximum disk . these are the vertical lines in fig . the extrapolation of the btf fit to the data in table 1 does an excellent job of predicting the data for these lower mass galaxies . the objects in table 5 follow the slope @xmath4 down to unprecedented low velocity . the btf remains valid over five decades in mass . 6 also illustrates why the slope has been difficult to constrain . the lower limit of other studies ( @xmath96 , @xmath97 : e.g. , bell & de jong 2001 ; courteau et al . 2003 ) is shown in the left hand panel . the data considered there extend over only a small fraction of the range studied here ( down to @xmath98 with the extreme dwarfs in table 5 ) . this lack of dynamic range probably dominates all other factors ( such as the mass determination method or the velocity estimator used ) in constraining the slope . indeed , if we were to truncate the data in table 1 at the same level , we would fail to perceive the break - point in the stellar mass tully - fisher relation . such a sample would be dominated by star - dominated galaxies , and fail to provide the constraint on @xmath1 which follows when gas - dominated objects are included . the steep slope of the btf should come as no surprise , as it is completely consistent with the results of mcgaugh et al . that study made use many low mass galaxies , 19 of which have @xmath99 . those objects are completely independent of the galaxies discussed here . the new , more accurate data in table 5 simply return the same result with less scatter . other workers investigating low mass galaxies have also inferred the need for a steep slope ( e.g. , gurovich et al . 2004 ; pizagno et al . 2004 ) . formally , a slope as shallow as @xmath81 deviates from the optimal btf by @xmath100 . this can be made less by changing @xmath1 , but only at the price of degrading the correlation and the the many consistency checks on @xmath1 . in order to recover a slope as shallow as @xmath81 , one requires @xmath101 or @xmath102 ( table 2 ) . such absurdly sub - maximal disks would fall considerably short of the mass which is directly observed in stars locally . consideration of the extreme dwarfs renders it even more difficult to reconcile a shallow slope with the data . while it is possible , at least in principle , to move massive galaxies down in mass by reducing their mass - to - light ratios in order to accomodate a shallow slope , it is not possible to move the extreme dwarfs very far up . even taking maximum disk in those cases makes little difference to the slope , and causes the curious situation that the imf in these low mass galaxies must be systematically heavier than that in giant galaxies . it is thus very difficult to reconcile a shallow ( @xmath81 ) slope for the btf with the data . one application of the result here is to quantify the degree to which galaxy disks are maximal . there is considerable debate as to whether high surface brightness disks are maximal ( e.g. , sellwood 1999 ; courteau & rix 1999 ) . there would seem little doubt that low surface brightness disks are dark matter dominated ( de blok & mcgaugh 1997 , 2001 ) , but an argument for maximal disks can be made even in these objects ( fuchs 2003 ) . it is therefor of considerable interest to investigate how maximal disks are , and how disk maximality varies with disk properties . for the mdacc mass - to - light ratios favored here , the fraction of maximum disk in each case is @xmath103 this is plotted against disk mass and surface density in fig . there is only a weak correlation of @xmath104 with disk mass ( @xmath105 ) which depends heavily on rather few points at low mass ( cf . persic & salucci 1988 ) . dynamical arguments stemming from the adherence of low surface brightness galaxies to the tully - fisher relation ( zwaan et al . 1995 ; sprayberry et al . 1995 ; hoffman et al . 1996 ) suggest that disk maximality @xmath104 should correlate with surface brightness ( tully & verheijen 1997 ; mcgaugh & de blok 1998a ; zavala et al . 2003 ) . we can improve on this by using the mass - to - light ratios @xmath35 to convert the observed central surface brightness into the central surface mass density of stars : @xmath106 as anticipated , there is a good correlation between @xmath104 and @xmath107 ( @xmath108 ) . a fit to the data in fig . 7 gives @xmath109 in terms of the more directly observable central surface brightness , this translates to @xmath110 . there is considerably greater scatter about this latter relation . irrespective of how we frame the relation , or what mass - to - light ratio prescription we prefer , it seems inevitable that the disk contribution must decline systematically as surface density declines . low surface brightness disks are inevitably dark matter dominated . in contrast , high surface density disks contribute a non - negligible fraction of the total mass at small radii for plausible @xmath1 . remarkably , this leaves no residual signature in the tully - fisher relation ( mcgaugh & de blok 1998a ; courteau & rix 1999 ) in spite of the generally modest radius at which rotation curves achieve @xmath15 . statistics of these data , divided into quartiles by @xmath107 , are given in table 6 . the typical @xmath111 in the highest surface density quartile . @xmath104 can not exceed unity , and is projected to saturate at @xmath112 . this is comparable to the highest surface brightness disks that exist ( marshall 2004 ) . in the lowest surface density quartile , the typical fraction of maximum disk drops to @xmath113 . this confirms and quantifies the well - known result that low surface brightness disks are sub - maximal ( de blok & mcgaugh 1997 ) . there is no empirical indication that we have reached a lower limit in @xmath104 . disks lower in surface brightness than the most extreme considered here do exist , though they have yet to be observed with sufficient accuracy to be included here . ccccc 1 & 15 & 23.31 & 21 & 0.25 + 2 & 15 & 22.31 & 99 & 0.48 + 3 & 15 & 21.52 & 295 & 0.74 + 4 & 15 & 20.41 & 964 & 0.78 + the meaning of @xmath104 for high surface brightness galaxies is subject to the caveats discussed in 3.1 . in particular , the effective definition of maximum disk typically accounts for 84% rather than 100% of the velocity at the peak of the disk contribution ( sackett 1997 ) . if the disks in the highest quartile have 78% of this mass , then they contribute 74% of the velocity at 2.2 scale lengths ( @xmath43 ) . this is not very different from the sub - maximal contribution of 63% advocated by bottema ( 1993 ) and is certainly within the galaxy - to - galaxy scatter . kregel , van der kruit & freeman ( 2005 ) find a slightly lower mean velocity contribution , but their sample is dominated by intermediate surface brightness galaxies , so such a result is consistent with the trend apparent in fig . 7 . the results in the literature seem broadly consistent , bearing in mind that a good deal depends on what is really meant by `` maximum disk . '' the most important point here is that the degree of maximality of a disk depends systematically upon its surface density . there is no magic value of @xmath104that is a fixed fraction for all disks ( bottema 1997 ; de blok & mcgaugh 1996 ) .

i give fits of the form . presumably , the prescription that comes closest to the correct value will minimize the scatter in the relation . this relation holds over five decades in mass . there is a systematic dependence of the degree of maximality of disks on surface brightness .

i investigate the baryonic tully - fisher relation for a sample of galaxies with extended 21 cm rotation curves spanning the range . a variety of scalings of the stellar mass - to - light ratio are considered . for each prescription for , i give fits of the form . presumably , the prescription that comes closest to the correct value will minimize the scatter in the relation . the fit with minimum scatter has and . this relation holds over five decades in mass . galaxy color , stellar fraction , and are correlated with each other and with , in the sense that more massive galaxies tend to be more evolved . there is a systematic dependence of the degree of maximality of disks on surface brightness . high surface brightness galaxies typically have of the maximum disk value , while low surface brightness galaxies typically attain of this amount .

astro-ph0506750

c

i have explored the baryonic tully - fisher relation for many choices of stellar mass - to - light ratios using a sample of high quality data spanning a large dynamic range in mass . i provide fits to the btf for each @xmath1 . there is a particular choice , based on the minimization of the scatter in the local mass - discrepancy acceleration relation ( the mdacc : mcgaugh 2004 ) , that also minimizes the scatter in the btf . this optimal btf is @xmath60 with @xmath15 in @xmath16 and the total baryonic mass of a galaxy in @xmath61 . this provides a remarkably precise method of estimating the mass of rotating galaxies by observation of a single global observable , the level at which the rotation curve becomes flat . the form in which the baryonic mass resides , stars or gas , makes no difference to the btf . only the sum matters . this strongly suggests that the btf is a fundamental relation between rotation velocity and baryonic mass . it further implies that there is no other large reservoir of baryons which matter to the sum : the stars and gas observed in spiral galaxies account for essentially all of the baryonic mass therein . the mass - to - light ratios determined for the optimal btf are in exceptionally good agreement with stellar population synthesis models . this consistency , together with the agreement between local and global empirical relations connecting baryonic mass to the observed dynamics , implies that the baryonic mass is well determined . this would appear to solve the long standing problem of the uncertainty in the mass of stellar disks . using these robust stellar mass estimates , i have examined a variety of evolutionary measures . the stellar fraction , mass - to - light ratio , and color all correlate with each other as one would expect . little evolved galaxies with low @xmath68 tend to have blue colors and low @xmath1 ; more evolved galaxies have higher stellar fractions , redder colors , and higher mass - to - light ratios . these quantities are also correlated with disk mass and rotation velocity : more massive disks tend to be more evolved . the degree to which disks are maximal varies systematically with stellar surface density . high surface brightness galaxies tend to be more nearly maximal , typically with @xmath114 of the maximum disk value at @xmath115 . low surface brightness galaxies are sub - maximal , with @xmath116 of maximum disk at @xmath117 . there is considerable variation from galaxy to galaxy . in no case is the stellar mass completely negligible at small radii , a fact that is important to mass models and constraints on the inner slope of the halo mass distribution ( core or cusp ) . the work of ssm is supported in part by nsf grant ast0206078 and nasa grant nag513108 . ssm is grateful for conversations on this subject with many people , especially greg bothun , bob sanders , brent tully , and rob swaters . ssm thanks the astronomy department of case western reserve university for its hospitality during a sabbatical visit when much of this work was done . barnes , e.i . , sellwood , j.a . , & kosowsky , a. 2004 , , 128 , 2724 begeman , k. g. , broeils , a. h. , & sanders , r. h. 1991 , mnras , 249 , 523 begum , a. , & chengalur , j.n . 2003 , , 409 , 879 begum , a. , & chengalur , j.n . 2004a , , 424 , 509 begum , a. , & chengalur , j.n . 2004b , , 413 , 525 begum , a. , chengalur , j.n . , & hopp , u. 2003 , new astronomy , 8 , 267 begum , a. , chengalur , j.n . , & karachentsev , i.d . 2005 , , 433 , l1 bell , e. f. & de jong , r. s. 2001 , , 550 , 212 bell , e. f. , mcintosh , d. h. , katz , n. , & weinberg , m. d. 2003 , , 149 , 289 bothun , g.d . , aaronson , m. , schommer , b. , mould , j. , huchra , j. ; sullivan , w.t . , iii 1985 , , 57 , 423 bottema , r. 1993 , , 275 , 16 bottema , r. 1997 , , 328 , 517 broeils , a. h. 1992 , ph.d . thesis , university of groningen courteau , s. , macarthur , l.a . , dekel , a. , van den bosch , f. , mcintosh , d.h . , & dale , d. 2003 , astro - ph/0310440 courteau , s. & rix , h .- w . 1999 , , 513 , 561 de blok , w.j.g . , & mcgaugh , s.s . 1996 , , 469 , l89 de blok , w.j.g . , & mcgaugh , s.s . 1997 , , 290 , 533 de blok , w.j.g . , & mcgaugh , s.s . 1998 , , 508 , 132 de blok , w.j.g . , mcgaugh , s.s . , & rubin , v.c . 2001 , , 122 , 2396 eder , j. , & schombert , j. m. 2000 , , 131 , 47 eisenstein , d. j. & loeb , a. 1996 , , 459 , 432 freeman , k.c . 1999 , in the low surface brightness universe , iau col . 171 , asp conference series 170 , 3 fuchs , b. 2003 , , 284 , 719 gurovich , s. , mcgaugh , s.s . , freeman , k.c . , jerjen , h. , staveley - smith , l. , & de blok , w.j.g . 2004 , pasa , 21 , 412 hoffman , g. l. , salpeter , e. e. , farhat , b. , roos , t. , williams , h. , & helou , g. 1996 , , 105 , 269 jackson , d.c . , skillman , e.d . , cannon , j.m . , & cote , s. 2004 , , 128 , 1219 juneau , s. , et al . 2005 , , 619 , l135 karachentsev , i. d. , et al . 2003 , , 398 , 479 kregel , m. , van der kruit , p.c . , & freeman , k.c . 2005 , , in press ( astro - ph/0501503 ) kroupa , p. & weidner , c. 2003 , , 598 , 1076 marshall , j. 2004 , ph.d . thesis , university of maryland matthews , l.d . , van driel , w. , & gallagher , j.s . 1998 , aj , 116 , 1169 mcgaugh , s.s . 2004 , , 609 , 652 mcgaugh , s.s . , & de blok , w.j.g . 1998a , , 499 , 41 mcgaugh , s.s . , & de blok , w.j.g . 1998b , , 499 , 66 mcgaugh , s.s . , rubin , v.c . , & de blok , w.j.g . 2001 , , 122 , 2381 mcgaugh , s. s. , schombert , j. m. , bothun , g. d. , & de blok , w. j. g. 2000 , , 533 , l99 milgrom , m. 1983 , , 270 , 371 milgrom , m. & braun , e. 1988 , apj , 334 , 130 mo , h. j. , & mao , s. 2004 , , 353 , 829 meurer , g. r. , mackie , g. , & carignan , c. 1994 , , 107 , 2021 navarro , j. f. & steinmetz , m. 2000a , , 528 , 607 navarro , j. f. & steinmetz , m. 2000b , , 538 , 477 palunas , p. & williams , t. b. 2000 , , 120 , 2884 persic , m. , & salucci , p. 1988 , , 234 , 131 pfenniger , d. , & revaz , y. 2005 , , in press ( astro - ph/0409621 ) pierce , m. j. , & tully , r. b. 1988 , , 330 , 579 pizagno , j. , blanton , m.r . , weinberg , d.h . , bahcall , n.a . , & brinkmann , j. 2004 , astro - ph/0410672 portinari , l. , sommer - larsen , j. , & tantalo , r. 2004 , , 347 , 691 sackett , p.d . 1997 , , 483,103 sakai , s. , et al . 2000 , , 529 , 698 sancisi , r. 2003 , iau symposium 220 , 192 sanders , r. h. 1996 , , 473 , 117 sanders , r.h . , & mcgaugh , s.s . 2002 , , 40 , 263 sanders , r. h. & verheijen , m. a. w. 1998 , , 503 , 97 schombert , j.m . , mcgaugh , s.s . , & eder , j. 2001 , , 121 , 2420 sellwood , j. a. 1999 , asp conf . ser . 182 : galaxy dynamics - a rutgers symposium , 351 sprayberry , d. , bernstein , g. m. , impey , c. d. , & bothun , g. d. 1995 , , 438 , 72 steinmetz , m. , & navarro , j.f . 1999 , , 513 , 555 swaters , r.a . , madore , b.f . , & trewhella , m. 2000 , , 2000 , , 531 , l107 treu , t. , ellis , r. s. , liao , t. x. , & van dokkum , p. g. 2005 , , 622 , l5 tully , r. b. & fisher , j. r. 1977 , , 54 , 661 tully , r. b. & verheijen , m. a. w. 1997 , , 484 , 145 van albada , t. s. & sancisi , r. 1986 , royal society of london philosophical transactions series a , 320 , 447 van den bosch , f. c. 2000 , , 530 , 177 verheijen , m. a. w. 1997 , ph.d . thesis , university of groningen verheijen , m. a. w. 2001 , , 563 , 694 verheijen , m. a. w. & sancisi , r. 2001 , , 370 , 765 warren , b.e . , jerjen , h. , & koribalski , b.s . 2004 , , 128 , 1152 zavala , j. , avila - reese , v. , hernndez - toledo , h. , & firmani , c. 2003 , , 412 , 633 zwaan , m.a . , van der hulst , j.m . , de blok , w.j.g . , & mcgaugh , s.s . 1995 , , 273 , l35

i investigate the baryonic tully - fisher relation for a sample of galaxies with extended 21 cm rotation curves spanning the range . galaxy color , stellar fraction , and are correlated with each other and with , in the sense that more massive galaxies tend to be more evolved . high surface brightness galaxies typically have of the maximum disk value , while low surface brightness galaxies typically attain of this amount .

i investigate the baryonic tully - fisher relation for a sample of galaxies with extended 21 cm rotation curves spanning the range . a variety of scalings of the stellar mass - to - light ratio are considered . for each prescription for , i give fits of the form . presumably , the prescription that comes closest to the correct value will minimize the scatter in the relation . the fit with minimum scatter has and . this relation holds over five decades in mass . galaxy color , stellar fraction , and are correlated with each other and with , in the sense that more massive galaxies tend to be more evolved . there is a systematic dependence of the degree of maximality of disks on surface brightness . high surface brightness galaxies typically have of the maximum disk value , while low surface brightness galaxies typically attain of this amount .

1512.01955

i

in many geophysical applications , in particular in the petroleum industry and in hydrology , distributed parameter estimation problems are often solved by means of iterative ensemble kalman filters @xcite . the basic methodology is to introduce an artificial dynamical system , to supplement this with observations , and to apply the ensemble kalman filter . the methodology is described in a basic , abstract form , applicable to a general , possibly nonlinear , inverse problem in @xcite . in this basic form of the algorithm regularization is present due to dynamical preservation of a subspace spanned by the ensemble during the iteration . the paper @xcite gives further insight into the development of regularization for these ensemble kalman inversion methods , drawing on links with the levenberg - marquardt scheme @xcite . in this paper our aim is to further the study of filters for the solution of inverse problems , going beyond the ensemble kalman filter to encompass the study of other filters such as 3dvar and the kalman filter itself see @xcite for an overview of these filtering methods . a key issue will be the implementation of regularization with the aim of deriving optimal error estimates . we focus on the linear inverse problem @xmath0 where @xmath1 is a compact operator acting between hilbert spaces @xmath2 and @xmath3 . the exact solution is denoted by @xmath4 and @xmath5 is a noise polluting the observations . we will consider two situations : * data model @xmath6 * where multiple observations are made in the form [ eq : base ] ; and * data model @xmath7 * where a single observation is made . for modelling purposes we will assume that the noise @xmath5 is generated by the gaussian @xmath8 , independently in the case of multiple observations . in each case we create a sequence @xmath9 ; for data model @xmath6 the elements of this sequence are i.i.d . @xmath10 whilst for data model @xmath7 they are @xmath11 , with @xmath12 a single draw from @xmath10 . the case where multiple independent observations are made is not uncommon in applications ( for example in electrical impedance tomography ( eit , @xcite ) and , although we do not pursue it here , our methodology also opens up the possibility of considering multiple instances with correlated observational noise , by means of similar filtering - based techniques . the artificial , partially observed linear dynamical system that underlies our methodology is as follows : @xmath13 in _ deriving _ the filters we apply to this dynamical system , it is assumed that the @xmath14 are i.i.d . from @xmath8 . note , however , that whilst the data sequence @xmath9 we use in data model @xmath6 is of this form , the assumption is not compatible with data model @xmath7 ; thus for data model @xmath7 we have a form of _ model error _ or _ model mis - specification _ @xcite . by studying the application of filtering methods to the solution of the linear inverse problem our aim is to open up the possibility of employing the filtering methodology to ( static ) inverse problems of the form [ eq : base ] , and nonlinear generalizations . we confine our analysis to the linear setting as experience has shown that a deep understanding of this case is helpful both because there are many linear inverse problems which arise in applications , and because knowledge of the linear case guide methodologies for the more general nonlinear problem @xcite . the last few decades have seen a comprehensive development of the theory of linear inverse problems , both classically and statistically see @xcite and the references therein . consider the tikhonov - phillips regularization method @xmath15 this can be reformulated from a probabilistic perspective as the map estimator for bayesian inversion given a gaussian smoothness prior , with mean @xmath16 and cameron - martin space @xmath17 compactly embedded into @xmath2 , and a gaussian noise model as defined above ; this connection is eludicated in @xcite . we note that from the point of view of tikhonov - phillips regularization only the parameter @xmath18 is relevant , but that each of @xmath19 and @xmath20 have separate interpretations in the overarching bayesian picture , the first as a scaling of the prior precision and the second as observational noise variance . in this paper we deepen the connection between the bayesian methodology and classical methods . the recent paper @xcite opens up the prospect for a statistical explanation of iterative regularization methods in the form of @xmath21 with a general kalman gain operator @xmath22 . in this paper , we establish the connection between iterative regularization methods ( c.f . @xcite ) and filter based methods @xcite with respect to an artificial dynamic system . more precisely , for a linear inverse problem , we verify that the iterative tikhonov regularization method @xmath23 is closely related to filtering methods such as 3dvar and the kalman filter when applied to the partially observed linear dynamical system [ eq : dynamic ] . the similarity between both schemes provides a probabilistic interpretation of iterative regularization methods , and allows the possibility of quantifying uncertainty via the variance . on the other hand , we will employ techniques from the convergence analysis arising in regularization theories @xcite to shed light on the convergence of filter based methods , especially when the linear observation operator is ill - posed . the paper is organized as follows . we first introduce filter based methods for the artificial dynamics [ eq : dynamic ] in section [ se_artidyna ] . section [ se_assumptions ] describes some general useful formulae which are relevant to all the filters we study , and lists our main assumptions on the inverse problem of interest . in sections [ se_kalman ] and [ se_3dvar ] respectively , detailed asymptotic analyses are given for the kalman filter method and 3dvar , for both data models . the final section [ se_num ] presents numerical illustrations confirming the theoretical predictions .

ensemble - based filtering methods have recently been used to solve inverse problems by introducing an artificial dynamical system . this opens up the possibility of using a range of other filtering methods , such as 3dvar and kalman based methods , to solve inverse problems , again by introducing an artificial dynamical system . the aim of this paper is to analyze such methods in the context of the ill - posed linear inverse problem . statistical linear inverse problems are studied in the sense that the observational noise is assumed to be derived via realization of a gaussian random variable . we investigate the asymptotic behavior of filter based methods for these inverse problems . rigorous convergence rates are established for 3dvar and for the kalman filters , including minimax rates in some instances . these analyses reveal a close connection between ( iterative ) regularization schemes in deterministic inverse problems and filter based methods in data assimilation . numerical experiments are presented to illustrate the theory .

ill - posed inverse problems are ubiquitous in applications . understanding of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem . in the applied communities ensemble - based filtering methods have recently been used to solve inverse problems by introducing an artificial dynamical system . this opens up the possibility of using a range of other filtering methods , such as 3dvar and kalman based methods , to solve inverse problems , again by introducing an artificial dynamical system . the aim of this paper is to analyze such methods in the context of the ill - posed linear inverse problem . statistical linear inverse problems are studied in the sense that the observational noise is assumed to be derived via realization of a gaussian random variable . we investigate the asymptotic behavior of filter based methods for these inverse problems . rigorous convergence rates are established for 3dvar and for the kalman filters , including minimax rates in some instances . blowup of 3dvar and a variant of its basic form is also presented , and optimality of the kalman filter is discussed . these analyses reveal a close connection between ( iterative ) regularization schemes in deterministic inverse problems and filter based methods in data assimilation . numerical experiments are presented to illustrate the theory .

0809.3178

i

the stellar absorption lines from the near - ir calcium triplet ( cat ) made their debut in the field of active galactic nuclei ( agn ) with the work of terlevich , daz & terlevich ( 1990 , hereinafter tdt ) . at that time , it was thought that the optical spectrum of seyfert 2s contained a featureless continuum ( fc ) from the agn , which , in light of unification scenarios ( antonucci 1993 ) , should be associated with scattered light from the hidden seyfert 1 nucleus ( cid fernandes & terlevich 1995 ) . tdt realized that this idea could not be fully correct , since their data indicated that , unlike for absorption lines in the optical , the strength of the cat in these sources shows no signs of dilution with respect to the values found in normal galaxies . their interpretation of this fact was that what was called a `` non - stellar fc '' was in fact a stellar component associated to young stellar populations . this conclusion was thoroughly confirmed by numerous studies in the past decade ( see cid fernandes 2004 for a review ) . since then , interest in the cat shifted towards its use as a tracer of stellar kinematics , particularly in agn . the location of the cat in a relatively clean spectral region makes it an ideal feature to measure stellar velocity dispersions ( @xmath6 ) , which trace the gravitational potential of the host galaxy s bulge . in an influential work , nelson & whittle ( 1996 ; nw ) used the cat in a comparison between stellar and gaseous kinematics of agn , finding that the typical velocity narrow line region ( nlr ) clouds ( @xmath3 ) correlates with @xmath6 , albeit with significant scatter . more recently , a strong correlation between @xmath6 and black - hole mass ( tremaine 2002 and references therein ) indirectly boosted interest in observations of the cat ( nelson 2000 ; botte 2004 ) . for completely different reasons , recent work on normal galaxies has also raised the interest in the cat . empirical investigations have revealed rather puzzling behavior of the cat in bulges and elliptical galaxies . firstly , detailed population synthesis models tend to over - predict the cat strength ( saglia 2002 ; cenarro 2003 , 2004 ) , particularly for giant ellipticals , though for dwarf ellipticals the match between data and models is satisfactory ( michielsen 2007 ) . secondly , while classic metallicity tracers like the mg@xmath7 index are known to correlate with @xmath6 ( eg , terlevich 1981 ) , tracing the well - known mass - metallicity relation , the strength of the cat appears to be _ anti - correlated _ with @xmath6 ( cenarro 2003 , 2004 ; falcn - barroso 2003 ; michielsen 2003 ) . the interpretation of these results is still not clear , and the situation is likely to be even more complex in systems with varied star formation histories like agn ( cid fernandes 2004 ; wild 2007 ) . one thus sees that , more than 15 years after tdt introduced the cat in agn research , there are still plenty of reasons to keep studying it . with this general motivation , in paper i we have carried out a spectroscopic survey of seyfert galaxies in the region including the cat and the [ siii]@xmath09069 emission line . paper i concentrated in the presentation of the data and the derivation of four main data products : stellar velocity dispersions ( @xmath6 ) , [ siii ] emission line widths ( @xmath8}$ ] , which is representative of the highly ionized component of the gas of the narrow line region in agns ) , [ siii ] equivalent widths ( @xmath9}$ ] ) , and the cat strength ( @xmath1 ) . here we use these data to address the following issues : ( 1 ) examine the contribution of a non - stellar component in the near - ir spectra of seyfert galaxies and test the consistency of @xmath9}$ ] and @xmath1 data with the unified model , ( 2 ) study the sensitivity of @xmath1 to stellar population properties , ( 3 ) investigate the connection between nlr and stellar kinematics and cat strength , and ( 4 ) report results of spatially resolved spectroscopy , not reported in paper i. to study these questions , we complement the data in paper i with values of the equivalent width of the caii k line ( @xmath4 ) obtained from previous studies . as shown by cid fernandes ( 2001 ) , the caii k line is a powerful tracer of stellar populations even in type 2 seyferts . by comparing @xmath1 with @xmath4 we can assess whether the cat is a useful stellar population tracer , and determine whether the combination of cak and cat strengths is explained as due to stars alone or if an fc component is necessary . we also add in literature information on the width ( @xmath10}$ ] ) of the [ oiii]@xmath05007 line , which is useful to test whether our results are somehow affected by the choice of [ siii]@xmath09069 as a tracer of nlr motions . this paper is organized as follows . section [ sec : cat_nonstellarlight ] presents a series of studies related to the cat strength . after showing cat observational properties in [ subsec : cat in sy ] , we compare @xmath1 with @xmath4 in [ subsec : dilution ] and investigate whether the location of the points in the @xmath1 versus @xmath4 diagram is consistent with the existence of an fc at near - ir wavelengths . in [ stellar models ] we use evolutionary synthesis models to track the behavior of both @xmath1 and @xmath4 as a function of age and metallicity , and overlay the models onto the data in the @xmath1 versus @xmath4 diagram . in [ subsec : spatial cat profiles ] we study the spatial behavior of @xmath2 and @xmath1 for about half of our sample . in section [ sec : kinematics ] we analyze stellar and ionized gas kinematics : stellar velocity dispersions and its relation to cat are studied in [ subsec : stellar velocity dispersions ] , while in [ subsec : stellar vs. nlr kinematics ] we discuss the link between stellar and gas kinematics . finally , section [ sec : summary ] summarizes our main results .

we analyze the cat strength ( ) , and kinematical products derived in that study , namely stellar ( ) and ionized gas ( ) velocity dispersions . our main results may be summarized as follows : ( 1 ) seyfert 2s show no sign of dilution in with respect to the values spanned by normal galaxies , even when optical absorption lines such as the caii k band at 3933 are much weaker than in old , bulge - like stellar populations . ( 2 ) the location of seyfert 2s in the- plane is consistent with evolutionary synthesis models . ( 3 ) in seyfert 1s , both}$ ] and tend to be diluted due to the presence of a non - stellar component , in agreement with the unification paradigm . ( 4 ) a comparison of with ( obtained from the _ core _ of the [ siii ] emitting line ) confirms the existence of a correlation between the typical velocities of stars and clouds of the narrow line region .

in a former paper ( garcia - rissmann 2005 ; hereafter paper i ) , we have presented spectra of 64 active , 9 normal and 5 starburst galaxies in the region around the near - ir calcium triplet absorption lines ( cat ) and the [ siii] line . in the present paper we analyze the cat strength ( ) , and kinematical products derived in that study , namely stellar ( ) and ionized gas ( ) velocity dispersions . our main results may be summarized as follows : ( 1 ) seyfert 2s show no sign of dilution in with respect to the values spanned by normal galaxies , even when optical absorption lines such as the caii k band at 3933 are much weaker than in old , bulge - like stellar populations . ( 2 ) the location of seyfert 2s in the- plane is consistent with evolutionary synthesis models . the implication is that the source responsible for the dilution of optical lines in these agn is a young stellar population , rather than an agn featureless continuum , confirming the conclusion of the pioneer study of terlevich , daz & terlevich . ( 3 ) in seyfert 1s , both}$ ] and tend to be diluted due to the presence of a non - stellar component , in agreement with the unification paradigm . ( 4 ) a comparison of with ( obtained from the _ core _ of the [ siii ] emitting line ) confirms the existence of a correlation between the typical velocities of stars and clouds of the narrow line region . the strength and scatter around this correlation are similar to those previously obtained from the [ oiii] line width .

0809.3178

i

in paper i we presented a spectroscopic atlas of 78 galaxies in the region of cat lines , and measured the equivalent widths of cat and [ siii]@xmath09069 lines , and stellar and gaseous velocity dispersions . in this paper we used these data , as other measurements , to investigate the cat strength and the kinematical properties of seyfert nuclei . our conclusions can be summarized as follows : 1 . the equivalent widths of cat and [ siii ] are diluted in seyfert 1s , due to the presence of a non - stellar component , while in seyfert 2s there is no sign of dilution . we show that the nuclear dilution of cat lines in seyfert 1s and the non observed dilution in seyfert 2s holds spatially , i.e. , within approximately the central kpc . at this distance the effects disappears , thus implying that the stellar lines are diluted due the nuclear non - stellar continuum directly seen in seyfert 1s . 2 . the cat strength turns out not to be a good tracer for the mean ages and metallicities of metal rich stellar populations . nonetheless , its combination with cak line yields a useful constraint on the nature of the continuum emission from optical to near - ir wavelengths . we show that the location of seyfert 2s in the cat - cak plane could be explained satisfactorily by stellar population synthesis models , by considering mixtures of an old plus very young stellar populations with a extinction of just two or three magnitudes . the hypothesis of seyfert 2 nuclei composition as a mixing of an old stellar population plus power - law central source can not account for the majority of the data . 4 . there is a correlation between nuclear @xmath6 and @xmath8}$ ] , as well as an anticorrelation between @xmath8}$]/@xmath2 and @xmath2 , both with substantial scatter . this means that care must be exercised when using @xmath8}$ ] as a proxy for @xmath6 . these results are compatible with previous results of nw and gh .

in a former paper ( garcia - rissmann 2005 ; hereafter paper i ) , we have presented spectra of 64 active , 9 normal and 5 starburst galaxies in the region around the near - ir calcium triplet absorption lines ( cat ) and the [ siii] line . in the present paper

in a former paper ( garcia - rissmann 2005 ; hereafter paper i ) , we have presented spectra of 64 active , 9 normal and 5 starburst galaxies in the region around the near - ir calcium triplet absorption lines ( cat ) and the [ siii] line . in the present paper we analyze the cat strength ( ) , and kinematical products derived in that study , namely stellar ( ) and ionized gas ( ) velocity dispersions . our main results may be summarized as follows : ( 1 ) seyfert 2s show no sign of dilution in with respect to the values spanned by normal galaxies , even when optical absorption lines such as the caii k band at 3933 are much weaker than in old , bulge - like stellar populations . ( 2 ) the location of seyfert 2s in the- plane is consistent with evolutionary synthesis models . the implication is that the source responsible for the dilution of optical lines in these agn is a young stellar population , rather than an agn featureless continuum , confirming the conclusion of the pioneer study of terlevich , daz & terlevich . ( 3 ) in seyfert 1s , both}$ ] and tend to be diluted due to the presence of a non - stellar component , in agreement with the unification paradigm . ( 4 ) a comparison of with ( obtained from the _ core _ of the [ siii ] emitting line ) confirms the existence of a correlation between the typical velocities of stars and clouds of the narrow line region . the strength and scatter around this correlation are similar to those previously obtained from the [ oiii] line width .

astro-ph0209099

i

the extreme properties of bl lac objects are explained in terms of relativistic beaming of the emission from a jet oriented close to the line of sight . this model implies the existence of a substantial ` parent population ' of sources whose jets are less favourably aligned , and it is widely accepted that this is the population of low - power radio galaxies ( browne 1983 ; urry & padovani 1995 ) . properties which are isotropic and unaffected by beaming should be similar in bl lac objects and low - power radio galaxies . this is broadly supported by observations of extended radio emission ( e.g. , antonucci & ulvestad 1985 , kollgaard et al . 1992 , perlman & stocke 1993 , 1994 ) , host galaxies ( e.g. , ulrich 1989 , abraham , mchardy & crawford 1991 ; wurtz , stocke & yee 1996 ; falomo 1996 ) and cluster environments ( pesce , falomo & treves 1995 ; smith , odea & baum 1995 ; wurtz , stocke & ellingson 1997 ) . in a series of papers ( padovani & urry 1990 ; padovani & urry 1991 ; urry , padovani & stickel 1991 ) , urry and co - workers made this model quantitative by predicting the luminosity function of bl lac objects based on that of radio galaxies . they used the analysis of urry & schafer ( 1984 ) and urry & padovani ( 1991 ) to calculate the expected luminosity function of a population of beamed objects given a parent ( unbeamed ) luminosity function . with the data on radio - galaxy and bl lac populations then available they were able to show reasonable agreement between the predictions of the model and the observed luminosity functions . they found that the luminosity function of radio - selected bl lac objects from the 1-jy sample ( stickel et al.1991 ) was consistent with that of radio galaxies from the 2-jy sample ( wall & peacock 1985 ) if the radio - emitting plasma in the cores had a bulk lorentz factor @xmath2 . the x - ray luminosity function and number counts of x - ray selected bl lac objects were consistent with the luminosity function of fri radio galaxies observed with _ einstein _ by fabbiano et al . ( 1984 ) if the x - ray emitting plasma has a somewhat lower bulk lorentz factor , @xmath3 . the issue of the relationship between radio galaxies and x - ray and radio - selected bl lac objects is only partially resolved by this work . the best - studied sample of x - ray selected bl lacs is the emss sample ( wolter et al . 1991 , rector et al . 2000 ) and the best radio - selected sample is the 1-jy sample ( stickel et al . 1991 , rector & stocke 2001 ) . when these samples are compared , a number of differences emerge . some perhaps as many as half of the 1-jy objects have radio structures , luminosities and emission - line properties similar to those of frii radio galaxies ( antonucci & ulvestad 1984 , kollgaard et al.1992 , rector & stocke 2001 ) while the emss bl lacs are all fri - like ( perlman & stocke 1993 ) . the luminosity functions of the two samples are also different ; the radio - selected objects show evidence for positive evolution ( i.e. sources were more numerous or more powerful at higher redshift ) while x - ray - selected sources appear to be _ negatively _ evolving . urry et al . were forced by the data then available to use an x - ray - selected sample of bl lacs for their comparison with the x - ray luminosity function of radio galaxies , and a radio - selected sample when considering the radio luminosity function . they were thus unable to say anything about the relation between radio galaxies and the two bl lac populations . radio - selected bl lacs are often considered to be more extreme than x - ray selected objects ; they have more prominent radio cores ( perlman & stocke 1993 , laurent - muehleisen et al . 1993 , rector & stocke 2001 ) , higher optical polarization with less stable position angle ( jannuzi , smith & elston 1994 ) and a lower optical starlight fraction ( stocke et al . 1985 ) . on the other hand , their environments and host galaxies are similar to x - ray selected sources ( wurtz , stocke & yee 1996 , wurtz et al . this has led to suggestions that radio - selected objects are more strongly affected by doppler boosting than x - ray selected objects , and so are being observed at smaller angles to the line of sight . since radio - selected and x - ray selected objects have similar x - ray luminosities , this requires that the x - ray - emitting regions be less strongly beamed , or even isotropic ( maraschi et al . 1986 ; celotti et al . 1993 ) ; the idea of weaker beaming is consistent with the difference in the doppler beaming factors found by urry et al . this in turn implies that x - ray - selected bl lacs should be the more numerous population , since they can be seen at larger angles to the line of sight , which celotti et al . ( 1993 ) argue is consistent with the x - ray luminosity functions of the two populations . models of this kind can either rely on differences in velocity between x - ray and radio - emitting regions ( e.g. , ghisellini & maraschi 1989 ) or differences in opening angle of the jet ( celotti et al . 1993 ) . however , these models do not account for the differences in evolutionary properties between the two samples . in section [ beaming ] of this paper we shall discuss whether they are consistent with observations of radio galaxies and with the x - ray and radio luminosity functions of the two classes . a description of bl lac objects in terms of the selection waveband does not necessarily reflect the underlying physics . an alternative approach is to refer to high - energy peaked bl lacs ( hbl ) and low - energy peaked bl lacs ( lbl ) ( e.g. , giommi & padovani 1994 , padovani & giommi 1995 ) , distinguishing between the two classes by their radio / x - ray flux ratios ; a typical dividing line is that hbl have @xmath4 , or , equivalently , @xmath5 , where @xmath6 is defined here and throughout the paper in the sense @xmath7 and @xmath8 denotes the radio - to - x - ray two - point spectral index . by selecting bright sources at one or the other waveband we may simply be picking up objects with extreme radio / x - ray flux ratios , which suggests various possible schemes for unifying the two populations ( e.g. , giommi & padovani 1994 , fossati et al . 1997 ) and is consistent with the discovery of ` intermediate ' bl lacs in deeper surveys ( laurent - muehleisen et al . 1999 ) . from multi - wavelength observations it has been found that the spectral energy distributions ( seds ) of bl lacs can be represented by a low - frequency peak ( assumed to be synchrotron radiation ) and a high - frequency peak ( perhaps inverse - compton radiation ) . there is evidence that the positions of these peaks shift to higher frequencies at lower bolometric luminosities ( sambruna , maraschi & urry 1996 , fossati et al . however , giommi , menna & padovani ( 1999 ) do not find the increase in the numbers of hbl at fainter radio fluxes that is expected in such a model . to try to resolve some of the outstanding issues in bl lac unification it is productive to learn more about the presumed parent population of many or all of the bl lac objects , namely the low - power radio galaxies . work to date has been hampered by the lack of a well - defined , low - frequency - selected sample of radio galaxies with well - known radio and x - ray properties . in a previous paper ( canosa et al . 1999 ) we presented results for the 40 members ( @xmath9 per cent ) of the b2 bright sample of radio galaxies which had been observed in pointed _ rosat _ observations . the high spatial resolution of _ rosat _ allowed us to separate the nuclear emission from extended emission due to the hot - gas environment of the radio source . in this paper we use these data to derive a new x - ray luminosity function for the nuclei of b2 radio sources , largely free from contamination from thermal emission from the sources hot - gas environments . we use numerical techniques to extend earlier work , first asking how well a simple beaming model can be used to link the x - ray and radio luminosity functions of radio galaxies , and then investigating the expected relationship between radio galaxies and bl lac objects when selection bias is taken into account . throughout the paper we use a cosmology in which @xmath10 and @xmath11 .

in an earlier paper we presented nuclear x - ray flux densities , measured with _ rosat _ , for the b2 bright sample of nearby low - luminosity radio galaxies . in this paper galaxies : active x - rays : galaxies bl lacertae objects : general galaxies : jets

in an earlier paper we presented nuclear x - ray flux densities , measured with _ rosat _ , for the b2 bright sample of nearby low - luminosity radio galaxies . in this paper we construct a nuclear x - ray luminosity function for the b2 radio galaxies , and discuss the consequences of our results for models in which such radio galaxies are the parent population of bl lac objects . based on our observations of the b2 sample , we use monte carlo techniques to simulate samples of beamed radio galaxies , and use the selection criteria of existing samples of bl lac objects to compare our simulated results to what is observed . we find that previous analytical results are not applicable since the bl lac samples are selected on beamed flux density . a simple model in which bl lacs are the moderately beamed ( ) counterparts of radio galaxies , with some random dispersion ( decades ) in the intrinsic radio - x - ray relationship , can reproduce many of the features of the radio - selected and x - ray - selected bl lac samples , including their radio and x - ray luminosity functions and the distributions of their radio - to - x - ray spectral indices . in contrast , models in which the x - ray and radio emission have systematically different beaming parameters can not reproduce important features of the radio - galaxy and bl lac populations , and recently proposed models in which the radio - to - x - ray spectral index is a function of source luminosity can not in themselves account for the differences in the slopes of the radio and x - ray - selected bl lac luminosity functions . the redshift distribution and number counts of the x - ray - selected emss sample are well reproduced by our best models , supporting a picture in which these objects are beamed fri radio galaxies with intrinsic luminosities similar to those of the b2 sample . however , we can not match the redshift distribution of the radio - selected 1-jy sample , and it is likely that a population of frii radio galaxies is responsible for the high - redshift objects in this sample , in agreement with previously reported results on the sample s radio and optical - emission - line properties . galaxies : active x - rays : galaxies bl lacertae objects : general galaxies : jets

astro-ph0209099

i

in this paper we have been trying to determine to what extent and under what assumptions b2 radio galaxies ( or , more accurately , the radio galaxy population represented by the b2 radio galaxies ) can be the parent population of two well - studied samples of bl lac objects ( the emss and 1-jy samples ) . following earlier work , we have characterized the properties of the populations using their luminosity functions : luminosity functions for the b2 and bl lac samples were constructed in sections [ b2lum ] and [ bllum ] . in section [ usmodl ] we discussed the analytical results of urry & schafer ( 1984 ) ; we argued that their models can not properly be applied to luminosity functions of samples with different selection criteria . instead , in sections [ mc ] and [ sim ] , we used monte carlo simulations to set up a parent population of beamed radio galaxies with b2-like properties and drew objects from them with selection criteria which as closely as possible matched those actually used in generating the emss and 1-jy samples . by adjusting the unknown parameters of the simulation ( section [ matching ] ) we were able to show that our simulated observations of a beamed population of radio galaxies matched to the b2 sample were able to reproduce reasonably well the observed numbers of bl lac objects and the slopes of the radio- and x - ray - selected bl lac luminosity functions , if low values ( @xmath197 ) of the beaming lorentz factor @xmath42 are adopted . in section [ dispersion ] we found that the introduction of a moderate dispersion in the rest - frame ratio of core x - ray to core radio luminosity ( for which there is some direct evidence in the observations of the b2 radio galaxies ) can help to explain the observed differences in the luminosity functions and radio - to - x - ray spectral indices of radio - selected and x - ray - selected bl lacs . this approach gives better results than other proposed ways of generating the differences between bl lac populations ( sections [ asymm ] [ ldep ] ) . these results therefore support a model in which the two apparently different bl lac populations are simply extreme objects drawn from a single parent population ( cf . laurent - muehleisen et al.1999 ) , although we have not attempted to reproduce all of the observed differences between radio - selected and x - ray - selected bl lacs , such as the apparent differences in cosmological evolution ( section [ intro ] ) . the beaming lorentz factors used here are much smaller than those inferred from superluminal motion or @xmath42-ray transparency in some bl lac objects . these typically require @xmath198 , which would grossly overpredict the number of bl lac objects that should be observed above the flux limit ( cf . table [ numbers ] ) . chiaberge et al . ( 2000 ) have previously pointed out that the nuclear luminosities of fri radio galaxies are a factor 1010@xmath199 too bright to be consistent with the ` de - beaming ' of bl lacs using these high lorentz factors . the solution they adopt , velocity structure in the nuclear jet , seems plausible in view of what we know about the existence of velocity - structures in the _ kiloparsec_-scale jets ( e.g. , laing 1996 ) . velocity structure in the jets should not significantly affect our general conclusions here . if jets have velocity structure , our values of @xmath42 parametrize the relationship between the observed luminosity and the angle to the line of sight , rather than describing real physical bulk velocities . however , the details of this parameterization make a difference to the predicted numbers of bl lac objects and the range in their luminosities . although attempting to determine a typical jet emissivity / velocity profile is beyond the scope of this paper , it is certainly the case that luminosity functions can be used to help to constrain it . the simulated observations fail to reproduce the real data in two important ways . firstly , although the simulated emss sample is a good match in redshift distribution to the observed objects ( fig.[redshifts ] , the simulated 1-jy sample contains far too few high - redshift objects . as discussed in section [ intro ] , the emss objects seem all to be fri - like in their radio structure and luminosity , while it is known that some 1-jy objects are frii - like ; since friis have higher luminosities than the parent population we use , it is not surprising that some of the 1-jy sample appear at higher redshifts . our models predict that essentially all the 1-jy objects whose parent population are fris should have redshifts less than @xmath200 ( fig . [ redshifts ] ) , which agrees well with the observations of rector & stocke ( 2001 ) . the fact that some of the 1-jy objects may have a different parent population may also help to explain the anomalously steep 1-jy x - ray luminosity function . secondly , the simulations predict a considerably larger number of bl lac objects than is observed ( by factors @xmath201 ) for @xmath202 or if a significant dispersion in intrinsic @xmath8 is introduced ; even the models which best reproduce other features of the population , such as the differences between the slopes of the x - ray and radio luminosity functions , overpredict the numbers of 1-jy bl lacs by a factor @xmath35 . the mismatch in numbers becomes even greater if some of the observed high - redshift 1-jy objects are not drawn from an fri parent population , as discussed above . we can attribute at least some of this effect to the optical selection criteria applied when defining bl lac samples . as pointed out by march et al . ( 1996 ) , a definition in terms of the strength of the 4000- break measures the strength of the optical non - thermal emission in terms of the starlight in the host galaxy , which may have very little to do with the agn , while a condition on the equivalent width of the strongest emission lines has little physical justification ( and may exclude objects which are in all other ways bl lac objects ; cf . vermeulen et al . 1995 ) . so some of the predicted objects may be present in the surveys , identified as something other than bl lacs . however , a search in the emss survey for objects intermediate between fris and traditional emss bl lacs ( rector et al . 1999 ) found relatively few candidates , and only a handful of emss sources are directly identified with radio galaxies . it remains possible that some of our simulated sources are identified as groups or clusters in the emss survey . if , as new _ chandra _ results ( section [ chandra - caveat ] ) suggest , we are overestimating the radio galaxies nuclear x - ray fluxes ( section [ chandra - caveat ] ) then we will also have overestimated the intrinsic x - ray core prominence ; correcting for this would result in a ( probably small ) reduction in the predicted total number of emss sources . in the 1-jy sample , there are additional optical magnitude and radio spectral selection criteria which are not modelled in our simulations , and so there is more scope for ` hiding ' the excess sources . on the other hand , we are extrapolating our b2 luminosity function to high redshifts to generate bl lac objects without including the effects of cosmological evolution of the fri population , now reasonably well - established ( e.g. , waddington et al . 2001 ) . because there is little evidence for evolution below @xmath203 , where most of our bl lac candidates are generated ( fig . [ redshifts ] ) , this does not have a strong effect on our models , but there may be up to an order of magnitude increase in the numbers of the most luminous sources at @xmath204 . taking this into account would lead our models to produce @xmath205 additional high - redshift 1-jy objects . without a detailed model for source evolution , we can not make this more quantitative . combining these factors with the large statistical uncertainties on the predicted and actual numbers of objects , we regard the degree of agreement between the simulations and observations as encouraging . it supports a model in which fri radio galaxies in the luminosity range of the b2 bright sample are the parent population of all the emss x - ray - selected bl lac objects , and of @xmath206 per cent of the radio - selected 1-jy objects . a higher - luminosity population , probably beamed friis , must be responsible for the remaining , higher - redshift , 1-jy objects .

we construct a nuclear x - ray luminosity function for the b2 radio galaxies , and discuss the consequences of our results for models in which such radio galaxies are the parent population of bl lac objects . based on our observations of the b2 sample , we use monte carlo techniques to simulate samples of beamed radio galaxies , and use the selection criteria of existing samples of bl lac objects to compare our simulated results to what is observed . a simple model in which bl lacs are the moderately beamed ( ) counterparts of radio galaxies , with some random dispersion ( decades ) in the intrinsic radio - x - ray relationship , can reproduce many of the features of the radio - selected and x - ray - selected bl lac samples , including their radio and x - ray luminosity functions and the distributions of their radio - to - x - ray spectral indices . in contrast , models in which the x - ray and radio emission have systematically different beaming parameters can not reproduce important features of the radio - galaxy and bl lac populations , and recently proposed models in which the radio - to - x - ray spectral index is a function of source luminosity can not in themselves account for the differences in the slopes of the radio and x - ray - selected bl lac luminosity functions . the redshift distribution and number counts of the x - ray - selected emss sample are well reproduced by our best models , supporting a picture in which these objects are beamed fri radio galaxies with intrinsic luminosities similar to those of the b2 sample . however , we can not match the redshift distribution of the radio - selected 1-jy sample , and it is likely that a population of frii radio galaxies is responsible for the high - redshift objects in this sample , in agreement with previously reported results on the sample s radio and optical - emission - line properties .

in an earlier paper we presented nuclear x - ray flux densities , measured with _ rosat _ , for the b2 bright sample of nearby low - luminosity radio galaxies . in this paper we construct a nuclear x - ray luminosity function for the b2 radio galaxies , and discuss the consequences of our results for models in which such radio galaxies are the parent population of bl lac objects . based on our observations of the b2 sample , we use monte carlo techniques to simulate samples of beamed radio galaxies , and use the selection criteria of existing samples of bl lac objects to compare our simulated results to what is observed . we find that previous analytical results are not applicable since the bl lac samples are selected on beamed flux density . a simple model in which bl lacs are the moderately beamed ( ) counterparts of radio galaxies , with some random dispersion ( decades ) in the intrinsic radio - x - ray relationship , can reproduce many of the features of the radio - selected and x - ray - selected bl lac samples , including their radio and x - ray luminosity functions and the distributions of their radio - to - x - ray spectral indices . in contrast , models in which the x - ray and radio emission have systematically different beaming parameters can not reproduce important features of the radio - galaxy and bl lac populations , and recently proposed models in which the radio - to - x - ray spectral index is a function of source luminosity can not in themselves account for the differences in the slopes of the radio and x - ray - selected bl lac luminosity functions . the redshift distribution and number counts of the x - ray - selected emss sample are well reproduced by our best models , supporting a picture in which these objects are beamed fri radio galaxies with intrinsic luminosities similar to those of the b2 sample . however , we can not match the redshift distribution of the radio - selected 1-jy sample , and it is likely that a population of frii radio galaxies is responsible for the high - redshift objects in this sample , in agreement with previously reported results on the sample s radio and optical - emission - line properties . galaxies : active x - rays : galaxies bl lacertae objects : general galaxies : jets

1309.7073

i

many biological systems involve mobile or fixed charges , the electrostatic response of which is key to our understanding of the physical behavior of such systems . nucleic acids and many proteins are charged in physiologically relevant conditions . the interactions that arise from the presence of these charges are crucial in the determination of the structure and function of these polymers @xcite . biological processes such as signaling in cells involve the creation of electrical potential differences and transport of ions across the cellular membrane @xcite . on the other hand , in the design and stabilization of many different synthetic structures , the electrostatic forces play a major role . examples include self - assembled colloidal dispersions @xcite , polynucleotide adsorption @xcite , dna precipitation in multivalent salts @xcite , overcharged surfaces @xcite , patterned surfaces @xcite , spontaneous adsorption of ions at liquid - liquid interfaces@xcite , faceted thin shells @xcite , viral assembly @xcite , and various dynamical processes including dna gel electrophoresis @xcite and related polyelectrolyte separation process @xcite . theoretical investigations of these interesting materials and biological systems must therefore accurately incorporate electrostatic interactions . under the conditions of high ionic concentration or in the presence of multivalent ions , when the finite size of ions and the inter - ionic correlations become significant , mean field theories are generally found inadequate to capture important electrostatic effects @xcite . for arbitrarily curved geometries or where the dielectric response of the medium is not homogeneous , the associated electrostatics problem gets too complicated even for the more sophisticated analytical treatments @xcite , and the use of numerical techniques becomes necessary . however , an accurate computer simulation involving electrostatic interactions presents its own challenges . the first challenge stems from the long range of the coulomb force which implies that every charge interacts with every other charge . thus , a system of @xmath0 charges requires an expensive @xmath1 force ( or energy ) calculation at every simulation step . attempts to ameliorate this scaling behavior have resulted in the development of several methods : e.g , ewald summation , particle - mesh methods , fast multipole methods @xcite , and local electrostatics algorithms @xcite . the other main challenge arises due to the presence of dielectric heterogeneities in the medium , and this constitutes the main focus of the present paper . free charges polarize their surrounding dielectric medium and the resulting net polarization and electric fields can have complex behavior . modeling of systems with electrostatic interactions should , ideally , incorporate this dielectric response of the medium . an explicit inclusion of the medium components ( molecules of the solvent , for example ) as a part of the model for the real system renders a prohibitively large number of degrees of freedom to simulate , such that even with the most efficient methods @xcite direct simulation becomes too computationally expensive . in many cases , the introduction of a spatially varying dielectric constant in the model is sufficient to capture the effects of polarizability and describe the dielectric response . in the simplest case of a uniform dielectric response , a single dielectric constant can describe a coarse - grained medium , and simulations can proceed as they would in free space , albeit with a scaled coulomb s law . however , most real situations involve regions with different dielectric response , as is the case for proteins within an aqueous cellular medium or for emulsions where oil and water are partitioned @xcite . in the presence of this varying dielectric response , the simplest form of coulomb s law breaks down and one has to accurately solve the poisson equation , at _ each _ simulation step , to obtain the necessary force ( energy ) information for the propagation of ionic coordinates . this adversely affects the stability and efficiency of the resulting numerical procedure . because of these computational challenges , the problem of treating dielectric heterogeneities in charge simulations continues to be a subject of intense research @xcite . a few previous attempts towards the solution of the problem of inhomogeneous dielectric response have involved a reformulation of electrostatics as a variational problem @xcite . here , the solution to the poisson equation is obtained not as a solution of a differential equation , but as the extremum of a suitably constructed functional @xcite . an important advantage of adopting a variational approach is that it offers the possibility of bypassing the effort to explicitly optimize the functional at each step by framing the problem in such a way that the very process of updating the simulation guarantees the optimization of the functional . in other words , since the optimization of the functional is equivalent to the solution of the poisson equation , we are offered the possibility of solving the poisson equation _ on - the - fly _ in tandem with the generation of the new charge configuration . however , this possibility arises only when the variational approach is based on an energy functional : a functional which _ minimizes _ to the _ true _ electrostatic energy . we note that in the literature , there is an abundance of functionals that are _ not _ energy functionals @xcite and therefore the numerical schemes associated with these functionals do not employ the ideas of dynamical optimization . in addition to the need for a true energy functional for an efficient numerical implementation of the variational procedure , it is also crucial to produce a functional with the appropriate function variable(s ) . in many cases a particular electrostatic variable offers distinct advantage over others . for example , a coarse - grained model often employed to study phenomena in both biological and synthetic settings is that of ions present in piecewise - uniform dielectrics separated by sharp interfaces ( see fig . [ fig1 ] ) . in this case , it is advantageous to choose the polarization charge density as the variable to solve for , rather than the electrostatic potential or the polarization vector . this is because when the dielectric response of the medium is piecewise uniform , the unknown polarization charge density resides only on the interface , and thus we are presented with the possibility to reduce the full three - dimensional electrostatic problem to a two - dimensional one . a uniform dielectric medium characterized by permittivity @xmath2 separated from another region of permittivity @xmath3 by a boundary that is treated as a thin interface . positive ( red ) and negative ( green ) ions are present in either media . coarse - grained models of this kind are often employed to study systems such as charged bio - macromolecules in aqueous solution or charged colloidal suspensions . ] in the light of the above discussion , it is clear that an energy functional of the polarization charge density would provide many advantages with regards to the numerical implementation of the variational method formulated to study problems involving dielectric heterogeneities . in the literature , one finds many functionals along with their associated numerical minimization procedures . though a functional of polarization density for a general system has been developed in ref . , it is not an energy functional . similarly , the functionals derived in refs . are energy functionals , but the basic field variables employed are vector fields such as the polarization vector @xcite or the electric field @xcite , not the polarization charge density . attard @xcite has provided an energy functional of the surface polarization charge density , but this functional is derived for a specific system that involves all free charges to be constrained in one uniform dielectric medium . in a recent paper ( ref . ) , we introduced a variational formulation of electrostatics that produced an energy functional of the polarization charge density . this functional reads : @xmath4&=\frac{1}{2}\iint \rho_{\mathbf{r}}g_{\mathbf{r},\mathbf{r ' } } \left(\rho_{\mathbf{r'}}+\omega_{\mathbf{r'}}[\omega]\right ) d^{3}r'd^{3}r\\ & - \frac{1}{2}\iint \omega_{\mathbf{r}}[\omega ] g_{\mathbf{r},\mathbf{r ' } } \left(\omega_{\mathbf{r ' } } - \omega_{\mathbf{r'}}[\omega ] \right ) d^{3}r'd^{3}r , \end{split}\ ] ] where @xmath5 is the polarization charge density and @xmath6 $ ] is both a functional of @xmath7 and a function of @xmath8 , and is defined as @xmath9 = \nabla\cdot\left ( \chi_{\mathbf{r}}\nabla\int g_{\mathbf{r},\mathbf{r ' } } \left ( \rho_{\mathbf{r ' } } + \omega_{\mathbf{r ' } } \right ) d^{3}r'\right).\ ] ] in the above equations @xmath10 is the susceptibility of the medium , @xmath11 is the free charge density , and @xmath12 is the green s function in free space . in our derivation we assumed that the medium polarization obeys linear response and also assumed the existence of dirichlet boundary conditions . both these assumptions are standard from the point of view of constructing electrostatic free energy functionals . @xmath13 $ ] is applicable to any configuration of free charges and works for arbitrary spatial variation in dielectric response . we also provided the expression of this functional for the important case of point charges present in piecewise - uniform dielectrics and developed a car - parrinello molecular dynamics scheme to study the equilibrium properties of such systems . as an application , we computed the density profiles for monovalent salt ions near a spherical emulsion droplet separating two liquids of different dielectric constants . in this paper , we present a detailed derivation of @xmath13 $ ] , showing steps that were omitted in ref . for the lack of space , and discuss the important features of our variational formulation that enable the production of an energy functional . also , we explore in detail , with several examples , the particular case of piecewise - uniform dielectric response . in addition , we provide the proofs that show that @xmath13 $ ] is an energy functional . in the supplementary information of ref . we proved the minimum property of this functional at its extremum . here we show that upon extremizing this functional one finds the usual electrostatic relation for the polarization charge density and the extremum value of the functional coincides with the true electrostatic energy of the system . for the sake of completeness we also include the proof of the functional becoming a minimum at its extremum . the paper is organized as follows . in sec . [ sec : vform ] we derive @xmath13 $ ] and discuss the key aspects of our variational formulation . in sec . [ sec : pud ] , we explicitly specialize @xmath13 $ ] to the case of sharp dielectric interfaces , and apply the resulting functional to some simple interfacial shapes . in sec . [ sec : numeric ] we demonstrate a grid - based numerical procedure to implement the functional minimization and some concluding remarks are made in sec . [ sec : conclusion ] . in appendix [ sec : ext ] we prove that @xmath13 $ ] is an energy functional . finally , appendix [ sec : app ] discusses the application of our variational principle to the simple case of a uniform dielectric .

in biological and synthetic materials , many important processes involve charges that are present in a medium with spatially varying dielectric permittivity . to accurately understand the role of electrostatic interactions in such systems , it is important to take into account the spatial dependence of the permittivity of the medium . however , due to the ensuing theoretical and computational challenges , this inhomogeneous dielectric response of the medium is often ignored or excessively simplified . the defining characteristic of a true energy functional is that at its minimum it evaluates to the actual value of the energy ; this is a feature not found in many commonly used electrostatic functionals . we demonstrate , in addition , that the functional has many properties that make it ideal for use in molecular dynamics simulations .

in biological and synthetic materials , many important processes involve charges that are present in a medium with spatially varying dielectric permittivity . to accurately understand the role of electrostatic interactions in such systems , it is important to take into account the spatial dependence of the permittivity of the medium . however , due to the ensuing theoretical and computational challenges , this inhomogeneous dielectric response of the medium is often ignored or excessively simplified . we develop a variational formulation of electrostatics to accurately investigate systems that exhibit this inhomogeneous dielectric response . our formulation is based on a true energy functional of the polarization charge density . the defining characteristic of a true energy functional is that at its minimum it evaluates to the actual value of the energy ; this is a feature not found in many commonly used electrostatic functionals . we explore in detail the charged systems that exhibit sharp discontinuous change in dielectric permittivity , and we show that for this case our functional reduces to a functional of only the surface polarization charge density . we apply this reduced functional to study model problems for which analytical solutions are well known . we demonstrate , in addition , that the functional has many properties that make it ideal for use in molecular dynamics simulations .

1309.7073

c

we have presented a variational formulation of electrostatics specifically designed to treat the problem of dielectric heterogeneities in charged systems . assuming only the condition of linear response , we constructed an energy functional that employs the polarization charge density as its sole variational field . this functional is applicable for any configuration of free charges and arbitrary spatial dependence of the dielectric response . we discussed in some depth the basic structure of our functional , drawing comparisons with past functionals and revealing how more energy functionals can be constructed using our variational approach . next , we focused on the important case of uniform dielectrics separated by sharp interfaces . we showed that under this piecewise - uniform dielectric response , our functional reduces to a functional of only the surface polarization charge density . such a reduction of the 3-dimensional electrostatic problem to a 2-dimensional one has many advantages from a computational perspective . we then obtained the specific expressions for this reduced functional , and subsequently the induced charge density , for the case of a point charge near a planar interface and for a point charge near a spherical dielectric . finally , in the view of applying our approach to more complicated systems , we discussed the numerical implementation of our minimizing variational principle for a system exhibiting piecewise - uniform dielectric response . we illustrated this procedure for a system of monovalent ions near a spherical dielectric ; obtaining the polarization charge density induced on the interface and finding excellent agreement with exact results . due to the fact that @xmath13 $ ] is an energy functional , its minimization can be carried out in conjunction with the update of the ionic configuration . in ref . we demonstrated such a dynamical minimization method . this is of tremendous significance with regards to md simulations of ions in heterogeneous media , as the explicit solution of the poisson equation at each step is avoided . detailed explorations of the dynamical optimization of our functional and the associated md simulations investigating diverse systems such as charged colloidal dispersions and liquid - liquid emulsions will be the subject of a future study . thanks r. sknepnek for many useful discussions . v.j . was funded by the department of defense research and engineering ( ddr&e ) and the air force office of scientific research ( afosr ) under award no . fa9550 - 10 - 1 - 0167 and f.j.s . was funded by the nsf grant numbers dmr-0805330 and dmr-0907781 .

we develop a variational formulation of electrostatics to accurately investigate systems that exhibit this inhomogeneous dielectric response . we explore in detail the charged systems that exhibit sharp discontinuous change in dielectric permittivity , and we show that for this case our functional reduces to a functional of only the surface polarization charge density .

in biological and synthetic materials , many important processes involve charges that are present in a medium with spatially varying dielectric permittivity . to accurately understand the role of electrostatic interactions in such systems , it is important to take into account the spatial dependence of the permittivity of the medium . however , due to the ensuing theoretical and computational challenges , this inhomogeneous dielectric response of the medium is often ignored or excessively simplified . we develop a variational formulation of electrostatics to accurately investigate systems that exhibit this inhomogeneous dielectric response . our formulation is based on a true energy functional of the polarization charge density . the defining characteristic of a true energy functional is that at its minimum it evaluates to the actual value of the energy ; this is a feature not found in many commonly used electrostatic functionals . we explore in detail the charged systems that exhibit sharp discontinuous change in dielectric permittivity , and we show that for this case our functional reduces to a functional of only the surface polarization charge density . we apply this reduced functional to study model problems for which analytical solutions are well known . we demonstrate , in addition , that the functional has many properties that make it ideal for use in molecular dynamics simulations .

1505.07194

i

conventional battery powered wireless communications systems require periodic recharging or replacement of the batteries , which incurs a high operation burden @xcite and can be cumbersome or even impossible ( e.g. , for biomedical devices implanted in the human body @xcite ) . recently , energy harvesting ( eh ) from the ambient radio - frequency ( rf ) signals has been developed as one of the attractive alternatives to prolong the lifetime of energy - constrained nodes in wireless networks @xcite . the dual use of rf signals for eh and information delivery ( i d ) has led to the novel architecture of simultaneous wireless information and power transfer ( swipt ) @xcite , which allows wireless nodes to scavenge energy as well as extract information simultaneously from the rf signals , thus constituting an appealing solution for energy - constrained applications such as wireless relay networks . practical swipt receiver architectures make use of two different circuits performing eh and i d individually @xcite . the receiver may either switch between the eh and i d circuits in a time - division fashion , a scheme known as time switching @xcite , or split the received rf signals into two streams fed to the eh and i d circuits at the same time , a scheme known as power splitting @xcite . typically , eh and i d circuits operate with rather different receiver power sensitivities , i.e. , @xmath1 dbm for information receivers and @xmath2 dbm for energy receivers @xcite . since the eh circuit is designed to maximize the eh efficiency while the i d circuit typically aims for maximum information rate , a fundamental _ rate - energy tradeoff _ exists for swipt systems @xcite . various resource allocation and beamforming schemes were designed to achieve different tradeoffs between rate and energy in swipt systems . in particular , the optimum power allocation maximizing the information rate subject to eh constraint was studied for broadband systems with perfect instantaneous channel state information ( csi ) @xcite . the optimum resource allocation with service differentiation between low- and high - priority data was studied for eh networks in @xcite . in @xcite , a joint optimization and game - theoretic framework was developed to optimize the packet delivery policy and cooperation strategy for delay tolerant networks with eh . moreover , beamforming schemes which maximize the information rate subject to eh constraint or maximize the harvested energy subject to rate constraint were studied under imperfect csi in @xcite and @xcite , respectively . recently , swipt has also been applied in wireless relay systems which allows energy - constrained relay nodes to harvest energy from the source rf signals and consequently brings in substantial benefits in wireless networks @xcite . various theoretical analysis and practical design have been conducted for eh relay systems in the literature . specifically , for dual - hop amplify - and - forward ( af ) networks , a greedy switching protocol between data relaying and eh was proposed in @xcite , and the joint relay selection and power allocation scheme was developed in @xcite . moreover , the outage probability and ergodic capacity for eh af relaying were derived for delay - limited and delay - tolerant applications , respectively , in @xcite . besides af relay systems , the eh has also been considered for decode - and - forward ( df ) networks . in particular , the outage probability of eh df relaying was studied , taking into account the spatial randomness of the source - destination pairs , for various network topologies in @xcite . the aforementioned studies on eh relay systems have either implicitly or explicitly assumed the instantaneous csi availability to allow for _ coherent _ information decoding . however , the coherent swipt requires the source to periodically send training symbols , which incurs an increased signaling overhead and processing burden . moreover , the relays may need to relay the training symbols and/or estimate the source - relay channels @xcite , which results in additional energy consumptions and poses serious issues especially for energy - constrained relay nodes . as a remedy , the _ noncoherent _ swipt eliminating the need for the instantaneous csi was first studied for the eh df relay systems @xcite , where two eh relaying protocols , namely , the power splitting noncoherent df ( ps - ncdf ) and time switching noncoherent df ( ts - ncdf ) were proposed , and the corresponding maximum - likelihood detectors ( mlds ) facilitating noncoherent swipt were obtained . however , these protocols and the detectors are applicable only for the df relay systems . it is still unknown about how the noncoherent af relaying can benefit from eh , and how the noncoherent af relaying performs as compared to the noncoherent df relaying in eh relay systems . in addition , for eh af relay systems , the noncoherent mld minimizing the symbol - error rate ( ser ) in noncoherent swipt is still unknown . realizing that none of the previous works have tackled the design challenges of noncoherent swipt in eh af relay systems , we aim to fill the gap . in this paper , we study the _ noncoherent _ eh relay systems consisting of multiple af relays , which can harvest energy from the ambient source signals and utilize the harvested energy to assist the communication . the main contributions of this paper are summarized as follows : * for arbitrary @xmath0-ary noncoherent frequency - shift keying ( fsk ) or differential phase - shift keying ( dpsk ) signalings , we propose a unified _ noncoherent _ swipt framework embracing two eh relaying protocols , namely , the power splitting noncoherent af ( ps - ncaf ) and time switching noncoherent af ( ts - ncaf ) . * following the proposed swipt framework , we develop noncoherent mlds for ps - ncaf and ts - ncaf in a _ unified _ form , which involves integral evaluations yet serves as the optimum performance benchmark for noncoherent swipt . to avoid integral computations , we also develop a _ closed - form _ gauss - legendre approximation based detector , which achieves almost identical ser to the mld at substantially lower complexity . it is demonstrated that the proposed eh - based noncoherent detectors achieve full diversity in rayleigh fading . in terms of the error performance , the proposed ps - ncaf and ts - ncaf may outperform conventional grid - powered noncoherent relay systems under the same total power constraint . * the choice of the time switching or power splitting parameters represents a tradeoff between eh and information transmission , and there exist unique optimum values of these parameters which minimize the ser . * the number of eh relay nodes is a key factor on the performance of the noncoherent eh relay systems : ps - ncaf outperforms ts - ncaf in the single - relay case , whereas ts - ncaf outperforms ps - ncaf in the multi - relay case . * the optimum relay position is closer to the source than to the destination , regardless of the eh relaying protocols ( this is in contrast to the conventional self - powered relay systems where the optimum relay position is closer to the destination for af and is closer to the source for df ) . furthermore , as the path - loss exponent increases , the optimum relay position shifts slightly towards the destination , but is still closer to the source . * the @xmath0-fsk signaling with @xmath3 is a more suitable solution for eh relay systems due to its higher energy efficiency compared to @xmath0-dpsk , regardless of the eh relaying protocols . * comparison of the af- and df - based eh relaying protocols demonstrates that the ser performance of af and df relaying is almost the same in noncoherent eh relay systems , irrespective of the swipt architecture ( e.g. , power splitting or time switching ) . this is in contrast to the conventional self - powered relay systems where either af or df may outperform each other depending on the relay locations . the remainder of the paper is organized as follows . section [ sec : sysmodel ] describes the system model and develops noncoherent eh relaying protocols . section [ sec : unifiedsysmodel ] obtains a unified noncoherent swipt framework for eh af relay system . section [ sec : mld ] derives the noncoherent detectors achieving swipt . section [ sec : numerical ] gains useful insights into the noncoherent swipt through simulations and section [ sec : con ] concludes the paper . _ notation _ : we use @xmath4 , @xmath5 , @xmath6 , @xmath7 , @xmath8 , @xmath9 , and @xmath10 to denote the conjugate , transpose , conjugate transpose , expectation , real part , 2-norm , and natural logarithm , respectively . also , @xmath11 , @xmath12 , and @xmath13 denote an all - zero column vector , an @xmath14 identity matrix , and a column vector with 1 at its @xmath15-th entry and 0 elsewhere , respectively . moreover , @xmath16 denotes that @xmath17 is defined by @xmath18 . finally , @xmath19 means that @xmath20 is a circularly symmetric complex gaussian ( cscg ) random vector with mean @xmath21 and covariance @xmath22 .

in energy harvesting ( eh ) relay networks , the _ coherent _ communication requires accurate estimation / tracking of the _ instantaneous _ channel state information ( csi ) which consumes extra power . as a remedy , we propose two _ noncoherent _ eh relaying protocols based on the amplify - and - forward ( af ) relaying , namely , power splitting noncoherent af ( ps - ncaf ) and time switching noncoherent af ( ts - ncaf ) , which do not require any instantaneous csi . we develop a _ noncoherent _ framework of simultaneous wireless information and power transfer ( swipt ) , embracing ps - ncaf and ts - ncaf in a _ unified _ form . for arbitrary-ary noncoherent frequency - shift keying ( fsk ) and differential phase - shift keying ( dpsk ) , we derive maximum - likelihood detectors ( mlds ) for ps - ncaf and ts - ncaf in a _ unified _ form , which involves integral evaluations yet serves as the optimum performance benchmark . to avoid expensive integral computations , we propose a _ closed - form _ detector using the gauss - legendre approximation , which achieves almost identical performance as the mld but at substantially lower complexity . these eh - based noncoherent detectors achieve full diversity in rayleigh fading . numerical results demonstrate that our proposed ps - ncaf and ts - ncaf may outperform the conventional grid - powered relay system under the same total power constraint . various insights which are useful for the design of practical swipt relaying systems are obtained . interestingly , ps - ncaf outperforms ts - ncaf in the single - relay case , whereas ts - ncaf outperforms ps - ncaf in the multi - relay case . energy harvesting , maximum - likelihood , noncoherent , simultaneous wireless information and power transfer ( swipt ) .

in energy harvesting ( eh ) relay networks , the _ coherent _ communication requires accurate estimation / tracking of the _ instantaneous _ channel state information ( csi ) which consumes extra power . as a remedy , we propose two _ noncoherent _ eh relaying protocols based on the amplify - and - forward ( af ) relaying , namely , power splitting noncoherent af ( ps - ncaf ) and time switching noncoherent af ( ts - ncaf ) , which do not require any instantaneous csi . we develop a _ noncoherent _ framework of simultaneous wireless information and power transfer ( swipt ) , embracing ps - ncaf and ts - ncaf in a _ unified _ form . for arbitrary-ary noncoherent frequency - shift keying ( fsk ) and differential phase - shift keying ( dpsk ) , we derive maximum - likelihood detectors ( mlds ) for ps - ncaf and ts - ncaf in a _ unified _ form , which involves integral evaluations yet serves as the optimum performance benchmark . to avoid expensive integral computations , we propose a _ closed - form _ detector using the gauss - legendre approximation , which achieves almost identical performance as the mld but at substantially lower complexity . these eh - based noncoherent detectors achieve full diversity in rayleigh fading . numerical results demonstrate that our proposed ps - ncaf and ts - ncaf may outperform the conventional grid - powered relay system under the same total power constraint . various insights which are useful for the design of practical swipt relaying systems are obtained . interestingly , ps - ncaf outperforms ts - ncaf in the single - relay case , whereas ts - ncaf outperforms ps - ncaf in the multi - relay case . energy harvesting , maximum - likelihood , noncoherent , simultaneous wireless information and power transfer ( swipt ) .

1601.07331

i

transition metal compounds ( tmcs ) , particularly in their nanostructured form , find applications in a diverse range of technological fields including photovoltaics and photocatalysis , magnetic storage and phosphorescent imaging.@xcite rational optimization of tmcs at the nanoscale requires an atomistic , quantum - mechanical description of these materials , which in principle can be provided by density - functional theory ( dft).@xcite unfortunately , the most widely - used approximations to the dft exchange - correlation ( xc ) energy , namely the local - density and generalized - gradient approximations ( lda / gga ) , have difficulty in describing the localized @xmath1-electrons of the transition metals.@xcite this difficulty has been ascribed to the unphysical self - interaction experienced by the electrons within the lda / gga , and a number of methods have been proposed to overcome it.@xcite one popular method is to supplement the lda / gga xc potential with orbital - dependent @xmath0 terms , designed to more accurately describe the on - site correlation of the @xmath1-electrons.@xcite such `` hubbard @xmath0 '' corrections have been found to give an improved description of the properties of tmcs like nio.@xcite a less widely - investigated approach to improving the lda / gga description of the tmcs is to obtain the xc energy as a combination of the `` exact '' hartree - fock exchange energy ( exx ) and the correlation energy calculated within the random - phase approximation ( rpa).@xcite such a scheme should benefit from the exx correction of self - interaction,@xcite and also from the non - local and dynamical description of correlation provided by the rpa . specifically , the rpa correlation energy should capture long - range dispersive interactions that are missing in the hubbard @xmath0 corrections.@xcite recent work has demonstrated the good performance of the rpa+exx approach for calculating the formation energies and relative stabilities of transition metal oxides.@xcite from the point of view of performing predictive calculations , the rpa+exx scheme carries the additional advantage of being essentially parameter - free . however , it is important to note that the most well - documented successes of this scheme for instance in describing non - local correlation in weakly - bonded systems , describing chemisorption and bonding in solids , or in the tmc examples above were performed non - self - consistently.@xcite that is , the xc potential felt by the non - interacting electrons was not the functional derivative of the xc energy , at variance with the standard kohn - sham ( ks ) formulation of dft.@xcite although self - consistent rpa calculations have been demonstrated , they remain a significant technical challenge.@xcite therefore a key question to ask is how the choice of xc potential in the single - particle hamiltonian affects the total energy calculated in a non - self - consistent rpa+exx scheme . an analogy can be drawn with one - shot calculations of quasiparticle energies within the @xmath3 approximation ( @xmath4 ) , where the green s function and screened coulomb interaction are usually constructed from lda / gga wavefunctions.@xcite here it has been established that the calculated quasiparticle energies ( e.g. the band gap ) can depend strongly on the xc potential used in the single - particle hamiltonian.@xcite studies which have explored this aspect for rpa+exx total energy calculations have usually focused on the differences between lda and gga or on the effect of including hartree - fock exchange.@xcite in most cases , the initial choice of xc potential has been found to play only a minor role ; a notable exception is the study of cerium in ref , and of molecular dissociation in refs . and . however , for tmcs it is natural to investigate the effect on the rpa+exx total energy of adding hubbard @xmath0 corrections to the xc potential . since such corrections can significantly change the character of the single - particle wavefunctions and their energy eigenvalues , one might expect to observe a dependence of the rpa+exx total energy on the parameter @xmath0 . indeed , one might even hope that including hubbard @xmath0 corrections in the xc potential might improve the quality of the subsequent rpa+exx calculation , if the resulting single - particle wavefunctions are closer to the exact ks form.@xcite on the other hand , it is important to note that the orbital - dependent hubbard @xmath0 corrections are non - local , and that the rpa correlation energy is strictly non - variational with respect to all possible non - local xc potentials.@xcite motivated by these considerations , we have performed a systematic study of the effects of hubbard @xmath0 corrections on the non - self - consistent rpa+exx total energy of tmcs . we present results for zns , tio@xmath2 and nio which , in terms of their 3@xmath1 states , display progressively more complex electronic structure . from the total energies we obtain lattice constants as a function of the @xmath0 parameter within the rpa approximation for the correlation energy , and compare the results to non - self - consistent exx , self - consistent gga+@xmath0 or lda+@xmath0 , and experiment . we also consider the energetics of the technologically - important tio@xmath2 polymorphs of anatase and rutile , and the heats of formation of tio@xmath2 and nio . the rest of our paper is organized as follows . in section [ sec.methods ] we outline the theory of the non - self - consistent rpa+exx scheme and describe our computational approach . in sections [ sec.zns ] , [ sec.tio2 ] and [ sec.nio ] we present our results for zns , tio@xmath2 and nio , including our calculations of the phase stability of tio@xmath2 in section [ sec.tio2_relstab ] . we provide a detailed analysis of the @xmath0-dependence of the total energy in sections [ sec.u_energies ] and [ sec.u_min ] , and consider the oxide heats of formation in section [ sec.heat_form ] . we present our conclusions in section [ sec.conclusions ] .

in non - self - consistent calculations of the total energy within the random - phase approximation ( rpa ) for electronic correlation , it is necessary to choose a single - particle hamiltonian whose solutions are used to construct the electronic density and non - interacting response function . here we investigate the effect of including a hubbard- term in this single - particle hamiltonian , to better describe the on - site correlation of 3 electrons in the transition metal compounds zns , tio and nio . we further demonstrate that the non - self - consistent rpa total energies of these materials have minima at nonzero . our rpa calculations find the rutile phase of tio to be more stable than anatase independent of , a result which is consistent with experiments and qualitatively different to that found from calculations employing-corrected ( semi)local functionals . however we also find that the + term can not be used to correct the rpa s poor description of the heat of formation of nio .

in non - self - consistent calculations of the total energy within the random - phase approximation ( rpa ) for electronic correlation , it is necessary to choose a single - particle hamiltonian whose solutions are used to construct the electronic density and non - interacting response function . here we investigate the effect of including a hubbard- term in this single - particle hamiltonian , to better describe the on - site correlation of 3 electrons in the transition metal compounds zns , tio and nio . we find that the rpa lattice constants are essentially independent of , despite large changes in the underlying electronic structure . we further demonstrate that the non - self - consistent rpa total energies of these materials have minima at nonzero . our rpa calculations find the rutile phase of tio to be more stable than anatase independent of , a result which is consistent with experiments and qualitatively different to that found from calculations employing-corrected ( semi)local functionals . however we also find that the + term can not be used to correct the rpa s poor description of the heat of formation of nio .

astro-ph9706210

c

the major axis measurements in ngc 253 pose an interesting problem . in fig . 6 , the `` rotation curve '' appears to flatten off before rising at a radius @xmath59 . this effect is seen for both the approaching and receding sides of the disk , with ( fig . 6@xmath60 ) or without ( fig . 6@xmath61 ) the correction for orbit inclination . in fig . 6@xmath51 , the taurus-2 measurements confirm and extend this trend out to @xmath62 . the outer taurus-2 values are somewhat higher than the azimuthally averaged hi rotation curve , but this is a distinctive feature of the approaching side of the disk ( fig . 6@xmath61 ) in that the outer hi measurements here are higher than average . if we assume that the distribution of mass has spherical symmetry , then from poisson s equation , @xmath63 where @xmath64 and @xmath65 are the local mass density and the circular velocity . for the flat region of @xmath65 , @xmath64 declines as @xmath66 ; the sudden rise requires the density profile to become much flatter or even constant with increasing radius . a slightly flattened potential gives the same result although the inferred total mass will be overestimated in this case . the inflexion in the rotation curve can be understood naturally to arise from the potential of an exponential stellar disk with a much larger dark halo ( e.g. carignan & freeman 1985 ) . to illustrate this , we show a variety of possible 3-component fits to the data . in the first model ( fig . 7@xmath61 ) , the hi and stellar disks have the same form . the dark halo is represented by an isothermal sphere , which is fully specified by any two of the halo central density , @xmath67 , the central velocity dispersion @xmath68 , or the core radius @xmath69 . the stellar disk is specified by a central surface density @xmath70 and a scale length @xmath71 . the hi surface density profile is given in pcvg ( fig . 5 ) ; the central hole within @xmath72 causes the gravitational force due to the gas to be directed outward ( e.g. staveley - smith 1990 ) . we have taken @xmath68 @xmath53 253 , @xmath73 kpc , @xmath74 kpc@xmath37 and @xmath75 kpc . these values compare well with pcvg except that the disk and halo scale lengths are 30% smaller than their values . in order to match the observed data , the model rotation curves have been projected to a plane inclined at 72 . we note that such a large core radius is normal for the dark halo of large disk galaxies ( freeman 1993 ) . in the second model ( fig . 7@xmath60 ) , the radial forms of the disk and halo are given by dehnen & binney ( 1997 ) . for the halo , we adopt @xmath76 with @xmath77 the halo parameters are the halo density normalization , @xmath78 , the halo scale radius , @xmath79 , the outer cut - off radius , @xmath80 , and the inner and outer power slopes @xmath81 and @xmath60 . apart from the halo axis ratio ( @xmath82 ) , all of these parameters were obtained from a fit to the rotation curve . both the stellar and gaseous disks are assumed to be exponential in form , i.e. @xmath83 for each of the disks , the adopted parameters are the surface density normalization , @xmath84 , the disk scale height , @xmath85 , and the disk scale radius and inner cut - off radius , @xmath86 and @xmath87 . for the hi disk , these were fixed at @xmath88 kpc@xmath37 , @xmath89 kpc , @xmath90 kpc , and @xmath91 kpc . for the stellar disk , @xmath92 kpc , @xmath93 kpc , and @xmath94 kpc as suggested by the photometry . the surface density normalization for the stellar disk was obtained from the least - squares fit . the fit , kindly undertaken by w. dehnen , ignored the last taurus-2 measurement to yield the following results : @xmath95 kpc@xmath37 , @xmath96 kpc@xmath97 , @xmath98 , @xmath99 , @xmath100 kpc and @xmath101 kpc . of these , @xmath60 was constrained to be greater than or equal to unity . 7@xmath60 shows that the rising halo contribution to the rotation curve gives a better fit to the data overall . but there are strong correlations between the various parameters and the fitted results depend critically on which of the taurus-2 points are included . the outermost taurus-2 measurement in figs . 6@xmath51 and 7 suggests that the rotation curve may be falling beyond a radius of about 10 kpc , but there are certainly other possible explanations for its low observed velocity . for example , _ ( i ) _ it may result from tidal distortion of the outermost regions of ngc 253 , or _ ( ii ) _ from accretion of a faint gas - rich object at large radius . in support of the accretion idea , a stacked photographic image by d. malin shows extended stellar light at faint levels ( @xmath4326 mag arcsec@xmath37 ) to the sw of the disk ; similar emission is not seen to the ne . _ ( iii ) _ while the emission may arise from an outer ionized envelope , it is conceivable that this emission is associated with the group itself . an extragalactic cloud has recently been discovered in the fornax cluster ( bland - hawthorn 1995 ) . mathewson , cleary & murray ( 1975 ) and arp ( 1985 ) found tentative evidence for hi clouds within the sculptor group ( cf . haynes & roberts 1979 ) . it is difficult , however , to reconcile the radial velocity ( @xmath12440 ) with the magellanic stream which passes in front of the sculptor group ( mathewson & ford 1984 ) . finally , we consider the possibility that the rotation curve of ngc 253 is indeed falling beyond 10 kpc . such a rapid decrease suggests that the dark halo may be truncated . we can illustrate the effect of such truncation with a simple model . we take the halo density distribution to be @xmath102 with the rotation curve @xmath103 given by @xmath104\ ] ] for @xmath105 and core radius @xmath106 kpc , the rotation curve for this model is very similar to that of the isothermal halo in fig . 7@xmath61 : the optical galaxy lies well within the core radius of the halo , and the halo rotation curve is close to solid - body . we now truncate the halo at @xmath107 kpc ; its rotation curve is then keplerian for @xmath108 kpc . 7@xmath51 shows how the resulting total rotation curve now provides an acceptable fit to all of the hi and taurus-2 data . the model is artificial ( the halo is sharply truncated , and we did not truncate the stellar and hi disks ) , but the point is obvious enough : truncation of the dark halo near the observed outer edge of the hi disk can produce the apparent falling rotation curve . if this is all correct so far , there are some interesting consequences . the properties of dark halos are best studied in disk galaxies for which the hi distribution extends well beyond the optical distribution . in the outer regions of these galaxies , the ratio of ( dark matter surface density)/(hi surface density ) is roughly constant ( bosma , 1978 ; carignan 1991 ) . ngc 253 is not such a galaxy . its hi extent is similar to its optical extent ( pcvg ) . our data provides the first hint that , in galaxies like ngc 253 where the hi and the light are co - extensive , the dark matter also may not extend much beyond the optical distribution . it is tentative evidence of the apparent link between the dark matter and the hi . we emphasize that the dark matter is still essential to generate the observed rotation curve for ngc 253 : the inferred mass ratio of dark matter to luminous matter is about 5 . our point is simply that the dark matter distribution in ngc 253 may be truncated at a radius of only 10 kpc , compared to the much larger dark halo distributions observed in our galaxy ( freeman 1996 ) and other large spirals ( zaritsky 1997 ) . the reduced chi square for the models presented in fig . 7@xmath61 and 7@xmath60 are 5.2 and 2.9 respectively . the latter model has the highest statistical significance of all models , but the basic assumptions are unlikely to be physical . a flat rotation curve given by equation [ arctan ] does not fit the measurements adequately . the reduced chi square is 6.3 and , more significantly , 10 of 12 points outside of @xmath59 miss the curve by more than 2@xmath38 . but the inclusion of a truncation radius lowers the reduced chi square to 3.9 and the curve now passes through all the outer points ( fig . 7@xmath51 ) . the most striking feature of the spectra presented in figs . 4 and 5 is the inferred high / ratios . in order to ensure that the whitelight calibration adequately removed the filter response over the field ( @xmath64 ) , we examined the line ratios in hii regions over the inner disk . where we have two interference rings that fall close together on the sky one from , the other from [ nii ] the hii regions appear weak in [ nii ] compared to , indicative of the order of magnitude difference expected for inner disk hii regions . if the outer hi gas has sub - solar abundances ( pagel 1989 ; diaz 1989 ) , the enhanced line ratio must arise from one or more excitation processes . however , to date , numerical models involving a single ionizing source have not managed to produce such an enhancement ( e.g. sokolowski 1994 ) . thus , we separate our discussion of ionization and excitation wherever possible . almost certainly , the anomalous ratio is indicative of a higher local electron temperature for which there are various mechanisms . in solar - abundance hii regions , this ratio rarely exceeds 0.15 ( evans & dopita 1985 ) : to substantially increase this ratio requires that we selectively heat the electrons without producing . the emission measure from the surface of a cloud embedded in a bath of ionizing radiation gives a direct gauge , independent of distance , of the intensity of the ambient radiation field beyond the lyman continuum ( lyc ) edge ( hogan & weymann 1987 ) . this assumes that the covering fraction _ seen by the ionizing photons _ is known and that there are sufficient gas atoms to soak up the incident ionizing photons . at electron temperatures of 10@xmath109k , collisional ionization processes are negligible . perpendicular to the surface , from equation [ ion_balance ] , the column recombination rate in equilibrium must equal the incident ionizing photon flux , @xmath110 , where is the rate at which lyman continuum photons arrive at a planar cloud surface ( phot @xmath4 s@xmath11 ) , and is the column density of ionized hydrogen . the emission measure produced by this ionizing flux is @xmath111 where @xmath112 ( bland - hawthorn & maloney 1997 , hereafter bm ) . for an optically thin cloud in an isotropic radiation field , the solid angle from which radiation is received is @xmath113 , while for one - sided illumination , @xmath114 . however , can be anisotropic and @xmath115 can be considerably less than @xmath116 . the measured surface brightness values for the emission lines in figs . 4 and 5 are as follows : for the line , 90@xmath565 mr ( @xmath117 ) , 46@xmath565 mr ( @xmath118 ) ; for the line , 81@xmath566 mr ( @xmath62 ) , 41@xmath568 mr ( @xmath119 ) . if the underlying hi is optically thick to the lyman continuum , the lines require an ionizing flux of @xmath120 and @xmath121 . the present upper limit on the metagalactic ionizing flux ( @xmath63.1 ) is @xmath122 ( @xmath30 ) which sets an upper limit on the one - sided ionizing flux at the surface of an optically thick hi sheet of @xmath123 , thereby ruling out the metagalactic background as the dominant ionizing source . the combined ionizing radiation from hot gas and galaxies within the sculptor group is also much too weak . sciama ( 1995 ) predicts an order of magnitude higher ionizing flux from decaying neutrinos which could conceivably account for much of the flux . however , the narrow energy bandpass of decaying neutrinos ( sciama 1996 ) at the lyman limit can not produce , and therefore requires an additional source of ionization . the most recent summary of the macho project indicates that as much as half of the dark matter in the galaxy out to the lmc is made up of solar mass objects . there is wide disagreement on whether the missing mass could comprise a halo population of white dwarfs ( adams & laughlin 1996 ; kawaler 1996 ; chabrier , segretain & mera 1996 ) . but most plausible models invoke a population which produces essentially no uv flux today . this is supported by high redshift observations of the precursor halo population ( charlot & silk 1995 ) . unlike ellipticals , spiral galaxy disks tend not to `` grow '' when photographic plates are stacked or amplified to reveal light at very faint levels ( malin 1983 ) . but a photographically amplified plate of ngc 253 ( malin 1981 ) reveals a faint blue disk extending to the limits of our outermost detection ( @xmath124 ) . following a suggestion from g.b . field , we now consider whether these could comprise an extended white dwarf population ( including the precursor population of central stars in planetary nebulae ) young enough to produce a significant uv disk flux . such a population was originally broached by lyon ( 1975 ) and bania & lyon ( 1980 ) . in fig . 8 , we consider whether white dwarfs are able to account for the diffuse line emission in concert with the faint stellar continuum at the hi edge in ngc 253 ( barred arrow ) . we present the expected emission measure versus @xmath50 surface brightness for an isothermal population of white dwarfs as a function of the disk surface density . the contribution to both of these quantities from white dwarfs in the solar neighbourhood is also shown ( filled symbols ) . the luminosity function is taken from liebert , dahn & monet ( 1988 ) and the luminosity@xmath7temperature conversion from wood ( 1990 ) . there are two basic problems in using white dwarfs to explain the disk ionization . in the solar neighbourhood , the combined effect of all white dwarfs could produce @xmath125 which fails to explain the reynolds layer emission by an order of magnitude or more , in agreement with nordgren , cordes & terzian ( 1992 ) . if we assume a comparable star formation history in the outer reaches of ngc 253 , this model could conceivably be used to explain the measured emission . this is particularly attractive in that the high temperatures of the white dwarf population produce elevated / ratios ( sokolowski & bland - hawthorn 1991 ) . however , if the luminosity function resembles the solar neighbourhood , the combined disk surface brightness at @xmath50 from the cooler white dwarfs is very much brighter than observed , particularly when one includes the contribution of early main sequence stars . alternatively , attempting to explain the low emission measure in terms of 2000 white dwarfs kpc@xmath37 at 45,000 k leads to a timing problem . we have measured an age - temperature relation from wood ( 1990 ) for which @xmath126 stars hotter than 40,000 k have left the asymptotic giant branch less than 10@xmath127 years ago which would require a highly contrived star formation history throughout the disk . ryan has suggested the possibility of hot horizontal branch stars , in particular , an isothermal population with temperatures around 15,000 k ( lee 1993 ) . if we assume comparable line blanketing with white dwarfs , fig . 8 illustrates that such a population will always produce too much blue light for the required ionizing flux , irrespective of the uncertain sizes and surface densities of both objects . the characteristic `` temperature '' of the ionizing source needs to be sufficiently high to fall within the strict @xmath50 band limit . interestingly , this is just what is needed to significantly enhance the / ratio as photons with higher mean energies produce higher electron temperatures . _ ram pressure heating . _ mathis ( 1986 ) has stressed the problems associated with shocks as a source of ionization and heating for the reynolds layer , particularly the near - uniformity of the emission . an interesting possibility is ram pressure heating as ngc 253 moves through an external medium where the disk is inclined at some angle to its direction of motion . the wake of ngc 7421 ( ryder 1996 ) suggests that such a process can take place . to ionize a column of 10@xmath3 atoms @xmath4 requires shock speeds close to 130 ( dopita & sutherland 1996 ) . a medium with pre - shock density @xmath128 @xmath33 moving through an ambient medium with the relatively high density @xmath129 @xmath33 at 400 could produce the necessary ram pressure . the post - shock temperature at a shock velocity of 130 is @xmath130 which is a factor of ten higher than the upper limit from the doppler parameter ( 22 ) of the observed line profiles . for and to have been collisionally ionized , the gas must have had time to cool . but groups with low velocity dispersions , like the sculptor group , tend to have very little intracluster medium ( fadda 1996 ) . therefore , the galaxy would need to be running into a large , external gas cloud for the shock model to remain plausible . there exists a wide range of ` exotic ' models for preferentially heating the electron population including turbulence - driven mhd wave heating ( raymond 1990 ) , and mixing layers driven by bulk flows ( slavin , shull & begelman 1993 ) . bulk flows and turbulence in the disk are thought to be maintained primarily by energy injection from star formation . the star formation rates at the hi edge are likely to be very small . an alternative possibility is that the outer disk is being rained on by galactic fountain material driven by the inner starburst ( e.g. benjamin & shapiro 1993 ) . it is unclear at present whether fountain models can generate the necessary heating through shocks . ferland & mushotsky ( 1984 ) have shown that under rather special conditions , low energy cosmic ray electrons can selectively heat ions and electrons through coulomb repulsion . however , sciama ( 1996 ) emphasizes the difficulties involved in cosmic rays penetrating gas clouds and these do not appear to be an important agent . the inner disk of ngc 253 hosts a young , stellar population producing copious amounts of ionizing photons . it is plausible that the outer disk sees this radiation either through dust scattering or through warps in the outer parts . for rayleigh scattering , we have repeated the calculations of jura ( 1980 ) using up - to - date dielectric phase functions ( martin & rouleau 1990 ; draine & lee 1984 ) and assuming a standard grain mixture and distribution ( mathis , rumpl & nordsieck 1977 ) . we adopt the henyey - greenstein ( 1941 ) phase function which relates the asymmetry parameter @xmath81 to photon energy . the expected ionizing flux at the hi edge is much less than 10@xmath131 due primarily to the highly forward - scattering behaviour ( @xmath132 ) of the grains at increasing energy towards the lyman limit . while there is some uncertainty as to the fraction of ionizing photons which escape a normal spiral galaxy , two independent lines of argument suggest that roughly 5% of ionizing photons escape the galaxy ( domgrgen & mathis 1994 ; bm ) . the absolute @xmath50 magnitude of ngc 253 is comparable to that inferred for the galaxy and thus , if the disk opacity is comparable in both cases , the same models in bm apply here . bothun ( personal communication ) suspects that the disk of ngc 253 may be more opaque than the milky way , in which case our predicted fluxes should be considered upper limits . to explain the flux at both outer positions ( 9 and 12 kpc ) requires an integral sign warp originating at 7 kpc reaching 20 at 10 kpc . it is difficult to rule this out on the basis of the hi data . at face value , fig . 8 of pcvg indicates such a warp starts at 7 kpc reaching @xmath1210 at 9 kpc . in the next section , we explore this model in more detail . after sokolowski ( 1994 ) , we attempt to simulate conditions at the hi edges of spiral galaxies ionized by the stellar radiation field from the central disk . this requires that the outer sw edge of ngc 253 is warped ( @xmath133 ) or flares up and therefore sees the central regions . we use the cloudy code ( ferland 1991 ) to ionize plane parallel slabs with cosmic abundances ( grevesse & anders 1989 ) . the physical state and emission spectrum of a low - density photoionized gas with a given composition are fixed by two parameters @xmath7 the shape of the ionizing continuum and the ionization parameter ( tarter , tucker & salpeter 1969 ) . for the ionization parameter , @xmath134 ( the ratio of ionizing photons to nucleons ) , we adopt @xmath135 where @xmath51 is the speed of light . in fig . 10 , the results for a range of emission - line diagnostics are presented as a function @xmath134 . the radiation - bounded models are truncated when the electron temperature @xmath136 falls below 4000k ; all models assume @xmath53 1 @xmath33 . the unabsorbed radiation field is a composite taking the form @xmath137 where @xmath138 is the current star formation rate , @xmath139 is the initial mass function , and @xmath140 is the main - sequence lifetime . the ionizing field is dominated by stars with @xmath141 ; we specify the upper mass cut - off to be @xmath142 . the stellar atmospheres are from mihalas ( 1972 ) and kurucz ( 1979 ) ; the solar metallicity evolutionary tracks are from maeder ( 1990 ) . for the massive star imf , we adopt @xmath143 which falls between the salpeter ( 1955 ) and the miller - scalo ( 1979 ) models . irrespective of the _ shape _ of the ionizing continuum , a dilute radiation field leads to enhanced emission from low ionization emission lines ( ferland & netzer 1983 ; halpern & steiner 1983 ) . but a general hardening of the ionizing field also produces the same trend ( e.g. sokolowski & bland - hawthorn 1991 ) . indeed , if the edges of spirals are ionized by the central stellar disk , the ionizing field is expected to be both dilute and hardened . there are at least two phenomena which serve to harden the local ionizing radiation field : interstellar opacity and metal depletion ( i.e. refractory elements ) onto grains . we assume that the ionizing photons have leaked from the young inner disk and that the ionizing spectrum has been hardened by intervening absorption ( @xmath144 perpendicular to the disk ) . we adopt the atomic photoionization cross - section for which the average interstellar opacity varies as @xmath145 above 13.6ev ( cruddace 1974 ) . in quiescent galaxies , the outer hi disk is expected to have sub - solar metallicities ( molla 1996 ) . but the ongoing nuclear starburst in ngc 253 ( beck & beckwith 1984 ; antonucci & ulvestad 1988 ) could conceivably enrich the outer disk through long - range galactic fountains ( corbelli & salpeter 1988 ) . on balance , we adopt solar abundances ( grevesse & anders 1989 ) modified by the known depletion rates for cold gas ( cowie & songaila 1986 ; jenkins 1987 ; savage & massa 1987 ) . the formation of grains depletes primarily ca , fe and si which in turn suppresses the dominant coolants from the singly - ionized stages of these atoms ( ferland 1992 ) . for example , at @xmath146 , 158@xmath8 m and 35@xmath8 m account for one quarter of the total nebular cooling . while c , n and o are not strongly depleted , the forbidden line emission from , , and is greatly enhanced by the increased temperature . in particular , mathis ( 1986 ) finds that the / ratio increases as @xmath147 . therefore , a 20% increase in the local electron temperature can effectively double this line ratio . we neglect grain heating and cooling processes ( reynolds & cox 1992 ) as these are only important in the high @xmath134 limit ( baldwin 1991 ; ferland 1992 ) . complete removal of the grain population from the depleted gas causes line strengths to change by no more than 5% ( shields 1992 ) . _ photoionization models . _ in fig . 9 , we show the detailed ionization and thermal structure within the gaseous slab . , and are closely coupled with slight differences due to charge exchange reactions . , and are therefore also closely linked , except that divergence can occur at the front of the slab if the radiation field is sufficiently strong to produce a higher state of ionization in n or o. the soft photons are soaked up and fully ionize the front of the slab ; the harder photons propagate further into the gas and set up a partially ionized zone . here , the electron temperature increases by 25% which boosts the emissivities of the , , and lines . the high energy photons are essential : cutting off the continuum just below the ionization potential of nii ( 29.6 ev ) produces / line ratios no higher than 0.25 . 10 shows the dependence of five important line diagnostics on both ionization parameter and the gas column density . the range of column densities shown are relevant to spiral edges . the line ratio / peaks at @xmath148 with a fivefold enhancement when compared with hii regions . in the warped disk model above , we expect @xmath149 . only the high end of this range is sufficient to explain the recombination emission . for a gas disk with a thickness of 1 kpc , @xmath53 0.1 implies @xmath150 @xmath33 , such that for a fully ionized gas , @xmath151 . the high end of this range is indeed where the / ratio peaks in fig . the observed ratio ( / @xmath12 1 ) implies / ( @xmath152 ) is a factor of two higher than the peak of the curve in fig . while this model may have some application to the hi edges of ngc 253 , a full explanation of the gas excitation requires an additional heat source . our attempt to explain the enhanced / ratios with the dilute , hardened radiation field is made much more difficult if the particle column density seen from the nucleus is much less than @xmath153 atoms @xmath4 . it is noteworthy that @xmath154 is produced deep within the slab compared to and . the relative strength of these lines exhibits a complex interdependence on the shape of the ionizing spectrum , the ionization parameter and , most crucially , the column density of the ionized gas . fig . 10 illustrates that , in fact , all emission lines exhibit some dependence on the gas column density . rand ( 1997 ) emphasizes the importance of the @xmath155/ and the / ratios , taken together , for constraining the he ionizing fraction and the ionizing spectrum . domgrgen & mathis ( 1994 ) predict a high he ionizing fraction if the enhanced emission is due to a dilute , hardened radiation field . a direct measurement of the kinetic temperature is possible from a detection of the @xmath156 line ( osterbrock 1989 ) . but these @xmath157 band lines are expected to be an order of magnitude fainter than which puts them at the limit of detectability ( btvs ) . finally , we summarize the steps that were taken to achieve the enhanced low ionization line ratios in fig . 10 . if / @xmath53 0.3 is typical for a high @xmath134 model ( e.g. hii region ) , a dilute radiation field ( @xmath158 ) in the neighbourhood of hot stars can double this ratio ( e.g. mathis 1986 ) . hardening the dilute radiation field with interstellar absorption can produce line ratios closer to unity ( e.g. sokolowski 1991 ) . an additional 50% increase is achieved with the known gas phase depletions of refractory elements . further enhancement of this ratio ( for a fixed abundance ) requires that we selectively heat the electrons without producing a higher ionization state of nitrogen .

it was anticipated that if the ambient radiation field is sufficiently strong , there exists a maximum radius beyond which the cold gas is unable to support itself against ionization . we have now succeeded in detecting ionized gas beyond the observed hi disk in spirals . here , we report on our findings for the sculptor galaxy ngc 253 . if this is correct , then it suggests that the dark halo of ngc 253 may be truncated near the hi edge , and provides further support for the link between dark matter and hi . the line ratios are anomalous with to h ratios close to unity . while metallicities at these large radii are uncertain , such enhanced ratios compared to solar - abundance hii regions ( / ) are likely to require selective heating of the electron population without further ionization of n . we discuss the most likely sources of ionization and heating , and the possible role of refractory element depletion ( e.g. ca , si , fe ) onto dust grains .

in spiral galaxies , the hi surface density declines with increasing radius to a point where it is seen to truncate dramatically in the best observed cases . it was anticipated that if the ambient radiation field is sufficiently strong , there exists a maximum radius beyond which the cold gas is unable to support itself against ionization . we have now succeeded in detecting ionized gas beyond the observed hi disk in spirals . here , we report on our findings for the sculptor galaxy ngc 253 . the hi disks in sculptor galaxies extend to only about 1.2 although we have detected ionized gas to the limits of our survey out to 1.4 . this has important ramifications for spiral galaxies in that it now becomes possible to trace the gravitational potential beyond where the hi disk ends . the detections confirm that the rotation curve continues to rise in ngc 253 , as it appears to do for other sculptor galaxies from the hi measurements , but there is a hint that the rotation curve may fall abruptly not far beyond the edge of the hi disk . if this is correct , then it suggests that the dark halo of ngc 253 may be truncated near the hi edge , and provides further support for the link between dark matter and hi . the line ratios are anomalous with to h ratios close to unity . while metallicities at these large radii are uncertain , such enhanced ratios compared to solar - abundance hii regions ( / ) are likely to require selective heating of the electron population without further ionization of n . we discuss the most likely sources of ionization and heating , and the possible role of refractory element depletion ( e.g. ca , si , fe ) onto dust grains .

astro-ph9706210

c

we have succeeded in detecting ionized gas at and beyond the hi cut - off radius in the nearby spiral galaxy , ngc 253 . this galaxy is a member of a small ensemble , the sculptor group , with a low internal dispersion and little or no associated hot medium . the detected emission measures of the and lines are sufficiently strong that it is unlikely the source of the ionization is the metagalactic uv background . the strength of the line with respect to the line argues for an enhanced electron temperature at large galactic radius compared with the inner hii regions . the dominant ionization mechanism is suspected to be due to hot young stars in the inner regions which see the warped outer hi disk . we present a composite ionization model which may have some application to the hi edges of ngc 253 , but a full explanation requires additional heat sources . the kinematic measurements confirm that the rotation curve is still rising at and beyond the hi edge . in some respects , since the hi disk ceases to be detectable at only 1.2 , this is not an ideal object for testing the original proposal of bochkarev & sunyaev ( 1977 ) . but there are a few objects which subtend a large solid angle on the sky and have hi disks extending to beyond 2 : these are the focus of subsequent papers . jbh wishes to thank oxford university for a visiting fellowship and for their hospitality during the preparation of this manuscript . we acknowledge extended dialogues with dennis sciama , jon weisheit and james binney . we are indebted to walter dehnen for his insights , and for carrying out a least - squares fit to our data . both an anonymous referee and the scientific editor , g.d . bothun , made substantive comments which improved the presentation of this manuscript . keith taylor and sylvain veilleux assisted in some of the observations and the etalon was loaned to us by brent tully . we acknowledge comments from george field communicated by dennis sciama . jbh wishes to thank jim sokolowski for permission to reproduce unpublished work arising from extensive collaborations . adams , f.c . & laughlin , g. 1996 , apj , 468 , 586 antonucci , r.r.j . & ulvestad , j.s . 1988 , apj , 330 , l97 arp , h. 1985 , aj , 90 , 1012 bahcall , j.n . 1991 , apj , 377 , l5 baldwin , j. 1991 , apj , 374 , 580 beck , s.c . & beckwith , s.v . 1984 , mnras , 207 , 671 benjamin , r.a . & shapiro , p.r . 1993 , in the evolution of galaxies and their environment , nasa ames publ . , p. 338 bica , e. & alloin , d. 1987 , a&a , 70 , 281 bland - hawthorn , j. 1997 , pasa , in press bland - hawthorn , j. , ekers , r.d . , van breugel , w. , koekemoer , a. & taylor , k. 1995 , apj , 447 , l77 bland - hawthorn , j. & maloney , p.r . 1997 , apj , in press bland - hawthorn , j. , taylor , k. , veilleux , s. & shopbell , p.l . 1994 , apj , 437 , l95 bochkarev , n.g . & sunyaev , r.a . 1977 , soviet astr . 21 , 542 ( originally 1975 , azh , 54 , 957 ) boggs , p.t . , byrd , r.h . & schnabel , r.b . 1987 , siam j. sci . & stat . computing , 8(6 ) , 1052 bosma , a. 1978 , university of groningen thesis . bowyer , s. 1991 , araa , 29 , 59 carignan , c. 1985 , apj , 299 , 59 carignan , c. 1991 , proc . workshop on dark matter , space telescope sci . carignan , c. & freeman , k.c . 1985 , 294 , 494 chabrier , g. , segretain , l. & mera , d. 1996 , apj , 468 , l21 charlot , s. & silk , j. 1995 , apj , 445 , 124 corbelli , e. & salpeter , e.e . 1988 , apj , 326 , 551 corbelli , e. , schneider , s.e . & salpeter , e.e . 1989 , aj , 97 , 390 cowie , l.l . & songaila , a. 1986 , araa , 24 , 499 cruddace , r. 1974 , apj , 187 , 497 dehnen , w. & binney , j. 1997 , mnras , in press diaz , a.i . 1989 , in evolutionary phenomena in galaxies , eds . beckman & b.e.j . pagel ( cambridge : cambridge university press ) , 377 domggen , h. & mathis , j.s . 1994 , apj , 428 , 647 dopita , m.a . & sutherland , r. 1996 , apjs , 102 , 161 dove , j.b . & shull , j.m . 1994 , apj , 423 , 196 draine , b.t . & lee , h.m . 1984 , apj , 285 , 89 evans , n. & dopita , m.a . 1985 , apjs , 58 , 125 fadda 1996 , apj , 473 , 670 ferland , g. & mushotsky , r. 1984 , apj , 286 , 42 ferland , g. & netzer , h. 1983 , apj , 264 , 105 ferland , g. 1991 , cloudy code , osu internal report , 91 - 01 ferland , g. 1992 , apj , 389 , l63 freeman , k.c . 1993 , in physics of nearby galaxies : nature or nurture , ed trinh thuan ( paris : editions frontieres ) , p 201 . freeman , k.c . 1996 , in unsolved problems of the milky way , ed l. blitz and p. teuben ( dordrecht : kluwer ) , p 645 . grevesse , n. & anders , e. 1989 , in cosmic abundances of matter , ( new york : aip ) , p. 1 haardt , f. & madau , p. 1996 , apj , 461 , 20 halpern , j.p . & steiner , j.e . 1983 , apj , 269 , l37 haynes , m.p . & roberts , m.s . 1979 , apj , 227 , 767 henyey , l.g . & greenstein , j.l . 1941 , apj , 93 , 70 henry , r.c . 1991 , araa , 29 , 89 hogan , c.j . & weymann , r.j . 1987 , mnras , 225 , 1p jenkins , e.b . 1987 , in interstellar processes , eds . hollenbach & h.a . thronson ( dordrecht : reidel ) , 533 jura , m. 1980 , apj , 241 , 965 kawaler , s. 1996 , apj , 467 , l61 kamphuis , j. 1993 , phd , groningen kondratyev , k. ya . 1969 , in radiation in the atmosphere , academic press , new york & london koribalski , b. , whiteoak , j.b . & houghton , s. 1995 , pasa , 12 , 20 kurucz , r.l . 1979 , apjs , 40 , 1 lee , y .- w . 1993 , in the globular cluster - galaxy connection , eds . smith & j.p . brodie , asp . 48 , 142 liebert , j. , dahn , c.c . & monet , d.g . 1988 , apj , 332 , 891 lyon , j.g . 1975 , apj , 201 , 168 bania , t.m . & lyon , j.g . 1980 , apj , 239 , 173 maeder , a. 1990 , a&as , 84 , 139 malin , d.f . 1981 , j. phot . , 29 , 199 malin , d.f . 1983 , in astronomy with schmidt - type telescopes , ed . m capaccioli , iau coll . 78 , 57 ( reidel : dordrecht ) maloney , p. 1993 , apj , 414 , 41 martin , p.g . & rouleau , f. 1990 , preprint mathewson , d.s . & ford , v.l . 1984 , in structure & evolution of the magellanic clouds ( reidel : dordrecht ) , iau symp . 108 , 125 mathewson , d.s . , cleary , m.n . & murray , j.d . 1975 , apj , 195 , l97 mathis , j. 1986 , apj , 301 , 423 mathis , j. , rumpl , w. & nordsieck , k.h . 1977 , apj , 217 , 425 mihalas , d. 1972 , non - lte model atmospheres for b & o stars ( ncar - tn / str-76 ) miller , g.e . & scalo , j.m . 1979 , apjs , 41 , 513 molla , m. , ferrini , f. & diaz , a.i . 1996 , apj , 466 , 668 nordgren , t.e . , cordes , j.m . & terzian , y. 1992 , aj , 104 , 1465 olling , r.p . 1995 , 110 , 591 osterbrock , d.e . & martel , a. 1992 , pasp , 104 , 76 osterbrock , d.e . 1989 , astrophysics of gaseous nebulae & active galactic nuclei , univ . books pagel , b.e.j . 1989 , in evolutionary phenomena in galaxies , eds . beckman & b.e.j . pagel ( cambridge : cambridge university press ) , 201 puche , d. & carignan , c. 1991 , apj , 378 , 487 puche , d. , carignan , c. & van gorkom , j. 1991 , aj , 101 , 456 rand , r. 1997 , apj , 474 , 129 raymond , j. 1990 , apj , 365 , 387 reynolds , r.j . & cox , d.p . 1992 , apj , 400 , l33 rots , a.h . 1975 , a&a , 45 , 43 ryder , s. 1996 , pasa , 14 , 81 ryu , d. , olive , k.a . & silk , j. 1990 , apj , 353 , 81 salucci , p. & frenck , c.s . 1989 , mnras , 237 , 247 salpeter , e.e . 1955 , apj , 121 , 161 sargent , w.l.w . & steidel , c.c . 1990 , in baryonic dark matter , eds . d. lynden - bell & g. gilmore ( dordrecht : kluwer ) , 223 savage , b.d . & massa , d. 1987 , apj , 314 , 380 schommer , r. 1993 , aj , 105 , 97 sciama , d.w . 1995 , mnras , 276 , l1 sciama , d.w . 1996 , modern cosmology & the dark matter problem ( cambridge : cambridge univ . press ) shields , j.c . 1992 , apj , 339 , l27 slavin , j.d . , shull , j.m . & begelman , m.c . 1993 , apj , 407 , 83 smith , g.p . 1963 , bull . neth . , 17 , 203 sokolowski , j. 1994 , preprint ( unpubl . ) sokolowski , j. & bland - hawthorn , j. 1991 , pasp , 103 , 911 spyromilio , j. 1995 , mnras , 277 , l59 staveley - smith , l. 1990 , apj , 364 , 23 sutherland , r.s . & dopita , m.a . 1993 , apjs , 88 , 253 tarter , c.b . , tucker , w.h . & salpeter , e.e . 1969 , apj , 156 , 943 van albada , t.s . , bahcall , j.n . , begeman , k. & sancisi , r. 1985 , apj , 295 , 305 van gorkom , j. 1993 , in environment & evolution of galaxies , eds . shull & h.a . thronson ( kluwer : dordrecht ) , p. 345 veilleux , s. 1988 , phd thesis , u. c. santa cruz vogel , s.n . , weymann , r. , rauch , m. & hamilton , t. 1995 , apj , 441 , 162 wakker , b.p . 1991 , aa&as , 90 , 495 wood , p. 1990 , jrasc , 84 , 150 yelle , r.v . & roesler , f. 1985 , jgr , 90 , 7568 zaritsky , d. , smith , r. , frenk , c. , & white , s.d.m . 1997 , apj , 478 , 39 * fig . 1 . * [ b_four ] taurus-2 5 fields ( sw1 , sw2 , sw3 , sw4 ) superimposed on a @xmath50 image of ngc 253 . the blue line occurs at smaller galaxian radii compared with the h@xmath0 line in the same field . there are four distinct fields with two emission lines occurring in each . at the central position , the etalon was used at two different spacings which meant that we obtained line detections at four discrete positions . * 2 . * [ hi_four ] same as fig . 1 except that the taurus-2 fields have been superimposed onto a deep atnf hi map ( koribalski , whiteoak & houghton 1995 ) . the outermost hi contour corresponds to a column density of @xmath159 @xmath4 . * [ zoom ] a magnified image of part of the sw3 field in figs . 1 and 2 . the field of view is rotated so that the vertical axis lies parallel to the galaxy major axis . clumpy and h@xmath0 emission is clearly visible . what is not easily rendered is the diffuse emission between and at large off - axis angles to the major axis . notice the extremely faint galaxy continuum ( @xmath160 mag arcsec@xmath37 ) over much of the field . the bright arcs are atmospheric oh lines . * 4 . * [ spec1 ] the emission - line spectrum at the hi edge ( field sw3 in figs . 1 and 2 ) compared with the off - field spectrum . the difference of these spectra is shown below . remarkably , the line has a surface brightness comparable to the h@xmath0 surface brightness , as compared with solar - abundance hii regions where the ratio is an order of magnitude smaller . this result holds after removing the dense knots in fig . 3 . the azimuthally averaged galaxy continuum underlies the spectrum and corresponds to roughly @xmath161 23 mag arcsec@xmath37 below falling to 25 mag arcsec@xmath37 below h@xmath0 . the equivalent widths of the lines are 0.60aa and 1.8 respectively . * [ spec2 ] the emission - line spectrum for the field beyond the hi edge ( field sw4 in figs . 1 and 2 ) . as we did not get a matching sky exposure , the spectra are shown from binning over two different opening angles . the top spectrum results from binning over 25 about the major axis from the optical axis ; the lower spectrum arises from binning over the entire field . the difference of these spectra is shown below . the emission is clearly seen in the top spectrum and , indeed , in a high contrast image . this line is completely washed out in the lower spectrum . the h@xmath0 emission is just visible in the high contrast image , and does not begin to appear until we sum over the entire field . the difference has been taken after weighting the top spectrum for its lower signal to noise ratio . again , we see a very faint galaxy continuum spectrum which is roughly @xmath161 26 mag arcsec@xmath37 after azimuthal binning below the line dropping to @xmath161 27 mag arcsec@xmath37 below the h@xmath0 line . the equivalent widths of the lines are 7.8 and 9.9 respectively . * fig . 6 . * [ v_observed ] kinematic measurements along the major axis of ngc 253 deduced from vla hi , taurus-2 and lines . in @xmath61 , the original rotation curve of pcvg has been projected onto the sky with their inferred orbit inclination at each radius . three sets of measurements are shown : these represent the approaching side ( open circles ) , receding side ( squares ) , and from fitting to the full velocity field ( filled circles ) . in @xmath60 , we show pcvg s original curves where the data have been deprojected with the measured inclination at each radius . in @xmath51 , the solid line is the same curve as the squares in @xmath61 . the filled squares are the taurus-2 measurements ; the circles are the measurements . * fig . 7 . * [ v_model ] representative fits to the pcvg and taurus-2 data using a 3-component mass model ( disk , halo , gas ) . the contribution from the hi surface density ( dotted line ) is the same in all models . in @xmath61 , we adopt an exponential disk ( short - dashed line ) and choose an isothermal sphere for the spherical halo ( long - dashed line ) using the numerical approach developed by carignan ( 1985 ) . in @xmath60 , we have used the disk - halo models of dehnen & binney ( 1997 ) : the least - squares fit was carried out by w. dehnen . in @xmath51 , we have truncated the halo at a radius of 10 kpc to demonstrate a possible explanation for the last measured point . * fig . 8 . * [ white_dwarf ] the predicted emission measure versus @xmath50 surface brightness for an isothermal population of white dwarfs as a function of surface density . the solid lines are isotherms for white dwarf temperatures in the range @xmath162 k. the dashed lines are isochoric lines indicating variations in white dwarf surface density in steps of 0.5 in dex starting at 1 pc@xmath37 at the top . the arrow indicates the average emission measure and disk surface brightness upper limit at the edge of the hi disk . the filled circles are the expected contribution to the @xmath50 band flux and emission measure for the white dwarf population in the solar neighbourhood ( assuming that all photons are absorbed ) . the galactic disk is assumed to be 600 pc thick and the white dwarf radius is assumed to be 0.14 r@xmath163 . * fig . 9 . * [ sok1 ] the lower panel shows the relative ionization fraction of important neutrals and ions , where the front of the gas slab ( @xmath164 ) is ionized by a dilute radiation field ( @xmath165 ) . the middle panel shows the temperature and mean electron density structure within the slab . the top panel shows the normalized line emissivities and illustrates the relative dependence on electron temperature , electron density , and ionization fraction . * fig . 10 . * [ sok2 ] the dependence of five important line diagnostics on the strength of the radiation field and hydrogen column density . the solid lines are radiation bounded models where all ionizing photons are soaked up by the gas . also shown are matter bounded models where the slab has been truncated at 1 , 2 , 5 , 10 and 20 @xmath39 10@xmath166 @xmath4 . the observed line ratio / is a factor of 2.98 smaller than /(veilleux 1988 ) . 9 gives some appreciation for the distinct trends shown by different lines ( e.g. vs. ) .

the hi disks in sculptor galaxies extend to only about 1.2 although we have detected ionized gas to the limits of our survey out to 1.4 . the detections confirm that the rotation curve continues to rise in ngc 253 , as it appears to do for other sculptor galaxies from the hi measurements , but there is a hint that the rotation curve may fall abruptly not far beyond the edge of the hi disk .

in spiral galaxies , the hi surface density declines with increasing radius to a point where it is seen to truncate dramatically in the best observed cases . it was anticipated that if the ambient radiation field is sufficiently strong , there exists a maximum radius beyond which the cold gas is unable to support itself against ionization . we have now succeeded in detecting ionized gas beyond the observed hi disk in spirals . here , we report on our findings for the sculptor galaxy ngc 253 . the hi disks in sculptor galaxies extend to only about 1.2 although we have detected ionized gas to the limits of our survey out to 1.4 . this has important ramifications for spiral galaxies in that it now becomes possible to trace the gravitational potential beyond where the hi disk ends . the detections confirm that the rotation curve continues to rise in ngc 253 , as it appears to do for other sculptor galaxies from the hi measurements , but there is a hint that the rotation curve may fall abruptly not far beyond the edge of the hi disk . if this is correct , then it suggests that the dark halo of ngc 253 may be truncated near the hi edge , and provides further support for the link between dark matter and hi . the line ratios are anomalous with to h ratios close to unity . while metallicities at these large radii are uncertain , such enhanced ratios compared to solar - abundance hii regions ( / ) are likely to require selective heating of the electron population without further ionization of n . we discuss the most likely sources of ionization and heating , and the possible role of refractory element depletion ( e.g. ca , si , fe ) onto dust grains .

1402.0195

i

polymer knots and links ( see ref . @xcite for a definition of knots and links ) have been actively studied since the discovery of interlocked polymer rings in dna in 1961 by frisch and wasserman @xcite . after then , linked dna molecules were identified in hela cell in 1967 @xcite . it has also been found that the probability that open circular dna molecules link with supercoiled molecules is quite large @xcite . also in the production of artificial knots and catenanes there has been a fast progress . the first artificial polymer knot , a trefoil , has been synthetized in 1989 @xcite . more recently , experiments have shown that bacterial dna often occurs in the form of knots that are sometimes heavily linked together . for example , dna molecules extracted from tailless mutants of phage p4 vir 1 del22 are highly knotted ( 95% ) @xcite . the mitochondrial dna of trypanosomes and related parasitic protozoa consists of networks of thousands of topologically interlocked dna rings @xcite . this abundance of knot and links in cells occurs because the probability of knotting increases with the degree of confinement @xcite . besides , a new mechanism of link formation in dna has been detected @xcite . due to the progress of technology , the thermal and mechanical properties of polymer knots and links can now be studied experimentally . the mechanical properties of single polymer knots have been investigated for almost two decades with the help of optical tweezers and atomic force microscope tips . it has been discovered in this way that polymer strands containing knots are much more breakable under tension than straight filaments @xcite . moreover , since a few years also the collective behavior of many polymer rings is accessible to experiments . the thermal properties of macromolecules forming knots and links may be analyzed using calorimetric techniques . for instance , in polymer fibers the presence of knots is revealed by irregularities in the thermogram @xcite . in artificial polymer materials , the existence of knots and links affects dramatically the viscoelastic properties of polymers . in @xcite melts composed by entangled polymer rings of an unprecedented purity , i. e. containing only a small fraction of linear chains , have been obtained . it has been found by observing the power law stress relaxation of these melts that they have a much lower viscosity than those containing linear polymers , of about one order of magnitude less . what it is interesting , is that even a very low amount of linear open chains inside the melt is able to introduce relevant influence in the viscosity . for that reason , polymer knots and links in artificial materials can be used to fine tune the elastic behavior of the produced materials in industrial applications . the rheological properties of polymer melts of rings are actively studied in connection with their significant implications to our understanding of polymer dynamics . the mechanical properties of systems containing a few polymer rings entangled together under the tensions exerted by external forces play a relevant role also in the physics of dna . more experimental results will come in the future thanks to more and more refined techniques of synthesis and separation of knotted polymers . already now , the formation of polymer knots and the effects of the topology in the intramolecular interactions can be investigated experimentally , see e. g.@xcite . the experiments mentioned above allow the comparison between the observations and the predictions coming from theoretical models . for this reason , they have attracted the interest of the community of theoretical physicists . theoretical models in turn provide a microscopic understanding of what is observed and can point out the directions of the future experimental research . many approaches to what can well be called the problem of topological entanglement in polymer physics have been proposed . as a matter of fact , polymers are already complex systems by themselves . when they are further knotted and linked together , to this complexity one should also add the topological complexity . this makes the treatment of systems containing polymer knots and links very hard . the reward for solving this problem and achieving a better understanding of polymer melts and materials composed by topologically entangled polymer rings will be huge . the formation of links and knots can result in fact in important effects in the physical behavior of polymer materials , see ref . @xcite for a review and further bibliography of this subject . in describing the topological entanglement of polymer rings , it is possible to take advantage of the progresses made in the previous century in the classification of knots and links . in particular , one should mention in this respect the construction of powerful knot and link invariants like the polynomials of alexander , homfly and conway or the invariants of arf - casson , vassiliev kontsevich and several others . following the seminal work of witten @xcite it has been possible to derive expressions of knot and link invariants using a particular class of field theories that are denominated topological . to convince oneself that the abstract methods of knot theory really matter in practical applications , it is sufficient to mention the example of the dna recombination procedure , during which the topology of dna can be changed . the changes are performed by particular enzymes called topoisomerases . the action of these proteins can not be observed directly , but it may be analyzed by the methods of knot theory , that have been indeed successfully applied in order to classify the effects of the topoisomerases @xcite . in polymer physics there has been always a nice interplay between experiments and theoretical approaches , both numerical and analytical . perhaps the most important example of this is provided by the works of de gennes and coworkers @xcite , that have led to a satisfactory understanding of the behavior of polymers in a solution thanks to the use of renormalization group techniques . a similar interplay occurs also in the research on polymer rings subjected to topological entanglement . the formation of knots in polymer systems is probably the most well studied subject of the statistical mechanics of polymer knots . it can be tackled analytically by means of renormalization group methods . nowadays there is a good agreement between analytical and numerical estimations of how the probability of formation of a knot of a given type scales with the length of the polymer @xcite . numerical simulations on this subject have been started already in the mid - seventies with the pioneering works @xcite . analytical methods are also able to predict the various scaling laws that characterize the asymptotic behavior of observables like the gyration radius . moreover , links between pairs of polymers can be analytically modeled by using as the knot invariant that takes into account the topology the gauss linking number . the model can be case in the form of a ginzburg - landau field theory which is similar to those appearing in the physics of critical systems . its main characteristic is that the scalar fields creating and annihilating the monomers of the polymer trajectories are coupled with an abelian bf model . the latter is a topological field theory and describes the `` reaction forces '' due to the presence of the topological constraints . these constraints are necessary because , physically , two polymer trajectories can not penetrate themselves unless the temperature is so high that the polymer melts down to single monomers or there are enzymes like the topoisomerases that allow the opening and the successive gluing back of the trajectories . it is intriguing the fact that bf models are invariant under parity and time reversal transformations and have been used for this reason as effective field theories in the description of high @xmath0 superconductors and topological insulators . with the help of the topological ginzburg landau model mentioned above it has been possible to formulate concrete predictions on the behavior of linked polymers . first of all , it has been shown that the presence of the topological constraints on the polymer rings does not affect their critical behavior @xcite . nevertheless , it affects the excluding volume interactions between the monomers by weakening them @xcite . the results of @xcite are valid in the approximation in which the monomer density is high and almost constant apart from small fluctuations . let us note that attractive forces associated to topological constraints have effectively been observed in an experiment @xcite . reviews on analytical methods can be found in @xcite and in kleinert s book @xcite . besides analytical calculations , very reliable numerical simulations allow to understand the behavior of polymer systems observed during experiments . a wealth of publications has been dedicated to the applications of polymer knots and links in biology and biochemistry , like for instance @xcite . more and more complex problems are solved . examples are the recent advances in understanding the behavior of knotted proteins under stretching @xcite and the breakability of physical knots @xcite . moreover , numerical simulations have shown that in localized knots as those studied in @xcite , the weakest points in the polymer strands are located at the two points in which the knot starts and ends @xcite . also numerical studies of the diffusion of polymer knots in gels have been able to reproduce the experimental results @xcite . let us remember that these studies are relevant for the particular application of the phenomenon of gel electrophoresis , that allows to extract polymer knots of given types out of a mixture of polymer rings , e. g. dna byproducts , having different topological configurations . the thermal properties of polymer knots in the stretched regime have been investigated very recently in @xcite . the latter works will be described in the next sections . very recently , some important advances in the statics and dynamics of polymer rings with or without entanglement have appeared in the literature @xcite . numerical simulations are also important to investigate phenomena that are hardly accessible by experiments . for instance , despite the progress in understanding the viscoelastic properties of melts of polymer rings mentioned above , it is still difficult to isolate possible effects due to the presence in the melt of knots or links . the rest of the paper is organized as follows . a short review on numerical approaches for treating the topological constraints of polymer knots is contained in section [ aaa ] . in section [ sectionpaeatici ] , we present two fast techniques , namely the paea and tici methods , which have been proposed in @xcite in order to preserve the topology of a polymer knot during the sampling procedure . the sampling is performed with the help of the wang - landau monte carlo algorithm , which is summarized in section [ sectionfd ] . the paea and tici methods allow the sampling of a huge set of knot conformations as it is required in the investigation of the thermal properties of unstretched polymer knots . some of the results obtained with these methods are discussed in section [ bbb ] . the original part of this work can be found in section [ sectionfd ] , where the conclusions are drawn and some further developments in the treatment of polymer knots with a large number of segments are presented .

in the first part of this work a summary is provided of some recent experiments and theoretical results which are relevant in the research of systems of polymer rings in nontrivial topological conformations . next , some advances in modeling the behavior of single polymer knots are presented . the numerical simulations are performed with the help of the wang - landau monte carlo algorithm . to sample the polymer conformation a set of random transformations called pivot moves is tackled with the help of two new techniques which are briefly explained . as an application , , original results are discussed concerning the use of parallelized codes to study polymers knots composed by a large number of segments within the wang - landau approach .

in the first part of this work a summary is provided of some recent experiments and theoretical results which are relevant in the research of systems of polymer rings in nontrivial topological conformations . next , some advances in modeling the behavior of single polymer knots are presented . the numerical simulations are performed with the help of the wang - landau monte carlo algorithm . to sample the polymer conformation a set of random transformations called pivot moves is used . the crucial problem of preserving the topology of the knots after each move is tackled with the help of two new techniques which are briefly explained . as an application , the results of an investigation of the effects of topology on the thermal properties of polymer knots is reported . in the end , original results are discussed concerning the use of parallelized codes to study polymers knots composed by a large number of segments within the wang - landau approach .

1401.0265

i

consider an observable , discrete - time stochastic process @xmath0 , @xmath1 , a latent and unobserved discrete - time stochastic process @xmath2 , @xmath3 , a parameter @xmath4 and i.i.d . sequence of random variables @xmath5 , @xmath6 , whose distribution can depend upon @xmath7 ( @xmath8 ) . this article is concerned with the class of statistical models , for @xmath9 , @xmath10 @xmath11 where @xmath12 , @xmath13 , @xmath14 is assumed null , which induces a joint lebesgue ( assumed for simplicty of presentation ) density of the model @xmath15 where we use @xmath16 to denote conditional and joint probability densities w.r.t . lebesgue measure and @xmath17 will denote the associated distribution . this collection of models is rather flexible and contains : 1 . i.i.d . models , when @xmath18 is null and @xmath19 does not depend on @xmath20 2 . observation - driven time series models ( odts ) ( e.g. @xcite ) , when @xmath18 is null 3 . hidden markov models ( hmms ) ( e.g. @xcite ) , when @xmath18 follows a markov chain and @xmath19 does not depend on @xmath20 4 . some non - linear time series models ( e.g. @xcite ) , such as causal and invertible bilinear time series models @xcite ( when @xmath18 is null ) . the class of models is quite large and includes many popular classes including some garch models ( @xcite ) , stochastic volatility models ( e.g. @xcite ) and partially observed markov jump process models ( e.g. @xcite ) . the list of applications is numerous ranging from economics , biology and engineering ; the reader is referred to the afore mentioned references for specific applications and details . the particular scenario of interest in this article is when one can exactly sample the process @xmath5 and evaluate for @xmath9 , @xmath19 , but that the density function @xmath21 is unknown up - to a positive and unbiased estimate ( this can occur see @xcite ) ; we will call the likelihood intractable . if the density function @xmath21 is known up - to a positive and unbiased estimate and suppose that this estimate is @xmath22 for some random variables @xmath23 where @xmath24= \prod_{i=1}^n p_{\theta}(y_i|y_{1:i-1},x_i)$ ] ( the expectation is w.r.t . the law of @xmath23 ) , then the approximation schemes we will discuss are not always needed as exact ( possibly monte carlo - based ) inference procedures are possible . later in the article , we will consider cases when @xmath25 is intractable in some way , but for now , we will assume , when it is in the model , that this density is known point - wise up - to a constant . we also remark , in section [ sec : approx ] , we will show that if one can evaluate the density of the noise terms @xmath26 then , indeed one does not require the ability to sample the @xmath27 . for the class of problems of interest , for either likelihood - based or bayesian inference methods , the complexity of the model is such that even when using advanced methods such markov chain monte carlo ( mcmc ) or sequential monte carlo ( smc ) exact statistical inference is seldom possible . one of the standard solutions to this problem is to introduce an approximation of the statistical model and an often adopted approach is that of using approximate bayesian computation , especially when taking a bayesian perspective to statistical estimation ; see for instance @xcite for a recent overview . before continuing , it is noted that the scenario of intractable likelihoods will occur in many applications . perhaps the most common is when @xmath5 is distributed according to a model which can be simulated , but @xmath28 is not known ; a good example is the stable distribution - this would find applications for i.i.d . models and hmms ( see @xcite ) applied in finanical contexts where the heavy tails of these distributions are a realistic modelling choice . other models used in practice include the lotka - voltera model @xcite used for stochastic - kinetic networks and the @xmath29 distribution used for ` non - standard ' data @xcite . suppose that one places a prior density @xmath30 on @xmath31 , the standard abc approximation ( see e.g. @xcite ) of the posterior associated to the likelihood in : @xmath32 is to take , for @xmath33 : @xmath34 where @xmath35 are _ auxiliary _ data , @xmath36 is as , @xmath37 is a _ summary _ of the data , @xmath38 is _ distance _ on the summary statistics . if the summary statistics are sufficient for the data , then one can show ( under minimal assumptions ) that as @xmath39 that the ( marginal ) abc posterior @xmath40 is in some sense exactly @xmath41 . it is remarked that if @xmath42 is countably infinite ( we assume this is not the case ) , then it is possible to take @xmath43 and if @xmath44 is sufficient , this leads to _ exact _ inference as proposed in @xcite . we note that the indicator function is used in , but it can be replaced with a kernel density ; we focus upon indicator functions in this article . the approximation is particularly amenable to inference , in that , in the framework of this article one can sample @xmath45 exactly from the true model ; this fact is very useful in that it would allow one to apply a number of computational algorithms such as rejection sampling , importance sampling , mcmc or smc ( this explained in detail later in the article ) . the problems with this approximation include : * if the statistics @xmath46 are not sufficient , one does not always recover the exact posterior , even if @xmath43 . this can make it difficult to characterize , mathematically , the bias in approximation . selecting summary statistics can then be challenging , although , there are approaches such as @xcite . * in many practical models , there is a trade - off between making @xmath47 small ( accuracy of the approximation ) and allowing a computational method to work well ( accuracy in computation ) . the approximation does not often help this former trade - off due to the factor @xmath48 , which may mean that @xmath47 has to be relatively large for a computational algorithm to produce reliable results . for example in a rejection algorithm which samples @xmath49 from @xmath50 the acceptance probability is @xmath48 ; if @xmath51 is large one may need to make @xmath47 quite large to yield reasonable acceptance rates . * in the context of this article , does not retain the probabilistic structure of the model . for example one does not have @xmath52 for some probability density @xmath53 . the issue with this is that the techniques of inference for the original model ( e.g. for hmms one often uses smc methods ) can not be used , without modification , which creates an additional difficulty . another issue is that a theoretical study of the abc approximation may be far more difficult than is the case when the probabilistic structure of the model is retained . although there are several results in the literature ( e.g. @xcite ) one could argue that a more precise analysis could be undertaken by retaining the structure of the model . the points here have been made in many other articles including @xcite . thus our objective is to use a different abc approximation which , to an extent , can deal with some of the deficiencies raised here . we note that there are a great deal of extensions of the standard abc approach ( such as regression adjustment @xcite ) , but the argument made in this article , is that the approximation to be reviewed and developed here , is very reasonable , especially for the case when @xmath54 is low to moderate . the abc - based approximation we consider is as follows , which can deal with some of the issues outlined above @xmath55 where @xmath56 and @xmath57 typically , one needs to be able to evaluate the abc posterior pointwise up - to a normalizing constant ( for example for monte carlo algorithms ) which is often not the case for @xmath40 . _ one particular choice _ is to define an abc posterior on an extended state - space from @xmath58 to @xmath59 , setting @xmath60 the probabilistic structure in is retained in . we note that the issue in the second bullet point for problems of standard abc approximations is dealt with to an extent ; it breaks the global dependence ( on the data i.e. the factor @xmath48 ) into a collection of smaller and possibly easier to handle ( from a computational perspective ) sub - problems ( i.e. the factors @xmath61 ) . this type of approximation has been studied in various special cases in @xcite , the actual intepretation will allow one , as we will explain later on in this article , to perform asymptotically in @xmath51 ( for some classes of models and under some assumptions and modifications ) consistent parameter estimation when taking a likelihood based ( i.e. trying to optimize @xmath62 $ ] ) or bayesian approach to this task . the approximation does not use any summary statistics ; this is only an option if @xmath54 is small to moderate - this latter scenario is sufficiently rich in that one does not always attempt to fit the original model ( i.e. approximation is not needed ) if this were not the case . this article will consider the abc approximation for a variety of special cases ( that is , the models 1.-3 . mentioned above ) . we will review and discuss both the inferential aspects associated to this approximation ( such as consistency in parameter estimation , bias and so fourth ) and the computational methods that can be used to fit the models . several original remarks are made along the way . it is remarked that a comprehensive comparison of ( some ) computational methods for abc approximations posteriors based upon and those based upon can be found in @xcite . the article is structured as follows . in section [ sec : rem_abc ] we investigate our abc approximation in more details , discuss the notion of abc and some alternative approximation schemes . in section [ sec : models ] we consider three classes of models which include i.i.d . models , odts models and hmms . we discuss the abc approximation and adjustments which can allow one to perform asymptotically consistent parameter estimation . in section [ sec : comp ] we give a variety of computational methods which can be used to fit the particular abc approximations discussed in section [ sec : models ] . we mainly consider smc and mcmc methods , of which we assume the reader has some familiarity . other approaches such as expectation - propagation are also considered . in section [ sec : summary ] the article is concluded and future research work is discussed . the appendix houses some proofs and assumptions of some propositions which are given in the article .

in the following article we consider approximate bayesian computation ( abc ) for certain classes of time series models . in particular , we focus upon scenarios where the likelihoods of the observations and parameter are intractable , by which we mean that one can not evaluate the likelihood even up - to a positive unbiased estimate . this paper reviews and develops a class of approximation procedures based upon the idea of abc , but , specifically maintains the probabilistic structure of the original statistical model . this idea is useful , in that it can facilitate an analysis of the bias of the approximation and the adaptation of established computational methods for parameter inference . + * keywords * : approximate bayesian computation ; hidden markov model ; observation driven time series . * + e-mail:`staja@nus.edu.sg `

in the following article we consider approximate bayesian computation ( abc ) for certain classes of time series models . in particular , we focus upon scenarios where the likelihoods of the observations and parameter are intractable , by which we mean that one can not evaluate the likelihood even up - to a positive unbiased estimate . this paper reviews and develops a class of approximation procedures based upon the idea of abc , but , specifically maintains the probabilistic structure of the original statistical model . this idea is useful , in that it can facilitate an analysis of the bias of the approximation and the adaptation of established computational methods for parameter inference . several existing results in the literature are surveyed and novel developments with regards to computation are given . + * keywords * : approximate bayesian computation ; hidden markov model ; observation driven time series . * approximate bayesian computation for a class of time series models * by ajay jasra department of statistics & applied probability , national university of singapore , singapore , 117546 , sg . + e-mail:`staja@nus.edu.sg `

0909.3349

i

the acceleration of cosmic rays up to @xmath1 ev has been attributed to supernova explosions and tev emission is expected from the remnants @xcite . the standard diffusive shock particle acceleration ( dsa ) model has been successful in explaining emissions from most supernova remnants @xcite . investigations of acceleration by a spectrum of turbulent plasma waves , the so - called stochastic particle acceleration ( sa ) , also have a long and resilient history @xcite . most authors prefer the use of relativistic leptons to account for the nonthermal radio , x - rays , and tev emissions from the remnants . the tev emission has also been attributed to energetic protons and ions @xcite . although the dsa can naturally give a universal power - law energetic particle distribution with the spectral index determined by the shock compression ratio for a linear model , it requires well - defined shock structure and efficient scatter of high - energy particles by small - scale turbulence @xcite . the initial acceleration of low - energy particles to a high enough energy for the shock to be effective , the so - called injection problem , is likely due to the sa by turbulence . @xcite showed that the sa by small - scale alfvn waves can be more efficient than the first order fermi acceleration by shocks . @xcite derived approximate diffusion coefficients and showed that stochastic interactions of particles with a spectrum of plasma waves can lead to efficient particle acceleration . over the past few decades , the sa has also been explored for broader astrophysical applications ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the essential challenges to the sa model are a self - consistent treatment of the nonlinear turbulence spectral evolution and the requirement of the same energy dependence of the acceleration and escape timescales for the production of a power - law particle distribution @xcite . recently gibbsian theory has been generalized to account for power - law distributions in marginally stable gibbsian equilibria @xcite . it remains to be shown how the physical processes of the sa are related to the ordering parameter @xmath2 of this statistics . most previous studies assume isotropic magnetohydrodynamic ( mhd ) waves for the turbulence @xcite . the anisotropy of the turbulence caused by cascade and damping processes has been considered recently @xcite . in particular , @xcite show that the scatter and acceleration rates of charged relativistic particles by fast - mode waves in a high-@xmath3 plasma may be much higher than those given by the standard quasi - linear theory with an isotropic wave power spectrum . over the past few years , detailed radio , x - ray , @xmath0-ray , and tev observations of a few shell - type tev supernova remnants ( sttsnrs ) pose several challenges to the classical dsa model in the hadronic scenario , where the tev emission is produced through neutral pion decays induced by proton - proton scatter @xcite . besides requiring efficient amplification of the magnetic field in the upstream plasma and a good correlation between the magnetic field and background plasma density @xcite , the model also implies a cosmic ray energy of @xmath4 ergs for each remnant and an electron acceleration efficiency more than 4 orders of magnitude lower than the ion acceleration efficiency @xcite . the high density of the upstream plasma in the model also implies significant thermal x - ray emission from the downstream , which may exceed the observed upper limit @xcite . a very hard proton spectrum is also required to fit the @xmath0-ray spectrum obtained recently with the _ fermi _ @xmath0-ray telescope @xcite . although these kinds of remnants may be atypical , detailed modeling can still have profound implications for our understanding of supernova shocks @xcite . in a previous paper , we showed that the sa of electrons by turbulent plasma waves in the shock downstream might naturally explain these observations @xcite . turbulence is expected given that the size of these remnants are many orders of magnitude larger than the dissipation scale of the ion inertial length @xcite . the dsa model proposes that particle acceleration occurs directly and predominantly at the ion inertial length or gyro - radius @xcite . this requires the absence of instabilities over a large range of spatial scales , which is highly idealized . @xcite showed that density fluctuations in the upstream can be amplified significantly by shock waves , resulting in strong turbulence in the downstream . magnetized turbulence appears to be a more generic and natural energy dissipation channel than the short - length - scale shock fronts ( sf ) . with the leptonic model , the tev emission is mostly produced by the inverse comptonization of the cosmic microwave background radiation by tev electrons @xcite . the magnetic field required to reproduce the observed x - ray flux by the same tev electrons through the synchrotron process implies a spectral cutoff in the hard x - ray band , which is in agreement with observations . the sa model also requires a much lower gas density than the dsa model , which not only explains the lack of thermal x - ray emission from the shell of the remnants , but also reduces the energetics of the supernovae . the required turbulence generation scale is comparable to the size of the observed x - ray filaments as well @xcite . the fast variability of small x - ray features may be attributed to rapid spatial diffusion of high energy electrons @xcite . as we will show in this paper , the agreement between preliminary results from _ fermi _ observations and the model prediction is also impressive @xcite . the sa by fast - mode waves has been studied by several authors @xcite . both resonant and nonresonant interactions have been considered . in this paper , we consider the nonresonant acceleration by compressional waves first studied by @xcite . compared with these original studies , our model has several distinct features : 1 ) most of the dissipated fast - mode turbulence energy is absorbed by thermal background ions ; 2 ) the residual fast - mode waves in the dissipation scales propagate along local magnetic fields and preferentially accelerate electrons in the background plasma ; 3 ) the plasma physics processes in the dissipation range in principle may lead to a self - consistent treatment of the electron injection process at low energies ; 4 ) the scatter mean - free - path of relativistic electrons , which is a free parameter in most of the previous studies , is determined by the characteristic length of the magnetic field , which in a high-@xmath3 plasma is reduced by strong turbulence motions significantly ; 5 ) the high - energy cutoff of the particle distribution is tied to the characteristic length of the magnetic field . in this paper , we first discuss the sa by decaying turbulence in general and show that fast - mode waves may account for observations of a few sttsnrs ( section [ ts ] ) . in section [ shock ] , we present the structure of the downstream turbulence with both the kolmogorov and kraichnan phenomenology for the turbulence cascade . the transit - time damping ( ttd ) by the thermal background particles of compressional fast - mode turbulence is considered in the dissipation range . the stochastic acceleration of relativistic electrons by fast - mode wave turbulence in the subsonic phase is discussed in section [ sa ] , where physical processes determine the acceleration of the highest energy electrons are discussed . the models are applied to the well - observed tev snr rx j1713.7 - 3946 in section [ application ] . although the inferred plasma density is much lower than that in the hadronic scenario , some models still have significantly higher densities than that derived from _ xmm - newton _ observations @xcite . in section [ disc ] , we discuss how the density may be further reduced by considering the turbulence generation processes and first - order fermi acceleration in the supersonic phase . conclusions are drawn in section [ con ] .

in the leptonic scenario for tev emission from a few well - observed shell - type tev supernova remnants ( sttsnrs ) , very weak magnetic fields are inferred . if fast - mode waves are produced efficiently in the shock downstream , we show that they are viable agents for acceleration of relativistic electrons inferred from the observed spectra even in the subsonic phase , in spite that these waves are subject to strong damping by thermal background ions at small dissipation scales . the turbulence evolution is modeled with both the kolmogorov and kraichnan phenomenology . processes determining the high - energy cutoff of nonthermal electron distributions are examined . the kraichnan models lead to a shallower high - energy cutoff of the electron distribution and require a lower downstream density than the kolmogorov models to fit a given emission spectrum . with reasonable parameters , the model explains observations of sttsnrs , including recent data obtained with the _ fermi _-ray telescope . more detailed studies of the turbulence generation and dissipation processes , supernova explosions and progenitors are warranted for better understanding the nature of supernova shocks . [ firstpage ] acceleration of particles mhd plasmas shock waves turbulence ism : supernova remnants .

in the leptonic scenario for tev emission from a few well - observed shell - type tev supernova remnants ( sttsnrs ) , very weak magnetic fields are inferred . if fast - mode waves are produced efficiently in the shock downstream , we show that they are viable agents for acceleration of relativistic electrons inferred from the observed spectra even in the subsonic phase , in spite that these waves are subject to strong damping by thermal background ions at small dissipation scales . strong collisionless non - relativistic astrophysical shocks are studied with the assumption of a constant aflvn speed in the downstream . the turbulence evolution is modeled with both the kolmogorov and kraichnan phenomenology . processes determining the high - energy cutoff of nonthermal electron distributions are examined . the kraichnan models lead to a shallower high - energy cutoff of the electron distribution and require a lower downstream density than the kolmogorov models to fit a given emission spectrum . with reasonable parameters , the model explains observations of sttsnrs , including recent data obtained with the _ fermi _-ray telescope . more detailed studies of the turbulence generation and dissipation processes , supernova explosions and progenitors are warranted for better understanding the nature of supernova shocks . [ firstpage ] acceleration of particles mhd plasmas shock waves turbulence ism : supernova remnants .

1512.02428

i

neutron stars ( nss ) are compact rotating relativistic objects . rotation allows nss to harbor inertial oscillation modes , the most interesting representatives of which are r modes . as it was shown by @xcite and @xcite , in the absence of dissipation r modes are subject to a gravitational driven instability ( the cfs instability ) at _ any _ ns spin frequency @xmath0 . an account for dissipative processes stabilizes nss to some extent , resulting in the appearance of the so called `` instability window '' in the @xmath1 @xmath0 plane , where @xmath1 is the redshifted internal stellar temperature . a typical instability window is shown in panel ( a ) of fig . [ fig : inst1 ] . in the region filled with gray nss are stable ( we call it `` stability region '' ) , in the white region they are unstable ( it is `` instability window '' ) . observations of nss in low mass x - ray binaries ( lmxbs ) revealed that many nss fall well outside the stability region ( see circles with error bars in panel ( a ) of fig . [ fig : inst1 ] and @xcite ) . at the same time , ns evolution models predict that a probability to find an ns in the instability window is negligibly small ( @xcite ) . this apparent contradiction was addressed in a number of papers ( e.g. , @xcite ) which attempted to reconcile theory with observations ( see @xcite for a short review of the existing ideas ) . in this paper we explore observational consequences of one such idea ( @xcite ) which , as we believe , allows one to explain the existing observations rather naturally . @xcite argued that a simultaneous account for superfluidity of nucleons in the cores of nss and finite - temperature effects substantially modifies the ns oscillation spectra and leads to a resonance interaction of r mode with superfluid inertial modes at some certain ns temperatures @xmath2 ( called `` resonance temperatures '' in what follows ) . this resonance interaction stabilizes r modes in the vicinity of @xmath2 . as a result , stability peaks appear in the @xmath3 plane . a typical instability window constructed allowing for the resonance interaction of the modes is demonstrated in panel ( b ) of fig . [ fig : inst1 ] ( the figure is taken from @xcite where it is discussed in detail ) . the evolution track of an ns in such instability window was studied by @xcite and is shown here by the solid thick line . it was found by @xcite that an ns spends substantial amount of time climbing up the left edge of the stability peak so that the probability to find it there is high . this presents a natural explanation for the existence of numerous nss in the region that was thought to be unstable with respect to r - mode excitation they climb up the stability peak . detailed analyzes of the evolution track revealed ( @xcite ) that it undergoes small oscillations ( in what follows we will call them @xmath4-oscillations ) near the edge of the peak ( unresolved on the scale of fig . [ fig : inst1 ] ) . these oscillations can , in principle , be detected and this paper discusses their possible observational manifestations . the paper is organized as follows . in section [ sec : generalequations ] we present basic equations governing evolution of nss in lmxbs , then in section [ sec : equations ] we analyze @xmath4-oscillation properties of a star climbing up / down the stability peak . in section [ sec : parameters ] we estimate different parameters of @xmath4-oscillations ( e.g. , oscillation period ) . section [ subsec : timing ] analyzes peculiar timing behavior of an ns attached to the stability peak . in section [ subsec : gravrad ] we discuss whether gravitational radiation from such stars can be detected . section [ sec : evidences ] inspects existing observations . we conclude in section [ sec : conclusions ] . plane , where @xmath5 . a region where nss are stable ( i.e. r - modes are not excited ) is filled with grey . circles with error bars show observational data for nss in lmxbs with measured @xmath0 and estimated @xmath1 . panel ( b ) presents an example of the instability window ( figure 5 of @xcite ) plotted allowing for the resonance interaction of r mode with superfluid inertial modes . the stability peak cd appears because of this interaction . evolution of the spin frequency @xmath0 and internal redshifted temperature @xmath1 is shown by thick solid line ( the track @xmath6 ) . see @xcite for more details . , width=576 ]

in the recent papers by a new scenario describing evolution of rapidly rotating neutron stars in low - mass x - ray binaries was proposed . the scenario accounts for a resonant interaction of normal r modes with superfluid inertial modes at some specific internal stellar temperatures ( `` resonance temperatures '' ) . [ firstpage ] stars : neutron stars : interiors pulsars

in the recent papers by a new scenario describing evolution of rapidly rotating neutron stars in low - mass x - ray binaries was proposed . the scenario accounts for a resonant interaction of normal r modes with superfluid inertial modes at some specific internal stellar temperatures ( `` resonance temperatures '' ) . this interaction results in an enhanced damping of r mode and appearance of the `` stability peaks '' in the temperature spin frequency plane , which split the r - mode instability window in the vicinity of the resonance temperatures . the scenario suggests that the hot and rapidly rotating nss spend most of their life climbing up these peaks and , in particular , are observed there at the moment . we analyze in detail possible observational signatures of this suggestion . in particular , we show that these objects may exhibit ` anti - glitches ' sudden frequency jumps on a time scale of hours - months . [ firstpage ] stars : neutron stars : interiors pulsars

hep-ph9707380

c

in a universe with domains which can have different values of some of the underlying parameters , life may only be able to develop in some of those domains . if this is the case , we would expect that the parameters of our domain should be typical of anthropically allowed range . if the anthropic principle accommodates such a large range that our values of the parameters are unnaturally small within this range , then the anthropic principle fails to help us understand the sizes of these parameters . however , we have found that within the overall structure of the standard model there is a relatively small acceptable range for the higgs parameter @xmath0 and the light quark masses . the physical values of these parameters are quite typical of this range , raising the possibility that the anthropic principle could be an explanation " of these magnitudes . the arguments behind this conclusion are summarized in fig . 1 . for @xmath0 negative , as in our universe , it seems that the whole range of values for the vacuum expectation value from @xmath275 down to about @xmath276 ( or perhaps even down to @xmath277 ) times the value in our universe can be excluded . for most of that range ( down to about @xmath278 ) the universe would consist of sterile , helium - like atoms whose nuclei were @xmath135 . there would be essentially no reactions either chemical or nuclear . for the lower part of the excluded range , there would be virtually no nuclei other than protons , and the @xmath279 and @xmath280 processes that are needed for nucleosynthesis would be endothermic as the deuteron would not be stable . for positive values of @xmath0 the condition that baryons still exist at the time biochemistry becomes possible forces @xmath0 to be many orders of magnitude smaller than the natural " planck scale . our arguments for smaller values of @xmath0 are less certain . it may be that long range nuclear forces cause all baryons to clump into superheavy nuclei with small charge , which does nt appear to be promising for life . if these forces are screened in a mesonic plasma , then light nuclei will continue to exist , and can burn in stars , and stars may ignite at sufficiently late times to fuel life . individual stars , however , will be extremely short lived compared to the cosmological time scales . if life is to develop in such a universe , the energy source is not likely to be the photoluminescence of an individual star . one can thus plausibly argue that for life to exist the @xmath0 parameter has to be negative and has to be close to the value it has in our universe . one of the interesting features of this argument is that it explains as no other approaches do at present the curious fact that the weak scale is near to the qcd scale . in order for protons and neutrons ( rather than @xmath135 ) to be the lightest baryons , @xmath281 has to be less than the chromodynamic energy which splits the baryon decuplet from the octet . for the deuteron to have large enough binding energy to save neutrons from virtual extinction in the early universe and also to allow the @xmath279 reactions to be exothermic , the pion has to have a long compton wavelength compared to the nucleon , and this in turn means that the @xmath78 and @xmath79 masses have to be not only less than but small compared to the qcd energy scale by about the amount seen in nature . this provides a possible resolution to the `` fine - tuning problem '' in an ensemble of different domains of the universe , the higgs mass parameter will occasionally fall into the anthropically allowed region without having to be fine - tuned in general . if the cosmological constant is confirmed to have a non - zero value close to present estimates , and no new physics is found in the tev energy region , we may be faced with de - facto evidence for the presence of fine - tuning . in such a situation , the anthropic or multiple - universe considerations become highly attractive . finally , let us comment on the ability of these ideas to be tested . negatively , we can say that if the weak scale is what it is for anthropic reasons , there would be no need to invoke supersymmetry or technicolor or other structure at the weak scale to make the fine - tuning natural " [ 1 ] . if no such structure is found , then , it would be a point in favor of anthropic explanations ; indeed , in that case there would be few if any alternatives to an anthropic explanation . positive evidence is harder to come by . of course , we are not able to explore other domains in the universe . however , theories which generate multiple domains may be testable by other , more conventional means . for example , the community is hoping to be able to test the details of inflationary theories through cosmological measurements . likewise , direct physical experimentation has the potential to eventually sort out the correct underlying theory . through standard means we may be able to learn if the fundamental theory in fact produces multiple domains , in which case anthropic considerations automatically become relevant . until the time that this happens , our conclusion must be modest : the observed values of the mass parameters are reasonably typical of the anthropically allowed ranges .

the requirement that complex elements be formed suggests that the higgs vacuum expectation value must have a magnitude less than 5 times its observed value , for , baryon stability requires that , the planck mass . we conclude that the observed value of is reasonably typical of the anthropically allowed range , and that anthropic arguments provide a plausible explanation for the closeness of the qcd scale and the weak scale . barr , john f. donoghue and d. seckel * + a)_bartol research institute + university of delaware , newark , de 19716 + _ b)_department of physics and astronomy , + university of massachusetts , amherst , ma 01003 + _ 0.4 in

in theories in which different regions of the universe can have different values of the the physical parameters , we would naturally find ourselves in a region which has parameters favorable for life . we explore the range of anthropically allowed values of the mass parameter in the higgs potential , . for , the requirement that complex elements be formed suggests that the higgs vacuum expectation value must have a magnitude less than 5 times its observed value , for , baryon stability requires that , the planck mass . smaller values of may or may not be allowed depending on issues of element synthesis and stellar evolution . we conclude that the observed value of is reasonably typical of the anthropically allowed range , and that anthropic arguments provide a plausible explanation for the closeness of the qcd scale and the weak scale . # 1#1 + 0.3 in * v. agrawal , s.m . barr , john f. donoghue and d. seckel * + a)_bartol research institute + university of delaware , newark , de 19716 + _ b)_department of physics and astronomy , + university of massachusetts , amherst , ma 01003 + _ 0.4 in

1606.04265

i

the area of @xmath0-calculus has in the last twenty years served as a bridge between mathematics and physics . recently , there is a significant increase of activities in the area of @xmath0-calculus due to its applications in various fields such as mechanics , mathematics and physics . the definitions and notations of @xmath0-calculus reviewed here are taken from @xcite . + the @xmath0-analogue of the shifted factorial @xmath3 is defined by @xmath4 the @xmath0-exponential function is defined as : @xmath10_{q}!},~0 < |q|<1.\ ] ] the @xmath0-derivative @xmath11 of a function @xmath12 at a point @xmath13 is defined as : @xmath14 the @xmath0-analogue of taylor series expansion of an arbitrary function @xmath15 for @xmath16 is defined as : @xmath17 where @xmath18 is the @xmath19 @xmath0-derivative of the function @xmath12 at point @xmath5 . the class of appell polynomials is characterized completely by appell @xcite in 1880 . in 1954 , sharma and chak @xcite introduced a @xmath0-analogue for the family of appell polynomials and called this sequence of polynomials as @xmath0-harmonic . further , in 1967 al - salaam @xcite introduced the family of @xmath0-appell polynomials @xmath20 and studied some of its properties . the @xmath1-degree polynomials @xmath21 are called @xmath0-appell provided they satisfy the following @xmath0-differential equation : @xmath22_q ~a_{n-1,q}(x),~n=0,1,2,\ldots~;~q \in \mathbb{c};~0<q<1.\ ] ] it is to be noted that @xmath25 is an analytic function at @xmath26 and @xmath27 are the @xmath0-appell numbers . also , there exists a sequence of numbers @xmath28 , such that the sequence @xmath21 satisfies the following relation @xcite : @xmath29 based on appropriate selection for the function @xmath25 , different members belonging to the family of @xmath0-appell polynomials can be obtained . these members are listed in table 1 . + * table 1 . certain members belonging to the @xmath0-appell family * + + + al - salaam showed that the class of all @xmath0-appell polynomials is a maximal commutative subgroup of the group of all polynomial sets , _ i.e. _ the class of all @xmath0-appell sequences is closed under the operation of @xmath0-umbral composition of polynomial sequences . if @xmath30 and @xmath31 are sequences of @xmath0-polynomials , then the @xmath0-umbral composition of @xmath21 with @xmath32 is defined to be the sequence @xmath33 under this operation the set of all @xmath0-appell sequences is an abelian group and it can be seen by considering the fact that every @xmath0-appell sequence is of the form @xmath34_q ! } d_{q}^k\right ) x^n\ ] ] and that the umbral composition of @xmath0-appell sequences corresponds to multiplication of these formal @xmath0-power series in the operator @xmath35 . in 1982 , srivastava @xcite gave several characterizations for the well known appell polynomials and for their basic analogues : the @xmath0-appell polynomials . in 1985 , roman proposed an approach similar to the umbral approach under the area of nonclassical umbral calculus which is called @xmath0-umbral calculus @xcite . the @xmath0-appell polynomials are studied using determinantal and umbral approaches , see for example @xcite . obtaining determinant forms for the @xmath0-appell polynomials and their members is an important aspect of such study . the determinant forms can be helpful for computation purposes and can also be useful in finding the solutions of general linear interpolation problems . + in this article , a family of the 2-iterated @xmath0-appell polynomials is introduced . the determinant forms and other properties of this family and also for certain members belonging to this family are established . in section 2 , the 2-iterated @xmath0-appell polynomials are introduced by means of generating function and series definition . certain members belonging to the 2-iterated @xmath0-appell family and some mixed type @xmath0-special polynomials and related numbers are also considered . in section 3 , the determinant forms of the 2-iterated and mixed type @xmath0-appell polynomials are derived . in section , 4 , the roots of the 2-iterated @xmath0-appell and mixed type @xmath0-appell polynomials are investigated and their graphs are drawn for suitable values of indices .

in this article , the 2-iterated-appell family is introduced . certain 2-iterated-appell and mixed type-special polynomials are considered as members of this family . the numbers related to these polynomials are obtained . the graphs of some 2-iterated-appell and mixed type-appell polynomials are drawn for different values of indices and the roots of these polynomials are also investigated for certain values of index by using matlab . finally , the approximate solutions of the real zeros of these polynomials are given . + * msc 2010 * : 33d45 , 33d99 , 33e20 .

in this article , the 2-iterated-appell family is introduced . certain 2-iterated-appell and mixed type-special polynomials are considered as members of this family . the numbers related to these polynomials are obtained . the determinant definitions for the 2-iterated-appell family and for the 2-iterated and mixed type-appell polynomials are established . the graphs of some 2-iterated-appell and mixed type-appell polynomials are drawn for different values of indices and the roots of these polynomials are also investigated for certain values of index by using matlab . finally , the approximate solutions of the real zeros of these polynomials are given . [ section ] [ thm]corollary [ thm]lemma [ thm]proposition [ thm]example [ thm]definition [ thm]remark + * subuhi khancorresponding author;e - mail : subuhi2006@gmail.com ( subuhi khan ) + second author ; e - mail : mumtazrst@gmail.com ( mumtaz riyasat ) ] and mumtaz riyasat * + department of mathematics + aligarh muslim university + aligarh , india + * _ keywords : _ * -appell polynomials ; 2-iterated-appell polynomials ;-bernoulli polynomials ;-euler polynomials . + * msc 2010 * : 33d45 , 33d99 , 33e20 .

1102.5241

i

the following model for a random walk in a random environment can be found in the physics literature ; see anshelevic and vologodskii ( @xcite ) , alexander _ et al . _ ( @xcite ) , kawazu and kesten ( @xcite ) . let @xmath0 be a family of positive i.i.d . random variables and @xmath1 the @xmath2-algebra generated by those random variables . let @xmath3 be a continuous - time random walk on @xmath4 having the following asymptotic transition rates for @xmath5 : @xmath6 in other words , the process @xmath3 is a birth death process with possibly negative population size , where , for a population with @xmath7 individuals , birth occurs at rate @xmath8 and death at rate @xmath9 . we will assume that the process @xmath3 starts at zero at time zero . the resulting process is symmetric , in the sense that the permeability of the edge connecting the vertices @xmath7 and @xmath10 does not depend on the direction of the motion . this physical background motivates the name ` random environment ' for the sequence @xmath11 . in what follows , we denote the distribution of the random environment on the sequence space by @xmath12 . the following convergence results are described in kawazu and kesten ( @xcite ) . if @xmath13<\infty$ ] , then for @xmath14-almost all environments , the distributions ( after conditioning on the environment ) of the processes @xmath15 converge weakly with respect to the skorohod topology toward the distribution of the process @xmath16 , where @xmath17 is standard brownian motion on @xmath18 . ( see also papanicolaou and varadhan ( @xcite ) for some related results . ) if there exists a slowly varying function @xmath19 such that @xmath20 then the distributions of the processes @xmath21 converge weakly with respect to the skorohod topology toward the distribution of standard brownian motion . if there exists a slowly varying function @xmath22 such that the sequence of random variables @xmath23 converges in distribution toward a one - sided stable distribution @xmath24 with index @xmath25 , then the distributions of the processes @xmath26 converge weakly with respect to the skorohod topology toward the distribution of a continuous self - similar process @xmath27 with scaling exponent @xmath28 . \(1 ) in the next section , we will give a representation for the process @xmath29 in terms of a standard brownian motion and a stable subordinator associated with the measure @xmath30 . \(2 ) we note that the results from kawazu and kesten ( @xcite ) are generalized in kawazu ( @xcite ) . he considered random walks in random environments defined by the following transition asymptotics : @xmath31 where @xmath32 is an i.i.d . family of positive random variables satisfying suitable assumptions . similarly to the situation studied in kawazu and kesten ( @xcite ) , the resulting random walks converge toward appropriate continuous processes after scaling . in kesten and spitzer ( @xcite ) , new classes of continuous self - similar processes are described . moreover , it was proven therein that those processes are weak limits of random walks in random scenery . those random walks are defined as follows . let @xmath33 and @xmath34 be two independent families of i.i.d . random variables , where the random variables @xmath35 are assumed to be @xmath36-valued . one can think of the sequence @xmath34 as increments of a classical @xmath36-valued random walk @xmath37 . the stationary sequence @xmath38 has some non - trivial long - range dependencies if the underlying random walk @xmath39 is recurrent . this is the case , for example , if @xmath40 is in the domain of attraction of an @xmath41-stable distribution with @xmath42 $ ] . the random sequence @xmath43 is called a _ random walk in random scenery_. in kesten and spitzer ( @xcite ) , the following convergence result was proven for those processes . if @xmath44 is in the domain of attraction of a @xmath45-stable distribution with @xmath46 $ ] and if @xmath40 is in the domain of attraction of an @xmath41-stable distribution with @xmath25 , then the distributions of the processes @xmath47 _ converge weakly with respect to the skorohod topology toward @xmath45-stable lvy motion . _ ( see also spitzer ( @xcite ) for a special case . ) if @xmath44 is in the domain of attraction of a @xmath45-stable distribution with @xmath46 $ ] and if @xmath40 is in the domain of attraction of an @xmath41-stable distribution with @xmath42 $ ] , then the distributions of the processes @xmath48 converge weakly with respect to the skorohod topology toward a continuous self - similar process @xmath49 with scaling exponent @xmath50 . the statement in ks1 corresponds to the transient case and is not difficult to prove since , in that case , the sequence @xmath38 has only weak dependencies . this is the reason why one obtains @xmath51-stable lvy noise in the limit . we also mention that the case @xmath52 is still open . there exist various generalizations of the results of kesten and spitzer ( @xcite ) . we will only mention shieh ( @xcite ) , where the limiting process is generalized to higher dimensions , lang and nguyen ( @xcite ) , which deals with multidimensional random walks and some special random scenery , maejima ( @xcite ) , where the random scenery belongs to the domain of attraction of an operator - stable distribution , arai ( @xcite ) , where the random scenery belongs to the domain of partial attraction of a semi - stable distribution , and saigo and takahashi ( @xcite ) , where the random scenery and the random walk belong to the domain of partial attraction of semi - stable and operator semi - stable distributions . in this article , we investigate whether it is possible to substitute the classical random walk in the result of kesten and spitzer ( @xcite ) by the random walk in random environment which was introduced in kawazu and kesten ( @xcite ) . we will restrict our attention to the result kk3 since this is the case where a new type of self - similar process arises at the end . for simplicity and in order to avoid complicating notation , we will assume that the slowly varying function @xmath22 which appears in kk3 is constant and equal to one . the general case involving non - constant @xmath22 can be treated in a similar way . we now fix a probability space @xmath53 which is sufficiently large to support a family of i.i.d . random variables @xmath0 , a birth death process @xmath3 with asymptotic transition rates given by equations ( 1)(3 ) and a family of i.i.d . random variables @xmath54 . we assume that the families @xmath54 and @xmath55 are independent and that @xmath56 is cadlag @xmath57-almost surely . further , we assume that @xmath58 is in the domain of normal attraction of a one - sided @xmath41-stable distribution @xmath30 with @xmath25 . moreover , we assume that @xmath44 is in the domain of normal attraction of a @xmath51-stable distribution @xmath59 with @xmath46 $ ] . its characteristic function is given by @xmath60 where @xmath61 and @xmath62 . for @xmath63 , it follows from those assumptions that @xmath64=0 $ ] . for @xmath52 , we make the further assumption that there exists a @xmath65 such that @xmath66}(\xi(0 ) ) \bigr ] \bigr|\leq k\qquad \mbox{for all } \rho>0 .\ ] ] we can now define the following continuous - time version of the random walk in random scenery : @xmath67 in the following , we will use the space @xmath68 with the skorohod topology . we will prove the following theorem . [ mt ] for @xmath69 and @xmath70 , the distributions of the processes @xmath71 converge weakly with respect to the skorohod topology toward the distribution of a self - similar stochastic process @xmath72 with scaling exponent @xmath73 . the stochastic process @xmath72 can be constructed as follows . let @xmath74 and @xmath75 be two independent copies of the @xmath51-stable lvy process which can be associated with the characteristic function @xmath76 further , let @xmath77 be the local time of the stochastic process @xmath78 ; that is , the random variable @xmath79 is the derivative with respect to @xmath80 of the occupation time @xmath81):=\int_0^\tau\mathbh{1}_{(-\infty , x]}(x_\ast(\sigma))\,\mathrm{d}\sigma.\ ] ] we will see in the next section that the local time exists for all but a countable number of points @xmath82 . moreover , for all @xmath83 , the processes @xmath84 are predictable with respect to the natural filtrations of @xmath74 ( resp . , @xmath85 ) . the following integral representation of the process @xmath86 can be given : @xmath87

in this article , we merge celebrated results of kesten and spitzer [ _ z . wahrsch . verw . gebiete _ * 50 * ( 1979 ) 525 ] and kawazu and kesten [ _ j . stat . phys . _ * 37 * ( 1984 ) 561575 ] . a random walk performs a motion in an i.i.d . environment and observes an i.i.d . scenery along its path . the resulting limit process is a self - similar stochastic process with non - trivial dependencies .

in this article , we merge celebrated results of kesten and spitzer [ _ z . wahrsch . verw . gebiete _ * 50 * ( 1979 ) 525 ] and kawazu and kesten [ _ j . stat . phys . _ * 37 * ( 1984 ) 561575 ] . a random walk performs a motion in an i.i.d . environment and observes an i.i.d . scenery along its path . we assume that the scenery is in the domain of attraction of a stable distribution and prove that the resulting observations satisfy a limit theorem . the resulting limit process is a self - similar stochastic process with non - trivial dependencies .

1004.0095

r

in this paper , we are interested in the convergence of a greedy algorithm for the minimization of high - dimensional nonlinear convex problems . we first introduce the general theoretical setting in which we prove the convergence , then describe two prototypical examples to which our analysis can be applied . throughout this article , @xmath11 and @xmath3 denote some positive integers , and @xmath51 and @xmath52 some open sets of @xmath53 and @xmath54 respectively . let @xmath42 and @xmath43 be hilbert spaces of real - valued functions respectively defined over @xmath51 and @xmath52 ( typically @xmath55 or sobolev spaces ) . let @xmath56 and @xmath57 be the norms of @xmath42 and @xmath43 . we introduce the following tensor product for all @xmath58 , @xmath59 which defines a real - valued function on @xmath60 . we also denote by @xmath61 . let @xmath22 be a hilbert space of real - valued functions defined on @xmath62 . the scalar product of @xmath22 is denoted by @xmath63 and the associated norm by @xmath64 . let @xmath46 be a differentiable real - valued functional defined on @xmath22 . for all @xmath65 , we denote by @xmath66 the gradient of @xmath46 at @xmath67 . we make the following assumptions : @xmath68 @xmath69 is a dense subset of @xmath22 for @xmath64 ; @xmath70 for all sequences of @xmath71 bounded in @xmath22 , there exists a subsequence which weakly converges in @xmath22 towards an element of @xmath71 ; @xmath72 the functional @xmath46 is strongly convex for @xmath64 , i.e. there exists a constant @xmath73 for which @xmath74 the functional @xmath46 is also said to be @xmath75-convex ; @xmath76 the gradient of @xmath46 is lipschitz on bounded sets : for each bounded subset @xmath77 of @xmath22 , there exists a nonnegative constant @xmath78 such that @xmath79 the unique global minimizer of @xmath46 on @xmath22 is denoted by @xmath39 . its existence and uniqueness are ensured by the @xmath75-convexity of the functional @xmath46 : @xmath80 we are going to study the following algorithm : the sequence @xmath81 is defined recursively by @xmath82 throughout this article , we will denote for all @xmath83 , @xmath84 our main result is the following theorem , whose proof is given in section 3 . under the assumptions @xmath68 , @xmath70 , @xmath72 and @xmath76 , the iterations of the algorithm are well - defined , in the sense that ( [ algorithm ] ) has at least one minimizer @xmath85 . moreover , the sequence @xmath86 strongly converges in @xmath22 towards @xmath39 . for each @xmath83 , the minimizer of ( [ algorithm ] ) is not unique in general . in particular , notice that the function @xmath87 is not convex . theorem 2.1 could be generalized to the case of tensor products of more than two hilbert spaces . indeed , let @xmath88 with @xmath89 . let @xmath90 be @xmath91 positive integers . let @xmath92 be @xmath91 open subsets of @xmath93 respectively . we consider @xmath91 hilbert spaces , @xmath94 of real - valued functions defined respectively on @xmath92 . let @xmath22 be a hilbert space of real - valued functions defined on @xmath95 . let @xmath46 be a real - valued differentiable functional defined on @xmath22 . we denote by @xmath96 . our algorithm can then easily be adapted provided that assumptions @xmath68 , @xmath70 , @xmath72 and @xmath76 are satisfied : @xmath97 are defined recursively by @xmath98 our convergence result also holds in this case . but for the sake of simplicity , we will limit our analysis to the case of only two hilbert spaces . let @xmath99 be the scalar product defined on @xmath69 as : for all @xmath100 , @xmath101 where @xmath102 and @xmath103 denote the scalar products of @xmath42 and @xmath43 respectively . let @xmath104 be the cross - norm associated to the scalar product @xmath99 . the tensor space of @xmath42 and @xmath43 , denoted as @xmath105 is then defined as the closure of @xmath69 for the product norm @xmath104 , @xmath106 let us point out that the hilbert space @xmath22 is not necessarily equal to @xmath105 , the tensor space of @xmath42 and @xmath43 associated to the tensor product ( [ tensor ] ) . indeed , an example where our analysis can be applied and where @xmath107 is given in section 2.2.2 ( see remark 2.5 . ) . however , the following inclusion relationship holds : @xmath108 . if @xmath42 and @xmath43 are discretized in finite - dimensional spaces of dimension @xmath7 and @xmath8 , our algorithm consists in solving several problems in dimension @xmath109 instead of solving one problem of dimension @xmath110 . thus , we can circumvent the curse of high - dimensionality . to prove that the general theoretical setting we described in section 2.1 is satisfied on the prototypical problems we present in this section , we need the following lemma , which is well - known in distribution theory@xcite . let @xmath111 be a distribution such that for any functions @xmath112 , @xmath113 then @xmath114 in @xmath115 . moreover , for any two sequences of distributions @xmath116 and @xmath117 such that @xmath118 in @xmath119 and @xmath120 in @xmath121 , @xmath122 in @xmath115 . an example of application of our algorithm is the study of uncertainty propagation on obstacle problems . we assume that uncertainty can be modeled by a set of @xmath11 random variables @xmath123 , @xmath124 , ... , @xmath125 , and that the random vector @xmath126 takes its values in @xmath51 . we consider also that the physical problem is defined over the domain @xmath52 , which is supposed to be a bounded subset of @xmath54 . if @xmath127 is a hilbert space of functions defined on @xmath52 , we denote by @xmath128 < + \infty \right\},\ ] ] where @xmath129 denotes the expectation with respect to the probability law of @xmath130 , and @xmath131 denotes the norm of @xmath127 . we endow @xmath132 with the scalar product defined by @xmath133 $ ] . a formulation of the obstacle problem with uncertainty is the following@xcite . let @xmath134 and @xmath135 . a membrane is stretched over the domain @xmath52 and is deflected by some random force having pointwise density @xmath136 for @xmath137 . at the boundary @xmath138 , the membrane is fixed and in the interior of @xmath52 the deflection is assumed to be bounded from below by the function @xmath139 ( a random obstacle ) . then the deflection @xmath140 is solution of the following obstacle problem with uncertainty ( see figure 1 ) : @xmath141 an equivalent formulation of this problem is the following . let us denote @xmath142 solving the obstacle problem ( [ form1 ] ) consists in solving the minimization problem @xmath143 where @xmath144 $ ] . one of the main difficulties of this kind of problems is their very high nonlinearity . many methods have been proposed to approximate the solution of these problems in the case without uncertainty@xcite . among them , penalization methods@xcite are among the most widely used . they consist in approximating the solution of a given obstacle problem by a sequence of solutions of penalized problems defined on the entire hilbert space . let @xmath145 be a parameter in @xmath146 . such a penalized problem associated with problem ( [ obstacle ] ) may be defined as @xmath147 where @xmath148_+^2 dx\right]$ ] . here and below , we denote by @xmath149_+$ ] the positive part of the real number @xmath150 , i.e. @xmath151_+ = 0 $ ] if @xmath152 and @xmath151_+ = a$ ] if @xmath153 . when @xmath145 goes to infinity , the solution @xmath154 of problem ( [ penalized ] ) strongly converges to the solution @xmath155 of problem ( [ obstacle ] ) . the goal of the algorithm we described in the previous section is to calculate the solution @xmath156 of this regularized problem for a given value of the parameter @xmath145 . let us check that the general theoretical setting we described in section 2.1 can be applied in this case . let us consider @xmath157 , @xmath158 , @xmath159 and @xmath160 for @xmath65 . we have @xmath161 . we endow @xmath162 with the scalar product defined by @xmath163 . in this case , we have @xmath164 and as a consequence assumption @xmath68 is obviously satisfied . besides , assumption @xmath70 is satisfied as well . if @xmath165 is such that @xmath166 is bounded , it is possible to extract a subsequence which weakly converges in @xmath22 towards an element @xmath167 . besides , there exists a non - negative constant @xmath168 such that for all @xmath169 , @xmath170 \\ & = & \mathbb{e}\left[|r_n(t)|^2\right ] \int_{\mathcal{x } } |\nabla_x s_n(x)|^2 dx \\ & = & \|r_n\|_{v_t}^2 \|s_n\|_{v_x}^2 \\ & \leq & c .\\\end{aligned}\ ] ] we can then choose @xmath171 such that @xmath172 and @xmath173 . the sequences @xmath174 and @xmath175 are then bounded in @xmath176 and @xmath162 respectively and we can extract subsequences which weakly converge in @xmath176 and @xmath162 towards @xmath177 and @xmath178 respectively . as the weak convergences in @xmath176 and @xmath162 imply the convergences in the distributional sense , the sequence @xmath172 necessarily converges towards @xmath179 in @xmath180 by lemma 2.1 . as the weak convergence in @xmath22 also implies the convergence in the sense of the distributions , we obtain , by uniqueness of the limit , @xmath181 . hence assumption @xmath70 is satisfied . the functional @xmath46 is differentiable and @xmath16-convex . indeed , for all @xmath65 , @xmath182_+^2dx\right]\right),\ ] ] is the sum of a @xmath16-convex function ( @xmath183 ) and of a convex function ( @xmath184_+^2dx\right]$ ] ) . the functional @xmath46 therefore obeys property ( [ alpha ] ) with @xmath185 . hence , assumption @xmath72 is satisfied . let us finally check that the gradient of @xmath46 is lipschitz . for all @xmath186 , @xmath187\right| \\ & & + \rho\left|\mathbb{e}\left [ \int_{\mathcal{x } } ( [ g(t , x)-v(t , x)]_+ - [ g(t , x ) -w(t , x)]_+)y(t , x)dx \right]\right| \\ & \leq & \|v - w\|_v\|y\|_v \\ & & + \rho \mathbb{e}\left [ \int_{\mathcal{x } } \left|[g(t , x)-v(t , x)]_+ - [ g(t , x ) -w(t , x)]_+\right| \left|y(t , x)\right|dx \right].\\\end{aligned}\ ] ] for @xmath188 , it can easily be seen that @xmath189_+-[b]_+|\leq |a - b|$ ] . this implies @xmath190 \\ & \leq & \|v - w\|_v\|y\|_v\\ & & + \rho \left(\mathbb{e}\left [ \int_{\mathcal{x } } |v(t , x)- w(t , x)]|^2 dx\right]\right)^{1/2}\left(\mathbb{e}\left [ \int_{\mathcal{x } } |y(t , x)]|^2 dx\right]\right)^{1/2 } .\\\end{aligned}\ ] ] the poincar inegality in @xmath191 implies that there exists a nonnegative constant @xmath192 such that for all @xmath193 , @xmath194|^2 dx\right]\right|^{1/2 } \leq d\|h\|_v.\ ] ] this yields @xmath195 hence , @xmath196 the functional @xmath46 then obeys property ( [ lipschitz ] ) with a constant @xmath197 independent of the bounded set considered . thus , our obstacle problem ( [ penalized ] ) falls into the general theoretical setting introduced in section 2.1 . there exist several variants of the obstacle problem which could be tackled with our algorithm . we refer to ref . @xcite or ref . @xcite for such examples . our algorithm may also be used to calculate the solution of other problems than obstacle problems . other examples are high - dimensional nonlinear poisson equations . a specific application where such high dimensional poisson equations arise is the calculation of the so - called committor function in molecular dynamics@xcite , which is an important quantity to compute reaction rates or to derive some effective dynamics for example . let @xmath198 . the committor is the solution to the following problem : @xmath199 where @xmath91 is typically large , @xmath17 and @xmath19 are disjoint smooth open sets of @xmath200 , @xmath201 is a given potential function such that @xmath202 and @xmath203 for @xmath204 , @xmath205 can be interpreted as the probability that the stochastic process @xmath206 solution to @xmath207 reaches @xmath208 before @xmath209 . here , @xmath210 denotes a @xmath91-dimensional brownian motion . let @xmath211 such that @xmath212 . in this example , we consider the case when @xmath213 is bounded . let @xmath51 and @xmath52 be open convex bounded subsets of @xmath53 and @xmath54 respectively such that @xmath214 and such that @xmath215 where @xmath216 denotes the lebesgue measure . we also assume that @xmath217 . in this case , the initial problem can be rewritten as a minimization problem set on @xmath218 instead of @xmath219 . indeed , as @xmath220 and @xmath221 is bounded , there exists constants @xmath222 such that for all @xmath223 , @xmath224 . and thus , we have @xmath225 if and only if @xmath226 , @xmath227 and @xmath228 . the penalized version of the committor problem then reads @xmath229 where @xmath230 for some @xmath231 . let us check that the general theoretical setting described in section 2.1 is relevant for this problem . in this case , we consider @xmath232 , @xmath233 and @xmath234 . the inner products that are defined over these hilbert spaces are the following . for all @xmath235 , @xmath236 , @xmath237 , @xmath238 @xmath239 @xmath240 let us point out that in this case , @xmath107 . indeed , for all @xmath241 , the @xmath22-norm of the tensor product @xmath242 reads @xmath243 which is not a cross - norm , equivalent to the norm induced by @xmath244 and @xmath245 over @xmath105 , which is @xmath246 indeed , let us consider @xmath247 , @xmath248 and @xmath249 for @xmath250 and @xmath251 . the sequence @xmath252 is bounded , but the sequence @xmath253 is not . assumption @xmath68 holds true , since @xmath254 is such that @xmath255 and @xmath256 is dense in @xmath257 . hence , @xmath258 is also dense in @xmath22 . let us prove that assumption @xmath70 also holds true . if @xmath165 is such that @xmath166 is bounded , we can extract a subsequence of @xmath259 which weakly converges in @xmath22 towards an element @xmath167 . besides , there exists a nonnegative constant @xmath168 such that for all @xmath169 , @xmath260 we can then choose @xmath171 such that @xmath172 and such that @xmath261 . the sequences @xmath174 and @xmath175 are then bounded in @xmath262 and @xmath263 and we can extract subsequences which weakly converge in @xmath262 and @xmath263 respectively towards @xmath264 and @xmath265 . as the weak convergences in @xmath262 and @xmath263 imply the convergences in the distributional sense , @xmath172 necessarily converges towards @xmath179 in the distributional sense by lemma 2.1 . as the weak convergence in @xmath22 also implies the convergence in the sense of the distributions , by uniqueness of the limit , @xmath266 . let us suppose @xmath267 . in that case , we have @xmath268 and @xmath269 . besides , we have @xmath270 hence @xmath271 as a consequence @xmath272 is finite and @xmath273 . hence @xmath274 . if @xmath275 , then obviously @xmath276 . hence , assumption @xmath70 holds true . the functional @xmath46 is differentiable and strongly convex . to prove this , it is sufficient to prove that there exists a constant @xmath277 such that for all @xmath278 , @xmath279 . indeed , there exists @xmath280 such that for all @xmath281 , @xmath282 . thus , there exists a constant @xmath283 such that , for all @xmath278 , @xmath284 to prove that the functional @xmath46 is strongly convex , it is sufficient to have the following inequality : there exists a constant @xmath285 such that for all @xmath286 , @xmath287 as @xmath51 and @xmath52 are bounded open convex subsets of @xmath53 and @xmath54 respectively , @xmath221 is then a bounded open convex subset of @xmath200 such that @xmath288 and inequality ( [ poinc ] ) is a well - known poincare - like inequality . hence , assumption @xmath72 is satisfied . let us check that the gradient of @xmath46 is lipschitz . for all @xmath289 , @xmath290 hence @xmath291 the functional @xmath46 therefore obeys property ( [ lipschitz ] ) with a constant @xmath292 independent of the bounded subset considered . thus , the committor problem falls into the general theoretical setting introduced in section 2.1 .

we illustrate this method on a prototypical example for uncertainty propagation on the obstacle problem . universit paris est , cole des ponts - paristech , cermics , + 6 & 8 avenue blaise pascal + 77455 marne - la - valle cedex 2 + france + \{cances , ehrlachv , lelievre}@cermics.enpc.fr + keywords : greedy algorithm ; high dimension ; obstacle problem ; uncertainty quantification .

in this article , we present a greedy algorithm based on a tensor product decomposition , whose aim is to compute the global minimum of a strongly convex energy functional . we prove the convergence of our method provided that the gradient of the energy is lipschitz on bounded sets . the main interest of this method is that it can be used for high - dimensional nonlinear convex problems . we illustrate this method on a prototypical example for uncertainty propagation on the obstacle problem . universit paris est , cole des ponts - paristech , cermics , + 6 & 8 avenue blaise pascal + 77455 marne - la - valle cedex 2 + france + \{cances , ehrlachv , lelievre}@cermics.enpc.fr + keywords : greedy algorithm ; high dimension ; obstacle problem ; uncertainty quantification .

1004.0095

c

in this article , we presented a greedy algorithm based on variable decomposition aiming at computing the global minimum of a strongly convex energy functional . we proved that , provided that the gradient of the energy is lipschitz on bounded sets , and that the hilbert spaces considered satisfy assumptions @xmath68 and @xmath70 , then the approximation given by our algorithm strongly converges towards the desired result . one of the main advantage of the algorithm is that it can deal with highly nonlinear problems . we also proved that in finite dimension , this algorithm converges exponentially fast . we applied this algorithm in the context of uncertainty quantification on obstacle problems . in this frame , we considered regularizations of this kind of problems by penalization methods . indeed , the obstacle problem can be approximated by a global minimization problem defined on the entire hilbert space of some strongly convex energy functional where the constraints of the initial problem are replaced by penalization terms in the expression of the functional . our algorithm gives a good approximation of the solutions of the regularized problem . however , the problem of ill - conditioned matrices , which is inherent to penalization methods , limits the accuracy with which we can approach the solution of the initial obstacle problem . one way to circumvent this problem is to use augmented lagrangian methods ( see ref . @xcite ) instead of penalization methods . indeed , the former algorithms converge towards the true solution of the initial obstacle problems . the adaptation of our algorithm to such methods is work in progress . another extension of our work would be to consider other problems than obstacle problems . in ref . @xcite , a similar algorithm based on proper generalized decomposition is used to study uncertainty quantification upon a burger type equation . we believe that it could be possible to extend our proof of convergence in the case of such hyperbolic systems .

in this article , we present a greedy algorithm based on a tensor product decomposition , whose aim is to compute the global minimum of a strongly convex energy functional . we prove the convergence of our method provided that the gradient of the energy is lipschitz on bounded sets . the main interest of this method is that it can be used for high - dimensional nonlinear convex problems .

in this article , we present a greedy algorithm based on a tensor product decomposition , whose aim is to compute the global minimum of a strongly convex energy functional . we prove the convergence of our method provided that the gradient of the energy is lipschitz on bounded sets . the main interest of this method is that it can be used for high - dimensional nonlinear convex problems . we illustrate this method on a prototypical example for uncertainty propagation on the obstacle problem . universit paris est , cole des ponts - paristech , cermics , + 6 & 8 avenue blaise pascal + 77455 marne - la - valle cedex 2 + france + \{cances , ehrlachv , lelievre}@cermics.enpc.fr + keywords : greedy algorithm ; high dimension ; obstacle problem ; uncertainty quantification .

cond-mat0007338

i

global optimization ( go ) is essentially a mathematical task . namely , for the class of go problems i will be particularly considering here , it is to find the absolute minimum ( or maximum ) of a cost function , @xmath0 , where @xmath1 belongs to a subset @xmath2 of euclidean n - space , @xmath3 @xcite , i.e.@xmath4 although the applications of global optimization span a wide range of fields from the economics of business in the travelling salesman problem to biophysics in the lowest - energy structure of a protein this does not take away from the essentially mathematical nature of the optimization problem . so why do i wish to discuss the _ physical _ aspects of global optimization ? to begin with we should realize that even for go problems that do not correspond to a physical system , physical properties can be associated with the system by thinking of the cost function as a potential energy function , @xmath5 . this allows the thermodynamics of the system to be defined . when the system is at equilibrium at a temperature @xmath6 each point @xmath1 in configuration space will be sampled with a probability proportional to its boltzmann weight , @xmath7 , where @xmath8 is the boltzmann constant . furthermore , for systems with continuous coordinates the forces , @xmath9 , associated with each coordinate can be obtained from the gradient of the cost function , i.e. @xmath10 . once masses are associated with each coordinate , the dynamics are then defined through newton s equations of motion . if one wishes the system s dynamics can then be simulated by integrating these equations of motion , as in the molecular dynamics method @xcite . even when the coordinates can only take discrete values , monte carlo ( mc ) simulations can still provide a pseudo - dynamics with the number of steps taking the role of time . of course , this connection to physics is most transparent , and most natural , when the system being optimized is a physical system , which has a real ( and potentially observable ) thermodynamics and dynamics . furthermore , in those cases where the cost function does truly correspond to the potential energy of the system , there is another physical dimension to the problem how is the structure of the global minimum determined by the physical interactions between the atoms and molecules that make up @xmath11 ? given that we have established that physical properties can be associated with any system being optimized , what relevance does this physics have to the task of global optimization ? firstly , many go algorithm have drawn their inspiration from physics . most famously , simulated annealing is analogous to the slow cooling of a melt to allow the formation of a near perfect crystal , the idea being that if equilibrium is maintained in the simulation as the system is cooled , then at zero temperature it must end up in the global minimum @xcite . there are many other physically - motivated go approaches . the extension of statistical thermodynamics to systems with non - extensive thermodynamics through the use of tsallis statistics @xcite has led to a generalized simulated annealing @xcite which is no longer tied to the boltzmann distribution and is often more efficient than standard simulated annealing . genetic algorithms imitate the biophysical evolution of the genome @xcite . and i could go on . however , this is not the link between physics and global optimization that is my focus here . rather , i wish to show how the ease or difficulty of global optimization is often intimately linked to the physics of the system . the insights obtained from understanding the physical basis for the success or failure of an algorithm not only provide an understanding of the limitations of the method and a basis for assessing the likelihood of success in future applications , but also aid the development of new algorithms by identifying the main physical challenges that need to be overcome to enable greater efficiency and suggesting the type of physical behaviour that would need to be incorporated into an improved algorithm . i will attempt to achieve this aim by concentrating on one class of problems , namely the global minimization of the potential energy of an atomic cluster . furthermore , i will mainly concentrate on model systems where the cost function is computationally cheap to evaluate , enabling the physical properties of these systems to be comprehensively examined and understood . as outlined by hartke elsewhere in this book @xcite , this class of problems is of great general interest to the chemical physics community , because the identification of a cluster s structure is often a prerequisite for understanding its other physical and chemical properties . in this chapter i start at the ` end ' , first showing the structures of the putative global minima for a number of cluster systems in order that the reader can understand some of the physical principles that determine the structure and how these relate to the interatomic interactions . furthermore , the structure provides a basis for understanding a cluster s thermodynamic and dynamic properties , especially when , as in some of our examples , the competition between different structural types plays an important role . i then consider some of the go algorithms that are most successful for these systems focussing on those that use the basin - hopping transformation of @xmath11 @xcite and on how the performance of these algorithms depend on the system and the cluster size . i then look at the physical properties of some of the clusters , relating these back to the ease or difficulty of global optimization . i firstly examine the topography of the multi - dimensional surface defined by @xmath11 ( the so - called potential energy surface ( pes ) or energy landscape ) , then the thermodynamics and dynamics . finally , i show why basin - hopping is able to locate the global minimum in those clusters where the pes has a multiple - funnel topography , and make some suggestions as to how further gains in efficiency might be secured .

in this chapter the physical aspects of the global optimization of the geometry of atomic clusters are elucidated . in particular , i examine the structural principles that determine the nature of the lowest - energy structure , the physical reasons why some clusters are especially difficult to optimize and how the basin - hopping transformation of the potential energy surface enables these difficult clusters to be optimized . atomic clusters , basin - hopping , multiple funnels

in this chapter the physical aspects of the global optimization of the geometry of atomic clusters are elucidated . in particular , i examine the structural principles that determine the nature of the lowest - energy structure , the physical reasons why some clusters are especially difficult to optimize and how the basin - hopping transformation of the potential energy surface enables these difficult clusters to be optimized . atomic clusters , basin - hopping , multiple funnels

1702.05841

i

an @xmath0th - order tensor @xmath1 is a multidimensional or @xmath0-way array , where @xmath2 is a field . a first - order tensor is a vector , a second - order tensor is a matrix , and tensors of order three or higher are called higher - order tensors . when @xmath3 , @xmath4 is called an @xmath5th - order , @xmath6-dimensional tensor . we denote the set of all @xmath0th - order , @xmath6-dimensional tensors on the field @xmath7 by @xmath8}$ ] . for a tensor @xmath9}$ ] , the tensor eigenvalues and eigenvectors have been considered in many literatures chang - qi - zhang:2013,lim:2005,qi:2005,qi:2007,qi - sun - wang:2007 , there are two particularly interesting definitions called z - eigenvalues and h - eigenvalues ( see the definition later on ) . tensor eigenproblems have found applications in automatic control anderson - bose - jury:1975,bose - kamt:1974,bose - newcomb:1974 , magnetic resonance imaging @xcite , spectral hypergraph theory @xcite , higher order markov chains @xcite , etc . unlike the matrix eigenvalue problem , computing eigenvalues of a general higher - order tensor is np - hard @xcite . recently , chen , han and zhou @xcite proposed a homotopy continuation method for finding all eigenpairs of a general tensor . for the tensors of a certain type , such as symmetric or nonnegative tensors , there are several algorithms for computing one or some eigenpairs ( including z - eigenpair and h - eigenpair ) . for the computation of z - eigenpairs , kolda and mayo @xcite proposed a shifted symmetric higher - order power method ( ss - hopm ) for real symmetric tensors . gleich , lim , and yu @xcite proposed , a always - stochastic newton iteration for finding nonnegative z - eigenpair of nonnegative tensors arising in a multilinear pagerank problem . for the computation of h - eigenpairs , ng , qi , and zhou @xcite proposed a power - type method , nqz algorithm , for the largest h - eigenvalue of weakly primitive nonnegative tensors . some modeled versions of the power - type method have been proposed in liu - zhou - ibrahim:2010,zhang - qi - xu:2012,zhou - qi - wu:2013 . recently , liu , guo and lin @xcite proposed a newton - noda iteration ( nni ) for finding the largest h - eigenvalue of weakly irreducible nonnegative tensors . for a high - order nonnegative tensor @xmath10}$ ] , @xmath4 has nonnegative z - eigenpairs and h - eigenpairs , but they are not unique ( see @xcite ) . in many applications @xcite , computing the nonnegative z-/h - eigenpairs is an important subject . therefore , a central concern is how to avoid computing all the eigenvalues to find a few nonnegative z - eigenpairs and h - eigenpairs . ss - hopm @xcite and nqz @xcite can be used to compute a nonnegative z - eigenpair and h - eigenpair , respectively , but the convergence may be quite slow . the always - stochastic newton s method @xcite is a fast - converging algorithm when the starting point is sufficiently close to a solution . however , it s interestingly enough that the authors @xcite also provided a nonnegative tensor with a unique nonnegative z - eigenpair , and the always - stochastic newton s method fails to find it . based on the reasons above mentioned , this motivates us to develop a continuation method to ensure the global convergence for nonnegative z - eigenpairs . the main contributions of this article are highlighted in the following items . * for _ nonnegative z - eigenpairs _ : we construct a linear homotopy @xmath11 , @xmath12 $ ] , where @xmath13 has only one positive solution , @xmath14 , and all real solutions of @xmath15 are z - eigenpairs of @xmath4 . * * we show that the solution curve of @xmath16 with initial @xmath17 is smooth . furthermore , we also show that the solution curve will reach a nonnegative solution of @xmath15 if all nonnegative solutions of @xmath15 are isolated ( see theorems [ thm2.6 ] and [ thm2.8 ] ) . hence , in this case , homotopy continuation method is guaranteed to compute the nonnegative z - eigenpair of @xmath4 . * * if @xmath4 is irreducible and all nonnegative solutions of @xmath18 are isolated , then we show that the number of positive z - eigenpairs of @xmath4 , counting multiplicities , is @xmath19 for some integer @xmath20 ( see corollary [ cor2.11 ] ) . * * we propose a novel homotopy continuation method to compute an odd number of positive z - eigenpairs for an irreducible nonnegative tenor @xmath21 ( see the flowchart in figure [ fig1 ] ) . * for _ nonnegative h - eigenpairs _ : we construct a linear homotopy @xmath22 , @xmath12 $ ] , where @xmath23 has only one positive solution , @xmath14 , and all real solutions of @xmath24 are h - eigenpairs of @xmath4 . we show that the solution curve of @xmath22 with initial @xmath25 can be parameterized by @xmath26 . if the nonnegative solutions of @xmath24 are isolated , then the solution curve will reach a nonnegative solution of @xmath27 ( see theorem [ thm2.3 ] ) , and hence , homotopy continuation method is guaranteed to compute the nonnegative h - eigenpair of @xmath4 . note that if @xmath4 is weakly irreducible , then @xmath24 has only one positive isolated solution ( see theorem [ thm2.4 ] ) . this paper is organized as follows . the notations and preliminary results are in section 2 . in section 3 , we develop homotopy continuation methods to compute the nonnegative z - eigenpairs and h - eigenpair of a nonnegative tensor @xmath4 and show that the continuation methods are guaranteed to compute the nonnegative eigenpairs . in section 4 , we propose a novel homotopy continuation method to compute an odd number of positive z - eigenpairs for an irreducible nonnegative tenor . some numerical results are presented in section 5 . conclusion of this paper is given in section 6 .

we show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair . additionally , using degree analysis a novel homotopy continuation method is proposed to compute an odd number of positive z - eigenpairs , and some numerical results are presented . continuation method , nonnegative tensor , z - eigenpair , h - eigenpair , tensor eigenvalue problem 65f15 , 65f50

in this paper , a homotopy continuation method for the computation of nonnegative z-/h - eigenpairs of a nonnegative tensor is presented . we show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair . additionally , using degree analysis , we show that the number of positive z - eigenpairs of an irreducible nonnegative tensor is odd . a novel homotopy continuation method is proposed to compute an odd number of positive z - eigenpairs , and some numerical results are presented . continuation method , nonnegative tensor , z - eigenpair , h - eigenpair , tensor eigenvalue problem 65f15 , 65f50

1303.6449

i

due to their importance in theory and applications , fine potential theoretical properties of lvy processes have been under intense study recently . the transition density @xmath8 of a lvy process is the heat kernel of the generator of the process . however , the transition density ( if it exists ) of a general lvy process rarely admits an explicit expression . thus obtaining sharp estimates on @xmath8 is a fundamental problem both in probability theory and in analysis . the generator of a discontinuous lvy process is an integro - differential operator and so it is a non - local operator . recently , quite a few people in pde are interested in problems related to non - local operators ; see , for example , @xcite and the references therein . when @xmath6 is a symmetric diffusion on @xmath7 whose infinitesimal generator is a uniformly elliptic and bounded divergence form operator , it is well - known that @xmath8 enjoys the celebrated aronson s gaussian type estimates . when @xmath6 is a pure jump symmetric process on @xmath7 , sharp estimates on @xmath8 have been studied in @xcite recently , which can be viewed as the counterpart of aronson s estimates for non - local operators . due to the complication near the boundary , two - sided estimates for the transition densities of discontinuous lvy processes killed upon leaving an open set @xmath0 ( equivalently , the dirichlet heat kernels ) have been established very recently for a few particular processes only . the first of such estimates is obtained in @xcite , where we succeeded in establishing sharp two - sided estimates for the heat kernel of the fractional laplacian @xmath9 with zero exterior condition on @xmath10 ( or equivalently , the transition density of the killed symmetric @xmath11-stable process ) in any @xmath2 open set @xmath0 . the approach developed in @xcite provides a road map for establishing sharp two - sided heat kernel estimates of other jump processes in open subsets of @xmath7 . the ideas of @xcite were adapted to establish sharp two - sided heat kernel estimates of relativistic stable processes and mixed stable processes in @xmath2 open subsets of @xmath7 in @xcite respectively . in all these cases , the characteristic exponents of these lvy processes admit explicit expressions , the boundary decay rates of the dirichlet heat kernels are suitable powers of the distance to the boundary . on the other hand , a varopoulos type two - sided dirichlet heat kernel estimate of symmetric stable processes in @xmath1-fat open sets was derived in @xcite ; this type of estimates is expressed in terms of surviving probabilities and the global transition density of the symmetric stable process . the objective of this paper is to establish sharp two - sided estimates on the transition density @xmath12 for a large class of purely discontinuous rotationally symmetric lvy processes . unlike the cases considered in @xcite , the characteristic exponents of the symmetric lvy processes considered in this paper are quite general , satisfying only certain mild growth condition at @xmath13 . moreover , the boundary decay rate of @xmath12 is no longer some power of the distance to the boundary . the analysis of the precise boundary behavior of @xmath12 is quite challenging and delicate . the main tools to obtain the precise boundary behavior of @xmath12 are two versions of the boundary harnack principle obtained in @xcite . in this paper we combine the approaches developed in @xcite with these boundary harnack principles to obtain sharp two - sided estimates for @xmath12 , which cover the main results in @xcite and much more . suppose that @xmath14 is a subordinator with laplace exponent @xmath4 , that is , @xmath15 is a nonnegative lvy process with @xmath16 and @xmath17=e^{-t\phi(\lambda)}$ ] for every @xmath18 . the function @xmath4 can be written in the form @xmath19 where @xmath20 and @xmath21 is a measure on @xmath22 satisfying @xmath23 . the constant @xmath24 is called the drift of the subordinator and @xmath21 the lvy measure of the subordinator ( or of @xmath4 ) . the function @xmath4 is a bernstein function , i.e. , it is @xmath25 , positive and @xmath26 for all @xmath27 . in particular , since @xmath28 and @xmath29 , the bernstein function @xmath4 has the property that @xmath30 the laplace exponent @xmath4 is said to be a complete bernstein function if the lvy measure @xmath21 of @xmath4 has a completely monotone density @xmath31 , i.e. , @xmath32 for every non - negative integer @xmath33 . for basic results on complete bernstein functions , we refer the reader to @xcite . throughout this paper , we assume that @xmath4 is a complete bernstein function satisfying the following growth condition at infinity ( see @xcite ) : * ( a ) : * there exist constants @xmath34 , @xmath35 , @xmath36 and @xmath37 such that @xmath38 note that it follows from the upper bound condition in * ( a ) * that @xmath4 has no drift . let @xmath39 be a brownian motion in @xmath7 independent of the subordinator @xmath15 . the subordinate brownian motion @xmath40 is defined by @xmath41 , which is a rotationally symmetric lvy process with lvy exponent @xmath42 . the infinitesimal generator of @xmath43 is @xmath44 . here and below for a function @xmath45 on @xmath46 , @xmath47 is defined as a pseudo differential operator in terms of fourier transform ; that is , @xmath48 , where @xmath49 is the fourier transform of a function @xmath50 on @xmath7 . it is known that the lvy measure of the process @xmath43 has a density given by @xmath51 where @xmath52 note that the function @xmath53 is continuous and decreasing on @xmath22 . we will assume that @xmath6 is a purely discontinuous rotationally symmetric lvy process with lvy exponent @xmath54 . because of rotational symmetry , the function @xmath5 depends on @xmath55 only , and by a slight abuse of notation we write @xmath56 . the infinitesimal generator of @xmath6 is @xmath57 . we further assume that the lvy measure of @xmath6 has a density with respect to the lebesgue measure on @xmath7 , which is denoted by @xmath58 . that is , @xmath59=e^{-t\psi(|\xi| ) } \quad \quad \mbox { for every } x\in \r^d \mbox { and } \xi\in \r^d,\ ] ] with @xmath60 we assume that @xmath61 is continuous on @xmath22 and that there is a constant @xmath62 such that @xmath63 this implies that @xmath64 and @xmath65 are comparable . clearly also implies that @xmath66 we remark that under the above assumptions , @xmath6 does not need to be a subordinate brownian motion because @xmath67 does not need to be monotone . for example , choose @xmath68 such that @xmath69 and a continuous function @xmath70 with @xmath71 , @xmath72 and @xmath73 for all @xmath74 . then @xmath75 is not monotone and its corresponding lvy process @xmath6 ( through lvy exponent ) is not a subordinate brownian motion . under the above setup , @xmath6 has a continuous transition density @xmath8 with respect to the lebesgue measure on @xmath7 ( see @xcite ) . clearly , @xmath8 is a function depending only on @xmath76 and @xmath77 , and so , by an abuse of notation , we also denote @xmath8 by @xmath78 . for every open subset @xmath79 , we denote by @xmath80 the subprocess of @xmath6 killed upon exiting @xmath0 . it is known ( see @xcite ) that @xmath80 has a transition density @xmath12 , with respect to the lebesgue measure , which is jointly locally hlder continuous . note that @xmath81 is the fundamental solution for @xmath82 in @xmath0 with zero exterior condition and so it can also be called the dirichlet heat kernel of @xmath83 in @xmath0 . the purpose of this paper is to establish sharp two - sided estimates on @xmath12 . the following two conditions will be needed for some of the results in this paper when @xmath0 is unbounded . * ( b ) * : there exist constants @xmath84 and @xmath85 $ ] such that @xmath86 \hbox { and } u\geq r>0.\ ] ] * ( c ) * : there exist constants @xmath87 and @xmath88 $ ] such that @xmath89 \hbox { and } r>0.\ ] ] throughout this paper we will use @xmath90 to denote the function [ e:1.9 ] ( r)=1(r^-2 ) , r>0 . note that in particular it follows from that [ e:1.8 ] ( 2r)= = 4(r ) r>0 . the inverse function of @xmath90 will be denoted by the usual notation @xmath91 . here and in the following , for @xmath92 , @xmath93 and @xmath94 . [ r:1.1 ] \(i ) the condition * ( b ) * is pretty mild . when @xmath6 is a rotationally symmetric lvy process such that @xmath95 is decreasing , condition * ( b ) * holds for all @xmath96 ( see ( * ? ? ? * proposition ) ) . in particular it holds for all subordinate brownian motions with @xmath97 . in this special case , we can also see this using the following elementary argument : when @xmath6 is a subordinate brownian motion , @xmath98 $ ] , where @xmath99 is the transition density of the brownian motion @xmath100 . it follows immediately that @xmath101 is decreasing in @xmath102 and so * ( b ) * holds with @xmath97 . \(ii ) under condition * ( a ) * , condition * ( b ) * is weaker than * ( c)*. under condition * ( a ) * , we will show in this paper that there exists @xmath103 such that @xmath104 \hbox { and } r>0\ ] ] ( see proposition [ p : new1 ] and theorem [ t : globalhke ] below ) . thus condition * ( c ) * amounts to say that there exist constants @xmath105 and @xmath106 $ ] such that for @xmath107 $ ] and @xmath74 , @xmath108 since @xmath109 is a decreasing function in @xmath102 , implies that condition * ( b ) * holds with @xmath110 and @xmath111 . \(iii ) assume that condition * ( a ) * holds . it follows from @xcite that , for every @xmath112 , there is a constant @xmath113 so that holds for @xmath114\times ( 0 , r]$ ] with @xmath115 . ( see proposition [ p : new1 ] below . ) so the assertions in conditions * ( b ) * and * ( c ) * are always satisfied for @xmath116 . \(iv ) by @xcite , @xmath117\times ( 0 , \infty),\ ] ] and consequently conditions * ( b ) * and * ( c ) * , hold for a large class of discontinuous processes including mixed stable - like processes ( with @xmath115 ) and relativistic stable - like processes ( with @xmath115 , see ( * ? ? ? * theorem 4.1 ) ) . before stating the main results of this paper , we need first to set up some notations . let @xmath118 . we denote the euclidean distance between @xmath119 and @xmath120 in @xmath7 by @xmath77 and denote by @xmath121 the open ball centered at @xmath122 with radius @xmath74 ; for any two positive functions @xmath50 and @xmath123 , @xmath124 means that there is a positive constant @xmath105 so that @xmath125 on their common domain of definition ; for any open @xmath126 and @xmath127 , @xmath128 stands for the diameter of @xmath0 and @xmath129 stands for the euclidean distance between @xmath119 and @xmath10 . [ def : ub ] let @xmath130 . we say that a open set @xmath0 is @xmath1-fat if there is @xmath131 such that for all @xmath132 and all @xmath133 $ ] , there is a ball @xmath134 . the pair @xmath135 is called the characteristics of the @xmath1-fat open set @xmath0 . the following factorization of the dirichlet heat kernel is the first main result of this paper . recall that @xmath136 and @xmath137 are the constants in condition * ( b)*. [ thm : oppz ] let @xmath6 be a purely discontinuous rotationally symmetric lvy process with lvy exponent @xmath5 and lvy density @xmath65 satisfying and respectively , where the complete bernstein function @xmath4 satisfies * ( a)*. suppose that @xmath0 is a @xmath1-fat open set with characteristics @xmath135 . \(i ) for every @xmath138 , there exists @xmath139 such that for @xmath140 , @xmath141 , @xmath142 \(ii ) if @xmath0 is unbounded , we assume in addition that condition * ( b ) * holds . for every @xmath138 , there exists @xmath143 such that for @xmath140 , @xmath141 , @xmath144 where @xmath145 . \(iii ) suppose in addition that @xmath0 is bounded . then there exists @xmath146 so that for all @xmath147 , @xmath148 where @xmath149 is the largest eigenvalue of the generator of @xmath80 . when @xmath6 is a rotationally symmetric @xmath11-stable process in @xmath7 , that is , when @xmath150 for some @xmath151 , parts ( i ) and ( ii ) of theorem [ thm : oppz ] are proved in @xcite . recall that @xmath152 and @xmath153 are the constants in condition * ( c)*. combining theorem [ thm : oppz](i)(ii ) and remark [ r:1.1](ii ) , we have the following corollary . [ c : main1 ] let @xmath6 be a purely discontinuous rotationally symmetric lvy process with lvy exponent @xmath5 and lvy density @xmath65 satisfying and respectively , where the complete bernstein function @xmath4 satisfies * ( a)*. suppose that @xmath0 is a @xmath1-fat open set with characteristics @xmath135 . if @xmath0 is unbounded , we assume in addition that condition * ( c ) * holds . for every @xmath138 , there exist @xmath154 and @xmath155 such that for @xmath140 , @xmath141 , @xmath156 where @xmath157 . the second main result of this paper is on explicit sharp dirichlet heat kernel estimates for subordinate brownian motions in @xmath158 open sets . so in the remainder of this section , we assume that @xmath159 , a subordinate brownian motion with lvy exponent @xmath160 . recall that an open set @xmath0 in @xmath161 ( when @xmath162 ) is said to be a ( uniform ) @xmath158 open set if there exist a localization radius @xmath163 and a constant @xmath164 such that for every @xmath165 , there exist a @xmath158-function @xmath166 satisfying @xmath167 , @xmath168 , @xmath169 , @xmath170 such that @xmath171 the pair @xmath172 is called the characteristics of the @xmath158 open set @xmath0 . note that a @xmath158 open set @xmath0 with characteristics @xmath172 can be unbounded and disconnected ; the distance between two distinct components of @xmath0 is at least @xmath173 . by a @xmath158 open set in @xmath174 we mean an open set which can be written as the union of disjoint intervals so that the minimum of the lengths of all these intervals is positive and the minimum of the distances between these intervals is positive . here is the second main result of this paper , which gives an affirmative answer to the conjecture posed in @xcite . in view of remark [ r:1.1 ] , it extends the main results of @xcite . recall that condition * ( b ) * holds with @xmath97 for any subordinate brownian motion . [ t : main ] suppose that @xmath6 is a subordinate brownian motion with lvy exponent @xmath160 with @xmath4 being a complete bernstein function satisfying condition * ( a)*. let @xmath0 be a @xmath158 open subset of @xmath161 with characteristics @xmath172 . \(i ) for every @xmath138 , there exists @xmath175 such that for all @xmath176\times d\times d$ ] , @xmath177 \(ii ) for every @xmath138 , there exists @xmath178 such that for all @xmath176\times d\times d$ ] , @xmath179 \(iii ) suppose in addition that @xmath0 is bounded . for every @xmath138 , there exists @xmath180 depending only on @xmath181 and @xmath182 so that for all @xmath183 , @xmath184 where @xmath149 is the largest eigenvalue of the generator of @xmath80 . recall that @xmath152 and @xmath153 are the constants in condition * ( c)*. combining theorem [ t : main](i)(ii ) and remark [ r:1.1](ii ) , we have the following corollary . [ c : main2 ] suppose that @xmath6 is a subordinate brownian motion with lvy exponent @xmath160 with @xmath4 being a complete bernstein function satisfying condition * ( a)*. let @xmath0 be a @xmath158 open subset of @xmath161 with characteristics @xmath172 . if @xmath0 is unbounded , we assume in addition that condition * ( c ) * holds . for every @xmath138 , there exist @xmath175 and @xmath185 such that for @xmath140 , @xmath141 , @xmath186 when @xmath6 is a rotationally symmetric @xmath11-stable process in @xmath7 , theorem [ t : main ] is first established in @xcite . sharp two - sided dirichlet heat kernel estimates in @xmath158 open sets are subsequently established in @xcite for censored stable processes , relativistic stable processes , mixed stable processes , and mixed brownian motion and stable processes , respectively . by integrating the two - sided heat kernel estimates in theorem [ t : main ] with respect to @xmath76 , we obtain the two - sided estimates on the green function @xmath187 ( see theorem [ t : gfe ] below ) , which extend ( * ? ? ? * theorem 1.1 ) . condition * ( a ) * is a very weak condition on the behavior of @xmath4 near infinity . using the tables at the end of @xcite , one can come up plenty of explicit examples of complete bernstein functions satisfying condition * ( a)*. here are a few of them . \(1 ) @xmath188 , @xmath189 $ ] ( symmetric @xmath11-stable process ) ; \(2 ) @xmath190 , @xmath191 and @xmath192 ( relativistic @xmath11-stable process ) ; \(3 ) @xmath193 , @xmath194 ( mixed symmetric @xmath11- and @xmath195-stable processes ) ; \(4 ) @xmath196 , @xmath191 , @xmath197 $ ] . now we give a way of constructing less explicit complete bernstein functions that have very general asymptotic behavior at infinity . suppose that @xmath191 and @xmath198 is a positive function on @xmath22 which is slowly varying at infinity . we further assume that @xmath199 is a right continuous increasing function with @xmath200 ( so @xmath201 ) . then the function @xmath202 is a stieltjes function , and so the function @xmath203 is a complete bernstein function ( see ( * ? ? ? * theorem 7.3 ) ) . it follows from ( * ? ? ? * lemma 6.2 ) that @xmath204 when @xmath205 . the rest of the paper is organized as follows . section [ s:2 ] recalls and collects some preliminary results that will be used in the sequel , including on - diagonal heat kernel estimates and the boundary harnack principle . section [ s:3 ] presents the interior lower bound heat kernel estimates , including an explicit lower bound estimate for symmetric lvy processes on @xmath7 . the proof of the short time factorization result for @xmath12 ( that is , theorem [ thm : oppz](i ) and ( ii ) ) is given in section [ s:4 ] , while the proof of theorem [ t : main](i ) and ( ii ) is given in section [ s:5 ] . the large time heat kernel estimates are proved in section [ s:6 ] . the green function estimates for subordinate brownian motions in bounded @xmath158 open sets are derived in section [ s:7 ] from the two - sided dirichlet heat kernel estimates in theorem [ t : main ] . the derivation , however , requires quite some effort . throughout this paper , @xmath206 and the constants @xmath207 , @xmath208 , @xmath173 , @xmath209 , @xmath1 , @xmath210 , @xmath211 , @xmath136 , @xmath137 , @xmath152 , @xmath153 , @xmath212 and @xmath213 will be fixed . we use @xmath214 to denote generic constants , whose exact values are not important and can change from one appearance to another . the labeling of the constants @xmath214 starts anew in the statement of each result . the dependence of the constant @xmath215 on the dimension @xmath216 will not be mentioned explicitly . we will use @xmath217 " to denote a definition , which is read as is defined to be " . we will use @xmath218 to denote a cemetery point and for every function @xmath50 , we extend its definition to @xmath218 by setting @xmath219 . we will use @xmath220 to denote the lebesgue measure in @xmath161 . for a borel set @xmath221 , we also use @xmath222 to denote its lebesgue measure .

in this paper , we consider a large class of purely discontinuous rotationally symmetric lvy processes . we establish sharp two - sided estimates for the transition densities of such processes killed upon leaving an open set . when is a-fat open set , the sharp two - sided estimates are given in terms of surviving probabilities and the global transition density of the lvy process . our results are the first sharp two - sided dirichlet heat kernel estimates for a large class of symmetric lvy processes with general lvy exponents . we also derive an explicit lower bound estimate for symmetric lvy processes on in terms of their lvy exponents . * ams 2000 mathematics subject classification * : primary 60j35 , 47g20 , 60j75 ; secondary 47d07 * keywords and phrases * : lvy processes , subordinate brownian motion , heat kernel , transition density , dirichlet transition density , green function , exit time , lvy system , boundary harnack inequality , parabolic harnack inequality

in this paper , we consider a large class of purely discontinuous rotationally symmetric lvy processes . we establish sharp two - sided estimates for the transition densities of such processes killed upon leaving an open set . when is a-fat open set , the sharp two - sided estimates are given in terms of surviving probabilities and the global transition density of the lvy process . when is a open set and the lvy exponent of the process is given by with being a complete bernstein function satisfying a mild growth condition at infinity , our two - sided estimates are explicit in terms of , the distance function to the boundary of and the jumping kernel of , which give an affirmative answer to the conjecture posted in . our results are the first sharp two - sided dirichlet heat kernel estimates for a large class of symmetric lvy processes with general lvy exponents . we also derive an explicit lower bound estimate for symmetric lvy processes on in terms of their lvy exponents . * ams 2000 mathematics subject classification * : primary 60j35 , 47g20 , 60j75 ; secondary 47d07 * keywords and phrases * : lvy processes , subordinate brownian motion , heat kernel , transition density , dirichlet transition density , green function , exit time , lvy system , boundary harnack inequality , parabolic harnack inequality

0809.2446

i

current wireless standards ( e.g. , ieee 802.11n and 802.16e ) have adopted mimo techniques @xcite-@xcite to achieve the benefits of transmit diversity ( using space - time coding ) and high data rates ( using spatial multiplexing ) . they , however , harness only a limited potential of mimo benefits since they use only a small number of transmit antennas ( e.g. , 2 to 4 antennas ) . significant benefits can be realized if large number of antennas are used ; e.g. , large - mimo systems with tens of antennas in communication terminals can enable multi - giga bit rate transmissions at high spectral efficiencies of the order of _ several tens of bps / hz_. key challenges in realizing such large - mimo systems include low - complexity detection and channel estimation , rf / if technologies , and placement of large number of antennas in communication terminals . our focus in this paper is on low - complexity detection and channel estimation for large - mimo systems . spatial multiplexing ( v - blast ) with large number of transmit antennas can offer high spectral efficiencies , but it does not give transmit diversity . on the other hand , well known orthogonal space - time block codes ( stbc ) have the advantages of full transmit diversity and low decoding complexity , but they suffer from rate loss for increasing number of transmit antennas @xcite,@xcite,@xcite . however , _ full - rate , non - orthogonal stbcs from cyclic division algebras ( cda ) _ @xcite are attractive to achieve high spectral efficiencies in addition to achieving full transmit diversity , using large number of transmit antennas . for example , a @xmath2 stbc matrix from cda has 1024 symbols ( i.e. , 32 complex symbols per channel use ) , and using this stbc along with 16-qam and rate-3/4 turbo code offers a spectral efficiency of 96 bps / hz . while maximum - likelihood ( ml ) decoding of orthogonal stbcs can be achieved in linear complexity , ml or near - ml decoding of non - orthogonal stbcs with large number of antennas at low complexities has been a challenge . channel estimation is also a key issue in large - mimo systems . in this paper , we address these two challenging problems ; our proposed solutions can potentially enable realization of large - mimo systems in practice . sphere decoding and several of its low - complexity variants are known in the literature @xcite-@xcite . these detectors , however , are prohibitively complex for large number of antennas . recent approaches to low - complexity multiuser / mimo detection involve application of techniques from belief propagation @xcite , markov chain monte - carlo methods @xcite , neural networks @xcite,@xcite,@xcite , etc . in particular , in @xcite,@xcite , we presented a powerful hopfield neural network based low - complexity search algorithm for detecting large - mimo v - blast signals , and showed that it performs quite close to ( within 4.6 db of ) the theoretical capacity , at high spectral efficiencies of the order of tens to hundreds of bps / hz using tens to hundreds of antennas , at an average per - symbol detection complexity of just @xmath3 , where @xmath4 and @xmath5 denote the number of transmit and receive antennas , respectively . in this paper , we present @xmath6 ) a low - complexity near - ml achieving detector , and @xmath7 ) an iterative detection / channel estimation scheme for large non - orthogonal stbc mimo systems having tens of transmit and receive antennas . our key contributions here can be summarized as follows : 1 . we generalize the 1-symbol update based _ likelihood ascent search _ ( las ) algorithm we proposed in @xcite,@xcite , by employing a low - complexity multistage multi - symbol update based strategy ; we refer to this new algorithm as multistage las ( @xmath0-las ) algorithm . we show that the @xmath0-las algorithm outperforms the basic las algorithm with some increase in complexity . we propose a method to generate soft outputs from the @xmath0-las output vector . soft outputs generation was not considered in @xcite,@xcite . the proposed soft outputs generation for the individual bits results in about 1 to 1.5 db improvement in coded bit error rate ( ber ) compared to hard decision @xmath0-las outputs . 3 . assuming i.i.d . fading and perfect channel state information at the receiver ( csir ) , our simulation results show that the proposed @xmath0-las algorithm is able to decode large non - orthogonal stbcs ( e.g. , @xmath1 and @xmath2 stbcs ) and achieve near single - input single - output ( siso ) awgn uncoded ber performance as well as near - capacity ( within 4 db from theoretical capacity ) coded ber performance . 4 . using the proposed detector , we decode and report the simulated ber performance of ` perfect codes ' @xcite-@xcite of large dimensions . 5 . presenting a ber performance and complexity comparison of the proposed cda stbc/@xmath0-las detection approach with other large - mimo / detector approaches ( e.g. , stacked alamouti codes / qostbcs and associated interference canceling receivers reported in @xcite ) , we show that the proposed approach outperforms the other considered approaches , both in terms of performance as well as complexity . we present simulation results that quantify the loss in ber performance due to spatial correlation in large - mimo systems , by considering a more realistic spatially correlated mimo fading channel model proposed by gesbert _ et al _ in @xcite . we show that this loss in performance can be alleviated by providing more receive dimensions ( i.e. , more receive antennas than transmit antennas ) . 7 . finally , we present a training - based iterative detection / channel estimation scheme for large stbc mimo systems . we report ber and nearness - to - capacity results when the channel matrix is estimated using the proposed iterative scheme and compare these results with those obtained using perfect csir assumption . the rest of the paper is organized as follows . in section [ sec2 ] , we present the stbc mimo system model considered . the proposed detection algorithm is presented in section [ sec3 ] . ber performance results with perfect csir are presented in section [ sec4 ] . this section includes the results on the effect of spatial correlation , ber performance of large perfect codes , and comparison of the proposed scheme with other large - mimo architecture / detector combinations . the proposed iterative detection / channel estimation scheme and the corresponding performance results are presented in section [ sec5 ] . conclusions are presented in section [ sec6 ] .

the fact that we could show such good results for large stbcs like and stbcs from cyclic division algebras ( cda ) operating at spectral efficiencies in excess of 20 bps / hz ( even after accounting for the overheads meant for pilot based training for channel estimation and turbo coding ) establishes the effectiveness of the proposed detector and channel estimator . large - mimo systems , low - complexity detection , channel estimation , non - orthogonal space - time block codes , high spectral efficiencies .

in this paper , we present a low - complexity algorithm for detection in high - rate , non - orthogonal space - time block coded ( stbc ) large - mimo systems that achieve high spectral efficiencies of the order of tens of bps / hz . we also present a training - based iterative detection / channel estimation scheme for such large stbc mimo systems . our simulation results show that excellent bit error rate and nearness - to - capacity performance are achieved by the proposed multistage _ likelihood ascent search _ (-las ) detector in conjunction with the proposed iterative detection / channel estimation scheme at low complexities . the fact that we could show such good results for large stbcs like and stbcs from cyclic division algebras ( cda ) operating at spectral efficiencies in excess of 20 bps / hz ( even after accounting for the overheads meant for pilot based training for channel estimation and turbo coding ) establishes the effectiveness of the proposed detector and channel estimator . we decode perfect codes of large dimensions using the proposed detector . with the feasibility of such a low - complexity detection / channel estimation scheme , large - mimo systems with tens of antennas operating at several tens of bps / hz spectral efficiencies can become practical , enabling interesting high data rate wireless applications . large - mimo systems , low - complexity detection , channel estimation , non - orthogonal space - time block codes , high spectral efficiencies .

0809.2446

c

we presented a low - complexity algorithm for the detection of high - rate , non - orthogonal stbc large - mimo systems with tens of antennas that achieve high spectral efficiencies of the order of several tens of bps / hz . we also presented a training - based iterative detection / channel estimation scheme for such large stbc mimo systems . our simulation results showed that the proposed 1-las detector along with the proposed iterative detection / channel estimation scheme achieved very good performance at low complexities . with the feasibility of low - complexity high - performance receivers , like the proposed detection / channel estimation scheme , large - mimo systems with tens of antennas at high spectral efficiencies can become practical , enabling interesting high data rate wireless applications ( e.g. , wireless iptv / hdtv distribution ) . this can motivate the inclusion of large - mimo architectures ( e.g. , @xmath337 , @xmath1 mimo systems , including those using stbcs from cda ) into wireless standards like ieee 802.11n / vht and ieee 802.16/lte - a in their evolution to achieve high data rates at increased spectral efficiencies .

in this paper , we present a low - complexity algorithm for detection in high - rate , non - orthogonal space - time block coded ( stbc ) large - mimo systems that achieve high spectral efficiencies of the order of tens of bps / hz . we also present a training - based iterative detection / channel estimation scheme for such large stbc mimo systems . our simulation results show that excellent bit error rate and nearness - to - capacity performance are achieved by the proposed multistage _ likelihood ascent search _ (-las ) detector in conjunction with the proposed iterative detection / channel estimation scheme at low complexities . we decode perfect codes of large dimensions using the proposed detector . with the feasibility of such a low - complexity detection / channel estimation scheme , large - mimo systems with tens of antennas operating at several tens of bps / hz spectral efficiencies can become practical , enabling interesting high data rate wireless applications .

in this paper , we present a low - complexity algorithm for detection in high - rate , non - orthogonal space - time block coded ( stbc ) large - mimo systems that achieve high spectral efficiencies of the order of tens of bps / hz . we also present a training - based iterative detection / channel estimation scheme for such large stbc mimo systems . our simulation results show that excellent bit error rate and nearness - to - capacity performance are achieved by the proposed multistage _ likelihood ascent search _ (-las ) detector in conjunction with the proposed iterative detection / channel estimation scheme at low complexities . the fact that we could show such good results for large stbcs like and stbcs from cyclic division algebras ( cda ) operating at spectral efficiencies in excess of 20 bps / hz ( even after accounting for the overheads meant for pilot based training for channel estimation and turbo coding ) establishes the effectiveness of the proposed detector and channel estimator . we decode perfect codes of large dimensions using the proposed detector . with the feasibility of such a low - complexity detection / channel estimation scheme , large - mimo systems with tens of antennas operating at several tens of bps / hz spectral efficiencies can become practical , enabling interesting high data rate wireless applications . large - mimo systems , low - complexity detection , channel estimation , non - orthogonal space - time block codes , high spectral efficiencies .

1004.2773

i

full diversity and low decoding complexity have been considered as two fundamental properties which a good space - time block code ( stbc ) should possess for multiple - input multiple - output ( mimo ) wireless communications . the first orthogonal stbc ( ostbc ) was proposed by alamouti which can achieve full transmit diversity for two transmit antennas@xcite . inspired by the alamouti scheme , seminal studies focused on the designs of ostbc for its unique orthogonal code structure which ensures a single symbol maximum likelihood ( ml ) decoding @xcite@xcite@xcite . however , ostbc suffers from the reduced symbol rate with an increase of the number of transmit antennas , especially when complex constellations are used @xcite . in spite of full diversity advantage , ostbc fails to achieve full channel capacity in mimo channels @xcite . to address the problem of low symbol rate and capacity loss in ostbc , linear dispersion code ( ldc ) was proposed as a full - diversity scheme that is constructed linearly in space and time @xcite @xcite . the ldc design can be viewed as a linear combination of a fixed set of dispersion matrices with the transmitted symbols ( or equivalently , combining coefficients ) . diagonal algebraic space - time ( dast ) block codes in @xcite and threaded algebraic space - time ( tast ) codes in @xcite were also proposed as two typical algebraic designs which can obtain both full diversity and full rate with moderate ml decoding complexity . however , it is noted that the aforementioned high - rate codes rely on ml decoding to collect full diversity which has high decoding complexity . efficient designs of stbc with low decoding complexity were proposed , such as coordinate interleaved orthogonal design ( ciod ) with single - symbol ml decoding in @xcite and quasi - orthogonal stbc ( qostbc ) in @xcite@xcite , but their rates are restricted by the rates of ostbc . recently , full diversity achieving stbc based on linear receivers , such as the minimum mean square error ( mmse ) receiver and zero - forcing ( zf ) receiver , were studied and proposed @xcite , @xcite . however , it was shown in @xcite that the rates of these stbc based on linear receivers are not more than one . to address the complexity and rate tradeoff , a general decoding scheme with code design criterion , referred to as partial interference cancellation ( pic ) group decoding algorithm , was proposed in @xcite . in the pic group decoding , the symbols to be decoded are divided into several groups after a linear pic operation and then each group is decoded separately with ml decoding . therefore , the pic group decoding can be viewed as an intermediate decoding between ml decoding and zf decoding . apparently , pic group decoding complexity depends on the number of symbols to be decoded in each group . moreover , a successive interference cancellation ( sic)-aided pic group decoding was proposed in @xcite . based on the design criterion of stbc with pic group decoding derived in @xcite , a systematic design of stbc achieving full diversity under pic group decoding was developed in @xcite . in subsequent work , a new design of stbc having an alamouti - toeplitz structure was proposed in @xcite which provides a lower pic decoding complexity compared with the design in @xcite . however , the decoding complexity of the stbc in @xcite is equivalent to a joint decoding of @xmath3 complex symbols . in this paper , we propose a design of stbc with pic group decoding that can achieve both full diversity and low decoding complexity . the decoding complexity is equal to a joint decoding of @xmath3 _ real _ symbols for @xmath0 transmit antennas , i.e. , only half decoding complexity of the stbc in @xcite . for the proposed stbc , real and imaginary parts of @xmath1 complex information symbols are parsed into @xmath2 diagonal layers and encoded by linear transform matrices , respectively . the full diversity can be achieved by the proposed stbc with @xmath6 under pic group decoding and with any @xmath2 under pic - sic group decoding , respectively . the code rate is equal to @xmath7 . in particular , for @xmath4 transmit antennas the code has real symbol pairwise ( i.e. single complex symbol ) decoding . furthermore , the code rate is @xmath5 . it should be noted that the existing stbc with single complex symbol ( or real symbol pairwise ) decoding , such as qostbc @xcite , @xcite , and ciod etc . in @xcite have symbol rates not larger than one . also the codes with linear receivers have single complex symbol decoding but their rates can not be above one either @xcite . simulation results show that the proposed code outperforms the ciod in @xcite and the qostbc with the optimal rotation in @xcite for @xmath4 transmit antennas at the same bandwidth efficiency . moreover , our code guarantees full diversity without performance loss compared with other pic group decoding based stbc in @xcite , @xcite and @xcite , but a half decoding complexity is reduced . it should be mentioned that the major difference between the code in @xcite and the one proposed in this paper is that a complex - valued linear transform matrix is used for input complex signal vector to construct the code in @xcite , whereas in this paper two real - valued linear transform matrices are used for real and imaginary parts of the signals , respectively . by doing so , half decoding complexity can be reduced . the rest of this paper is organized as follows . the system model is outlined in section ii . in section iii , a systematic design of stbc is proposed and a few code design examples are also given . the full diversity is proved under pic group decoding in section iv . in section v , simulation results are presented . finally , we conclude the paper in section vi . the following notations are used throughout this paper . column vectors ( matrices ) are denoted by boldface lower ( upper ) case letters . superscripts @xmath8 , @xmath9 and @xmath10 stand for conjugate , transpose , and conjugate transpose , respectively . @xmath11 denotes the field of complex numbers and @xmath12 denotes the real field . @xmath13 denotes the @xmath14 identity matrix , and @xmath15 denotes the @xmath16 matrix whose elements are all @xmath17 . additionally , @xmath18 and @xmath19 represent the real part and the imaginary part of variables , respectively .

the proposed codes can be applied to any number of transmit antennas and admit a low decoding complexity while achieving full diversity . for transmit antennas , in each codeword real and imaginary parts of complex information symbols are parsed into diagonal layers and then encoded , respectively . in particular , for transmit antennas , the code has real symbol pairwise ( i.e. , single complex symbol ) decoding that achieves full diversity and the code rate is . simulation results demonstrate that the full diversity is offered by the newly proposed stbc with the pic group decoding .

in this paper , we propose a systematic design of space - time block codes ( stbc ) which can achieve high rate and full diversity when the partial interference cancellation ( pic ) group decoding is used at receivers . the proposed codes can be applied to any number of transmit antennas and admit a low decoding complexity while achieving full diversity . for transmit antennas , in each codeword real and imaginary parts of complex information symbols are parsed into diagonal layers and then encoded , respectively . with pic group decoding , it is shown that the decoding complexity can be reduced to a joint decoding of real symbols . in particular , for transmit antennas , the code has real symbol pairwise ( i.e. , single complex symbol ) decoding that achieves full diversity and the code rate is . simulation results demonstrate that the full diversity is offered by the newly proposed stbc with the pic group decoding . 4.6ex mimo systems , space - time block codes , partial interference cancellation , decoding complexity

1004.2773

c

in this paper , we proposed a systematic design of stbc that can achieve full diversity with the pic group decoding . by coding the real and imaginary parts of the complex symbols vector independently , the proposed code has a reduced pic group decoding complexity , which is equivalent to a joint decoding of @xmath3 real symbols for @xmath0 transmit antennas . the full diversity of the proposed stbc with @xmath2 diagonal layers was proved for pic group decoding with @xmath6 and pic - sic group decoding with any @xmath2 , respectively . it is worthwhile to mention that for @xmath4 transmit antennas the code admits real symbol pairwise decoding and the code rate is @xmath5 . simulation results show that our proposed code can achieve full diversity with a lower decoding complexity than other existing codes .

in this paper , we propose a systematic design of space - time block codes ( stbc ) which can achieve high rate and full diversity when the partial interference cancellation ( pic ) group decoding is used at receivers . with pic group decoding , it is shown that the decoding complexity can be reduced to a joint decoding of real symbols .

in this paper , we propose a systematic design of space - time block codes ( stbc ) which can achieve high rate and full diversity when the partial interference cancellation ( pic ) group decoding is used at receivers . the proposed codes can be applied to any number of transmit antennas and admit a low decoding complexity while achieving full diversity . for transmit antennas , in each codeword real and imaginary parts of complex information symbols are parsed into diagonal layers and then encoded , respectively . with pic group decoding , it is shown that the decoding complexity can be reduced to a joint decoding of real symbols . in particular , for transmit antennas , the code has real symbol pairwise ( i.e. , single complex symbol ) decoding that achieves full diversity and the code rate is . simulation results demonstrate that the full diversity is offered by the newly proposed stbc with the pic group decoding . 4.6ex mimo systems , space - time block codes , partial interference cancellation , decoding complexity

0805.4047

i

applications of phase - transforming materials such as shape memory alloys ( smas ) and shape memory polymers are very broad . for example , they have been used to make satellite dampers , golf club heads and snake - like robots and so on . in particular , these materials have been used to design many minimal surgery devices ( pelton _ et al . a deep and thorough understanding of the behaviour of this type of phase - transforming material is essential in the manufacturing and designing of these devices . systematic experiments on uniaxial extensions of superelastic niti alloy ( a kind of shape memory alloys and also one kind of phase - transforming materials ) wires and strips ( shaw @xmath0 kyriakides 1995 , 1997 , 1998 ) showed the measured engineering stress - strain curves have the key features : the nucleation stress occurs at a local maximum which is significantly larger than the maxwell stress ; following the nucleation stress there is a sharp stress drop ; and afterwards there is a stress plateau . these features were also observed in experiments done by others ( sun _ et al . _ 2000 , tse @xmath0 sun 2000 , favier _ et al . _ 2001 and li @xmath0 sun 2002 ) . theoretically , solid - solid phase transitions have also been studied for a long time in the context of both continuum and lattice theories . the seminal work of ericksen ( 1975 ) , which considered a continuum one - dimensional stress problem , made clear that for a non - convex strain energy function the solution with two phases can arise and there are multiple solutions . based on the lattice model for a two - phase martensitic material , it is possible to deduce in the related continuum model the strain - energy function has double wells ; see ball @xmath0 james ( 1992 ) . in general , it is now understood that in the continuum scale for a material whose strain - energy function is non - convex phase transitions can take place ( see also , abeyaratne _ et al . _ 2001 ) . with a proper choice of a strain - energy function , phase transitions can be modeled through a continuum theory . still , to justify this point of view , it is desirable ( probably necessary ) to compare the analytical solutions based on this type of energy functions with experimental results . but , the difficulty is that we lack mathematical theories for mixed type equations that typically arise from non - convex energy functions . analytical solutions for boundary - value problems are very few . in the classical paper of ericksen ( 1975 ) , analytical solutions were constructed for a static problem based on a pure one - dimensional stress model , which neglects the effect from other dimensions . however , a one - dimensional model appears to be not sophisticated enough to capture some key features observed in experiments . we give the explanations below . in the experiments ( shaw @xmath0 kyriakides 1995 , 1997 ; li @xmath0 sun 2002 ) , it was observed that after the nucleation stress was reached the nucleation process began and accompanying with it there was a radial contraction ( necking ) . also , after the two - phase state was formed , the deformation was inhomogeneous , one part being thin and one part being thick . as pointed out by chang _ et al . _ ( 2006 ) that the axial extent of the transformation front is of the order of the radius . thus , to model the nucleation process and the inhomogeneous deformation of different thicknesses , one should consider the radial deformation . theoretically , if one treats the problem as a one - dimensional stress one , there is a discontinuous interface between two phases with two different strain values . the thicknesses of the cylinder at two phases are different , thus the shear strain @xmath1 ( @xmath2 is the radial displacement and @xmath3 is the axial coordinate ) is nonzero ( infinite at the phase boundary ) . the traction - free boundary conditions require the two stress components @xmath4 ( depending on @xmath5 up to the second order ) and @xmath6 ( depending on @xmath1 ) to be zero at the lateral surface , which can not be satisfied . thus , it appears that to model phase transitions by a one - dimensional stress approximation violates the traction - free boundary conditions . in the papers of dai @xmath0 cai ( 2006 ) and cai @xmath0 dai ( 2006 ) , phase transitions in a slender cylinder composed of a _ special _ _ incompressible _ elastic material was considered . a novel series - asymptotic approach is utilized to reduce the field equations . a proper asymptotic model equation is derived , which takes into account the influences of the radial deformation and traction - free boundary conditions . the solutions for two boundary - value problems are obtained , and they could capture the key features observed in experiments . in this paper , we study the phase transitions in a slender cylinder composed of a _ general _ _ compressible _ elastic material due to tension / extension . also , different from the previous studies on _ incompressible _ materials , here we further consider the coupling effect of the material nonlinearity and geometrical size . another important new feature is that we consider the more practical clamped end conditions instead of the natural boundary conditions used in cai @xmath0 dai ( 2006 ) . we consider the problem in a three - dimensional setting , different from the one - dimensional stress problem studied by ericksen ( 1975 ) . however , the strain - energy function is assumed to have the same property as that in ericksen ( 1975 ) , i.e. , for a one - dimensional stress problem the stress - strain curve has a peak - valley combination ( cf . figure 1 ) . we aim at constructing the asymptotic solutions and using them to explain the experimental results . mathematically , to deduce the analytical solutions for the present problem is a very difficult task . one need to deal with coupled nonlinear partial differential equations ( pde s ) together with complicated boundary conditions . further , the existence of multiple solutions ( corresponding to the instability phenomena ( e.g. , stress drop ) observed in experiments ) makes the problem even harder to solve . here , the analysis is carried out by a novel methodology developed earlier ( dai @xmath0 huo 2002 ; dai @xmath0 fan 2004 ; dai @xmath0 cai 2006 ) , which is capable of treating the global bifurcation problem of nonlinear pde s and obtaining the post - bifurcation solutions . we construct the solutions and extract from them important information on the deformation configurations , the nucleation stress , the instability phenomena and the transformation front . comparisons with experimental results are made , which show that the asymptotic solutions can capture the key features of the experimental engineering stress - strain curves and the instability phenomena as observed in experiments . the qualitative agreements give supporting evidence that a non - convex strain energy function can be used to describe solid - solid phase transitions and the instability phenomena in phase transformations are mainly due to the non - convexity of the strain energy function . this paper is arranged as follows . in section 2 , we formulate the field equations by treating the slender cylinder as a three - dimensional object . in section 3 , we carry out a non - dimensionalization process to extract the important small variable and two small parameters which characterize this problem . then we derive the normal form equation of the original governing nonlinear pde s in section 4 , through series and asymptotic expansions . in section 5 , we show that the euler - lagrange equation can also lead to the same normal form equation , which justifies our method in deriving this equation . in section 6 , we propose the clamped boundary conditions . in section 7 , we construct the asymptotic solutions for both a force - controlled problem and a displacement - controlled problem . we also use the solutions obtained to explain some experimental results . finally , some conclusions are drawn .

the engineering stress - strain curve plotted from the asymptotic solutions can capture the key features of the curve measured in a few experiments ( e.g. , the stress drop , the stress plateau , and the small stress valley ) . also , an important feature of this work is that we consider the clamped end conditions , which are more practical but rarely used in literature for phase transition problems . * key words * : phase transformation ; hyperelastic material ; asymptotic analysis ; cylinder ; bifurcations of pde s

in this paper , we study phase transitions in a slender circular cylinder composed of a compressible hyperelastic material with a non - convex strain energy function . we aim to construct the asymptotic solutions based on an axisymmetrical three - dimensional setting and use the results to describe the key features ( in particular , instability phenomena ) observed in the experiments by others . the difficult problem of the solution bifurcations of the governing nonlinear partial differential equations ( pde s ) is solved through a novel approach . by using a methodology involving coupled series - asymptotic expansions , we derive the normal form equation of the original complicated system of nonlinear pde s . by writing the normal form equation into a first - order dynamical system and with a phase - plane analysis , we manage to deduce the global bifurcation properties and to solve the boundary - value problem analytically . the asymptotic solutions ( including post - bifurcation solutions ) in terms of integrals are obtained . the engineering stress - strain curve plotted from the asymptotic solutions can capture the key features of the curve measured in a few experiments ( e.g. , the stress drop , the stress plateau , and the small stress valley ) . it appears that the asymptotic solutions obtained shed certain light on the instability phenomena associated with phase transitions in a cylinder , in particular the role played by the radius - length ratio . also , an important feature of this work is that we consider the clamped end conditions , which are more practical but rarely used in literature for phase transition problems . * key words * : phase transformation ; hyperelastic material ; asymptotic analysis ; cylinder ; bifurcations of pde s

0805.4047

c

we consider phase transitions induced by axial tension / extension in a slender circular cylinder composed of a general compressible hyperelastic material with a non - convex strain energy function under clamped end conditions . in order to capture the macroscopic phenomena observed in the experiments by others , the problem is formulated in a three - dimensional setting and as a result it is governed by a system of coupled nonlinear pde s with complicated nonlinear boundary conditions . a novel approach involving coupled series - asymptotic expansions is developed to derive the normal form equation ( nfe ) of the original system . by conducting the phase - plane analysis on this nfe , we manage to deduce the global bifurcation properties of its solutions . the solutions ( including those for post - bifurcation solutions ) for both a force - controlled problem and a displacement - controlled problem are obtained . these asymptotic solutions demonstrate the essential features of phase transitions in a cylinder and are consistent with the experimental data qualitatively . specifically , the engineering stress - strain curve is shown to have the same features as observed in experiments . these qualitative agreements with experiments give strong supporting evidence that a non - convex strain energy function can be used to describe phase transitions and the non - convexity of the strain energy function is the main cause of the instability phenomena associated with phase transitions in a slender cylinder . an important finding is that under the clamped end conditions , there exists a critical stress value @xmath229 , which depends on the radius - length ratio and larger than the maxwell stress , such that phase transition can only happen when the engineering stress is larger than this value . this is different from the case of the nature boundary condition that phase transition can happen as long as the engineering stress is larger than the maxwell stress . * acknowledgments * the work described in this paper was fully supported by two grants from the research grants council of the hksar , china ( project numbers : cityu 100804 and cityu 100807 ) . @number#1 addtoreset#1sectionnamedefthe#1 . @nostar@section .@em @empty@section @numberequation@numberfigure@numbertable @star@section@empty@section@section @numberequation@numberfigure@numbertable

in this paper , we study phase transitions in a slender circular cylinder composed of a compressible hyperelastic material with a non - convex strain energy function . the difficult problem of the solution bifurcations of the governing nonlinear partial differential equations ( pde s ) is solved through a novel approach . by using a methodology involving it appears that the asymptotic solutions obtained shed certain light on the instability phenomena associated with phase transitions in a cylinder , in particular the role played by the radius - length ratio .

in this paper , we study phase transitions in a slender circular cylinder composed of a compressible hyperelastic material with a non - convex strain energy function . we aim to construct the asymptotic solutions based on an axisymmetrical three - dimensional setting and use the results to describe the key features ( in particular , instability phenomena ) observed in the experiments by others . the difficult problem of the solution bifurcations of the governing nonlinear partial differential equations ( pde s ) is solved through a novel approach . by using a methodology involving coupled series - asymptotic expansions , we derive the normal form equation of the original complicated system of nonlinear pde s . by writing the normal form equation into a first - order dynamical system and with a phase - plane analysis , we manage to deduce the global bifurcation properties and to solve the boundary - value problem analytically . the asymptotic solutions ( including post - bifurcation solutions ) in terms of integrals are obtained . the engineering stress - strain curve plotted from the asymptotic solutions can capture the key features of the curve measured in a few experiments ( e.g. , the stress drop , the stress plateau , and the small stress valley ) . it appears that the asymptotic solutions obtained shed certain light on the instability phenomena associated with phase transitions in a cylinder , in particular the role played by the radius - length ratio . also , an important feature of this work is that we consider the clamped end conditions , which are more practical but rarely used in literature for phase transition problems . * key words * : phase transformation ; hyperelastic material ; asymptotic analysis ; cylinder ; bifurcations of pde s

gr-qc9901061

i

in classical general relativity there are many solutions of einstein equations with closed timelike curves ( ctcs ) @xcite . however , some early calculations of vacuum polarization in spacetimes with ctcs indicated that the renormalized stress - energy tensor diverged at the cauchy horizon or the polarized hypersurfaces @xcite . hawking thus proposed the chronology protection conjecture which stated that physical laws do not allow the appearance of ctcs @xcite . but , many counter - examples to the chronology protection conjecture have been found @xcite . in particular , li and gott @xcite have found a self - consistent vacuum for a massless conformally coupled scalar field in misner space ( see also @xcite ) , which gives an example of a time machine ( i.e. a spacetime with ctcs ) at the semi - classical level ( i.e. the background spacetime is classical but the matter fields are quantized ) . of more interest , recently gott and li have discovered that ctcs could play an important role in the early universe : if we trace backward the history of time , we may enter an early epoch of ctcs , which means that there is no earliest event in time @xcite . according to the theory of quantum foam @xcite , in the early universe ( at the planck epoch ) , quantum fluctuations of spacetime should be very important and the spacetime might have a very complicated topology . very strong fluctuations in the metric of spacetime could cause the lightcones to distribute randomly , which could give rise to a sea of ctcs in the early universe . therefore , we might expect that at very early epochs , the universe could have a tangled network of ctcs . one model of the creation of the universe is the model of tunneling from nothing " @xcite . in this model the universe is supposed to be a lorentzian spacetime [ with signature @xmath1 glued to an early euclidean space [ with signature @xmath2 , thus the universe has a beginning in time ( i.e. the beginning of the lorentzian section ) . this model of tunneling from nothing " has some shortcomings ( see @xcite , and penrose in @xcite ) . contrasting with the model of tunneling from nothing " , in the model of gott and li @xcite , the universe does not need a signature change and has no beginning in time . gott and li s universe is always a lorentzian spacetime but at a very early epoch there is a loop of time . the universe could thus be its own mother and create itself . the model of gott and li has some additional interesting features : the present epoch of the universe is separated from the early ctcs epoch by a past chronology horizon . the only self - consistent solution with this geometry has pure retarded potentials , creating naturally an arrow of time in our current universe , which is consistent with our experience @xcite . thus , ctcs have potentially important applications in the early universe . anti - de sitter space is a spacetime which has ctcs everywhere . it is a solution of the vacuum einstein equation with a negative cosmological constant and has maximum symmetry @xcite . anti - de sitter space plays a very important role in theories of supergravity and superstrings @xcite . if we unfold " anti - de sitter space and go to its covering space , the ctcs disappear . however , if we identify the events related by boost transformations in the covering space of anti - de sitter space , we will get a spacetime with an infinite number of regions with ctcs and an infinite number of regions without ctcs , where the regions with ctcs and the regions without ctcs are separated by chronology horizons . the causal structure is similar to that of misner space , except that misner space has only two regions with ctcs and two regions without ctcs . for misner space , li and gott have found a self - consistent vacuum for a massless conformally coupled scalar field , which is an `` adapted '' rindler vacuum ( i.e. a rindler vacuum with multiple images ) @xcite . in this paper we will show that a self - consistent vacuum also exists for a massless conformally coupled scalar field in the misner - like anti - de sitter space constructed above , which is simply the conformal transformation of li and gott s adapted rindler vacuum . in 1993 , li , xu , and liu constructed a time machine in a space with a complex metric @xcite . in this paper we will show that the lorentzian section of that solution is just the misner - like anti - de sitter space described above . inflation theory proposes that during an early epoch the universe was in a state with an effective positive cosmological constant at the gut ( or planck ) scale @xcite , which is well - described as a de sitter phase . by transition to a zero cosmological constant ( through either quantum tunneling or classical evolution ) , the universe then enters a friedmann big bang stage . but , if there is a transition to a negative cosmological constant ( it does not seem physical theories exclude a negative cosmological constant especially since in supergravity and superstring theories anti - de sitter space is the only known self - consistent solution besides minkowski space @xcite ) , the universe could enter an anti - de sitter phase where ctcs exist . in this paper we will consider some models describing the transition between a de sitter space and an anti - de sitter space , which are obtained by gluing a de sitter space to an anti - de sitter space along a bubble wall , and we will show that self - consistent vacua for these solutions also exist . the generalization to the case of electromagnetic fields and massless neutrinos will also be considered . it is argued that , in order to be consistent with euclidean quantization , a new renormalization procedure for quantum fields in misner - type spaces is required . self - consistent " renormalization procedure is then proposed . with this renormalization procedure , self - consistent vacua exist for massless conformally coupled scalar fields , electromagnetic fields , and massless neutrinos in the misner - type spaces .

in this paper time machines are constructed from anti - de sitter space . self - consistent vacua for a massless conformally coupled scalar field are found for these time machines , whose renormalized stress - energy tensors are finite and solve the semi - classical einstein equations . the extensions to electromagnetic fields and massless neutrinos are discussed . it is argued that , in order to make the results consistent with euclidean quantization , a new renormalization procedure for quantum fields in misner - type spaces ( misner space , misner - like de sitter space , and misner - like anti - de sitter space ) is required . such a self - consistent " renormalization procedure is proposed . with this renormalization procedure , self - consistent vacua exist for massless conformally coupling scalar fields , electromagnetic fields , and massless neutrinos in these misner - type spaces . #

in this paper time machines are constructed from anti - de sitter space . one is constructed by identifying points related via boost transformations in the covering space of anti - de sitter space and it is shown that this misner - like anti - de sitter space is just the lorentzian section of the complex space constructed by li , xu , and liu in 1993 . the others are constructed by gluing an anti - de sitter space to a de sitter space , which could describe an anti - de sitter phase bubble living in a de sitter phase universe . self - consistent vacua for a massless conformally coupled scalar field are found for these time machines , whose renormalized stress - energy tensors are finite and solve the semi - classical einstein equations . the extensions to electromagnetic fields and massless neutrinos are discussed . it is argued that , in order to make the results consistent with euclidean quantization , a new renormalization procedure for quantum fields in misner - type spaces ( misner space , misner - like de sitter space , and misner - like anti - de sitter space ) is required . such a self - consistent " renormalization procedure is proposed . with this renormalization procedure , self - consistent vacua exist for massless conformally coupling scalar fields , electromagnetic fields , and massless neutrinos in these misner - type spaces . #

gr-qc9901061

c

from the covering space of anti - de sitter space , a misner - like anti - de sitter space can be constructed . this misner - like anti - de sitter space has ctcs but the regions with ctcs are separated from the regions without ctcs by chronology horizons . in the appropriate coordinates , this misner - like anti - de sitter space is just the lorentzian section of the complex space with ctcs constructed by li , xu , and liu in 1993 @xcite . for a massless conformally coupled scalar field in this space , a self - consistent vacuum is found , whose renormalized stress - energy tensor is like that of a positive cosmological constant which when added to an appropriate negative bare cosmological constant can self - consistently solve the semi - classical einstein equations . by gluing a de sitter space to an anti - de sitter space along a bubble wall , another new spacetime with ctcs is obtained . this spacetime could describe the transition between de sitter space and anti - de sitter space . in this spacetime , the region with ctcs and the region without ctcs are separated via chronology horizons . for the de sitter / anti - de sitter invariant vacua in these spacetimes , the renormalized stress - energy tensors are like positive cosmological constants . a self - consistent solution can be obtained if there is a single negative bare cosmological constant in the two regions with the renormalized stress - energy tensor of vacuum polarization adding different positive cosmological constants to the two sides of the bubble wall so that the effective cosmological constant ( bare @xmath318 renormalized ) is positive on one side and negative on the other . on the hypersurface separating de sitter space from anti - de sitter space , in order that the einstein equations are satisfied , a surface stress - energy tensor should be induced . if the hypersurface is timelike , the surface stress - energy tensor is like that of a three - dimensional positive cosmological constant . the self - consistent solutions of the semi - classical einstein equations with cosmological constant and the renormalized stress - energy tensor of vacuum polarization in de sitter / anti - de sitter space are investigated . if the bare cosmological constant is positive , there are two self - consistent solutions , both of them are de sitter spaces . if the bare cosmological constant is zero then there are two self - consistent solutions one is minkowski space and the other is a planckian scale de sitter space . if the bare cosmological constant is negative , there are also two self - consistent solutions , one of them is an anti - de sitter space , but the other is a sub - planckian scale de sitter space . and , at the sub - planckian scale , self - consistent solutions ( either de sitter space or anti - de sitter space ) exist only for a bare negative cosmological constant . the generalization to electromagnetic fields and massless neutrinos in spacetimes with ctcs are discussed . it is argued that , for misner - type spacetimes , in order that the semi - classical einstein equations are preserved under continuation between the euclidean and lorentzian sections , a new renormalization procedure should be introduced . we have proposed such a self - consistent renormalization procedure , with which self - consistent vacua for electromagnetic fields and neutrinos are found . k. gdel , rev . mod * 21 * , 447 ( 1949 ) . a. h. taub , ann . math . * 53 * , 472 ( 1951 ) . e. t. newman , l. tamburino , and t. j. unti , j. math . * 4 * , 915 ( 1963 ) . c. w. misner , in _ relativity theory and astrophysics i : relativity and cosmology _ , edited by j. ehlers , lectures in applied mathematics , vol . 8 ( american mathematical society , providence , 1967 ) , p. 160 . m. s. morris , k. s. thorne , and u. yurtsever , phys . lett . * 61 * , 1446 ( 1988 ) . j. r. gott , phys . lett . * 66 * , 1126 ( 1991 ) . w. a. hiscock and d. a. konkowski , phys . d * 26 * , 1225 ( 1982 ) . v. p. frolov , phys . d * 43 * , 3878 ( 1991 ) . kim and k. s. thorne , phys . d * 43 * , 3929 ( 1991 ) . j. d. e. grant , phys . rev . d * 47 * , 2388 ( 1993 ) . s. w. hawking , phys . d * 46 * , 603 ( 1992 ) . d. g. boulware , phys . d * 46 * , 4421 ( 1992 ) . li , j. -m . xu , and l. liu , phys . rev . d * 48 * , 4735 ( 1993 ) . li , phys . d * 50 * , r6037 ( 1994 ) . t. tanaka and w. a. hiscock , phys . d * 52 * , 4503 ( 1995 ) . li , class . quantum grav . * 13 * , 2563 ( 1996 ) . s. v. krasnikov , phys . d * 54 * , 7322 ( 1996 ) . s. v. sushkov , class . quantum grav . * 14 * , 523 ( 1997 ) . m. visser , phys . d * 55 * , 5212 ( 1997 ) . m. j. cassidy , class . quantum grav . * 14 * , 3031 ( 1997 ) . li and j. r. gott , phys . lett * 80 * , 2980 ( 1998 ) . j. r. gott and l. -x . li , phys . d * 58 * , 023501 ( 1998 ) . j. a. wheeler , phys . rev . * 97 * , 511 ( 1955 ) . a. vilenkin , phys . b * 117 * , 25 ( 1982 ) . j. b. hartle and s. w. hawking , phys . d * 28 * , 2960 ( 1983 ) . s. hawking and r. penrose , _ the nature of space and time _ ( princeton university press , princeton , 1996 ) . s. w. hawking and g. f. r. ellis , _ the large scale structure of space - time _ ( cambridge university press , cambridge , 1973 ) . l. castellani , r. dauria , and p. fr , _ supergravity and superstrings : a geometric perspective _ ( world scientific , singapore , 1991 ) . e. witten , preprint hep - th/9805112 ( 1998 ) . a. h. guth , phys . d * 23 * , 347 ( 1981 ) . a. d. linde , phys . 108b * , 389 ( 1982 ) . a. albrecht and p. j. steinhardt , phys . lett * 48 * , 1220 ( 1982 ) . s. w. hawking , in _ general relativity : an einstein centenary survey _ , edited by s. w. hawking and w. israel ( cambridge university press , cambridge , 1979 ) , p. 746 . s. w. hawking , phys . d * 52 * , 5681 ( 1995 ) . n. d. birrell and p. c. w. davies , _ quantum fields in curved space _ ( cambridge university press , cambridge , 1982 ) . j. r. gott , nature * 295 * , 304 ( 1982 ) . j. r. gott , in _ inner space /outer space _ , edited by e. w. kolb et al ( university of chicago press , chicago , 1986 ) . s. coleman , phys . d * 15 * , 2929 ( 1977 ) . s. coleman and f. de luccia , phys . rev . d * 21 * , 3305 ( 1980 ) . c. w. misner , k. thorne , and j. a. wheeler , _ gravitation _ ( w. h. freeman and company , san francisco , 1973 ) . e. schrdinger , _ expanding universes _ ( cambridge university press , london , 1956 ) . c. j. s. clarke and t. dray , class . quantum grav . * 4 * , 265 ( 1987 ) . c. barrabes and w. israel , phys . d * 43 * , 1129 ( 1991 ) . j. r. gott , ap . j. 288 , 422 ( 1985 ) . w. a. hiscock , phys . d * 31 * , 3288 ( 1985 ) . li and j. r. gott , phys . d * 58 * , 103513 ( 1998 ) . j. s. dowker , quantum field theory around conical defects , in _ the formation and evolution of cosmic strings _ , edited by g. gibbons , s. hawking , and t. uachaspati ( cambridge university press , 1990 ) . d. iellici , preprint gr - qc/9805058 , ph.d . m. j. cassidy and s. w. hawking , phys . d * 57 * , 2372 ( 1998 ) .

one is constructed by identifying points related via boost transformations in the covering space of anti - de sitter space and it is shown that this misner - like anti - de sitter space is just the lorentzian section of the complex space constructed by li , xu , and liu in 1993 .

in this paper time machines are constructed from anti - de sitter space . one is constructed by identifying points related via boost transformations in the covering space of anti - de sitter space and it is shown that this misner - like anti - de sitter space is just the lorentzian section of the complex space constructed by li , xu , and liu in 1993 . the others are constructed by gluing an anti - de sitter space to a de sitter space , which could describe an anti - de sitter phase bubble living in a de sitter phase universe . self - consistent vacua for a massless conformally coupled scalar field are found for these time machines , whose renormalized stress - energy tensors are finite and solve the semi - classical einstein equations . the extensions to electromagnetic fields and massless neutrinos are discussed . it is argued that , in order to make the results consistent with euclidean quantization , a new renormalization procedure for quantum fields in misner - type spaces ( misner space , misner - like de sitter space , and misner - like anti - de sitter space ) is required . such a self - consistent " renormalization procedure is proposed . with this renormalization procedure , self - consistent vacua exist for massless conformally coupling scalar fields , electromagnetic fields , and massless neutrinos in these misner - type spaces . #

1204.5589

i

in quantum information several entropic functionals ( the so called quantum capacities ) have been introduced that provide a sort of inverse measures " of the noise level associated with a given process , see e.g. refs . @xcite . in this approach the evolution of the system of interest @xmath1 is described as a linear , completely positive , trace preserving mapping ( cpt ) , the quantum channel @xmath2 , which associates a final state @xmath3 to each possible initial density matrix @xmath4 of @xmath1 . the quantum capacities of @xmath2 have a clear operational meaning as they gauge the optimal communication transmission rates achievable when operating in parallel on multiple copies of @xmath1 : consequently the noisier the channel is , the lower are its associated quantum capacities . unfortunately however , even for small systems , these quantities are also extremely difficult to evaluate since require optimization over large coding spaces , e.g. see ref . @xcite . in this paper we introduce an alternative way to determine how disruptive a channel might be which , while still having a simple operational interpretation , it is easier to compute than the quantum capacities . the starting point of our analysis is to use entanglement - breaking ( eb ) channels @xcite as the fundamental benchmarks for evaluating the noise level of a transformation . we remind that a map operating on a system @xmath1 , is said to be entanglement - breaking if for all its extensions to an ancillary system @xmath5 it annihilates the entanglement between the system and the ancilla @xcite . from the point of view of quantum information , the action of these maps represents hence the most disruptive form of noise a quantum mechanical system can undergo . a reasonable way to quantify the noise level of a generic map @xmath2 can then be introduced by computing how much extra noise we need to add " to it before the resulting transformation becomes entanglement - breaking . the intuitive idea behind this approach is that channels which are less disruptive on @xmath1 should require larger amount of extra noise to behave like an entanglement - breaking map . in the following we analyze two different mechanisms of noise addition . the first one assumes to form convex combinations @xmath6 of the input channel @xmath2 with generalized completely depolarizing channels @xmath7 ( these are the most drastic examples of entanglement - breaking channels which bring every state of @xmath1 into a unique output configuration @xmath8 the fixed point of the map ) . in this approach the level of noise associated with the original map @xmath2 is gauged by the minimum value @xmath9 of the mixing parameter @xmath10 which transforms @xmath6 into an entanglement - breaking map ( as we will see a proper characterization of this measure requires an optimization upon @xmath8 ) . the second mechanisms of noise addition we consider assumes instead the reiterative application of @xmath2 on @xmath1 . in this case the noise level is determined by the minimum value @xmath11 of iterations needed to transform @xmath2 in an entanglement - breaking map ( _ if _ such minimum exists ) . as we shall see , due to the lack of monotonicity under concatenation with other maps , this second functional can not be considered a proper measure of the noise level introduced by @xmath2 ( regularized version of @xmath11 _ do _ however retain this property ) . nonetheless @xmath11 captures some important aspects of the dynamics associated with @xmath2 : namely it counts the number of discrete time evolutions induced by the map that a system can sustain before its entanglement with an external ancilla is completely destroyed . the definition of @xmath11 gives us also the opportunity of introducing the set @xmath12 of the entanglement - breaking channels of order @xmath0 , and the notion of _ amendable _ channels . the former is composed by all cpt maps @xmath2 which , when applied @xmath0 times , are entanglement - breaking . vice - versa a channel @xmath2 is amendable if it can be prevented from becoming entanglement - breaking after @xmath11 iterations via a proper application of intermediate quantum channels a similar problem was also discussed in ref . @xcite . in the following we will discuss some general features of the functional @xmath9 and @xmath11 computing their exact values for some special class of channels . specifically in sec . [ sec : critmu ] we introduce the functionals and characterize some general properties . in sec . [ sec : qubit ] we will restrict our attention to qubit channels computing the value of @xmath9 and @xmath11 for the set of unital maps and for the generalized amplitude - damping channels . also using examples from these sets we will show that the set @xmath12 is not convex for @xmath13 and provide evidence of the existence of amendable maps . in sec . [ sec : gaussian ] we will consider the analogous of qubit maps for continuous variable systems , that is one - mode gaussian channels , and in particular we will evaluate the functional @xmath11 for attenuation and amplification channels . conclusions and final remarks are given in sec . [ par : summary and conclusions ] .

in this paper we introduce a way to quantify the noise level associated to a given quantum transformation . the key mechanism lying at the heart of the proposal is _ noise addition _ : in other words we compute the amount of extra noise we need to add to the system , through convex combination with a reference noisy map or by reiterative applications of the original map , before the resulting transformation becomes entanglement - breaking . explicit examples are analyzed in the context of qubit and one - mode gaussian channels .

in this paper we introduce a way to quantify the noise level associated to a given quantum transformation . the key mechanism lying at the heart of the proposal is _ noise addition _ : in other words we compute the amount of extra noise we need to add to the system , through convex combination with a reference noisy map or by reiterative applications of the original map , before the resulting transformation becomes entanglement - breaking . we also introduce the notion of entanglement - breaking channels of order ( i.e. maps which become entanglement - breaking after iterations ) , and the associated notion of amendable channels ( i.e. maps which can be prevented from becoming entanglement - breaking after iterations by interposing proper quantum transformations ) . explicit examples are analyzed in the context of qubit and one - mode gaussian channels .

1204.5589

c

in our analysis we have introduced two new functionals ( @xmath9 and @xmath11 ) that can be used to quantify the noise level of a map . these have been characterized in terms of general properties and have been explicitly evaluated for some class of channels . along the way we have also introduced the notion of amendable channels showing how there exist maps which can be prevented from becoming entanglement - breaking after subsequent applications by interposing some extra transformations . for the sake of simplicity in our study we have only considered the case in which the _ same _ unitary transformation is interposed between successive channel uses . this however is not the only possibility and it is an interesting question of quantum control to determine what are the optimal operations one has to perform in order to guarantee that after certain number of reiterations entanglement will not be destroyed in the system . we finally notice that when introducing the functionals @xmath11 and @xmath9 we started from the identification of the entanglement - breaking channels as a benchmark set to evaluate the noise level of other quantum transformations ( the choice being operationally motivated by the extreme deteriorating effects that eb maps have on the system ) . again this however is not the only possibility . for instance another reasonable choice is to replace the entanglement - breaking channels with the set formed by the positive partial transpose ( or _ binding _ ) maps @xcite producing new noise measures @xmath456 and @xmath457 for @xmath2 . we remind that a channel is said to be ppt if when extended on an ancilla a the only entanglement one can find in the output of @xmath458 is non - distillable @xcite . similarly to the case of eb maps , also the ppt set is stable under convex convolution and iteration : therefore @xmath456 and @xmath457 will again assume the minimum allowed values on the benchmark set guarantying that they are well defined quantities for all @xmath2 . now , since for qubits the entanglement is always distillable @xcite , when @xmath1 has dimension 2 we have @xmath459 and @xmath460 ( a property we explicitly exploited when computing the values of @xmath9 and @xmath11 for qubit channels ) . on the contrary when @xmath1 has larger dimensions , @xmath461 and @xmath462 need not to reduce to @xmath42 and @xmath114 yielding a qualitatively new way of gauging the noise level of @xmath2 . this work was supported by miur through firb- ideas project no . rbid08b3fm .

we also introduce the notion of entanglement - breaking channels of order ( i.e. maps which become entanglement - breaking after iterations ) , and the associated notion of amendable channels ( i.e. maps which can be prevented from becoming entanglement - breaking after iterations by interposing proper quantum transformations ) .

in this paper we introduce a way to quantify the noise level associated to a given quantum transformation . the key mechanism lying at the heart of the proposal is _ noise addition _ : in other words we compute the amount of extra noise we need to add to the system , through convex combination with a reference noisy map or by reiterative applications of the original map , before the resulting transformation becomes entanglement - breaking . we also introduce the notion of entanglement - breaking channels of order ( i.e. maps which become entanglement - breaking after iterations ) , and the associated notion of amendable channels ( i.e. maps which can be prevented from becoming entanglement - breaking after iterations by interposing proper quantum transformations ) . explicit examples are analyzed in the context of qubit and one - mode gaussian channels .

0903.0634

i

understanding the activity of galaxies , their morphologies , and the interplay between the two are key problems in galaxy evolution and are tightly correlated with the problem of understanding whether such properties depend on the initial physical conditions of a galaxy ( e.g. , its mass ) or , rather , result from evolutionary processes driven by the environment in which they live , such as mergers , gravitational and gas - gas interactions . models of galaxy formation and evolution have tried to explain the differences in the features of galaxies for decades , mostly unsuccessfully . hierarchical cold dark matter models , which have been shown to describe successfully large - scale structure formation , currently fail to describe properly many salient properties of galaxies , such as the color - magnitude relation , the bimodal distribution in colors , the luminosity function , and downsizing " ( i.e. , the earlier quenching of star formation in more massive objects ) . furthermore such models inadequately describe the formation of small bulge - less spirals , the most common galaxies in the universe . it is unclear if the problems that these models encounter are given by a simplistic treatment of the complex baryonic physics governing the observable parameters or if the models are not appropriate for the description of galaxy formation and evolution . explaining the mechanisms which initiate and regulate star - formation and agn activity in galaxies along the hubble diagram has proven as challenging . galaxies show very different rates and histories of star - formation activity and host agn with very different characteristics ( narrow and/or broad emission lines , point - like radio emission and large radio jets , to name a few ) , making the modeling of such activity quite complex . the interplay between star - formation and agn activity is also poorly understood . using the sdss , @xcite showed that active galactic nuclei selected on the basis of their emission lines preferentially reside in massive , bulge - dominated systems with traces of recent star - formation , possibly a consequence of the presence of a reservoir of cold gas which triggers both star - formation and agn activity . using the goods survey , however , @xcite showed that x - ray agn activity persists in many @xmath1 red - sequence galaxies , well after the star - formation has quenched , suggesting that the presence of a cold reservoir of gas may not be a necessary ingredient in the triggering of agn activity . the role of the environment surrounding a galaxy in initiating activity is also quite controversial . interactions and mergers among galaxies are known to trigger bursts of star formation in galaxies ( e.g. , * ? ? ? * ) , yet the trigger for the onset of star - formation on galactic scales in isolated spiral galaxies calls for a different explanation . in clusters , @xcite have shown that the environment produces a significant effect in the later evolution of galaxies , lowering their star - formation rates substantially , while @xcite using the sdss sample conclude the opposite , i.e. that the cluster environment may be irrelevant to the bulk of the transformation of galaxies . mergers and close interaction between galaxies have also been suggested as possible triggers of agn activity @xcite ; however , @xcite using the goods survey and two chandra deep fields have shown that there is no close connection between galaxy mergers and moderate - luminosity agn activity out to appreciable look - back times approaching the epoch of peak agn activity in the universe ( @xmath2 ) . this result is supported by the study of @xcite who showed that x - ray - selected agn tend to reside in undisturbed pairs of early type galaxies with no direct evidence of gravitational perturbation or interactions , suggesting that the activation mechanism of agn is not primarily galaxy interaction . the role of secular evolution in triggering star - formation and agn activity , as well as the morphological transformation of galaxies by means of a re - arrangement of energy and mass through collective phenomena such as bars @xcite and/or spiral waves @xcite is unclear , but there is increasing observational evidence of its importance in shaping galaxy features @xcite . interestingly , many properties observed in the local universe are observed also in the high- redshift population of galaxies investigated by recent deep galaxy surveys . using the goods survey , @xcite have shown that the well - known correlation between size of a galactic bulge and the mass of the supermassive black hole residing at its center @xcite is in place at early epochs ( z@xmath31.3 ) . @xcite , using the cosmos survey , have studied the morphological content and environmental dependence of the galaxy color - magnitude relation at @xmath4 and found that the red and blue sequences of galaxies found in the nearby universe are found at @xmath4 as well . by comparing the high- and low - redshift populations , they conclude that the local red sequence is adequately reproduced by passive evolution , suggesting that a fraction of the galaxies in the high - redshift blue sequence eventually evolve into red - sequence galaxies . they also confirm the result of @xcite , who showed that the slope and the normalization of such color - magnitude relations are substantially invariant with respect to local density when galaxies are separated into early and late types , arguing that secular star - formation is driven more by galaxy mass than by environment . the color - density correlation found by other authors ( e.g. , * ? ? ? * ) at high redshift , with bluer galaxies found in regions of greater over - density , is interpreted as an excess of more late - type galaxies in denser environments which evolve into red - sequence galaxies at the present time . these studies are in agreement with older results @xcite which showed a variation in the fractional abundance of different morphological types in galaxy cluster populations as a function of redshift . the study of @xcite is not limited to clusters , suggesting that a transformation of galaxies might also occur in the absence of mechanisms such as the gas - gas and gravitational interactions typical of dense cluster environments . these results are at odds with the work of @xcite who have used the sdss sample to show that close interaction among galaxies is the most likely mechanism leading to the density - morphology correlation observed . in a series of three papers based on the sloan digital sky survey @xcite and the first survey @xcite we examine the population of broad and narrow emission - line active galactic nuclei ( agn ) in the local universe in order to explore the physical and environmental properties of galaxies . in paper i @xcite we described the multiwavelength database built for this analysis and the systematics affecting the spectroscopic selection of agn . we presented evidence of the existence of a large population of radio - emitting radio agn which lack optical spectroscopic signatures and show that , at all luminosities , galaxies with redder colors are more likely to show weaker emission lines . in this second paper we further explore the interplay between galaxy properties and agn features , focusing on the interplay between morphology , star - formation , and nuclear activity , including its evolution over cosmic times . in a following paper we will present a comparative analysis of the radio and spectroscopic properties of narrow- and broad - lined agn and their evolution . the structure of the paper is the following : in section [ sample_ch3 ] we present the sample used for this analysis , while in [ evolution ] we show our evidence of co - evolution of galaxy activity and morphology , and in [ aging_radio ] we map the aging of the radio power associated with agn . in [ aging_spectro ] we illustrate the aging of the spectroscopic features of agn , in [ environment ] we study the correlation between environment , activity and morphology . we discuss our results in [ discussion_ch3 ] and present our conclusions in [ conclusion_ch3 ] .

such evolution appears more substantial for less luminous systems , and is possibly the low - redshift tail of the downsizing in star - formation , agn activity and supermassive black hole build - up observed in higher redshift surveys.this suggests that the differences in intrinsic properties of galaxies along the hubble sequence may arise from the difference in the depth of their potential wells which leads to different evolutionary paths because of different timescales for gas infall . this primordial infall and the following secular evolution mediated by bar and density wave instabilities may bring galaxies of different mass to have the different activity levels and morphological features in the local universe shown in this study . in agreement with such a hypothesis

in this second paper of a series of papers based on the first and sdss surveys we investigate the evolution of galaxy morphology and nuclear activity in the look - back time of the sdss ( 2 gyrs ) for a sample of 150000 galaxies in the local universe . we demonstrate an evolution in the strength of the radio power and the spectroscopic emission - lines typical of agn , as well as in the morphology of their hosts . such evolution appears more substantial for less luminous systems , and is possibly the low - redshift tail of the downsizing in star - formation , agn activity and supermassive black hole build - up observed in higher redshift surveys.this suggests that the differences in intrinsic properties of galaxies along the hubble sequence may arise from the difference in the depth of their potential wells which leads to different evolutionary paths because of different timescales for gas infall . this primordial infall and the following secular evolution mediated by bar and density wave instabilities may bring galaxies of different mass to have the different activity levels and morphological features in the local universe shown in this study . in agreement with such a hypothesis , we find that star - formation as traced by radio emission is progressively more centrally concentrated in more evolved star - forming galaxies and we show that the environment in which a galaxy resides plays a lesser role in shaping the features and activity for the majority of systems .

0903.0634

c

in this study based on the sdss and first surveys , we have investigated the evolution of galaxy properties withing the sdss look - back time ( @xmath0 2 gyr ) for a sample of @xmath0 150000 galaxies in the local universe . we have shown a transformation of the activity and morphology of galaxies over the look - back time of the sdss and have further demonstrated that this transformation is more significant for lower luminosity systems , in agreement with the notion of downsizing in star formation , agn activity and bulge formation over cosmic time . the intensity of the h@xmath8 and radio emission has significantly dropped over the last 1 gyr in emission - line agn , a fact in agreement with the progressive fading of active nuclei from high to low redshift traced by other surveys . the hosts of these nuclei have substantially transformed towards more concentrated stellar distributions typical of more bulgy systems . the fact that systems of different luminosity evolve differently over this look - back time supports the claim that , for the bulk of galaxies , transformation is unlikely the product of environment - driven mechanisms , but rather depends on the mass / size of the host itself . this is further supported by the direct study of the galaxy environment presented in this paper . we have shown that galaxies show increasing bulge - to - disk ratio with increasing density and that this increase is accompanied by a transition in the type of activity from star - formation - dominated to composite to agn - dominated and eventually to passive systems . this transition accompanies the well - know density - morphology relation , into regions well beyond the cluster cores where it was originally discovered ( dressler 1980 ) . we argue that these two trends with densities are unlikely driven by environment - driven mechanisms , but rather depend on the mass / size of the host itself and different evolution timescales for galaxies associated to different potential wells . we note that if over - densities of all sizes were formed at early epochs instead of being hierarchically formed over time , the infall time of gas would be much faster for the largest over - densities and correspondingly slower for the smaller ones . a fast infall / collapse of material in bigger over - densities would more likely resemble a monolithic collapse . these over - densities would form big bulges and big ellipticals ( and supermassive black holes within ) . a slow accretion phase typical of small over - densities would most likely find a thin disk equilibrium configuration , forming smaller bulge - less spiral galaxies over longer timescales . galaxies with intermediate potential wells would have both and be a less stable configuration . in agreement with this we have shown that big bulge - dominated galaxies and star - forming disks are stable configurations , while galaxies with intermediate bulges hosting agn tend to evolve towards bulgier systems . this rapid transformation of systems of intermediate luminosity into earlier type systems with more prominent bulges demonstrated here , suggests that the intermediate phase may be short - lived compared to the star - forming disk phase and the red elliptical phase , thus explaining the dichotomy between red- and blue - sequence galaxies . the progressive infall of gas from the outer regions to the inner regions of a galaxy potential well can be traced using the size of radio emission as an indicator of the star - formation region within galaxies . we have shown that a progressive concentration of star - formation activity towards the inner regions of redder star - forming galaxies is found , in agreement with early work of hummels ( 1981 ) , suggesting a picture in which gas is progressively transported by instabilities towards the inner regions . as the gas is funneled towards the center , star - formation is triggered , followed by nuclear activity . as this cold gas reservoir is exhausted the agn activity is progressively brought to a halt , explaining the anti - correlation that we find between line - strength of active nuclei and galaxy color ( and other indicators of star - formation activity ) , which is an extension of the results of @xcite . from this point of view the density - morphology relation and the density - activity relation discussed in this study is the by - product of different formation and evolution timescales for galaxies associated with different primordial over - densities , and the fact that the biggest galaxy - scale over - densities were formed within the denser large - scale structure over - densities .

in this second paper of a series of papers based on the first and sdss surveys we investigate the evolution of galaxy morphology and nuclear activity in the look - back time of the sdss ( 2 gyrs ) for a sample of 150000 galaxies in the local universe .

in this second paper of a series of papers based on the first and sdss surveys we investigate the evolution of galaxy morphology and nuclear activity in the look - back time of the sdss ( 2 gyrs ) for a sample of 150000 galaxies in the local universe . we demonstrate an evolution in the strength of the radio power and the spectroscopic emission - lines typical of agn , as well as in the morphology of their hosts . such evolution appears more substantial for less luminous systems , and is possibly the low - redshift tail of the downsizing in star - formation , agn activity and supermassive black hole build - up observed in higher redshift surveys.this suggests that the differences in intrinsic properties of galaxies along the hubble sequence may arise from the difference in the depth of their potential wells which leads to different evolutionary paths because of different timescales for gas infall . this primordial infall and the following secular evolution mediated by bar and density wave instabilities may bring galaxies of different mass to have the different activity levels and morphological features in the local universe shown in this study . in agreement with such a hypothesis , we find that star - formation as traced by radio emission is progressively more centrally concentrated in more evolved star - forming galaxies and we show that the environment in which a galaxy resides plays a lesser role in shaping the features and activity for the majority of systems .

0906.0892

i

this is work the second of a pair of articles on mesoscopic transport through chaotic quantum dots with spatial symmetries ( see ref . @xcite for part i ) . in both works we use recent advances in semiclassical techniques to address the effect of spatial symmetries on weak localization ( wl ) corrections and universal conductance fluctuations ( ucfs ) . the aim of the first article was to identify the microscopic origin of properties that were earlier only known from phenomenological random - matrix theory ( rmt ) @xcite , and furthermore to extend the considerations to situations in which rmt is not easily applicable . in particular , this includes scenarios where symmetries are only partially preserved . to this end , the first article @xcite also considered the combined effects of magnetic fields , a finite ehrenfest time , and dephasing on symmetric systems and also discussed the reduction of symmetry - related interference effects by deformations of the dots . in the present paper , we contrast this ` internal ' symmetry breaking with symmetry breaking which is due to the position or shape of the leads ( for examples of such situations see fig . [ fig : asymmleads ] ) . we ask what happens to the transport if we take a symmetric dot coupled to leads which respect the symmetry , and then start moving one of the leads . in the fully symmetric situation , the magnitude of ucfs is doubled for each independent symmetry , while the weak localization correction can be either increased or reduced ( sometimes remain unaffected ) depending on the spatial symmetry in question @xcite . are these symmetry - induced effects modified when the leads are deformed or displaced ? if so , are they sensitive to displacement on a quantum scale ( of order of a fermi wavelength ) or a classical scale ( of order of a lead width ) ? the present literature does not offer much guidance to answer these questions indeed , the knowledge on transport in spatially symmetric systems with displaced leads is rather limited . reference @xcite reports that the distribution of transmission eigenvalues of a left - right symmetric dot with completely asymmetrically - placed leads differs slightly from the distribution of a completely asymmetric dot . because the difference is small , symmetric systems ( such as stadium billiards ) with displaced leads are indeed often used as representatives of completely asymmetric systems ( see , e.g. , refs.@xcite ) . recent works of one of the authors , on the other hand , identify a huge conductance peak in weakly coupled mirror - symmetric double - dots which still remains large even when the leads are not placed symmetrically @xcite . a simple consideration of weak localization quickly convinces us that it could never be as robust as the above - mentioned huge conductance peak in double dots . in systems without spatial symmetries , weak localization is the counter - part of coherent backscattering particle conservation guarantees that one can not have one without the other . systems with spatial symmetries have addition coherent back- and forward - scattering contributions ( as discussed in the first of this pair of articles @xcite ) . these contributions rely on interference between paths that are related by spatial symmetry . if those paths do not both couple to the leads , they can not generate an interference contribution to conductance . thus , if we displace one lead so much that there is no intersection with its spatially symmetric partner ( @xmath0 in fig . [ fig : asymmleads ] ) then the contributions to coherent forward scattering due to the spatial symmetries must vanish . the precise distance by which one has to move the lead to substantially suppress the symmetry - related contributions depends on the detailed position dependence of the coherent forward- and backscattering peaks . in principle , these coherent interference patterns could oscillate on a scale of a wavelength , and thus one might imagine that a small displacement of that order would suffice . the calculations and numerical computations presented by us here show that this is not the case . instead , the coherent forward- and backscattering peaks have a width of order the lead width , and do not oscillate on the scale of a wavelength . these considerations entail that the displacement of leads in internally symmetric systems offers a unique means to study coherent forward- and backscattering processes . from photonic systems it is known that the shape of the coherent backscattering cone provides valuable information on the multiple scattering in a sample @xcite . based on the results of the present work , transport measurements with gradually displaced leads promise to give similar insight into the dynamics of electronic systems . this work is organized as follows . section [ sec : backgrd ] introduces notation and provides a condensed review of the basic semiclassical concepts elaborated in more detail in the first of this pair of articles @xcite . the following sections describe the consequences of displaced leads for the weak localization correction in systems with left - right symmetry ( sec.[sect : lr ] ) , inversion symmetry ( sec . [ sect : inv ] ) , up - down symmetry ( sec . [ sect : ud ] ) and four - fold symmetry ( sec.[sect:4f ] ) . in sec . [ sect : ucfs ] we study the magnitude of universal conductance fluctuations for all types of symmetry . finally , in section [ sect : rmt ] we generalize the phenomenological rmt model of symmetry breaking ( presented in @xcite ) to the case of displaced leads , and compare the results of numerical computations to the semiclassical predictions . our conclusions are collected in section [ sect : conclusions ] . the appendix contains some further details on the semiclassical calculation of universal conductance fluctuations .

in this work the second of a pair of articles we consider transport through spatially symmetric quantum dots with leads whose widths or positions do not obey the spatial symmetry . finally , we develop a random - matrix theory model which enables us to numerically confirm these results .

in this work the second of a pair of articles we consider transport through spatially symmetric quantum dots with leads whose widths or positions do not obey the spatial symmetry . we use the semiclassical theory of transport to find the symmetry - induced contributions to weak localization corrections and universal conductance fluctuations for dots with left - right , up - down , inversion and four - fold symmetries . we show that all these contributions are suppressed by asymmetric leads , however they remain finite whenever leads intersect with their images under the symmetry operation . for an up - down symmetric dot , this means that the contributions can be finite even if one of the leads is completely asymmetric . we find that the suppression of the contributions to universal conductance fluctuations is the square of the suppression of contributions to weak localization . finally , we develop a random - matrix theory model which enables us to numerically confirm these results .

1702.07762

i

internal gravity waves play a primary role in geophysical fluids @xcite : they contribute significantly to mixing in the ocean @xcite and they redistribute energy and momentum in the middle atmosphere @xcite . the generation and propagation mechanisms are fairly well understood , as for instance in the case of oceanic tidal flows @xcite . by contrast , the dissipation mechanisms , together with the understanding of observed energy spectra resulting from nonlinear interactions between those waves , are still debated @xcite . several routes towards dissipation have been identified , from wave - mean flow interactions to cascade processes , but this remains a fairly open subject from both theoretical @xcite and experimental points of view @xcite . the objective of this review is to present important recent progress that sheds new light on the nonlinear destabilization of internal wave beams , bridging part of the gap between our understanding of their generation mechanisms based mostly on linear analysis , and their subsequent evolution through nonlinear effects . until recently , most studies were focused on plane wave solutions , which are introduced in classical textbooks @xcite . strikingly , such plane waves are not only solutions of the linearized dynamics , but also of the nonlinear equations @xcite . however , spatially and temporally monochromatic internal wave trains are not a satisfactory description of most geophysical internal gravity waves @xcite . indeed , oceanic field observations have rather reported internal gravity beams with a confined profile @xcite . in the atmosphere , gravity waves due to thunderstorms also often form beam - like structures @xcite . oceanic wave beams arise from the interaction of the barotropic tide with sea - floor topography , as has been recently studied theoretically and numerically @xcite , taking into account transient , finite - depth and nonlinear effects , ignored in the earlier seminal work by @xcite . the importance of those beams has also been emphasized recently in quantitative laboratory experiments @xcite . from these different works , it is now recognized that internal wave beams are ubiquitous in the geophysical context . the interest for internal gravity beams resonates with the usual pedagogical introduction to internal waves , the saint andrew s cross , which comprises four beams generated by oscillating a cylinder in a stratified fluid @xcite . thorough studies of internal wave beams can be found in @xcite . moreover , @xcite have realized that an inviscid uniformly stratified boussinesq fluid supports time - harmonic plane waves invariant in one transverse horizontal direction , propagating along a direction determined by the frequency ( and the medium through the buoyancy frequency ) , with a general spatial profile in the cross - beam direction . these wave beams are not only fundamental to the linearized dynamics but , like sinusoidal wavetrains , happen to be exact solutions of the nonlinear governing equations . remarkably , @xcite showed that the steady - state similarity linear solution for a viscous beam @xcite is also valid in the nonlinear regime . in light of the recent experimental and analytical studies of those internal gravity wave beams , it is thus timely to study their stability properties . the structure of the review is the following . first , in section [ sectionintroductive ] , we introduce the subject by presenting concepts , governing equations and approximations that lead to the description of gravity waves in stratified fluids . we dedicate a special emphasis on the peculiar role of nonlinearities to explain why internal gravity wave beams are ubiquitous solutions in oceans and middle atmospheres . then , in section [ triadicresonanceinstability ] , we discuss the classic triadic resonant instability that corresponds to the destabilization of a primary wave with the spontaneous emission of two secondary waves , of lower frequencies and different wave vectors . in addition to the simple case of plane waves , we discuss in detail the generalization to wave beams with a finite width . section [ streaminginstability ] is dedicated to the streaming instability , the second important mechanism for the instability of internal gravity waves beams through the generation of a mean flow . finally , in section [ conclusionsperspectives ] , we draw some conclusions and discuss main future issues .

internal gravity waves play a primary role in geophysical fluids : they contribute significantly to mixing in the ocean and they redistribute energy and momentum in the middle atmosphere . until recently , most studies were focused on plane wave solutions . however , these solutions are not a satisfactory description of most geophysical manifestations of internal gravity waves , and it is now recognized that internal wave beams with a confined profile are ubiquitous in the geophysical context . i ) the triadic resonant instability generating two secondary wave beams .

internal gravity waves play a primary role in geophysical fluids : they contribute significantly to mixing in the ocean and they redistribute energy and momentum in the middle atmosphere . until recently , most studies were focused on plane wave solutions . however , these solutions are not a satisfactory description of most geophysical manifestations of internal gravity waves , and it is now recognized that internal wave beams with a confined profile are ubiquitous in the geophysical context . we will discuss the reason for the ubiquity of wave beams in stratified fluids , related to the fact that they are solutions of the nonlinear governing equations . we will focus more specifically on situations with a constant buoyancy frequency . moreover , in light of recent experimental and analytical studies of internal gravity beams , it is timely to discuss the two main mechanisms of instability for those beams . i ) the triadic resonant instability generating two secondary wave beams . ii ) the streaming instability corresponding to the spontaneous generation of a mean flow . internal waves , instability , mean - flow

1702.07762

c

we have presented several recent experimental and theoretical works that have renewed the interest of internal wave beams . after emphasizing the reason for their ubiquity in stratified fluids they are solutions of the nonlinear governing equations this review has presented the two main mechanisms of instability for those beams : \i ) triadic resonant instability . we have shown that this instability produces a direct transfer of energy from large scales ( primary waves ) to smaller scales ( subharmonic ones ) for inviscid plane waves , but that it is no longer true for internal wave beams since the most unstable triad may combine subharmonic waves with larger and smaller wavelength . moreover , the effects of the finite size and envelope shape for the onset of triadic resonant instability have been overlooked . these features have to be taken into account to safely reproduce the complete nonlinear transfer of energy between scales in the ocean interior or in experimental analog @xcite , and therefore to find its stationary state , the so - called garrett and munk spectrum @xcite or its possible theoretical analog , the zakharov spectrum for the wave turbulence theory @xcite . \ii ) streaming instability . now that the mechanism underlying streaming instability and the conditions for its occurrence have been identified , several other examples will probably be reported in the coming years . for example , such a mean - flow generation has also been observed in a recent experiment @xcite for which the reflection of internal gravity waves in closed domains lead to an internal wave attractor . two lateral stokes boundary layers generate indeed a fully three - dimensional interior velocity field that provides the condition for the mean flow to appear . with a perturbation approach , @xcite confirmed this theoretically and showed that the generated 3d velocity field damps the wave beam at high wave numbers , thereby providing a new mechanism to establish an energetic balance for steady state wave attractors . @xcite have also recently studied experimentally the generation of a mean flow by a progressive internal gravity wave in a simple two - dimensional geometry , revisiting an experimental analog of the quasi - biennial oscillation @xcite . they study the feedback of the mean flow on the wave , an essential ingredient of the quasi - biennial oscillation . which is the dominant mechanism ? @xcite have recently suggested that streaming instability are central to three - dimensional internal gravity wave beam dynamics in contrast to the tri of sinusoidal wave train relevant to uniform beams , the special case of a internal plane wave with confined spatial profile . this review reinforces therefore the need for more three - dimensional experiments studying wave - induced mean flow . in particular , the conditions that favor mean - flow generation with respect to triadic resonant interaction remains largely unknown . angles of propagation ? three - dimensionality ? this is an important question that needs to be addressed . in an incompressible non - rotating linearly stratified boussinesq fluid , 1 . plane waves are solutions of the linear and nonlinear equations for any amplitude . 2 . internal wave beams , which correspond to the superposition of plane waves with wave vectors of different magnitude but pointing in the same direction , are solutions of the linear and nonlinear equations . 3 . plane waves solutions are always unstable by tri . general localized internal wave beams are stable while ( quasi ) spatial - harmonic internal wave beams are unstable if the beam is wide enough . 5 . in presence of rotation , beams of general spatial profile are more vulnerable to tri especially close to the critical latitude where nearly - stationary wavepackets remain in the interaction region for extended durations , facilitating energy transfer . 6 . internal gravity wave beams with confined spatial profile are linearly unstable to three - dimensional modulations . when the wave beam is attenuated along its direction of propagation and when the wave - envelop varies in the transverse horizontal direction , nonlinear interactions of the wave beam with itself induce the emergence of a horizontal mean - flow with vertical vorticity .

we will discuss the reason for the ubiquity of wave beams in stratified fluids , related to the fact that they are solutions of the nonlinear governing equations . moreover , in light of recent experimental and analytical studies of internal gravity beams , it is timely to discuss the two main mechanisms of instability for those beams .

internal gravity waves play a primary role in geophysical fluids : they contribute significantly to mixing in the ocean and they redistribute energy and momentum in the middle atmosphere . until recently , most studies were focused on plane wave solutions . however , these solutions are not a satisfactory description of most geophysical manifestations of internal gravity waves , and it is now recognized that internal wave beams with a confined profile are ubiquitous in the geophysical context . we will discuss the reason for the ubiquity of wave beams in stratified fluids , related to the fact that they are solutions of the nonlinear governing equations . we will focus more specifically on situations with a constant buoyancy frequency . moreover , in light of recent experimental and analytical studies of internal gravity beams , it is timely to discuss the two main mechanisms of instability for those beams . i ) the triadic resonant instability generating two secondary wave beams . ii ) the streaming instability corresponding to the spontaneous generation of a mean flow . internal waves , instability , mean - flow

astro-ph0509742

i

lccccccc vdb - hagen 176 ( bh176 ) & 15:39:05.4 & @xmath950:03:01.7 & 328.4100 & @xmath104.3418 & 2.3 & 0.70 & 1 + berkeley 20 ( be20 ) & 05:32:37.0 & @xmath1000:11:30.0 & 203.4803 & @xmath917.3711 & 2.0 & 0.16 & 2 + berkeley 29 ( be29 ) & 06:53:04.2 & @xmath1016:55:39.0 & 197.9493 & @xmath107.9802 & 2.0 & 0.10 & 3 + berkeley 39 ( be39 ) & 07:46:51.0 & @xmath904:40:30.0 & 223.5465 & @xmath1010.0915 & 7.0 & 0.11 & 4 + saurer 1 ( sa1 ) & 07:20:56.0 & @xmath1001:48:29.0 & 214.6894 & @xmath107.3862 & 1.3 & 0.18 & 5 ( * ? ? ? * hereafter f04 ) noted that the outermost open clusters in the milky way seem to lie in a string - like configuration that can be fit to an orbital plane coincident with the galactic anticenter stellar structure ( gass ) . the presence of this arc - like structure was inferred from excesses of various types of stars @xcite beyond the apparent limit of the galactic disk , and has also been used to argue for the presence of a distinct , extended stellar structure wrapping around the disk at low latitudes . the feature has been referred to as the `` monoceros ring '' @xcite or gass @xcite . however , because of its unfortunate location behind considerable extinction , the system s true shape , orientation , extent , etc . have been difficult to ascertain . even the location of the structure s center ( presumably corresponding to a `` nucleus '' ) remains uncertain and controversial . for example , this stellar stream has been argued to be associated with the postulated canis major @xcite or argo dwarf galaxies @xcite . previous work @xcite on this stellar arc has determined some characteristics including : ( 1 ) a velocity - longitude trend that indicates a slightly non - circular orbit , ( 2 ) a velocity dispersion that is smaller than even that of disk stars , and ( 3 ) a wide metallicity spread from [ fe / h]@xmath11 dex ( y03 ) to at least [ fe / h]@xmath12 dex . f04 found that at least five globular clusters and one open cluster ( tombaugh 2 ) have positions and radial velocities ( rvs ) suggesting an association with gass ( see also * ? ? ? * ; * ? ? ? * ) , but pointed to other clusters with spatial coincidence with gass that still have unknown rvs . as a result , we sought to derive the kinematics and chemistry for these other clusters . in this work , the clusters berkeley 29 ( be29 ) , saurer 1 ( sa1 ) , and vdb - hagen 176 ( bh176 ) from the f04 list of postulated gass clusters are investigated . table 1 gives the positional data for these clusters , as well as for old , outer open clusters berkeley 20 ( be20 ) and berkeley 39 ( be39 ) , which we also observed as metallicity calibrators . medium resolution spectra for all five clusters are used to determine their bulk rvs and metallicities via measurement of the infrared triplet lines . these data are used to test whether these clusters are consistent with the observed dynamical and chemical trends of the gass system . while @xcite and @xcite suggest the metallicity and rv data are insufficient to prove membership in gass , they are sufficient to identify clusters with properties inconsistent with those observed for gass . lcccccc bh176 & lco 2.5-m & 0.259 & 1998 jun 30 & & + be29 & fmo 1.0-m & 0.367 & 2003 nov 21 & @xmath13 & @xmath13 + sa1 & fmo 1.0-m & 0.367 & 2004 nov 21 & @xmath13 & @xmath14 lccccccc be20 & lco 1.0-m & 0.697 & 2000 dec 05 & @xmath15 & @xmath15 & @xmath16 + be39 & lco 1.0-m & 0.697 & 2000 dec 05 & @xmath15 & @xmath15 & @xmath16 + sa1 & fmo 1.0-m & 0.367 & 2004 feb 28 & @xmath13 & @xmath14 & @xmath17 in 2 we analyze photometry for the clusters be20 , be29 , be39 , sa1 , and bh176 . this photometry is used to select targets for spectroscopy . in 3 , we discuss the spectroscopic observations and use rvs derived from the spectra to determine the clusters bulk rvs . the derived mean cluster rvs are used to clarify the positions of the giant branches of the clusters in the color - magnitude diagram and compare our work to previous studies in 4 . finally in 5 , we explore each cluster s likelihood of belonging to gass and discuss the implications these clusters have for gass and open cluster studies in the galaxy in general .

it has been previously proposed that some distant open clusters in the milky way may have been accreted during a dwarf galaxy merger , perhaps associated with the same event that led to the formation of the galactic anticenter stellar structure ( gass ) , also known as the `` monoceros ring '' . we have obtained and washington photometric and medium resolution ( ) multi - fiber spectroscopic data for the three distant old open clusters berkeley 29 , saurer 1 , and vdb - hagen 176 ( bh 176 ) . these clusters are spatially coincident with gass , but radial velocities and spectroscopic metallicities had not been available during previous studies of the gass candidate cluster system . similar data for the clusters berkeley 20 and berkeley 39 have been obtained for calibration purposes .

it has been previously proposed that some distant open clusters in the milky way may have been accreted during a dwarf galaxy merger , perhaps associated with the same event that led to the formation of the galactic anticenter stellar structure ( gass ) , also known as the `` monoceros ring '' . we have obtained and washington photometric and medium resolution ( ) multi - fiber spectroscopic data for the three distant old open clusters berkeley 29 , saurer 1 , and vdb - hagen 176 ( bh 176 ) . these clusters are spatially coincident with gass , but radial velocities and spectroscopic metallicities had not been available during previous studies of the gass candidate cluster system . similar data for the clusters berkeley 20 and berkeley 39 have been obtained for calibration purposes . we provide the first _ reliable _ radial velocity for bh 176 ( km s ) . we also find that and km s , for saurer 1(a ) and berkeley 29 , respectively . we show that-enhanced isochrones , while spectroscopically motivated , provide a poor fit to be29 in contrast to previous findings . we find that the clusters berkeley 29 and saurer 1 are consistent with the previously reported characteristics for gass candidate clusters and the gass stellar stream as derived from m - giant observations . however , the radial velocity and photometric metallicity ( [ fe / h ] dex ) for bh 176 suggests that a connection of this cluster with the putative gass cluster system is unlikely . we reassess the age - metallicity relation for the most likely members of the gass clusters system for which spectroscopic metallicities are now available .

astro-ph0509742

r

the photometrically identified , most likely rgb and rc stars unambiguously reveal the bulk rv of each cluster , as shown by the rv distributions in the left panels ( a e ) of figure 4 . since these rgb and rc stars are the most likely to provide the `` purest '' samples of cluster members , we use these samples to define one measure of the mean cluster rv and observed dispersion ( the top values of table 11 with subscript rgb " ) . with this version of the mean rv established for each cluster , we can search for other potential cluster members identified on the basis of similar rv . the rv histograms for all stars in the cluster fields with spectra are shown in the right panels ( f i ) of figure 4 . when the left and right panels of figure 4 are compared we see the usefulness of photometric pre - screening to identify the _ best _ cluster rgb candidates for these sparse , highly field star contaminated clusters : e.g. , in the cases of bh176 , be20 , and sa1 the true rv of the cluster would remain somewhat uncertain were only the rv distributions in the right panels available . we can now rederive bulk cluster rvs using all stars with rvs indicating likely cluster membership . for this purpose , we limit the cluster member range to @xmath67 7 km s@xmath4 about the mean defined by @xmath68 , values guided by the typical individual stellar rv errors and the small expected velocity dispersions of these systems ( @xmath69-@xmath70 km s@xmath4 ) . because of this imposed selection bias , the dispersions given in table 11 should be interpreted only as a guide to the observed tightness of the rvs used to define the mean rv , not as the true intrinsic dispersions of the clusters . the mean rvs for the clusters using these enlarged samples are also given in table 11 ( middle values with subscript all " ) . note that while these rv values average over a larger sample of stars and therefore might be expected to give a more accurate measure of the mean cluster rv , it is also the case that a higher fraction of interloping field stars with similar rvs may enter , and perturb , the average . the rvs we have calculated for the five clusters using the rgb " and the all " samples agree to within 2 km s@xmath4 , which is less than half the observed dispersions . these rvs also agree in general with other recent determinations for these clusters ( bottom values , denoted as pub " in table 11 ) , but an offset of unknown origin is also found for sa1 ( see 4.4 below ) . the cmds and color - color diagrams for these clusters with observed and member stars marked are shown in figures 58 . we match isochrones to our clusters while constraining the metallicity to spectroscopically determined values . we explore a range in metallicities centered on the spectroscopically determined value for each cluster . additionally , our radial velocity data help clarify the actual positions of the the cluster rgbs to improve model isochrone fits for each cluster . through these techniques , we re - derive age and distance estimates for the clusters be29 , bh 176 , and sa1 . the derived cmds for these three gass candidate clusters are compared to theoretical isochrones from @xcite . we use as free parameters the cluster s age , @xmath30 , @xmath71 , and [ fe / h ] . we must stress that given the confused appearance of the cmds for these sparse clusters in heavily contaminated backgrounds , especially for sa1 , we must be careful not to over - interpret the results of these matches . nevertheless , useful information can still be extracted from these comparisons , and it is a useful exercise to compare these results with previously published values . in the analysis that follows , visual matching of isochrones covering a range in ages and metallicities is carried out after simultaneously varying @xmath30 and the distance modulus @xmath71 to get the best fit for any given combination of age and metallicity . we have used the following equation from @xcite : @xmath72 } = { \rm log_{10}}~(z ) + 1.72125\ ] ] to convert between the observed metallicities and the total metallicity @xmath73 values used for the @xcite isochrones . additionally , we tested @xcite @xmath7-enhanced isochrone for be29 , see 4.3 below . we measure the first reliable rv for bh176 ( @xmath74 km s@xmath4 ) based on 9 stars . this measurement is significantly different and better than our single star measurement given in f04 , which was of poorer quality and lower resolution than our new data . the photometric data used for bh176 were obtained from @xcite , where these authors carried out isochrone matching using @xcite isochrones . we rederive the cluster parameters for the same photometric dataset , but now use the isochrones from @xcite . figure 9 shows the matched isochrones when we adopt @xmath75 ( [ fe / h ] = @xmath76 ) , @xmath77 ( [ fe / h ] = @xmath78 ) and @xmath79 ( [ fe / h ] = @xmath80 ) , with clusters members , determined from the spectroscopy , marked as solid triangles . the best results are achieved for the highest of these metallicities , which is also the most metal rich value available from @xcite . a range of ages ( 5.6 and 7.1 gyrs ) seems to match fairly well the msto , the slope of the rgb , and the position of the rc , suggesting the age is not well constrained photometrically . outside this age range a poor match is obtained when trying to match these three cmd features simultaneously . an @xmath30 from 0.64 to 0.68 is therefore derived , resulting in a heliocentric distance of 15.2 - 15.8 kpc ( table 12 ) . we find similar cluster parameters ( based on our new isochrone matches with updated stellar evolution models ) to those obtained by @xcite using the same photometry . we agree with the findings of @xcite that , based on current , _ photometrically_-determined [ fe / h ] , bh176 does not seem to follow the gass amr , in fact it is quite the opposite . we have also noted that the rv for bh176 is also not strongly correlated to the gass rv trend , so , collectively , the present evidence makes bh 176 unlikely to be a member of the putative gass cluster system . analysis of the rv find that it consistent with an object ( open cluster ) rotating with the flat rotation curve of the galactic disk . however , this result could also be consistent with a globular cluster passing through the disk . if bh176 is found spectroscopically to have [ fe / h ] @xmath81 , and it is actually a globular cluster ( as it has been cataloged ; * ? ? ? * ) , bh176 could provide important new constraints on milky way globular cluster formation scenarios . the rv determinations for be 29 is within the errors ( @xmath82 ) of other published findings ( see table 11 ) . for be29 , the measured spectroscopic metallicity is @xmath73=0.005 ( @xmath83}= -0.44 $ ] ; * ? ? ? * hereafter cbvmpr ) . we explored @xmath73=0.004 ( @xmath83}= -0.68 $ ] ) , @xmath73=0.008 ( @xmath83}= -0.38 $ ] ) and @xmath73=0.019 ( @xmath83}= + 0.0 $ ] ) @xcite isochrones . figure 10 shows the cmd for be29 with the matched isochrones for the different adopted metallicities and for three different ages ( 3.2 , 3.5 and 4.0 ) gyrs . it is evident from the figure that both @xmath84 and @xmath77 isochrones do a poor job matching the slope of the rgb . the best matches are obtained for @xmath75 , and we can see that the three ages seem to do similarly well matching the rather poorly defined msto , subgiant branch , and position of the rc . ages outside this range fail to reproduce the msto and the position of the rc simultaneously . together , the isochrone matches suggest a probable age range of 3.2 - 4.0 gyrs , and @xmath30 ranging from 0.08 to 0.10 . these values yield a heliocentric distance of 13.1 - 14.5 kpc . the resulting `` revised '' cluster parameters ( table 12 ) are roughly consistent with previous work . we find a similar age , reddening and distance for be29 to that found by @xcite , though we find a lower reddening and thereby farther distance when compared with ( * ? ? ? * e(@xmath25)=0.10 , @xmath85 kpc ) . using the same isochrones for be29 and sa1 , we find that be29 _ is _ the most distant known open cluster ( @xmath86 ) in the galaxy , as found by ( * ? ? * see table 12 ) . the isochrone - fitted metallicity is in agreement , within our errors , to the spectroscopic , detailed chemical abundances of cbvmpr and @xcite . however , ( * ? ? ? * hereafter aat ) pointed out in their comparison of ngc 2243 to be29 , that the findings of cbvmpr show that be29 is somewhat @xmath7-enhanced . in figure 11 , we refit the cmd using the padova @xmath7-enhanced isochrones @xcite . aat matched @xmath7-enhanced isochrones to be29 providing a reasonably good fit within previous determinations of the cluster redding and metallicity , although they do not have stars on the rgb higher than the rc . however as shown in figure 11 , our matches to @xmath7-enhanced isochrones are markedly different . while some of the differences can be attributed to the different isochrones used , the primary difference comes from trying to match our 2 spectroscopically confirmed member stars above the rc . matching the entire cmd with @xmath7-enhanced isochrones requires one to make be29 have _ solar _ [ fe / h ] . while this match is consistent with previous reddening determinations , it is very inconsistent with previously determined _ spectroscopic _ metallicities which range from @xmath83}= -0.4 $ ] ( cbvmpr ) to @xmath83}= -0.7 $ ] @xcite . an additional method that comes near to matching the cmd , is to decrease the age to @xmath87 gyr , however this match is inconsistent with the finding of aat , who find that the age difference of be29 and ngc 2243 ( @xmath88 gyr ) can not be more than 0.5 gyr . additionally the reddening determined must be 50% higher that the highest previous estimate and double that found by aat . we find that be29 can not be consistently fit with @xmath7-enhanced isochrones , therefore to account for the variable @xmath7 element enhancements found in cbvmpr more complex models are needed . we refer the reader to 6.2 in @xcite for further discussion of the high resolution studies . using the same isochrones for be29 and sa1 ( see below ) , we find that be29 _ is _ the most distant known open cluster ( @xmath89 ) in the galaxy , as found by ( * ? ? ? * see table 12 ) . our sa1 rv ( @xmath90 km s@xmath4 ) is smaller by @xmath91 9 km s@xmath4 than the sa1 velocity obtained by cbvmpr . we note that two of our sa1 stars 572 and 693 were the only stars observed by cbvmpr for this cluster ; cbvmpr find rvs of ( 104.4 , 104.8 ) km s@xmath4 for these two stars , respectively , while our survey finds ( 98.2 , 95.3 ) km s@xmath4 . thus , while both studies find small rv differences between the two stars , the relatively large rv offset between studies persists and is apparently not related to a difference in the stellar samples . while cbvmpr does observe at much higher @xmath49 than we do , the magnitude of the rv offset is significantly larger than the estimated uncertainty in the mean cluster motion for the two surveys . moreover , we have found no net zero point offset in checks of our standard star rvs by comparison to the iau values to our measurements , as shown in table 4 . the same template stars were used for the rv determination of all of the clusters and no large offset is found in be20 , 29 , 39 or bh176 . thus , the origin of the systematic offset between the surveys is not clear . however , since we observed the same stars as cbvmpr , we can determine that the four stars selected as members are indeed consistent with the work of cbvmpr . the sparse cmd of sa1 , and lack of bright giants , limits our ability to achieve a reliable isochrone match , though our rv members provide crucial benchmarks at the magnitude of the red clump . to improve the photometry depth and provide a better match , we used the photometry of @xcite within 2 @xmath46 of the cluster center and added our confirmed members . the spectroscopic metallicity for sa1 gives a @xmath75 ( @xmath83}= -0.38 $ ] ; cbvmpr ) . we fit the ages 4 , 4.5 and 5 gyrs , with the fixed @xmath75 metallicity , are studied as shown in figure 13 . an age of 4.5 - 5 gyr is derived , since the 4 gyr isochrones do not match well the msto . this match results in an @xmath30 that ranges from 0.19 to 0.24 . the corresponding heliocentric distance for these values ranges from 11.8 to 13.5 kpc ( see table 12 ) . we find that we are in relative agreement about the cluster parameters with other photometric studies of sa1 @xcite . @xcite find an older age ( 6.3 gyr ) based on the morphological age index @xcite , which is known to yield older age estimates than those derived from isochrone matching . with defined rv - member " samples , we may examine the membership reliability of stars selected to be cluster member candidates by our photometric pre - screening . this information is useful because a large number of our candidates have not been observed spectroscopically , but if we have confidence that the photometrically - selected candidates are likely to be members , they can potentially help constrain the likely positions of the rgb and rc sequences in the cluster cmds as well as point to the effectiveness of these kinds of selections for picking spectroscopic samples in future studies . the rv membership success rate among washington@xmath1 selected rgb stars with rvs is ( 100% , 53% , 100% ) for ( sa1 , be39 , and be20 ) respectively . ergb stars were added to our analysis for be20 but none were found to be members . the membership success rate for the @xmath0 selected rgb stars was 71% for bh176 ( 60% for rgb+rc+ergb ) and 75% for be29 . in previous studies of dwarf spheroidal galaxies ( e.g. , * ? ? ? * ; * ? ? ? * ) , the washington@xmath1 technique has been found to improve the selection reliability of star system rgb stars over cmd - only selection techniques by a significant factor , even with samples selected over larger areas , to the low density extremities of the clusters . the present use of the washington@xmath1 technique is not completely analogous to these dsph studies , because here we have targeted _ any _ giant star candidates for spectroscopic follow - up without regard to cmd position ( because in some cases the location of the rgb was not certain ) , whereas the dsph studies applied both washington@xmath1 selected of giant candidates _ and _ specific cmd location pre - filtering on the stars samples . nevertheless , we do find that use of the washington@xmath1 filters has apparently improved our success rate relative to simply picking targets based on cmd position . for further discussion of the washington@xmath1 selection technique the reader is directed to @xcite . lcrrrrr # members & ( rgb ) & 4 & 4 & 6 & 18 & 4 + @xmath68 & ( km s@xmath4 ) & 9.1 & 75.6 & 27.1 & 55.0 & 95.4 + @xmath92 & ( km s@xmath4 ) & 4.6 & 2.5 & 3.8 & 2.9 & 3.6 + @xmath93 & ( km s@xmath4 ) & @xmath9103.3 & @xmath922.0 & @xmath951.2 & @xmath9107.1 & @xmath941.4 + # members & ( all ) & 9 & 5 & 11 & 24 & 4 + @xmath94 & ( km s@xmath4 ) & 11.2 & 75.7 & 28.4 & 55.0 & 95.4 + @xmath95 & ( km s@xmath4 ) & 5.3 & 2.4 & 3.6 & 2.5 & 3.6 + @xmath96 & ( km s@xmath4 ) & @xmath9101.2 & @xmath921.8 & @xmath949.7 & @xmath9107.1 & @xmath941.4 + @xmath97 & ( km s@xmath4 ) & 85.0 & 78.0 & 24.7 & 58.0 & 104.0 + @xmath98 & ( km s@xmath4 ) & 30 & 5 & 0.1 & 2 & 0.1 + ref . & & 1 & 2 & 3 & 2 & 4 lcccccccc bh176 & 6.3 @xmath67 1.0 & 15.8 @xmath67 0.5 & 9.9 & 0.70 & & @xmath1011.2 & @xmath9101.2 & ? ? ? + berkeley 29 & 3.7 @xmath67 0.5 & 13.4 @xmath67 0.4 & 21.1 & 0.09 & @xmath90.44 & @xmath1028.4 & @xmath949.7 & yes + saurer 1 & 4.5 @xmath67 1.0 & 13.1 @xmath67 0.4 & 20.2 & 0.22 & @xmath90.38 & @xmath1095.4 & @xmath941.4 & yes

we provide the first _ reliable _ radial velocity for bh 176 ( km s ) . we also find that and km s , for saurer 1(a ) and berkeley 29 , respectively . we show that-enhanced isochrones , while spectroscopically motivated , provide a poor fit to be29 in contrast to previous findings . however , the radial velocity and photometric metallicity ( [ fe / h ] dex ) for bh 176 suggests that a connection of this cluster with the putative gass cluster system is unlikely . we reassess the age - metallicity relation for the most likely members of the gass clusters system for which spectroscopic metallicities are now available .

it has been previously proposed that some distant open clusters in the milky way may have been accreted during a dwarf galaxy merger , perhaps associated with the same event that led to the formation of the galactic anticenter stellar structure ( gass ) , also known as the `` monoceros ring '' . we have obtained and washington photometric and medium resolution ( ) multi - fiber spectroscopic data for the three distant old open clusters berkeley 29 , saurer 1 , and vdb - hagen 176 ( bh 176 ) . these clusters are spatially coincident with gass , but radial velocities and spectroscopic metallicities had not been available during previous studies of the gass candidate cluster system . similar data for the clusters berkeley 20 and berkeley 39 have been obtained for calibration purposes . we provide the first _ reliable _ radial velocity for bh 176 ( km s ) . we also find that and km s , for saurer 1(a ) and berkeley 29 , respectively . we show that-enhanced isochrones , while spectroscopically motivated , provide a poor fit to be29 in contrast to previous findings . we find that the clusters berkeley 29 and saurer 1 are consistent with the previously reported characteristics for gass candidate clusters and the gass stellar stream as derived from m - giant observations . however , the radial velocity and photometric metallicity ( [ fe / h ] dex ) for bh 176 suggests that a connection of this cluster with the putative gass cluster system is unlikely . we reassess the age - metallicity relation for the most likely members of the gass clusters system for which spectroscopic metallicities are now available .

astro-ph0008006

i

seyfert nuclei are typical active galactic nuclei ( agns ) in the nearby universe . they have been broadly classified into two types based on presence or absence of broad emission lines in their optical spectra ( khachikian & weedman 1974 ) ; seyferts with broad lines are type 1 ( hereafter s1 ) while those without broad lines are type 2 ( s2 ) . these two types of seyfert nuclei are now unified by introducing the viewing angle dependence toward the central engine surrounded by the geometrically and optically thick dusty torus ( antonucci & miller 1985 ; see for a review antonucci 1993 ) . in addition to these typical types , narrow - line seyfert 1 galaxies ( nls1s ) have also been recognized as a distinct type of seyfert nuclei . the optical emission - line properties of nls1s are summarized as follows ( e.g. , osterbrock & pogge 1985 ) . ( 1 ) the balmer lines are only slightly broader than the forbidden lines such as [ o iii]@xmath05007 ( typically less than 2000 km s@xmath1 ) . this property makes nls1s a distinct type of ordinary broad - line s1s ( bls1s ) . ( 2 ) the [ o iii]@xmath05007/h@xmath2 intensity ratio is smaller than 3 . this criterion was introduced to discriminate s1s from s2s by shuder & osterbrock ( 1981 ) . and , ( 3 ) they present strong fe ii emission lines which are often seen in s1s but generally not in s2s . moreover , the x - ray spectra of nls1s are very steep ( puchnarewicz et al . 1992 ; boller , brandt , & fink 1996 ; wang , brinkmann , & bergeron 1996 ; vaughan et al . 1999 ; leighly 1999b ) and highly variable ( boller et al . 1996 ; turner et al . 1999 ; leighly 1999a ) . because of these complex properties , it is still not understood what nls1s are in the context of the current agn unified model . in order to understand what nls1s are , it is important to investigate the narrow - line regions ( nlrs ) of nls1s because of the following two reasons . first , the intrinsic spectral energy distribution ( sed ) of the nuclear radiation of nls1s is rather different from that of bls1s ; i.e. , the soft and hard x - ray spectra of nls1s are steeper than those of bls1s ( boller et al . 1996 ; brandt , mathur , & elvis 1997 ; vaughan et al . 1999 ; leighly 1999b ) . it is often considered that the nlrs are photoionized by the nonthermal continuum radiation from central engines ( yee 1980 ; shuder 1981 ; cohen 1983 ; cruz - gonzlez et al . 1991 ; osterbrock 1993 ; evans et al . 1999 ) though shock ionization may play an important role of ionization of the nlr ( e.g. , contini & aldrovandi 1983 ; viegas - aldrovandi & contini 1989 ; dopita & sutherland 1995 ) . if the dominant mechanism of ionization is the photoionization , the degree or the structure of ionization of nlrs in nls1s may be different from that of bls1s . such difference can be probed by forbidden emission - line ratios . second , it is known that there are some differences between the nlr properties of s1s and s2s , for example , the gas temperature in the [ o iii ] zone ( e.g. , heckman & balick 1979 ; shuder & osterbrock 1981 ) . although the reason of such differences has not yet been understood fully , it is meaningful to investigate how the nlrs in nls1s share the properties with those in s1s or those in s2s . analyzing optical spectra of 7 nls1s and 16 bls1s , recently , rodrguez - ardila , pastoriza , & donzelli ( 2000b ) and rodrguez - ardila et al . ( 2000a ) reported that the nlrs of nls1s are less excited than those of the bls1s . they suggested that this is due to the difference in the shape of the seds of nuclear radiation between nls1s and bls1s . in their analysis they used the intensities of the forbidden lines normalized by the narrow components of balmer lines . however , it is not clear whether or not the `` narrow components '' of the balmer lines of nls1s are radiated from only the nlrs . for example , line widths of the balmer lines radiated from broad - line regions ( blrs ) may be narrow like nlr emission if we see nls1s from a nearly pole - on viewing angle ( taniguchi , murayama , & nagao 1999 and reference therein ) . therefore it seems better to use some combinations among forbidden emission lines . in this paper , we present the comparisons of some emission - line flux ratios among nls1s and bls1s ( see nagao , taniguchi , & murayama 2000c for highly ionized emission lines ) using the data compiled from the literature .

it is known that the spectral energy distribution ( sed ) of the nuclear radiation of narrow - line seyfert 1 galaxies ( nls1s ) has different shapes with respect to that of ordinary broad - line seyfert 1 galaxies ( bls1s ) , particularly in wavelengths of x - ray . , we have compiled the emission - line ratios of 36 nls1s and 83 bls1s from the literature .

it is known that the spectral energy distribution ( sed ) of the nuclear radiation of narrow - line seyfert 1 galaxies ( nls1s ) has different shapes with respect to that of ordinary broad - line seyfert 1 galaxies ( bls1s ) , particularly in wavelengths of x - ray . this may cause some differences in the ionization degree and the temperature of gas in narrow - line regions ( nlrs ) between nls1s and bls1s . this paper aims to examine whether or not there are such differences in the physical conditions of nlr gas between them . for this purpose , we have compiled the emission - line ratios of 36 nls1s and 83 bls1s from the literature . comparing these two samples , we have found that the line ratios of [ o i]/[o iii] and [ o iii]/[o iii] , which represent the ionization degree and the gas temperature respectively , are statistically indistinguishable between nls1s and bls1s . based on new photoionization model calculations , we show that these results are not inconsistent with the difference of the sed between them . the influence of the difference of seds on the highly ionized emission lines is also briefly discussed .

1610.08004

i

the concept of network coding came into light in the year 2000 by a seminal work of ahlswede _ et al._. in @xcite the authors showed that the min - cut bound in a multicast network can be achieved if the intermediate nodes are allowed to do operations on incoming messages before forwarding . this kind of operation of intermediate nodes has been termed as network coding . linear network coding refers to the scheme when all such operations are linear . in subsequent works it has been shown that linear network coding is sufficient to achieve the capacity of multicast networks @xcite . moreover , a capacity achieving network code can be designed efficiently @xcite . as far as a multicast network is concerned , a scalar linear network code over a sufficiently large finite field suffices to achieve the capacity . however , the requirement of field size can be reduced if vector linear network coding is used @xcite . in @xcite , it was shown that binary field is sufficient if the vector length is large enough . these results related to multicast networks were known by the year 2005 . after a decade later , there has been a few interesting works related to intricacies involved in linear network coding for multicast network . in one such result it has been shown that a multicast network being linearly solvable over a sufficiently large finite field does not necessarily mean that over all larger fields it is also solvable @xcite . it was also shown that existence of a vector linear solution for a certain vector dimension does not necessarily mean that there exists a vector linear solution for all larger vector dimensions @xcite . it is important to note that for a multicast network , the characteristic of the finite field does not play an important role in the sense that there does not exist a multicast network which has a scalar / vector linear solution only over a finite field of certain characteristic . the non - multicast networks have very different properties . for non - multicast networks it has been shown that there exists a network where better throughput ( capacity ) can be achieved if the nodes are allowed to do non - linear operations @xcite . there are non - multicast networks where scalar / vector linear solution not only depends on the size of the field but also on the characteristic of the field @xcite . in particular , it has been shown in @xcite that for any system of polynomial equations over integers , there exists a network which has a scalar linear network solution over a finite field if and only if the system of polynomial equation has a root in the same finite field . therefore , there exist networks which are solvable only over fields of certain characteristics . interesting examples are the fano and non - fano network presented in @xcite . the fano network has a vector linear solution for any vector dimension if and only if the characteristic of the finite field is even . over a finite field of odd characteristic it has linear coding capacity equal to @xmath2 . the non - fano network has a vector linear solution for any vector dimension if and only if the characteristic of the finite field is odd . if the characteristic is even then its linear coding capacity is equal to @xmath3 . in the references @xcite and @xcite the authors considered networks where all terminals demand the sum of the symbols generated at the sources . such networks have been given the name sum - networks . in @xcite it was shown that for any finite set of primes there exists a sum - network which has a vector linear solution for any vector dimension if and only if the characteristic of the finite field belongs to the given set . in @xcite it was shown that for any sum - network , there exists a multiple - unicast network which has a rate @xmath0 solution if and only if the sum - network has a rate @xmath0 solution . they also show that for any co - finite set of primes there exists a sum - network which has a vector linear solution for any vector dimension if and only if the characteristic of the finite field belong to the given set @xcite . thus , these three results when combined , shows that for any given finite / co - finite set of primes there exists a multiple - unicast network which has a vector linear solution if and only if the characteristic of the finite field belong to the given set . however , in the works of @xcite , the dependency on the characteristic of the field is shown only for either scalar linear network coding @xcite or vector linear network coding of any vector length @xcite . in this paper , we generalise the previous results to show that for any non - zero positive rational number @xmath1 and for any given finite / co - finite set of prime numbers , there exists a non - multicast network which has a rate @xmath1 fractional linear network code solution if and only of the characteristic of the finite belongs to the given finite / co - finite set of primes . the organization of the paper is as follows . in section [ sec2 ] we reproduce the standard definitions of fractional linear network coding , vector linear network and scalar linear network coding . in section [ sec3 ] we show that for any non - zero positive rational number @xmath1 , and for any finite / co - finite set of primes , there exists a network which has a rate @xmath1 fractional linear network coding solution if and only if the characteristic of the finite field belongs to the given set . in section [ sec4 ] we extend the results of section [ sec2 ] to multiple - unicast networks . the paper is concluded in section [ sec5 ] .

it is known that there exists a multiple - unicast network which has a rate linear network coding solution if and only if the characteristic of the finite field belongs to a given finite or co - finite set of primes . in this paper , we show that for any non - zero positive rational number , there exists a multiple - unicast network which has a rate fractional linear network coding solution if and only if the characteristic of the finite field belongs to a given finite or co - finite set of primes .

it is known that there exists a multiple - unicast network which has a rate linear network coding solution if and only if the characteristic of the finite field belongs to a given finite or co - finite set of primes . in this paper , we show that for any non - zero positive rational number , there exists a multiple - unicast network which has a rate fractional linear network coding solution if and only if the characteristic of the finite field belongs to a given finite or co - finite set of primes .

0911.1403

i

an unsatisfactory feature of all theories of gravity is that the field equations do not have any direct physical interpretation . the lack of an elegant principle which can lead to the dynamics of gravity ( `` how matter tells spacetime to curve '' ) is quite striking when we compare this situation with the kinematics of gravity ( `` how spacetime makes the matter move '' ) . the latter can be determined through the principle of equivalence by demanding that all freely falling observers , at all events in spacetime , must find that the equations of motion for matter reduce to their special relativistic form . our first aim will be to remedy this and provide a physical interpretation to field equations describing gravity in any diffeomorphism invariant theory . this , in turn , will lead us to the possibility of _ deriving _ the gravitational field equations from a thermodynamic variational principle without using the metric as a dynamical variable . the alternative interpretation is based on the thermodynamics of horizons . several recent investigations have shown that there is indeed a deep connection between gravitational dynamics and horizon thermodynamics ( for a review , see @xcite ) . for example , studies have shown that : * gravitational field equations in _ a wide variety of theories _ , when evaluated on a horizon , reduce to a thermodynamic identity @xmath0 . this result , first pointed out in ref.@xcite , has now been demonstrated @xcite in several cases like the stationary axisymmetric horizons and evolving spherically symmetric horizons in einstein gravity , static spherically symmetric horizons and dynamical apparent horizons in lovelock gravity , and three dimensional btz black hole horizons , frw cosmological models in various gravity theories and even @xcite in the case horava - lifshitz gravity . it is not possible to understand , in the conventional approach , why the field equations should encode information about horizon thermodynamics . * gravitational action functionals in a wide class of theories have a a surface term and a bulk term . in the conventional approach , we _ ignore _ the surface term completely ( or cancel it with a counter - term ) and obtain the field equation from the bulk term in the action . any solution to the field equation obtained by this procedure is logically independent of the nature of the surface term . but when the _ surface term _ ( which was ignored ) is evaluated at the horizon that arises in any given solution , it gives the entropy of the horizon ! ( again , this result extends far beyond einstein s theory to situations in which the entropy is not just proportional to horizon area . ) this is possible only because there is a specific holographic relationship @xcite between the surface term and the bulk term which , however , is an unexplained feature in the conventional approach to gravitational dynamics . since the surface term has the thermodynamic interpretation as the entropy of horizons , and is related holographically to the bulk term , we are again led to an indirect connection between spacetime dynamics and horizon thermodynamics . based on these features _ which have no explanation in the conventional approach _ one can argue that there is a conceptual reason why we need to relate horizon thermodynamics with gravitational dynamics ( in a wide class of theories far more general than just einstein gravity ) and revise our perspective towards spacetime . to set the stage for this future discussion , we begin by recalling the implications of the existence of temperature for horizons . in the study of normal macroscopic systems like , for example , a solid or a gas one can _ deduce _ the existence of microstructure just from the fact that the object can be heated . this was the insight of boltzmann which led him to suggest that heat is essentially a form of motion of the microscopic constituents of matter . that is , the existence of temperature is sufficient for us to infer the existence of microstructure even without any direct experimental evidence . the non - zero temperature of a horizon shows that we can actually heat up a spacetime , just as one can heat up a solid or a gas . an unorthodox way of doing this would be to take some amount of matter and arrange it to collapse and form a black hole . the hawking radiation @xcite emitted by the black hole can be used to heat up , say , a pan of water just as though the pan was kept inside a microwave oven . in fact the same result can be achieved by just accelerating through the inertial vacuum carrying the pan of water which will eventually be heated to a temperature proportional to the acceleration @xcite . these processes show that the temperatures of all horizons are as real as any other temperature @xcite . since they give rise to a class of hot spacetimes , it follows _ la _ boltzmann that the spacetimes should possess microstructure . in the case of a solid or gas , we know the nature of this microstructure from atomic and molecular physics . hence , in principle , we can work out the thermodynamics of these systems from the underlying statistical mechanics . this is not possible in the case of spacetime because we have no clue about its microstructure . however , one of the remarkable features of thermodynamics in contrast to statistical mechanics is that the thermodynamic description is fairly insensitive to the details of the microstructure and can be developed as a fairly broad frame work . for example , a thermodynamic identity like @xmath1 has a universal validity and the information about a _ given _ system is only encoded in the form of the entropy functional @xmath2 . in the case of normal materials , this entropy arises because of our coarse graining over microscopic degrees of freedom which are not tracked in the dynamical evolution . in the case of spacetime , the existence of horizons for a particular class of observers makes it mandatory that these observers integrate out degrees of freedom hidden by the horizon . to make this notion clearer , let us start from the principle of equivalence which allows one to construct local inertial frames ( lif ) with coordinates @xmath3 , around any event in an arbitrary curved spacetime . given the lif , we can now construct a local rindler frame ( lrf ) by boosting along one of the directions with an acceleration @xmath4 , thereby locally transforming the metric to a form given by : @xmath5 where @xmath6 and @xmath7 . the observers at rest ( with @xmath8 constant ) in the lrf will perceive the @xmath9 null surface as a horizon @xmath10 ( fig 1 ) . these local rindler observers and the freely falling inertial observers will attribute different thermodynamical properties to matter in the spacetime . for example , they will attribute different temperatures and entropies to the vacuum state as well as excited states of matter fields . when some matter with energy @xmath11 moves close to the horizon say , within a few planck lengths because it formally takes infinite rindler time for matter to actually cross @xmath10 the local rindler observer will consider it to have transfered an entropy @xmath12 to the horizon degrees of freedom . we will show ( in sec . 3 ) that , when the metric satisfies the field equations of any diffeomorphism invariant theory , this transfer of entropy can be given @xcite a geometrical interpretation as the change in the entropy of the horizon . this result allows us to associate an entropy functional with the null surfaces which the local rindler observers perceive as horizons . we can now demand that the sum of the horizon entropy and the entropy of matter that flows across the horizons ( both as perceived by the local rindler observers ) , should be an extremum for all observers in the spacetime . this leads to a constraint on the geometry of spacetime which can be stated , in @xmath13 , as @xmath14 for all null vectors @xmath15 in the spacetime . the general solution to is given by @xmath16 where @xmath17 has to be a constant because of the conditions @xmath18 . hence the thermodynamic principle leads uniquely to einstein s equation with a cosmological constant in 4-dimensions . notice , however , that has a new symmetry which the standard einstein s theory does not posses ; viz . , it is invariant under the transformation @xmath19 . this has important implications for the cosmological constant problem which we will discuss in sec . 4.3 . in @xmath20 , the same entropy maximization leads to a more general class of theories called lanczos - lovelock models ( see sec . 4.2 ) . the constraint on the background geometry in arises from our demand that the thermodynamic extremum principle should hold for _ all _ local rindler observers . this is identical to the manner in which freely falling observers are used to determine how gravitational field influences matter . demanding the validity of special relativistic laws for the matter variables , as determined by all the freely falling observers , allows us to determine the influence of gravity on matter . in a similar manner , demanding the maximization of entropy of horizons ( plus matter ) , as measured by all local rindler observers , leads to the dynamical equations of gravity . in this approach , both the entropy of horizons as well as the entropy of matter flowing across the horizon will be observer dependent thereby introducing a new level of observer dependence in thermodynamics . in particular , observers in different states of motion will have different regions of spacetime accessible to them ; for example , an observer falling into a black hole will not perceive its horizon in the same manner as an observer who is orbiting around it . therefore we are forced to accept that the notion of entropy is an observer dependent concept . ( at a conceptual level this is no different from the fact different freely falling observers will measure physical quantities differently ; but in this case , standard rules of special relativity allow us to translate the results between the observers . we do not yet have a similar set of rules for quantum field theory in noninertial frames . ) all these features suggest a deep relationship between quantum theory , thermodynamics and gravity which forms the main theme of this article . the rest of the article is organized as follows : in the next section , i briefly review some of the background results needed for our discussion . section 3 describes an interpretation of gravitational field equations in a general , diffeomorphism invariant , theory of gravity . using these results , it is possible to introduce an entropy maximization principle from which one can obtain the same field equations without using the metric as a dynamical variable . this is done in sec . 4 and the last section summarizes the results .

this insight , in turn , leads us to the possibility of deriving the gravitational field equations from another variational principle without using the metric as a dynamical variable . i review this approach and discuss its implications . address = iucaa , pune university campus , + ganeshkhind , pune 411007 , india . + email : nabhan@iucaa.ernet.in

it is possible to provide a thermodynamic interpretation for the field equations in any diffeomorphism invariant theory of gravity . this insight , in turn , leads us to the possibility of deriving the gravitational field equations from another variational principle without using the metric as a dynamical variable . i review this approach and discuss its implications . address = iucaa , pune university campus , + ganeshkhind , pune 411007 , india . + email : nabhan@iucaa.ernet.in

1012.4385

i

although the standard model ( sm ) is successful in describing almost all experimental results of high energy physics in terms of gauge theory , the dynamics responsible for the elerctroweak symmetry breaking is unknown . in the minimal version of the higgs sector , one higgs doublet field is introduced as an effective description of the dynamics below some cutoff scale @xmath27 . constraints from electroweak precision measurements indicate that @xmath27 is at least beyond 3 tev . on the other hand , this scale already introduces a fine - tuning problem of the higgs mass term at the @xmath28 % level . this is called a little hierarchy problem @xcite . little higgs models @xcite were proposed as a solution to the little hierarchy problem . in these models , the higgs doublet field appears as pseudo nambu - goldstone ( ng ) bosons of new strong dynamics at the cutoff scale . a remarkable property is that the one - loop quadratic divergence to the renormalization of the higgs mass term is cancelled by a proper choice of global and local symmetries , so that the cutoff scale can be pushed to @xmath29tev without a severe fine - tuning . a simple case is called the littlest higgs model @xcite where the higgs field is realized as a part of the ng bosons associated with the global symmetry breaking of su(5 ) to so(5 ) and the gauge symmetry is [ su(2)@xmath30u(1)]@xmath31 . then the quadratic divergence of the higgs mass term in the sm is cancelled by the extra gauge bosons and the heavy partner of the top quark . subsequent studies @xcite , however , showed that these heavy partners need to be heavier than several tev to satisfy severe constraints imposed by precise electroweak measurements , hence reintroducing some degree of the fine - tuning problem . in the littlest higgs model with t parity ( lht ) @xcite , the model is extended to have a @xmath32 parity so that the heavy gauge bosons assigned to be t - odd particles do not directly couple with a pair of the sm fermions , and the phenomenological constraints are somewhat relaxed . flavor physics provides an interesting possibility to explore the lht . in order to assign t parity , we need to introduce extra fermions ( t - odd fermions ) which are left - handed su(2 ) doublets . then , the flavor transition can arise in the vertices of heavy gauge bosons , t - odd fermions and ordinary sm fermions . there are two 3@xmath303 unitary matrices describing these flavor transitions associated with quark and lepton sectors besides the ordinary flavor mixing matrices in the quark and lepton sectors i.e. the cabibbo - kobayashi - maskawa ( ckm ) @xcite and pontecorvo - maki - nakagawa - sakata ( pmns ) @xcite matrices . these matrices are new sources of flavor changing neutral current ( fcnc ) processes in the quark sector and lepton flavor violating ( lfv ) processes in the charged lepton sector . in the early literature on this subject various observable quantities of fcnc and lfv processes were calculated in the lht and showed that the effects of t - odd partners can be sizable and the correlations among various observable quantities can be different from other new physics model such as supersymmetric ( susy ) models @xcite . it was pointed out later that calculations missed a type of diagrams and the logarithmic dependences on the cutoff scale in the fcnc and lfv amplitudes disappear thanks to new contributions @xcite , thus reducing theoretical ambiguity associated with the physics at the ultraviolet cutoff scale . branching ratios of various fcnc and lfv processes were reevaluated including the new contributions @xcite . the qualitative feature turned out to be similar to the previous calculation though there were sizable changes at the quantitative level . in this paper , we present the results of further studies in tau and muon lfv processes . in addition to branching fractions , we also study observables defined with the help of polarizations of the initial muon and tau lepton @xcite . polarized muon experiments can be done using surface muon beams that are 100% polarized in the opposite direction of the @xmath33 momentum . in fact , a @xmath34 experiment with initial muon polarization is under consideration @xcite . in the tau pair production at @xmath35 colliders , the polarization information can be obtained by taking an angular correlation with tau decays on the opposite side @xcite . the study of polarized tau decays is also being considered for the @xmath7 process at the cern large hadron collider ( lhc ) where we can utilize the tau polarization from @xmath36 decays @xcite . in the following , we consider the processes @xmath2 , @xmath3 , @xmath4 ( @xmath37 al , ti , au and pb ) , @xmath6 , @xmath7 , @xmath8 , @xmath9 ( @xmath38 , @xmath12 and @xmath13 ) , @xmath14 ( @xmath39 , @xmath17 and @xmath18 ) , @xmath19 , @xmath20 , @xmath21 , @xmath22 , @xmath23 , @xmath24 and , @xmath25 . we define a parity asymmetry in two - body decays and two parity and one time - reversal asymmetries in three - body decays . in addition , we can define forward - backward asymmetry and forward - backward - angular asymmetries in the cases of @xmath40 and @xmath21 . we show that the parity asymmetries of two - body decays reflect the characteristic chirality structure of the lfv interactions . for three - body decays , we find that there are useful relations among various asymmetries . we calculate the rates of @xmath1-@xmath41 conversions for different muonic atoms and show that the ratios of the conversion rates can vary within 1 order of magnitude over most of the lht model parameter space . these features , as well as correlations of various branching ratios , can be useful in discriminating different new physics models . this paper is organized as follows : section ii is a brief review of the lht . lfv processes are classified and various asymmetries are defined in sec . numerical results on the various observable quantities are shown in sec . section v is the conclusion . appendix a shows the general formulae of branching ratios and asymmetries for the processes studied . functions for the wilson coefficients are given in appendix b. useful formulae to perform the consistency test of the lht are presented in appendix c.

lepton flavor violation in and processes is studied in the littlest higgs model with t parity . correlations among branching ratios and asymmetries are shown in the following lepton flavor violation processes : , , ( = al , ti , au and pb ) , , , , ( = , and ) , ( = , and ) , , , , , , and . it is shown that large parity asymmetries and time - reversal asymmetries are allowed in . for lepton flavor violation processes , sizable asymmetries are possible reflecting characteristic chirality structure of lepton flavor violating interactions in this model .

lepton flavor violation in and processes is studied in the littlest higgs model with t parity . we consider various asymmetries defined in polarized and decays . correlations among branching ratios and asymmetries are shown in the following lepton flavor violation processes : , , ( = al , ti , au and pb ) , , , , ( = , and ) , ( = , and ) , , , , , , and . it is shown that large parity asymmetries and time - reversal asymmetries are allowed in . for lepton flavor violation processes , sizable asymmetries are possible reflecting characteristic chirality structure of lepton flavor violating interactions in this model .

math0402139

i

let @xmath0 be a connected , linear algebraic group defined over @xmath1 , @xmath2 a @xmath18-dimensional vector space over @xmath3 with @xmath1-structure @xmath4 , and @xmath19 a @xmath1-rational representation of @xmath0 on @xmath2 with a zariski - dense @xmath0-orbit . the triple @xmath20 then represents a prehomogeneous vector space , and we denote the dual prehomogeneous vector space by @xmath21 . in case that @xmath0 is reductive , and the singular set @xmath11 is an irreducible hypersurface , there exists an irreducible , homogeneous polynomial @xmath22 such that @xmath23 , and @xmath24 . the singular set @xmath25 of the dual prehomogeneous vector space is then also an irreducible hypersurface given as the set of zeros of a homogeneous , irreducible polynomial @xmath26 satisfying @xmath27 . the rational functions @xmath22 and @xmath26 are called relative invariants . set @xmath28 , @xmath29 , denote by @xmath7 the group of @xmath1-rational points of @xmath0 , and let @xmath30 be the connected component containing the unit element . @xmath13 and @xmath31 decompose into the same number of connected components denoted by @xmath32 , respectively @xmath33 , @xmath34 , each of them being a @xmath35-orbit . the fundamental theorem of prehomogeneous vector spaces @xcite , regarding the fourier transform of a complex power of a relative invariant , then states that for rapidly decreasing functions @xmath36 , @xmath37 on @xmath4 , respectively @xmath38 , the integrals @xmath39 which converge for @xmath40 , can be extended analytically to meromorphic functions on the whole complex @xmath17-plane , and satisfy the functional equations @xmath41 where @xmath42 is given by a product of @xmath43-functions , and the @xmath44 are entire functions . originally , the theory of prehomogeneous vector spaces developed from an attempt to construct dirichlet series satisfying functional equations in a systematic way . since every smooth affine algebraic variety @xmath45 which carries the action of a reductive algebraic group @xmath35 , and posesses an open orbit , is isomorphic to a homogeneous vector bundle @xmath46 , where @xmath47 is a reductive subgroup of @xmath35 , and @xmath48 is a locally homogeneous @xmath47-vector bundle , the investigation of such @xmath35-varieties can be reduced to the study of locally transitive linear actions of connected reductive groups . in classical representation theory , for every admissible irreducible representation @xmath49 of @xmath35 on some hilbert space @xmath47 , the continuous linear operators @xmath50 , defined by @xmath51 , where @xmath10 is some test function on @xmath35 , and @xmath52 denotes haar measure on @xmath35 , are of trace class , and the global character of @xmath53 is defined in terms of this trace as a distribution on @xmath35 . in this paper , we will consider the left regular representation @xmath6 of the group @xmath7 on the banach space @xmath8 of continuous functions on @xmath4 vanishing at infinity , and our main goal will consist in giving a description of the corresponding operators @xmath54 , where @xmath10 is a rapidly decreasing function on @xmath35 . since we will work in a @xmath55 framework , avoiding hilbert space theory entirely , we will rely on the theory of pseudodifferential operators in order to formulate our results . it turns out that , for arbitrary prehomogeneous vector spaces , the restriction of @xmath9 to @xmath56 is a pseudodifferential operator with smooth kernel . in case that @xmath0 is reductive , and both @xmath11 and @xmath14 are irreducible hypersurfaces , each of the components @xmath32 is a @xmath55 manifold with boundary @xmath57 , the latter being smooth outside its intersection with the set of non - regular points @xmath58 of @xmath14 . as we will show , the restriction of @xmath9 to @xmath59 is a totally characteristic pseudodifferential operator lying in the class @xmath60 . these operators are locally given as oscillatory integrals @xmath61 where @xmath62 , and @xmath63 is a lacunary symbol . here @xmath64 are the standard coordinates in @xmath65 . the kernels of such operators are no longer smooth , and become singulare along @xmath66 . in the case of a smooth operator acting on a @xmath55 manifold , a trace can be defined in a natural way by restricting its kernel to the diagonal , which yields a density on the underlying manifold . if the manifold is compact , it can be integrated , and the so defined trace coincides with the usual @xmath67-trace . in our situation , the restriction of the schwartz kernel of @xmath9 to the diagonal defines a distribution on @xmath13 given by expressions of the form for some critical exponent @xmath17 , and its extension to @xmath68 , and the complex @xmath17-plane , satisfies functional equations according to . a trace of @xmath9 can then be defined by subtracting the singular contributions of the poles of the meromorphic extension . as an application , we consider the holomorphic semigroup @xmath69 of bounded linear operators on @xmath8 generated by a strongly elliptic differential operator associated with the representation @xmath6 . the latter is a differential operator of euler type , and the corresponding semigroup can be characterized by a convolution semigroup of complex measures , which are absolutely continuous with respect to haar measure . denoting the corresponding radon - nikodym derivative by @xmath70 , one has @xmath71 , and since @xmath72 is analytic in @xmath73 and @xmath74 , as well as rapidly decreasing , we can apply the above considerations . in particular , we get explicit expressions for the schwartz kernel of the operators @xmath75 , and their restrictions to the diagonal .

let be a connected , linear algebraic group defined over , acting regularly on a finite dimensional vector space over with-structure . we consider the left regular representation of the group of-rational points on the banach space of continuous functions on vanishing at infinity , and study the convolution operators , where is a rapidly decreasing function on the identity component of . it turns out that the restriction of to is a smooth operator . we then investigate the restriction of the schwartz kernel of to the diagonal . it defines a distribution on given by some power of a relative invariant of and , as a consequence of the fundamental theorem of prehomogeneous vector spaces , its extension to , and the complex-plane , satisfies functional equations . a trace of can then be defined by subtracting the singular contributions of the poles of the meromorphic extension .

let be a connected , linear algebraic group defined over , acting regularly on a finite dimensional vector space over with-structure . assume that posseses a zariski - dense orbit , so that becomes a prehomogeneous vector space over . we consider the left regular representation of the group of-rational points on the banach space of continuous functions on vanishing at infinity , and study the convolution operators , where is a rapidly decreasing function on the identity component of . denote the complement of the dense orbit by , and put . it turns out that the restriction of to is a smooth operator . furthermore , if is reductive , and and are irreducible hypersurfaces , corresponds , on each connected component of , to a totally characteristic pseudodifferential operator . we then investigate the restriction of the schwartz kernel of to the diagonal . it defines a distribution on given by some power of a relative invariant of and , as a consequence of the fundamental theorem of prehomogeneous vector spaces , its extension to , and the complex-plane , satisfies functional equations . a trace of can then be defined by subtracting the singular contributions of the poles of the meromorphic extension .

1011.5731

i

i am very glad to submit a paper for the special issue of the journal of geometric mechanics in honour of tudor ratiu . i followed his scientific work for several years ; i specially praise the superb book he wrote with juan - pablo ortega @xcite . i hope that he will find some interest in the present work . the kepler problem is a completely integrable hamiltonian system with important applications in the physical world : it provides a very accurate model of the motion of planets in the solar system , and its quantized equivalent provides a good model of the hydrogen atom . moreover , several features of the kepler problem make it very interesting for the mathematician : some of its motions ( those in which there is a collision of the moving point with the attractive centre ) are not defined for all times , but the system can be regularized , _ i.e. _ mapped into a new hamitonian system whose motions are defined for all times ; the lie algebra of infinitesimal symmetries of a given energy level of the phase space depends on that energy level . in section [ conformallyfields ] some results in symplectic geometry are presented . these results will be used in section [ kepler ] to explain why a diffeomorphism between the phase space of the kepler problem , restricted to negative values ( resp . positive values ) of the energy , and an open subset of the cotangent space to a 3-dimensional sphere ( resp . , a 3-dimensional two - sheeted hyperboloid ) is symplectic . that diffeomorphism was discovered by gyrgyi @xcite ( 1968 ) , re - discovered by ligon and schaaf @xcite ( 1976 ) and discussed by cushman and duistermaat @xcite ( 1997 ) , who have shown that it is characterized by the three very natural properties : 1 . it maps the set of points in the phase space of the kepler problem where the energy is negative ( resp . , positive ) onto the tangent bundle of the @xmath9-sphere ( resp . , the two - sheeted @xmath9-dimensional revolution hyperboloid ) with its zero section removed . 2 . it intertwines the kepler and delaunay vector fields ( a rescaling of the geodesic vector field on the @xmath9-sphere , or on the @xmath9-dimensional hyperboloid ) . 3 . it intertwines the @xmath10-momentum mappings of the kepler and delauney vector fields . we will see that the remarkable properties of that diffeomorphism appear as very natural consequences of the results presented in section [ conformallyfields ] . we will also discuss the weak infinitesimal symmetries of the kepler problem , and we will show that their set is a lie algebroid with a zero anchor map , rather than a lie algebra . after completion and submission of the present paper , the work of gert heckman and tim de laat @xcite , recently posted on arxiv , was indicated to us . the method used by these authors to explain the properties of the gyrgyi - ligon - schaaf diffeomorphism rests on the same ideas as ours . we also learnt that conformally hamiltonian vector fields were used , in the theory of bi - hamiltonian vector fields , by a.j . maciejewski , m. prybylska and a.v . tsiganov @xcite .

this result explains why the diffeomorphism of the phase space of the kepler problem restricted to the negative ( resp . two - sheeted hyperboloid ) , discovered by gyrgyi ( 1968 ) , re - discovered by ligon and schaaf ( 1976 ) , is a symplectic diffeomorphism . infinitesimal symmetries of the kepler problem are discussed , and it is shown that their space is a lie algebroid with zero anchor map rather than a lie algebra .

let be a hamiltonian vector field defined on a symplectic manifold , a nowhere vanishing smooth function defined on an open dense subset of . we will say that the vector field is _ conformally hamiltonian_. we prove that when is complete , when is hamiltonian with respect to another symplectic form defined on , and when another technical condition is satisfied , then there is a symplectic diffeomorphism from onto an open subset of , which maps each orbit to itself and is equivariant with respect to the flows of the vector fields on and on . this result explains why the diffeomorphism of the phase space of the kepler problem restricted to the negative ( resp . positive ) values of the energy function , onto an open subset of the cotangent bundle to a three - dimensional sphere ( resp . two - sheeted hyperboloid ) , discovered by gyrgyi ( 1968 ) , re - discovered by ligon and schaaf ( 1976 ) , is a symplectic diffeomorphism . cushman and duistermaat ( 1997 ) have shown that the gyrgyi - ligon - schaaf diffeomorphism is characterized by three very natural properties ; here that diffeomorphism is obtained by composition of the diffeomorphism given by our result about conformally hamiltonian vector fields with a ( non - symplectic ) diffeomorphism built by a variant of moser s method . infinitesimal symmetries of the kepler problem are discussed , and it is shown that their space is a lie algebroid with zero anchor map rather than a lie algebra . charles - michel marle ( communicated by the associate editor name )

1308.6497

i

we start out with a few definitions from group theory . let @xmath4 be a group . we say that _ @xmath4 splits over the subgroup @xmath5 _ if @xmath4 admits an hnn decomposition with base group @xmath6 and amalgamating subgroup @xmath5 . more precisely , @xmath4 splits over the subgroup @xmath5 if there exists an isomorphism @xmath7 where @xmath8 are subgroups of @xmath4 and @xmath9 is a monomorphism . in this notation , relations of @xmath6 are implicit . we will write such a presentation more compactly as @xmath10 in this paper we are interested in splittings of knot groups . given a knot @xmath11 we denote the knot group @xmath12 by @xmath2 . we denote by @xmath13 the genus of the knot , the minimal genus of a seifert surface @xmath14 for @xmath0 . it follows from the loop theorem and the seifert - van kampen theorem that we can split the knot group @xmath2 over the free group @xmath15 of rank @xmath16 . the _ rank _ @xmath17 of a group @xmath18 is the minimal size of a set of generators for @xmath18 . it is well known that if @xmath0 is a fibered knot , that is , the knot complement @xmath19 fibers over @xmath20 , then the group @xmath2 splits only over free groups of rank @xmath16 . ( see , for example , lemma [ lem : fibsplit ] . ) we show that this property characterizes fibered knots . in fact , we can say much more . [ thm : fibsplitintro ] let @xmath0 be a non - fibered knot . then @xmath2 splits over non - free groups of arbitrarily large rank . neuwirth ( * ? ? ? * problem l ) asked whether there exists a knot @xmath0 such that @xmath2 splits over a _ free _ group of rank other than @xmath16 . by the above , such a knot would necessarily have to be non - fibered . lyon ( * ? ? ? * theorem 2 ) showed that there does in fact exist a non - fibered genus - one knot @xmath0 with incompressible seifert surfaces of arbitrarily large genus . this implies in particular that there exists a knot @xmath0 for which @xmath2 splits over free groups of arbitrarily large rank . we give a strong generalization of this result . [ freesplitting ] let @xmath0 be a non - fibered knot . then for any integer @xmath21 there exists a splitting of @xmath2 over a free group of rank @xmath22 . note that an incompressible seifert surface gives rise to a splitting over a free group of _ even rank_. the splittings over free groups of _ odd rank _ in the theorem are therefore not induced by incompressible seifert surfaces . feustel and gregorac @xcite showed that if @xmath23 is an aspherical , orientable @xmath24-manifold such that @xmath25 splits over the fundamental group of a _ closed _ surface @xmath26 , then this splitting can be realized topologically by a properly embedded surface . ( more splitting results can be found in ( * ? ? ? * proposition 2.3.1 ) . ) the fact that fundamental groups of non - fibered knots can be split over free groups of odd rank shows that the result of feustel and gregorac does not hold for splittings over fundamental groups of surfaces with boundary . theorems [ thm : fibsplitintro ] and [ freesplitting ] can be viewed as strengthenings of stallings s fibering criterion . we refer to section [ section : stallings ] for a precise statement . our third main theorem shows that theorem [ freesplitting ] is optimal . [ mainthm][mainthm3 ] if @xmath0 is a knot , then @xmath2 does not split over a group of rank less than @xmath16 . the case @xmath27 follows from the kneser conjecture and work of waldhausen @xcite , as we show in section [ section : genusone ] . however , to the best of our knowledge , the classical methods of 3-manifold topology do not suffice to prove theorem [ mainthm ] in the general case . we use the recent result @xcite that wada s invariant detects the genus of any knot . this result in turn relies on the seminal work of agol @xcite , wise @xcite , przytycki wise @xcite and liu @xcite . theorem [ mainthm ] is of interest for several reasons : it gives a completely group - theoretic chararcterization of the genus of a knot , namely @xmath28 a different group - theoretic characterization was given by calegari ( see the proof of proposition 4.4 in @xcite ) in terms of the ` stable commutator length ' of the longitude . theorem [ mainthm ] fits into a long sequence of results showing that minimal - genus seifert surfaces ` stay minimal ' even if one relaxes some conditions . for example , gabai @xcite showed that the genus of an _ immersed _ surface cobounding a longitude of @xmath0 is at least @xmath13 . furthermore , minimal - genus seifert surfaces give rise to surfaces of minimal complexity in the 0-framed surgery @xmath29 ( see @xcite ) and in most @xmath20-bundles over @xmath29 ( see @xcite ) . given a closed @xmath24-manifold @xmath23 it is obvious that @xmath30 is a lower bound for the heegaard genus @xmath31 of @xmath23 . in light of theorem [ mainthm ] one might hope that this is in an equality ; that is , that @xmath32 . this is not the case , though , as was shown by various authors ( see @xcite and @xcite ) . the paper is organized as follows . in section [ section : hnnsplittings ] we discuss several basic facts about hnn decompositions of groups . in section [ section : splitk ] we recall that incompressible seifert surfaces give rise to hnn decompositions of knot groups and we characterize in lemma [ lem : fibsplit ] the splittings of fundamental groups of fibered knots . in section [ section:52 ] we consider the genus - one non - fibered knot @xmath33 . we give explicit examples of splittings of the knot group over a non - free group and over the free group @xmath34 of rank 3 , and inequivalent splittings of the knot group over @xmath35 . section [ section : splitnonfree ] contains the proof of theorem [ thm : fibsplitintro ] , and in section [ section : splitfree ] we give the proof of theorem [ freesplitting ] . in section [ section : stallings ] we show that these two theorems strengthen stallings s fibering criterion . in section [ section : genusone ] we give a proof of theorem [ mainthm ] for genus - one knots . the proof relies mostly on the kneser conjecture and a theorem of waldhausen . in section [ section : wada ] we review the definition of wada s invariant of a group . finally , in section [ section : proof ] we prove theorem [ thm : technical ] , which combined with the main result of @xcite provides a proof of theorem [ mainthm ] for all genera . we conclude this introduction with two questions . the precise notions are explained in section [ section : hnnsplittings ] . let @xmath4 be a word hyperbolic group and let @xmath36 be an epimorphism such that @xmath37 is not finitely generated . does @xmath38 admit splittings over ( infinitely many ) pairwise non - isomorphic groups ? ( the group @xmath39 satisfies these conditions if @xmath0 is a non - fibered knot . ) let @xmath0 be a non - fibered knot of genus @xmath1 . does @xmath2 admit ( infinitely many ) inequivalent splittings over the free group @xmath40 on @xmath3 generators ? all groups are assumed to be finitely presented unless we say specifically otherwise . all @xmath24-manifolds are assumed to be connected , compact and orientable . given a submanifold @xmath41 of a @xmath24-manifold @xmath23 , we denote by @xmath42 an open tubular neighborhood of @xmath41 in @xmath23 . given @xmath43 we denote by @xmath44 the free group on @xmath22 generators . the first author wishes to thank the university of sydney for its hospitality . we are also very grateful to eduardo martinez - pedroza , saul schleimer and henry wilton for very helpful conversations .

let be a knot of genus . if is fibered , then it is well known that the knot group splits only over a free group of rank . if is not fibered , then splits over every free group of rank at least . however , can not split over a group of rank less than .

let be a knot of genus . if is fibered , then it is well known that the knot group splits only over a free group of rank . we show that if is not fibered , then splits over non - free groups of arbitrarily large rank . furthermore , if is not fibered , then splits over every free group of rank at least . however , can not split over a group of rank less than . the last statement is proved using the recent results of agol , przytycki wise and wise .

math0211386

i

take real polynomials @xmath18 $ ] and let @xmath19 , @xmath13 , be a continuous family of ovals . for sufficiently small @xmath20 and generic @xmath21 the limit cycles of the perturbed plane hamiltonian system @xmath22 which tend to certain ovals from the continuous family when @xmath23 , are in one - to - one correspondence with the zeros of the complete abelian integral @xmath24 for this reason the problem of finding the zeros of @xmath14 in terms of the degrees of @xmath25 was called by arnold @xcite the _ weakened 16th hilbert problem _ " ( compare to hilbert @xcite , see also arnold @xcite ) . note that the level sets @xmath26 will contain in general several continuous families of ovals which need be considered separately . it follows from the varchenko - khovanskii theorem that the number of the zeros of @xmath14 is bounded by a constant @xmath27 , uniformly in all @xmath25 , such that @xmath28 , @xmath29 , @xmath30 . in the so called hyperelliptic case " ( @xmath2 ) it was proved by novikov and yakovenko@xcite that there exists an algorithm producing a function @xmath31 such that @xmath32 , which is given by a tower function ( an iterated exponent ) of height at least five . their proof is based on the analytic properties of a suitable picard - fuchs system satisfied by abelian integrals ( including the magnitude of the coefficients of the system and some restrictions on its monodromy group ) . the progress in solving the weakened 16th hilbert problem ( finding the _ exact _ number of the zeros of @xmath14 ) concerned so far the elliptic case " only ( the complex algebraic curve @xmath4 is of genus at most one ) . it was proved for instance that in several cases , the vector space @xmath33 of abelian integrals of degree @xmath34 polynomials along the ovals of @xmath11 , obeys the so called _ chebyshev property _ ( the number of the zeros of each integral is smaller than the dimension of the vector space @xmath33 ) , see @xcite . in this relation arnold asked in ( * ? ? ? * the 7th problem ) whether the @xmath9-dimensional vector space of abelian integrals @xmath35 where @xmath36>1 , $ ] is chebyshev . in an attempt to solve this problem givental @xcite obtained a non - oscillation theorem for lagrangian planes of the picard - fuchs system satisfied by the abelian integrals @xmath37 . he used the fact that every picard - fuchs system has a hamiltonian ( or poisson ) structure . he failed , however , to produce bounds for the zeros of the abelian integrals . in the present paper we try to explore the algebro - geometrical properties of the abelian integrals , without using the picard - fuchs system . our main result is theorem [ main ] in which we show that when @xmath17 and @xmath38 , exceptional families of ovals @xmath8 , @xmath39 , exist such that every abelian integral of the form @xmath40 has at most one simple zero on the interval @xmath16 . at a first sight this seems to be an easy observation ( equivalent to the claim that @xmath41 is monotonous on @xmath16 ) . this is , however , the first result of such a kind for non - elliptic curves @xmath4 . the proof uses the riemann bilinear relations on differentials of the first kind together with the fact that a jacobian variety with its polarization can not be a direct product of principally polarized abelian varieties . our arguments can be adapted to other situations ( for instance when the degree of @xmath0 is @xmath42 ) , but we shall not do this here . we give also a negative answer ( proposition [ nocheb ] ) to the initial question posed by arnold : it turns out that there exist abelian integrals of the form ( [ question ] ) with exactly @xmath15 - 1 $ ] zeros in a neighborhood of the origin .

we show that the-dimensional real vector space of these integrals is not chebyshev in general : for any , there are hyperelliptic hamiltonians and continuous families of ovals , , such that the abelian integral can have at least - 1 $ ] zeros in . our main result is theorem [ main ] in which we show that when , exceptional families of ovals exist , such that the corresponding vector space is still chebyshev .

let be a real polynomial of degree , and be an oval contained in the level set . we study complete abelian integrals of the form where are real and is a maximal open interval on which a continuous family of ovals exists . we show that the-dimensional real vector space of these integrals is not chebyshev in general : for any , there are hyperelliptic hamiltonians and continuous families of ovals , , such that the abelian integral can have at least - 1 $ ] zeros in . our main result is theorem [ main ] in which we show that when , exceptional families of ovals exist , such that the corresponding vector space is still chebyshev .

1701.07947

i

suppose @xmath14 is an elliptic surface defined over a number field @xmath1 , so @xmath2 is a smooth projective curve and all but finitely many fibers @xmath15 , @xmath16 , are smooth elliptic curves . we let @xmath17 denote the nron - tate canonical height of @xmath18 viewed as an elliptic curve over the function field @xmath19 ; we let @xmath20 denote the canonical height on the fibers for ( all but finitely many ) @xmath21 . suppose that @xmath22 is a section defined over @xmath1 for which @xmath23 , so , in particular , the points @xmath8 on the fiber are not torsion in @xmath15 for all @xmath24 . tate showed that the function @xmath25 is a weil height on @xmath6 , up to a bounded error @xcite . more precisely , there exists a divisor @xmath26 of degree equal to @xmath27 so that @xmath28 where @xmath29 is a weil height on @xmath6 associated to @xmath30 . in a series of three articles @xcite , silverman refined statement ( [ elliptic variation ] ) by analyzing the nron decomposition of the canonical height on the fibers @xmath31 where @xmath32 denotes the set of places of the number field @xmath1 , and @xmath33 are the integers appearing in the product formula @xmath34 for all @xmath35 . in this article , we explain how silverman s conclusions about the local functions @xmath36 are precisely the input needed to show that @xmath37 is a good " height function on the base curve @xmath2 , from the point of view of equidistribution . combining his work with methods from complex dynamics , as in @xcite , and the inequalities of zhang on successive minima @xcite , we prove : [ good height ] let @xmath1 be a number field and @xmath38 for a smooth projective curve @xmath2 defined over @xmath1 . fix any elliptic surface @xmath14 defined over @xmath1 and point @xmath39 satisfying @xmath40 . then @xmath41 for @xmath24 with smooth fibers , is the restriction of a height function on @xmath6 induced from an adelically metrized ample line bundle @xmath42 , with continuous metrics of non - negative curvature , satisfying @xmath43 theorem [ good height ] implies that our height function on @xmath2 satisfies the hypotheses of the equidistribution theorems of thuillier and yuan for points of small height on curves @xcite , and we deduce the following : [ equidistribution on b ] let @xmath1 be a number field and @xmath38 for a smooth projective curve @xmath2 defined over @xmath1 . fix any elliptic surface @xmath14 defined over @xmath1 and point @xmath39 satisfying @xmath40 . there is a collection of probability measures @xmath44 on the berkovich analytifications @xmath45 such that for any infinite , non - repeating sequence of @xmath46 such that @xmath47 as @xmath48 , the discrete measures @xmath49 converge weakly on @xmath45 to the measure @xmath50 at each place @xmath51 of @xmath1 . [ measures ] the measures @xmath50 of corollary [ equidistribution on b ] are not difficult to describe , at least at the archimedean places . at each archimedean place @xmath51 , there is a canonical positive @xmath52-current @xmath53 on the surface @xmath54 ( with continuous potentials away from the singular fibers ) which restricts to the haar measure on each smooth fiber @xmath55 . the measure @xmath50 on @xmath9 is just the pull - back of this current by the section @xmath12 . moreover , at every place , the measure @xmath50 is the laplacian of the local height function @xmath56 , away from its singularities . we give more details about ( and a dynamical perpective on ) the construction of the current @xmath53 in section [ dynamics ] . as a consequence of theorem [ good height ] , and combined with the work of masser and zannier @xcite , we obtain the so - called bogomolov extension of their theorems . suppose @xmath57 and @xmath58 are elliptic surfaces over a curve @xmath2 , defined over @xmath59 , and assume that at least one is non - isotrivial . we consider sections @xmath12 of the fiber product @xmath60 defined over @xmath59 . we say that a section @xmath61 is _ special _ if either * @xmath62 is torsion on @xmath63 for some @xmath64 , or * @xmath65 and @xmath66 are isogenous and there exists a pair of nonzero integers @xmath67 so that @xmath68 on a common cover @xmath18 of @xmath63 . if a family of abelian surfaces @xmath13 is isogenous to a fiber product ( after performing a base change @xmath69 if needed ) , we say that a section of @xmath70 is special if it is special on the fiber product . it is well known , assuming both @xmath65 and @xmath66 are non - isotrivial , that a special section will always pass through infinitely many torsion points in the fibers @xmath71 . that is , there are infinitely many @xmath72 for which @xmath73 if one of the curves , say @xmath66 , is isotrivial then a special section will pass through infinitely many torsion points unless the component @xmath74 is torsion and @xmath75 is constant and non - torsion on @xmath66 . is isotrivial if there exist a finite @xmath69 , an elliptic curve @xmath76 , and a birational @xmath77 . now let @xmath12 be a section of @xmath78 and denote by @xmath79 its extension to @xmath80 . then we say that @xmath12 is constant if @xmath81 is constant on @xmath80 . ] for proofs of these statements , see ( * ? ? ? * chapter 3 ) or , for dynamical proofs , see @xcite . the converse statement is also true , but it is much more difficult : masser and zannier proved that if @xmath82 for infinitely many @xmath83 , then the section @xmath12 must be special @xcite . we extend these results of masser - zannier from points of height 0 to points of small height : [ zhang language ] let @xmath2 be a quasiprojective smooth algebraic curve defined over @xmath59 . suppose @xmath84 is a non - isotrivial family of abelian varieties of dimension 2 defined over @xmath59 with a non - simple generic fiber . let @xmath42 be a line bundle on @xmath70 which restricts to an ample and symmetric line bundle on each fiber @xmath85 , and let @xmath86 be the induced nron - tate canonical height on @xmath85 , for each @xmath83 . for each non - special section @xmath87 defined over @xmath59 , there is a constant @xmath88 so that @xmath89 is finite . to put theorem [ zhang language ] in context , recall that ullmo and zhang proved the bogomolov conjecture @xcite , extending the manin - mumford conjecture ( a theorem of raynaud @xcite ) to points of small height on abelian varieties defined over @xmath59 . that is , for any abelian variety @xmath90 and choice of ample , symmetric line bundle @xmath42 on @xmath70 , and for any subvariety @xmath91 which is not itself an abelian subvariety or torsion translate of one , there is a positive constant @xmath92 so that @xmath93 is not zariski dense in @xmath94 . a key ingredient in their proofs is the equidistribution theorem of szpiro , ullmo , and zhang @xcite . in his 1998 icm lecture notes @xcite , zhang presented a conjecture about geometrically simple families of abelian varieties , which stated , in its most basic form : [ zhang ] [ zhang conj ] let @xmath2 be a quasiprojective smooth algebraic curve defined over @xmath59 . suppose @xmath84 is a non - isotrivial family of abelian varieties with fiber dimension @xmath95 , defined over @xmath59 with a simple generic fiber . let @xmath42 be a line bundle on @xmath70 which restricts to an ample and symmetric line bundle on each fiber @xmath85 , and let @xmath86 be the induced nron - tate canonical height on @xmath85 , for each @xmath83 . for each non - torsion section @xmath87 defined over @xmath59 , there is a constant @xmath88 so that @xmath89 is finite . when the dimension of the fibers @xmath85 is equal to 2 , the finiteness of @xmath96 for sections as in conjecture [ zhang conj ] was established recently by masser and zannier in @xcite . it is well known that the conclusion of conjecture [ zhang conj ] can fail to hold if @xmath70 is not simple and certainly fails if it is a family of elliptic curves , as mentioned above . however , the results of masser and zannier in their earlier work @xcite suggested a formulation of zhang s conjecture for the non - simple case in relative dimension 2 ; this is what we proved in our theorem [ zhang language ] . theorem [ good height ] , corollary [ equidistribution on b ] , and theorem [ zhang language ] were obtained in the special case of the legendre family @xmath97 over @xmath98 and the abelian variety @xmath99 , for sections @xmath12 with @xmath100-coordinates in @xmath101 in @xcite , using methods from complex dynamical systems , without appealing to silverman and tate s results on the height function . moreover , restricting further to sections @xmath12 with constant @xmath100-coordinate ( in @xmath102 ) , theorem [ zhang language ] was obtained without relying on the theorems of masser and zannier and gave an alternate proof of their result . this includes the special case treated by masser and zannier in their article @xcite . for sections with constant @xmath100-coordinate , the hypothesis on @xmath12 ( that @xmath40 ) is equivalent to asking that @xmath103 ( * ? ? ? * proposition 1.4 ) . the result of theorem [ zhang language ] extends to non - isotrivial families of abelian varieties @xmath13 in higher dimensions that split as a product @xmath104 of @xmath105 elliptic curves . indeed , if @xmath106 is a section , and if there exists an infinite sequence @xmath107 so that @xmath108 , then in fact @xmath109 for all @xmath64 , and we can reduce to theorem [ zhang language ] by considering pairs @xmath110 , @xmath111 . we conclude that every pair @xmath112 is special as a section of @xmath110 . * comments and acknowledgements . * this project was motivated , in part , by experiments to visualize silverman s results on the variation of canonical height @xcite in terms of the measures @xmath50 at archimedean places , and to examine their dependence on @xmath12 . in particular , the measure detects the failure of the local height function @xmath56 to be harmonic ; compare the comments on non - analyticity preceding theorem i.0.3 of @xcite . the images appearing in section [ experiment ] were first presented at the conference in honor of silverman s birthday , august 2015 . we thank charles favre , dragos ghioca , robert rumely , joseph silverman , and amaury thuillier for helpful suggestions and inspiring conversations . our research was supported by the national science foundation and the simons foundation .

applying theorems of thuillier and yuan , we obtain the equidistribution of points where is torsion , and we give an explicit description of the limiting distribution on . finally , combined with results of masser and zannier , we show there is a positive lower bound on the height , after excluding finitely many points , for any non - special " section of a family of abelian varieties that split as a product of elliptic curves .

let be an elliptic surface defined over a number field , where is a smooth projective curve , and let be a section defined over with canonical height . in this article , we show that the function on is the height induced from an adelically metrized line bundle with non - negative curvature on . applying theorems of thuillier and yuan , we obtain the equidistribution of points where is torsion , and we give an explicit description of the limiting distribution on . finally , combined with results of masser and zannier , we show there is a positive lower bound on the height , after excluding finitely many points , for any non - special " section of a family of abelian varieties that split as a product of elliptic curves .

1409.1486

i

the thompson group @xmath0 is the group of homeomorphisms @xmath14\to[0,1]$ ] for which : * the endpoints satisfy @xmath15 , @xmath16 , * it is piecewise linear with finitely many break points on the diadic numbers @xmath17\cap ( 0,1)$ ] , * all slopes of @xmath18 are in the set @xmath19 . @xmath0 is a countable group , and it is generated by the elements @xmath20 whose graphs are shown in fig . [ f : generatorsaboff ] . of @xmath0.[f : generatorsaboff],title="fig : " ] of @xmath0.[f : generatorsaboff],title="fig : " ] moreover , it has a finite presentation in terms of @xmath20 , namely @xmath21=[ab^{-1},a^{-2}ba^2]=e\rangle,\ ] ] where the group commutator @xmath22=ghg^{-1}h^{-1}$ ] is defined as usual . recall that elementary amenability implies amenability , and a copy of the free group @xmath23 ( on two generators ) inside a group implies non - amenability of the group . it is known that @xmath0 is not elementary amenable , i.e. @xmath0 can not be obtained from finite or abelian groups by taking subgroups , quotients , extensions , and direct limits . on the other hand , by a result of brin and squier @xcite , @xmath0 does not contain a copy of @xmath23 . for more information on the thompson group @xmath0 , see the survey paper by cannon , floyd and perry @xcite . it is a main open problem to decide whether the thompson group @xmath0 is amenable . recently , monod @xcite has constructed examples of groups of homeomorphisms of @xmath24 $ ] which are non - amenable , but which also do not contain a copy of @xmath23 . these groups resemble @xmath0 . moreover , olesen and the second named author has shown in @xcite that if the reduced @xmath25-algebra @xmath26 of the ( non - amenable ) thompson group @xmath27 is simple , then @xmath0 is non - amenable . both of the above mentioned results suggest that @xmath0 might not be amenable , and extrapolations of our computational results point in the same ( non - amenability ) direction . the present paper grew out of an attempt to test the amenability problem for @xmath0 by using computers to estimate norms of certain elements in the group ring @xmath5 of @xmath0 . by the norm @xmath28 ( see also section [ s : two ] ) of an element @xmath29 in the group ring of a discrete group @xmath30 we mean @xmath31 where @xmath32 is the left regular representation of @xmath30 . as explained in section [ s : two ] , it is standard to write @xmath33 instead of @xmath34 , for any @xmath35 , and we will continue with this tradition . our starting point is the following two theorems due to kesten and lehner : ( see section [ s : six ] for a more detailed discussion ) . [ t:1.2 ] let @xmath30 be a discrete group with a generating set @xmath36 such that @xmath37 and @xmath38 . then , @xmath39 moreover , the upper bound is attained if and only if @xmath30 is amenable , and the lower bound is attained if and only if @xmath40 generates @xmath30 freely . [ t:1.3 ] let @xmath30 be a discrete group with a generating set @xmath36 such that @xmath37 and @xmath41 . then , @xmath42 moreover , the upper bound is attained if and only if @xmath30 is amenable , and the lower bound is attained if and only if @xmath40 generates @xmath30 freely . hence for the thompson group @xmath0 we get [ c:1.4 ] let @xmath43 and @xmath44 be the standard generators of @xmath0 , and let @xmath45 denote the unit element of @xmath0 . then @xmath46 @xmath47 moreover , in both cases the upper bound is attained if and only if @xmath0 is amenable . let @xmath48 denote the von neumann algebra of a discrete group @xmath30 , i.e. @xmath48 is the von neumann algebra in @xmath49 generated by @xmath50 . then @xmath51 defines a normal faithful tracial state on @xmath48 ( see e.g. section 6.7 in @xcite ) . hence @xmath52 ( cf . section [ s : four ] ) . hence if we knew all the numbers @xmath53 we could also compute the norm @xmath54 . in practice we can only compute a finite number of the moments @xmath55 . in this paper , we develop efficient methods , both mathematically and computationally to compute the numbers @xmath55 in the case @xmath56 for any finite set @xmath57 in a discrete group @xmath30 . we then apply the methods to the elements @xmath58 and @xmath59 in the group ring @xmath5 of the thompson group @xmath0 given by @xmath60 as a result , we have been able to compute the moments @xmath61 for @xmath62 and the moments @xmath63 for @xmath64 . using the spectral theorem to the self - adjoint operators @xmath65 ( cf . section [ s : two ] ) , one gets that there are unique probability measures @xmath66 to @xmath67 with @xmath68 $ ] such that @xmath69 is invariant under the reflection @xmath70 , and such that @xmath71 moreover , @xmath72 . using methods from the theory of orthonormal polynomials applied to these two measures ( cf . section [ s : four ] ) we obtain from our moment calculations good lower bounds for @xmath73 , @xmath74 , namely @xmath75 and @xmath76 in fact for each @xmath77 ( resp . @xmath78 ) , we find a lower estimate of @xmath79 ( resp . @xmath80 ) , and a suitable extrapolation of those two finite series of numbers suggests that the actual norms are much closer to 3 ( resp 4 ) , namely @xmath81 furthermore , based on our moment calculations , we have also been able to estimate the lebesgue densities of the measures @xmath82 and @xmath83 with fairly high precision . this shows that the measures @xmath82 and @xmath83 are very close to zero on the interval @xmath84 $ ] and @xmath85 $ ] respectively , but we can not rule out , that the measures have very thin tails " stretching all the way up to @xmath86 and @xmath87 , respectively , which would imply that @xmath0 is amenable ( cf . corollary [ c:1.4 ] ) . in comparison , one gets for the free group @xmath23 on two generators @xmath88 that @xmath89 and @xmath90 the measures @xmath82 , @xmath83 based on @xmath88 instead of @xmath20 , will be denoted by @xmath91 ( @xmath74 ) , and they can be computed explicitly ( see section [ s : six ] ) : @xmath92}(x ) \ , dx\\ & & \mu_2^{\mathrm{free}}= \frac 2{\pi } \frac{\sqrt{12-x^2}}{16-x^2 } 1_{[-2\sqrt 3,2\sqrt3]}(x ) \ , dx.\end{aligned}\ ] ] since 2007 a number of papers has been published about computational approaches to problems related to the thompson group @xmath0 , including the amenability problem ( cf . @xcite,@xcite,@xcite,@xcite,@xcite ) . our paper is the first that considers the moments of @xmath93 for @xmath94 . in @xcite burillo , cleary and wiest use probabilistic methods to estimate the moments of @xmath63 for @xmath95 for @xmath96 . moreover , elder , rechnitzer and wong compute in @xcite the first 22 cogrowth coefficients of @xmath0 with respect to the symmetric set of generators @xmath97 , from which the exact values of @xmath98 @xmath99 can easily be computed . we will comment in more detail on the results of @xcite and @xcite at the end of section [ s : four ] . the thompson group @xmath0 has been the key motivation for the research presented in this paper . however , we should stress , that the methods developed in this paper can be applied to do similar computations in any other finitely generated group , provided there is a reasonable fast algorithm to decide whether two words in the generators correspond to the same element of the group . the rest of the paper is organized as follows : section [ s : two ] contains background material on the reduced @xmath25-algebra @xmath100 and the group von neumann algebra @xmath48 associated to a discrete group @xmath30 . in section [ s : three ] , we consider for any given finite set @xmath57 in a discrete group @xmath30 , the element @xmath101 and explain how one can compute the moments @xmath102 from computing much smaller number @xmath103 , @xmath104 , @xmath105 , @xmath106 ( @xmath107 ) associated to the pair @xmath108 . we next apply this to the special case of @xmath109 , the thompson group @xmath0 , and @xmath110 or @xmath111 in order to compute numerically the moments @xmath112 for @xmath113 in the first case and for @xmath114 for the second case . in sections [ s : four ] and [ s : fourb ] we apply methods from the theory of orthogonal polynomials to estimate the norms @xmath115 and @xmath116 , and to estimate the probability measures @xmath82 , @xmath83 , associated to @xmath117 and @xmath118 via formula ( [ e:4plus ] ) above . the sections [ s : five ] and [ s : six ] are the main theoretical sections of the paper . in the general setting of a finite subset @xmath57 of a discrete group @xmath30 , we derive in section [ s : five ] the formulas ( used in section [ s : three ] ) , that allow us to pass back and forth between the 5 sequences of numbers @xmath103 , @xmath104 , @xmath105 , @xmath106 and @xmath112 ( @xmath107 ) . in section [ s : six ] we formulate and explain kesten s and lehner s results ( theorem [ t:1.2 ] and theorem [ t:1.3 ] ) in the setting of leinert sets ( cf . theorem [ t : lowerboundleinersetsupperboundamenability ] ) . moreover , we make comparison between our numbers @xmath103 , @xmath104 , @xmath105 , @xmath106 ( @xmath107 ) and the cogrowth coefficients due to cohen @xcite and grigorchuk @xcite , and show that amenability of the group @xmath119 generated by @xmath120 can be decided from the asymptotics of each of the 4 sequences mentioned above ( cf . corollary [ c:7.9 ] ) .

let denote the thompson group with standard generators , . it is a long standing open problem whether is an amenable group . by a result of kesten from 1959 , amenability of is equivalent to and to where in both cases the norm of an element in the group ring is computed in via the regular representation of . by extensive numerical computations , oafpg 247321 , and partially supported by the danish national research foundation ( dnrf ) through the centre for symmetry and deformation at the university of copenhagen , and the danish council for independent research , natural sciences . ] supported by the erc advanced grant no . oafpg 247321 , and by the center for experimental mathematics at the university of copenhagen . ]

let denote the thompson group with standard generators , . it is a long standing open problem whether is an amenable group . by a result of kesten from 1959 , amenability of is equivalent to and to where in both cases the norm of an element in the group ring is computed in via the regular representation of . by extensive numerical computations , we obtain precise lower bounds for the norms in and , as well as good estimates of the spectral distributions of and of with respect to the tracial state on the group von neumann algebra . our computational results suggest , that it is however hard to obtain precise upper bounds for the norms , and our methods can not be used to prove non - amenability of . supported by the erc advanced grant no . oafpg 247321 , and partially supported by the danish national research foundation ( dnrf ) through the centre for symmetry and deformation at the university of copenhagen , and the danish council for independent research , natural sciences . ] supported by the erc advanced grant no . oafpg 247321 , and by the center for experimental mathematics at the university of copenhagen . ]

1409.1486

m

let @xmath30 be a discrete group and let @xmath125 be a finite set with @xmath187 elements ( @xmath188 ) . our main example will be @xmath109 , the thompson group , and @xmath57 either @xmath189 or @xmath97 , but we will for some time stick to the general case in order to treat the two particular cases in a similar way . our goal is to compute as many as possible of the moments @xmath190 where @xmath191 and @xmath11 is the trace on @xmath123 coming from the group von neumann algebra @xmath48 as in section [ s : two ] . recall that @xmath192 hence @xmath193 , and for @xmath107 , the numbers @xmath194 are @xmath195 where @xmath196 denotes the number of elements in a set @xmath40 . for composing elements of the thompson group @xmath0 , we used the belk and brown forest algorithm from @xcite . consider the subsets @xmath197 @xmath198 @xmath199 we say that @xmath200 is cyclic " as all the cyclic rotations of each element in @xmath200 are contained in the set itself . since these subsets are smaller , it takes less time to compute the reduced " numbers @xmath201 and even less time to compute the cyclic " numbers @xmath202 the relationship between these numbers and the moments are derived in section [ s : five ] . in particular , we have @xmath203 which shows that the first @xmath204 moments ( @xmath205 , , @xmath112 ) can be computed from either @xmath206 or @xmath207 . in the case of a symmetric set @xmath57 , i.e. @xmath208 , the reduced numbers @xmath105 are the even co - growth coefficients @xmath209 introduced by cohen @xcite and grigorchuk @xcite . in the notation of elder - rechnitzer - wong @xcite , @xmath210 and @xmath211 . ( still for a symmetric set @xmath212 in cohen words , @xmath105 is the number of reduced " words in @xmath57 of length @xmath213 which represent the unit element in @xmath30 . it is much faster to compute the @xmath105 s or @xmath106 s , than to compute the moments @xmath112 directly from ( [ e : mncomp ] ) . however , we found a different approach to compute the moments , which speeded up the computations much further : let @xmath214 and recall that @xmath215 is the 2-norm on @xmath48 associated with the trace @xmath11 . then @xmath216 and the reduced number @xmath105 can be computed from the square of the 2-norm of @xmath217 by the following two equations @xmath218 ( cf . section [ s : five ] ) , and hence the moment series @xmath219 can also be computed from the numbers @xmath220 . in practice we computed @xmath103 as follows . note first that @xmath221 where @xmath222 is the set of all distinct terms in the sum ( [ e:3.5 ] ) , and @xmath223 is the multiplicity of the occurrence of @xmath224 in the sum ( [ e:3.5 ] ) . note that @xmath225 , @xmath226 , @xmath227 , @xmath228 , etc . since @xmath229 we have @xmath230 the advantage of computing the squared 2-norms @xmath103 instead of the reduced numbers @xmath105 or the cyclic numbers @xmath106 is that we only have to consider @xmath231 words of length @xmath204 instead of @xmath232 words of length @xmath213 . this made it possible for us to almost double the number of moments we could compute in the two cases @xmath110 and @xmath233 for the thompson group @xmath0 . the only drawback was that we need first to store all the terms of the sum ( [ e:3.5 ] ) , and next to sort the list in order to compute the multiplicities @xmath234 , @xmath224 . we wrote two programs , both using parallel computing , to calculate the squared 2-norms @xmath103 , which can be downloaded at : + + https://github.com/shaagerup/thompsongroupf/ + https://github.com/mariars/thompsongroupf/ + http://www.math.ku.dk/~haagerup/thompsongroupf/ + http://www.math.ku.dk/~mrs/thompsongroupf/ + .the series of numbers for @xmath235 ( case 1).[t : case1seriesofnumbers ] [ cols="<,<,<,<,<",options="header " , ] .[f : iabgraphs ] ] [ f : abainvbinvgraphs ] ] recall that from proposition [ p:4.1 ] and proposition [ p:4.7 ] that @xmath236 and all three sequences on the left hand side converges monotonically to @xmath54 as @xmath237 . note that in both cases @xmath238 and @xmath239 are poor lower estimates ( see tables [ t : case1numbersforestimatingthenorm ] , [ t : case2numbersforestimatingthenorm ] and figs . [ f : iabgraphs ] , [ f : abainvbinvgraphs ] ) . for the listed range of integers @xmath204 , they both stay well below the known lower bound @xmath240 in case 1 , ( resp . @xmath241 in case 2 ) , while the lower estimates @xmath242 stay above this value for @xmath243 in case 1 ( resp . for @xmath244 in case 2 ) . the best exact lower bound for @xmath54 in case 1 ( @xmath245 ) we can obtain from our results is @xmath246 note however that by proposition [ p:4.4 ] , @xmath247 and since @xmath248 appear to be monotonically increasing for @xmath249 our computation results make it very likely that actually @xmath250 to get some prediction of the actual value of @xmath115 , we made a least squares fitting of the 26 numbers @xmath251 to a function of the following form @xmath252 and found that the optimal values of the parameters @xmath253 were @xmath254 in particular , this extrapolation argument predicts that @xmath255 however , we can in no way rule out that @xmath256 , i.e. that @xmath0 is amenable . in the same way , we get in case 2 , ( @xmath257 ) the precise lower bound @xmath258 and that most likely we have @xmath259 moreover , by making a least squares fitting of the @xmath260 numbers @xmath261 to a function of the form @xmath262 we found the values of @xmath253 to be @xmath263 in particular , this extrapolation method predicts that @xmath264 but again we can not rule out that @xmath0 is amenable . in @xcite , burillo , cleary and wiest used probabilistic methods to estimate the moments @xmath112 in case 2 ( @xmath265 ) for @xmath266 . in their notation , @xmath267 and @xmath268 . they found that ( see table 1 in @xcite ) @xmath269 and @xmath270 since @xmath271 is increasing slowly for @xmath272 we also have @xmath273 their estimates are based on random samples of words in the generators , and are therefore not precise lower bound for @xmath116 . in comparison , we found an exact lower bound @xmath274 of the norm based only on @xmath275 and a very likely lower bound @xmath276 based on the same list of moments . in @xcite , elder , rechnitzer and wong also worked on estimating the norm @xmath116 . they found the lower bound @xmath277 based on computing numerically the largest eigenvalue of the adjacency matrix for the cayley graph of @xmath0 restricted to balls in @xmath0 of size @xmath278 , which corresponds to consider elements of @xmath0 of distance up to @xmath279 from the identity element . moreover , they computed cohen s cogrowth coefficients @xmath280 for @xmath281 ( cf . table 3 in @xcite ) . note that @xmath280 is equal to our reduced " number @xmath105 ( cf . section [ s : three ] ) . in the notation of @xcite , @xmath282 , and @xmath210 , and they use a different method ( based on power series ) to pass from the @xmath283-series to the @xmath284-series .

we obtain precise lower bounds for the norms in and , as well as good estimates of the spectral distributions of and of with respect to the tracial state on the group von neumann algebra . our computational results suggest , that it is however hard to obtain precise upper bounds for the norms , and our methods can not be used to prove non - amenability of . supported by the erc advanced grant no .

let denote the thompson group with standard generators , . it is a long standing open problem whether is an amenable group . by a result of kesten from 1959 , amenability of is equivalent to and to where in both cases the norm of an element in the group ring is computed in via the regular representation of . by extensive numerical computations , we obtain precise lower bounds for the norms in and , as well as good estimates of the spectral distributions of and of with respect to the tracial state on the group von neumann algebra . our computational results suggest , that it is however hard to obtain precise upper bounds for the norms , and our methods can not be used to prove non - amenability of . supported by the erc advanced grant no . oafpg 247321 , and partially supported by the danish national research foundation ( dnrf ) through the centre for symmetry and deformation at the university of copenhagen , and the danish council for independent research , natural sciences . ] supported by the erc advanced grant no . oafpg 247321 , and by the center for experimental mathematics at the university of copenhagen . ]

1506.05129

c

ngc 1271 harbors a black hole with @xmath128 and has a stellar mass - to - light ratio of @xmath129 . we note that the final uncertainty on the black hole mass we use is comparable to the formal 3@xmath43 statistical uncertainty . some @xcite have suggested 3@xmath43 statistical errors should be used in place of 1@xmath43 errors as a conservative way in which to account for the effect of unknown systematics on @xmath7 . with a black hole mass of @xmath130 and adopting 276 km s@xmath0 for the bulge stellar velocity dispersion ( see section [ subsec : bhrels ] ) , @xmath131 044 . thus , the nifs observations have resolved the black hole sphere of influence . below we discuss the galaxy s orbital structure and place the galaxy on the @xmath7@xmath8host galaxy relations . in addition to determining the mass of the black hole in ngc 1271 , the schwarzschild models provide information about the galaxy s orbital structure . using our best - fit model in section [ sec : results ] , we show the ratio @xmath132 as a function of radius in figure [ fig : orbstructure ] . the tangential velocity dispersion is defined as @xmath133 , and @xmath134 are the usual spherical coordinates . we find that ngc 1271 is roughly isotropic at all radii covered by our kinematic measurements , deviating by at most 30% from @xmath135 , but we observe a trend in which @xmath132 declines at radii outside the black hole sphere of influence . as expected , short - axis tube orbits dominate in this oblate system , making up more than 85% of the orbits at all radii . long - axis tube orbits , which are important for triaxial and prolate systems , are negligible , while the fraction of box orbits increases at small radii but still make up only 15% of the orbits near the nucleus . furthermore , we use our best - fit stellar dynamical model to examine the mass distribution as a function of average radius , @xmath136 , and spin , @xmath137 , of the orbits , where @xmath138 . here , @xmath139 is the average angular momentum along the @xmath140-direction and @xmath141 is the average second moment of the orbit . ngc 1271 shows several dynamical components , as can be seen in figure [ fig : massdens ] , including a clear non - rotating bulge ( with @xmath142 ) , a highly co - rotating component ( with @xmath1430.5 ) , and a maximally co - rotating component ( with @xmath144 ) . the bulge component accounts for 12% of the mass , whereas the rotating components total 75% of the mass within the radial extent of the kinematic measurements . qualitatively these components agree with the classification of ngc 1271 as a fast - rotating s0 galaxy with a classical bulge . although the dynamical decomposition from the best - fit stellar dynamical model presented above can be used to place ngc 1271 on the @xmath7 bulge relationships , we follow the more common approach of carrying out a photometric decomposition to determine the galaxy s bulge luminosity and bulge effective radius . using galfit , we find a single srsic component fit is an insufficient description of the galaxy , with the percent difference between the model and data reaching as high as 60% . the fit is significantly improved with the addition of one or two other srsic components , and in the later case the percent difference between the model and data is under 15% . in table [ tab : galfitresults ] , we present the best - fit parameters of galfit models with one , two , and three srsic components , as well as the f160w luminosity for each component . the three - component model provides the best match to the _ hst _ image , but it is difficult to unambiguously identify a `` bulge '' component because the components all have rather low srsic indices . therefore , we conservatively assume that the innermost component of the three - component model provides a lower limit on the bulge luminosity and effective radius , while the innermost component of the two - component model gives an upper limit . this yields a @xmath1-band bulge luminosity of @xmath145 when correcting for galactic extinction using the @xcite wfc3 f160w value of @xmath146 , assuming an @xmath147 color of @xmath148 @xcite , and a @xmath1-band solar absolute magnitude of @xmath149 . alternatively , the bulge has a mass of @xmath150 when applying the best - fit mass - to - light ratio from our dynamical models to the luminosities in table [ tab : galfitresults ] . the corresponding bulge effective radius ranges between 06 and 52 ( or @xmath151 kpc ) . ccccccccccc 1 & & 10.72 & & 7.7@xmath152 & & 5.56 & & 4.78 & & 0.41 + + 1 & & 10.95 & & 6.2@xmath152 & & 5.23 & & 6.54 & & 0.54 + 2 & & 12.47 & & 1.5@xmath152 & & 6.63 & & 0.93 & & 0.20 + + 1 & & 12.39 & & 1.6@xmath152 & & 0.61 & & 2.12 & & 0.68 + 2 & & 11.80 & & 2.8@xmath152 & & 5.24 & & 1.17 & & 0.27 + 3 & & 11.90 & & 2.6@xmath152 & & 10.46 & & 1.30 & & 0.62 in order to determine the bulge stellar velocity dispersion for ngc 1271 , we use the best - fit stellar dynamical model from section [ sec : results ] and predict the luminosity - weighted second moment within a circular aperture whose radius equals the galaxy s bulge effective radius , following the approach used by @xcite . due to the uncertainty in the bulge effective radius for ngc 1271 , we measure the effective stellar velocity dispersion ( @xmath153 ) for three different bulge effective radii corresponding to the largest @xmath10 estimate from the galfit decomposition , the smallest estimate of @xmath10 , and the average of the two . additionally , some previous black hole studies have chosen to exclude data within @xmath89 when determining @xmath153 because the stellar kinematics are under the direct influence of the black hole in this region ( e.g. , @xcite ) . when excluding the region within @xmath89 , we find effective stellar velocity dispersions of @xmath154 km s@xmath0 , @xmath155 km s@xmath0 , and @xmath156 km s@xmath0 , whereas when the region within @xmath89 is included we measure @xmath157 km s@xmath0 , @xmath158 km s@xmath0 , and @xmath159 km s@xmath0 , for bulge effective radii of 52 , 29 , and 06 , respectively . as a comparison , the het massive galaxy survey reports a central velocity dispersion of 317 km s@xmath0 @xcite , which is the observed stellar velocity dispersion within a 35 aperture from the major axis long - slit data . figure [ fig : bhrels ] shows the location of ngc 1271 on the most recent versions of the @xmath160 and @xmath161 relations by @xcite . for the purposes of placing ngc 1271 on the @xmath7 @xmath15 correlation , we use @xmath162 km s@xmath0 with uncertainties that include the @xmath163 measurements made for bulge effective radii of 52 and 06 when excluding data within @xmath89 . when placing ngc 1271 on the @xmath7 @xmath16 relation , we set the faint end of the bulge luminosity error bar assuming the luminosity of the innermost component of the three - component srsic fit to the _ hst _ image and the high end of the error bar assuming the luminosity of the innermost component of the two - component srsic fit . we adopt a @xmath1-band bulge luminosity of @xmath164 , which is the midpoint of the range of possible bulge luminosities . we find that ngc 1271 consistent with the @xmath7 @xmath15 relation , but is an order of magnitude above the black hole mass prediction from the @xmath7 @xmath16 correlation . in order to demonstrate that the black hole in ngc 1271 must be larger than that expected from @xmath165 , in figure [ fig : comparemodels ] we present the nifs observations of the velocity dispersion and @xmath45 along with the predictions from the best - fitting model with a black hole mass of @xmath166 and a @xmath167 black hole . the @xmath167 black hole is expected from @xmath7 @xmath16 when conservatively using the galaxy s total @xmath1-band luminosity of @xmath168 , which is derived from the single srsic fit to the _ hst _ image , after correcting for galactic extinction and assuming a @xmath169 . clear differences between the kinematic predictions and the observations can be seen by eye . the best - fit model with @xmath170 is able to nicely reproduce the sharp rise in the velocity dispersion and the slight peak in @xmath45 at the nucleus , while the less massive black hole predicted from @xmath7 @xmath16 fails to do so . ngc 1271 has an apparent ellipticity of @xmath171 and a specific stellar angular momentum of @xmath172 within one effective radius based on the ppak data . here , @xmath173 , @xmath42 , and @xmath43 are the radius , velocity , and velocity dispersion and the brackets denote a luminosity weighted average @xcite . using the dividing line between slow and fast rotators from the atlas@xmath174 survey , such that fast rotators have @xmath175 @xcite , ngc 1271 falls well within in this fast rotator regime . ngc 1271 appears similar to the other compact galaxies ngc 1277 , ngc 1332 , ngc 4342 , ngc 4486b , and m60-ucd1 . all six of these early - type galaxies have small sizes , are rotating , show large stellar velocity dispersions for their luminosities , and have black holes that are too massive for their host galaxy s bulge luminosity . the black holes , however , are consistent with @xmath7 @xmath15 given the intrinsic scatter of the relation . in the case of m60-ucd1 , @xcite suggest that the ultracompact dwarf galaxy ( ucd ) was once the nucleus of a larger galaxy that has since been tidally stripped by the giant elliptical m60 , whose center lies at a projected distance of just 6.6 kpc away from the ucd . while tidal stripping is a natural explanation for the presence of an over - massive black hole , in the case of ngc 1271 , we do not see signs of active stripping in the _ hst _ image . the isophotes appear extremely regular , and no massive galaxies immediately neighbor ngc 1271 like in the case of m60-ucd1 . ngc 1271 is @xmath9270 kpc in projection from the bcg of perseus . further evidence could come from counting the number of globular clusters , as the galaxy would be stripped of its globular clusters first . while ngc 1271 appears not to have been stripped with our current data , we can not rule out an event in the distant past . interestingly , the behavior of the compact , high - dispersion galaxies being consistent with @xmath7 @xmath15 but being large positive outliers on @xmath7 @xmath16 could be in conflict with recent observations of bcgs , which instead may hint that black hole mass becomes independent of @xmath15 at high black hole mass while the @xmath7 @xmath16 correlation remains unchanged at large luminosities @xcite . clearly , more compact , high - dispersion galaxies and bcgs / giant ellipticals need to be examined . there could be systematic differences in the scaling relations between the two types of galaxies , thereby imply different mechanisms for black hole growth . since the compact , high - dispersion galaxies like ngc 1271 look similar to the quiescent @xmath19 red nuggets , they could be relics that somehow avoided the same fate that ultimately produced the giant ellipticals observed today . perhaps the compact , high - dispersion galaxies are left over from an era when the local black hole scaling relations did not apply and galaxies instead contained over - massive black holes .

we find that the galaxy is rapidly rotating and exhibits a sharp rise in the velocity dispersion . through the use of orbit - based stellar dynamical models , more compact , high - dispersion galaxies need to be studied using high spatial resolution observations to securely determine black hole masses , as there could be systematic differences in the black hole scaling relations between these types of galaxies and the bcgs / giant ellipticals , thereby implying different pathways for black hole and galaxy growth .

located in the perseus cluster , ngc 1271 is an early - type galaxy with a small effective radius of 2.2 kpc and a large bulge stellar velocity dispersion of 276 km s for its-band luminosity of . we present a mass measurement for the black hole in this compact , high - dispersion galaxy using observations from the integral field spectrograph nifs on the gemini north telescope assisted by laser guide star adaptive optics , large - scale integral field unit observations with ppak at the calar alto observatory , and _ hubble space telescope _ wfc3 imaging observations . we are able to map out the stellar kinematics both on small spatial scales , within the black hole sphere of influence , and on large scales that extend out to four times the galaxy s effective radius . we find that the galaxy is rapidly rotating and exhibits a sharp rise in the velocity dispersion . through the use of orbit - based stellar dynamical models , we determine that the black hole has a mass of and the-band stellar mass - to - light ratio is ( uncertainties ) . ngc 1271 occupies the sparsely - populated upper end of the black hole mass distribution , but is very different from the brightest cluster galaxies ( bcgs ) and giant elliptical galaxies that are expected to host the most massive black holes . interestingly , the black hole mass is an order of magnitude larger than expectations based on the galaxy s bulge luminosity , but is consistent with the mass predicted using the galaxy s bulge stellar velocity dispersion . more compact , high - dispersion galaxies need to be studied using high spatial resolution observations to securely determine black hole masses , as there could be systematic differences in the black hole scaling relations between these types of galaxies and the bcgs / giant ellipticals , thereby implying different pathways for black hole and galaxy growth .

1506.05129

c

to summarize , we obtained ao - assisted gemini nifs observations of ngc 1271 to map out the stellar kinematics on scales comparable to the black hole sphere of influence , and large - scale ifu data with ppak , which are useful for constraining the galaxy s stellar mass - to - light ratio and orbital distribution . using an _ hst _ wfc3 @xmath4-band image along with the spectral information , we constructed orbit - based stellar dynamical models . we measure @xmath176 and @xmath177 . the quoted errors combine the 1@xmath43 model fitting uncertainties with some common sources of systematic uncertainty that affect stellar dynamical models . the black hole in ngc 1271 is at the upper end of the black hole mass distribution ( @xmath178 ) . yet , this compact , rapidly rotating galaxy , with a high stellar velocity dispersion for its luminosity is very different from the giant elliptical galaxies and bcgs that are expected to harbor the most massive black holes in the universe . such host galaxy environments have yet to be widely explored on the @xmath7 host galaxy relations . with our mass measurement , we find that the black hole is too large for the galaxy s @xmath1-band bulge luminosity of @xmath179 , falling an order of magnitude above the expectation from the @xmath7 @xmath16 correlation , but the black hole mass is consistent with expectations from the @xmath7 @xmath15 relationship assuming @xmath180 km s@xmath0 . this behavior has also been observed in the few other compact galaxies that have dynamical black hole mass measurements to date . carrying out more black hole mass measurements in similar galaxies using high spatial resolution observations from _ hst _ and ao is necessary in order to determine if there are systematic differences in the black hole scaling relations between the large ellipticals / bcgs and these compact , high - dispersion galaxies . the compact , high - dispersion galaxies could be remnants of the @xmath19 red nugets that for some reason did not evolve into the largest ellipticals observed today , and instead reflect a time when black holes were too large for their bulges . more broadly , additional black hole mass measurements are needed in order to enlarge and better fill in undersampled regions of galaxy parameter space . targeting such a large and carefully selected sample with high spatial resolution facilities is a natural step toward gaining a more complete census of local black holes and a better understanding of the role that black holes play in galaxy evolution . j. l. w. has been supported by an nsf astronomy and astrophysics postdoctoral fellowship under award no . 1102845 . based on observations obtained at the gemini observatory , which is operated by the association of universities for research in astronomy , inc . , under a cooperative agreement with the nsf on behalf of the gemini partnership : the national science foundation ( united states ) , the national research council ( canada ) , conicyt ( chile ) , the australian research council ( australia ) , ministrio da cincia , tecnologia e inovao ( brazil ) and ministerio de ciencia , tecnologa e innovacin productiva ( argentina ) , under program gn-2012b - q-51 . also based on observations made with the nasa / esa hubble space telescope , obtained at the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nas 5 - 26555 . these observations are associated with program # 13050 . this work is further based on observations collected at the centro astronmico hispano alemn ( caha ) at calar alto , operated jointly by the max - planck institut fr astronomie and the instituto de astrofsica de andaluca ( csic ) . the authors acknowledge the texas advanced computing center ( tacc ; http://www.tacc.utexas.edu ) at the university of texas at austin for providing hpc resources that have contributed to the research results reported within this paper . the authors also made use of the grant - funded cyberinfrastructure at indiana university . this material is based upon work supported by the national science foundation under grant no . cns-0723054 , and in part by lilly endowment , inc . , through its support for the indiana university pervasive technology institute , and in part by the indiana metacyt initiative . the indiana metacyt initiative at indiana university is also supported in part by lilly endowment , inc . this research has made use of the nasa / ipac extragalactic database which is operated by the jet propulsion laboratory , california institute of technology , under contract with nasa .

located in the perseus cluster , ngc 1271 is an early - type galaxy with a small effective radius of 2.2 kpc and a large bulge stellar velocity dispersion of 276 km s for its-band luminosity of . we are able to map out the stellar kinematics both on small spatial scales , within the black hole sphere of influence , and on large scales that extend out to four times the galaxy s effective radius . ngc 1271 occupies the sparsely - populated upper end of the black hole mass distribution , but is very different from the brightest cluster galaxies ( bcgs ) and giant elliptical galaxies that are expected to host the most massive black holes . interestingly , the black hole mass is an order of magnitude larger than expectations based on the galaxy s bulge luminosity , but is consistent with the mass predicted using the galaxy s bulge stellar velocity dispersion .

located in the perseus cluster , ngc 1271 is an early - type galaxy with a small effective radius of 2.2 kpc and a large bulge stellar velocity dispersion of 276 km s for its-band luminosity of . we present a mass measurement for the black hole in this compact , high - dispersion galaxy using observations from the integral field spectrograph nifs on the gemini north telescope assisted by laser guide star adaptive optics , large - scale integral field unit observations with ppak at the calar alto observatory , and _ hubble space telescope _ wfc3 imaging observations . we are able to map out the stellar kinematics both on small spatial scales , within the black hole sphere of influence , and on large scales that extend out to four times the galaxy s effective radius . we find that the galaxy is rapidly rotating and exhibits a sharp rise in the velocity dispersion . through the use of orbit - based stellar dynamical models , we determine that the black hole has a mass of and the-band stellar mass - to - light ratio is ( uncertainties ) . ngc 1271 occupies the sparsely - populated upper end of the black hole mass distribution , but is very different from the brightest cluster galaxies ( bcgs ) and giant elliptical galaxies that are expected to host the most massive black holes . interestingly , the black hole mass is an order of magnitude larger than expectations based on the galaxy s bulge luminosity , but is consistent with the mass predicted using the galaxy s bulge stellar velocity dispersion . more compact , high - dispersion galaxies need to be studied using high spatial resolution observations to securely determine black hole masses , as there could be systematic differences in the black hole scaling relations between these types of galaxies and the bcgs / giant ellipticals , thereby implying different pathways for black hole and galaxy growth .

1312.5528

i

viruses are the most numerous organisms on earth . they play diverse roles in the biotic component of practically any ecosystem . especially remarkable is the case of marine ecosystems . marine viruses are important sources of mortality at every trophic level . potential hosts range from whales and commercial fish species to zooplankton , heterotrophic bacteria and microbial autotrophs @xcite . viruses are key components of the microbial loop and , therefore , the biogeochemical cycle of elements such as nitrogen or phosphorus @xcite . they are responsible for more than @xmath0 of marine bacterial mortality @xcite , contributing importantly to shaping the community @xcite . the relevance of _ virioplankton _ not only stems from the `` predatory '' pressure they exert , but also from the subsequent release of organic nutrients ( able to supply a considerable amount of the nutrient demand of , e.g. heterotrophic bacterioplankton @xcite ) ; or their contribution to microbial genetic diversity in the ocean through horizontal gene transfer @xcite . the vast majority of these roles are assumed by marine viruses that eventually kill the host cell @xcite . the standard _ lytic infection _ can be summarized in the following steps @xcite : _ i ) _ free viruses diffusing in the medium encounter and attach to cells at a certain _ adsorption rate _ ; _ ii ) _ after injecting its nucleic acid into the host cell , the virus takes control of the host synthesis machinery in order to replicate its genetic material ( dna or rna , depending on the type of virus @xcite ) and produce the proteins that will form the components of the viral offspring ( _ eclipse period _ ) ; _ iii ) _ during the _ maturation _ stage ( or _ rise period _ ) , the new _ virions _ are assembled ; _ iv ) _ finally , the virus synthesizes the _ holin _ protein , which perforates the plasma membrane allowing viral endolysins ( lysoenzymes ) to reach and lyse the cell wall , thereby releasing offspring and cellular organic compounds to the medium . the _ latent period _ ( steps _ ii_-_iv _ above ) , controlled by the so - called _ gene t _ ( or holin gene ) @xcite , is one of the most important viral life - history traits . so are the _ burst size _ ( offspring number , intimately related to the duration of the infection ) , and the adsorption rate . the latent period is studied intensively in the viral literature not only due to its ecological importance , but also owing to the small pleiotropic effect that its evolutionary change has on other phenotypic traits @xcite . on the other hand , the latent period links ecological and evolutionary change , as mutations in this trait influence the demography of the population and the environment influences which latent periods are favored by selection @xcite , closing in this way an eco - evolutionary feedback loop @xcite . furthermore , the short generation times and numerous offspring of viruses facilitate rapid evolution @xcite , and a possible overlap between ecological and evolutionary timescales . all these factors provide evidence for the importance of using a proper description of the ecological interactions between virus and host in order to make reliable evolutionary predictions . in the theoretical literature for marine viruses , mostly centered on viruses that infect bacteria ( _ bacteriophages _ ) , host - virus interactions are represented in two different ways . one approach explicitly considers the latent period imposing a fixed delay between the adsorption and the release of the offspring @xcite . in the other approach , new viruses are continuously released at a certain _ lytic rate _ , with cells that are simultaneously infected bursting at different post - infection times , exponentially distributed @xcite . thus , in the delay model the survival of each and every infected cell is ensured up to an infection age that equals the fixed latent period , whereas survival responds to a probabilistic rule in the rate model . the latter can actually be seen as a simplification of the former that facilitates mathematical and computational analysis of the interactions . indeed , the ecological outcome of the two approaches seems to be , a priori , qualitatively similar in spite of the obvious difference in the timing of the infection @xcite . while in the delay model progeny show periods of no release ( e.g. initial stages of viral culture experiments ) , in the rate model viral offspring are liberated at all times . however , little attention has been paid to quantifying thoroughly how these differences affect the long - term predictions by the two kinds of models . here , we aim to fill this gap . in this paper , we focus on the eco - evolutionary differences between the two approaches to the description of the lytic infection cycle . this comparison may prove very useful to assess the evolutionary consequences of the simplifying assumptions in these models , and therefore the long - term reliability of a whole group of different models for host - virus dynamics available in the literature . the rate - based approach is used to model not only diverse aspects of host - lytic virus interactions @xcite , but also other types of viral infection cycles such as lysogeny @xcite or shedding @xcite . in the latter , viruses continuously produce and release virions during the entire infection period . some examples include filamentous phages , and viruses of an enormous importance for humans such as ebola , sars , smallpox , varicella - zoster virus , and hiv @xcite . in some retroviruses such as hiv , both burst and continuous production modes have actually been suggested @xcite . thus , this question transcends purely technical matters such as model selection . indeed , this study can potentially serve to compare the evolutionary strategies of a wide selection of viruses with very different infection cycles . as a model case , we use bacteriophages , due to their importance for biogeochemical cycles ; it also allows us to resort to the extensive modeling bibliography available , in which the two approaches to the infection cycle are used . on the other hand , we consider mutations only in the holin gene , in order to isolate the effects of evolution on the key differentiating trait for the two strategies : the latent period ( or , equivalently , lysis rate ) . thus , we first present the two models for lytic infection . after briefly comparing them from an ecological perspective , we turn our attention to their evolutionary divergences . under this framework , we discuss the ecological and evolutionary contrast between the two forms for the life - history _ trade - off _ between latent period and burst size that have been proposed in the literature . finally , we comment on the implications of all the above for the descriptions of host - virus interactions in general , and marine bacteriophages in particular . this study will contribute to the reliability of long - term predictions regarding the interaction between a wide variety of viruses and their hosts .

they are , thus , a key determinant of the most important biogeochemical cycles in the planet . therefore , a correct description of the ecological and evolutionary behavior of these viruses is essential to make reliable predictions about their role in marine ecosystems . , the latter description is widely used as a simplification of the former . however , it is still unclear how the dichotomy `` delay versus rate description '' affects long - term predictions of host - virus interaction models . here , we study the ecological and evolutionary implications of using one or the other approaches , applied to marine microbes . to this end , we use mathematical and eco - evolutionary computational analysis . we show that the rate model exhibits improved competitive abilities from both ecological and evolutionary perspectives in steady environments . however , rate - based descriptions can fail to describe properly long - term microbe - virus interactions . moreover , additional information about trade - offs between life - history traits is needed in order to choose the most reliable representation for oceanic bacteriophage dynamics .

marine viruses shape the structure of the microbial community . they are , thus , a key determinant of the most important biogeochemical cycles in the planet . therefore , a correct description of the ecological and evolutionary behavior of these viruses is essential to make reliable predictions about their role in marine ecosystems . the infection cycle , for example , is indistinctly modeled in two very different ways . in one representation , the process is described including explicitly a fixed delay between infection and offspring release . in the other , the offspring are released at exponentially distributed times according to a fixed release rate . by considering obvious quantitative differences pointed out in the past , the latter description is widely used as a simplification of the former . however , it is still unclear how the dichotomy `` delay versus rate description '' affects long - term predictions of host - virus interaction models . here , we study the ecological and evolutionary implications of using one or the other approaches , applied to marine microbes . to this end , we use mathematical and eco - evolutionary computational analysis . we show that the rate model exhibits improved competitive abilities from both ecological and evolutionary perspectives in steady environments . however , rate - based descriptions can fail to describe properly long - term microbe - virus interactions . moreover , additional information about trade - offs between life - history traits is needed in order to choose the most reliable representation for oceanic bacteriophage dynamics . this result affects deeply most of the marine ecosystem models that include viruses , especially when used to answer evolutionary questions . = -1 bacteriophage ; phytoplankton ; latency period ; burst size ; evolutionarily stable strategy ; eco - evolutionary dynamics .

1409.2385

i

let @xmath13 and @xmath14 be symplectic manifolds . a _ symplectic embedding _ of @xmath13 into @xmath14 is a smooth embedding @xmath15 such that @xmath16 . it is interesting to ask when one symplectic manifold embeds into another . for example , define the ( open ) four - dimensional symplectic _ @xmath17 and define the ( open ) _ symplectic ball _ these inherit symplectic forms by restricting the standard form @xmath19 on @xmath20 in @xcite , mcduff and schlenk determined exactly when a four - dimensional symplectic ellipsoid @xmath0 embeds symplectically into a symplectic ball , and found that if @xmath21 is small , then the answer involves an infinite staircase " determined by the odd index fibonacci numbers , while if @xmath21 is large then all obstructions vanish except for the volume obstruction . to give another example , define the ( open ) four - dimensional _ polydisc _ @xmath22 where @xmath23 are real numbers and the symplectic form is again given by restricting the standard symplectic form on @xmath24 . frenkel and mller determined in @xcite exactly when a four - dimensional symplectic ellipsoid symplectically embeds into a _ cube _ @xmath25 and found that part of the expression involves the pell numbers . cristofaro - gardiner and kleinman @xcite studied embeddings of four - dimensional ellipsoids into scalings of @xmath26 and also found that part of the answer involves an infinite staircase determined by a recursive sequence . here we study symplectic embeddings of an open four - dimensional symplectic ellipsoid @xmath0 into an open four - dimensional symplectic polydisc @xmath1 . by scaling , we can encode this embedding question as the function @xmath27 where , @xmath28 and @xmath8 are real numbers that are both greater than or equal to @xmath29 . the function @xmath30 always has a lower bound , @xmath31 , the volume obstruction . our first theorem states that for fixed @xmath8 , if @xmath28 is sufficiently large then this lower bound is sharp , i.e. all embedding obstructions vanish aside from the volume obstruction : [ thm : rigidity ] if @xmath32 , then @xmath33 . this is an analogue of a result of buse - hind @xcite concerning symplectic embeddings of one symplectic ellipsoid into another . from the previously mentioned work of mcduff - schlenk , frenkel - mller , and cristofaro - gardiner - kleinman , one expects that if @xmath28 is small then the function @xmath30 should be more rich . our results suggest that this is indeed the case . for example , we completely determine the graph of @xmath34 ( see figure 1 ) : [ thm:13/2 ] for @xmath35 , @xmath36 and is equal to this lower bound for all @xmath28 except on the following intervals : \(i ) @xmath37 for all @xmath38 $ ] \(ii ) for @xmath39 , @xmath40 : @xmath41 , \\ \\ \dfrac{26 + 4k}{25 + 2k } & \quad a\in[13 + 2k,\beta_{k } ] , \end{array } \right.$ ] where @xmath42 , @xmath43 , @xmath44 , @xmath45 , @xmath46 , @xmath47 , @xmath48 , @xmath49 , @xmath50 , and @xmath51 . interestingly , the graph of @xmath52 has only finitely many nonsmooth points , in contrast to the infinite staircases in @xcite . this appears to be the case for many values of @xmath8 . for example , we conjecture what the function @xmath30 is for all @xmath53 see conjecture [ conj2 ] . our proofs rely on the following remarkable theorem of frenkel and mller @xcite . let @xmath54 be the sequence ( indexed starting at @xmath55 ) of all non - negative integer linear combinations of @xmath28 and @xmath8 , arranged with repetitions in non - decreasing order , and let @xmath56 be the sequence whose @xmath57 term is @xmath58 where @xmath59 . write @xmath60 if each term in the sequence @xmath54 is less than or equal to the corresponding term in @xmath61 . frenkel and mller show that embeddings of an ellipsoid into a polydisc are completely determined by the sequences @xmath62 and @xmath63 : ( frenkel - mller @xcite ) [ them:(frenkel - muller ) ] there is a symplectic embedding @xmath64 if and only if @xmath60 . to motivate the sequences @xmath62 and @xmath63 , note that @xmath63 is the sequence of _ ech capacities _ of the symplectic ellipsoid @xmath0 while @xmath62 is the sequence of ech capacities of the symplectic polydisc @xmath1 . the ech capacities are a sequence of nonnegative ( possibly infinite ) real numbers , defined for any symplectic four - manifold , that obstruct symplectic embeddings . we will not discuss ech capacities here ; see @xcite for a survey . theorem [ them:(frenkel - muller ) ] is equivalent to the statement that the ech capacities give sharp obstructions to embeddings of an ellipsoid into a polydisc . we wish to thank daniel cristofaro - gardiner for his helpful explanations , reference suggestions , encouragement and patience . we also thank the nsf , michael hutchings and uc berkeley for providing the opportunity to work on symplectic embedding problems this summer .

mcduff and schlenk have recently determined exactly when a four - dimensional symplectic ellipsoid symplectically embeds into a symplectic ball . similarly , frenkel and mller have recently determined exactly when a symplectic ellipsoid symplectically embeds into a symplectic cube . symplectic embeddings of more complicated structures , however , remain mostly unexplored . we study when a symplectic ellipsoid symplectically embeds into a polydisc . we prove that there exists a constant depending only on ( here , is assumed greater than ) such that if is greater than , then the only obstruction to symplectically embedding into is the volume obstruction . we also conjecture exactly when an ellipsoid embeds into a scaling of for greater than or equal to , and conjecture about the set of such that the only obstruction to embedding into a scaling of is the classical volume .

mcduff and schlenk have recently determined exactly when a four - dimensional symplectic ellipsoid symplectically embeds into a symplectic ball . similarly , frenkel and mller have recently determined exactly when a symplectic ellipsoid symplectically embeds into a symplectic cube . symplectic embeddings of more complicated structures , however , remain mostly unexplored . we study when a symplectic ellipsoid symplectically embeds into a polydisc . we prove that there exists a constant depending only on ( here , is assumed greater than ) such that if is greater than , then the only obstruction to symplectically embedding into is the volume obstruction . we also conjecture exactly when an ellipsoid embeds into a scaling of for greater than or equal to , and conjecture about the set of such that the only obstruction to embedding into a scaling of is the classical volume . finally , we verify our conjecture for .

1611.05224

c

in this paper , we have discussed the divergence based model adequacy tests and its link with some new divergence families . we have shown that the recent general family of the @xmath0-divergence can also be obtained from suitable model adequacy tests . we have also considered a more general model adequacy test based on the @xmath0-divergence measures which further generates a much larger superfamily of divergences that contains the @xmath0-divergence family and also the well - know generalized kullback - leibler divergence family as its special case , among others . we have also discussed several interesting properties of this new divergence family that we call the generalized @xmath0-divergence family ( gsd ) . we have indicated also the potential application of the gsd family in robust parametric inference ; derived the asymptotic properties of the minimum gsd estimators and illustrated their robustness through influence function analysis and suitable numerical illustrations . in this pursuit , we have observed and demonstrated the limitations of the first order influence function in assessing the robustness of these minimum divergence estimators . the research of this paper in fact opens up a lots of interesting questions for future researchers , both mathematicians and statisticians . the new generalized @xmath0-divergence family is seen to have several interesting properties with some identical members within this family . so , it would be an interesting future problem to investigate the topological properties of the gsd measures to characterize the distinct members of this divergence family . further , the application of the minimum gsd estimators in several statistical inference problems other than parametric estimation will also provide a great value addition to the literature of the robust inference . however , the most interesting future work in this case would be to generalize the connection between the model adequacy test and resulting divergence family . we have seen that starting from a model adequacy test based on one particular divergence one gets a one - parameter family of divergences ( pd family or the gkl family ) ; the model adequacy test based on a one parameter divergence family ( skl or sld ) generates a two - parameter divergence family ( @xmath0-divergence family ) and staring from the model adequacy test based on the two parameter @xmath0-divergence family we obtained a three - parameter divergence family . up to this point it seems meaningful since each time we generate a divergence which is better than the existing ones in terms of combining good efficiency and robustness properties . so , a natural question in this regard is how long we can extend this fact to generate even larger and larger superfamily of divergences . noting that all the members of the three parameter gsd family are not distinct , this process may eventually end after finite steps where we will get the largest such divergence family including all possible distinct divergences ; however this needs many more research to arrive at any such conclusions . we hope to pursue some of these extensions in our future endeavors .

we consider tubular model adequacy tests , and demonstrate that the new divergences that are generated in the process are very useful in robust statistical inference . in particular we show that family of-divergences can be alternatively developed using the tubular model adequacy tests ; a further application of the paradigm generates a larger superfamily of divergences .

minimum divergence methods are popular tools in a variety of statistical applications . we consider tubular model adequacy tests , and demonstrate that the new divergences that are generated in the process are very useful in robust statistical inference . in particular we show that family of-divergences can be alternatively developed using the tubular model adequacy tests ; a further application of the paradigm generates a larger superfamily of divergences . we describe the properties of this larger class and its potential applications in robust inference . along the way , the failure of the first order influence function analysis in capturing the robustness of these procedures is also established .

1401.8208

c

in the present work we have used a reconstruction scheme for new holographic dark energy model with energy density given by @xmath168 in the framework of brans - dicke cosmology taking the ansatz @xmath169 . outcomes of the study are : * considering @xmath170 in the first modified field equation of bd theory leads to a linear differential equation which could be solved analytically to have a solution for the reconstructed hubble parameter in terms of scale factor @xmath73 ; when plotted against redshift @xmath91 , it exhibited decaying pattern with the evolution of the universe ( i.e. , decreases in @xmath84 ) and this is consistent with the accelerated expansion of the universe . * the nhde energy density , as reconstructed through hubble parameter , when plotted against @xmath84 , is found to increase with evolution of the universe and it is consistent with the evolution of the universe from matter to dark energy domination . * violation of strong energy condition , as expected in the framework of einstein gravity , has also been found for the reconstructed nhde model in the framework of bd gravity . * the reconstructed equation of state ( eos ) parameter has been found to exhibit phantom "- like behavior , i.e. @xmath171 . * considering three different combinations of the parameters @xmath61 and @xmath62 , namely @xmath85 , @xmath86 and @xmath87 and setting the other parameters as @xmath88 and the bd parameter @xmath31 following @xcite , we have computed the reconstructed eos parameter for the reconstructed nhde . observational results coming from sneia data suggest a limit of the eos parameter as @xmath89 @xcite . using a set of variations in the values of @xmath61 and @xmath62 in eq . ( [ eos ] ) we found that the results are in good agreement with observations of @xcite ( see table i ) . in the following phase of the study , we considered the correspondence between the reconstructed new holographic dark energy in the framework of bd gravity and some scalar field dark energy models in a manner under which the two scenarios can be simultaneously valid . this type of approach is available in cosmological literature ( e.g. , @xcite ) . we have constructed the potentials and the scalar fields of these models . we observed that @xmath172 for all of the reconstructed scalar field models upt o @xmath165 and , at very late stage , ( i.e. , @xmath173 ) , we have @xmath174 . moreover , @xmath175 for all of the models . in summary , by generalizing the previous works @xcite to the nhde model with @xmath0 in the framework of chameleon brans - dicke cosmology , we have obtained the evolution of eos . following @xcite we have considered @xmath63 , @xmath27 and @xmath64 in power - law form and accordingly reconstructed hubble parameter . this approach differs from @xcite in the sense that instead of considering brans - dicke cosmology , we have considered chameleon brans - dicke with coupling function @xmath64 . we have tested sec and wec conditions and interpreted evolution of eos from them . with some choice of the model parameters we computed eos and found the the computed values of eos are consistent with the observational results coming from sneia data that suggest a limit of the eos parameter as @xmath89 @xcite . subsequently we examined the stability for the obtained solutions of the crossing of the phantom divide under a quantum correction of massless conformally - invariant fields and we have seen that quantum correction could be small when the phantom crossing occurs and the obtained solutions of the phantom crossing could be stable under the quantum correction . in the subsequent phase , we have established a correspondence between the nhde model and the quintessence , the dbi - essence and the tachyon scalar field models in the framework of chameleon brans - dicke cosmology . we reconstruct the potentials and the dynamics for these three scalar field models we have considered . the reconstructed potentials are found to increase with evolution of the universe and in a very late stage they are observed to decay . it is also observed through @xmath176 plot that the potential is increasing with @xmath64 , which indicates that the potential increases as the matter - chameleon coupling gets stronger with evolution of the universe .

a _ , * 26 * , 191 ( 2011 ) , we report a study on the new holographic dark energy ( nhde ) model with energy density given by in the framework of chameleon brans - dicke cosmology . we have studied a correspondence between the quintessence , the dbi - essence and the tachyon scalar field models with the nhde model in the framework of chameleon brans - dicke cosmology . furthermore , we have examined the stability for the obtained solutions of the crossing of the phantom divide under a quantum correction of massless conformally - invariant fields and we have seen that quantum correction could be small when the phantom crossing occurs and the obtained solutions of the phantom crossing could be stable under the quantum correction . it has also been noted that the potential increases as the matter - chameleon coupling gets stronger with the evolution of the universe .

motivated by the work of yang et al . , _ mod . phys . lett . a _ , * 26 * , 191 ( 2011 ) , we report a study on the new holographic dark energy ( nhde ) model with energy density given by in the framework of chameleon brans - dicke cosmology . we have studied a correspondence between the quintessence , the dbi - essence and the tachyon scalar field models with the nhde model in the framework of chameleon brans - dicke cosmology . deriving an expression of the hubble parameter and , accordingly , in the context of chameleon brans - dicke chameleon cosmology , we have reconstructed the potentials and dynamics for these scalar field models . furthermore , we have examined the stability for the obtained solutions of the crossing of the phantom divide under a quantum correction of massless conformally - invariant fields and we have seen that quantum correction could be small when the phantom crossing occurs and the obtained solutions of the phantom crossing could be stable under the quantum correction . it has also been noted that the potential increases as the matter - chameleon coupling gets stronger with the evolution of the universe .

astro-ph0212354

i

the giant region n66 is the largest , brightest star forming region in the small magellanic cloud ( smc ) . the populous star cluster ngc346 embedded in the nebula is home to several dozen early type stars including a dozen of spectral types o7 and earlier . two arcminutes to the east lies the massive , luminous wn+ob system hd5980 which underwent a luminous blue variable ( lbv ) outburst in 1994 @xcite . these stars are the main source of ionization in the nebula . n66 also contains at least one known supernova remnant ( snr ) , snr0057@xmath07226 . _ einstein _ x - ray observations showed a bright source in n66 tentatively identified as a snr @xcite . radio observations by @xcite showed bright , extended , thermal emission at 408 , 843 and 5000 mhz corresponding to the region , but no clear sign of the snr . optical observations also showed only the extremely bright nebular emission but no filamentary structure associated with the snr . however , @xcite discovered faint , high - velocity h@xmath1 emission in a long - slit spectrum across n66 and suggested the existence of a snr . subsequently , @xcite subtracted smoothed h@xmath1 data from 843 mhz radio continuum observations and revealed a remnant @xmath23.2 ( @xmath255 pc at an smc distance of 59 kpc ) in diameter and confirmed the remnant snr0057@xmath07226 . x - ray spectroscopy of snr0057@xmath07226 with asca @xcite showed that the spectrum can be modeled as a hot thermal plasma . high - resolution x - ray observations of n66 with the _ chandra x - ray observatory _ @xcite show a 130@xmath3100 region of extended , center - bright , thermal emission corresponding to the snr . these high - resolution data show snr0057@xmath07226 to have relatively uniform surface brightness and no clear temperature gradient from center to rim . difference imaging techniques applied to recent radio observations @xcite at 1.42 , 2.37 , and 4.80 ghz ( 20 , 13 and 6 cm ) show snr0057@xmath07226 to be a non - thermal , limb - brightened shell with a spectral index of approximately @xmath1=@xmath00.17 ( s@xmath4 ) . the x - ray and radio emitting regions are similar in extent at a resolution of @xmath220 . hence , the @xcite estimate of angular size is probably too large , and the x - ray / radio snr is roughly 36 @xmath3 28 pc in extent . thus , snr0057@xmath07226 may be a member of the `` mixed morphology '' class of snrs @xcite , with a radio shell and filled - center x - ray emission , although the presence of hd 5980 along the sight line confuses the situation . @xcite resolve x - ray emission from hd 5980 itself for the first time , and note similarities with the galactic object @xmath5 carinae , which has diffuse surrounding x - ray emission @xcite . @xcite mention a possible association of hd 5980 and snr0057@xmath07226 , but fuv absorption studies have clearly determined that hd 5980 is behind the snr . fuv observations toward hd5980 show the expected galactic and smc absorption at @xmath60 km s@xmath7 and @xmath6@xmath8150 km s@xmath7 , respectively , as well as high - velocity absorption indicating the receding shell of an intervening snr . absorption at @xmath8300 km s@xmath7 was found in iue spectra by @xcite ; this was later confirmed by @xcite who suggested an intervening snr . @xcite detected absorption systems at @xmath8300 and @xmath8330 km s@xmath7 in , and several other ions in high - resolution _ hst _ stis spectra . they also see very weak components at @xmath820 and @xmath850 km s@xmath7 , possibly consistent with the approaching side of the remnant if indeed these features are real . @xcite also see absorption at @xmath2@xmath8300 km s@xmath7 in and in _ fuse _ observations of hd5980 and conclude that the star must lie behind the receding shell of snr0057@xmath07226 . @xcite also find that a _ fuse _ spectrum of sk80 ( av232 ) , an o7ia star @xmath21 southeast of hd5980 but also seen in projection within the x - ray emission , shows none of the high - velocity absorption seen toward hd5980 . since sk80 lies closer to the x - ray edge of the remnant , we might expect a lower line - of - sight velocity for snr gas in this sight line . however , the absorption profile near the smc systemic velocity ( @xmath2150 km s@xmath7 ) is indistinguishable from that of hd5980 . thus , sk80 must either lie within or in front of the remnant . far - ultraviolet ( fuv ) observations are useful in the study of snrs . several strong emission lines including @xmath91548,1550 , @xmath91238,1242 , and especially @xmath91032,1038 are good shock diagnostics and are produced in regions where the temperature is lower than typical x - ray producing regions and higher than regions of bright optical emission @xcite . emission , in particular , arises in gas at temperatures near @xmath10 k a condition almost never reached by photoionization and is thus a sensitive tracer of shock - heated material . in this paper we present a _ fuse _ observation of emission at the x - ray edge of snr0057@xmath07226 that shows strong emission in @xmath91032,1038 and @xmath11977 . we also present new longslit echelle observations showing high- and low - velocity material in h@xmath1 across the face of snr0057@xmath07226 . the observations are described in 2 . in 3 , we discuss the snr kinematics as revealed by the optical and fuv data . in 4 , we compare the , , and h@xmath1 measurements with the predictions of shock models to derive shock velocity , preshock density and ram pressure at one location in the snr . using the same models with the fuv absorption data of @xcite and @xcite , we derive similar values for material on the sight line toward hd5980 . we propose a physical picture for snr0057@xmath07226 in relation to n66 . finally we discuss the implications these observations have for the detection of snrs in bright nebulae and ob associations . a summary is presented in 5 .

n66/ngc346 is the largest and brightest region in the small magellanic cloud and contains at least one known supernova remnant snr0057 . we also present high - resolution , long - slit h spectra across n66 showing high- and low - velocity emission corresponding closely to the x - ray boundaries of the supernova remnant . we use these fuv and optical data to determine the physical parameters of the shock and interaction geometry with n66 .

n66/ngc346 is the largest and brightest region in the small magellanic cloud and contains at least one known supernova remnant snr0057 . optical emission from the remnant is overwhelmed by the bright photoionized emission from the nebula , but the remnant has been detected by way of far ultraviolet absorption lines . here we present data from the far ultraviolet spectroscopic explorer ( _ fuse _ ) satellite showing strong and emission from a position at the edge of snr0057 . we also present high - resolution , long - slit h spectra across n66 showing high- and low - velocity emission corresponding closely to the x - ray boundaries of the supernova remnant . we use these fuv and optical data to determine the physical parameters of the shock and interaction geometry with n66 . we find that ionizing photons from the many massive cluster stars nearby likely affect the ionization balance in the post - shock gas , hindering the production of lower - ionization and neutral species . we discuss the importance and inherent difficulty of searching for supernova remnants in or near bright regions and suggest that the far ultraviolet provides a viable means to discover and study such remnants .

astro-ph0212354

c

the detection of emission as well as the kinematics present in the h@xmath1 echelle data imply the presence of a strong shock in n66 associated with snr0057@xmath07226 . the snr shock model was also favored by @xcite for the high velocity absorption towards hd5980 . detection of the front side of snr0057@xmath07226 has not been clearly established because the low velocity components cited by @xcite were detected at such a marginal level . in any event , the near side of the snr is considerably more difficult to detect both in emission and absorption than the back side . optical emission from the region complicates the situation and masks the morphology of the snr . in the following discussion we adopt a working model of the physical association of various components in the n66 region . a roughly spherical snr is located on the near side of n66 . the rear side of the snr is propagating into relatively denser nebula while the near side is propagating through the more rarefied smc ism . hd5980 lies behind the remnant , embedded within n66 . the ngc346 cluster stars lie outside the snr , also embedded within n66 . we determine the shock velocity , preshock hydrogen density and ram pressure of the shock wave using the emission and absorption sight lines toward snr0057@xmath07226 . by examining the surface brightness ratio between and h@xmath1 , we measure the `` completeness '' of the shock . then we discuss the relationship between the snr and its surroundings and the implications of this analysis for observing snrs in other regions . in the n66 reference frame ( v@xmath26=@xmath8158 km s@xmath7 ) , the material at position 1 has a radial velocity of @xmath870 km s@xmath7 while toward hd5980 , @xmath45 km s@xmath7 . from x - ray and radio images , we choose the center of the remnant to be ( j2000 ) @xmath1=00:59:27 , @xmath46=@xmath072:10:15 , about 20 south of hd5980 . this position is also consistent with the location of the highest - velocity h@xmath1 emission ( figure 3 ) . using the projected distances from this center and the two radial velocity measurements , we derive a radius of curvature for the shock front of 80@xmath47 and an expansion velocity for the gas of v@xmath48 km s@xmath7 . this places the observed x - ray edge on the eastern side of the shock front inclined @xmath260 to our line of sight . the expansion velocity of 147 km s@xmath7 is not the shock speed , but rather the bulk velocity of the postshock material which should be between 0.75 and 1.0 times the shock speed . first we caculate shock models for comparison against the observations . the models were calculated using an updated version of the code described by @xcite . the main input parameters are the shock velocity , the preshock density and the elemental abundances . we ran models for shock velocities between 140 and 200 km s@xmath7 spaced by 10 km s@xmath7 . a preshock hydrogen number density of 1 @xmath49 , and smc elemental abundances @xcite were used in all the models . the calculation is followed until the the recombination zone is complete and the gas temperature has reached about 1000 k. we present the intensities of selected lines from the shock models in table 3 . the intensities are relative to h@xmath1=100 and the flux from nearby multiplet lines of an ion have been summed . the line flux produced by a shock increases sharply as a function of shock velocity in the range 150 200 km s@xmath7 . shocks below @xmath2160 km s@xmath7 do not produce much and thus this represents a lower limit to the actual shock velocity in the snr . over this same range of shock velocities , the flux remains nearly constant . the changing ratio of i()/i ( ) is due to the increasing ionization of oxygen at higher velocities . as discussed in 3.1 , the is strongly affected by absorption and scattering , and so it is not possible for us to derive an accurate assessment of the intrinsic ratio of i()/i ( ) in the spectrum of position 1 . however , we note that using the total ( corrected ) flux with the observed flux places an upper limit of f()/f()@xmath503 . ignoring the effect of differential reddening for the moment , this clearly points us toward the lower end of the velocity range where is produced . based on this ratio , the observed expansion velocity and the shock velocity requirements for production , we adopt 160 km s@xmath7 as a representative shock velocity at position 1 and use details from the model at this velocity below . we now compare the observed and calculated surface brightnesses to estimate the preshock density required to produce the observed flux . the model predicts an surface brightness ( in both lines of the doublet ) of i@xmath51 erg s@xmath7 @xmath13 into 2@xmath52 steradians ( for v@xmath53=160 km s@xmath7 , @xmath54=1 @xmath49 , he / h=0.08 ) or i@xmath55 erg s@xmath7 @xmath13 arcsec@xmath43 . in the optically thin limit , intensity will scale with density so we can write @xmath56 where @xmath57 is the reddening correction factor at 1035 , @xmath58 is the surface area of shock ( in arcseconds@xmath59 ) within the aperture and @xmath60 is the preshock density in units of @xmath49 . i@xmath61 is the total flux in both lines which we estimate by multiplying the corrected @xmath111032 flux by 1.5 , thus i@xmath62 erg s@xmath7 @xmath13 . from figure 1 , we estimate that @xmath2@xmath63 of the lwrs aperture is filled with x - ray emission . if the emission follows the same pattern and the shock front is tilted 60 from our line of sight , then the aperture sampled emission from 600 arcseconds@xmath59 of shock front . reddening is a potential source of uncertainty . @xcite found the mean e(b@xmath0v)=0.14 for the ngc346 stellar population . however , since the snr lies in front of the bulk of the cluster , this may overestimate the extinction to the snr . on the other hand , using the spectral type and observed colors of sk80 , one can derive e(b@xmath0v)=0.11 . we adopt this value and assume r@xmath64=3.1 ( typical for the diffuse ism ) and the extinction curve of @xcite ( e(1035@xmath0v)/e(b@xmath0v)=18 ) . this yields a reddening correction c@xmath65=4.5 . solving the above equation , we get n@xmath66 @xmath49 at position 1 , similar to an azimuthally - averaged electron density of 7 @xmath49 at the radius of position 1 derived by @xcite . the dynamical pressure is then @xmath67 dyne @xmath13 . if more reddening is assumed and e(b@xmath0v ) is raised to 0.14 ( c@xmath65=6.8 ) , the changes are minor : n@xmath68 @xmath49 and @xmath69 dyne @xmath13 . less reddening ( e(b@xmath0v)=0.08 , c@xmath65=3.0 ) would yield n@xmath70 @xmath49 , @xmath71 dyne @xmath13 . this pressure is higher than those seen in regions of the vela snr . @xcite derive n@xmath72 @xmath49 and p=3.7@xmath73 dyne @xmath13 for a x - ray bright , nearly face - on shock . @xcite find p=1.6@xmath74 dyne @xmath13 for an edge - on shock . @xcite find p=2 - 4@xmath73 dyne @xmath13 for another locations in vela while @xcite find p@xmath21@xmath73 dyne @xmath13 for a region of diffuse x - ray emission . this variation in pressures within the same remnant suggests local density and pressure enhancements caused by reverse shocks from blastwave - cloud interactions . we have only two widely - separated measurements for snr0057@xmath07226 and can say nothing so specific but the high pressure and density at position 1 as well as the x - ray emission morphology suggest similar shock - cloud interactions . the shock models discussed above predict the total column depths of ions produced in the post - shock flow . @xcite measured the column depths of several highly ionized species in the high - velocity component toward hd5980 ( their table 1 ) and conclude that a snr shock is the most likely production mechanism for these ions in the observed quantities . @xcite presented data on other ions not available to _ fuse_. in figure 5 , we present the observed column depths of these fuv ions and the values predicted by the models with v@xmath75=160 , 180 and 200 km s@xmath7 . the ions are ordered according to the ionization potential needed to produce them . the relative column depths of all the ions down to are well matched by the 160 km s@xmath7 model . the higher velocity models predict too much relative to the other high ionization ions . the column depths scale linearly with preshock density ( all the models were run with n@xmath76 = 1 @xmath49 ) . the offset between the 160 km s@xmath7 model and the observations is @xmath77 dex , so a preshock density of @xmath78 can reproduce the observed column depths for the high ionization lines . the shock velocity and preshock density toward hd5980 are thus in good agreement with our measurements for position 1 . the behavior of the low ionization lines is drastically different . for and , all the models predict column densities that are an order of magnitude higher than the observations ( see figure 5 ) . this dearth of low - ionization material can also be seen by comparing the observed and calculated ratio of and h@xmath1 . the shock models ( which have been calculated to the point of complete recombination ) predict i()/i(h@xmath1)=3.3 for @xmath79=160 km s@xmath7 and smc abundances . the observed ratio at position 1 is @xmath80 where @xmath81 indicates the surface brightness and @xmath82 the aperture filling factor of the relevant emission . we assume the reddening correction @xmath57=4.5 as discussed above ; reddening at h@xmath1 is moderate and we adopt @xmath83=1.24 . the filling factor @xmath82 for each aperture is more uncertain . we assume @xmath84 as discussed above . it is difficult to say where emission does and does not appear at a fine scale in the low s / n echelle data . the h@xmath1 aperture was chosen carefully to encompass only the faint emission in figure 3 , but we estimate that @xmath85 is still @xmath2@xmath86 . these values give i()/i(h@xmath1)@xmath3718 . uncertainties in the filling factors , reddening , and surface brightnesses probably make this ratio uncertain by a factor of 2 , but the ratio is still significantly higher than the predicted ratio of 3.3 . the weakness of h@xmath1 emission compared with at position 1 suggests the presence of an incomplete shock . there are many cases where incomplete shocks are observed in individual filaments or small portions of snrs @xcite ; however , these regions are all at sub - parsec scales . the lwrs aperture at position 1 is sampling a region of snr0057@xmath07226 roughly 8 pc across . furthermore , the observed h@xmath1 surface brightness does not vary strongly between different portions of the snr implying that the conditions at position 1 are typical of the remnant as a whole . in figure 3 , we see weak snr h@xmath1 emission or none at all . this is a large object with moderate shock velocities implying that it is a middle - aged remnant like the cygnus loop or the vela snr ; most of the optical emission from these remnants comes from complete , radiative shocks and these remnants are bright in h@xmath1 . if some portions of snr0057@xmath07226 were recombinationally complete , we would expect to see h@xmath1 emission @xmath210 times brighter than is observed . thus , it appears that there is a global effect preventing the cooler parts of the recombination flow from forming . we argue that the gas at the back end of the post - shock flow is being prevented from recombining by the ionizing flux from the bright stars in n66 . there are eleven stars of spectral type o6.5 or earlier located 2 ( 35 pc , in projection ) to the west of snr0057@xmath07226 . the combined ionizing flux from ngc346 is 4.0@xmath310@xmath87 erg s@xmath7 @xcite or @xmath21.5@xmath310@xmath88 ionizing photons s@xmath7 . hd5980 itself contributes @xmath89 ionizing photons s@xmath7 . using basic ionization / recombination equations from @xcite we find that this photon flux in a medium with density @xmath25 @xmath49 will yield an ionized sphere over 100 pc in radius . indeed , @xcite find that n66 is density bounded and that 45% of the ionizing photons from cluster stars escape to ionize the general smc ism . this zone of ionization could encompass snr0057@xmath07226 and affect the ionization balance in the recombining post - shock gas . the dynamical time scale of the shock is of order a few hundred years . the photoionization time scales are much shorter ( @xmath2100 days ) , while the recombination times are longer ( of order 10,000 yr ) . thus the ionizing flux will suppress h@xmath1 emission . the strength and spectral energy distribution of the local ionizing flux will affect the column densities of the low and moderately ionized species . in theory , much of the discrepancy between the modeled and observed and columns towards hd5980 ( figure 5 ) could be due to iron and silicon being ionized to higher ionization stages . if the best fit model is scaled up to n@xmath90 @xmath49 , the column is underpredicted by about 0.3 dex . this is clearly not enough to explain the 1.9 dex discrepancy in the column , but the stellar spectrum extends out to @xmath250 ev @xcite and the local flux could be producing . however , no such discrepancies are seen in the and columns . a more likely scenario is that the sight line to hd5980 is passing through a small region where the swept up column is lower than average for snr0057@xmath07226 . while the zone is complete , the zone would be incomplete regardless of ionizing radiation . a self - consistent shock model calculation that includes a photoionizing field is necessary to predict the column densities and the h@xmath1 flux accurately . while such modeling is beyond the scope of this paper , we conclude that the local ionizing field must have a significant effect on the observed characteristics of snr0057@xmath07226 as a whole . the emission and absorption data discussed here lead to a schematic structure for the n66snr region shown in figure 6 . snr0057@xmath07226 lies on the near side of n66 and is encountering the denser nebular material on its back side . position 1 is located at the edge of the x - ray emission ( figure 1 ) . the observed radial velocity of and h@xmath1 emission at position 1 is @xmath2225 km s@xmath7 . this is lower than the observed velocity of absorption ( @xmath8300 km s@xmath7 ) toward hd5980 which lies projected closer to the center of the remnant . also it is @xmath275 km s@xmath7 higher than the systemic velocity of n66 ( @xmath8158 km s@xmath7 ) , which we would expect for material viewed tangentially at the edge of the expanding remnant . either the systemic velocity of the snr and n66 differ by @xmath270 km s@xmath7 , or the observed x - ray edge ( a portion of which is position 1 ) does not represent the actual limb of the snr shock . the latter is assumed in figure 6 . we propose that the x - ray emission arises over a spherical cap where the shock has encountered and heated denser material . the remnant is not yet even half - way submerged in the n66 material , and thus the observed radius of x - ray emission is smaller than the actual blast wave radius . the observed x - ray edge at position 1 is inclined to our line of sight by @xmath260 . hd5980 and the other uv - bright stars are located within n66 and have ionized a region of surrounding material . the combined stellar winds and thermal pressure have formed a slowly expanding envelope around the cluster core . since high - velocity absorption is not seen in the spectrum of sk80 @xcite , it must lie within or in front of the snr . hd5980 lies behind the remnant and affects the ionization balance in the swept - up gas , preventing the formation of , , , and other low - excitation species . the bright nebular emission seen surrounding the uv bright stars of n66 arises in dense material behind an ionized layer . the approaching snr material is apparent in h@xmath1 in figure 3 , but has not been conclusively identified in fuv spectra . if the far side of the remnant is seen near @xmath2300 km s@xmath7 and if the snr is centered at the smc systemic velocity of @xmath2155 km s@xmath7 , we expect the nearside absorption to be seen near v=10 km s@xmath7 . this region is essentially masked by galactic absorption making it difficult to detect the snr . @xcite compared the spectra of sk80 and hd5980 near zero velocity and found no difference . however , both of these sight lines are toward the remnant and may contain nearly identical foreground columns . the four _ fuse _ targets in ngc346 lie less than 2 from hd5980 and are outside the snr sight line . a comparison of the averaged , normalized profiles from these four targets and the two sight lines projected within the snr is shown in figure 7 . we find a small but systematic excess in absorption near v=0 km s@xmath7 in the two remnant profiles . the difference represents an extra column density of about @xmath91 @xmath13 or about @xmath92 that of the backside value reported by @xcite . we also find that the velocity centroid of the hd5980/sk80 zero velocity absorption is shifted by about @xmath810 km s@xmath7 with respect to the ngc346 galactic absorption . this is not too different from the velocity found by @xcite for and absorption features that they attribute to front - side snr material . recent work by @xcite on galactic halo absorption has shown significant variations in column over as little as 3 . the variation in n ( ) between the four ngc346 targets ( mean separation 19 ) is 9% ( the maximum variation between two measurements is 12% ) while the variation between the two snr sight lines ( separation @xmath931 ) is only 8% , comparable to the uncertainties due to continuum placement , noise , and limits of integration . however , the cluster and snr stars show a relative difference of 53% in the zero - velocity column over @xmath22 . because of the potential galactic halo variation on small scales , the matter of frontside absorption remains inconclusive . however , it is plausible we are seeing front side absorption near v=@xmath810 km s@xmath7 in the hd5980/sk80 data . if true , then sk80 would be inside snr0057@xmath07226 , as shown in figure 6 . even if it is not , we can place an upper limit of n()@xmath94 @xmath13 for the frontside column density , much less than is observed from the back side of snr0057@xmath07226 . in a recent paper , @xcite model the collision of a snr shock with a wind - blown bubble around an evolved star and suggest that the far side of snr0057@xmath07226 is interacting with the stellar wind of hd5980 . the x - ray image of the system @xcite does , in fact , show some resemblance to the models and there is reasonable agreement between predicted and observed x - ray fluxes . our observations allow us to further test this wind - snr model . the velzquez et al . wind - blown bubble has a radius of @xmath210 pc while our position 1 ( at the rim of the snr ) is at least twice that distance ( in projection ) from hd5980 ; thus , position 1 is sampling the ism , not stellar wind . in 4.1 we derived a preshock density of @xmath26 @xmath49 for the material at both position 1 and in the shock toward hd5980 , at least two orders of magnitude higher than the interior of the modeled wind bubbles ( see figures 1 and 2 of * ? ? ? * ) . furthermore , the @xmath8300 km s@xmath7 component exhibits an ionization structure expected for a single snr shock @xcite . if this component arose in a turbulent region between snr and stellar wind shock fronts , as suggested by @xcite , we might not expect to see the kinematics structure observed by @xcite . clearly , higher resolution spectral observations and detailed shock models are required . core - collapse supernovae arise from massive stars often formed in clusters and associations the same massive stars which photoionize their surrounding gas and create bright regions . massive sn progenitors can not migrate far from their birth places in their short lifetimes and thus snrs associated with h ii regions should occur frequently . to various degrees , this is not seen in optical snr surveys of nearby galaxies . the primary optical method for detecting snrs , especially in galaxies beyond the magellanic clouds , is to compare h@xmath1 to [ ] emission , and pick out objects with [ ] /h@xmath1@xmath95 0.4 ( cf . * ? ? ? * ; * ? ? ? * and references therein ) . in recent years , as the sensitivity and resolution of radio and x - ray observations has become competitive with optical ground - based observations , independent searches at these wavelengths have been undertaken and compared against the optical snr lists @xcite . these multiwavelength surveys and comparisons provide a more complete survey method , but in general do not find many of the same snrs . discussions of selection effects usually point toward `` confusion '' as being responsible for incompleteness of optical snr surveys in crowded and complex regions of emission . clearly this is plausible at some level , but the denser conditions in regions might also be expected to cause brighter optical ( radiative ) snrs since the shock emissivity increases as the density squared . scanning through the optical snr catalogs of nearby galaxies ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * to name a few ) , one can find a number of stunning counter examples to the `` confusion '' hypothesis . there are often bright optical snrs found in confused regions and adjacent to bright region emission . the mechanism we propose in 4.2 seems to be a more plausible explanation for why the optical snr searches miss some snrs and not others in confused regions . if a supernova occurs close enough to ionizing stars , the potential bright optical snr emission in h@xmath1 and is prevented from forming and no optical snr can be detected , especially against bright nebular emission . our investigation of snr0057@xmath07226 , however , demonstrates that bright fuv emission lines are still present in such a situation and may provide an alternate way of not only detecting but studying such snrs in detail . detecting snrs with higher ions circumvents the problems of truncated recombination and bright background emission . stellar photoionization will not prevent the production of high ions nor will they be contaminated significantly by surrounding nebular emission . our observations have shown that in a bright region , the detection of localized emission from high - ionization species such as can provide a clear signature of snr emission . position 1 lies on the edge of the snr and shows strong emission in and . position 2 lies outside the remnant but still within bright optical emission ; yet no line emission is present . in conjunction with radio and x - ray data , such a detection is conclusive . we note however that the use of the fuv is restricted to lines of sight where extinction is low . nearby extragalactic targets such as the magellanic clouds and local group galaxies will be the easiest to investigate with this technique .

we find that ionizing photons from the many massive cluster stars nearby likely affect the ionization balance in the post - shock gas , hindering the production of lower - ionization and neutral species . we discuss the importance and inherent difficulty of searching for supernova remnants in or near bright regions and suggest that the far ultraviolet provides a viable means to discover and study such remnants .

n66/ngc346 is the largest and brightest region in the small magellanic cloud and contains at least one known supernova remnant snr0057 . optical emission from the remnant is overwhelmed by the bright photoionized emission from the nebula , but the remnant has been detected by way of far ultraviolet absorption lines . here we present data from the far ultraviolet spectroscopic explorer ( _ fuse _ ) satellite showing strong and emission from a position at the edge of snr0057 . we also present high - resolution , long - slit h spectra across n66 showing high- and low - velocity emission corresponding closely to the x - ray boundaries of the supernova remnant . we use these fuv and optical data to determine the physical parameters of the shock and interaction geometry with n66 . we find that ionizing photons from the many massive cluster stars nearby likely affect the ionization balance in the post - shock gas , hindering the production of lower - ionization and neutral species . we discuss the importance and inherent difficulty of searching for supernova remnants in or near bright regions and suggest that the far ultraviolet provides a viable means to discover and study such remnants .

astro-ph0212354

i

we see strong emission in and at a position on the eastern x - ray edge of snr0057@xmath07226 . absorption in these same ions is seen at @xmath2300 km s@xmath7 toward the bright lbv system hd5980 which lies behind the remnant . another position away from the remnant but within the bright nebular extent of n66 shows no fuv line emission . the remnant lies on the near side of n66 and the is formed in shocks as the blast wave encounters the denser material of the nebula . seven longslit echelle spectra in h@xmath1 and [ ] show that n66 has turbulence similar to other magellanic regions . two slowly expanding features are seen : the compact region n66c and a bright shell around the core of ngc346 . three of the echelle spectra show faint patches of h@xmath1 emission at high and low velocities which appear as a rough expansion feature corresponding spatially and kinematically to snr0057@xmath07226 . observed and flux compared with shock models allows us to estimate the shock velocity and determine the ambient density and ram pressure at position 1 . we use observed column depths from @xcite and @xcite to derive the shock velocity and density of the snr shock toward hd5980 . these values are in good agreement with each other and with other values in the literature . weak h@xmath1 emission as well as low column densities of low - ionization species such as show that the ionization balance in the post - shock gas is affected by ionizing stellar photons . the ionizing flux from the many hot stars in ngc346 is sufficient to keep swept - up material out of ionization equilibriuim . this highlights the importance and inherent difficulty of looking for snrs in bright regions . direct optical identification is complicated by the bright nebular emission . fuv emission and absorption , along with x - ray and radio observations , are good ways to circumvent these difficulties . the authors wish to acknowledge useful discussion with charles hoopes , miroslav filipovi , lister staveley - smith and alex fullerton . mike corcoran provided the x - ray images . chris smith supplied the interference filters used in the schmidt imagery . bryan dunne helped with the echelle observations . robert kennicutt supplied the flux - calibrated image of n66 . john raymond made available the shock code used in calculating the models . we would also like to recognize ctio for providing the excellent observing facilities and travel support . this work contains data obtained for the guaranteed time team by the nasa - cnes - csa _ fuse _ mission operated by the johns hopkins university . financial support has been provided by nasa contract nas5 - 32985 . n66snr barba , r. h. , niemela , v. s. , baume , g. , & vazquez , r. a. 1995 , , 446 , l23 blair , w. p. , et al . 1991 , , 379 , l33 blair , w. p. , & long , k. s. 1997 , , 108 , 261 blair , w. p. , raymond , j. c. , danziger , j. , matteucci , f. 1989 , , 338 , 812 blair , w. p. , sankrit , r. , & tulin , s. m. 2002 , , 140 , 367 chu , y - h . , & kennicutt , r. c. 1988 , , 95 , 1111 chu , y - h . , & kennicutt , r. c. 1994 , , 216 , 253 danforth , c. w. , blair , w. p. , & raymond , j. c. , 2001 , , 122 , 938 danforth , c. w. , howk , j. c. , fullerton , a. w. , blair , w. p. , & sembach , k. r. 2002 , , 139 , 81 de boer , k. s. , & savage , b. d. 1980 , , 238 , 86 fesen , r. a. , blair , w. p. , & kirshner , r. p. 1982 , , 262 , 171 filipovi , m. , staveley - smith , l. , ried , w. , & danforth , c. w. , 2003 , in prep . fitzpatrick , e. l. & savage , b. d. 1983 , , 267 , 93 gordon , s. m. , duric , n. , kirshner , r. p. , goss , w. m. , & viallefond , f. 1999 , , 120 , 247 gordon , s. m. , kirshner , r. p. , long , k. s. , blair , w. p. , duric , n. , & smith , r. c. 1998 , , 117 , 89 hoopes , c. g. , sembach , k. r. , howk , j. c. , & blair , w. p. 2001 , , 558 , l35 hutchings , j. b. , & giasson , j. 2001 , , 113 , 1205 howk , j. c. , savage , b. , sembach , k. r. , & hoopes , c. g. 2002 , , 572 , 264 inoue , h. , koyama , k. , & tanaka , y. 1983 , iaus , 101 , 535 jenkins , e. b. , & wallerstein , g. 1995 , , 440 , 227 kahn , s. m. , gorenstein , p. , harnden , f. r. , & seward , f. d. 1985 , , 299 , 821 kennicutt , r. c. 1984 , , 287 , 116 kennicutt , r. c. , & hodge , p. 1986 , , 306 , 130 koenigsberger , g. , guinan , e. , auer , l. , & georgiev , l. 1995 , , 452 , l107 koenigsberger , g. , et al . 2001 , , 121 , 267 lacey , c. k. , duric , n. , & goss , w. m. 1997 , , 108 , 417 long , k. s. , blair , w. p. , kirshner , r. p. , & winkler , p. f. 1990 , , 72 , 61 massey , p. , parker , j. w. , & garmany , c. d. 1989 , , 98 , 1305 matonick , d. m. , & fesen , r.a . 1997 , , 112 , 49 mills , b. y. , little , a. g. , durdin , j. m. , & kesteven , m. j. 1982 , , 200 , 1007 moos , h. w. , et al . 2000 , , 538 , l1 naz , y. , et al . 2002 , , in press osterbrock , d. e. 1989 , `` astrophysics of gaseous nebulae and active galactic nuclei '' , university science books , mill valley , ca pannuti , t. g. , duric , n. , lacey , c. k. , goss , w. m. , hoopes , c. g. , walterbos , r. a. m. , & magnor , m. a. 2000 , , 544 , 780 pannuti , t. g. , duric , n. , lacey , c. k. , ferguson , a. n. m. , magnor , m. a. , & mendelowitz , c. 2002 , , 565 , 966 parker , j. w. , et al . 1998 , , 116 , 180 raymond , j. c. 1979 , , 39 , 1 raymond , j. c. , blair , w. p. , long , k. s. , vancura , o. , edgar , r. j. , morse , j. , hartigan , p. , & sanders , w. t. 1997 , , 482 , 881 rela~ no , m. , peimbert , m. , & beckman , j. 2002 , , 564 , 704 rho , j. , & petre , r. 1998 , , 503 , l167 russell , s. c. , & dopita , m. a. 1990 , , 74 , 93 sahnow , d. j. , et al . 2000 , , 538 , l7 sankrit , r. , shelton , r. l. , blair , w. p. , sembach , k. r. , & jenkins , e. b. 2001 , , 549 , 416 seward , f. d. , & mitchell , m. 1981 , , 243 , 736 shull , j. m. , et al . 2000 , , 538 , l73 smith , m. g. , & weedman , d. w. 1970 , , 161 , 33 smith , m. g. , & weedman , d. w. 1971 , , 169 , 271 smith , m. g. , & weedman , d. w. 1973 , , 179 , 461 sutherland , r. s. , & dopita , m. a. 1993 , , 88 , 253 tumlinson , j. , et al . 2002 , , 566 , 857 velzquez , p. f. , koenigsberger , g. , & raga , a. c. 2003 , , 584 , in press wang , q. , & wu , x. 1992 , , 78 , 391 ye , t. , turtle , a. j. , & kennicutt , r. c. 1991 , , 249 , 722 yokogawa , j. , imanishi , k. , tsujimoto , m. , nishiuchi , m. , koyama , k. , nagase , f. , & corbet , r. h. d. 2000 , , 128 , 491 llllllcrl ngc346-wb6 & 00 58 57.74 & @xmath072 10 33.6 & o4v((f ) ) & p20305&mdrs & 5&10992&2001-sep-25 + ngc346-wb4 & 00 59 00.39 & @xmath072 10 37.9 & o5 - 6v & p20304&mdrs & 6&11853&2001-aug-25 + ngc346-wb3 & 00 59 01.09 & @xmath072 10 28.2 & o2iii(f * ) & p20303&mdrs & 3 & 8482&2001-aug-25 + ngc346-wb1 & 00 59 04.81 & @xmath072 10 24.8 & o4iii(n)(f ) & p20302&mdrs & 3 & 4625&2001-aug-25 + hd5980 & 00 59 26.55 & @xmath072 09 53.8 & wn var & p10301 & lwrs & 4 & 5734 & 2000-jul-02 + sk80 & 00 59 31.95 & @xmath072 10 45.8 & o7 iaf+ & p10302 & lwrs & 4&11699 & 2000-jul-02 + n66-pos1 & 00 59 42 & @xmath072 09 49 & & p20305 & lwrs & 5&10992 & 2001-sep-25 + n66-pos2 & 00 59 37 & @xmath072 07 57 & & p20302 & lwrs & 3 & 4625 & 2001-aug-25 + lllrrc hd5980 ns & 00 59 26.55 & -72 09 53.8 & 0 & 1200 & 2001-dec-24 + hd5980 ew & 00 59 26.55 & -72 09 53.8 & 90 & 1200 & 2001-dec-25 + sk80 ns & 00 59 31.95 & -72 10 45.8 & 0 & 1200 & 2001-dec-26 + sk80 ew & 00 59 31.95 & -72 10 45.8 & 90 & 600 & 2000-dec-10 + ngc346-wb6 & 00 58 57.74 & -72 10 33.6 & 90 & 600 & 2000-dec-10 + ngc346-wb3 + 4 & 00 59 01.09 & -72 10 28.2 & 197 & 600 & 2000-dec-10 + ngc346-wb1 & 00 59 04.81 & -72 10 24.8 & 0 & 600 & 2001-dec-26 + lrrrrrrr h@xmath1 6563 & 100 & 100 & 100 & 100 & 100 & 100 & 100 + s vi 937 & 12 & 19 & 18 & 20 & 23 & 27 & 30 + c iii 977 & 352 & 304 & 275 & 258 & 247 & 239 & 232 + n iii 991 & 17 & 13 & 12 & 11 & 10 & 10 & 10 + ne vi 1006 & 0 & 1 & 4 & 12 & 27 & 45 & 58 + o vi 1034 & 9 & 90 & 334 & 708 & 996 & 1156 & 1236 + s iv 1070 & 11 & 8 & 8 & 7 & 7 & 7 & 7 + ne v 1146 & 3 & 8 & 13 & 18 & 24 & 27 & 28 + n v 1240 & 17 & 27 & 23 & 23 & 24 & 24 & 24 + si iv 1397 & 31 & 28 & 26 & 25 & 24 & 24 & 23 + o iv ] 1402 & 100 & 112 & 108 & 101 & 97 & 94 & 92 + n iv ] 1490 & 9 & 7 & 6 & 5 & 5 & 5 & 5 + c iv 1549 & 211 & 174 & 156 & 148 & 145 & 142 & 140 + o iii ] 1662 & 59 & 52 & 47 & 44 & 42 & 41 & 40 + n iii ] 1748 & 6 & 5 & 4 & 4 & 4 & 4 & 4 + i(h@xmath1 ) & 1.268 & 1.551 & 1.819 & 2.048 & 2.249 & 2.431 & 2.622 +

optical emission from the remnant is overwhelmed by the bright photoionized emission from the nebula , but the remnant has been detected by way of far ultraviolet absorption lines . here we present data from the far ultraviolet spectroscopic explorer ( _ fuse _ ) satellite showing strong and emission from a position at the edge of snr0057 .

n66/ngc346 is the largest and brightest region in the small magellanic cloud and contains at least one known supernova remnant snr0057 . optical emission from the remnant is overwhelmed by the bright photoionized emission from the nebula , but the remnant has been detected by way of far ultraviolet absorption lines . here we present data from the far ultraviolet spectroscopic explorer ( _ fuse _ ) satellite showing strong and emission from a position at the edge of snr0057 . we also present high - resolution , long - slit h spectra across n66 showing high- and low - velocity emission corresponding closely to the x - ray boundaries of the supernova remnant . we use these fuv and optical data to determine the physical parameters of the shock and interaction geometry with n66 . we find that ionizing photons from the many massive cluster stars nearby likely affect the ionization balance in the post - shock gas , hindering the production of lower - ionization and neutral species . we discuss the importance and inherent difficulty of searching for supernova remnants in or near bright regions and suggest that the far ultraviolet provides a viable means to discover and study such remnants .

0809.1066

i

in the study of the demographics of supermassive black holes , one important unresolved problem is the observational census of black holes in very late - type disk galaxies . the masses of supermassive black holes in elliptical and early - type spiral galaxies appear to be well correlated with the bulge properties of their host galaxies @xcite . these correlations naturally lead to the question of whether supermassive black holes can form in disk galaxies that lack bulges , and if so , how the black hole mass in bulgeless galaxies might be related to the properties of the host . the nearest example of a bulgeless disk galaxy , m33 , does not contain a massive black hole , with an extremely tight upper limit of @xmath6 @xmath3 determined from stellar - dynamical observations and modeling @xcite . it is not yet known whether the absence of a massive black hole is a typical property of bulgeless spirals in general , however , because very few late - type disk galaxies are near enough for stellar - dynamical measurements to yield such stringent constraints on the black hole mass . it has long been recognized that many spiral galaxies contain photometrically and dynamically distinct central star - cluster nuclei , with the m33 nucleus being one of the best - studied examples ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the _ hubble space telescope _ ( _ hst _ ) made it possible to survey the properties of nuclear star clusters in more distant galaxies ( e.g. , * ? ? ? * ; * ? ? ? * ) , and _ hst _ imaging programs have demonstrated that the majority of very late - type spirals ( hubble types scd sd ) contain compact star - cluster nuclei at or very close to their isophotal centers @xcite . spectroscopic observations have revealed that the nuclear clusters in late - type spirals typically have stellar velocity dispersions of @xmath7 km s@xmath1 @xcite , effective radii of a few parsecs @xcite , and dynamical masses of @xmath8 @xmath3 @xcite . the spectra also reveal composite stellar populations indicative of multiple star formation episodes , with most clusters containing a population component with an age of @xmath9 myr @xcite . the discovery of scaling relationships between nuclear cluster masses and host galaxy properties , both in spirals @xcite and in dwarf ellipticals @xcite , offers an intriguing hint of a connection between the processes that govern the growth of nuclear clusters and black holes . @xcite speculate that the formation of nuclear star clusters and massive black holes might be mutually exclusive , such that black holes are able to form only in galaxies above some critical mass . however , the only nuclear star clusters in which the presence of a massive black hole can be ruled out at any significant level are in the local group or within a few mpc . optical spectroscopic surveys have shown that active galactic nuclei ( agns ) do occur in some nuclear star clusters in nearby galaxies @xcite , so black holes and nuclear clusters can apparently coexist . evidence that black holes can occur in at least some very late - type disk galaxies comes from the detection of a small number of agns in scd and sd - type spirals . the best example is the sd galaxy ngc 4395 , which contains a seyfert 1 nucleus @xcite ; it remains the only clear identification of a broad - lined agn in a bulgeless disk galaxy . in addition , a few examples of type 2 agns in very late - type spirals have been detected recently in optical spectroscopic surveys , such as ngc 1042 @xcite and ugc 6192 @xcite . in both ngc 4395 and ngc 1042 the agns occur in nuclear star clusters ( it is not known whether ugc 6192 contains a nuclear cluster ) . a recent _ spitzer _ spectroscopic observation of the sd galaxy ngc 3621 by @xcite led to the discovery of an active nucleus , based on the detection of [ ] emission lines at 14.3 and 24.3 . since photon energies greater than 95 ev are required for photoionization of ne@xmath10 to ne@xmath11 , ordinary regions are not expected to be significant sources of [ ] emission , but a hard agn continuum can easily provide the necessary ionizing photons . emission lines from a range of ionization states of neon are observable in the mid - infrared , and the relative strengths of these lines are useful as diagnostics of the ionization conditions within agn narrow - line regions ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? @xcite used the results of new photoionization models to argue that the strength of the [ ] emission in ngc 3621 can only be plausibly explained by the presence of an agn , and not by an ordinary burst of nuclear star formation . the detection of an agn in ngc 3621 is of significant interest because it is one of the few very late - type spirals known to host an active nucleus , making it an important target for further observations to constrain its black hole mass and agn energetics . @xcite note that there is no previously published optical spectrum of the nucleus of ngc 3621 suitable for emission - line classification . in this paper , we use archival _ hst _ images to show that ngc 3621 contains a well - defined and compact nuclear star cluster . a new optical spectrum of this star cluster is used to examine the classification of the active nucleus , and to measure the stellar velocity dispersion of the cluster . we describe dynamical modeling of the nuclear cluster and the resulting constraints on the masses of both the cluster and the central black hole . we also examine the structure of ngc 3621 using near - infrared images from 2mass in order to search for a bulge component in this late - type galaxy . for the distance to ngc 3621 , we adopt @xmath12 mpc , based on the cepheid measurements of @xcite . at this distance , 1corresponds to 32.0 pc .

ngc 3621 is a late - type ( sd ) spiral galaxy with an active nucleus , previously detected through mid - infrared [ ] line emission . archival _ hubble space telescope _ ( _ hst _ ) images reveal that the galaxy contains a bright and compact nuclear star cluster . we present a new high - resolution optical spectrum of this nuclear cluster , obtained with the esi spectrograph at the keck observatory . ngc 3621 provides one of the best demonstrations that very late - type spirals can host both active nuclei and nuclear star clusters , and that low - mass black holes can occur in disk galaxies even in the absence of a substantial bulge .

ngc 3621 is a late - type ( sd ) spiral galaxy with an active nucleus , previously detected through mid - infrared [ ] line emission . archival _ hubble space telescope _ ( _ hst _ ) images reveal that the galaxy contains a bright and compact nuclear star cluster . we present a new high - resolution optical spectrum of this nuclear cluster , obtained with the esi spectrograph at the keck observatory . the nucleus has a seyfert 2 emission - line spectrum at optical wavelengths , supporting the hypothesis that a black hole is present . the line - of - sight stellar velocity dispersion of the cluster is km s , one of the largest dispersions measured for any nuclear cluster in a late - type spiral galaxy . combining this measurement with structural parameters measured from archival _ hst_images , we carry out dynamical modeling based on the jeans equation for a spherical star cluster containing a central point mass . the maximum black hole mass consistent with the measured stellar velocity dispersion is . if the black hole mass is small compared with the cluster s stellar mass , then the dynamical models imply a total stellar mass of , which is consistent with rough estimates of the stellar mass based on photometric measurements from _ hst _ images . from structural decomposition of 2mass images , we find no clear evidence for a bulge in ngc 3621 ; the galaxy contains at most a very faint and inconspicuous pseudobulge component ( mag ) . ngc 3621 provides one of the best demonstrations that very late - type spirals can host both active nuclei and nuclear star clusters , and that low - mass black holes can occur in disk galaxies even in the absence of a substantial bulge .

0809.1066

i

our main conclusions are as follows . 1 . ngc 3621 has a seyfert 2 optical spectrum , consistent with the agn identification based on its mid - infrared spectrum by @xcite . this adds further support for the hypothesis that a black hole is present . 2 . for the nuclear star cluster , we find an effective radius of @xmath176 pc , a line - of - sight stellar velocity dispersion of @xmath0 km s@xmath1 , and an absolute magnitude of @xmath177 mag ( uncorrected for internal extinction ) . simple estimates based on the available _ hst _ photometry suggest a stellar mass of @xmath178 @xmath3 . 3 . from two - dimensional image decomposition of 2mass images , we find that the galaxy is dominated by an exponential disk , with at most a very faint possible pseudobulge component being present . we derive an upper limit of @xmath179 mag to the luminosity of any bulge or pseudobulge component . 4 . from stellar - dynamical modeling of the nuclear cluster , we find an upper limit to the black hole mass of @xmath180 . this result is insensitive to possible velocity anisotropy within the cluster . the upper limit is based on the extreme assumption of @xmath181 for the stellar population . with improved photometric and spectroscopic observations it would be possible to better constrain the stellar mass - to - light ratio and reduce the upper limit on @xmath129 . assuming that the cluster s black hole mass is small in comparison with its stellar mass , the dynamical models give a stellar mass of @xmath4 @xmath3 for the cluster . these results add to the emerging body of evidence that some late - type , bulgeless galaxies do contain low - mass central black holes , and that black holes can be found inside some nuclear star clusters . it remains the case , however , that there are only a few late - type spirals in which a the presence of a massive black hole has been either confirmed ( based on nuclear activity ) or ruled out ( from dynamical modeling ) . further observations of the ngc 3621 nuclear cluster will lead to a more complete picture of the properties of this object . the most pressing observational need is for x - ray observations , to provide more definitive confirmation of the agn interpretation and a better estimate of the agn luminosity . improved measurements of the stellar content of the nuclear cluster can be obtained from high - resolution , high - s / n spectra extending farther to the blue than our esi data , in addition to improved multi - band _ hst _ imaging covering the near - ultraviolet to near - infrared . future extremely large ground - based telescopes with adaptive optics may make it possible to spatially resolve the kinematic substructure of the nuclear cluster , and this could lead to dramatically improved constraints on the black hole mass . research by a.j.b . and is supported by nsf grant ast-0548198 , and research by l.e.s . is supported by nsf grant ast-0607746 . we thank rachel kuzio de naray for helpful conversations , and an anonymous referee for suggestions that improved this work . data presented herein were obtained at the w.m . keck observatory , which is operated as a scientific partnership among caltech , the university of california , and nasa . the observatory was made possible by the generous financial support of the w.m . keck foundation . the authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of mauna kea has always had within the indigenous hawaiian community . we are most fortunate to have the opportunity to conduct observations from this mountain . this publication is based on observations made with the nasa / esa hubble space telescope , obtained from the data archive at the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nas 5 - 26555 . these observations are associated with programs 5446 , 9492 , and 11080 . this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation . this research has made use of the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration .

the nucleus has a seyfert 2 emission - line spectrum at optical wavelengths , supporting the hypothesis that a black hole is present . the maximum black hole mass consistent with the measured stellar velocity dispersion is . if the black hole mass is small compared with the cluster s stellar mass , then the dynamical models imply a total stellar mass of , which is consistent with rough estimates of the stellar mass based on photometric measurements from _ hst _ images . from structural decomposition of 2mass images , we find no clear evidence for a bulge in ngc 3621 ; the galaxy contains at most a very faint and inconspicuous pseudobulge component ( mag ) .

ngc 3621 is a late - type ( sd ) spiral galaxy with an active nucleus , previously detected through mid - infrared [ ] line emission . archival _ hubble space telescope _ ( _ hst _ ) images reveal that the galaxy contains a bright and compact nuclear star cluster . we present a new high - resolution optical spectrum of this nuclear cluster , obtained with the esi spectrograph at the keck observatory . the nucleus has a seyfert 2 emission - line spectrum at optical wavelengths , supporting the hypothesis that a black hole is present . the line - of - sight stellar velocity dispersion of the cluster is km s , one of the largest dispersions measured for any nuclear cluster in a late - type spiral galaxy . combining this measurement with structural parameters measured from archival _ hst_images , we carry out dynamical modeling based on the jeans equation for a spherical star cluster containing a central point mass . the maximum black hole mass consistent with the measured stellar velocity dispersion is . if the black hole mass is small compared with the cluster s stellar mass , then the dynamical models imply a total stellar mass of , which is consistent with rough estimates of the stellar mass based on photometric measurements from _ hst _ images . from structural decomposition of 2mass images , we find no clear evidence for a bulge in ngc 3621 ; the galaxy contains at most a very faint and inconspicuous pseudobulge component ( mag ) . ngc 3621 provides one of the best demonstrations that very late - type spirals can host both active nuclei and nuclear star clusters , and that low - mass black holes can occur in disk galaxies even in the absence of a substantial bulge .

1502.04107

i

different from other fundamental quantities such as mass and charge , spin is a dynamical quantity , and its dynamics have been widely studied and applied in science and technology . in particular , recent rapid growth of spintronics provides a stage where deeper understandings of spin dynamics directly lead to practical applications . the dynamics of spin are governed by the spin berry phase @xcite , and its equation of motion includes only the first - order time derivative of spin . this is natural because spin is an angular momentum and its equation of motion takes the familiar form : the time - derivative of the angular momentum ( i.e. spin ) is given by the torque acting on it . without any torque , the solution of the equation of motion of spin is only a static one . this is in contrast with , for example , the case of a massive point particle , which has inertia and can move at non - zero speed as its free motion . in this sense , spin does not have inertia . however , for systems where spin interacts with other environmental degrees of freedom , spin dynamics are affected by those environmental degrees of freedom , and the dynamical law of spin is changed to be an effective one . for example , in metallic ferromagnets , conduction electrons affect the dynamics of localized spins ( i.e. spins of atoms on lattice cites ) . a typical effect is spin - damping ( e.g. @xcite ) , where the energy and the angular momentum of spins are transferred to the environmental degrees of freedom and , as the result , spins relax to their ground state within a certain time scale . without this effect , spins undergo the larmor precession around the applied magnetic field forever . in this respect , the existence of the degrees of freedom other than spins changes the dynamical behavior of spins significantly . in the equation of motion of spins , this damping is represented by the gilbert damping term @xcite . this damping term includes only the first - order time derivative of spins . therefore , spin still does not have inertia even when we take into account the gilbert damping effect . the effects of the environments other than the gilbert damping can be studied systematically by the derivative expansion , where the effects are expanded in powers of the time ( and spatial ) derivative of spin . from that point of view , the gilbert damping term gives the leading order term in that expansion . in the higher orders , there appear terms which include the second - order time derivative , the third - order time derivative and so on , in the equation of motion of spin . these terms with higher order time derivatives are interesting in that , like the gilbert damping term , they change the dynamical law of spin itself , more than give additional torque on spin . in particular , from a comparison with the form of the newton s equation of motion of a massive point particle , the term with the second - order time derivative of spin plays the role of the inertia of spin . such spin inertia has been discussed in the literature ( e.g. ref.@xcite ) . in particular , recent progress in ultrafast magnetization @xcite motivated several works . in refs.@xcite , the inertia of spin was introduced phenomenologically and was shown to give additional nutation to the motion of spin . the time scale where the effect of the inertia is significant was discussed , based on the work of brown @xcite , to be sub - picosecond order . in ref.@xcite , the equivalence between the dynamics of spin with inertia and a spinning top was discussed . microscopic derivation of spin inertia was performed in refs.@xcite and @xcite . in ref.@xcite , an extended breathing fermi surface model was used , and the relation between the gilbert damping coefficient and the spin inertia was given in terms of physical quantities ( such as fermi - dirac occupation numbers ) of conduction electrons . the time scale for the nutational motion to be damped by the gilbert damping was estimated to be sub - picosecond order . in ref.@xcite , a general expression of the contribution of the conduction electrons to spin dynamics was discussed . the spin effective dynamics was shown to be non - local in general , which can be approximated as local dynamics by the derivative expansion of spin . the inertial term of spin arises in that derivative expansion and its general expression was given in term of the green s function of the conduction electrons . since the inertia of spin is conceptually interesting in its own and gives the first step toward the understanding of non - adiabatic contribution of environmental degrees of freedom to spin effective dynamics , further investigations are worthwhile . although the expressions of the inertia of spin were given as integral forms @xcite , an explicit expression of the inertia of spin in terms of parameters of a model has not been obtained so far . furthermore , the effect of the inertia of spin on the dynamics of spin has been discussed only for spatially homogeneous spin system under time - independent magnetic field . in this paper , we present detailed theoretical study of the effects induced by the spin inertia based on an @xmath4 model . in section [ sec : effective action ] , we derive a concrete expression of spin inertia in terms of the parameters in the @xmath4 model . in section [ sec : spin and spinning top ] , the basic behavior of spin with finite inertia is studied with the help of its two equivalents : a symmetric spinning top and a massive charged particle on a sphere subject to a monopole field . in section [ sec : phenomena ] , we study spatially inhomogeneous system , and discuss that spin waves and magnetic domain walls acquire an additional oscillation mode due to spin inertia . we also study the behavior of spin under large and time - dependent magnetic field , and find an unusual behavior of spin where the velocity of spin is parallel to the direction of the time - derivative of magnetic field .

non - adiabatic contribution of environmental degrees of freedom yields effective inertia of spin in effective spin dynamics . in this paper , we study several aspects of the inertia of spin in metallic ferromagnets . ( ii ) dynamical behavior of spin with inertia , discussed from viewpoints of a spinning top and of a particle on a sphere . ( iii ) behavior of spin waves and domain walls in the presence of inertia , and behavior of spin with inertia in the case of a time - dependent magnetic field .

non - adiabatic contribution of environmental degrees of freedom yields effective inertia of spin in effective spin dynamics . in this paper , we study several aspects of the inertia of spin in metallic ferromagnets . ( i ) a concrete expression of the spin inertia : , where is the spin polarization of conduction electrons and is the coupling constant . ( ii ) dynamical behavior of spin with inertia , discussed from viewpoints of a spinning top and of a particle on a sphere . ( iii ) behavior of spin waves and domain walls in the presence of inertia , and behavior of spin with inertia in the case of a time - dependent magnetic field .

1201.4965

i

experimental data on high energy physics say that elementary particles are complex systems with internal degrees of freedom . fundamental particle which in certain relation can pretend to simplicity , on the one hand , and underlie all known interactions , on the other hand , is the electron . nonexistence of the electron , being a source of electromagnetic field , in the maxwell theory and its generalizations is paradoxical . it may be explained by that the maxwell theory describes macroscopical averaged fields created by systems consisting of large quantity of moving charges . therefore the electron theory , whose foundations were laid by lorentz , is necessary for the description of the majority of the electromagnetic phenomena in material systems . the electron theory has been developing in classical trend after discovery of the electron by j.j.thomson in cathode rays . the theory by abraham @xcite , based on the maxwell - lorentz electrodynamics , became the first theory considering internal structure of the electron . during two decades preceding experience by stern - gerlach and the kronig - uhlenbeck - goudsmit hypothesis about electron spin , there were appeared a few alternative theories and guesses about electron structure . it should be mentioned here works by compton @xcite- @xcite , influenced by both the paper by parson @xcite and stereoscopic photos of tracks of the @xmath1-rays , made by wilson , some of which had almost ideal form of a helix . compton has come to a conclusion that the model of the electron , `` spinning like a tiny gyroscope '' , can eliminate difficulties in an explanation of curvature of these tracks , as well as of richardson - barnett effect and diffraction of x - rays by magnetic crystals . nevertheless , the parson - compton theory continuing early idea of vortex atoms , going back to greek atomists , kepler , descartes , leibnitz , svedenborg , boskovich , ampere , kelvin , and theories of some other researchers had rather natural philosophic and empirical nature , than they gave any mathematical instrument for future theory . the first mathematical realization of the parson - compton theory was the work by frenkel @xcite , where the electron was considered as a point with six - vector of magnetic moment , what has allowed to explain the anomalous zeeman effect . after creation of quantum mechanics , especially after works by pauli and dirac , the electron theory began to develop chiefly in quantum direction . in 1930 schrdinger has shown that the trembling motion ( zitterbewegung ) of the electron takes place in the dirac theory where eigenvalues of any component of the velocity operator are equal to @xmath2 . microscopic trembling motion with the velocity of light of imaginary center of the cloud of charge , whose amplitude is about half compton wave length , is imposed on translational macroscopic motion of the center of mass of the electron . as shrdinger talks , `` exclusively entangled relations , which are present according to the dirac equation already at free movement of a mass point , seem to me worthy of enunciating though i can not present some completed result of this research '' @xcite . in 1952 huang has shown that zitterbewegung of a free dirac electron may be looked upon as a circular motion about the direction of the electron spin that in turn may be interpreted as the `` orbital angular momentum '' of this motion . as a result the electric current produced by zitterbewegung is seen to give rise to the intrinsic magnetic moment of the electron @xcite . however , as early as in 1937 mathisson has written down general relativistic equations of motion for systems possessed multipole momenta @xcite . he has shewed also , that their application to a particle with spin treated as a dipole gives rise to equations of motion , describing zitterbewegung @xcite . mathisson has considered the motion of a free uncharged particle with spin and free electron taking account of the reaction of radiation . here he has assumed spin to be a constant ( pseudo-)vector , what was rather stringent assumption , for spin direction in general can change . nevertheless , having associated trembling motion of the electron with the de broglie s wave , he has obtained the well - known value of a spin @xmath3 . following basic articles by schrdinger and mathisson a lot of works were appeared , developing both quantum and classical electron theory and establishing connection between them . sufficiently full list of references one may find in the books @xcite , @xcite . despite a considerable quantity of researches devoted to the theory of the electron , there are many unclear matters associated both with radiation of the electron and with dependence of its trajectory from its spin ( see , e.g. , @xcite ) . an interest in classical theory of the electron has especially increased at the recent years , and this work contains some arguments in favour of a classical origin of zitterbewegung . relating of the electron spin with its proper rotation allows considering the electron as non - inertial object which can be described as a mass point with internal degrees of freedom @xcite , @xcite . the formalism of such description based on generalization of the second newton s law is considered in 2 . here the equations of motion of the point interacting with an external field described by the potential function depending on relative variables are obtained . consequence of the equation of motion is the equation of balance of energy which is integral of motion only if a certain condition is fulfilled . non - conservation of the energy , in general , seems to be caused by the fact that mass point in question is non - inertial system . it is supposed that internal degrees of freedom are described by the pseudo - vectors @xmath4 and @xmath5 connected both with internal structure of the point , and with its interaction with external fields . it is shown in 3 that equation of motion of free mass point reduces to a conservation of the velocity of the center of inertia . to obtain solutions natural equations of motion are introduced for internal degrees of freedom describing precession of pseudo - vectors @xmath4 and @xmath5 round the direction of the velocity of the center of inertia . all solutions of the equation of motion for a free mass point ( when @xmath6 and @xmath7 ) in the center - of - inertia reference frame are found in 4 . the center of inertia proves to be does not coincide with the center of mass . as a result , the center of mass moves by a complicated trajectory round the direction of motion of the center of inertia . some solutions in the center - of - inertia reference frame are infinite . it is shown that they become finite at zero energy of the mass point . it is of interest that equation of motion admits also solutions for zero mass and transversal polarization . in 5 equation of moments is considered and speculations are contained about the physical sense of pseudo - vectors @xmath8 and @xmath9 and their relation with spin whose equation of motion in general case we deal with in 6 , which contains also conclusive remarks on possible interpretation of obtained solutions .

the equation for energy , which is an integral of motion when satisfies to certain differential condition , is derived for the general case . for a free mass point all solutions of the equations of motion in the center - of - inertia reference frame , moving with constant velocity , are found . as a result , the center of mass follows along helical and more complicated trajectories round a direction of motion of the center of inertia .

nonrelativistic formalism is developed , which allows describing systems with internal degrees of freedom in the scalar potential field , which is a function both on relative coordinates and time , and on relative speed and accelerations . the equation for energy , which is an integral of motion when satisfies to certain differential condition , is derived for the general case . for a free mass point all solutions of the equations of motion in the center - of - inertia reference frame , moving with constant velocity , are found . as a result , the center of mass follows along helical and more complicated trajectories round a direction of motion of the center of inertia . this motion can be interpreted as trembling movement ( zitterbewegung ) . on this basis a conclusion is done that zitterbewegung has purely classical origin , arising even in a nonrelativistic case if internal degrees of freedom are taken into account . the general equation of motion for a spin which can be interpreted from positions of a classical mechanics is written down . application of the obtained results to the electron leads to new conception of electric charge , sign of which corresponds to a sign of spin polarization . pacs numbers : 14.60cd , 45.20.d , 45.50.j keywords : classical mechanics , internal degrees of freedom , equations of motion , energy conservation , electron

astro-ph0309458

i

in the past decade , observations of x - ray emission from accreting neutron stars and black holes have introduced new possibilities for astrophysical tests of fundamental physics . recent discoveries made by satellites such as asca , rxte , bepposax , chandra , and xmm - newton provide direct evidence for strong - field gravitational effects in compact binary systems and active galactic nuclei ( agn ) . these results include doppler - broadened iron k@xmath0 fluorescent emission from microquasars @xcite and millisecond variability of the x - ray flux from black holes in low - mass x - ray binaries @xcite . these measurements give the exciting prospect for determining a black hole s mass and spin , as well as tests of general relativity in the strong - field regime . the strong gravitational fields near a black hole ( bh ) introduce significant deviations from newtonian physics , including the existence of an inner - most stable circular orbit ( isco ) , a feature absent in the classical kepler problem . since accreting gas can efficiently lose energy and angular momentum only outside of the isco , the hydrodynamic and radiative behavior of the inner accretion disk should be strongly dependent on the structure of the space - time metric near the isco . the famous `` no hair '' theorem states that the only observable features of an electrically neutral black hole are functions of its mass @xmath1 and specific angular momentum @xmath2 . by understanding the behavior of matter near the isco , we can determine the mass and angular momentum , and thus completely describe the black hole . many authors have approached the problem of accretion in compact binaries with a variety of different methods , including early analytic models by @xcite and @xcite . some have simplified the hydrodynamics in favor of a flat , thin , steady - state disk and a more detailed treatment of general relativistic effects @xcite . to include dynamic effects , essential for modeling qpos , others have included magnetohydrodynamics ( mhd ) in a pseudo - newtonian model @xcite or with smoothed particle hydrodynamics @xcite . a family of perturbative models has given rise to the field of diskoseismology @xcite , where different global modes in the disk oscillate with different frequencies . @xcite propose a magnetic coupling between the rotating black hole and the accretion disk as a means of producing high - frequency qpos , analogous to the blandford - znajek process @xcite used to describe agn . recent observations of commensurate relationships in the high - frequency qpos of black hole accretion disks @xcite , as well as the longstanding puzzles of the frequency variability of qpo peaks and their correlations with x - ray flux and energy @xcite , motivate more detailed study of the qpo phenomenon as a means to determining the black hole parameters . we have developed a model that is a combination of many of the above approaches in which additional physics ingredients can be added incrementally to a framework grounded in general relativity . the model does not currently include scattering , radiation pressure , magnetic fields , or hydrodynamic forces , instead treating the disk as a collection of cold test particles radiating isotropically in their respective rest frames . the trajectories of emitted photons are integrated through the metric to a distant observer to construct time - dependent images and spectra of the disk . the dynamic model uses the geodesic trajectory of a massive particle as a guiding center for a small region of excess emission , a `` hot spot , '' that creates a time - varying x - ray signal , in addition to the steady - state background flux from the disk . this hot spot model is motivated by the similarity between the qpo frequencies and the black hole ( or neutron star ) coordinate frequencies near the isco @xcite as well as the suggestion of a resonance leading to integer commensurabilities between these coordinate frequencies @xcite . @xcite investigated primarily the qpo frequency pairs found in lmxbs with a neutron star ( ns ) accretor , but their basic methods can be applied to black hole systems as well . @xcite have presented a thorough analysis of this hot spot model for a collection of ns binaries for which pairs of qpos have been observed . based on a number of experimental and theoretical arguments , they conclude that the geodesic hot spot model is not a physically viable explanation for the observed ns qpos . for low to moderate eccentricity orbits , the coordinate frequencies simply do not agree with the qpo data . for highly eccentric geodesics , they argue that the relative power in the different frequency modes are qualitatively at odds with the observations . furthermore , they show that hydrodynamical considerations place strong constraints on the possible size , luminosity , coherency , and trajectories of the hot spots . many of these points are addressed in our version of the hot spot model . also , by including full 3-dimensional ( 3d ) ray - tracing , we can quantitatively predict how much qpo power will be produced by a hot spot of a given size and emissivity moving along a geodesic orbit near the isco . along with the special relativistic beaming of the emitted radiation , we find that strong gravitational lensing can cause high - amplitude modulations in the light curves , even for relatively small hot spots . the issues of differential rotation and shearing of the emission region are addressed below when we consider the generalization of the hot spot model to include arcs and non - planar geometries . perhaps the most powerful feature of this hot spot model is the facility with which it can be developed and extended to more general accretion disk geometries . in addition to providing a possible explanation for the commensurate hfqpos in at least two systems ( xte j1550 - 564 and gro j1655 - 40 ) , the hot spot model with full general relativistic ray - tracing is a useful building block toward any other viable model of a dynamic 3d accretion disk . within the computational framework of the kerr metric , we can investigate many different emission models and compare their predicted x - ray spectra and light curves with observations . for example , our ray - tracing code could be used in conjunction with a 3d mhd calculation of the accretion disk to simulate the time - dependent x - ray flux and spectrum from such a disk . it is with this motivation that we present the initial results of the model . section 2 describes the relativistic ray - tracing methods and discusses numerical techniques . in section 3 , we develop the basic model of a steady - state disk with the potential application to broad iron k@xmath0 emission . section 4 introduces the basic hot spot model for circular geodesics and shows the effect of binary inclination and black hole spin on the qpo power spectrum . in section 5 the model is extended to trajectories with non - zero eccentricity and inclination , as well as elongated hot spots or arcs , giving a set of model parameters that best fit the qpo data from a large number of outbursts from xte j1550 - 564 . in section 6 we present our conclusions and a discussion of future work .

using the exact geodesic equations for the kerr metric , we calculate the trajectories of massive test particles , which are treated as isotropic , monochromatic emitters in their rest frames . photons are traced from the accretion disk to a distant observer to produce time- and frequency - dependent images of the orbiting hot spot and background disk . the observed power spectra allow us to infer values for the black hole mass and angular momentum , and also constrain the parameters of the model , such as the hot spot size and luminosity .

observations from the rossi x - ray timing explorer have shown the existence of high frequency quasi - periodic oscillations ( hfqpos ) in the x - ray flux from accreting black hole binary systems . in at least two systems , these hfqpos come in pairs with a 2:3 frequency commensurability . we propose a simple `` hot spot '' model to explain the position and amplitude of the hfqpo peaks . using the exact geodesic equations for the kerr metric , we calculate the trajectories of massive test particles , which are treated as isotropic , monochromatic emitters in their rest frames . photons are traced from the accretion disk to a distant observer to produce time- and frequency - dependent images of the orbiting hot spot and background disk . the power spectrum of the x - ray light curve consists of multiple peaks at integral combinations of the black hole coordinate frequencies . in particular , if the radial frequency is one - third of the azimuthal frequency ( as is the case near the inner - most stable circular orbit ) , beat frequencies appear in the power spectrum at two - thirds and four - thirds of the fundamental azimuthal orbital frequency , in agreement with observations . we also model the effects of shearing the hot spot in the disk , producing an arc of emission that also follows a geodesic orbit , as well as the effects of non - planar orbits that experience lens - thirring precession around the black hole axis . by varying the arc length , we are able to explain the different qpo features observed in `` type a '' and `` type b '' x - ray outbursts from xte j1550 - 564 . in the context of this model , the observed power spectra allow us to infer values for the black hole mass and angular momentum , and also constrain the parameters of the model , such as the hot spot size and luminosity .

0906.0588

i

forming high - mass o and b stars with a surface temperature larger than @xmath1 k emit most of their radiation in far uv ( fuv ) wavelengths . after a not yet well defined point of the evolution , also x - rays are emitted . when still deeply embedded in their natal cloud , most of this high - energy radiation is absorbed by the large column density of gas and dust towards the protostar . it is thus not available to direct observation but does influence the composition of the molecular envelope through heating and photoionization . an essential ingredient of star formation are bipolar outflows transporting the excess angular momentum outwards . when the fast , low - density gas of molecular outflows or jets expand into the surrouding molecular cloud , large cavities may result ( e.g. @xcite ) . along these outflow cavities , fuv radiation may escape and irradiate the high density material at the border of the cavity . + a surprisingly large amount of co@xmath0 has been detected in the high - mass star forming region afgl 2591 by @xcite . their radiative transfer calculations indicate fractional abundances of order @xmath2 , much higher than @xmath3 predicted by dark cloud models . co@xmath0 has previously not been detected towards envelopes of young stellar objects ( ysos ) , but has been seen in photo dominated regions ( pdrs , e.g. @xcite or @xcite ) . strong far uv ( fuv ) radiation in these regions heats the gas and drives a peculiar chemistry which enhances the abundance of co@xmath0 . the detection of co@xmath0 in envelopes of ysos is thus strong evidence for the feedback of the protostar on the envelope by high - energy irradiation . in this work , we will study co@xmath0 as a prototypical species enhanced by fuv irradiation in high - mass ysos . + chemical models solve for the evolution of the abundances of molecules and atoms . they simulate a network of species reacting with each other . the network consists of different types of chemical reactions . in dark clouds for example , all fuv radiation is shielded by a large column density of dust and the chemistry is dominated by cosmic ray ionization and reactions between neutral and ionized species ( e.g. @xcite ) . in the innermost part of a yso envelope , x - rays may dominate the ionization ( @xcite ) . they influence the chemistry mainly by secondary fast photoelectrons hitting molecules and atoms . x - ray induced chemistry is very similar to cosmic ray induced chemistry ( @xcite ) . in regions with a strong fuv irradiation , direct photoionization of species with ionization potential @xmath4 ev drive the chemistry . the influence of fuv radiation on the envelope of ysos has been studied by @xcite . + so far , a spherically symmetric structure of the envelope has been assumed for chemical models of envelopes of high - mass star forming regions ( e.g. @xcite , @xcite , @xcite ) . while the abundances derived using this spherical model agree for many species with observations of specific sources , they fail to explain the amount of co@xmath0 . due to the attenuation by dust , fuv radiation can not escape the innermost few hundred au and the volume of gas where co@xmath0 may be formed is too small in spherical models to reproduce the observations . another possible formation mechanism of co@xmath0 is x - ray irradiation . unlike fuv photons , x - rays are mainly attenuated by geometrical dilution ( @xmath5 ) due to their smaller absorption cross - section proportional to @xmath6 . x - ray radiation can thus penetrate much deeper into the envelope on scales of a few thousand au . protostellar x - ray luminosities of up to @xmath7 erg s@xmath8 in the 1 - 100 kev band are observed ( @xcite ) . for this luminosity however , the x - ray flux is too low to enhance co@xmath0 sufficiently to match with observations . + the interaction zone between outflow and infall has been proposed before as sites of anomalous chemistry and molecular excitation . @xcite have explained the strong co(6 - 5 ) emission in narrow lines observed towards many low - mass ysos by heating of the cavity wall through protostellar fuv photons . compact emission of hco@xmath0 associated with the outflow wall has been detected by @xcite in the class 0 object l 1527 . a possible explanation is mixing of partially ionized gas from the outflow with infalling material leading to a thin layer of dense and ionized gas , where species with a high dipole moment ( e.g. hco@xmath0 or hcn ) can be excitet efficiently by collisions with electrons ( @xcite ) . detailed 3d radiative transfer studies by @xcite on the other hand prefer a scenario with an enhanced abundance of hco@xmath0 due to shock liberation and photoprocessing of molecular material stored in ice mantles . observational evidence for such an interaction layer in a high - mass star forming region are found by @xcite by studying the line profiles of different molecular species . recently , @xcite find evidence for uv photons escaping through the outflow cones and impacting the walls for the low - mass protostar hh 46 . + in this work , we will introduce a chemical model that implements a non - spherical density structure taking an outflow cavity into account . a proper treatment of the fuv irradiated outflow walls requires two - dimensional chemical models with high spatial resolution . this is however computationally excessively expensive , especially if the temperature structure is calculated self - consistently with the chemical abundances . in the first paper of this series ( @xcite ) , we have introduced a new method for fast chemical modelling . a precalculated grid of chemical abundances depending on different physical parameters like the density , temperature or fuv flux is calculated and the abundances can then be obtained by interpolation in this database . using different benchmark tests , we found very good agreement between fully calculated chemical abundances and interpolated values , while the interpolation approach is more than 5 orders of magnitudes faster . this speed - up allows to quickly construct detailed chemical models with a complex geometry . + we construct a detailed two - dimensional chemical model of the high - mass star forming region afgl 2591 . the goal is to explain the high abundance of co@xmath0 measured by the jcmt single - dish telescope ( @xcite ) as well as the non - detection by the submillimeter array ( sma ) interferometer ( @xcite and new data , reported in sect . [ sec : compsma ] ) . in this paper , we assume a fixed geometry and consider only co@xmath0 . the next part of this series of papers is dedicated to a study of the influence of geometry for a larger sample of species . + the paper is organized as follows : in the first section of the paper , we briefly discuss the chemistry of co@xmath0 . the next section introduces the two - dimensional model of afgl 2591 : we describe the modelling process , the radiative transfer of the fuv radiation and the calculation of the temperature structure . in section [ sec : results ] , we present results of the chemical model . modeled fluxes and synthetic maps are compared to jcmt and sma observations .

observations of the high - mass star forming region afgl 2591 reveal a large abundance of co , a molecule known to be enhanced by far uv ( fuv ) and x - ray irradiation . in chemical models assuming a spherically symmetric envelope , the volume of gas irradiated by protostellar fuv radiation is very small due to the high extinction by dust . , fuv photons can escape through an outflow region and irradiate gas at the border to the envelope . thus , we introduce the first 2d axi - symmetric chemical model of the envelope of a high - mass star forming region to explain the co observations as a prototypical fuv tracer . a grid of precalculated chemical abundances , introduced in the first part of this series of papers , is used to quickly interpolate chemical abundances . single - dish and interferometric observations are simulated and the model results are compared to published and new jcmt and sma observations . the two - dimensional model of afgl 2591 is able to reproduce the jcmt single - dish observations and also explains the non - detection by the sma .

observations of the high - mass star forming region afgl 2591 reveal a large abundance of co , a molecule known to be enhanced by far uv ( fuv ) and x - ray irradiation . in chemical models assuming a spherically symmetric envelope , the volume of gas irradiated by protostellar fuv radiation is very small due to the high extinction by dust . the abundance of co is thus underpredicted by orders of magnitude . in a more realistic model , fuv photons can escape through an outflow region and irradiate gas at the border to the envelope . thus , we introduce the first 2d axi - symmetric chemical model of the envelope of a high - mass star forming region to explain the co observations as a prototypical fuv tracer . the model assumes an axi - symmetric power - law density structure with a cavity due to the outflow . the local fuv flux is calculated by a monte carlo radiative transfer code taking scattering on dust into account . a grid of precalculated chemical abundances , introduced in the first part of this series of papers , is used to quickly interpolate chemical abundances . this approach allows to calculate the temperature structure of the fuv heated outflow walls self - consistently with the chemistry . + synthetic maps of the line flux are calculated using a raytracer code . single - dish and interferometric observations are simulated and the model results are compared to published and new jcmt and sma observations . the two - dimensional model of afgl 2591 is able to reproduce the jcmt single - dish observations and also explains the non - detection by the sma . we conclude that the observed co line flux and its narrow width can be interpreted by emission from the warm and dense outflow walls irradiated by protostellar fuv radiation .

astro-ph0203041

c

the early evolution ( within @xmath341 days ) of the light curves of sn 1999el indicates that this is one of the most rapidly declining type iin sn among those studied so far . it is useful to compare its features with those of sn 1998s , the other recent and extensively observed type iin sn ( fassia et al . 2000 ) . in the @xmath182 band , sn 1999el exhibits a luminosity decrease even faster than that of sn 1998s and is more similar to a type ii linear sn than to previously studied type iin sne , such as sn 1998z or sn 1997ab . the light curves at various wavelengths of sn 1999el , with their steep decline , are closer to those of sne 1994aj ( benetti et al . 1999 ) and 1996l ( benetti et al . 1998 ) than to that of sn 1995 g ( pastorello et al . 2002 ) , whose spectrum is on the contrary very similar to that of sn 1999el , as noted in sect . [ spec : res ] . therefore , the indication of interaction with the csm arising from the spectrum is not supported by the rapidly declining light curve . consequently , type iin sne seem to embrace a wide range of characteristics . therefore the differences between sn 1999el and sn 1998s are worth noting . it appears that the sn 1998s lcs attain a maximum in the nir some days after those in the optical bands ( however , the precise times of occurrence for the optical maxima are uncertain since measurements appear to have begun when the optical light curve had already started declining ) . conversely , in the case of sn 1999elthe maximum emission in the nir @xmath43 and @xmath44 bands occurs before that in the optical bands , whose maxima almost coincide with that in the nir @xmath42 band . the exact time of maxima at @xmath43 and @xmath44 bands is uncertain but they seem to have occurred some time before the beginning of our observations . the differences may be appreciated by looking at the color curves shown in fig . [ f : fig3 ] . as previously noted , the evolution of @xmath161 and @xmath162 for sn 1999el exhibits an early appearance of a nir excess ( around day 5 ) and a nir blueing effect in the first @xmath163 days . this seems observationally well established , since here the nir lcs sample the sn when it was much brighter than the nearby sources c2 and c3 ( see fig . [ gal : sn ] ) , and thus are easily measurable even though sometimes only partially resolved on swircam images . although maxima at nir wavelengths do appear to have been missed for sn 1998s , nevertheless there is no evidence for an early blueing effect in this case . furthermore , a nir excess from sn 1998s is not apparent at early epochs . one possible origin of the quoted differences , in particular of the early nir excess may be due to an ir echo from pre - existing dust in the vicinity of sn 1999elnot evaporated at the moment of the shock outburst . this would suggest that dust clumps near sn 1999el are distributed differently than those near sn 1998s which may be devoid of nearby dust entirely . for sn 1998s this is supported by leonard et al . ( 2000 ) whose spectroscopic observations suggest that the progenitor of sn 1998s underwent a major mass - loss episode that ended some 60 years before the explosion , followed by a weaker scarcely detectable mass - loss activity in the last seven years before the explosion . if a mass - loss wind associated with the sn 1999el progenitor had not ceased at the time of explosion , the density of the csm around it would be much larger than in the case of sn 1998s . in the above scenario , the interaction of the uv flash with the csm around sn 1999el would have led to heating , destruction and sublimation of dust . the extent of the region where grain sublimation and destruction can occur may be estimated as ( see , e. g. , waxman & draine 2000 ) @xmath342 where @xmath343 is the grain absorption efficiency at uv wavelengths , @xmath344 the maximum luminosity in the range 17.5 ev in units of @xmath345 erg s@xmath1 ( optical - uv flash ) and @xmath346 the mean size of grains in units of @xmath347 @xmath13 m . assuming @xmath348 and @xmath349 , @xmath350 cm is obtained for a maximum luminosity of @xmath351 erg s@xmath1 ( the greatest value indicated in table [ lboltab ] ) , a distance which is two orders of magnitude larger than the largest photospheric radius attained by the supernova ( see table [ lboltab ] ) , but also somewhat greater than the estimate based on the occurrence of the nir excess very early ( see sect . [ lc : d ] ) . since the grain distruction and sublimation due to the uv flash imply also the unlocking of fe ions ( if they exist in the dust ) , we have been tempted to ascribe the early 45 days blueing to [ feii ] line emission . the [ feii ] lines which may affect @xmath42 and @xmath43 bands result from the transitions involving metastable levels @xmath352d@xmath353@xmath354d@xmath355 ( @xmath356 @xmath13 m , a@xmath357 s@xmath1 ) and @xmath354f@xmath353@xmath352d@xmath355 ( @xmath358 @xmath13 m , a@xmath359 s@xmath1 ) , collisionally excited by free electrons ( see mouri , kawara , & taniguchi 2000 , and references therein ) . very large line integrated fluxes ( up to 0.51 times the continuum flux integrated on the @xmath44 band ; see fig . [ f : cc ] ) would be required to produce the observed changes in colors , indicating that [ feii ] lines alone can not account for it . in addition , since relative luminosity of the main [ feii ] lines in the j and h windows is constant , the contribution of this mechanism to the color evolution is definitively ruled out . if the early ir excess of sn 1999el is due to the presence of a csm generated by a continuous wind of the progenitor star , it might be reasonable to expect its signature in the optical light curves . this seems not to be the case . roscherr and schaefer ( 2000 ) analysed theoretically the modifications of optical lcs supernovae produced by echo processes . they assume spherical symmetry for the dust and find that critical parameters are @xmath360 , @xmath361 and @xmath362 , where @xmath360 and @xmath361 are the inner and outer radii of the dust shell and @xmath362 the optical depth in the @xmath16 band for a purely radial photon trajectory , a quantity directly related with the total mass of dust . roscherr and schaefer ( 2000 ) find that , in the case of thick shells , @xmath362 is the more sensitive parameter . changes in @xmath362 effect changes in the luminosity of light maxima in various bands whose amounts depend on the wavelength range . even the time at which the light maximum is attained may be shifted ( by up to several days ; roscherr , private communication ) according to its wavelength . unfortunately , these computations do not address the nir bands . the decline rate is also strongly affected by changes in @xmath362 at levels once again dependent on wavelength . in this respect a relevant parameter is the @xmath363 index which corresponds to the luminosity drop in 100 days in the @xmath182 band . therefore the @xmath363 index can provide information on the presence of a csm around the sn . observational data provide a value of @xmath363 greater than 4 mag for both sn 1999el and 1998s . a comparison with the theoretical results quoted above suggests the surprising result that the expected amount of dust surrounding both sn 1999el and sn 1998s should be vanishingly small . ( or that almost all the pre - existing dust is evaporated at the moment of the uv flash ) . for sn 1999el this result is in contrast with the suggestion that the early ir excess is due to an ir echo caused by near - by dust . we suggest that the failure of the @xmath363 index to display the presence of csm around sn 1999el may be ascribed to the assumption made to derive theoretically this index , namely the assumption of spherically distributed dust . the theoretical results of emmering and chevalier ( 1988 ) on the ir echo light originated by an asymmetric csm distribution around a sn progenitor clearly illustrate how many parameters influence the observed results . indeed they find that ir light curves can substantially change by varying the geometrical properties of a given non - spherical ( but still axi - symmetric ) csm distribution and/or its orientation relative to the line of sight . even if not explicitly accounted for in their work it can be nevertheless deduced that additional parameters , such as a non - radial density profile of the dust , play an additional pivotal role . we intend in the future to provide a tentative model of the dust distribution around sn 1999el . finally we note that both for sn 1998s ( fassia et al . 2000 ) and sn 1999el the observations do not rule out a scenario of dust formation after the explosion . in the case of sn 1999elan occurrence like this would imply that the signature of dust appears both at early and also at late stages . in particular , for sn 1999el assuming a@xmath169 @xmath364 mag , the dereddened @xmath44 magnitude on jd+691 ( see table [ nir : phot ] ) yields an observed flux of @xmath365 erg @xmath171 s@xmath1 @xmath13m@xmath1 . as in sect . [ lc : d ] , we can determine the radius of a blackbody - emitting surface for a temperature of 1500 k , which is roughly the sublimation temperature for dust grains . this amounts to @xmath366 cm , of the order of the largest photospheric radius attained ( see table [ lboltab ] ) , a distance that might be covered by dust formed in the ejecta moving with a velocity @xmath367 km s@xmath1 . therefore the scenario we propose embraces the evolution of the progenitor star in that cold , high - luminosity , mass loss from evolved massive stars may proceed in episodes with asymmetric distributions . it is however conceivable that single mass - loss episodes are not completely stochastic in duration , periodicity and intensity . over long temporal intervals , possibly covering several cycles of activity , it is possible to define mean wind properties , such as , for example , the dependence of the mean mass - loss rate on the main structural parameters such as temperature and luminosity . if the sn explosion occurs during a long pause in mass - loss we observe a normal type ii sn , otherwise the typical features of the type iin sne will appear with varying degrees of visibility .

spectroscopic observations are also discussed . using as a distance calibrator the type ia sn 2000e , which occurred some months later in the same galaxy , and fitting a blackbody law to the photometric data we obtain a maximum bolometric luminosity for sn 1999el of erg s . in general , the photometric properties of sn 1999el are very similar to those of sn 1998s , a bright and well studied type iin sn , showing a fast decline in all observed bands similar to those of type ii - l sne . the differences with sn 1998s are analyzed and ascribed to the differences in a pre - existing circumstellar envelope in which dust was already present at the moment of the sn outburst . we infer that light echoes may play a possibly significant role in affecting the observed properties of the light curves , although improved theoretical models are needed to account for the data . we conclude that mass loss in the progenitor rg stars is episodic and occurs in an asymmetric way . this implies that collapsing massive stars appear as normal type ii sn if this occurs far from major mass loss episodes , whereas they appear as type iin sne if a large mass loss episode is in progress .

optical and near - infrared light curves of the type iin supernova 1999el in ngc 6951 are presented . a period of 220 days ( 416 days in the near - infrared ) is covered from the first observation obtained a few days before maximum light . spectroscopic observations are also discussed . using as a distance calibrator the type ia sn 2000e , which occurred some months later in the same galaxy , and fitting a blackbody law to the photometric data we obtain a maximum bolometric luminosity for sn 1999el of erg s . in general , the photometric properties of sn 1999el are very similar to those of sn 1998s , a bright and well studied type iin sn , showing a fast decline in all observed bands similar to those of type ii - l sne . the differences with sn 1998s are analyzed and ascribed to the differences in a pre - existing circumstellar envelope in which dust was already present at the moment of the sn outburst . we infer that light echoes may play a possibly significant role in affecting the observed properties of the light curves , although improved theoretical models are needed to account for the data . we conclude that mass loss in the progenitor rg stars is episodic and occurs in an asymmetric way . this implies that collapsing massive stars appear as normal type ii sn if this occurs far from major mass loss episodes , whereas they appear as type iin sne if a large mass loss episode is in progress . [ firstpage ]

astro-ph0410065

i

in rich clusters of galaxies , virial mass estimates agree well with independent determinations of the cluster mass made from the x - ray flux of hot intracluster gas , and from weak gravitational lensing effects . a typical ratio of the total mass - to - blue luminosity for rich clusters , @xmath9 , extrapolated over the whole volume of the universe , yields the mean density of matter @xmath100.25 , in the excellent concordance with parameters of the standard @xmath11cdm model : @xmath6 = 0.27 , @xmath12 = 0.73 ( spergel et al . 2003 ) . however , about 85% of galaxies are situated outside the rich clusters . roughly a half of them belong to groups of different size and population , while the remaining half are scattered in diffuse ( unvirialized ) `` clouds '' and `` filaments '' usually called the `` field '' . until recently , application of the virial theorem to galaxy groups remained the only way to trace the dark matter distribution on scales of 0.1 1 mpc measurements of the total mass of individual groups via their x - ray flux or weak gravitational lensing have not lead yet to distinct results . in the case of our local group ( lg ) , lynden - bell ( 1981 ) and sandage ( 1986 ) proposed to determine its total mass using a method , which is based on a measurement of the radius of the `` zero - velocity surface '' , @xmath13 , where the overdensity of the group has halted expansion and infall is about to commence . under the assumption of spherical symmetry the total mass of a group can be expressed in terms of the radius @xmath13 , the age of the universe @xmath14 , and the gravitational constant @xmath15 as @xmath16 application of this method to the lg as well to other groups requires accurate distances and radial velocities for all galaxies surrounding a group . such data is now accessible for several nearby groups by using the luminosity of stars at the tip of the red giant branch ( trgb ) as standard candles . over the last 5 years , searches for additional nearby dwarf galaxies , made on the poss - ii & eso / serc plates by karachentseva & karachentsev ( 1998 ; 2000 ) , and also results of `` blind '' hi surveys of the southern sky , and the zone of avoidance by the hipass team ( kilborn et al . 2002 ) , as well as other wide - field sky surveys , lead to a doubling of the population of known galaxies in the local volume . basic observational data on 450 local volume galaxies with distances less than 10 mpc are presented in the catalog of neighboring galaxies ( karachentsev et al . . the new quantity and quality of observational data on nearby galaxy distances and radial velocities allowed us to determine virial and total masses of four of the nearest complexes : milky way+m31 ( karachentsev et al . 2002c ) , m81+ngc2403 ( karachentsev et al . 2002a ) , cena+m83 ( karachentsev et al . 2002b ) , and ic342+maffei ( karachentsev et al . 2003d ) , as well as of two other nearby scattered galaxy systems : m96 = the canes venatici i cloud ( karachentsev et al . 2003a ) and ngc253 = the sculptor filament ( karachentsev et al . below we discuss the results of mass determination for all six nearest groups made via internal and external galaxy motions .

over the last few years , rapid progress has been made in distance measurements for nearby galaxies based on the magnitude of the tip of red giant branch stars . the values of for the virialized groups turn out to be close each other , in the range of 0.9 1.3 mpc . as a result ,

over the last few years , rapid progress has been made in distance measurements for nearby galaxies based on the magnitude of the tip of red giant branch stars . current ccd surveys with hst and large ground- based telescopes bring%-accurate distances for roughly a hundred galaxies within 5 mpc . the new data on distances to galaxies situated in ( and around ) the nearest groups : the local group , m81 group , cena / m83 group , ic342/maffei group , sculptor filament , and canes venatici cloud allowed us to determine their total mass from the radius of the zero- velocity surface , , which separates a group as bound against the homogeneous cosmic expansion . the values of for the virialized groups turn out to be close each other , in the range of 0.9 1.3 mpc . as a result , the total masses of the groups are close to each other , too , yielding total mass - to - blue luminosity ratios of 10 40 . the new total mass estimates are 3 5 times lower than old virial mass estimates of these groups . because about half of galaxies in the local volume belong to such loose groups , the revision of the amount of dark matter ( dm ) leads to a low local density of matter , , which is comparable with the global baryonic fraction , but much lower than the global density of matter , . to remove the discrepancy between the global and local quantities of , we assume the existence of two different dm components : 1 ) compact dark halos around individual galaxies and 2 ) a non - baryonic dark matter `` ocean '' with and , respectively .

0809.2342

c

in summary , we calculated the asymptotic forms of the pair - connection probability , the distributions of the total resistance and fractal masses of the backbone , the red bonds and the shortest , the longest and the average self - avoiding walk between any two points on a cluster . our analysis drew solely on general , structural features of the underlying diagrammatic perturbation theory , and hence our results for the form of the distributions are valid to arbitrary loop order , although the critical exponents featured in these distributions are known only to finite order , of course . the distributions of the transport quantities such as the total resistance or the backbone mass etc . are essentially all of the same form . in this sense , these distributions share a high degree of universality . as far as future directions are concerned , we think it is worthwhile to study the renormalizability - problem for @xmath363 discussed in sec . [ shortdistanceexpansion ] and its implications in more detail . it would be interesting to have field theoretic results for distribution functions in directed and dynamic percolation . also , it would be interesting to see experimental or simulation results for distribution functions in any kind of percolation that might be compared to our results presented here or to future results . we hope that our work stimulates further interest in this subject . see , e.g. , d.j . amit , _ field theory , the renormalization group , and critical phenomena _ ( world scientific , singapore , 1984 ) ; j. zinn - justin , _ quantum field theory and critical phenomena _ ( clarendon , oxford , fourth edition 2002 ) . k.g . wilson , phys . rev . * 179 * , 1499 ( 1969 ) ; l. kadanoff , phys . * 23 * , 1430 ( 1969 ) ; w. zimmermann : in _ lectures on elementary particles and quantum field theory _ , edited by deser , grisaru and pendleton ( mit press , cambridge , mass . , 1970 )

our study includes the pair - connection probability , the distributions of the fractal masses of the backbone , the red bonds and the shortest , the longest and the average self - avoiding walk between any two points on a cluster , as well as the distribution of the total resistance in the random resistor network . our analysis draws solely on general , structural features of the underlying diagrammatic perturbation theory , and hence our main results are valid to arbitrary loop order .

percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions . using renormalized field theory , we determine the asymptotic form of various of such distribution functions in the limits where certain scaling variables become small or large . our study includes the pair - connection probability , the distributions of the fractal masses of the backbone , the red bonds and the shortest , the longest and the average self - avoiding walk between any two points on a cluster , as well as the distribution of the total resistance in the random resistor network . our analysis draws solely on general , structural features of the underlying diagrammatic perturbation theory , and hence our main results are valid to arbitrary loop order .

nucl-th9701032

i

one of the oldest but still most challenging problems of nuclear physics is an adequate description of collective motion at finite excitations . as the prime example one may quote nuclear fission which has attracted the attention of both experimentalists as well as theoreticians since its discovery . to date it is still an open question which type of configurations the system undergoes on its way from the potential minimum over the saddle region down to scission . whereas in the early days those of the compound model were clearly favoured in theoretical pictures , after the discovery of the shell model that of independent particle motion came into fashion more and more . this development was enhanced after computers got fast enough such that hartree - fock type computations could be done in every lab . however , there can be little doubt that this picture fails to describe collective motion at finite excitations where one is compelled almost by experimental evidence that the dynamics shows irreversible behaviour , not only by the very nature of the decay process itself but by the appearance of frictional forces . it is more than questionable that this feature can adequately be met by introducing simple minded collision terms . decent descriptions of fission in terms of the one body density operator most likely require to consider correlations beyond the independent particle picture , together with non - markovian effects . this is a difficult problem in itself , not to mention the computational task of solving this equation of motion for the one body density . for these reasons it may still be interesting and worth while to start from a more phenomenological point of view introducing the shape parameters as collective variables . it is true that in this way again the picture of independent particles will serve as a starting point , in the form of the deformed shell model . however , the latter is simple and flexible enough to allow one considering residual interactions , in one way or other . as we shall see , it may be possible to gain insight into their importance by studying dynamical aspects . likewise , we may be able to get information on the complexity of the configurations which are to be considered . such a task becomes more feasible in case collective motion is sufficiently slow . then one may exploit the quasi - static picture which reduces the complexity of the full problem drastically . under such circumstances one may actually linearize the problem and treat collective motion locally within a harmonic approximation . in this way one may take advantage of the benefits of linear response theory . one of the major problems in theories of this type is to find a decent guess for the relevant macroscopic variables , a problem which is familiar almost from all transport theories . for nuclear fission there exists some kind of guiding principle through the liquid drop model . the latter is known to represent the static energy for temperatures above @xmath8 . since at these temperatures one expects motion to be strongly damped , it will most likely follow somehow the line of steepest decent . possible shapes which a fissioning nucleus may assume on its way to scission have been looked for in @xcite by minimizing the liquid drop energy . this minimization has been done for some realistic energy density functional under the constraint of fixing a parameter which measures the distance between the evolving fragments . incidentally , it is the same parameter which we are going to exploit later on in our approach . it so turns out that the shapes found in this way can be approximated fairly well by the cassini ovaloids introduced to nuclear physics in @xcite . later in @xcite a single particle model has been constructed for such a parameterization of shapes , which was based on the woods - saxon potential . in this paper we are going to use this model for computations of transport coefficients , after some suitable modifications which are necessary to incorporate the effects mentioned above . one of our goals will be to study average motion along the fission path for different temperatures , as it is reflected in the associated transport coefficients of inertia , friction and local stiffness . in this sense the aim of our present work is similar to the one of @xcite , where a two center shell model was used . the latter feature renders the previous model simpler on the computational level . on the other hand , the parameterization of the shape by means of cassini ovaloids opens the possibility of treating more realistic shapes , which are perhaps better suited to describe the later stages of a fission process . furthermore , it is fair to say that the woods - saxon potential may be supposed to resemble more the `` true '' mean field . for cassini ovaloids commonly a few parameters suffice to treat in simple terms a whole variety of realistic shapes including very compact ones as well as strongly deformed ones with a well developed neck , or even those corresponding to separated fragments . in this sense this parameterization may be considered superior to expansions in terms of spherical harmonics ( see @xcite ) . in the ideal case one would then be able to compute transport tensors for all the parameters , the collective degrees of freedom , one claims to be relevant . this is a tremendous task and so far has been carried through only for a two dimensional model @xcite , without utilizing though the full microscopic potential of linear response theory . in this paper we want to restrict ourselves to the one dimensional case . the main reason for that is found , of course , in the simplification one gains by this restriction . however , it may be said that at present most of the applications of macroscopic equations of motion to fission at finite excitation adhere to a similar confinement , see e.g. @xcite - @xcite . evidently one then needs to rely on the `` right '' guess of the fission path . as said before and for arguments given there we presume it to be represented well enough by the line along the valley of the static energy . possible improvements have to be left for future studies .

previous computations of the potential landscape with the shapes parameterized in terms of cassini ovaloids are extended to collective dynamics at finite excitations . taking fission as the most demanding example of large scale collective motion , transport coefficients are evaluated along a fission path . their expressions are formulated within a locally harmonic approximation and the help of linear response theory . special attention is paid to an appropriate definition of the deformation of the nuclear density and its relation to that of the single particle potential . for temperatures above also friction exhibits large fluctuations along the fission path for small excitations .

previous computations of the potential landscape with the shapes parameterized in terms of cassini ovaloids are extended to collective dynamics at finite excitations . taking fission as the most demanding example of large scale collective motion , transport coefficients are evaluated along a fission path . we concentrate on those for average motion , namely stiffness , friction and inertia . their expressions are formulated within a locally harmonic approximation and the help of linear response theory . different approximations are examined and comparisons are made both with previous studies , which involved different descriptions of single particle dynamics , as well as with macroscopic models . special attention is paid to an appropriate definition of the deformation of the nuclear density and its relation to that of the single particle potential . for temperatures above the inertia agrees with that of irrotational flow to less than a factor of two , but shows larger deviations below , in particular in its dependence on the shape . also friction exhibits large fluctuations along the fission path for small excitations . they get smoothed out above where attains values in the range of the wall formula . for the inverse relaxation time turns out to be rather insensitive to the shape and increases with . addtoresetequationsection pacs numbers : 21.60.ev , 21.60.cs , 24.10pa , 24.75+i * to appear in prc *

astro-ph0610205

i

to date , seven papers have been published providing listings and finding charts for faint uv - bright sources identified on plates from the sandage two - color survey of the galactic plane . the most recently published paper , paper vii ( @xcite ) , included proper motions for many of the sources found using information extracted from the usno - b1.0 catalog @xcite . the combination of the magnitude , color and proper motion values available for these sources provides important additional data that may lead to the detection of previously unidentified white dwarfs . the usno - b1.0 catalogue was not available prior to publication of paper vii . therefore , it was considered worthwhile to go back and examine all previously identified lanning uv - bright sources in hopes of finding additional evidence to identify the best candidates for new white dwarfs in the published catalogues . as noted in the previous papers devoted to this survey project , the sandage two - color survey consists of more than 100 plates measuring 6.6 degrees on a side and centered on the galactic plane . plates were double - exposed with one image taken in the uv and the second image in the blue separated by 12 arcseconds . while the original goal of the sandage project was to identify the optical counterparts to x - ray sources found by the x - ray satellite , the uv - bright sources found during this analysis do not necessarily correspond to previously discovered x - ray sources . they do represent a comprehensive survey of the entire 43 square degree field on each schmidt plate examined .

proper motions with values mas yr or mas yr have been extracted from the usno - b1.0 and tycho ii catalogues for all lanning uv - bright sources identified in the sandage two - color survey of the galactic plane and presented in papers i - vi . of the 572 sources examined , we find at least 213 which exhibit a significantly large proper motion . based on the location of the sources in a reduced proper motion diagram , we demonstrate that about two thirds of the high proper motion sources are likely or very likely to be heretofore unidentified white dwarfs .

proper motions with values mas yr or mas yr have been extracted from the usno - b1.0 and tycho ii catalogues for all lanning uv - bright sources identified in the sandage two - color survey of the galactic plane and presented in papers i - vi . of the 572 sources examined , we find at least 213 which exhibit a significantly large proper motion . based on the location of the sources in a reduced proper motion diagram , we demonstrate that about two thirds of the high proper motion sources are likely or very likely to be heretofore unidentified white dwarfs .

q-bio0603014

i

critical to understanding how information is processed in the brain is the form of the neural coding that underlies the storage and recall of memories . is there a local , or gnostic @xcite , code colloquially called a grandmother - cell ( gm - cell ) representation in which the firing of a single neuron ( or group of neurons ) exclusively codes recognition of a particular object , person or memory ? or is the code much more distributed ? although it is generally accepted [ e.g. , @xcite ] that gm representations are not used in reality , experiments @xcite often find localist responses by individual neurons . most dramatically , @xcite have recently found many neurons in humans that , within the limits of the measurements , behave like classic gm cells . in this paper , we therefore quantitatively re - examine the viability of gm - cell representations , with the outcome that we refute the standard quantitative arguments against them , both theoretical and phenomenological . the information - theoretic argument is that gm representations need far too many neurons for the information coded @xcite . we show that this argument fails when one examines the information storage capacity of the synapses rather than the representational capacity of neurons for input stimuli . the standard efficiency argument applies only to the input representation , needed to represent any of the myriad possible stimuli . for storage , a gm representation can be optimally efficient . the phenomenological argument is that gm cells should fire in response to a much smaller fraction of stimuli than has been deduced from measurements of neural responses @xcite . a gm cell can be regarded as a categorizer , and the data appear to imply that any apparent gm cell responds to many categories of stimuli rather than to one category . however , our information theoretic argument shows that associated with any gm - cell population , with its ultra - low sparsity , is a more conventional population with a much higher sparsity . this two - population property , always a part of the gm - cell idea @xcite , was not allowed for in older analyses , including that @xcite by the group responsible for the new data @xcite . we devise a very general method of analyzing neural systems with multiple sparsities , and apply it to the data of @xcite . it enables us to quantify the biases against experimental detection of gm - like cells , most of which simply appear as unreported silent cells , and whose estimated numbers @xcite may be a factor of 30 more than the reported cells . we find that the two - population property holds , and that less than @xmath1 of _ detected _ cells are in the distributed - code population : the vast majority of the cells can be gm - like . then we find that the number of categories coded by the gm - like cells can be @xmath0 or more . uncertainties are minor relative to the orders of magnitude involved . the data of @xcite therefore appear in strong quantitative agreement with the gm - cell hypothesis . the biases against detecting gm cells are enough to allow consistency with previous @xcite measurements and analyses that use a single - population model and that quantitatively argued against gm cells . we will examine other arguments against gm representations in the discussion section .

quian quiroga et al . [ nature * 435 * , 1102 ( 2005 ) ] have recently discovered neurons that appear to have the characteristics of grandmother ( gm ) cells . here we quantitatively assess the compatibility of their data with the gm - cell hypothesis . we quantify the strong biases against detection of gm cells , and show consistency of our results with previous measurements that find only distributed coding . and neural representations ; grandmother cells ; distributed coding ;

quian quiroga et al . [ nature * 435 * , 1102 ( 2005 ) ] have recently discovered neurons that appear to have the characteristics of grandmother ( gm ) cells . here we quantitatively assess the compatibility of their data with the gm - cell hypothesis . we show that , contrary to the general impression , a gm - cell representation can be information - theoretically efficient , but that it must be accompanied by cells giving a distributed coding of the input . we present a general method to deduce the sparsity distribution of the whole neuronal population from a sample , and use it to show there are two populations of cells : a distributed - code population of less than about 5% of the cells , and a much more sparsely responding population of putative gm cells . with an allowance for the number of undetected silent cells , we find that the putative gm cells can code for or more categories , sufficient for them to be classic gm cells , or to be gm - like cells coding for memories . we quantify the strong biases against detection of gm cells , and show consistency of our results with previous measurements that find only distributed coding . we discuss the consequences for the architecture of neural systems and synaptic connectivity , and for the statistics of neural firing . and neural representations ; grandmother cells ; distributed coding ;

q-bio0603014

c

the results of @xcite clearly suggest the detection of grandmother cells in the classic sense . many other experiments have detected individual cells with strikingly specific responses ( e.g. , @xcite ) . therefore it is useful to hypothesize that some of these cells are indeed gm - like cells , even though the concept of gm - cell may need to be extended and modified . a purely experimental direct test of the idea needs too many stimuli to be practical , cf . so other arguments must be brought in , of which we have provided two . one uses an estimate of the actual storage requirements for a memory system . we showed that gm systems can be optimally efficient in the use of synapses and neurons . the usual efficiency argument applies only to the input representation , but now carries the implication that in a gm - like system there must be two populations of cells with widely different sparsities . our second argument is a method to analyze neural responses . a particular aim is to measure whether they are quantitatively consistent there being separate neurons coding for each recognized person , or , alternatively , for each individual declarative memory . our method enables one to determine whether or not individual cells necessarily code for multiple persons or memories . we derived a general formula eq . ( [ eq : binomial.combo ] ) for the neural responses in terms of an underlying distribution of sparsity . our expansion is a new result and is applicable independently of any detailed theory or model of neural function . in effect , the formula enables us to extrapolate from limited data to obtain the fraction to stimuli to which cells respond . it also allows us to compensate for the strong biases involved in detecting cells when sparsities differ by very large factors . thus we obtain valid estimates of the numbers of cells of different kinds . we thereby solve some of the issues raised by @xcite concerning the publication of data only about responsive cells . one primary remaining bias is that different neurons may have different electrical characteristics , with a consequent different maximum distance from the electrodes for detectability of spikes . but this is presumably a milder effect than that caused by orders of magnitude differences in sparsities . from the data we find indeed that the two - population property is obeyed . not only does the ultra - low - sparsity population comprise the vast majority of cells in the brain regions concerned ( hippocampus , etc ) , but its sparsity can be in a range compatible with the hypothesis of a gm - like system : roughly @xmath84 with a repertoire of @xmath0 . an important role is played by the many silent cells . it is obviously unreasonable to assume they have no function . but on the gm - cell hypothesis they naturally are to be interpreted as the majority of gm cells that are not relevant to the particular stimuli used in an experiment . the large number of these cells is what enables one to overcome the strong biases against detecting a response of any one gm cell to a limited set of stimuli . now the group responsible for the analyzed data argue @xcite that their data do not support the gm cell idea . in @xcite , they say `` if we assume that a typical adult recognizes between 10,000 and 30,000 discrete objects ( biederman , 1987 ) , @xmath85 implies that each neuron fires in response to 50 150 distinct representations . '' [ @xmath86 should be replaced by @xmath60 in the notation of the present paper . ] however their analysis assumed a single value of sparsity . while this is a suitable approximation for conventional mechanisms of distributed memory , it is very bad for gm - like systems . even though the explicit aim of @xcite was to test the gm - cell hypothesis , the use of a single sparsity in effect imposed an assumption that the hypothesis is wrong . we showed that the single - population hypothesis is a bad fit to the data . since our expansion ( [ eq : binomial.combo ] ) is very general , the fault is in the single - population hypothesis not in any assumption about neural properties . the rather low value of sparsity given by waydo et al . is merely a compromise between the widely different sparsities of the two populations . our results are consistent with an even higher number of recognized objects than in the estimates of @xcite . indeed , even _ without _ allowing for the silent cell correction , our fits allow a gm - cell population with a sparsity of @xmath87 corresponding to a number of objects not far from the lower edge of biederman s range . note that our basic estimate of the number of categories , @xmath0 , assumes that the cells are classic gm cells , each responding to a single individual person . but the number of categories could be substantially higher . if the cells are general memory cells , in the style of the model of @xcite , they could respond to images of several people . it could also be that more familiar stimuli , with richer associations , have more cells . in that case measurements with familiar stimuli , as is the case in the data , would be biased towards these memories with unusually large numbers of cells , with a corresponding reduction in our estimate of the number of categories compared with the true number . in gm systems , like the model of @xcite , the number of gm cells is very much larger than that of the input cells , as is consistent with the numbers we have deduced . an immediate implication is that each gm cell receives input from a modest number of input cells , but that each input cell sends output to a much larger number of memory cells . given also our finding that the gm cells in the relevant regions are in the vast majority , there are some striking anatomical implications . in fact striking disparities in synapse number are well known in the hippocampus @xcite : for example , each ca3 pyramidal cell gets about 50 input synapses from dentate granule cells , while other connections have tens of thousands of synapses . note that hippocampal neurogenesis results in dentate granule cells , highly appropriate if they are gm - like . however , general - purpose memories need a wider variety of ( processed ) input than does a face recognition system , and hippocampal - related regions are sufficiently complex that the real picture is undoubtedly much more complicated . even so , a careful analysis of the disparities in synapse number should provide critical information on neural function and the viability of gm - like systems . other less quantitative arguments have been advanced against the reality of gm systems , e.g. , @xcite . for example , distributed memory systems are said to be robust against partial destruction , since there is no single location for a single memories . but we do know that memories disappear . if there are multiple gm cells for a memory in different places , then we can overcome the robustness argument by simple redundancy . moreover memories form a network of knowledge , so that individual items of semantic memory can be readily reconstructed from other knowledge . episodic memory is really an ordered sequence of individual episodes , not necessarily remembered at all precisely . any one episode that disappears can be approximately filled in from neighboring episodes . distributed memory systems are also said to be good at filling in missing parts of input data , as in reconstructing a full remembered image from a stimulus containing only a part of the image . but this property can also be true for gm - like systems . for example , when the bmw architecture @xcite is used with a sparse input representation and suitable dynamics for its gm cells , it also performs pattern completion ; the completion property is actually associated with properties of sparse representations used for input data . it has been said that new memories are harder to construct in gm systems than in distributed - memory systems . but now that adult neurogenesis in the hippocampus is well established , it may well be that there is actually a pool of new neurons available for at least some uses that could include being gm - like cells for new memories . the new neuron rate may however be excessively small . in addition , it is possible that the gm nodes are on dendritic tree rather than being whole neurons . it is known that there can be substantial changes in dendritic topology , which could easily include the formation of new nodes . here the fundamental mode of operation is of a gm - like system while the neural code of memory neurons takes on some of the aspects of distributed memory . in any case , there are potential realistic mechanisms for the formation of new gm nodes , so that there is no insuperable obstacle here .

we present a general method to deduce the sparsity distribution of the whole neuronal population from a sample , and use it to show there are two populations of cells : a distributed - code population of less than about 5% of the cells , and a much more sparsely responding population of putative gm cells . with an allowance for the number of undetected silent cells ,

quian quiroga et al . [ nature * 435 * , 1102 ( 2005 ) ] have recently discovered neurons that appear to have the characteristics of grandmother ( gm ) cells . here we quantitatively assess the compatibility of their data with the gm - cell hypothesis . we show that , contrary to the general impression , a gm - cell representation can be information - theoretically efficient , but that it must be accompanied by cells giving a distributed coding of the input . we present a general method to deduce the sparsity distribution of the whole neuronal population from a sample , and use it to show there are two populations of cells : a distributed - code population of less than about 5% of the cells , and a much more sparsely responding population of putative gm cells . with an allowance for the number of undetected silent cells , we find that the putative gm cells can code for or more categories , sufficient for them to be classic gm cells , or to be gm - like cells coding for memories . we quantify the strong biases against detection of gm cells , and show consistency of our results with previous measurements that find only distributed coding . we discuss the consequences for the architecture of neural systems and synaptic connectivity , and for the statistics of neural firing . and neural representations ; grandmother cells ; distributed coding ;

astro-ph0601716

i

the current generation of ground - based interferometers , such as the palomar testbed interferometer ( pti ) @xcite , the naval prototype optical interferometer ( npoi)@xcite , the infrared optical telescope array ( iota3)@xcite , and the center for high angular resolution in astronomy ( chara ) array @xcite , is advancing stellar astronomy in a number of ways . @xcite , for example , reviewed the state of optical and infrared interferometry . one direction of progress is the increasing number of spectroscopic binaries that are being resolved as visual binaries . this allows the determination of their three - dimensional orbits and the derivation of accurate masses for the component stars and distances to the systems , distances that in many cases are more accurate than those from the _ hipparcos _ satellite . in recognition of this development we have started a program to determine substantially improved spectroscopic orbits for bright , field spectroscopic binaries . the program has two benefits : the provision of new radial velocities and spectroscopic orbits of a quality that matches or exceeds the prospective interferometric observations and , for some binaries , the detection of the secondary spectrum and measurement of secondary radial velocities for the first time . we now briefly consider these two points in turn . while some interferometric studies , such as that of 12 boo @xcite , include complementary new radial velocities , the usual practise is to take the radial velocities for the binary concerned from the literature . the precision of such velocities often falls short of that needed to match the interferometric observations . for example , in their recent determination of the three - dimensional orbit of the bright spectroscopic binary @xmath17 psc , @xcite had to complement their interferometric measurements with radial velocities observed in 1944 and 1945 @xcite . their resulting best - fit solution for the three - dimensional orbit has rms velocity residuals of 4.8 and 3.6 km s@xmath13 for the primary and secondary , respectively . orbits with large velocity residuals are not exceptional because of the generally lower resolution and low signal - to - noise ratio of spectra obtained in the first roughly three - quarters of the twentieth century , for example , of the first 100 systems in the _ eighth catalogue of the orbital elements of spectroscopic binaries _ @xcite , 63 have orbits that were published in 1980 or earlier and 24 have orbits that were published in 1950 or earlier , long before the advent of radial velocity spectrometers and charge - coupled device detectors , which can produce spectra with very high signal - to - noise ratios . similar proportions must apply for all 1469 systems in the catalogue . while these proportions will have improved as a result of the substantial number of new spectroscopic binary orbits that have been published since 1989 @xcite , most such orbits are for newly discovered binaries . with respect to the detection of the secondary spectrum , we note that without secondary radial velocities and a determination of the secondary s spectroscopic orbit , the linear separation between the binary components is unknown and the determination of the three - dimensional orbit is incomplete . increasing the pool of double - lined spectroscopic binaries ( sb2s ) thus increases the number of spectroscopic binaries available for fruitful interferometric observation . in addition , binary systems with components of significantly different masses provide the greatest constraints on evolutionary models . considering that the majority of spectroscopic binaries are single - lined spectroscopic binaries ( sb1s ) , there is ample opportunity here . @xcite , for example , found that two - thirds of the spectroscopic binaries in their _ ninth catalogue _ ( there is no reason to think the catalogue s incompleteness affects this statistic much . ) our program uses new , high - resolution , red - wavelength spectra obtained with the 2.1 m telescope at mcdonald observatory of the university of texas and the coud feed telescope at kitt peak national observatory ( kpno ) . @xcite provided a preliminary description of our program and an initial list of observed stars , which has now been expanded to over 40 systems . these come primarily from a sample of 130 candidate systems obtained by searching the _ eighth catalogue _ for sb2 systems that could profit from renewed spectroscopic observation and sb1 systems with large enough mass functions to suggest that high signal - to - noise ratio spectra might transform them into sb2 systems ( e.g. , * ? ? ? the stars are north of @xmath1840 in declination and generally brighter than @xmath19 mag . others have also seen the need for improved radial velocities for spectroscopic binaries . for example , @xcite has successfully applied the iodine absorption - cell method for determining very precise radial velocities to the measurement of radial velocities of _ both _ components in sb2s . hitherto , this technique , which uses an iodine absorption cell to impose a reference spectrum on the stellar spectrum and is notable for its use in the discovery of extrasolar planets , has been restricted to the radial velocities of single stars or stars with companions of insignificant relative brightness . his pioneering investigation , which was carried out on the keck i telescope with the hires spectrograph , was limited to five objects including a radial - velocity standard and two sb2s . among the latter was 64 psc ( hd 4676 ) , a well - known , bright spectroscopic binary ( f8v , @xmath20 days ) with a three - dimensional orbit determined by @xcite , using their own interferometric observations made with pti and radial velocities from @xcite . konacki s combined fit of his new radial velocities and the @xcite interferometric data leads to better - determined orbital and physical parameters for 64 psc . in particular , the rms velocity residual of 24 m s@xmath13 , determined from his new fit , is a striking improvement compared to the rms residual of 810 m s@xmath13 ( average @xmath21 m s@xmath13 ) given by @xcite for their radial - velocity solution . our new velocities are not as precise as the iodine - cell velocities from the keck i telescope we will see that for 12 boo , which has a similar spectral type to 64 psc , the rms residual for our velocities is 110 m s@xmath13 but their quality is still a good match with that of current interferometric observations . there is thus ample opportunity for radial velocities from small and medium - sized telescopes , measured by traditional methods , to make a worthwhile contribution . here we report new orbit determinations for three bright spectroscopic binaries , rr lyn , 12 boo , and hr 6169 . analysis of our new velocities provides significant improvements in the orbital elements of the systems . indeed , in the case of hr 6169 some of the revisions are substantial . table 1 gives basic data for the systems ; all three are known sb2s , have orbital periods near 10 days , and eccentric orbits . we now briefly look at each system individually . rr lyn has long been known as both an eclipsing and spectroscopic binary . its orbit has a period of 9.95 days and a modest eccentricity , @xmath22 . the star s peculiar abundances are indicated in its metallic - lined spectral classification , which reflects primarily the spectral type of the primary . @xcite classified it as a3/a8/a6 , based on its ca ii k line , its hydrogen balmer lines , and its metallic lines , respectively , while @xcite called the hydrogen lines a7 and the metallic lines f0 . @xcite compared the two components with evolutionary tracks and also used their photoelectric photometry on the @xmath23 system @xcite to place the components of rr lyn in a @xmath24 diagram . from those results they estimated individual spectral types of a6 iv for the primary and f0 v for the secondary . thus , the primary has already begun to leave the main sequence , while the secondary is still ensconced within it . the metallic - line status of the primary is not in doubt @xcite , while that of the secondary remains uncertain , although the abundances of @xcite indicate possible metallicism . @xcite published the first spectroscopic orbit . more recent , but now quite old orbits were published by @xcite and @xcite . kondo s orbit has the advantages that it sampled the primary and secondary radial velocity curves more fully than popper s and that it has a single systemic velocity , while popper determined different systemic velocities for the primary and secondary . photoelectric light curves of rr lyn have been reported by @xcite , @xcite , @xcite , @xcite , @xcite , and @xcite . the last of these studies used precise photometry in the @xmath25 and @xmath26 bandpasses @xcite , which are based on but somewhat different from the johnson @xmath27 and @xmath26 photometric bandpasses . @xcite showed that the primary and secondary eclipse depths in @xmath4 are @xmath28 and @xmath29 , respectively , the fractional luminosities , also in @xmath4 , are @xmath30 , @xmath31 , and the orbital inclination is @xmath32 . both @xcite and @xcite needed the addition of third light to solve the light curves , while @xcite , who also did a photometric analysis , found no requirement for third light . this last result is supported by @xcite , who demonstrated that their observations in all filters are fitted by the same geometry and that their model matches the observations without any need to invoke third light . in a later paper , however , @xcite presented new evidence for a third body , based _ not _ on an analysis of the light curve , but on the times of the eclipse minima . the presence of the third star , which @xcite suggested is a very low - mass , low - luminosity object that contributes an insignificant amount of light to the system , is inferred from quasi - periodic oscillations in the times of primary and secondary minima . they proposed an extemely eccentric orbit ( @xmath33 ) with a rather long orbital period of @xmath34 years for it . the 64-year timespan of the published photoelectric minima amounts to only one - and - a - half orbital periods , however , so the case for the third body can not yet be regarded as conclusive . the sb2 system 12 boo is the only one in our trio that already has a determination of its three - dimensional orbit @xcite . the two components have an orbital period of 9.60 days and are of very similar mass , having a secondary to primary mass ratio of 0.97 . the system s combined spectral type is f8 iv @xcite or f8 v @xcite . @xcite found that the primary is leaving the main sequence , and with @xmath35 k it is now marginally _ cooler _ than the secondary ( @xmath36 k ) . @xcite was the first to determine its spectroscopic orbit . newer orbital elements have been published by @xcite and @xcite . @xcite presented the newest set of radial velocities as well as interferometric observations . details for these more recent spectroscopic orbits , including the present investigation , are summarised in table 2 . prior to its publication , we were unaware of the new investigation of 12 boo by @xcite . thus , in spite of the element of ( unintentional ) redundancy here , our own study of 12 boo , based on radial velocities acquired from 2002 to 2005 , is still of interest because our velocities turn out to be significantly more precise , allowing us to determine improved spectroscopic orbital elements . compared to rr lyn and 12 boo , the previous work on hr 6169 has been quite modest . this binary has a combined spectral type of a2 v @xcite or a1 iv @xcite . the first and , to date , only spectroscopic orbit is that of @xcite , which was based on radial velocities from blue photographic spectrograms obtained at the cassegrain focus of the 1.8 m telescope at the dominion astrophysical observatory ( dao ) . this sb2 system has an orbit with a period of 10.56 days and a moderate eccentricity , @xmath37 .

radial velocities from the 2.1 m telescope at mcdonald observatory supplemented with radial velocities from the coud feed telescope at kpno provide new precise orbits for the double - lined spectroscopic binaries rr lyn ( a3/a8/a6 ) , 12 boo ( f8iv ) , and hr 6169 ( a2v ) . our analysis of hr 6169 has produced a major improvement in its orbital elements .

radial velocities from the 2.1 m telescope at mcdonald observatory supplemented with radial velocities from the coud feed telescope at kpno provide new precise orbits for the double - lined spectroscopic binaries rr lyn ( a3/a8/a6 ) , 12 boo ( f8iv ) , and hr 6169 ( a2v ) . we derive orbital dimensions ( and ) and minimum masses ( and ) with accuracies of 0.06 to 0.9% . the three systems , which have magnitudes of 5.54 , 4.83 , and 6.42 , respectively , are all sufficiently bright that they are easily within the grasp of modern optical interferometers and so afford the prospect , when our spectroscopic observations are complemented by interferometric observations , of fully - determined orbits , precise masses , and distances . in the case of rr lyn , which is also a detached eclipsing binary with a well - determined orbital inclination ( ; khaliullin et al . 2001 ) , we are able to determine the semimajor axis of the relative orbit ,r , primary and secondary radii ofr andr , respectively ; and primary and secondary masses ofm andm , respectively . comparison of our new systemic velocity determination , km s , with the earlier one of , km s , shows no evidence of any change in the systemic velocity in the 40 years separating the two measurements , a null result that neither confirms nor contradicts the presence of the low - mass third component proposed by . our spectroscopic orbit of 12 boo is more precise that that of but confirms their results about this system . our analysis of hr 6169 has produced a major improvement in its orbital elements . the minimum masses of the primary and secondary are 2.20 0.01 and 1.64 0.02 m , respectively . although all three systems have eccentric orbits , the six components of the systems are either pseudosynchronously rotating or very nearly so .

astro-ph0601716

r

all three systems have eccentric orbits , so we obtained simultaneous solutions of the primary and secondary radial velocities by the lehmann filhes method to determine the orbits . a preliminary to the orbit calculation was the assignment of suitable weights for the various velocities . typically the primary and secondary spectra are of different quality because the components can differ , sometimes markedly , as to strength of lines , line width , and number of available lines , resulting in primary and secondary velocities that are of different weight . also , the mcdonald velocities , because of the higher resolution by a factor of two and the substantially greater wavelength coverage of the mcdonald spectra , resulting in a larger number of available lines , are somewhat more precise than the kpno velocities and therefore have higher weight . for each system there are , thus , four different sets of velocity , each with its own weight . these weights , which are given in table 3 , were chosen so as to approximately equalize the products of the weights and the mean square velocity residuals for the different sets of velocity . once the weights were assigned , the velocities were then solved to determine the spectroscopic orbits . the velocity residuals ( table 3 ) for the orbital solutions , given to two decimal places to facilitate our examination , allow a straightforward check on the consistency of the radial velocities from the two observatories . any systematic difference between the mcdonald and kpno velocities will manifest itself as a corresponding difference between the average residuals , calculated with regard to sign , for the two types of velocity , while if they are consistent then their average residuals , apart from statistical fluctuations , will be identical and equal to zero . a comparison of the residuals for the mcdonald and kpno radial velocities is given in table 4 . although the differences are all smaller than or similar to their estimated errors , they all have the same sign , thus suggesting an offset of order 0.1 0.2 km s@xmath13 between the mcdonald and kpno velocities . we attach the most importance , however , to the primaries of rr lyn and 12 boo because of the six stars in our three systems these two have the most well - determined radial velocities , and in both cases there is no evidence of an offset . this simple check , therefore , indicates the possible presence of an offset of 0.1 0.2 km s@xmath13 between the mcdonald and kpno velocities , but the results are inconclusive . in the absence of clear evidence of an offset , we decided not to adjust either set of velocities . we now look at the results for the individual systems . table 5 gives the spectroscopic orbital elements of rr lyn obtained from the solution of our radial velocities . for comparison , the elements of @xcite and the photometrically - based elements of @xcite are also listed . figure [ fig1 ] shows our radial velocities along with the calculated radial - velocity curves for our orbital elements . although the photometrically determined orbital period is more precise than our spectroscopically measured value , the difference between the two 10-day periods corresponds to less than 1 second . we have retained the spectroscopic period for the determination of our spectroscopic orbit , since adopting the photometric period does not change the orbital elements . examining the solutions in table 5 , one sees that to within the uncertainties all three investigations give the same eccentricity of 0.08 . this agreement is especially pleasing in the case of @xcite because their photometric determination of the eccentricity is completely independent of our spectroscopic one . we note that our determination of @xmath45 ( 1794 @xmath15 06 ) is the first accurate measurement of this element and that to within its uncertainty , it is @xmath46 , which means the major axis of the true orbit and the line of nodes coincide . also of interest , we find that our and kondo s determinations of @xmath47 and @xmath48 are the same to within the uncertainties . we will compare the two @xmath49-velocity determinations shortly . the minimum masses are also in agreement , with our uncertainties being about 10 times smaller than kondo s . as we have seen , rr lyn is also a detached eclipsing binary so the photometric and spectroscopic orbital elements can be combined to provide the sizes and masses of the components as well as the linear separation between the primary and secondary . this is done in table 6 . the new mass determinations of @xmath50 m@xmath7 and @xmath51 m@xmath7 are extremely precise , having uncertainties of only 0.4% and 0.3% , respectively . although our new determinations of the masses and radii of the primary and secondary are more precise than those of @xcite , our values differ only slightly from theirs . the new primary and secondary masses are just 0.037m@xmath7 and 0.017m@xmath7 larger , respectively , than theirs , while the new primary and secondary radii differ from theirs by 0.00 r@xmath7 and 0.01 r@xmath7 , respectively . we will not rediscuss , therefore , the evolutionary state of rr lyn because our new results would have little impact on the conclusions of @xcite in this regard . instead , we note that insofar as our new masses and radii confirm theirs , so we support their determinations of other derived quantities . in particular we confirm their photometric estimate of the system s distance , 73.5 @xmath15 2.8 pc , and its age , @xmath52 billion years . we now look at the question of the third body in the system . as already mentioned , @xcite proposed the presence of a third star in an extremely eccentric orbit ( @xmath53 ) with a period of 39.7 years as an explanation of variations in the times of minima of the primary and secondary eclipses . the proposed star is of low mass , estimated to be 0.10m@xmath7 if its orbit is coplanar with that of the eclipsing pair . thus , it would make a negligible contribution to the spectrum , but its presence would cause a regular variation of the systemic velocity of the eclipsing pair as the center - of - mass of the eclipsing pair orbits the center - of - mass of the entire system . in view of the long interval between the observations of @xcite and ours , it is natural to compare kondo s systemic velocity with ours to see if there is a variation . the difference between our and kondo s @xmath49-velocities is insignificant . from table 5 we see that it is @xmath54 with the estimated uncertainty being set by the uncertainty in kondo s result . the observations thus set an upper limit of @xmath55 km s@xmath13 on any difference between the two @xmath49-velocities . what is the predicted difference that would be caused by the proposed third star ? to answer this question we note that we do _ not _ need to know the ( unknown ) systemic velocity of the entire system ; calculation of the _ orbital motion _ alone , of the center of mass of the eclipsing pair , is sufficient to provide the predicted @xmath49-velocity _ difference _ that we want . @xcite have provided estimates of all the orbital elements needed to calculate the predicted variation of the @xmath49-velocity of the eclipsing pair , with the exception of @xmath56 , and , from the information they give , one can infer @xmath57 km s@xmath13 . we can thus calculate the predicted variation of the @xmath49-velocity of the eclipsing pair due to its motion in the proposed 39.7-year orbit , and this is shown in figure [ fig2 ] . it is apparent from that figure that the predicted difference of @xmath49-velocities is tiny , only @xmath58 km s@xmath13 . the smallness of the difference results from the extreme eccentricity of the proposed orbit , so the velocity variation outside of periastron passage is slight , and because , by chance , kondo s observations and ours are separated by almost exactly one orbit and thus are at the same phase . our null result , therefore , is consistent with the predicted minute change in the @xmath49-velocity of the eclipsing pair of stars caused by the presence of the proposed low - mass third star . of course , the result is also consistent with the absence of such a body , and so we are unable to either confirm or deny its existence . as can be seen in figure [ fig2 ] , the extreme eccentricity of the 39.7-year orbit means that usually the @xmath49-velocity of the eclipsing pair changes very gradually . so , during most of the orbit , radial velocities are almost impervious to the presence or absence of the third body . near periastron it is a different story , however , as the third star swoops toward the eclipsing pair , and their @xmath49-velocity suffers an abrupt change with a total amplitude of 2.5 km s@xmath13 . at the next periastron passage in 2028 one or two precise radial velocities will readily confirm or refute the existence of the third star . in their recent investigation of the 12 boo system @xcite combined their interferometric observations of the visual orbit and complementary , new radial velocities to make an accurate determination of the system s three - dimensional orbit and the masses and radii of its components . they then use these basic parameters to discuss the system s evolutionary status . although our own work duplicates theirs to some extent , our radial velocities are more precise , so our results provide a useful check on the spectroscopic component of their investigation . table 7 lists the spectroscopic orbital elements from the combined interferometric and radial velocity solution of @xcite with our new radial - velocity solution . the two sets of orbital elements are in excellent agreement , and the uncertainties of our elements are usually smaller than those of @xcite . with the exception of the period , for which our observational timespan is quite short , all our elements are improved determinations and for four of them ( @xmath59 , @xmath47 , @xmath48 , and @xmath49 ) the improvement is a factor of two . there is also good agreement between the two @xmath49 velocities , where we find @xmath60 km s@xmath13 , while they find @xmath61 km s@xmath13 , which argues that our and their radial velocities have the same zero point . to make the most of the radial velocities , we also obtained a combined solution of our radial velocities and theirs , making no adjustment to either set of velocities . ( the weights for our velocities in this solution are given in table 3 , while the weights for theirs were 0.1 and 0.05 for the primary and secondary , respectively . ) the elements from this combined spectroscopic solution are also listed in table 7 . they represent an all - round improvement , with the period determination , in particular , being sharpened thanks to the longer timespan , 1987 to 2005 , of the combined observations . figure [ fig3 ] shows our radial velocities and those of @xcite along with the calculated radial velocity curves for the combined solution of the two sets . with the help of the inclination , @xmath62 , from the orbit of @xcite we determine new values of the stellar masses and the semi - major axis of the relative orbit . we find @xmath63m@xmath7 , @xmath64m@xmath7 , and @xmath65 gm . these results certainly confirm those of @xcite , which are @xmath66m@xmath7 , @xmath67m@xmath7 , but are more precise . finally we look at the orbital parallax , @xmath68 , and distance of the system . the orbital parallax is simply @xmath69 ( arcsec)/@xmath69 ( au ) where @xmath69 denotes both the angular and linear sizes , respectively , of the true orbit . the angular size of the orbit , @xmath70 mas , of course , comes from the visual - orbit determination @xcite . we note , however , that the uncertainty in the angular size of the orbit , which is 0.5% and is much bigger than the uncertainties in the determinations of the linear size of the orbit ( 0.1% for theirs and 0.06% for ours ) , dominates the uncertainty in the orbital parallax . thus , although we have improved the determination of the linear size of the orbit , there are no corresponding improvements in the orbital parallax or distance of 12 boo , so we content ourselves with restating the results of @xcite @xmath71mas and a distance to the system of @xmath72pc . table 8 lists the orbital elements of hr 6169 , derived from the solution of our radial velocities , as well as the elements obtained by @xcite . in figure [ fig4 ] our radial velocities and those of @xcite are compared with the radial velocity curves calculated from our elements alone . for hr 6169 , in the yellow and red region of the spectrum where we measured our radial velocities , the only useful lines representing the primary are the two siii lines at 6347 and 6371 and a smattering of very weak feii lines , while the secondary is represented by lines of neutral and ionised species that are both more numerous and sharper . for this reason the _ secondary _ velocities are more precise than those of the primary . it follows that the secondary velocities have much higher weight than those of the primary ( see table 3 ) , the secondary radial - velocity curve is better defined than that of the primary , and @xmath48 is better determined than @xmath47 . comparison of our results with young s reveals some very significant discrepancies , especially for the @xmath49 velocity . at first sight the large difference of @xmath73 km s@xmath13 between our @xmath49 velocity ( @xmath74 km s@xmath13 ) and young s ( @xmath75 km s@xmath13 ) suggests the presence of an unseen third star , which must have changed the @xmath49 velocity of the spectroscopic - binary pair in the 84 years between the two measurements . a glance at figure [ fig4 ] , however , shows there is no need to invoke a third star . instead , a simpler explanation of the difference can be found because of a systematic error in young s @xmath49 velocity , caused by blending of the primary and secondary lines in his spectra . @xcite remarked that in his spectra with smaller primary - secondary velocity separations the primary lines and their secondary counterparts were blended , so that he was only able to measure a single blend velocity , which he adopted as the primary velocity . inspection of figure [ fig4 ] shows that these blended primary velocities cluster around the smaller velocity extremum associated with the nodal passage near apastron . they mostly fall below the @xmath49 velocity and , being dragged upwards and towards it , are too positive and , not being balanced by the few velocities that are dragged downwards , their presence in young s orbit solution made his @xmath49 velocity too positive . similar considerations account for his semi - amplitude of the primary being too small , @xmath76 km s@xmath13 compared with our value of @xmath77 km s@xmath13 . unlike our other two systems , rr lyn , which is an eclipsing system , and 12 boo , for which interferometric observations have been used to determine a visual orbit , hr 6169 has no direct determination of its orbital inclination . thus , at present we can only compute the minimum masses of its two components , which are 2.20 @xmath15 0.01 and 1.64 @xmath15 0.02 m@xmath16 for the primary and secondary , respectively .

the three systems , which have magnitudes of 5.54 , 4.83 , and 6.42 , respectively , are all sufficiently bright that they are easily within the grasp of modern optical interferometers and so afford the prospect , when our spectroscopic observations are complemented by interferometric observations , of fully - determined orbits , precise masses , and distances . in the case of rr lyn , which is also a detached eclipsing binary with a well - determined orbital inclination ( ; khaliullin et al . 2001 ) , we are able to determine the semimajor axis of the relative orbit ,r , primary and secondary radii ofr andr , respectively ; and primary and secondary masses ofm andm , respectively . comparison of our new systemic velocity determination , km s , with the earlier one of , km s , shows no evidence of any change in the systemic velocity in the 40 years separating the two measurements , a null result that neither confirms nor contradicts the presence of the low - mass third component proposed by . the minimum masses of the primary and secondary are 2.20 0.01 and 1.64 0.02 m , respectively . although all three systems have eccentric orbits , the six components of the systems are either pseudosynchronously rotating or very nearly so .

radial velocities from the 2.1 m telescope at mcdonald observatory supplemented with radial velocities from the coud feed telescope at kpno provide new precise orbits for the double - lined spectroscopic binaries rr lyn ( a3/a8/a6 ) , 12 boo ( f8iv ) , and hr 6169 ( a2v ) . we derive orbital dimensions ( and ) and minimum masses ( and ) with accuracies of 0.06 to 0.9% . the three systems , which have magnitudes of 5.54 , 4.83 , and 6.42 , respectively , are all sufficiently bright that they are easily within the grasp of modern optical interferometers and so afford the prospect , when our spectroscopic observations are complemented by interferometric observations , of fully - determined orbits , precise masses , and distances . in the case of rr lyn , which is also a detached eclipsing binary with a well - determined orbital inclination ( ; khaliullin et al . 2001 ) , we are able to determine the semimajor axis of the relative orbit ,r , primary and secondary radii ofr andr , respectively ; and primary and secondary masses ofm andm , respectively . comparison of our new systemic velocity determination , km s , with the earlier one of , km s , shows no evidence of any change in the systemic velocity in the 40 years separating the two measurements , a null result that neither confirms nor contradicts the presence of the low - mass third component proposed by . our spectroscopic orbit of 12 boo is more precise that that of but confirms their results about this system . our analysis of hr 6169 has produced a major improvement in its orbital elements . the minimum masses of the primary and secondary are 2.20 0.01 and 1.64 0.02 m , respectively . although all three systems have eccentric orbits , the six components of the systems are either pseudosynchronously rotating or very nearly so .

astro-ph0612461

i

recent estimates of the kerr parameters @xmath0 for two soft x - ray transients ( sxts ) @xcite , gro j1655@xmath140 ( nova sco ) and 4u 1543@xmath147 ( il lupi ) , facilitate a test of stellar evolution , in that the spins of the black holes in these binaries should be produced in common envelope evolution which begins with the evolving massive giant and companion donor , and ends up in helium - star donor binary , the hydrogen envelope of the massive star having been stripped off and the helium having been burned . @xcite ( hereafter denoted as lbw ) assumed common envelope evolution to begin only after he core burning has been completed ; i.e. , case c mass transfer @xcite . otherwise the he envelope , if laid bare , would blow away to such an extent that the remaining core would not be sufficiently massive to evolve into a black hole @xcite . the black - hole - progenitor star , in which the helium core burning has been completed , is tidally locked with the donor ( secondary star ) so the spin period of the helium star is equal to the orbital period of the binary . in this tidal locking , lbw assumed uniform rotation of he star by assuming that the inner and outer parts of he are strongly connected due to the presence of a strong magnetic field . the c - o core of the helium star drops into a rapidly spinning black hole due to angular momentum conservation . in this process , the spin of the black hole depends chiefly on the mass of the donor because the orbital period chiefly depends on the donor mass as we explain later ( in section [ sec - lmd2ham ] ) . lbw calculated this kerr parameter ( @xmath0 ) as a function of binary orbital period . the results are given in their fig . 12 which we reproduce as fig . [ fig12 ] . the agreement of the natal kerr parameters with the @xcite measured ones means that only a small amount of angular momentum energy could have been lost after the formation of the black hole . the good agreement in this comparison supports the assumption of case c mass transfer and the tidal locking at the donor - he star stage assumed in the lbw calculations . in the lbw calculation , the @xmath0 for nova sco was slightly greater than for il lupi . combining this with observation , @xmath8 would be our best estimate for both binaries . in this report we also note that lbw predicted @xmath9 for 7 soft x - ray transient sources with main sequence companions and @xmath10 for xte j1550@xmath1564 and gs 2023@xmath11338 ( v404cygni ) with evolved companions . the maximum available energy in the blandford - znajek formalism for @xmath6 gives @xmath7ergs , orders of magnitude larger than observed in the grb and hypernova explosion . based on this observation , we interpret the soft x - ray transients to be relics of grbs and hypernovae . it should be noted that the way in which the hypernova explodes can be similar to the woosley collapsar model . the main advantage in our scenario is that the h envelope in our binary is removed by the donor and the rotational energy is naturally produced in the common envelope evolution . the necessity for case c mass transfer , given galactic metallicity , and the measured system velocity lock us into the kerr - parameter values we find . in section [ casec ] we elaborate on the determination of the kerr parameters of soft x - ray transient black - hole binaries discussed above , which could be read off the figures of lbw by a discussion of tidal locking , and the connection of tidal locking to case c mass transfer . we also discuss the energetics for grbs and hypernovae based on the black - hole spin . in section [ sec - lmd2ham ] we show that the angular - momentum energy of the black - hole binary is determined mainly by the mass of the donor . we discuss 12 galactic transient sources with angular - momentum energies @xmath12ergs , so that all of these are relics of grbs and hypernovae . the energies of the grb and hypernova explosion powered by these , as we shall develop , should be subtracted from the natal rotational energies , to give the explosion energy .

recent measurements of the kerr parameters for two black - hole binaries in our galaxy , gro j1655 and 4u 1543 of and , respectively , fitted well the predictions of , of . in this report we also note that predicted for 80% of the soft x - ray transient sources . the maximum available energy in the blandford - znajek formalism for givesergs , orders of magnitude larger than the energy needed for the grb and hypernova explosion . we interpret the soft x - ray transients to be relics of grbs and hypernovae , but most of them were subluminous ones which could use only a small part of the available rotational energy .

recent measurements of the kerr parameters for two black - hole binaries in our galaxy , gro j1655 and 4u 1543 of and , respectively , fitted well the predictions of , of . in this report we also note that predicted for 80% of the soft x - ray transient sources . the maximum available energy in the blandford - znajek formalism for givesergs , orders of magnitude larger than the energy needed for the grb and hypernova explosion . we interpret the soft x - ray transients to be relics of grbs and hypernovae , but most of them were subluminous ones which could use only a small part of the available rotational energy .

1202.2874

i

the origin of ultra - high - energy cosmic rays ( uhecrs ) with energies @xmath7 ev is an intriguing mystery in modern astrophysics . their sources are generally believed to be extragalactic objects , although some galactic objects may also be viable . in either case , the maximum energy of @xmath8 ev can only be achieved in extreme environments @xcite . prominent source candidates suggested so far include active galactic nuclei ( agn ) @xcite , gamma - ray bursts ( grbs ) @xcite , neutron stars or magnetars @xcite and clusters of galaxies @xcite . if uhecrs with energies above @xmath9 ev are mainly protons , their propagation distance should be limited by interactions with cosmic microwave background ( cmb ) photons @xcite , the so - called greisen - zatsepin - kuzmin ( gzk ) mechanism , so that they are observable only from sources sufficiently nearby ( typically @xmath10 mpc ) . since all known astrophysical objects are distributed inhomogeneously at such distances in the local universe , anisotropies in the distribution of uhecr arrival directions are expected as long as cosmic magnetic fields are weak enough to allow quasi - rectilinear propagation of the uhecrs . searches for correlations between the arrival directions and the celestial positions of potential source candidates should then provide valuable clues to reveal their origin @xcite . the pierre auger observatory ( pao ) operating in the southern hemisphere has reported possible evidence of a gradual increase in the average mass of uhecr particles with energies above @xmath11 ev by analyzing the average depth of the shower maximum @xmath12 and the root mean square of the shower - to - shower fluctuations of @xmath13 ( @xmath14 ) , assuming that current hadronic interaction models are realistic at these energies @xcite . this is in contrast to measurements of similar quantities for the northern sky by the high resolution fly s eye ( hires ) experiment that are consistent with an uhecr composition dominated by protons @xcite . if uhecrs consisted mainly of heavy nuclei rather than protons as indicated by the pao results , their deflections during propagation in magnetized extragalactic and galactic environments would be much larger than those for protons , and the hopes for observing anisotropy may be considerably weakened . on the other hand , pao has seen statistically significant correlations between the arrival directions of uhecrs with energies above @xmath9 ev and the projected positions of agn with @xmath15 within an angular scale of @xmath16 @xcite . this does not necessarily point to agn as the true sources , since they may only be tracers of the more numerous population of galaxies that make up the anisotropic , local cosmic matter distribution , and there are also considerable uncertainties in the angular displacement due to deflections by both the extragalactic magnetic field ( egmf ) and the galactic magnetic field ( gmf ) . nevertheless , this does imply that uhecr sources are associated with the matter distribution . independent analyses of the pao data have confirmed the correlations of uhecr arrival directions with various kinds of nearby astrophysical objects @xcite . such correlations were predicted in several theoretical studies under the assumption of protons as the primary uhecr particles @xcite . we must beware that at the moment , the positional correlations ( or anisotropy ) are observed only _ above _ @xmath9 ev , whereas the pao results on the composition are available only _ up to _ @xmath9 ev due to the lack of event statistics . we can not rule out the possibility that protons become dominant above this energy and produce the anisotropy . however , there are presently no hints of such a sudden change in the composition , and the simplest extrapolation of the measured trends of @xmath12 and @xmath14 to higher energies would entail a composition dominated by heavy nuclei . since the appearance of anisotropies or cross correlations with astrophysical objects in the case of uhecr nuclei is not trivial , deeper , relevant studies of uhecr propagation are warranted in order to achieve a consistent interpretation of the current data set as well as to quantify the prospects for future observations . propagation of uhe nuclei has been studied previously by many authors from various perspectives @xcite . many have studied the photodisintegration process and consequent spectra in detail without accounting for magnetic fields , but only a few have focused on the effects of the magnetic fields . ref . @xcite calculated the propagation of uhe nuclei in a uniform turbulent egmf model and examined their trajectories and photodisintegration interactions in intergalactic photon fields , concluding that a characteristic feature in the spectrum may result . @xcite discussed the propagation of nuclei in a structured egmf model obtained through a numerical simulation of cosmological structure formation , showing that while heavy nuclei can be strongly deflected ( @xmath17 ) by the egmf , nuclei ( and their secondaries ) with relatively small deflections can generate anisotropy on intermediate angular scales . in this paper , we study the propagation of uhecr nuclei in cosmic radiation and magnetic fields under different assumptions for the source properties and the fields , focusing on the resulting distribution of arrival directions . in addition to a detailed treatment of the photopair , photomeson and photodisintegration interactions of uhe nuclei with background photons , deflections in gmf and egmf are taken into account for both primary nuclei as well as secondary nuclei arising from photodisintegration . by statistically analyzing the calculated arrival distributions , we discuss the implications for current and future observations of anisotropy and cross correlations with sources . motivated by the recent pao result , we adopt a model for the uhecr source distribution that follows the density of large - scale structure actually observed in the local universe . this is in contrast to refs . @xcite who took the sources to be related to the matter distribution in a numerical simulation , but not reflecting the actual universe . because photodisintegration limits the propagation distance of heavy nuclei in a way similar to the gzk mechanism for protons , a realistic account of local source inhomogeneity is essential . unlike most previous work on the subject , here we also account for the gmf as well as the egmf , since the former unavoidably affects all uhecrs arriving at earth . concerning the uhecr source composition , a wide variety of possibilities are currently allowed that are consistent with both the observed spectrum and the composition indicators @xmath13 and @xmath14 ( e.g. , @xcite ) . this study assumes a pure iron composition , which can also reproduce the highest - energy spectrum , and which would be the most pessimistic situation for producing anisotropy or source correlations in view of their large magnetic deflections . this paper is laid out as follows . in section [ method ] we describe our models and methods of calculation and statistical analysis . parametrization of photodisintegration cross sections to calculate the mean free paths of nuclei in cosmic background radiation fields is summarized in section [ method_pd ] . section [ method_mf ] is dedicated to our models for the gmf and egmf . a method of calculation for nuclear propagation is introduced in section [ method_prop ] , and that for uhecr arrival distribution is presented in section [ method_ad ] . the contents of these two subsections are essentially based on ref . @xcite that dealt with uhe proton propagation in intergalactic space , and here we extend their methods to heavy nuclei . we describe our statistical methods for studying anisotropy and cross correlations with sources in section [ method_stat ] . in section [ results ] , we present our simulation results , compare with the current data @xcite , and discuss the implications thereof for the sources of uhe nuclei . we also give special attention to centaurus ( cen ) a , for which several pao events positionally correlate @xcite . we summarize in section [ summary ] .

recent results from the pierre auger observatory ( pao ) indicate that the composition of ultra - high - energy cosmic rays ( uhecrs ) with energies above ev may be dominated by heavy nuclei . we have simulated the propagation of uhecr nuclei including models for both the extragalactic magnetic field ( egmf ) and the galactic magnetic field ( gmf ) . we find that the gmf is particularly crucial for suppressing the anisotropy as well as source correlations . ultra - high - energy cosmic rays

recent results from the pierre auger observatory ( pao ) indicate that the composition of ultra - high - energy cosmic rays ( uhecrs ) with energies above ev may be dominated by heavy nuclei . an important question is whether the distribution of arrival directions for such uhecr nuclei can exhibit observable anisotropy or positional correlations with their astrophysical source objects despite the expected strong deflections by intervening magnetic fields . for this purpose , we have simulated the propagation of uhecr nuclei including models for both the extragalactic magnetic field ( egmf ) and the galactic magnetic field ( gmf ) . we find that the gmf is particularly crucial for suppressing the anisotropy as well as source correlations . assuming that only iron nuclei are injected steadily from sources with equal luminosity and spatially distributed according to the observed large scale structure in the local universe , at the number of events published by the pao so far ( 69 events above ev ) , the arrival distribution of uhecrs would be consistent with no auto - correlation at 95% confidence if the mean number density of uhecr sources mpc , and consistent with no cross - correlation with sources within 95% errors for mpc . on the other hand , with 1000 events above ev in the whole sky , next generation experiments can reveal auto - correlation with more than 99% probability even for mpc , and cross - correlation with sources with more than 99% probability for mpc . in addition , we find that the contribution of centaurus a is required to reproduce the currently observed uhecr excess in the centaurus region . secondary protons generated by photodisintegration of primary heavy nuclei during propagation play a crucial role in all cases , and the resulting anisotropy at small angular scales should provide a strong hint of the source location if the maximum energies of the heavy nuclei are sufficiently high . ultra - high - energy cosmic rays

1202.2874

c

we have investigated the anisotropy in the arrival directions of uhecr nuclei and their positional correlations with source objects , on the basis of propagation calculations conducted under various assumptions for the source properties and cosmic magnetic fields . although @xmath20 ev was fiducially assumed in the previous section , the results depend somewhat on @xmath189 . since only iron nuclei above @xmath185 ev can produce secondary protons above @xmath1 ev ( @xmath190 [ @xmath191 ev ] ev ) , the threshold energy for the published pao events and also adopted in this study , secondary protons do not contribute to the total flux of uhecrs above it if @xmath192 ev . [ fig : acoremax ] shows the probability curves as discussed in fig . [ fig : cprob_auto1000 ] , but for @xmath193 , @xmath194 , and @xmath185 ev , in order to check the dependence on @xmath189 . the probability for the appearance of a positive excess of events is the highest for @xmath20 ev at small angular scales , and the angular scale of the peak is smaller for higher @xmath189 . these reflect the fact that secondary protons contribute only in the case of @xmath20 ev . furthermore , the probability is slightly higher at small angular scales for @xmath195 ev than for @xmath193 ev because light and/or high energy nuclei are included above the threshold in the former case . therefore , positive anisotropy at small angular scales is weakened when @xmath192 ev , owing to the lack of secondary protons above threshold , but the probability at intermediate angular scales is still greater than 95% . we have considered a rather extreme case where only iron nuclei are emitted from sources . however , other nuclei and/or protons may also plausibly constitute the composition of uhecr sources ( e.g. , a mixed composition model @xcite or a wolf - rayet star model @xcite ) . the other elements can affect the spectral shape as mentioned in section [ introduction ] due to different energy losses and magnetic deflections . although the source composition is highly uncertain at the moment , further studies of anisotropy and correlations under more realistic assumptions for the source composition are in order . for instance , assuming a mixed composition and a simple rigidity scaling for the maximum energies , protons can produce anisotropy at low energies comparable to or stronger than the anisotropy due to heavy nuclei at the highest energies , because a proton with energies @xmath183 times smaller than an iron nucleus propagates along the same trajectory @xcite . thus , if cen a is an uhecr source , anisotropy at low energies may also be expected . however , pao has reported the lack of significant anisotropy at low energies toward the direction of the excess highest energy events @xcite . this result implies that 1 ) a significant fraction of uhecrs may be nuclei even at lower energies , 2 ) the anisotropy at the highest energies is actually weaker than reported , 3 ) the composition at high energies is not as heavy nuclei - dominant as indicated from the xmax measurements , or some combination of these three possibilities . furthermore , strong magnetic fields could modify the theoretical expectation through the extension of the propagation distance as mentioned in @xcite , so magnetic fields may also be important in this context . although we have adopted simple models for the gmf and egmf to avoid the uncertainties with their structure , the details of these fields can actually play important roles in the propagation of uhecrs and their arrival directions at earth , as has been well studied for uhe protons @xcite . in particular , as discussed in ref . @xcite for protons , the structures actually observed near the galaxy are also relevant when searching for the evidence of nearby uhecr sources . whether the positional information in the sky is lost or not during propagation depends on the egmf strength and structures in local universe . the effect of the gmf is inevitable , but the deflection angles and directions of uhecrs strongly depend on the region of the sky , reflecting the structure of the gmf , as studied in refs . @xcite for iron nuclei . thus more realistic gmf models should be applied for correlation studies , although such gmf models also have significant uncertainties . the dependence of the anisotropy signals on different models for the gmf and egmf will be investigated in future work . in addition to cen a , m87 is also an interesting object as an uhecr source candidate . since it is more distant than cen a ( @xmath196 mpc ) , the contribution of m87 to the anisotropy is smaller , depending on the egmf strength . if the power of uhecr injection from m87 is comparable to that of typical fr i galaxies , it is not expected to contribute strongly to the anisotropy . however , if its power is an order of magnitude stronger or @xmath118 is smaller , anisotropy can appear in the direction of m87 even for @xmath152 ng . secondary protons should also be a good source indicator in this case . this study has assumed the sources of uhecrs to be steady . on the other hand , it is also very much possible that transient phenomena like grbs or agn flares produce uhecrs . transient scenarios are especially relevant for accelerating protons up to @xmath8 ev in outflows because not many steady sources satisfy the luminosity requirement for uhecr acceleration @xcite . for transient sources , the arrival distribution of uhecrs will be different from that in the case of steady source scenarios . the time delay of uhecrs by the gmf and egmfs leads to apparent durations of uhecr bursts longer than their intrinsic duration . if the apparent duration is longer than the observation timescale of human beings , we would misperceive an uhecr burst as a steady source @xcite . however , since the arrival time of uhecrs depends on the uhecr energies , features of anisotropy may be strongly energy - dependent @xcite . this will be evidence for the transient generation of uhecrs . even in transient scenarios , anisotropy of ( secondary ) protons at small angular scale should still be a strong hint of uhecr sources . to summarize , we have calculated the propagation of uhe nuclei above @xmath1 ev , taking into account magnetic fields in the universe on the assumption that only iron nuclei are injected by steady sources , and examined the anisotropy in the distribution of uhecr arrival directions and positional correlation between uhecrs and their sources in local universe . we found that both the anisotropy and correlation are dominantly suppressed by the gmf rather than by egmfs . assuming the current pao status ( 69 events above @xmath1 ev ) , the arrival distribution of uhecrs is consistent with isotropy within 95% errors for @xmath2 mpc@xmath3 and is consistent with no correlation within 95% errors for @xmath4 mpc@xmath3 when the gmf and egmf are taken into account . we also discussed whether future experiments improve these situation . 1000 events above @xmath1 ev in the whole sky would reveal positive anisotropy with more than 99% probability at intermediate angular scales even for @xmath197 mpc@xmath3 , and correlation between uhecrs and their sources in local universe would appear with more than 99% at small angular scales for @xmath6 mpc@xmath3 . in addition , we found that the contribution of cen a is required to reproduce the observed uhecr excess around the centaurus region . secondary protons from primary heavy nuclei are working positively to produce anisotropy at small angular scales , which would provide a strong hint of the source location , depending on the maximum energy at the uhecr source . we thank d. allard , g. medina - tanco , and f. takahara for useful comments . this work is supported by grant - in - aid no . 22540278 ( si ) from the ministry of education , culture , sports , science and technology of japan . 121 natexlab#1#1[2]#2 , ( ) . , , ( ) ( ) . , , ( ) . , , , ( ) . , ( ) . , , , ( ) . , , ( ) . , , , , available from arxiv:1107.5576 , ( ) . , ( ) . , , , , ( ) . , , , , ( ) . , , , ( ) . , ( ) . , , , ( ) . , ( ) . , , , ( ) . , , , ( ) . , , , , available from astro - ph/0701167 , ( ) . , , ( ) . , ( ) . , , ( ) . , , , , ( ) . , , , ( ) . , , , , , , , , , , , ( ) . , et al . , ( ) . , et al . , ( ) . , et al . , ( ) . , et al . , ( ) . , et al . , ( ) . , , ( ) . , , , , , ( ) . , , , , , ( ) . , , , , ( ) . , , , , ( ) . , , ( ) . , , ( ) . , , , , ( ) . , , , , , ( ) . , , , ( ) . , , , , , ( ) . , , , ( ) . , , ( ) . , , , , , ( ) . , , , , , , , , ( ) . , , , ( ) . , , , ( ) . , , , ( ) . , , , , , ( ) . , , , , , ( ) . , , , ( ) . , , , ( ) . , , , available from arxiv:0802.4452 , , , , , ( ) . , , , available from arxiv:1006.2484 , , , , ( ) . , , , , , , , , , , , ( ) . , , , , , ( ) . , , , , ( ) . , , , ( ) . , , , ( ) . , , , , ( ) . , , , , ( ) . , , ( ) . , , , ( ) . , , , , ( ) . , , , ( ) . , , , ( ) . , , , , ( ) . , , , , ( ) . , , , , , , ( ) . , , , , ( ) . , , available from arxiv:1110.3245 , ( ) . , , , , ( ) . , , , , ( ) . , , , , ( ) . , , ( ) . , , , , , ( ) . , , , ( ) . , et al . , ( ) . , , , ( ) . , , ( ) , , , , , ( ) . , , ( ) . , ( ) . , , , ( ) . , , , ( ) . , , ( ) . , , , , ( eds . ) , , . , , , ( ) . , , ( ) . , ( ) . , , , , , , , , , , , available from arxiv:1009.1855 , , ( ) . , in : proc . 30th icrc ( melida ) , 2007 , 10451048 , ( ) . , , , , ( ) . , , , , ( ) . , , , ( ) . , , ( ) . , , , ( ) . , , ( ) . , , , , , , , , , , , ( ) . , ( ) . , , ( ) .

an important question is whether the distribution of arrival directions for such uhecr nuclei can exhibit observable anisotropy or positional correlations with their astrophysical source objects despite the expected strong deflections by intervening magnetic fields . for this purpose , assuming that only iron nuclei are injected steadily from sources with equal luminosity and spatially distributed according to the observed large scale structure in the local universe , at the number of events published by the pao so far ( 69 events above ev ) , the arrival distribution of uhecrs would be consistent with no auto - correlation at 95% confidence if the mean number density of uhecr sources mpc , and consistent with no cross - correlation with sources within 95% errors for mpc . on the other hand , with 1000 events above ev in the whole sky , next generation experiments can reveal auto - correlation with more than 99% probability even for mpc , and cross - correlation with sources with more than 99% probability for mpc . in addition , we find that the contribution of centaurus a is required to reproduce the currently observed uhecr excess in the centaurus region . secondary protons generated by photodisintegration of primary heavy nuclei during propagation play a crucial role in all cases , and the resulting anisotropy at small angular scales should provide a strong hint of the source location if the maximum energies of the heavy nuclei are sufficiently high .

recent results from the pierre auger observatory ( pao ) indicate that the composition of ultra - high - energy cosmic rays ( uhecrs ) with energies above ev may be dominated by heavy nuclei . an important question is whether the distribution of arrival directions for such uhecr nuclei can exhibit observable anisotropy or positional correlations with their astrophysical source objects despite the expected strong deflections by intervening magnetic fields . for this purpose , we have simulated the propagation of uhecr nuclei including models for both the extragalactic magnetic field ( egmf ) and the galactic magnetic field ( gmf ) . we find that the gmf is particularly crucial for suppressing the anisotropy as well as source correlations . assuming that only iron nuclei are injected steadily from sources with equal luminosity and spatially distributed according to the observed large scale structure in the local universe , at the number of events published by the pao so far ( 69 events above ev ) , the arrival distribution of uhecrs would be consistent with no auto - correlation at 95% confidence if the mean number density of uhecr sources mpc , and consistent with no cross - correlation with sources within 95% errors for mpc . on the other hand , with 1000 events above ev in the whole sky , next generation experiments can reveal auto - correlation with more than 99% probability even for mpc , and cross - correlation with sources with more than 99% probability for mpc . in addition , we find that the contribution of centaurus a is required to reproduce the currently observed uhecr excess in the centaurus region . secondary protons generated by photodisintegration of primary heavy nuclei during propagation play a crucial role in all cases , and the resulting anisotropy at small angular scales should provide a strong hint of the source location if the maximum energies of the heavy nuclei are sufficiently high . ultra - high - energy cosmic rays

hep-th9504007

i

the classical and quantum propagation of strings in curved spacetimes has attracted a great deal of interest in recent years . the main complication , as compared to the case of flat minkowski spacetime , is related to the non - linearity of the equations of motion . it makes it possible to obtain the complete analytic solution only in a very few special cases like conical spacetime @xcite and plane - wave / shock - wave backgrounds @xcite . there are however also very general results concerning integrability and solvability for maximally symmetric spacetimes @xcite and gauged wzw models @xcite . these are the exceptional cases ; generally the string equations of motion in curved spacetimes are not integrable and even if they are , it is usually an extremely difficult task to actually separate the equations , integrate them and finally write down the complete solution in closed form . fortunately , there are several different ways to `` attack '' a system of coupled non - linear partial differential equations . the systematic study of string dynamics in curved spacetimes and its associated physical phenomena was started in refs.@xcite . besides numerical methods , which will not be discussed here , approximative [ 7 - 10 ] and exact [ 11 - 14 ] methods for solving the string equations of motion and constraints in curved spacetimes , have been developed . classical and quantum string dynamics have been investigated in black hole backgrounds [ 15 - 18 ] , cosmological spacetimes [ 7 , 11 - 14 , 17 - 21 ] , cosmic string spacetime @xcite , gravitational wave backgrounds @xcite , supergravity backgrounds ( which are necessary for fermionic strings ) @xcite , and near spacetime singularities @xcite . physical phenomena like the hawking - unruh effect in string theory @xcite , horizon string stretching @xcite , particle transmutation @xcite , string scattering @xcite , mass spectrum and critical dimension @xcite , string instability [ 7 , 11 - 13 , 16 , 21 ] and multi - string solutions [ 11 - 13 , 28 ] have been found . in a generic @xmath2-dimensional curved spacetime with metric @xmath3 and coordinates @xmath4 the string equations of motion and constraints are : @xmath5 @xmath6 where dot and prime stand for derivative with respect to the world - sheet coordinates @xmath7 and @xmath8 respectively and @xmath9 are the christoffel symbols with respect to the metric @xmath10 in the following we present recent results [ 26 - 29 ] on solutions to eqs.(1.1)-(1.2 ) in a variety of curved spacetimes from cosmology , gravitation and string theory . we obtain explicit ( exact and/or approximate ) mathematical solutions , discuss the corresponding physical properties , we quantize the solutions in different ways ( canonical quantization , semi - classical quantization ) and find the physical content : the mass spectrum . the presentation is organized as follows : in section 2 , we discuss the classical string dynamics in the @xmath0 black hole anti de sitter ( bh - ads ) spacetime , recently found by baados et al @xcite . we compare with the string dynamics in ordinary cosmological and black hole spacetimes . this clarifies the geometry ( as seen by a string ) of the bh - ads spacetime . in section 3 , generalizing results from section 2 , we derive the quantum string mass spectrum in ordinary @xmath2-dimensional anti de sitter spacetime . we discuss , in particular , the sectors of low and very high mass states . new physical phenomena arise like the fine - structure effect at all levels beyond the graviton and the non - existence of a hagedorn critical temperature . the results are compared with corresponding results obtained in minkowski and de sitter spacetimes . sections 4 and 5 are devoted to the investigation of the more general underlying structure of solutions to eqs.(1.1)-(1.2 ) . in section 4 , we find new classes of exact string and multi - string solutions in cosmological and black hole spacetimes , while in section 5 , we consider the effects of a non - zero spatial curvature on the classical and quantum string dynamics in friedmann - robertson - walker ( frw ) universes .

recent results on classical and quantum strings in a variety of black hole and cosmological spacetimes , in various dimensions , are presented . furthermore , using a canonical quantization procedure , we find the string mass spectrum in de sitter and anti de sitter spacetimes . we discuss the physical implications of these results . finally , we consider the effect of spatial curvature on the string dynamics in robertson - walker spacetimes .

recent results on classical and quantum strings in a variety of black hole and cosmological spacetimes , in various dimensions , are presented . the curved backgrounds under consideration include the black hole anti de sitter spacetime and its dual , the black string , the ordinary black holes with or without a cosmological constant , the de sitter and anti de sitter spacetimes and static robertson - walker spacetimes . exact solutions to the string equations of motion and constraints , representing circular strings , stationary open strings and dynamical straight strings , are obtained in these backgrounds and their physical properties ( length , energy , pressure ) are described . the existence of _ multi - string _ solutions , describing finitely or infinitely many strings , is shown to be a general feature of spacetimes with a positive or negative cosmological constant . generic approximative solutions are obtained using the string perturbation series approach , and the question of the stability of the solutions is addressed . furthermore , using a canonical quantization procedure , we find the string mass spectrum in de sitter and anti de sitter spacetimes . new features as compared to the string spectrum in flat minkowski spacetime appear , for instance the _ fine - structure effect _ at all levels beyond the graviton in both de sitter and anti de sitter spacetimes , and the _ non - existence _ of a hagedorn temperature in anti de sitter spacetime . we discuss the physical implications of these results . finally , we consider the effect of spatial curvature on the string dynamics in robertson - walker spacetimes .

gr-qc9801036

i

we were very much surprised when we learned during the 8@xmath2 marcel grossmann meeting in jerusalem @xcite that kaniel & itin @xcite were able to propose a gravitational model which looks viable at a first sight even if it had neither an einstein - hilbert type of lagrangian nor the schwarzschild metric as an exact solution . their gravitational potential is represented by a quartet of 1-forms @xmath3 or , for short , by @xmath1 , which constitutes the coframe field of spacetime . their vacuum field equation is simply the wave equation with an additional ` massive ' contribution depending on some scalar field @xmath4 : @xmath5\vartheta^\alpha=0\,.\ ] ] they show that the yilmaz - rosen metric @xcite solves the _ tracefree _ part of exactly . let us be a bit more specific : the yilmaz - rosen metric , in isotropic coordinates , is given by @xmath6 where @xmath7 . if we introduce an orthonormal coframe , @xmath8 then the following coframe , up to arbitrary local lorentz transformations , represents the yilmaz - rosen metric : @xmath9 the tracefree part of will be determined in sec . [ sec:44 ] and turns out to be @xmath10\vartheta^\alpha=0\,.\ ] ] the coframe solves the tracefree field equation exactly . we have verified this by means of our computer algebra program kaniti.exi displayed in the appendix in sec . [ sec : ca ] . kaniel & itin tried to derive the field equation from a suitable lagrangian . for that purpose they had to assume specifically that the variation @xmath11 of the coframe @xmath1 commutes with the hodge star : @xmath12 . however , such a commutativity is only valid for internal yang - mills fields . it is violated for the coframe and the metric . therefore the kaniel - itin model is based on somewhat shaky foundations . in the light of the results mentioned so far , the following questions come to mind : ( i ) what is the source on the right hand side of the field equation ? ( ii ) can the yilmaz - rosen metric also be adjusted to the trace part of and , more generally , to a possible source term on the right hand side of ? ( iii ) is there a consistent variational principle available which would allow to derive , including a source term , from a suitable lagrangian ? ( iv ) what is the ( geometrical ? ) meaning of the constrained variations of kaniel & itin ? the purpose of this article is to try to answer these questions . moreover , along our way , we will discuss some unclear points on the commutativity of variation and hodge star which led to some ( so far uncorrected ) mistakes in the literature. in sec . [ sec : model - ki ] we provide some background material on how to derive wave equations of the general type from lagrangians in maxwell s theory and in theories of other internal fields . here and in the following _ internal _ fields are those which do not depend on the spacetime geometry ( in contrast to @xmath1 and @xmath13 ) . in this way we are able to understand how the lagrangian of kaniel - itin comes up in the first place . but since they identify the _ gravitational potential _ with the _ coframe _ , we run into trouble from the point of view of finding a suitable lagrangian . any reasonable gauge approach to gravity contains in some way the gauging of the translation group . the simplest gauge theories of gravity are teleparallel theories with only the translation group as gauge group . they already require the knowledge of how to vary the hodge dual of forms . in a teleparallel theory , spacetime can be described by an _ coframe @xmath1 as the only gravitational field variable , which is interpreted as translational gauge potential , see @xcite . and this gauge potential was used by kaniel - itin in their model . accordingly , their lagrangian is a special teleparallelism lagrangian with the additional postulate of constrained variations . the commutativity of @xmath14 and @xmath15 is , in general , _ not _ fulfilled for gauge theories of _ external _ ( or spacetime ) groups , i.e. , for gravitational gauge theories . in this case it is important to know the commutator @xmath16 of the variation @xmath14 and the hodge star @xmath17 . therefore , in sec . [ sec : hodge ] we will derive the master formula for @xmath16 . we will include general variations of the components @xmath13 of the riemannian metric @xmath18 besides those of a ( not necessarily orthonormal ) coframe @xmath1 . if we _ insist _ , in accordance with the kaniel - itin postulate , on commutativity of @xmath14 and @xmath17 , then the variations @xmath19 of the components of the metric are no longer independent and can be expressed in terms of the variation @xmath11 of the coframe , see . in sec . [ sec : tele ] we give a short overview of teleparallelism theories and the relevant quadratic lagrangians . we will discuss the viable set of lagrangians and display the results in table 1 . we will show that the ki - lagrangian , for arbitrary variations , is not viable . some errors in the literature ( see schweitzer et al . @xcite ) are rectified . in sec . [ sec : ki ] , we evaluate the model of kanin & itin @xcite . the field equation of the constrained variational principle is the _ antisymmetric part _ of a wave equation for @xmath1 , in contrast to the full wave equation as claimed by kaniel and itin . the yilmaz - rosen metric , found by yilmaz ( * ? ? ? * eqs.(18 ) and ( 20 ) ) in 1958 as a solution in the context of a scalar field theory of gravitation , also turned out to be a solution of the bi - metric theory of gravitation of rosen @xcite ; cf . also @xcite . and , in the kaniel - itin model , it solves the tracefree wave equation . in sec . [ sec : yr - sol ] we compare the yilmaz - rosen with the schwarzschild metric and give , in sec . [ yr - mot ] , a motivation for the emergence of the yilmaz - rosen metric . finally , we investigate the implications that would arise if the yilmaz - rosen metric is considered to be a solution of the field equation of kaniel & itin including its trace . in sec . 6 we collect our arguments .

recently kaniel & itin proposed a gravitational model with the wave type equation\vartheta^\alpha=0 $ ] as vacuum field equation , where denotes the coframe of spacetime . they found that the viable yilmaz - rosen metric is an exact solution of the tracefree part of their field equation . this model belongs to the _ teleparallelism _ class of gravitational gauge theories . of decisive importance for the evaluation of the kaniel - itin model is the question whether the variation of the coframe commutes with the hodge star . we find a master formula for this commutator and rectify some corresponding mistakes in the literature . then we turn to a detailed discussion of the kaniel - itin model . _ file kaniel21.tex , 1998 - 01 - 12 _ keywords : gravity , gauge theory , teleparallelism , variation , hodge duals

recently kaniel & itin proposed a gravitational model with the wave type equation\vartheta^\alpha=0 $ ] as vacuum field equation , where denotes the coframe of spacetime . they found that the viable yilmaz - rosen metric is an exact solution of the tracefree part of their field equation . this model belongs to the _ teleparallelism _ class of gravitational gauge theories . of decisive importance for the evaluation of the kaniel - itin model is the question whether the variation of the coframe commutes with the hodge star . we find a master formula for this commutator and rectify some corresponding mistakes in the literature . then we turn to a detailed discussion of the kaniel - itin model . _ file kaniel21.tex , 1998 - 01 - 12 _ keywords : gravity , gauge theory , teleparallelism , variation , hodge duals

1407.5484

i

during mitosis , the cell equally divides into two daughter cells , each getting a copy of the original genetic material . successful division requires that the two identical sister chromatids of mitotic chromosomes attach to the plus - ends of spindle microtubules ( mts ) via their kinetochores @xcite . this process is critical because incorrect attachments lead to mitotic errors giving rise to genetic instabilities , also involved in cancer @xcite . to ensure accurate chromosome segregation , correct mt - kinetochore attachments should remain stable while faulty attachments should be destabilized and corrected @xcite . mts are composed by a number of protofilaments ( pfs ) , typically thirteen , and polymerize by the addition of tubulin dimers in their gtp - bound state . growing mts switch to a shrinkage phase when all or most gtp - bound tubulin is hydrolysed , a process known as catastrophe , while the switch back to a growing state is known as resuce . these two processes constitute the _ dynamic instability _ of mts.@xcite . gtp - hydrolysis also induces a change in conformation of mt protofilaments from a straight to a curved state @xcite which eventually leads to depolymerization , since curved pfs tend to peel from the mt while straight filaments are stable . indeed electron micrographs of microtubules show that individual pfs can be seen curving outwards from the ends @xcite . mechanical measurements of the rigidity of mts show that their young s modulus is two orders of magnitude smaller than the shear modulus @xcite . this implies that tubulin dimers interact strongly along the pf and weakly along the transverse direction . all these structural , mechanical and kinetic aspects have been included in theoretical and computational models that describe with great accuracy the main features of the stability and dynamic instability of mts @xcite . mt - kinetochore attachments vary in different organisms , but all seem to share a common feature @xcite : fibrils extending from the kinetochore either link directly to curling mt - pfs , as in most higher eukaryotes @xcite , or fibrils linking to a ring , known as the @xmath01 complex @xcite , form around the attached mt , as in budding yeast @xcite . once the attachment has been formed , mt depolymerization @xcite provides a force that is strong enough to carry kinetochore - attached loads @xcite , even in the absence of motor proteins . the precise nature of the attachment between kinetochore fibrils and mts has been the object of intense experimental investigation suggesting that binding occurs through the ndc80 complex which interacts with tubulin by weak electrostatic forces @xcite . other experiments show that the ndc80 complex acts like a curvature sensor and binds preferentially to straight mt pfs , typical of polymerizing mts @xcite . on the other hand , electron micrographs illustrate vividly that kinetochore fibrils directly connect to the tips of _ curling _ pfs @xcite . in a recent paper , akiyoshi et al . @xcite have shown that yeast kinetochores form _ catch - bonds _ with mts . _ catch - bonds _ become stronger under a pulling force @xcite , thus providing a possible stabilizing mechanism needed for chromosome segregation . akiyoshi et al . also show that the kinethocore forms _ catch - bonds _ only with depolymerizing mts , whereas it forms standard force - weakening bonds with polymerizing mts @xcite . the authors encompass this information into a simple two - states kinetic model that is able to fit well the experimentally measured detachment times @xcite . the physical mechanism by which a _ catch - bond _ forms remains , however , still unclear . it is easy to understand that electrostatic interactions alone , even if protein complexes act cooperatively @xcite , would not give rise to a _ catch - bond _ : pulling charges apart leads to a weakening of the bond and should therefore increase the detachment rate . thus electrostatic interactions reasonably account for the experimentally observed increase of detachment rate for polymerizing mts under tension , but can not explain at the same time the decreasing detachment rate observed for depolymerizing mts . models of mt - kinetochore interactions are abundant ranging from the classical sleeve model @xcite to curling models @xcite and syntheses of both @xcite as well as incorporation of motor proteins @xcite , but none of them provide insight into the observed _ catch - bond _ behavior . in this paper , we resolve this puzzle by combining existing experimental evidence into a model of mt - kinetochore attachment that can explain the formation of _ catch - bonds_. we consider the interaction of a microtubule with a set of kinetochore fibrils with tips that can directly bind to straight mt - protofilaments and to neighbor fibril tips as suggested in ref . @xcite for the ndc80 complex . similarly , the fibrils can be effectively cross linked by other protein complexes as e.g. the @xmath1 complex in budding yeast or the mis12 complex in ptk@xmath2 cells @xcite . hence , when a polymerizing mt approaches the kinetochore , fibrils attach to its surface due their direct interactions . this attachment is a standard force - weakening bond as expected , but the mutual interactions or cross - linking between fibrils naturally leads to the formation of fibril loops . when mts depolymerize , the direct fibril - mt binding force is strongly suppressed @xcite , but the tips of curling pfs can easily entangle in the fibril loops . this attachment is now a _ catch - bond _ , since it becomes stronger under tension . the mechanism we propose is very general and could also involve other kinetochore proteins , such as cenp - e @xcite , cenp - t @xcite , cenp - f @xcite or the ska complex @xcite , rather than just ndc80 , which is too short to account for the fibrils alone . finally , the entangled organization of the observed in vertebrate kinetochores @xcite , provides another striking example where a velcro - like attachment , such as the one we propose , could naturally take place . we illustrate the formation of a conformational attachment by three dimensional simulations of a single depolymerizing mt interacting with a set of kinetochore fibrils . once we are confident that a conformational attachment is formed , we can reduce the computational complexity of the problem by focusing on a two - dimensional representation of the interaction between a pf and a fibril loop . numerical results of the two dimensional model reproduce with good accuracy the _ catch - bond _ behavior reported experimentally in ref . we also study the stability of the mt attachment and find that it crucially depends on the local conformation of the mt . by changing the intrinsic curvature of the mt - pf , the attachment is destabilized and the _ catch - bond _ disappears . our results suggest that the experimentally observed tension - induced stabilization of mt - kinetochore attachments could be explained by a conformational mechanism although chemical affinities between mts and kinetochore proteins may also play a role .

here we introduce and simulate a mechanical model of mt - kinetochore interactions in which the stability of the attachment is ruled by the geometrical conformations of curling mt - protofilaments entangled in kinetochore fibrils . the model allows us to reproduce with good accuracy in vitro experimental measurements of the detachment times of yeast kinetochores from mts under external pulling forces . key words : _ microtubule ; catch bond ; numerical simulation ; kinetochore ; mitosis . _ _ abbreviations : _ _ mt , microtubule ; pf , protofilament

regulating the stability of microtubule(mt)-kinetochore attachments is fundamental to avoiding mitotic errors and ensure proper chromosome segregation during cell division . while biochemical factors involved in this process have been identified , its mechanics still needs to be better understood . here we introduce and simulate a mechanical model of mt - kinetochore interactions in which the stability of the attachment is ruled by the geometrical conformations of curling mt - protofilaments entangled in kinetochore fibrils . the model allows us to reproduce with good accuracy in vitro experimental measurements of the detachment times of yeast kinetochores from mts under external pulling forces . numerical simulations suggest that geometrical features of mt - protofilaments may play an important role in the switch between stable and unstable attachments . _ key words : _ microtubule ; catch bond ; numerical simulation ; kinetochore ; mitosis . _ _ abbreviations : _ _ mt , microtubule ; pf , protofilament

0806.2658

i

in this paper we have carried out a synoptic analysis of the different observational features that have to do with the uv luminosity excess in elliptical galaxies . as far as the canonical picture is assumed , with old stellar populations dominating early - type galaxy luminosity , the appearence of the `` uv upturn '' should readily call for a profound change in the c - m diagram of galaxy stellar populations , not only involving the hot stellar component of the galaxy but also reverberating on red - giant evolution at the low - temperature regime . as we mainly deal with distant , unresolved stellar populations , our analysis has to rely on a combined approach , matching infrared and ultraviolet diagnostic tools in order to probe the main features of the stellar c - m diagram , starting with integrated galaxy photometry . theory of surface - brightness fluctuations provides , in this sense , a natural and quite powerful way to go deep inside the problem and , as far as the infrared wavelength interval is considered , we have demonstrated theoretically that a straight and very clean relationship is in place between a macroscopic measure , such as the galaxy fluctuation magnitude , and the corresponding individual magnitude of the brightest stars in turn at the tip of the red - giant ( agb+rgb ) phases ( fig . 2 ) . played in the @xmath28 band , this correlation leads , from a measurement of @xmath0 , to a value for @xmath34 : @xmath86 with a @xmath87 mag internal uncertainty . as we showed in sec . 2 , our ssp theoretical predictions find full support from the observations , and a direct check on the mc star clusters confirms the @xmath0 vs. @xmath34 relationship to be a much more general and deeply intrinsic property of stellar populations , virtually independent from any assumption about age , metallicity , imf , and mass loss parameters . given its nature , this relationship can not , by itself , help disentangle the problem of age / metallicity degeneracy ; however , quite fruitfully , it provides us with a very direct probe of agb properties , in a number of relevant details that directly deal with the mass - loss impact and the mass of dying stars ( fig . our effort toward exploring the infrared side of galaxy seds has a twofold aim since , as a consequence of the basic principle of energy conservation , any gram of stellar fuel spent to feed ultraviolet luminosity can not ( and will not ) be spent at longer wavelengths . this has led to the key issue of this paper , summarized in fig . 6 , that the _ strengthening of the uv rising branch is always seen to correspond to a weakening in the agb luminosity extension _ , as traced by galaxy @xmath28 fluctuation magnitude . this `` shortening '' in agb deployment is mainly recognized among giant ellipticals ( @xmath0 becomes fainter with increasing galaxy velocity dispersion , @xmath76 , see fig . 7 ) , and could mainly be ascribed to an age effect , as the agb tip naturally fades in luminosity with increasing age of the system ( fig . 3 ) , and high - mass galaxies are recognized to be older than systems of lower mass ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? however , the relationship in place likely calls for a more elaborated physical scenario , once the full range of observing evidences is added to our analysis . vs. lick mg@xmath67 index , for the galaxy sample in table [ tab_tot ] . the lick index is assumed to trace galaxy metallicity according to the @xcite calibration , as reported on the top axis of the plot . the observed decrease in @xmath34 with increasing @xmath88 $ ] can be mostly explained if more metal - rich galaxies are also older , as in a standard monolythic scenario for galaxy formation . the dashed line on the plot marks the minimum luminosity required for stars to experience the thermal pulsing phase along their agb evolution , and thus end their evolution as pne . ] _ ( a ) _ besides being old , `` uv upturn '' galaxies are also metal rich ( i.e. , stronger in mg@xmath67 lick index ) . disregarding any change in mass - loss rate , stellar tracks predict slightly more massive stars to evolve off the ms at a fixed age , with increasing metallicity ( e.g. , * * ; * ? ? ? this leads to correspondingly more massive agb stars and a brighter agb luminosity . facing the observed trend in galaxy distribution , as summarized in fig . 12 , metallicity effects evidently enter by mitigating the dimming action of age on @xmath34 with increasing galaxy mass . in any case , the interplay between age and metal abundance actually makes the derived range for the reimers mass - loss parameter ( i.e. @xmath74 , as discussed in sec . 3 ) a safe upper limit . in fact , it suggests that metal abundance does _ not _ modulate by orders of magnitude mass - loss efficiency via stellar winds .. conversely , also from data of single stars , @xcite argues that @xmath89 is metallicity - independent . from a theoretical point of view , @xcite models suggest that , if mass - loss is really proportional to metallicity , its effect to dim near - ir effective luminosities on average almost exactly offsets the brightening effect of metallicity itself . ] _ ( b ) _ a match of galaxy @xmath0 data with the calibration of fig . 5 confirms that , all the way , brightest stars in ellipticals are genuine agb members , reaching the thermal - pulsing phase ( see also fig . 12 ) , and with the agb tip exceeding the rgb tip by some 0.5 - 1.5 mag . in the temperature range of m giant stars , a major fraction of bolometric luminosity is emitted through the @xmath28 band , and bolometric correction is a nearly constant quantity that we can estimate from @xmath90 mag @xcite ; we can therefore straightforwardly translate the galaxy fluctuation magnitude into an estimate of the bolometric tip luminosity , @xmath91 , and therefrom of the corresponding stellar core mass . from our previous calibration ( eq . [ eq : calib ] ) , we can write then @xmath92\ ] ] ( where the sun has magnitude m@xmath93 ) . following @xcite , from the assumed core mass - luminosity relation for the solar metallicity range , this leads to @xmath94 . \label{mctip}\ ] ] figure 13 reports the inferred core - mass distribution , at the pn onset , for our galaxy sample . note that this is the _ maximum _ actual mass allowed to luminous stars in each galaxy environment , and demonstrates that the _ mass of dying stars tends to decrease with increasing uv - upturn strength _ , being in general @xmath95 m@xmath2 among giant ellipticals . for this mass range , pn lifetime is the largest possible , but the timescale for the nebula to be visible is critically constrained by the transition time ( @xmath96 ) needed by the post - agb stellar core to be hot enough to `` fire up '' the ejected envelope and become a hard uv emitter @xcite . the evident drop of @xmath77 among strong uv - upturn galaxies ( fig . 8) might be a direct consequence , therefore , of an increasing blocking effect of @xmath96 along the inferred @xmath97 range ( i.e. , the stellar core takes longer to heat - up than the shell to evaporate ; * ? ? ? * ) , to which one has to further add a size cut in the overall pn population , as a result of the ehb progenitors ( m@xmath98 m@xmath2 ) evolving as _ agb - manqu _ stars and therefore skipping the nebula event . _ ( c ) _ we remarked , in sec . 3 , the importance of the integrated @xmath82 index as a fairly selective tracer of the warm ( t@xmath99 k ) stellar component in the galaxy stellar population . a proper assessment of the photometric contribution from this range of temperatures is of paramount importance in the framework of early - type galaxy evolution , in order to single out any signature of recent ( i.e. , in the last few gyr or so ) star formation or , conversely , of intervening evolution of the hb morphology among old ssps , as in a more standard canonical scenario . as far as uv - upturn galaxies are concerned , the study of @xmath82 distribution clearly points to _ a substantial lack of a - type stars _ in the galaxy mix ( see fig . while , on one hand , this definitely secures the `` quiescent '' nature of these galaxies , it also poses , on the other hand , a stringent constraint on hb morphology in their old - age context . in fact , a bimodal temperature distribution is required for the hb to assure , at a time , both an enhanced uv emission _ and _ a conveniently low @xmath82 feature . thus , in these systems the expected prevailing bulk of red hb stars should be accompanied , at some point , by a residual population of blue ( metal - poor ? ) hb objects ( coincident with ehb stars in the current empirical classification scheme ) , peaked at about 20000 - 40000 k , in a proportion of , roughly , @xmath100 $ ] . on the other hand , to complete the picture , one can not neglect the masking effects of age distribution , facing a recognized evidence for low - mass ellipticals to display a more silent but also more continuous star formation along their entire galaxy life , that naturally feeds the a - star contribution , thanks to the bluer ms turn - off point ( msto ) exhibited by ssps in the @xmath101 gyr age range , and leads to a younger average " age , compared to high - mass systems . this is what we observe , for instance , among the resolved stellar populations of the local group dwarf spheroidals @xcite ( see , in this regard , the illustrative location of m32 in fig . 9 , and also consider the discussion by * ? ? ( d ) _ along with our discussion of the @xmath0 vs. @xmath66 relation , we noticed , in fig . 6 , the presence of a few outliers about 0.7 mag brighter at infrared magnitudes , or alternatively @xmath102 mag `` bluer '' in the @xmath66 color , than the main galaxy population . in order to further investigate this issue , we tracked the relevant objects also in other figures , whenever possible . if galaxy mass ( _ alias _ @xmath103 ) is considered as the leading physical parameter to compare outlier location with respect to the bulk of the galaxy distribution ( see , for instance fig . 7 ) , one must conclude that both ngc 4552 and ngc 1389 seem to have a brighter agb tip rather than a bluer @xmath66 color . with regard to ngc 1389 , @xcite find that the @xmath104 sbfs of ngc 1389 are also too bright compared to its ( @xmath105 ) color , a fact that would be consistent with either a higher than average metallicity given the age of its most recent burst of star formation or a longer lifetime of its tp - agb stars @xcite . in the case of ngc 4552 , however , @xcite contribute an interesting piece of information . these authors measure near - ir sbfs for several galaxies in virgo , and their results are systematically fainter than those obtained by @xcite . unfortunately , the two groups use slightly different filters ( jensen et al . employ @xmath106 , vs. @xmath40 of pahre & mould ) , but the discrepancy is larger than can be ascribed to the effect of the filters . in particular , jensen et al . find @xmath107 for ngc 4552 ; assuming @xmath108 , ngc 4552 would no longer be deviant in the @xmath104 vs. ( @xmath109 ) plane . concerning ngc 1387 , the dearth of data for this galaxy in the literature ( see table 2 ) makes it hard to propose an origin for its departure from the @xmath104 vs. ( @xmath109 ) sequence . vs. ( @xmath105 ) correlation determined by @xcite . ] on the other hand , ngc 1387 and ngc 1389 are lenticular galaxies , like the merger remnant ngc 1316 , but so are ngc 3384 and ngc 4406 , both of which do not deviate from the correlation . at any rate , ngc 1387 and ngc 1389 constitute privileged candidates for any future `` in - depth '' investigation . we would like to thank gustavo bruzual for providing us with his latest ssp models , in advance of publication , and livia origlia , for useful discussions . the anonymous referee is also acknowledged for his / her competent suggestions , that greatly helped refine the main focus of the paper . partial financial support is acknowledged from the italian miur , under grant inaf - prin05 1.06.08.03 , and mexican conacyt , under grant no . 48589-f , and dgapa , under grant in111007 . bailyn , c. d. 1995 , , 33 , 133 blakeslee , j. p. , vazdekis , a. , & ajhar , e. a. 2001 , , 320 , 193 boothroyd , a. i. , & sackmann , i .- 1988 , , 328 , 641 bressan , a. , chiosi , c. , & fagotto , f. 1994 , , 94 , 63 bressan , a. , chiosi , c. , & tantalo , r. 1996 , , 311 , 425 brodie , j. p. , & huchra , j. p. 1990 , , 362 , 503 brown , t. m. 2004 , astrophys . space sci . , 291 , 215 brown , t. m. , ferguson , h. c. , davidsen , a. f. , dorman , b. 1997 , 482 , 685 brown , t. m. , ferguson , h. c. , stanford , s. a. , deharveng , j .- m . 1998 , , 504 , 113 brown , t. m. , bowers , c. w. , kimble , r. a. , sweigart , a. v. , & ferguson , h. c. 2000 , , 532 , 308 brown , t. m. , ferguson , h. c. , smith , e. , bowers , c. w. , kimble , r. a. , renzini , a. , & rich , r. m. 2003 , , 584 , l69 brown , d. , yi , s. , han , z. , & yoon , s .- j . 2006 , baltic astronomy , 15 , 13 bruzual , g. , 2007 , in proc . of the iau symp . 241 `` stellar populations as building blocks of galaxies '' , eds . a. vazdekis and r. peletier ( cambridge : cambridge univ . press ) , p.125 ( see also astro - ph/0703052 ) bruzual , g. , & charlot , s. 2003 , , 344 , 1000 buonanno , r. , corsi , c. , bellazzini , m. , ferraro , f. r. , & pecci , f. f. 1997 , , 113 , 706 burstein , d. , bertola , f. , buson , l. m. , faber , s. m. , & lauer , t. r. 1988 , , 328 , 440 buson , l. m. , bertone , e. , buzzoni , a. , & carraro , g. 2006 , baltic astronomy , 15 , 49 busso , g. , moehler , s. , zoccali , m. , heber , u. , & yi , s. k. 2005 , , 633 , l29 buzzoni , a. 1989 , , 71 , 817 buzzoni , a. 1993 , , 275 , 433 buzzoni , a. 1995 , , 98 , 69 buzzoni , a. 1998 in t. zanzu , v. testa & m. bellazzini eds . , evolving evolution , oss . di cagliari , cagliari , p. 13 ( see also astro - ph/9811382 ) buzzoni , a. 2008 , in d. valls - gabaud & m. chavez eds . , `` resolved stellar populations '' , asp conf . ( asp : san francisco ) , in press ( see also astro - ph/0509602 ) buzzoni , a. , gariboldi , g. , & mantegazza , l. 1992 , , 103 , 1814 buzzoni , a. , mantegazza , l. , & gariboldi , g. 1994 , , 107 , 513 buzzoni , a. , arnaboldi , m. , & corradi , r. l. m. 2006 , , 368 , 877 cantiello , m. , raimondo , g. , brocato , e. , & capaccioli , m. 2003 , , 125 , 2783 castellani , v. , & renzini , a. 1968 , , 2 , 310 castellani m. , & tornamb a. 1991 , apj , 381 , 393 castellani , v. , giannone , p. , & renzini , a. 1970 , , 9 , 418 castellani m. , limongi m. , tornamb a. 1992 , , 389 , 227 castellani , v. , iannicola , g. , bono , g. , zoccali , m. , cassisi , s. , & buonanno , r. 2006 , , 446 , 569 catelan , m. , ferraro , f. r. , & rood , r. t. 2001 , , 560 , 970 cervio , m. , & luridiana , v. 2006 , , 451 , 475 cervio , m. , luridiana , v. , & castander , f. j. 2000 , , 360 , l5 cervio , m. , valls - gabaud , d. , luridiana , v. , & mas - hesse , j. m. 2002 , , 381 , 51 chabrier , g. 2003 , , 115 , 763 charbonnel , c. , meynet , g. , maeder , a. , & schaerer , d. 1996 , , 115 , 339 chiosi , c. , bertelli , g. , bressan , a. 1992 , , 30,235 code , a. d. , & welch , g. a. 1979 , , 228 , 95 cohen j. g. 1982 , , 258 , 143 colina , l. , bohlin , r. c. , & castelli , f. 1996 , instrument science report cal / scs-008 ( baltimore , stsci ) cox , j.p . & giuli , r.t . 1968 principles of stellar structure , gordon & breach sci . ltd , new york . dcruz , n. l. , dorman , b. , rood , r. t. , & oconnell , r. w. 1996 , , 466 , 359 dcruz , n. l. , morgan , s. m. , bhm - vitense , e. 2000 , , 120 , 990 demleitner , m. , accomazzi , a. , eichhorn , g. , grant , c. s. , kurtz , m. j. , & murray , s. s. 2001 , in astronomical data analysis software and systems x , asp conf . 238 , eds . f. r. harnden , jr . , francis a. primini , and harry e. payne ( san francisco : asp ) , p.321 de vaucouleurs , g. , de vaucouleurs , a. , corwin , h.g . , buta , r.j . , paturel , g. , fouque , p. 1991 , third reference catalog of bright galaxies . springer verlag , heidelberg dorman , b. , rood , r.t . , oconnell , r.w . 1993 , , 419 , 596 dorman , b. , oconnell , r. w. , & rood , r. t. 1995 , , 442 , 105 demarque , p. , mengel , j. g. , & sweigart , a. v. 1972 , , 173 , l27 elson , r. a. w. , & fall , s. m. 1985 , , 299 , 211 elson , r. a. , & fall , s. m. 1988 , , 96 , 1383 ferguson , h.c . , & davidsen , a.f . 1993 , , 408 , 92 frogel , j.a . , mould , j. , & blanco , v.m . 1990 , , 352 , 96 fusi pecci , & f. , renzini , a. 1976 , , 46 , 447 gonzlez , r. a. , liu , m. c. , & bruzual a. , g. 2004 , , 611 , 270 height0.4pt depth0.0pt width1.0 in .2005 , , 621 , 557 gonzlez - lpezlira , r. a. , albarrn , m. y. , mouhcine , m. , liu , m . c. , bruzual - a . , g. , & de batz , b. 2005 , , 363 , 1279 greggio , l. , & renzini , a. 1990 , , 364 , 35 groenewegen , m. a. t. , smith , c. h. , wood , p. r. , omont , a. , & fujiyoshi , t. 1995 , , 449 , l119 hui x. , ford h.c . , ciardullo r. , jacoby g.h . 1993 , apj , 414 , 463 iben , i. j. , & rood , r. t. 1970 , , 161 , 587 iben , i. , jr . , & renzini , a. 1983 , , 21 , 271 jensen , j. b. , luppino , g. a. , & tonry , j. l. 1996 , , 468 , 519 jensen , j. b. , tonry , j. l. , & luppino , g. a. 1998 , , 505 , 111 jensen , j. b. , tonry , j. l. , barris , b. j. , thompson , r. i. , liu , m. c. , rieke , m. j. , ajhar , e. a. , & blakeslee , j. p. 2003 , , 583 , 712 johnson , h. l. 1966 , , 4 , 193 kaluzny , j. , & udalski , a. 1992 , acta astronomica , 42 , 29 kobayashi , c. , & arimoto , n. 1999 , , 527 , 573 kuntschner , h. , lucey , j. r. , smith , r. j. , hudson , m. j. , & davies , r. l. 2001 , , 323 , 615 larson , r.b . 1974 , , 166 , 585 lee , m. g. , freedman , w. l. , & madore , b. f. 1993 , , 417 , 553 lee , y .- w . , ree , c. h. , rich , r.m . , et al . 2005 , , 619 , l103 liu , m. c. , graham , j. r. , & charlot , s. 2002 , , 564 , 216 maraston , c. , greggio , l. , & thomas , d. 2001 , , 276 , 893 marigo , p. , girardi , l. , weiss , a. , groenewegen , m. a. t. , & chiosi , c. 2004 , , 423 , 995 marigo , p. , & girardi , l. 2007 , , 469 , 239 mateo , m. l. 1998 , , 36 , 435 mouhcine , m. , gonzlez , r. a. , & liu , m. c. 2005 , , 362 , 1208 oconnell , r. w. 1980 , , 236 , 430 oconnell , r. w. 1999 , , 37 , 603 paczyski , b. 1970 , acta astronomica , 20 , 47 pahre , m. a. , de carvalho , r. r. , & djorgovski , s. g. 1998 , , 116 , 1606 pahre , m. a. , & mould , j. r. 1994 , , 433 , 567 park , j .- h . , & lee , y .- w . 1997 , , 476 , 28 paturel , g. , petit , c. , prugniel , p. , theureau , g. , rousseau , j. , brouty , m. , dubois , p. , & cambrsy , l. 2003 , , 412 , 45 peimbert m. 1990 , rev . , 20 , 119 persson , s. e. , murphy , d. c. , krzeminski , w. , roth , m. , & rieke , m. j. 1998 , , 116 , 2475 piersanti , l. , tornamb , a. , & castellani , v. 2004 , , 353 , 243 raimondo , g. , brocato , e. , cantiello , m. , & capaccioli , m. 2005 , , 130 , 2625 recio - blanco , a. , aparicio , a. , piotto , g. , de angeli , f. , & djorgovski , s. g. 2006 , , 452 , 875 ree , c. h. , lee , y .- w . , sohn , y .- j . , yi , s. k. , yoon , s .- j . , & the galex science team 2006 , baltic astronomy , 15 , 5 reimers , d. 1975 , mem . soc . lige , 6th ser . , 8 , 87 renzini , a. 1977 , in advanced stages in stellar evolution i. , eds . iben jr . , a. renzini , d.n . schramm ( heidelberg : springer verlag ) . renzini , a. 2006 , , 44 , 141 renzini , a. , & buzzoni , a. 1986 , in spectral evolution of galaxies , eds . c. chiosi & a. renzini ( dordrecht : reidel ) , p. 195 renzini , a. , & fusi pecci , f. 1988 , , 1988 , 26 , 199 rich , r. m. , et al . 1997 , , 484 , l25 rose , j.a . , & deng , s. 1999 , , 117 , 2213 schnberner , d. 1983 , , 272 , 708 schiavon , r.p . , caldwell , n. , & rose , j.a . 2004 , , 127,1513 searle , l. , wilkinson , a. , & bagnuolo , w. g. 1980 , , 239 , 803 seidel , e. , da costa , g. s. , & demarque , p. 1987 , , 313 , 192 skrutskie , m. f. et al . 1997 , assl vol . 210 : the impact of large scale near ir sky surveys , 25 stanghellini , l. , & renzini , a. 2000 , , 542 , 308 sweigart , a. v. 1997 , , 474 , l23 sweigart , a. v. , & gross , p. g. 1976 , , 32 , 367 sweigart , a. v. , brown , t. m. , lanz , t. , landsman , w. b. , hubeny , i. 2002 in omega centauri , a unique window into astrophysics . asp conf . , vol . 265 . f. van leeuwen , j. d. hughes , & g. piotto ( san francisco : asp ) p.261 tantalo , r. , chiosi , c. , bressan , a. , & fagotto , f. 1996 , , 311 , 361 tonry , j. l. 1991 , , 373 , l1 tonry , j. , & schneider , d. p. 1988 , , 96 , 807 unglaub , k. , bues , i. 2001 , , 374 , 570 van den bergh , s. 1962 , , 67 , 486 van loon , j. t. 2000 , , 354 , 125 worthey , g. 1993 , , 409 , 530 worthey , g. 1994 , , 95 , 107 yi , s. k. , & yoon , s .- j . 2004 , , 291 , 205 yi s. , demarque p. , oemler a. j. 1998 , , 492 , 480

we find that the uv - upturn actually signals a profound change in the c - m diagram of stellar populations in elliptical galaxies , involving both the hot stellar component and red - giant evolution . first , we encounter that the strengthening of the uv rising branch is always seen to correspond to a shortening in agb deployment ; this trend can be readily interpreted as an age effect , perhaps mildly modulated by metal abundance . a comparison between galaxy magnitudes and population synthesis models confirms that , all the way , brightest stars in ellipticals are genuine agb members , reaching the thermal - pulsing phase , and with the agb tip exceeding the rgb tip by some 0.5 - 1.5 mag . the inferred core mass of these stars is found to be m among giant ellipticals .

relying on infrared surface brightness fluctuactions to trace agb properties in a sample of elliptical galaxies in the virgo and fornax clusters , we assess the puzzling origin of the `` uv - upturn '' phenomenon , recently traced down to the presence of a hot horizontal branch ( hb ) stellar component . we find that the uv - upturn actually signals a profound change in the c - m diagram of stellar populations in elliptical galaxies , involving both the hot stellar component and red - giant evolution . first , we encounter that the strengthening of the uv rising branch is always seen to correspond to a shortening in agb deployment ; this trend can be readily interpreted as an age effect , perhaps mildly modulated by metal abundance . a comparison between galaxy magnitudes and population synthesis models confirms that , all the way , brightest stars in ellipticals are genuine agb members , reaching the thermal - pulsing phase , and with the agb tip exceeding the rgb tip by some 0.5 - 1.5 mag . the inferred core mass of these stars is found to be m among giant ellipticals . coupled with the recognized severe deficiency of planetary nebulae in these galaxies , this result strongly calls for an even more critical blocking effect due to a lengthy transition time needed by the post - agb stellar core to become a hard uv emitter and eventually `` fire up '' the nebula . the combined study of galaxy color and integrated h index points , as an explanation for the uv - upturn phenomenon , to a composite hb with a bimodal temperature distribution , i.e. with both a red clump and an extremely blue component , in a relative proportion of roughly [ n(rhb):n(bhb ) ] [ 80:20 ] . as far as metallicity of the bhb stellar population is concerned , we find that [ fe / h ] values of either dex or may provide the optimum ranges to feed the needed low - mass stars ( m m ) , that at some stage begin to join the standard red - clump stars .

hep-ph0606106

i

gauge theories on spaces with noncommuting coordinates , @xmath2=i\,\theta^{\mu\nu } \ , \ ] ] provide a very interesting new class of quantum field theories with intriguing and sometimes unexpected features . these noncommutative models can arise naturally as low - energy effective theories from string theory and d - branes . as field theories they must satisfy a number of restrictive constraints detailed below , and this makes them particularly interesting and challenging for purposes of particle physics model building . for general reviews of noncommutative gauge theories the reader can consult e.g. refs . @xcite . there are two distinct approaches used in the recent literature for constructing quantum field theories on noncommutative spaces . the first approach uses the weyl - moyal star - products to introduce noncommutativity . in this case , noncommutative field theories are defined by replacing the ordinary products of all fields in the lagrangians of their commutative counterparts by the star - products @xmath3 noncommutative theories in the weyl - moyal formalism can be viewed as field theories on ordinary commutative spacetime . for example , the noncommutative pure gauge theory action is @xmath4 where the commutator in the field strength also contains the star - product . the important feature of this approach is the fact that phase factors in the star - products are not expanded in powers of @xmath5 and the @xmath5 dependence in the lagrangian is captured entirely . this ability to work to all orders in @xmath5 famously gives rise to the ultraviolet / infrared ( uv / ir ) mixing @xcite in the noncommutative quantum field theory which we will review below . the second indirect approach to noncommutativity does not employ star - products . it instead relies @xcite on the seiberg - witten map which represents noncommutative fields as a function of @xmath5 and ordinary commutative fields . this approach essentially reduces noncommutativity to an introduction of an infinite set of higher - dimensional ( irrelevant ) operators , each suppressed by the corresponding power of @xmath5 , into the action . there are two main differences compared to the weyl - moyal approach . first , in practice one always works with the first few terms in the power series in @xmath5 and in this setting the uv / ir mixing can not be captured . second , the seiberg - witten map is a non - linear field transformation . therefore , one expects a non - trivial jacobian and possibly a quantum theory different from the one obtained in the weyl - moyal approach . in this paper we will use the original direct formulation of the theory on a noncommutative space in terms of the weyl - moyal star product . in the context of weyl - moyal noncommutative standard model building , a number of features of noncommutative gauge theories have to be taken into account which are believed to be generic @xcite : 1 . the mixing of ultraviolet and infrared effects @xcite and the asymptotic decoupling of u(1 ) degrees of freedom @xcite in the infrared ; 2 . the gauge groups are restricted to u(@xmath6 ) groups @xcite or products of thereof ; 3 . fields can transform only in ( anti-)fundamental , bi - fundamental and adjoint representations @xcite ; 4 . the charges of matter fields are restricted @xcite to @xmath7 and @xmath8 , thus requiring extra care in order to give fractional electric charges to the quarks . building upon an earlier proposal by chaichian _ @xcite , the authors of ref . @xcite constructed an example of a noncommutative embedding of the standard model with the purpose to satisfy all the requirements listed above . the model of @xcite is based on the gauge group @xmath9 with matter fields transforming in noncommutatively allowed representations . higgs fields break the noncommutative gauge group down to a low - energy commutative gauge theory which includes the standard model group @xmath10 . the @xmath11 group here corresponds to ordinary qed , or more precisely to the hypercharge @xmath12 abelian gauge theory . the generator of @xmath11 was constructed from a linear combination of _ traceless _ diagonal generators of the microscopic theory @xmath13 because of this , the uv / ir effects which can affect only the overall trace-@xmath14 subgroup of each @xmath15 were not contributing to the hypercharge @xmath16 however some of the overall trace-@xmath17 degrees of freedom can survive the higgs mechanism and thus contribute to the low - energy effective theory , in addition to the standard model fields . these additional trace-@xmath14 gauge fields logarithmically decouple from the low - energy effective theory and were neglected in the analysis of ref . @xcite . here , we take these effects into account . we will find that the noncommutative model building constraints , and , specifically , the uv / ir mixing effects in the trace - u(1 ) factors in the item 1 above , lead to an unacceptable defective behavior of the low - energy theory , when we try to construct a model having the photon as the only massless colourless u(1 ) gauge boson . our findings pose extremely severe constraints on such models effectively ruling them out . one way out is to modify some of the assumptions . we will discuss the introduction of universal extradimensions and modifications of the noncommutative field theory at very high energy scales . the uv / ir mixing in noncommutative theories arises from the fact that certain classes of feynman diagrams acquire factors of the form @xmath18 ( where @xmath19 is an external momentum and @xmath20 is a loop momentum ) compared to their commutative counter - parts . these factors directly follow from the use of the weyl - moyal star - product ( [ stardef ] ) . at large values of the loop momentum @xmath20 , the oscillations of @xmath18 improve the convergence of the loop integrals . however , as the external momentum vanishes , @xmath21 the divergence reappears and what would have been a uv divergence is now reinterpreted as an ir divergence instead . this phenomenon of uv / ir mixing is specific to noncommutative theories and does not occur in the commutative settings where the physics of high energy degrees of freedom does not affect the physics at low energies . there are two important points concerning the uv / ir mixing @xcite which we want to stress here . first , the uv / ir mixing occurs only in the trace - u(1 ) components of the noncommutative @xmath22 theory , leaving the @xmath23 degrees of freedom unaffected . second , there are two separate sources of the uv / ir mixing contributing to the dispersion relation of the trace - u(1 ) gauge fields : the @xmath24 effects and the @xmath25 effects , as will be explained momentarily . a study of the wilsonian effective action , obtained by integrating out the high - energy degrees of freedom using the background field method , and keeping track of the uv / ir mixing effects , has given strong hints in favour of a non - universality in the infrared @xcite . in particular , the polarisation tensor of the gauge bosons in a noncommutative @xmath22 gauge theory takes a form @xcite @xmath26 here @xmath27 are adjoint labels of @xmath22 gauge fields , @xmath28 , such that @xmath29 correspond to the overall @xmath14 subgroup , i.e. to the trace - u(1 ) factor . the term in ( [ poltensor ] ) proportional to @xmath30 would not appear in ordinary commutative theories . it is transverse , but not lorentz invariant , as it explicitly depends on @xmath31 nevertheless it is perfectly allowed in noncommutative theories . it is known that @xmath25 vanishes for supersymmetric noncommutative gauge theories with unbroken supersymmetry , as was first discussed in @xcite . in general , both @xmath24 and @xmath25 terms in ( [ poltensor ] ) are affected by the uv / ir mixing . more precisely , as already mentioned earlier , the uv / ir mixing affects specifically the @xmath32 components and generates the @xmath33 components in ( [ poltensor ] ) . the uv / ir mixing in @xmath32 affects the running of the trace - u(1 ) coupling constant in the infrared . for a pure noncommutative gauge theory in 4 continuous dimensions one finds , @xmath34 leading to a logarithmic decoupling of the trace - u(1 ) gauge fields from the @xmath23 low - energy theory , see refs . @xcite for more detail . for nonsupersymmetric theories , @xmath33 can present more serious problems . in theories without supersymmetry , @xmath35 at small momenta , and this leads to unacceptable quadratic ir singularities @xcite . in theories with softly broken supersymmetry ( i.e. with matching number of bosonic and fermionic degrees of freedom ) the quadratic singularities in @xmath33 cancel @xcite . however , the subleading contribution @xmath36 survives @xcite unless the supersymmetry is exact . for the rest of the paper we will concentrate on noncommutative standard model candidates with softly broken supersymmetry , in order to avoid quadratic ir divergencies . in this case , @xmath37 is a measure of susy breaking . ] as explained in @xcite . the presence of such @xmath25 effects will lead to unacceptable pathologies such as lorentz - noninvariant dispersion relations giving mass to only one of the polarisations of the trace - u(1 ) gauge field , leaving the other polarisation massless . the presence of the uv / ir effects in the trace - u(1 ) factors makes it pretty clear that a simple noncommutative u(1 ) theory taken on its own has nothing to do with ordinary qed . the low - energy theory emerging from the noncommutative u(1 ) theory will become free at @xmath38 ( rather than just weakly coupled ) and in addition will have other pathologies @xcite . however , one would expect that it is conceivable to embed a commutative @xmath23 theory , such as e.g. qcd or the weak sector of the standard model into a supersymmetric noncommutative theory in the uv , but some extra care should be taken with the qed u(1 ) sector @xcite . we will show that the only realistic way to embed qed into noncommutative settings is to recover the electromagnetic u(1 ) from a _ traceless _ diagonal generator of some higher @xmath22 gauge theory . so it seems that in order to embed qed into a noncommutative theory one should learn how to embed the whole standard model @xcite . we will see , however , that the additional trace - u(1 ) factors remaining from the noncommutative @xmath22 groups will make the resulting low - energy theories unviable ( for the 4 dimensional models considered in the first half of this paper ) . in order to proceed we would like to disentangle the mass - effects due to the higgs mechanism from the mass - effects due to non - vanishing @xmath39 hence we first set @xmath40 ( this can be achieved by starting with an exactly supersymmetric theory ) . it is then straightforward to show ( see @xcite ) that the higgs mechanism alone can not remove all of the trace - u(1 ) factors from the massless theory . more precisely , the following statement is true : _ consider a scenario where a set of fundamental , bifundamental and adjoint higgs fields breaks @xmath41 such that @xmath42 is non - trivial . then there is at least one generator of the unbroken subgroup @xmath42 with _ non - vanishing trace_. this generator can be chosen such that it generates a u(1 ) subgroup . _ we can now count all the massless u(1 ) factors in a generic noncommutative theory with @xmath40 and after the higgs symmetry breaking . in general we can have the following scenarios for massless u(1 ) degrees of freedom in @xmath42 : 1 . [ possa]@xmath43 is traceless and in addition there is one or more factors of trace - u(1 ) in @xmath42 . [ possb ] @xmath43 arises from a mixture of traceless and trace - u(1 ) generators of the noncommutative product group @xmath44 3 . [ possc ] @xmath43 has an admixture of trace - u(1 ) generators as in ( [ possb ] ) plus there are additional massless trace - u(1 ) factors in @xmath42 . in the following sections we will see that none of these options lead to an acceptable low - energy theory once we have switched on @xmath45 , i.e. once we have introduced mass differences between superpartners . it is well - known @xcite that @xmath45 leads to strong lorentz symmetry violating effects in the dispersion relation of the corresponding trace - u(1 ) vector bosons , and in particular , to mass - difference of their helicity components . if option ( [ possa ] ) was realised in nature , it would lead ( in addition to the standard photon ) to a new colourless vector field with one polarisation being massless , and one massive due to @xmath39 the options ( b ) and ( c ) are also not viable since an admixture of the trace - u(1 ) generators to the photon would also perversely affect photon polarisations and make some of them massive . in the rest of this note we will explain these observations in more detail . we end this section with some general comments on noncommutative standard modelling . in an earlier analysis @xcite the trace - u(1 ) factors were assumed to be completely decoupled in the extreme infrared and , hence , were neglected . however , it is important to keep in mind that the decoupling of the trace - u(1 ) s is logarithmic and hence slow . for a 4 dimensional continuum theory one finds that even in presence of a huge hierarchy between the noncommutative mass scale @xmath46 , say of the order of the planck scale @xmath47 , and the scale @xmath48 ( electroweak and qcd scale , respectively ) , where the su(@xmath6 ) subgroup becomes strong , the ratio @xmath49 is not negligible . in particular , the above inequality holds for any @xmath50 . hence , the complete decoupling of the trace - u(1 ) degrees of freedom at small non - zero momenta does not appear to be fully justified and the trace - u(1 ) would leave its traces in scattering experiments at accessible momentum scales @xmath51 ( see sect . 2 for more detail ) . however , eq . ( [ ration1 ] ) already gives us a hint how one can avoid that the trace - u(1 ) s leave observable traces . the logarithms in eq . ( [ ration1 ] ) are a typical property of the 4 dimensional theory . adding universal extra dimensions ( where gauge fields can propagate into the extra dimensions ) one expects that one gets a much faster power like decoupling . we will explore this possibility in in sect . [ powerlaw ] . finally , starting from the original motivation from string theory another possibility to avoid the conclusions stated above presents itself . viewed as originating from string theory , the noncommutative field theory is only a low energy limit . at very high scales the noncommutative field theory is not necessarily a good description anymore . we discuss a simple ( but not too unreasonable ) modification and study its consequences in sect . [ birefringence ] .

we pay particular attention to overall trace - u(1 ) factors of the gauge group which are affected by the ultraviolet / infrared mixing . unobservable would require making the effects of noncommutativity tiny , . this severely limits the phenomenological prospects of such models . however , adding additional universal extra dimensions the trace - u(1 ) factors decouple with a power law and the constraint on the noncommutativity scale is weakened considerably . finally , we briefly mention some interesting properties of the photon that could arise if the noncommutative theory is modified at a high energy scale .

restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet / infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the standard model . we study a general class of noncommutative models consistent with these restrictions . specifically we consider models based upon a gauge theory with the gauge group coupled to matter fields transforming in the ( anti)-fundamental , bi - fundamental and adjoint representations . we pay particular attention to overall trace - u(1 ) factors of the gauge group which are affected by the ultraviolet / infrared mixing . typically , these trace - u(1 ) gauge fields do not decouple sufficiently fast in the infrared , and lead to sizable lorentz symmetry violating effects in the low - energy effective theory . in a 4-dimensional theory on a continuous space - time making these effects unobservable would require making the effects of noncommutativity tiny , . this severely limits the phenomenological prospects of such models . however , adding additional universal extra dimensions the trace - u(1 ) factors decouple with a power law and the constraint on the noncommutativity scale is weakened considerably . finally , we briefly mention some interesting properties of the photon that could arise if the noncommutative theory is modified at a high energy scale . desy 06 - 087 + ippp/06/34 + dcpt/06/68

hep-ph0606106

c

noncommutative gauge symmetry in the weyl - moyal approach leads to two main features which have to be taken into account for sensible model building . first , there are strong constraints on the dynamics and the field content . the only allowed gauge groups are u(@xmath6 ) . in addition , the matter fields are restricted to transform as fundamental , bifundamental and adjoint representations of the gauge group . second , there are the effects of ultraviolet / infrared mixing . those lead to asymptotic infrared freedom of the trace - u(1 ) subgroup and , if the model does not have unbroken supersymmetry , to lorentz symmetry violating terms in the polarisation tensor for this trace - u(1 ) subgroup . for a 4 dimensional continuum theory we have demonstrated that , although the trace - u(1 ) decouples in the limit @xmath264 , the coupling is not negligibly small at finite momentum scales @xmath19 , as they appear , for example , in scattering experiments . therefore , observations rule out additional unbroken ( massless ) trace - u(1 ) subgroups . noncommutativity explicitly breaks lorentz invariance . therefore an additional lorentz symmetry violating structure is allowed in the polarisation tensor . this structure is absent only in supersymmetric models . if supersymmetry is ( softly ) broken , this additional structure is present in the polarisation tensor of the trace - u(1 ) . it leads to an additional mass @xmath284 for one of the transverse polarisation states @xcite . the tight constraints on the photon mass therefore exclude trace - u(1 ) s as a candidate for the photon . it turns out that even a small admixture of a trace part to a traceless part ( unaffected by these problems ) is fatal . the only way out seems to be the construction of the photon from a completely traceless generator . a group theoretic argument shows , that this is impossible whithout having additional unbroken u(1 ) subgroups . however , those are already excluded from the arguments given above . this result severely restricts the possibilities to construct a noncommutative standard model extension . if all of the constraints given at the beginning are fulfilled the noncommutativity scale is pushed to scales far beyond @xmath285 . in general there is no reason to assume that the simple noncommutative model used here describes correctly the physics at energies ranging from a few ev up to the planck mass . in fact , due to the ultraviolet / infrared mixing , a different ultraviolet embedding of the theory would modify the theory not only in the ultraviolet , but also in the infrared which can drastically alter these conclusions . e.g. , a powerlike decoupling of the trace - u(1 ) can effectively hide them from observation . we have demonstrated that in a noncommutative u(@xmath6 ) gauge theory with compact extra dimensions , the ultraviolet / infrared mixing effects lead to such a fast power - like decoupling of the trace - u(1 ) degrees of freedom . in such a setting the bounds are weakened considerably if the compactification scale is small enough . as an alternative to extra dimensions we have discussed a modification obtained by simply cutting off all fluctuations with momenta larger than a cutoff @xmath248 . the presence of an ultraviolet cutoff @xmath78 induces an effective infrared scale @xmath286 below which the theory behaves essentially like a commutative gauge theory and the theory shows strong effects of noncommutativity at all scales . ] . in particular , up to threshold effects the running is that of a commutative field theory . if supersymmetry is broken , we have a lorentz symmetry violating mass term at scales @xmath287 in accord with @xcite . however , below @xmath288 the mass term turns into a modification of the phase velocity of plane wave solutions , leading to birefringence . nevertheless , if such a trace - u(1 ) gauge boson is to be interpreted as ( part of ) a photon a mass is not acceptable and birefringence must be smaller than the experimental limits . using the most stringent limits from cosmological observations one obtains a rather strong limit of @xmath289 . if we use the more conservative astrophysical or laboratory limits the same argument yields only @xmath290 . in this setting high precision measurements of the properties of light are a wonderful tool to test ( nearly ) planck scale physics .

restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet / infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the standard model . typically , these trace - u(1 ) gauge fields do not decouple sufficiently fast in the infrared , and lead to sizable lorentz symmetry violating effects in the low - energy effective theory . in a 4-dimensional theory on a continuous space - time making these effects

restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet / infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the standard model . we study a general class of noncommutative models consistent with these restrictions . specifically we consider models based upon a gauge theory with the gauge group coupled to matter fields transforming in the ( anti)-fundamental , bi - fundamental and adjoint representations . we pay particular attention to overall trace - u(1 ) factors of the gauge group which are affected by the ultraviolet / infrared mixing . typically , these trace - u(1 ) gauge fields do not decouple sufficiently fast in the infrared , and lead to sizable lorentz symmetry violating effects in the low - energy effective theory . in a 4-dimensional theory on a continuous space - time making these effects unobservable would require making the effects of noncommutativity tiny , . this severely limits the phenomenological prospects of such models . however , adding additional universal extra dimensions the trace - u(1 ) factors decouple with a power law and the constraint on the noncommutativity scale is weakened considerably . finally , we briefly mention some interesting properties of the photon that could arise if the noncommutative theory is modified at a high energy scale . desy 06 - 087 + ippp/06/34 + dcpt/06/68

physics0702192

i

blackbody radiation ( bbr ) is known to strongly affect the populations of atoms in highly excited rydberg states @xcite . it has also been shown that at the ambient temperature of 300 k bbr can photoionize rydberg atoms with @xmath1 at astonishingly high rates ( @xmath2 ) @xcite . strong effect of bbr on rydberg atoms is related to large matrix elements of bound - bound and bound - free transitions between rydberg states in the microwave and far infrared spectral range @xcite . interaction of rydberg atoms with bbr has been studied earlier in various contexts . farley and wing @xcite calculated the dynamic stark shifts and depopulation rates of rydberg levels of alkali atoms with @xmath3 at 300 k. the temperature dependence of bbr - induced transitions rates from the 19s state of sodium was calculated and measured by spencer et al @xcite . galvez et al @xcite have studied bbr - induced cascade transitions from the initially populated @xmath4=24 - 29 states of na , both theoretically and experimentally . although interaction of rydberg atoms with blackbody radiation has been studied for years , both theoretically and experimentally , only a few works were devoted to bbr - induced ionization of rydberg atoms itself . the temperature dependence of the bbr - induced ionization rate of na 17d state was numerically calculated using the quantum defect method in a coulomb approximation and experimentally measured by spencer et al @xcite . a simple scaling law for bbr ionization rates was also introduced in that work . more recently , the interest to bbr - induced ionization of rydberg atoms has been related to the spontaneous formation of ultracold plasma in dense samples of cold rydberg atoms @xcite , and to the prospects of its use as a convenient reference signal in absolute measurements of collisional ionization rates @xcite . even nowadays , however , the studies of spontaneous evolution of ultracold rydberg atoms to a plasma caused by bbr @xcite use the simple estimates of bbr ionization rates taken from the well - known work @xcite . the numerical calculations of direct bbr photoionization rates were performed by lehman @xcite for h and na rydberg states with @xmath4=10 - 40 using a herman - skillman potential with an additional term to account for core polarization . however , the theoretical data for rb atoms , which are widely investigated in experiments on ultracold plasma , are lacking . no systematic experimental studies of the @xmath4-dependences of bbr ionization rates of alkali - metal rydberg atoms in a wide range of principal quantum numbers are known . a major problem in the interpretation of measured ionization rates of rydberg atoms is related to the fact that populations of rydberg states are affected by bbr - induced processes to an unknown ( or , at least , not straightforwardly predictable ) extent , which depends on the combination of specific experimental conditions ( principal quantum numbers _ n _ , ambient temperature , duration of measurements , extracting electric field strengths , etc . ) . therefore , a more detailed study of bbr - induced ionization of rydberg atoms under typical experimental conditions is required , especially for higher rydberg states that are often explored in the experiments with cold atoms . in this article we present the results of numerical calculations of bbr ionization rates of rb and na rydberg atoms for the most commonly used _ _ n__s , _ _ n__p and _ _ n__d states with _ _ n__=8 - 65 at the ambient temperatures of 77 , 300 and 600 k. in these calculations we take into account two phenomena that may affect the observed ionization rates : the time - dependent bbr - induced population redistribution between rydberg states prior to photoionization and the selective field ionization ( sfi ) of high - lying rydberg states by the electric field applied for extraction of ions from the excitation zone . although both phenomena were mentioned in some of the earlier studies @xcite , their effects have not yet been studied in sufficient detail neither theoretically , nor experimentally . in particular , in the measurements of direct bbr photoionization rate of the sodium 17d state @xcite with effective lifetime 4 @xmath5s at the ambient temperature of 300 k , the effect of population redistribution was diminished due to the short measurement time of 500 ns and weak electric field used for extraction of ions . however , for rydberg states with @xmath6 and effective lifetimes less than 500 ns even this very short time interval is insufficient to avoid mixing with neighboring states , so that mixing processes must be necessarily accounted in calculations . in the present study we address to both phenomena and provide the useful analytical formulae , which can be applied to any rydberg atom for estimates of the direct bbr - induced ionization rates and of the contribution of the sfi . the simplest ( but often insufficient ) way of considering bbr - induced ionization after the excitation of an atom _ a _ to a given _ nl _ rydberg state is to limit the problem to the direct photoionization of the initial _ nl _ state in one step by absorption of bbr photons : @xmath7 where @xmath8 is the energy of absorbed bbr photon , @xmath9 is the atomic ion , and @xmath10 is the free electron emitted in the ionization . in the reality , however , ionization of rydberg atoms exposed to bbr is a complex process , in which the following main components can be identified [ see fig . 1(a ) ] : ( i ) direct photoionization of atoms from the initial rydberg state via absorption of bbr photons , ( ii ) field ionization by extraction electric field pulses of high rydberg states , which are populated from the initial rydberg state by absorption of bbr photons , ( iii ) direct bbr - induced photoionization of atoms in the neighboring rydberg states , which are populated due to absorption and emission of bbr photons prior to photoionization , and ( iv ) field ionization of other high - lying states , which are populated via population redistribution involving two or more steps of bbr photon absorption and/or emission events . our calculations show that all these processes can contribute to the total ionization rate to a comparable extent , and , therefore , none of them can be disregarded . in what follows we will consider the above processes separately and calculate the total bbr ionization rates , both analytically and numerically .

results of theoretical calculations of ionization rates of rb and na rydberg atoms by blackbody radiation ( bbr ) are presented . calculations have been performed for _ n__=8 - 65 and at three ambient temperatures of 77 , 300 and 600 k. a peculiarity of our calculations is that we take into account the contributions of bbr - induced redistribution of population between rydberg states prior to photoionization and field ionization by extraction electric field pulses . we also present the useful analytical formulae for quick estimation of bbr ionization rates of rydberg atoms .

results of theoretical calculations of ionization rates of rb and na rydberg atoms by blackbody radiation ( bbr ) are presented . calculations have been performed for _ _ n__s , _ _ n__p and _ _ n__d states of na and rb , which are commonly used in a variety of experiments , at principal quantum numbers _ _ n__=8 - 65 and at three ambient temperatures of 77 , 300 and 600 k. a peculiarity of our calculations is that we take into account the contributions of bbr - induced redistribution of population between rydberg states prior to photoionization and field ionization by extraction electric field pulses . the obtained results show that these phenomena affect both the magnitude of measured ionization rates and shapes of their dependences on _ n_. the calculated ionization rates are compared with the results of our earlier measurements of bbr - induced ionization rates of na _ _ n__s and _ _ n__d rydberg states with _ _ n__=8 - 20 at 300 k. a good agreement for all states except _ _ n__s with is observed . we also present the useful analytical formulae for quick estimation of bbr ionization rates of rydberg atoms .

physics0702192

c

we have calculated the total bbr - induced ionization rates of na and rb _ _ n__s , _ _ n__p and _ _ n__d rydberg states for principal quantum numbers _ _ n__=8 - 65 at the ambient temperatures of 77 , 300 and 600 k. our calculations take into account the effect of bbr - induced mixing of rydberg states and their field ionization by extracting electric field pulses . useful analytical formulae have been derived , which allow for quick estimation of ionization rates and their dependences on the principal quantum number _ n_. the numerical results are in a good agreement with our recent experiment data on na _ _ n__s and _ _ n__d states , except for _ _ n__s states with @xmath0 , which is most probably associated with the cooper minimum in the photoionization cross - section . the obtained results show that bbr - induced redistribution of population over rydberg states and their field ionization by extracting electric fields affect both the magnitudes of total ionization rates and shapes of their dependencies on the principal quantum number . this suggests that these processes are important and can not be ignored in the calculations and measurements of bbr ionization rates . equations ( [ eq16])-([eq20 ] ) , as well as the analytical formulae ( [ eq9 ] ) and ( [ eq15 ] ) , can be used to calculate total ionization rates @xmath113 under particular experimental conditions . the obtained numerical results may be helpful to the analysis of ionization signals measured in experiments on collisional ionization and spontaneous formation of ultracold plasma , since bbr - induced ionization is the main channel of delivering atomic ions . at the same time , as we have revealed that theoretical data for na @xmath4s - states noticeably disagree with experiment at @xmath120 , new experimental data for na and rb in a broader range of principal quantum numbers would be of interest for the further improvement of theory , especially for the non - hydrogen - like states . this work was supported by intas grant no . 04 - 83 - 3692 , russian foundation for basic research ( grants no . 05 - 02 - 16181 , 05 - 03 - 33252 ) , siberian branch of ras , eu fp6 tok project lamol , european social fund , latvian science council , and nato grant eap.rig.981387 . @|c|c|c|c|c|c|c|c|c| + & & & & & & & & + @xmath4&@xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 100v / cm & 200v / cm & & 100v / cm & 200v / cm & 100v / cm & 200v / cm + & & & & & & & & + 10 & @xmath121 & @xmath122 & @xmath123 & @xmath124 & @xmath125&@xmath126 & @xmath127&@xmath128 + 15 & 0.009 & 0.019 & 0.042 & 0.002 & 0.003 & 0.006 & 0.033&0.059 + 20 & 0.805 & 1.655 & 3.83 & 0.059 & 0.118 & 0.240 & 2.64&4.94 + 25 & 4.04 & 10.23 & 25.29 & 0.185 & 0.420 & 0.891 & 14.9&30.4 + 30 & 8.45 & 27.12 & 81.09 & 0.257 & 0.706 & 1.689 & 36.5&91.5 + & & & & & & & & + & @xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 5v / cm & 10v / cm & & 5v / cm & 10v / cm & 5v / cm & 10v / cm + 35 & 11.8 & 2.47 & 5.20 & 0.267 & 0.0488 & 0.107 & 14.6&17.4 + 45 & 14.6 & 4.12 & 9.09 & 0.195 & 0.0466 & 0.106 & 19.0&24.0 + 55 & 14.1 & 5.76 & 13.9 & 0.124 & 0.0412 & 0.102 & 20.1&28.3 + 65 & 12.6 & 8.01 & 23.6 & 0.0773 & 0.0377 & 0.111 & 20.7&36.4 + + & & & & & & & & + @xmath4&@xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 100v / cm & 200v / cm & & 100v / cm & 200v / cm & 100v / cm & 200v / cm + & & & & & & & & + 10 & @xmath129 & @xmath130 & @xmath131 & @xmath132 & @xmath133 & @xmath134 & @xmath135&@xmath136 + 15 & 0.0996 & 0.195 & 0.389 & 0.00111 & 0.00200 & 0.00409 & 0.298 & 0.493 + 20 & 5.22 & 10.2 & 20.5 & 0.0217 & 0.0455 & 0.0977 & 15.4&25.8 + 25 & 22.1 & 50.8 & 107 & 0.0545 & 0.132 & 0.308 & 73.1&130 + 30 & 42.4 & 120 & 290 & 0.0662 & 0.197 & 0.554 & 163&333 + & & & & & & & & + & @xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 5v / cm & 10v / cm & & 5v / cm & 10v / cm & 5v / cm & 10v / cm + 35 & 57.0 & 10.5 & 22.9 & 0.0726 & 0.0144 & 0.0318 & 67.6 & 80.0 + 45 & 66.2 & 16.2 & 37.1 & 0.0514 & 0.0135 & 0.0313 & 82.5&103 + 55 & 61.9 & 21.6 & 53.7 & 0.0320 & 0.0117 & 0.0297 & 83.5&116 + 65 & 53.8 & 28.6 & 86.5 & 0.0186 & 0.00997 & 0.0304 & 82.4&140 + + & & & & & & & & + @xmath4&@xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 100v / cm & 200v / cm & & 100v / cm & 200v / cm & 100v / cm & 200v / cm + & & & & & & & & + 10 & @xmath137 & @xmath138 & @xmath139 & @xmath140 & @xmath141 & @xmath142&@xmath143 & @xmath144 + 15 & 0.251 & 0.483 & 0.947 & 0.00270 & 0.00472 & 0.00953&0.742&1.21 + 20 & 6.59 & 12.7 & 25.2 & 0.0371 & 0.0762 & 0.158&19.4 & 32.0 + 25 & 22.6 & 50.0 & 104 & 0.0926 & 0.215 & 0.467&72.9 & 127 + 30 & 39.0 & 107 & 256 & 0.120 & 0.331 & 0.812&146 & 296 + & & & & & & & & + & @xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 5v / cm & 10v / cm & & 5v / cm & 10v / cm & 5v / cm & 10v / cm + 35 & 49.3 & 8.88 & 19.4 & 0.131 & 0.0239 & 0.0527&58.3 & 68.8 + 45 & 54.6 & 13.0 & 29.6 & 0.0995 & 0.0230 & 0.0528&67.7&84.3 + 55 & 49.8 & 16.7 & 41.5 & 0.0663 & 0.0204 & 0.0503&66.7 & 91.5 + 65 & 42.7 & 21.8 & 65.9 & 0.0424 & 0.0180 & 0.0519&64.6&109 + @|c|c|c|c|c|c|c|c|c| + & & & & & & & & + @xmath4&@xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 100v / cm & 200v / cm & & 100v / cm & 200v / cm & 100v / cm & 200v / cm + & & & & & & & & + 10 & 7.50 & 1.33 & 2.34 & 13.6 & 3.02 & 4.88&25.5&28.3 + 15 & 114 & 39.4 & 70.2 & 78.6 & 24.2 & 39.6 & 256 & 302 + 20 & 223 & 99.2 & 185 & 77.6 & 29.2 & 49.2 & 429 & 534 + 25 & 254 & 155 & 314 & 53.6 & 26.2 & 46.9 & 489 & 669 + 30 & 242 & 218 & 537 & 34.2 & 23.2 & 46.9 & 518 & 861 + & & & & & & & & + & @xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 5v / cm & 10v / cm & & 5v / cm & 10v / cm & 5v / cm & 10v / cm + 35 & 217 & 19.3 & 39.5 & 22.6 & 1.55 & 3.29 & 261 & 283 + 45&166&22.8 & 49.1 & 10.2 & 1.04 & 2.30 & 200 & 227 + 55 & 126&27.3 & 64.2 & 5.15 & 0.780 & 1.87 & 159 & 197 + 65 & 97.4&35.0 & 100 & 2.80 & 0.652 & 1.86 & 136 & 202 + + & & & & & & & & + @xmath4&@xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 100v / cm & 200v / cm & & 100v / cm & 200v / cm & 100v / cm & 200v / cm + 10 & 79.92 & 15.99 & 25.84 & 2.426 & 0.8949 & 1.456 & 99.23 & 109.6 + 15 & 778.2 & 240.9 & 393.6 & 17.82 & 5.476 & 9.174&1042 & 1199 + 20 & 1295 & 501.8 & 845.4 & 19.05 & 6.384 & 11.24 & 1823 & 2171 + 25 & 1374 & 709.0 & 1272 & 13.50 & 5.610 & 10.76 & 2102 & 2670 + 30 & 1253 & 932.0 & 1919 & 8.444 & 4.660 & 10.56 & 2198 & 3191 + & & & & & & & & + & @xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 5v / cm & 10v / cm & & 5v / cm & 10v / cm & 5v / cm & 10v / cm + 35 & 1090 & 79.97 & 169.6 & 6.145 & 0.3428 & 0.7388 & 1177 & 1267 + 45 & 795.2 & 89.28 & 198.3 & 2.830 & 0.2290 & 0.5203 & 887.5&996.9 + 55 & 586.0 & 102.1 & 247.0 & 1.419 & 0.1679&0.4172 & 689.7 & 834.8 + 65 & 441.8 & 124.9 & 366.0 & 0.7254 & 0.1267 & 0.3768&567.5 & 808.9 + + & & & & & & & & + @xmath4&@xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 100v / cm & 200v / cm & & 100v / cm & 200v / cm & 100v / cm & 200v / cm + 10 & 157.5 & 37.01 & 59.22 & 13.71 & 2.596 & 4.237 & 210.8 & 234.7 + 15 & 890.1 & 268.2 & 434.4 & 39.52 & 8.003 & 13.30&1206 & 1377 + 20 & 1253 & 467.7 & 782.0 & 36.76 & 8.176 & 14.05 & 1765 & 2086 + 25 & 1244 & 613.5 & 1094 & 26.17 & 6.907 & 12.61 & 1891 & 2377 + 30 & 1099 & 774.0 & 1592 & 17.38 & 5.679 & 11.70 & 1896 & 2720 + & & & & & & & & + & @xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 5v / cm & 10v / cm & & 5v / cm & 10v / cm & 5v / cm & 10v / cm + 35 & 936.2 & 65.00 & 137.7 & 12.31 & 0.4207 & 0.8980 & 1014 & 1087 + 45 & 666.5 & 70.18 & 155.6 & 6.040 & 0.2783 & 0.6197&743.0 & 828.8 + 55 & 483.1 & 78.52 & 189.6 & 3.240 & 0.2025 & 0.4856&565.1 & 676.4 + 65 & 360.0 & 94.60 & 277.3 & 1.849 & 0.1557 & 0.4332&456.6 & 639.6 + @|c|c|c|c|c|c|c|c|c| + & & & & & & & & + @xmath4&@xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 100v / cm & 200v / cm & & 100v / cm & 200v / cm & 100v / cm & 200v / cm + 10 & 284.4 & 41.90 & 71.08 & 1396 & 187.6 & 294.9 & 1910 & 2046 + 15 & 910.1 & 185.6 & 321.5 & 1396 & 237.4 & 378.9 & 2729 & 3007 + 20 & 991.5 & 290.5 & 526.8 & 770.7 & 175.8 & 289.9 & 2229 & 2579 + 25 & 874.7 & 378.8 & 748.8 & 411.1 & 130.9 & 229.0 & 1796 & 2264 + 30 & 728.5 & 489.6 & 1172 & 229.0 & 105.5 & 208.4 & 1553 & 2338 + & & & & & & & & + & @xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 5v / cm & 10v / cm & & 5v / cm & 10v / cm & 5v / cm & 10v / cm + 35 & 601 & 42.9 & 87.6 & 139 & 7.04 & 14.8 & 790 & 843 + 45&416&48.3 & 104 & 57.1 & 4.46 & 9.82 & 526 & 586 + 55&299&56.5 & 132 & 27.5 & 3.25 & 7.76 & 386 & 467 + 65&222&71.3 & 203 & 14.6 & 2.67 & 7.57 & 311 & 448 + + & & & & & & & & + @xmath4&@xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 100v / cm & 200v / cm & & 100v / cm & 200v / cm & 100v / cm & 200v / cm + 10 & 2580 & 353.0 & 554.1 & 190.1 & 31.47 & 49.95 & 3155 & 3374 + 15 & 6054 & 1054 & 1681 & 279.2 & 45.01 & 73.60 & 7433 & 8088 + 20&5900 & 1433 & 2364 & 173.8 & 34.97 & 60.14 & 7541 & 8497 + 25&4884 & 1715 & 3015 & 96.59 & 26.01 & 48.63 & 6722 & 8044 + 30&3898 & 2077 & 4183 & 52.98 & 19.78 & 43.40 & 6048 & 8178 + & & & & & & & & + & @xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 5v / cm & 10v / cm & & 5v / cm & 10v / cm & 5v / cm & 10v / cm + 35 & 3115 & 177.6 & 375.1 & 35.25 & 1.458 & 3.135 & 3330 & 3529 + 45 & 2049 & 188.9 & 417.8 & 14.72 & 0.9238 & 2.094 & 2254 & 2484 + 55 & 1426 & 210.8 & 508.0 & 7.008 & 0.6582 & 1.632 & 1644 & 1942 + 65 & 1029 & 254.5 & 742.4 & 3.470 & 0.4856 & 1.439 & 1288 & 1777 + 35 & 3115 & 177.6 & 375.1 & 35.25 & 1.458 & 3.135 & 3330 & 3529 + + & & & & & & & & + @xmath4&@xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 100v / cm & 200v / cm & & 100v / cm & 200v / cm & 100v / cm & 200v / cm + 10 & 3679 & 506.3 & 787.9 & 750.7 & 68.35 & 108.5 & 5004 & 5326 + 15 & 6226 & 1052 & 1666 & 631.2 & 58.47 & 94.75 & 7968 & 8618 + 20 & 5547 & 1286 & 2106 & 368.8 & 40.12 & 67.39 & 7242 & 8090 + 25 & 4405 & 1458 & 2549 & 211.4 & 28.43 & 50.80 & 6103 & 7216 + 30 & 3434 & 1709 & 3438 & 124.9 & 21.11 & 42.54 & 5288 & 7039 + & & & & & & & & + & @xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 5v / cm & 10v / cm & & 5v / cm & 10v / cm & 5v / cm & 10v / cm + 35 & 2702 & 143.5 & 302.9 & 81.66 & 1.594 & 3.390 & 2929 & 3090 + 45 & 1733 & 148.1 & 327.0 & 36.94 & 0.9921 & 2.202 & 1919 & 2099 + 55 & 1185 & 162.0 & 389.4 & 19.08 & 0.6971 & 1.667 & 1367 & 1595 + 65 & 844.1 & 192.7 & 562.0 & 10.72 & 0.5188 & 1.438 & 1048 & 1418 + @|c|c|c|c|c|c|c|c|c| + & & & & & & & & + @xmath4&@xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 5v / cm & 10v / cm & & 5v / cm & 10v / cm & 5v / cm & 10v / cm + & & & & & & & & + 10 & @xmath145 & @xmath146 & @xmath147 & @xmath148 & @xmath149 & @xmath150 & @xmath151 & @xmath152 + 20 & 0.2826 & 0.04174 & 0.08730 & 0.005807 & @xmath153 & 0.001622 & 0.3309 & 0.3773 + 30 & 6.541 & 1.108 & 2.343 & 0.04932 & 0.006986 & 0.01519&7.706 & 8.949 + 40 & 12.61 & 2.740 & 5.967 & 0.04750 & 0.008213 & 0.01840&15.41 & 18.64 + 50 & 13.91 & 4.201 & 9.678 & 0.03120 & 0.007135 & 0.01687&18.15 & 23.64 + 60 & 12.97 & 5.813 & 14.96 & 0.01917 & 0.006156 & 0.01615&18.81 & 27.97 + 65 & 12.21 & 6.863 & 19.53 & 0.01502 & 0.005856 & 0.01688&19.10 & 31.78 + + & & & & & & & & + 10 & @xmath154 & @xmath155 & @xmath156 & @xmath157 & @xmath158 & @xmath159 & @xmath160 & @xmath161 + 20 & 0.489 & 0.0636 & 0.136 & 0.00443 & @xmath162 & 0.00132 & 0.558 & 0.631 + 30 & 7.21 & 1.02 & 2.22 & 0.0412 & 0.00656 & 0.0139&8.28 & 9.49 + 40 & 11.8 & 2.08 & 4.65 & 0.0447 & 0.00887 & 0.0193 & 14.0 & 16.5 + 50 & 11.9 & 2.83 & 6.70 & 0.0321 & 0.00854 & 0.0195&14.8 & 18.7 + 60&10.5 & 3.60 & 9.49 & 0.0212 & 0.00797 & 0.0201&14.1 & 20.0 + 65 & 9.65 & 4.09 & 11.9 & 0.0171 & 0.00785 & 0.0217&13.8 & 21.6 + + & & & & & & & & + 10 & @xmath163 & @xmath164 & @xmath165 & @xmath166 & @xmath167 & @xmath168 & @xmath169 & @xmath170 + 20 & 1.66 & 0.227 & 0.475 & 0.0149 & 0.00207 & 0.00442 & 1.90 & 2.15 + 30 & 15.7 & 2.46 & 5.19 & 0.0710 & 0.0110&0.0237 & 18.2 & 21.0 + 40 & 24.7 & 4.99 & 10.8 & 0.0662 & 0.0127&0.0280 & 29.7 & 35.6 + 50 & 25.4 & 7.15 & 16.5 & 0.0450 & 0.0113 & 0.0264 & 32.6 & 41.9 + 60 & 22.9 & 9.60 & 24.9 & 0.0287 & 0.0101&0.0260 & 32.5 & 47.8 + 65 & 21.3 & 11.3 & 32.5 & 0.0229 & 0.00969&0.0277 & 32.6 & 53.9 + @|c|c|c|c|c|c|c|c|c| + & & & & & & & & + @xmath4&@xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 5v / cm & 10v / cm & & 5v / cm & 10v / cm & 5v / cm & 10v / cm + 10 & 0.604 & 0.0195 & 0.0390 & 0.408 & 0.0113 & 0.0228&1.04&1.07 + 20 & 183 & 7.58 & 15.3 & 20.8 & 0.633 & 1.30 & 212 & 220 + 30&235&14.8 & 30.3 & 9.25 & 0.390 & 0.819 & 260 & 276 + 40&189&18.5 & 39.2 & 3.70 & 0.227 & 0.492 & 211 & 232 + 50&143&21.9 & 49.1 & 1.67 & 0.150 & 0.344 & 167 & 194 + 60&109&26.7 & 67.0 & 0.842 & 0.113 & 0.288 & 137 & 177 + 65&96.1&30.3 & 83.9 & 0.619 & 0.103 & 0.287 & 127 & 181 + + 10 & 3.69 & 0.102 & 0.206 & 0.0598 & 0.00432 & 0.00873 & 3.85 & 3.96 + 20 & 300 & 9.25 & 19.0 & 8.14 & 0.311 & 0.626 & 317 & 327 + 30 & 294 & 13.0 & 27.3 & 4.87 & 0.255 & 0.520 & 312 & 327 + 40&207 & 13.8 & 30.0 & 2.20 & 0.173 & 0.363 & 223 & 240 + 50&144&14.7 & 33.8 & 1.07 & 0.126 & 0.278 & 160 & 179 + 60&103&16.5 & 42.3 & 0.568 & 0.103 & 0.246 & 120 & 146 + 65&87.8&18.0 & 51.0 & 0.426 & 0.0965 & 0.251 & 106 & 140 + + 10 & 27.8 & 0.782 & 1.58 & 2.73 & 0.0532 & 0.108 & 31.4 & 32.2 + 20 & 540 & 18.7 & 37.6 & 21.4 & 0.626 & 1.28 & 581 & 600 + 30&517&27.3 & 55.9 & 10.4 & 0.439 & 0.908 & 555 & 584 + 40&381&31.6 & 66.9 & 4.60 & 0.282 & 0.600 & 418 & 453 + 50&277&36.2 & 81.2 & 2.25 & 0.199 & 0.444 & 315 & 360 + 60&205&43.5 & 110 & 1.20 & 0.157 & 0.385 & 250 & 316 + 65&179&49.1 & 138 & 0.904 & 0.146 & 0.391 & 229 & 318 + @|c|c|c|c|c|c|c|c|c| + & & & & & & & & + @xmath4&@xmath110&@xmath71&@xmath71&@xmath112&@xmath18&@xmath18&@xmath114&@xmath114 + & direct & 5v / cm & 10v / cm & & 5v / cm & 10v / cm & 5v / cm & 10v / cm + 10 & 81.20 & 1.429 & 2.838 & 177.4 & 2.395 & 4.806 & 262.4&266.2 + 20 & 941.6 & 26.22 & 52.51 & 259.5 & 4.569 & 9.340 & 1232 & 1263 + 30 & 734.1 & 35.55 & 72.58 & 68.99 & 1.925 & 4.022 & 840.6 & 879.7 + 40 & 500.8 & 40.35 & 85.19 & 23.30 & 1.009 & 2.181 & 565.4 & 611.4 + 50 & 350.5 & 45.92 & 102.7 & 9.740&0.6394 & 1.458 & 406.8&464.4 + 60 & 255.3 & 54.93 & 137.1 & 4.738&0.4709 & 1.188 & 315.4&398.3 + 65 & 220.8 & 61.92 & 170.6 & 3.445&0.4253 & 1.176 & 286.6&396.0 + 10 & 373.9 & 5.011 & 10.06 & 20.19 & 0.6466 & 1.299 & 399.7 & 405.5 + 20 & 1690 & 30.95 & 63.33 & 100.7 & 2.073&4.156 & 1824&1858 + 30 & 1009 & 30.95 & 64.80 & 35.35 & 1.170&2.375 & 1077&1112 + 40 & 592.4 & 30.00 & 64.98&13.44 & 0.7148&1.488 & 636.5&672.3 + 50 & 374.1 & 30.71 & 70.43 & 6.029 & 0.4986 & 1.086 & 411.3 & 451.6 + 60 & 252.3 & 33.85 & 86.50&3.076 & 0.3940&0.9362 & 289.6 & 342.8 + 65 & 211.3 & 36.78 & 103.7&2.279 & 0.3675&0.9453 & 250.7&318.2 + + 10 & 1263 & 17.45 & 34.98 & 279.7 & 2.919 & 5.900&1563 & 1584 + 20 & 2696 & 57.56 & 115.5 & 220.0 & 3.948 & 8.007&2978 & 3040 + 30 & 1681 & 63.97 & 130.5&71.48&2.059 & 4.235&1819 & 1887 + 40 & 1051 & 68.29 & 144.0 & 27.59 & 1.211 & 2.556&1148 & 1225 + 50 & 699.6 & 75.56 & 168.9&12.59 & 0.8201 & 1.814 & 788.6 & 883.0 + 60 & 492.7 & 89.13 & 223.8 & 6.510 & 0.6320 & 1.534 & 589.0 & 724.5 + 65 & 420.5 & 100.1 & 280.1 & 4.847 & 0.5827 & 1.544&526.1 & 706.9 + r. f. stebbings , c. j. latimer , w. p. west , f. b. dunning , and t. b. cook , phys . a * 12 * , 1453 ( 1975 ) ; t. ducas , m. g. littman , r. r. freeman , and d. kleppner , phys . lett . * 35 * , 366 ( 1975 ) ; t. f. gallagher , l. m. humphrey , r. m. hill , and s. a. edelstein , phys . rev . lett . * 37 * , 1465 ( 1976 ) .

the obtained results show that these phenomena affect both the magnitude of measured ionization rates and shapes of their dependences on _ n_. the calculated ionization rates are compared with the results of our earlier measurements of bbr - induced ionization rates of na _ _ n__s and _ _ n__d rydberg states with _

results of theoretical calculations of ionization rates of rb and na rydberg atoms by blackbody radiation ( bbr ) are presented . calculations have been performed for _ _ n__s , _ _ n__p and _ _ n__d states of na and rb , which are commonly used in a variety of experiments , at principal quantum numbers _ _ n__=8 - 65 and at three ambient temperatures of 77 , 300 and 600 k. a peculiarity of our calculations is that we take into account the contributions of bbr - induced redistribution of population between rydberg states prior to photoionization and field ionization by extraction electric field pulses . the obtained results show that these phenomena affect both the magnitude of measured ionization rates and shapes of their dependences on _ n_. the calculated ionization rates are compared with the results of our earlier measurements of bbr - induced ionization rates of na _ _ n__s and _ _ n__d rydberg states with _ _ n__=8 - 20 at 300 k. a good agreement for all states except _ _ n__s with is observed . we also present the useful analytical formulae for quick estimation of bbr ionization rates of rydberg atoms .

hep-ex9905041

c

we have measured the optical properties of seventy - four pure cesium iodide crystals that were polished and wrapped in the diffuse teflon reflector . the results are summarized separately for the full - sized and half - sized crystals in tables [ tab1 ] and [ tab2 ] . the deduced light yields parameterized by two axial and one transverse light collection nonuniformity coefficients constitute a minimum set of parameters necessary for a realistic monte carlo simulation of the modular csi calorimeter . the predicted energy resolutions fwhm@xmath129 for @xmath770@xmath4mev positrons and photons in the full pibeta calorimeter with the ideal , optically uniform csi modules with specified luminosities were shown to be close , 3.7@xmath4mev and 4.0@xmath4mev , respectively . the upper limit of the low energy tail contributions in the region between 5@xmath4mev and 55@xmath4mev were calculated to be 6.9@xmath4% and 8.7@xmath4% for the positrons and gammas in an optically homogeneous detector , respectively . after applying the 5@xmath4mev calorimeter veto cut , these tail corrections decrease to 2.2@xmath4% and 4.5@xmath4% . the average deduced axial light nonuniformities of real csi crystals wrapped in a teflon sheet had negative slopes , @xmath1050.18@xmath4%/cm and @xmath1051.6@xmath4%/cm , for the front and back half of the crystal volume , respectively . the corresponding geant simulation of the nonuniform pibeta apparatus for 68.9@xmath4mev @xmath126 and 70.8@xmath4mev @xmath23 s shows that both energy responses will be broadened to the average fwhm@xmath129 of 5.9@xmath4% and 6.9@xmath4% while the associated tail contributions will change only for photon spectra , increasing the low - energy tail by @xmath70.3@xmath4% . the simulated calorimeter adc spectra are shown in figs . [ fig : tails1 ] and [ fig : tails2 ] . the nonlinearity of the measured energy scale caused by the optical nonuniformity is @xmath942.8@xmath4% throughout the relevant @xmath126/@xmath23 energy range . this spread is consistent with the precision of energy calibration required to extract the tail corrections with the systematic uncertainty of @xmath70.2@xmath4% . the predicted adc spectra of the monoenergetic positrons , electrons and tagged photons in the energy range 1070@xmath4mev will be compared with the measured responses of the partial csi calorimeter arrays in a forthcoming publication @xcite .

seventy - four individual crystals , polished and wrapped in teflon foil , were examined in a multiwire drift chamber system specially designed for transmission cosmic muon tomography . imposing the 5 mev calorimeter veto cut to suppress the electromagnetic losses , geant - evaluated positron and photon lineshape tail fractions summed over all above - threshold adcs were found to be 2.36.05(stat).20(sys)% and 4.68.07(stat).20(sys)% , respectively .

scintillation properties of pure csi crystals used in the shower calorimeter being built for precise determination of the decay rate are reported . seventy - four individual crystals , polished and wrapped in teflon foil , were examined in a multiwire drift chamber system specially designed for transmission cosmic muon tomography . critical elements of the apparatus and reconstruction algorithms enabling measurement of spatial detector optical nonuniformities are described . results are compared with a monte carlo simulation of the light response of an ideal detector . the deduced optical nonuniformity contributions to the fwhm energy resolution of the pibeta csi calorimeter for the 69.8mev positrons and the monoenergetic 70.8mev photons were 2.7% and 3.7% , respectively . the upper limit of optical nonuniformity correction to the 69.8mev positron low - energy tail between 5mev and 55mev was.2% , as opposed to the.3% tail contribution for the photon of the equivalent total energy . imposing the 5 mev calorimeter veto cut to suppress the electromagnetic losses , geant - evaluated positron and photon lineshape tail fractions summed over all above - threshold adcs were found to be 2.36.05(stat).20(sys)% and 4.68.07(stat).20(sys)% , respectively . pacs numbers : 87.59.f ; 29.40.mc ; 24.10.lx _ keywords : _ computed tomography ; scintillation detectors ; monte carlo simulations psfig.sty , , , , , , , , , , , ,

1401.1183

i

suppose @xmath2 is a real - valued , @xmath0th - order , @xmath1-dimensional tensors and @xmath8 is a real - valued @xmath1-vector . we let @xmath9 denote the @xmath1-vector defined by @xmath10 we let @xmath11 denote the scalar defined by @xmath12 . we say the tensor @xmath2 is _ symmetric _ if its entries are invariant under permutation . we say the tensor @xmath2 is _ positive definite _ if @xmath13 for all @xmath14 . the notion of generalized eigenpairs has been defined for tensors by chang , pearson , and zhang @xcite as follows . let @xmath2 and @xmath3 be real - valued , @xmath0th - order , @xmath1-dimensional symmetric tensors . assume further that @xmath0 is even and @xmath3 is positive definite . we say @xmath15 is a _ generalized eigenpair _ ( also known as a _ @xmath3-eigenpair _ ) if @xmath16 taking the dot product with @xmath8 , it is clear that any solution satisfies @xmath17 the advantage of the generalized eigenpair framework is that it nicely encapsulates multiple definitions of tensor eigenvalues , as follows . a _ z - eigenpair _ @xcite is defined as a pair @xmath18 such that @xmath19 this is equivalent to a generalized tensor eigenpair with @xmath20 , the identity tensor such that @xmath21 for all @xmath22 @xcite . note that , unlike ordinary tensor z - eigenpairs , generalized tensor eigenpairs allow arbitrary rescaling of the eigenvector @xmath8 with no effect on the eigenvalue @xmath23 . in this way , the generalized tensor eigenvalue problem preserves the homogeneity of the corresponding matrix eigenproblem . an _ h - eigenpair _ is defined as a pair @xmath15 such that @xmath24}.\ ] ] here @xmath25}$ ] denotes elementwise power , i.e. , @xmath26})_i \equiv { { { \bm { \mathbf{\makelowercase{x}}}}}}_i^{m-1}$ ] , for @xmath27 . this is equivalent to a generalized tensor eigenpair with @xmath28 @xcite . let @xmath29 be a symmetric @xmath30 matrix and assume @xmath31 . we say @xmath32 is a _ d - eigenpair _ @xcite if @xmath33 this is equivalent to a @xmath3-eigenpair where @xmath3 is the symmetrized tensor outer product of @xmath29 with itself @xcite . in this paper , we describe a method for computing generalized eigenpairs . our method is a generalization of the shifted symmetric higher - order power method ( ss - hopm ) that we previously introduced for computing z - eigenvalues @xcite . in addition to generalizing the method , we have also significantly improved it by adding an adaptive method for choosing the shift . to derive the method , we reformulate the generalized eigenproblem , , as a nonlinear program such that any generalized eigenpair is equivalent to a kkt point in . we develop an adaptive , monotonically convergent , shifted power method for solving the optimization problem in . we call our method the generalized eigenproblem adaptive power ( geap ) method . in , we show that the geap method is much faster than the ss - hopm method for finding z - eigenpairs due to its adaptive shift selection . furthermore , the geap method is shown to find other types of generalized eigenpairs , by illustrating it on examples from related literature as well as a randomly generated example . this is the only known method for finding generalized eigenpairs besides direct numerical solution ; we survey related work in .

several tensor eigenpair definitions have been put forth in the past decade , but these can all be unified under generalized tensor eigenpair framework , introduced by chang , pearson , and zhang ( 2009 ) . different choices for yield different versions of the tensor eigenvalue problem . we present our generalized eigenproblem adaptive power ( geap ) method for solving the problem , which is an extension of the shifted symmetric higher - order power method ( ss - hopm ) for finding z - eigenpairs . a major drawback of ss - hopm was that its performance depended in choosing an appropriate shift , but our geap method also includes an adaptive method for choosing the shift automatically . tensor eigenvalues , e - eigenpairs , z - eigenpairs ,-eigenpairs , generalized tensor eigenpairs , shifted symmetric higher - order power method ( ss - hopm ) , generalized eigenproblem adaptive power ( geap ) method 15a18 , 15a69 adaptive shifted power method for computing generalized tensor eigenpairs

several tensor eigenpair definitions have been put forth in the past decade , but these can all be unified under generalized tensor eigenpair framework , introduced by chang , pearson , and zhang ( 2009 ) . giventh - order ,-dimensional real - valued symmetric tensors and , the goal is to find and such that . different choices for yield different versions of the tensor eigenvalue problem . we present our generalized eigenproblem adaptive power ( geap ) method for solving the problem , which is an extension of the shifted symmetric higher - order power method ( ss - hopm ) for finding z - eigenpairs . a major drawback of ss - hopm was that its performance depended in choosing an appropriate shift , but our geap method also includes an adaptive method for choosing the shift automatically . tensor eigenvalues , e - eigenpairs , z - eigenpairs ,-eigenpairs , generalized tensor eigenpairs , shifted symmetric higher - order power method ( ss - hopm ) , generalized eigenproblem adaptive power ( geap ) method 15a18 , 15a69 adaptive shifted power method for computing generalized tensor eigenpairs

cond-mat0311362

c

before concluding this paper , it is intructive to compare effective ac susceptibilities of @xmath0-(bedt - ttf)@xmath204khg(scn)@xmath2 determined using different methods in fig . [ comparison ] . in fig [ comparison]a , @xmath208 is obtained by fitting the bean model ( as described above- see eq . [ beanman ] ) to many hysteresis loops over an extended region of magnetic field . the imaginary component @xmath209 , which accounts for losses , is obtained from the loop areas . in fig . [ comparison]b , the susceptibility is estimated using @xmath210 the most clear aspect of fig . [ comparison ] is that the magnitudes of the real and imaginary susceptibilitiies due to free currents @xmath5 , estimated from the ac hall potential , agree more closely with the high frequency ac susceptibility measurements made in ref . @xcite ( shown in fig . [ comparison]c ) than with the magnetic torque measurements . this indicates that the ac susceptibility made at frequencies @xmath211 hz consists mostly of free currents @xmath5 , which are shown ( above , and in the appendix ) to be confined to the sample edges . the data in fig . [ times ] shows that @xmath5 can persist for times as long as @xmath212 ms for sufficiently small values of the hall potential @xmath213v in a sample of @xmath140 mm@xmath52 cross - section at @xmath123 t and @xmath214 k. in spite of the fact that the corresponding susceptibility in fig . [ comparison]b is much larger than that for the torque measurements in fig . [ comparison]a , the magnetization @xmath215 am@xmath92 due to free currents is actually smaller . free currents therefore have insufficient duration to contribute a significant amount to the irreversible steady magnetic torque in fig . [ loops ] . by contrast , magnetic currents observed in the torque experiments last for an indefinite period of time @xcite . the combined induction of free and magnetic currents @xmath216 can therefore be understood as follows : for small changes in magnetic field @xmath217 mt , the greatest contribution to the susceptibility initially originates from free currents at the surface that attempt to screen changes in magnetic flux density from within the bulk . these currents quickly saturate , however , as dissipation sets in , possibly assisted by zener tunneling . at that point , changes in magnetic flux density enter the bulk which cause the landau level structure and chemical potential to change , causing the cdw to depart from equilibrium , as described in the appendix . the stored energy increases quadratically with @xmath197 , eventually causing the cdw to collapse at the edges , initiating the critical state . in conclusion , hall potential and magnetic torque measurements on @xmath0-(bedt - ttf)@xmath1hg(scn)@xmath2 ( @xmath3 k , rb ) show that two types of screening currents occur within the high - field , low - temperature cdw@xmath4 phase in response to changing magnetic fields . the first , which gives rise to the induced hall potential , is a free current ( @xmath5 ) , weighted mostly towards the edge of the sample . the time constant for the decay of these currents is longer than that expected from the sample resistivity . the second component of the current appears to be magnetic ( @xmath6 ) , in that it is a microscopic , quasi - orbital bulk effect ; it is evenly distributed within the sample upon saturation . a simple model ( appendix ) , describing a new type of quantum fluid comprising a cdw coexisting with a two - dimensional fermi - surface pocket , is able to account for the origins of the currents . taken together , these findings are able to reconcile the body of experimental evidence @xcite which had previously been interpreted in terms of the quantum hall effect @xcite or superconductivity @xcite .

the data show that two types of screening currents occur within the high - field , low - temperature cdw phases of these salts in response to time - dependent magnetic fields . the first , which gives rise to the induced hall potential , is a free current ( ) , present at the surface of the sample . the time constant for the decay of these currents is much longer than that expected from the sample resistivity . the second component of the current appears to be magnetic ( ) , in that it is a microscopic , quasi - orbital effect ; it is evenly distributed within the bulk of the sample upon saturation . to explain these data , we propose a simple model invoking a new type of quantum fluid comprising a cdw coexisting with a two - dimensional fermi - surface pocket which describes the two types of current . the model and data are able to account for the body of previous experimental data which had generated apparently contradictory interpretations in terms of the quantum hall effect or superconductivity .

single crystals of the organic charge - transfer salts-(bedt - ttf)hg(scn) have been studied using hall - potential measurements (k ) and magnetization experiments ( k , rb ) . the data show that two types of screening currents occur within the high - field , low - temperature cdw phases of these salts in response to time - dependent magnetic fields . the first , which gives rise to the induced hall potential , is a free current ( ) , present at the surface of the sample . the time constant for the decay of these currents is much longer than that expected from the sample resistivity . the second component of the current appears to be magnetic ( ) , in that it is a microscopic , quasi - orbital effect ; it is evenly distributed within the bulk of the sample upon saturation . to explain these data , we propose a simple model invoking a new type of quantum fluid comprising a cdw coexisting with a two - dimensional fermi - surface pocket which describes the two types of current . the model and data are able to account for the body of previous experimental data which had generated apparently contradictory interpretations in terms of the quantum hall effect or superconductivity .

astro-ph9912207

i

soft gamma ray repeaters ( sgrs ) are neutron stars whose multiple bursts of gamma rays distinguish them from other gamma ray burst sources ( e.g @xcite for a recent review ) . sgrs are also unusual x ray pulsars in that they have spin periods clustered in the interval @xmath2 s , and they all appear to be associated ( @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) with supernova remnants ( snrs ) , which limits their average age to approximately @xmath3 kyr ( @xcite ) . the angular offsets of the sgrs from the apparent centers of their associated supernova remnant shells indicate that sgrs are endowed with space velocities @xmath4 km s@xmath5 , which are greater than the space velocities of most radio pulsars ( @xcite ) . anomalous x ray pulsars ( axps ) are similar to sgrs in that they are radio quiet x ray pulsars with spin periods clustered in the range @xmath6 s , and have similar persistent x ray luminosities as the sgrs ( @xmath7 ergs s@xmath5 , see e.g. @xcite for a recent review ) . most of the axps appear to be associated with supernova remnants , and therefore they are also thought to be young neutron stars like the sgrs . the spin periods of both axps and sgrs are increasing with time ( spinning - down ) , and show no evidence for intervals of decreasing spin period ( spin - up ) , although the spin - down rates of many of the sgrs and axps appear to be variable or `` bumpy '' ( e.g. @xcite ; @xcite ; @xcite ; @xcite ; although for a different viewpoint see @xcite ) . the lack of identified companions at non x ray wavelengths ( e.g. @xcite ) and doppler shifts associated with binary orbital motion ( @xcite ) , together with the problem of accelerating binaries to space velocities @xmath8 km s@xmath5 ( @xcite ) , imply that sgrs and axps are not members of high mass binary systems , although low mass systems with neutron star companions of @xmath9 are not constrained in most cases . if sgrs and axps spin - down primarily via the emission of magnetic dipole radiation ( mdr ) , as do radio pulsars , then they must have surface dipole fields of @xmath10 g or greater ( i.e. `` magnetars '' ; e.g. @xcite ) . observations of the sgrs 180620 ( @xcite ) and 1900 + 14 ( @xcite ; @xcite ) , however , indicate that the present - day spin - down rates of these sgrs are inconsistent with simple mdr , given the ages of their associated supernova remnants ( @xcite ; @xcite ) , and imply that the spin - downs are due to winds . magnetar - strength fields might still be possible in these sources , however , if alfvn wave wind emission is infrequent and intermittent ( @xcite , so that the presently observed spin - down rates are atypical . alternative scenarios for sgrs and axps involving typical pulsar magnetic fields ( @xmath11 g ) have been proposed ( @xcite ; alpar 2000 ; chatterjee , hernquist & narayan 2000 ; chatterjee & hernquist 2000 ) . in these models , the sgrs and axps have spun - down rapidly via magnetospheric accretion torques from outflowing `` propeller effect '' winds . the assumed sources of the magnetospheric material are either fallback accretion disks ( alpar 2000 ; chatterjee , hernquist & narayan 2000 ; chatterjee & hernquist 2000 ) , or fossil disks formed from expanding supernova ejecta intercepted by high velocity neutron stars ( @xcite ; @xcite ) . here we present a fresh look at evidence which suggests that sgrs and axps are born into unusually dense environments . we show that the environments of the sgr and axp progenitors into which their snrs expand are the dense , warm and cool phases of the interstellar medium ( ism ) , and not the hot tenuous phase of the ism where most of the neutron - star - producing , core collapse supernovae of massive o and b stars occur and where most young radio pulsars are found . this implies that there is an environmental factor influencing the development of sgrs and axps . the structure of this paper is as follows . we first discuss the typical environments of supernova progenitors in @xmath12 , and then supernova remnants associated with sgrs and axps in @xmath13 , followed by a discussion of the sgr and axp ages and distances are in @xmath14 . in @xmath15 the density of the sgr and axp progenitor environments is discussed , and in @xmath16 a similar analysis is done for the snrs associated with young radio pulsars . in @xmath17 we discuss the statistical significance of the results and the implications for magnetar and propeller - based models for sgrs and axps . finally , the appendix contains a short discussion of the ages , distances , and other information for each sgr and axp .

soft gamma ray repeaters ( sgrs ) and anomalous x ray pulsars ( axps ) are young and radio - quiet x - ray pulsars which have been rapidly spun - down to slow spin periods clustered in the range s. most of these unusual pulsars also appear to be associated with supernova shell remnants ( snrs ) with typical ages kyr . by examining the sizes of these remnants versus their ages , we demonstrate that the interstellar media which surrounded the sgr and axp progenitors and their snrs were unusually dense compared to the environments around most young radio pulsars and snrs .

soft gamma ray repeaters ( sgrs ) and anomalous x ray pulsars ( axps ) are young and radio - quiet x - ray pulsars which have been rapidly spun - down to slow spin periods clustered in the range s. most of these unusual pulsars also appear to be associated with supernova shell remnants ( snrs ) with typical ages kyr . by examining the sizes of these remnants versus their ages , we demonstrate that the interstellar media which surrounded the sgr and axp progenitors and their snrs were unusually dense compared to the environments around most young radio pulsars and snrs . we explore the implications of this evidence on magnetar and propeller - based models for the rapid spin - down of sgrs and axps . we find that evidence of dense environments is not consistent with the magnetar model unless a causal link can be shown between the development of magnetars and the external ism . propeller - driven spin - down by fossil accretion disks for sgrs and axps appears to be consistent with dense environments since the environment can facilitate the formation of such a disk . this may occur in two ways : 1 ) formation of a `` pushback '' disks from the innermost ejecta pushed back by prompt reverse shocks from supernova remnant interactions with massive progenitor wind material stalled in dense surrounding gas , or 2 ) acquisition of disks by a high velocity neutron stars , which may be able to capture a sufficient amounts of co - moving outflowing ejecta slowed by the prompt reverse shocks in dense environments .

astro-ph9912207

i

we have shown that soft gamma ray repeaters ( sgrs ) and anomalous x ray pulsars ( axps ) are born in regions of the interstellar medium which are denser than the environments typical of young neutron stars . this suggests that the development of sgrs and axps may be related to their environments , and we examine the implications of this on magnetar and propeller - based models for sgrs and axps . the evidence of dense progenitor environments would be consistent with the magnetar model only if magnetars are born exclusively in dense environments , which does not appear to be the case if magnetars form only from the most massive stars . propeller - based models for sgrs and axps involving the formation of accretion disks from supernova ejecta appear to be consistent with the evidence for dense progenitor environments since these environments may induce the formation of such disks . this may occur in two ways . _ pushback _ disks may be formed from the infall of the innermost ejecta , pushed back towards the neutron stars by prompt reverse shocks from the interactions of the expanding remnants with massive progenitor winds confined close to the stars by dense surrounding gas producing rapid deceleration of the expanding ejecta and strong prompt reverse shocks ( truelove & mckee 1999 ) . fossil disks may also form around high velocity neutron stars accreting from nearly co - moving supernova ejecta , slowed by the strong prompt reverse shocks in such dense environments ( van paradijs et al . 1995 ) . we acknowledge helpful suggestions from anonymous referees which led to improvements in the paper . this research made extensive use of nasa s astrophysics data system abstract service . this work was performed while one of the authors ( dm ) held a national research council - gsfc research associateship . rer acknowledges support by nasa contract nas5 - 30720 , and rel support from the astrophysical theory program .

we explore the implications of this evidence on magnetar and propeller - based models for the rapid spin - down of sgrs and axps . we find that evidence of dense environments is not consistent with the magnetar model unless a causal link can be shown between the development of magnetars and the external ism . propeller - driven spin - down by fossil accretion disks for sgrs and axps appears to be consistent with dense environments since the environment can facilitate the formation of such a disk . this may occur in two ways : 1 ) formation of a `` pushback '' disks from the innermost ejecta pushed back by prompt reverse shocks from supernova remnant interactions with massive progenitor wind material stalled in dense surrounding gas , or 2 ) acquisition of disks by a high velocity neutron stars , which may be able to capture a sufficient amounts of co - moving outflowing ejecta slowed by the prompt reverse shocks in dense environments .

soft gamma ray repeaters ( sgrs ) and anomalous x ray pulsars ( axps ) are young and radio - quiet x - ray pulsars which have been rapidly spun - down to slow spin periods clustered in the range s. most of these unusual pulsars also appear to be associated with supernova shell remnants ( snrs ) with typical ages kyr . by examining the sizes of these remnants versus their ages , we demonstrate that the interstellar media which surrounded the sgr and axp progenitors and their snrs were unusually dense compared to the environments around most young radio pulsars and snrs . we explore the implications of this evidence on magnetar and propeller - based models for the rapid spin - down of sgrs and axps . we find that evidence of dense environments is not consistent with the magnetar model unless a causal link can be shown between the development of magnetars and the external ism . propeller - driven spin - down by fossil accretion disks for sgrs and axps appears to be consistent with dense environments since the environment can facilitate the formation of such a disk . this may occur in two ways : 1 ) formation of a `` pushback '' disks from the innermost ejecta pushed back by prompt reverse shocks from supernova remnant interactions with massive progenitor wind material stalled in dense surrounding gas , or 2 ) acquisition of disks by a high velocity neutron stars , which may be able to capture a sufficient amounts of co - moving outflowing ejecta slowed by the prompt reverse shocks in dense environments .

1208.1381

i

understanding the processes by which molecules and particles on surfaces absorb and scatter electromagnetic radiation is an area of considerable scientific importance . information may be needed because of an intrinsic desire to study surface physics , because an active surface forms part of an electronic device , or because of the need to locate defects and identify contaminants . examples include the dynamics of adsorbed biomolecules @xcite , the adhesion and movement of droplets @xcite , the plasmonic behaviour of nanoparticles @xcite , and the photonic response of patterned films @xcite . surface processes have traditionally been studied through infrared and optical microscopy , spectroscopy , and scattering , with afm playing a key role in recent years . often , the information needed has to be acquired indirectly through measurements made at inappropriate wavelengths , or through models that are hard to extrapolate . crucially , it is necessary to measure the state of coherence of the field to which a system is sensitive in order to fully characterize its behaviour : for example when calculating radiative heat transfer between nanoparticles @xcite . measurements made with a single source only gain access to a subset of the information available . of particular importance are those cases where the ability of a surface to absorb energy is central to the operation of a device . for example , complex schemes are being explored to increase the efficiency of photovoltaics @xcite , to optimize the sensitivity of infrared and optical sensors @xcite , and to develop frequency selective surfaces , high - power mirrors , and hyperspectral black absorbers . in all cases , the physics of the absorption process is intimately related to the existence of coherent phenomena such as resonant dipole interactions , surface plasmon coupling @xcite , and surface phonon exchange . even in the case of apparently simple structures , such as planar dielectric and metallic interfaces , the near - field spatial and polarimetric correlations contain a wealth of information @xcite . a typical set of questions is as follows : what are the scale sizes and forms of the dynamical modes responsible for absorbing energy ? how many modes are involved in the absorption process ? what are their responsivities ? what physical mechanisms mediate the collective behaviour ? in this paper we argue that it is possible to measure the state of coherence of the electromagnetic field to which any system is sensitive , and thereby determine the spatial forms , polarizations , and relative strengths of the individual modes responsible for absorbing energy . because the electromagnetic modes are intimately related to dynamical modes of the system , it is possible to accrue direct information about the dynamical modes themselves , and thereby reveal the existence of collective phenomena . the basic technique can be used at any wavelength , and can be implemented in a number of different ways . the basic idea is to illuminate the structure under test ( sut ) with a pair of phase - locked , near - field or far - field point sources . as the differential phase between the sources is rotated , the _ total _ absorbed power displays a fringe . if the complex visibility of this fringe is measured for different pairs of source locations , the dynamical forms of the modes responsible for absorbing the energy can be found . in the case of detectors and photovoltaics , the scheme is particularly easy to implement because the degrees of freedom responsible for generating the measured output are those of practical significance . although the technique is applicable to a wide range of problems , we illustrate the method by showing how it provides information about the collective behaviour of systems of surface dipoles . the sut is modeled by using the discrete dipole approximation ( dda ) @xcite , together with a polarizability that allows for bound states and damping to the substrate . dda was originally devised @xcite to model light extinction by astrophysical particles , but has since been developed in areas as diverse as modeling the aggregation of irregular particles from colloids @xcite , the scattering of light by particles on surfaces @xcite , the scattering of light by periodic targets @xcite , and the optical properties of viruses , proteins , dna , and blood cells @xcite . formulating our measurement procedure in terms of dda opens the way to predicting the interferometric response of a wide variety of complex objects such as biomolecules , droplets , and nanoparticles , and thereby creating representative dynamical models of measured interferometric data . other simulation methods , such as mom , can be used . as an aside , a variant of eai can be used with dda purely as a numerical tool for determining the state of coherence , and therefore the incident electromagnetic modes , to which any irregular dielectric body is sensitive . the scheme differs from the usual method for determining the state of coherence of thermally radiated fields , through @xmath0 where @xmath1 is the electric green s dyadic of the whole system including scattering , because ( [ a ] ) requires the object to be in thermal equilibrium with its surroundings , and therefore includes the blackbody environment and scattered fields . as a consequence , even lossless dielectric objects display near - field coherence effects , as discussed by yannopapas in the context of chains of spheres @xcite . in contrast , eai only includes those degrees of freedom responsible for absorbing energy . in section [ sec : basic_scheme ] we present the theory of energy absorption interferometry ( eai ) , and then in section [ sec : simulations ] illustrate how it can be used to recover the dynamical modes of ring - like and linear chains of coupled dipoles , with and without defects . linear chains of dipoles @xcite , spheres @xcite , and cylinders @xcite are of practical importance , and exhibit complex forms of spatial and spectral coherence . we show how eai can reveal large - scale collective behaviour , and how the response of a discrete system transitions to that of a continuous system when the sut contains many dipoles per wavelength . in section [ sec : practical ] , we discuss practical implementation . a collection of particles on a surface . the individual particles have dipole moments @xmath2 . the system is illuminated by a pair of phase - locked sources , which can have any polarisation and position . the experiment measures the complex visibility of the absorbed power as the differential phase between the sources is varied . ]

spatial interferometry , based on the measurement of total absorbed power , can be used to determine the state of coherence of the electromagnetic field to which any energy - absorbing structure is sensitive . the measured coherence tensor can be diagonalized to give the amplitude , phase , polarization patterns , and responsivities of the individual electromagnetic modes through which the structure can absorb energy . because the electromagnetic modes are intimately related to dynamical modes of the system , information about collective excitations can be found . we present simulations , based on the discrete dipole approximation ( dda ) , showing how the dynamical modes of systems of surface dipoles can be recovered . interactions are taken into consideration , leading to long - range coherent phenomena , which are revealed by the method . the use of dda enables the interferometric response of a wide variety of objects to be modeled , from patterned photonic films to biological macromolecules .

spatial interferometry , based on the measurement of total absorbed power , can be used to determine the state of coherence of the electromagnetic field to which any energy - absorbing structure is sensitive . the measured coherence tensor can be diagonalized to give the amplitude , phase , polarization patterns , and responsivities of the individual electromagnetic modes through which the structure can absorb energy . because the electromagnetic modes are intimately related to dynamical modes of the system , information about collective excitations can be found . we present simulations , based on the discrete dipole approximation ( dda ) , showing how the dynamical modes of systems of surface dipoles can be recovered . interactions are taken into consideration , leading to long - range coherent phenomena , which are revealed by the method . the use of dda enables the interferometric response of a wide variety of objects to be modeled , from patterned photonic films to biological macromolecules .

1403.5813

i

in recent years , the interest in plastic electronics has grown considerably . the realization of devices such as organic field - effect transistors ( ofet ) represents a key step in this field . single - crystal ofet made of ultrapure small molecule semiconductors are characterized by mobilities up to one order of magnitude larger then those typical of thin film transistors @xcite . the most promising are those based on oligoacenes , such as pentacene and rubrene , which exhibit a strong anysotropy and the largest mobility measured in organic semiconductors @xcite . in spite of many applications based on such devices , the intrinsic transport mechanism acting in high mobility organic semiconductors is not fully understood . transport measurements from @xmath0 k to room temperature in single crystal semiconductors , such as rubrene , show a behaviour of the charge carrier mobility @xmath1 which can be defined band - like ( @xmath2 , with the exponent @xmath3 close to two ) similar to that observed in crystalline inorganic semiconductors @xcite . however , the order of magnitude of mobility is much smaller than that of pure inorganic semiconductors , and the mean free path for the carriers has been theoretically estimated to be comparable with the molecular separation at room temperature @xcite . therefore , the ioffe - regel limit is reached with increasing temperature . moreover , in some systems , starting from room temperature , a crossover from band - like to activated hopping behavior can take place @xcite . the crossover has been interpreted as due to the formation of the polaron , that is the quasi - particle formed by the electron ( or hole ) and the surrounding phonon cloud @xcite . for example , in naphthalene and anthracene , while the mobility along the @xmath4 and @xmath5 axis shows only a slightly change with the temperature , that along the @xmath6 axis is characterized by a temperature activated behavior at higher temperature with energy barrier of the order of @xmath7 mev @xcite . the experimental data in these compounds suggest that the coherent band transport is gradually destroyed and the transport due to polaron hopping evolves as a parallel channel dominating at sufficiently high temperature ( which can be larger than room temperature ) @xcite . sketch about the interplay between low frequency inter - molecular and high frequency intra - molecular vibrational modes in a crystal of naphtalene . the charge carrier deforms the benzene ring when it is on the molecule . moreover , the charge carrier displaces two neighbor molecules when it jumps.,scaledwidth=75.0% ] in systems with polarizable gates , scaling laws of the mobility as a function of the dielectric constant of solid @xcite and liquid @xcite gates have been discovered pointing out that the nearby dielectric has a strong influence . actually , if the difference between the dielectric constant of the organic semiconductor and of the gate is small , at temperatures close or higher than @xmath0 k , the mobility @xmath1 of these systems exhibits the power - law band - like behavior . on the other hand , if the dielectric constant mismatch is high , an activated insulating behavior is found with much smaller values of mobility at room temperature @xcite . a possible explanation of this behavior is that the injected charge carriers undergo a polaronic localization due to the interaction with modes at the interface with the polarizable dielectric gate @xcite . extended vs. localized features of charge carriers appear also in spectroscopic observations . angle resolved photoemission spectroscopy ( arpes ) supports the extended character of states @xcite showing that the quasi - particle energy dispersion does exhibit a weak mass renormalization even if the width of the peaks of the spectral function increases significantly with temperature . for pentacene , the bandwidth is reduced only by about @xmath8 going from @xmath9 to @xmath10 indicating moderate values of electron - phonon coupling . on the other hand , some spectroscopic probes , such as electron spin resonance ( esr ) @xcite , thz @xcite , and modulated spectroscopy @xcite are in favor of states localized within few molecules . actually , in rubrene and in pentacene , to ascribe the presence of localized features to small polarons is not likely since the electron - phonon coupling is not large enough to justify the polaron formation @xcite . therefore , one of the main theoretical problems is to conciliate band - like with localized features of charge carriers @xcite . first - principle calculations have pointed out that charge carriers are affected by the coupling to inter - molecular modes with low frequency in comparison with typical electron hoppings @xcite . a model that is to some extent close to the su - schrieffer - heeger ( ssh ) @xcite hamiltonian has been recently introduced to take into account this interaction @xcite . it is a minimal one - dimensional ( 1d ) system , valid for the most conductive crystal axis of high mobility systems , where the effect of the electron - phonon coupling is reduced to a modulation of the transfer integral @xcite . a dynamic approach where vibrational modes are treated as classical variables has been used in 1d and in a recent generalization to two dimensions ( 2d ) @xcite . within this method , the temperature dependence of computed mobility is in agreement with experimental results . however , the role of dimensionality of the system is not clear : in fact , in the 1d case , one has @xmath11 , while , in the 2d case , the decrease of the mobility with temperature is intermediate between @xmath11 and @xmath12 . in any case , the computed mobility is larger than that measured ( at least a factor of two ) . moreover , the dynamics of only one charge particle is studied neglecting completely the role of the chemical potential . finally , the effects on charge carrier dynamics due to the coupling with vibrational modes are included in an approximate way @xcite and the corresponding coupled dynamics do not recover the right thermal equilibrium on long times . recently , the transport properties of the 1d ssh model have been analyzed within a different adiabatic approach @xcite mapping the problem onto that of a single quantum particle in a random potential ( generalized anderson problem @xcite ) . very recently , some of us have made a systematic study of this 1d model including the vertex corrections into the calculation of the mobility @xcite . while finite frequency quantities are properly calculated in this 1d model , the inclusion of vertex corrections leads to a vanishing mobility unless an ad - hoc broadening of the energy eigenvalues is assumed . it is clear that 1d adiabatic models suffer of severe limitations , of which the main is that electronic states are always localized @xcite . moreover , features such as band anisotropy , small but finite carrier density are necessary for a correct description of the systems . therefore , in this review , we first analyze a generic three - dimensional ( 3d ) model such as the anisotropic holstein model @xcite in order to discuss the relevant issue of the band anisotropy at finite carrier density . this model is studied within the adiabatic approach focusing on the weak to intermediate el - ph coupling regime which is relevant for high mobility organic semiconductors @xcite . next , we analyze a realistic model for rubrene which represents an extension of the 1d ssh model to the quasi 2d case since this is the relevant geometry for ofet @xcite . spectral and transport properties calculated within these two models are discussed in this review . the spectral functions show peaks which are weakly renormalized in comparison with those of the bare bands . however , with increasing temperature , the width of the spectral functions gets larger and larger making the quasi - particles less defined . the marked width of the spectral functions gives rise to densities of states with a low energy exponential tail increasing with temperature . at low temperatures , this tail corresponds to localized states and gives rough indications for the energy position of the mobility edge . with increasing temperature , in the regime of low carrier doping appropriate to most ofet , the chemical potential always enters the energy region of the tail . the features of the spectral function and the behavior of the chemical potential allow to reconcile the band - like description ( arpes data ) with the finding that charge carriers appear more localized at high temperature ( esr and modulated spectroscopy data ) . the study of spectral properties also clarifies that the states that mainly contribute to the conduction process have low momentum and are not at the chemical potential . the mobility @xmath1 is studied as a function of the electron - phonon coupling , the temperature and particle density . not only the order of magnitude and the anisotropy ratio between different directions are in agreement with experimental observations , but also the temperature dependence of @xmath1 is correctly reproduced in the model for rubrene since it scales as a power law @xmath13 , with @xmath3 close or larger than two . the inclusion of vertex corrections in the calculation of the mobility is relevant , in particular , to get a transport lifetime one order smaller than the spectral lifetime of the states involved in the transport mechanism . moreover , with increasing temperature , the ioffe - regel limit is reached since the contribution of itinerant states to the conduction becomes less and less relevant . _ ab - initio _ calculations have clarified that charge carriers in organic semiconductors are not only coupled to low frequency inter - molecular modes , but also to intra - molecular modes with high frequency in comparison with typical electron hoppings @xcite ( see fig . [ naphta ] for a sketch in naphtalene crystal ) . an important point is that the reorganization energy ( related to the polaron binding energy ) decreases with increasing the number of benzene rings in oligoacenes ( for example , going from naphthalene to pentacene ) . in order to fully explore the effects of the different modes on prototype single crystal organic semiconductors , such as oligoacenes , a model with intermediate coupling to both intra- and inter - molecular modes is analyzed in this review @xcite . we will show that the interplay between local and non local electron - phonon interactions is able to provide a very accurate description of the mobility and to shed light on the intricate mechanism of band narrowing with increasing temperature @xcite . when the organic semiconductor is grown on a polarizable gate , it is important to analyze the effects of electron coupling to surface vibrational modes of the gate at the interface with the semiconductor mediated by a long - range electron - phonon interaction @xcite . in this review , we analyze a model which combines the effects of interface and intrinsic bulk electron - phonon couplings on the transport properties at finite temperature . we show that the coupling to the organic semiconductor bulk phonon modes affects the behavior of mobility below room temperature enhancing the coherent contribution , but it is ineffective on the incoherent small polaron contribution dominated by the interface coupling at high temperatures . in order to improve the modeling of organic semiconductors , the effect of a weak disorder due to bulk and interface traps is included @xcite . in particular , the interplay between long - range electron - phonon interactions and disorder effects is investigated within a model . the disorder effects are able to enhance the hopping barriers of the activated mobility and to drive the small polaron formation to lower values of electron - phonon interactions . we point out that disorder is a key factor to get agreement with experimental data in rubrene ofet grown on polarizable gate dielectrics , such as the @xmath14 oxide @xcite . the paper is organized in the following way . in section ii , the effects of electron coupling to low frequency vibrational modes on the spectral and transport properties are discussed in high - dimensional holstein - like and ssh - like models . in section iii , the effects of electron coupling to both low frequency inter - molecular and high frequency intra - molecular modes on the spectral and transport properties are investigated . in section iv , the influence of gates made of polarizable dielectrics and the interplay between electron - phonon couplings and disorder strength on the transport properties are emphasized . in section v , conclusions and final discussions .

spectral and transport properties of small molecule single - crystal organic semiconductors have been theoretically analyzed focusing on oligoacenes , in particular on the series from naphthalene to rubrene and pentacene aiming to show that the inclusion of different electron - phonon couplings is of paramount importance to interpret accurately the properties of prototype organic semiconductors . while , in the case of rubrene , the coupling between charge carriers and low frequency inter - molecular modes is sufficient for a satisfactory description of spectral and transport properties , the inclusion of electron coupling to both low frequency inter - molecular and high frequency intra - molecular vibrational modes is needed to account for the temperature dependence of transport properties in smaller oligoacenes . the mobility along different crystallographic directions has been calculated , including vertex corrections that give rise to a transport lifetime one order of magnitude smaller than the spectral lifetime of the states involved in the transport mechanism . the mobility always exhibits a power - law behavior as a function of temperature in agreement with experiments in rubrene . + in systems gated with polarizable dielectrics , the electron coupling to interface vibrational modes of the gate has to be included in addition to the intrinsic electron - phonon interaction . while the intrinsic bulk electron - phonon interaction affects the behavior of mobility in the coherent regime below room temperature , the coupling with interface modes is dominant for the activated high temperature contribution of localized polarons .

spectral and transport properties of small molecule single - crystal organic semiconductors have been theoretically analyzed focusing on oligoacenes , in particular on the series from naphthalene to rubrene and pentacene aiming to show that the inclusion of different electron - phonon couplings is of paramount importance to interpret accurately the properties of prototype organic semiconductors . while , in the case of rubrene , the coupling between charge carriers and low frequency inter - molecular modes is sufficient for a satisfactory description of spectral and transport properties , the inclusion of electron coupling to both low frequency inter - molecular and high frequency intra - molecular vibrational modes is needed to account for the temperature dependence of transport properties in smaller oligoacenes . + for rubrene , a very accurate analysis in the relevant experimental configuration has allowed to clarify the origin of the temperature dependent mobility observed in these organic semiconductors . with increasing temperature , the chemical potential moves into the tail of the density of states corresponding to localized states , but this is not enough to drive the system into an insulating state . the mobility along different crystallographic directions has been calculated , including vertex corrections that give rise to a transport lifetime one order of magnitude smaller than the spectral lifetime of the states involved in the transport mechanism . the mobility always exhibits a power - law behavior as a function of temperature in agreement with experiments in rubrene . + in systems gated with polarizable dielectrics , the electron coupling to interface vibrational modes of the gate has to be included in addition to the intrinsic electron - phonon interaction . while the intrinsic bulk electron - phonon interaction affects the behavior of mobility in the coherent regime below room temperature , the coupling with interface modes is dominant for the activated high temperature contribution of localized polarons . + finally , the effects of a weak disorder largely increase the activation energies of mobility and induce the small polaron formation at lower values of electron - phonon couplings in the experimentally relevant temperature window .

1403.5813

c

in this review , we have theoretically analyzed the effects of different electron - phonon couplings on spectral and transport properties of small molecule single - crystal organic semiconductors . focus has been on oligoacenes , in particular on the series from naphthalene to rubrene and pentacene . first , we have discussed the effects of the electron coupling to low frequency inter - molecular vibrational modes on the spectral and transport properties . the resulting adiabatic models have been studied through numerical approaches with varying electron - phonon coupling and temperature . for rubrene , the model has considered the role of the electron - phonon coupling leading to a modulation of the particle hopping integral . with increasing temperature , the density of states is characterized by a larger exponential tail corresponding to localized states . consequently , the chemical potential moves into the tail of the density of states , but this is not enough to drive the system into an insulating state . not only the order of magnitude and the anisotropy ratio between different directions are accurate , but also the temperature dependence of the mobility is correctly reproduced in the model for rubrene . with increasing temperature , the ioffe - regel limit is reached since the contribution of itinerant states to the conduction becomes less and less relevant . then , we have analyzed the effects of electron coupling to both low frequency inter - molecular and high frequency intra - molecular modes on the spectral and transport properties . the interplay between local and non local electron - phonon interactions has been able to provide a very accurate description of the mobility of oligoacenes and to shed light on the intricate mechanism of band narrowing with increasing temperature . the band narrowing is a complicated phenomenon which could also be affected by the thermal expansion of the crystal structure @xcite ( an effect which has not been analyzed in this review ) . in the last part of the review , we have considered the influence of gates made of polarizable dielectrics on the transport properties . this effect has been studied in a model which has combined bulk and long - range interface electron - phonon couplings . we have pointed out that the bulk coupling affects the behavior of mobility below room temperature enhancing the coherent contribution , but it is ineffective on the incoherent small polaron contribution dominated by the interface coupling at high temperatures . finally , we have emphasized the interplay between electron - phonon couplings and disorder strength on the transport properties . the presence of disorder is important to improve the modeling of the materials studied in this review . in particular , for systems gated with polarizable dielectrics , we have shown that disorder effects are able to enhance the hopping barriers of the activated mobility and to drive the small polaron formation at lower values of electron - phonon interactions . therefore , disorder represents a key factor to get agreement with experimental data . some issues have not been covered in this review . indeed , the transport properties could be affected by the nonlocal electron coupling not only to optical but also acoustic vibrations @xcite . the coupling to acoustic vibrations should be effective at low temperatures where it would be interesting also to investigate the role of quantum lattice fluctuations . these quantum effects are small in the adiabatic limit , however , they could be important in the regime where the presence of traps also influences the transport properties . finally , we believe that concepts and methods discussed in this review can be a starting point for the study of related ( such as durene crystals @xcite ) and more complex systems @xcite . 1 t. hasegawa and j. takeya , _ sci . technol . adv . mater . _ * 2009 * , _ 10 _ , 24314 . m. e. gershenson , v. podzorov and a. f. morpurgo , _ rev . _ * 2006 * , _ 78 _ , 973 . y. c. cheng , r. j. silbey , d. a. da silva filho , j. p. calbert , j. cornil , and j. l. bredas , _ j. chem * 2003 * , _ 118 _ , 3764 . v. coropceanu , j. cornil , d.a . da silva filho , y. olivier , r. silbey , and j .- l . bredas , _ chem . rev . _ * 2007 * , _ 107 _ , 926 . y. c. cheng and r. j. silbey , _ j. chem . phys . _ * 2008 * _ 128 _ , 114713 . f. ortmann , f. bechstedt , and k. hannewald , _ new j. phys . _ * 2010 * , _ 12 _ , 023011 . a. s. alexandrov and j. t. devreese , _ advances in polaron physics _ ; springer verlag , berlin heidelberg , 2010 . w. warta and n. karl , _ phys . b _ * 1985 * _ 32 _ , 1172 ; n. karl , xith molecular crystal symposium , lugano , 1985 , p. 135 ; n. karl , _ synthetic metals _ * 2003 * _ 133 - 134 _ , 649 . a. f. stassen , r. w. i. de boer , n. n. iosad and a. f. morpurgo , _ app . lett . _ * 2004 * , _ 85 _ , 3899 . i. n. hulea , s. fratini , h. xie , c. l. mulder , n. n. iossad , g. rastelli , s. ciuchi and a. f. morpurgo , _ nat . _ * 2006 * , _ 5 _ , 982 . s. ono , k. miwa , s. seki and j. takeya , _ app . lett . _ * 2010 * , _ 94 _ , 063301 . s. fratini , h. xie , i. n. hulea , s. ciuchi and a. f. morpurgo , _ new j. phys . _ * 2008 * , _ 10 _ , 033031 . h. ding , c. reese , a. j. makinen , z. bao , and y. gao , _ appl . lett . _ * 2010 * , _ 96 _ , 222106 . s. i. machida , y. nakayama , s. duhm , q. xin , a. funakoshi , n. ogawa , s. kera , n. ueno , and h. ishii , _ phys . lett . _ * 2010 * _ 104 _ , 156401 . r. c. hatch , d. l. huber , and h. hchst , _ phys . lett . _ * 2010 * _ 104 _ , 047601 . k. marumoto , s. kuroda , t. takenobu , and y. iwasa , _ phys . _ * 2006 * _ 97 _ , 256603 . k. marumoto , n. arai , h. goto , m. kijima , k. murakami , y. tominari , j. takeya , y. shimoi , h. tanaka , s. kuroda , t. kaji , t. nishikawa , t. takenobu , and y. iwasa , _ phys . b _ * 2011 * _ 83 _ , 075302 . h. a. v. laarhoven , c. f. j. flipse , m. koeberg , m. bonn , e. hendry , g. orlandi , o. d. jurchescu , t.t.m . palstra , and a. troisi , _ j. chem . phys . _ * 2008 * _ 129 _ , 044704 . t. sakanoue and h. sirringhaus , _ nat . mater . _ * 2010 * _ 9 _ 736 . a. troisi and g. orlandi , _ phys . _ * 2006 * _ 96 _ , 086601 . r. s. sanchez carrera , p. paramonov , g. m. day , v. coropceanu , and j .- l . bredas , _ j. am . soc . _ * 2010 * , _ 132 _ , 14437 . w. p. su , * et al . * , _ phys . rev . lett . _ * 1979 * , _ 42 _ , 1698 . a. troisi , _ adv . _ * 2007 * , _ 19 _ , 2000 . a. troisi , _ j. chem . phys . _ * 2011 * , _ 134 _ , 034702 . y. li , v. coropceanu , and j .- l . phys . _ * 2013 * , _ 138 _ , 204713 . s. fratini and s. ciuchi , _ phys . lett . _ * 2009 * , _ 103 _ , 266601 . p. w. anderson , _ phys . rev . _ * 1958 * , _ 109 _ , 1492 . v. cataudella , g. de filippis , and c. a. perroni , _ phys . b _ * 2011 * , _ 83 _ , 165203 . f. ortmann , f. bechstedt , and k. hannewald , _ phys . b _ * 2009 * , _ 79 _ , 235206 . c. a. perroni , a. nocera , v. marigliano ramaglia , and v. cataudella , _ phys . rev . b _ * 2011 * , _ 83 _ , 245107 . f. gargiulo , c. a. perroni , v. marigliano ramaglia , and v. cataudella , _ phys . b _ * 2011 * , _ 84 _ , 245204 . k. hannewald and p. a. bobbert , _ appl . phys . lett . _ * 2004 * _ 85 _ , 1535 ; k. hannewald and p. a. bobbert , _ phys . b _ * 2004 * , _ 69 _ , 075211 . c.a . perroni , v. marigliano ramaglia , and v. cataudella , _ phys . b _ * 2011 * , _ 84 _ , 014303 . c. a. perroni and v. cataudella , _ phys . rev . b _ * 2012 * _ 85 _ , 155205 . c. a. perroni and v. cataudella , _ europhys . lett . _ * 2012 * _ 98 _ , 47004 . t. holstein , _ ann . _ * 1959 * , _ 8 _ , 325 . t. holstein , _ ann . phys . _ * 1959 * , _ 8 _ , 343 . a. shehu , s. d. quiroga , p. dangelo , c. albonetti , f. borgatti , m. murgia , a. scorzoni , p. stoliar , and f. biscarini , _ phys . _ * 2010 * , _ 104 _ , 246602 . a. girlando , l. grisanti , and m. masino , _ phys . b _ * 2010 * , _ 82 _ , 035208 . e. venuti , i. billotti , r. g. della valle , a. brillante , p. ranzieri , m. masino and a. girlando , _ j. phys c _ * 2008 * _ 112 _ , 17416 . a. nocera , c. a. perroni , v. marigliano ramaglia , and v. cataudella , _ phys . b _ * 2011 * , _ 83 _ , 115420 . a. nocera , c. a. perroni , v. marigliano ramaglia , and v. cataudella , _ phys . rev . b _ * 2012 * , _ 86 _ , 035420 . a. nocera , c. a. perroni , v. marigliano ramaglia , g. cantele , and v. cataudella , _ phys . b _ * 2013 * , _ 87 _ , 155435 . c. a. perroni , a. nocera , and v. cataudella , _ europhys . lett . _ * 2013 * _ 103 _ , 58001 . c. a. perroni , f. romeo , a. nocera , v. marigliano ramaglia , r. citro , and v. cataudella , _ arxiv:1307.6834v1 _ * 2013*. g. d. mahan , _ many - particle physics _ 2nd ed . ; plenum press , new york , 1990 . e. n. economou , _ green s functions in quantum physics _ ; springer verlag , berlin , 1983 . c. a. perroni , e. piegari , m. capone , and v. cataudella , _ phys . b _ * 2004 * , _ 69 _ , 174301 . o. gunnarsson , m. calandra , and j. e. han , _ rev . mod . phys . _ * 2003 * , _ 75 _ , 1085 . k. hannewald and p. a. bobbert , _ phys . b _ * 2004 * , _ 69 _ , 075212 . h. ishii , n. kobayashi , and k. hirose , _ phys . b _ * 2013 * , _ 88 _ , 205208 . f. ortmann , f. bechstedt , and k. hannewald , _ j. phys . : condens . matter _ * 2010 * , _ 22 _ , 465802 . e. piegari , c. a. perroni , and v. cataudella , _ eur . j. b _ * 2005 * , _ 44 _ , 415 . s. ciuchi and s. fratini , _ phys * 2011 * , _ 106 _ , 166403 . i. j. lang and yu . a. firsov , _ sov . . jetp _ * 1963 * , _ 16 _ , 1301 . a. iorio , c. a. perroni , v. marigliano ramaglia , and v. cataudella , _ phys . b _ * 2011 * _ 83 _ , 085107 . n. vukmirovic , c. bruder , and vladimir m. stojanovic , _ phys . lett . _ * 2012 * _ 109 _ , 126407 . n. kirova and m .- n . bussac , _ phys . b _ * 2003 * , _ 68 _ , 235312 . y. li , v. coropceanu , and j .- l . bredas , _ j. phys lett . _ * 2012 * , _ 3 _ , 3325 . f. ortmann , k. hannewald , and f. bechstedt , _ app . lett . _ * 2008 * , _ 93 _ , 222105 . f. ortmann , k. hannewald , and f. bechstedt , _ j. phys . chem . b _ * 2009 * , _ 113 _ , 7367 .

+ for rubrene , a very accurate analysis in the relevant experimental configuration has allowed to clarify the origin of the temperature dependent mobility observed in these organic semiconductors . with increasing temperature , the chemical potential moves into the tail of the density of states corresponding to localized states , but this is not enough to drive the system into an insulating state . + finally , the effects of a weak disorder largely increase the activation energies of mobility and induce the small polaron formation at lower values of electron - phonon couplings in the experimentally relevant temperature window .

spectral and transport properties of small molecule single - crystal organic semiconductors have been theoretically analyzed focusing on oligoacenes , in particular on the series from naphthalene to rubrene and pentacene aiming to show that the inclusion of different electron - phonon couplings is of paramount importance to interpret accurately the properties of prototype organic semiconductors . while , in the case of rubrene , the coupling between charge carriers and low frequency inter - molecular modes is sufficient for a satisfactory description of spectral and transport properties , the inclusion of electron coupling to both low frequency inter - molecular and high frequency intra - molecular vibrational modes is needed to account for the temperature dependence of transport properties in smaller oligoacenes . + for rubrene , a very accurate analysis in the relevant experimental configuration has allowed to clarify the origin of the temperature dependent mobility observed in these organic semiconductors . with increasing temperature , the chemical potential moves into the tail of the density of states corresponding to localized states , but this is not enough to drive the system into an insulating state . the mobility along different crystallographic directions has been calculated , including vertex corrections that give rise to a transport lifetime one order of magnitude smaller than the spectral lifetime of the states involved in the transport mechanism . the mobility always exhibits a power - law behavior as a function of temperature in agreement with experiments in rubrene . + in systems gated with polarizable dielectrics , the electron coupling to interface vibrational modes of the gate has to be included in addition to the intrinsic electron - phonon interaction . while the intrinsic bulk electron - phonon interaction affects the behavior of mobility in the coherent regime below room temperature , the coupling with interface modes is dominant for the activated high temperature contribution of localized polarons . + finally , the effects of a weak disorder largely increase the activation energies of mobility and induce the small polaron formation at lower values of electron - phonon couplings in the experimentally relevant temperature window .

1310.2283

i

spectral methods have been used recently for solving partial differential equations on the unit disk , unit ball , or other domains with cylindrical or spherical geometry . their increasing popularity on these domains lies partially in various applications in earth sciences , disk or sphere shaped mirrors and lenses , fluid flow in a pipe or rotating cylinder , accretion disks in planetary astronomy , to name a few . in @xcite , poisson equation on an axisymmetric domain is transformed into a system of two - dimensional problems by the polar transformation , and the axisymmetric problems are then approximated by an appropriate spectral - galerkin method . fast spectral - galerkin methods for helmholtz equations on a disk or a cylinder are proposed in @xcite , using the polar transformation with essential pole conditions and the chebyshev or legendre polynomial bases in the radial direction . subsequently , these types of spectral galerkin methods have been extended to other domains with spherical geometries , including the 3-dimensional ball @xcite . meanwhile , mixed jacobi - fourier spectral method are presented for elliptic equations on a disk @xcite and a mixed jacobi - harmonic spectral approximation is proposed in @xcite for a navier - stokes equation in a ball . see @xcite for a comprehensive review of spectral methods and their special treatments in polar / spherical coordinates . moreover , an alternative approach for solving differential equations in a smooth domain is to map the domain into the unit ball and then apply a spectral method @xcite . however , apparent disadvantages and difficulties in such a type of spectral - galerkin method lie in : ( i ) . the polar transformation introduces variable coefficients in the reduced problem in polar / spherical coordinates , which increases the bandwidth of the discrete linear system ; ( ii ) . the enforcement of pole conditions induces artificial singularities at the pole either explicitly or implicitly , which brings about extra difficulties to both the design of efficient approximation schemes and the corresponding numerical analysis @xcite ; ( iii ) . as the numerical analysis is concerned , the approximation errors are measured and estimated in anisotropic , instead of genuine , sobolev norms . initiated by direct and efficient spectral method of atkinson and his collaborators that uses orthogonal polynomials to solve on linear elliptic equations on the disk with both homogeneous dirichlet and neumann boundary conditions @xcite . the second author of this paper studied sobolev orthogonal polynomials on a unit ball @xcite , which leads to a tri - diagonal linear system for second order elliptic equation with constant coefficients , as can be seen below . it this also give challenges to researchers on spectral approximations on the unit ball and its applications in direct and efficient spectral methods on the unit ball . one of the challenging problems in the spectral methods on the unit ball is to measure and estimate the errors of approximation in genuine , instead of anisotropic , sobolev norms . such estimates were established for the product domain in @xcite but has been lacking in most of the works on the unit disk or the unit ball . the problem of characterizing best approximation by the smoothness of functions is intensively studied in approximation theory . the two problems are closely related but not exactly the same as we shall explain below . the purpose of this paper is to conduct a comprehensive study for the spectral approximation on the unit ball @xmath3 of @xmath4 , making use of recent advances in both approximation theory , orthogonal polynomials , and spectral methods . spectral approximation for solving an elliptic equation on @xmath3 looks for approximate solutions that are polynomials written in terms of certain orthogonal basis on the ball and their coefficients are determined by the galerkin method . to understand the convergence of such an approximation process , it is necessary to study polynomial approximation in the sobolev space @xmath2 , where @xmath5 is a positive integer , that consists of functions whose derivatives up to @xmath5-th order are all in @xmath6 . in some literatures , the space @xmath2 is called @xmath7 . for @xmath8 , let @xmath9 denote its best polynomial approximation of degree at most @xmath10 . for spectral approximation , the desired estimate for @xmath11 is of the form @xmath12 where @xmath13 denotes the norm of @xmath14 defined by @xmath15 one of the main result of this paper is to establish this estimate and , more generally , establish its analogue in the space @xmath16 for @xmath17 . the difficulty of quantifying the error of polynomial approximation on the unit ball lies in the strong influence of the boundary of the ball on the approximation behavior . this is well documented for approximation on a closed interval on the real line . a complete characterization of best approximation on the unit ball is only carried out recently . in @xcite , two moduli of smoothness and their equivalent @xmath18-functionals were introduced and used to establish both direct and inverse theorems that characterize the behavior of best approximation on the unit ball . in @xcite , approximation in the sobolev space was studied and estimate for @xmath19 was established , more generally for @xmath20 ( ( * ? ? ? * corollary 5.4 ) ) , and the derivative estimates were established for angular derivatives , which however do not imply . what we can prove relatively effortless ( see theorem [ eq : approx - weight ] below ) is the following estimate @xmath21 where @xmath22 vanishes on the boundary sphere @xmath23 of @xmath24 and @xmath25 is the partial sum of the fourier orthogonal expansion in @xmath6 . this estimate , however , is weaker than because of the power of @xmath26 in its left hand side . it tuns out that what we need for proving is the orthogonal structure of the soblolev space @xmath2 , not the orthogonal structure of @xmath6 . an essential step in our study is to study orthogonal polynomials for with respect to the inner product @xmath27 of @xmath2 , which we call the sobolev orthogonal polynomials . initially motivated by direct and efficient spectral method of atkinson and his collaborators that uses orthogonal polynomials to solve linear elliptic equations on the disk @xcite , the sobolev orthogonal polynomials on the ball with respect to @xmath28 were studied in @xcite and those with respect to @xmath29 were studied in @xcite . in these works , sobolev orthogonal bases were constructed in terms of the orthogonal polynomials for @xmath30 with @xmath31 and @xmath32 , respectively , where the weight function @xmath33 , which are given explicitly in terms of spherical harmonics and the jacobi polynomials @xmath34 that are orthogonal polynomials with respect to @xmath35 on @xmath36 $ ] . for larger @xmath5 , however , the orthogonal structure is more complicated , and we need to extend the orthogonal basis for @xmath30 to allow @xmath37 to be negative integers , which in turn requires us to use extensions of the jacobi polynomials with negative indexes . this is prompted by the realization that the sobolev orthogonal polynomials for @xmath38 and @xmath39 in @xcite can be expressed in terms of orthogonal polynomials for @xmath30 with @xmath40 and @xmath41 , and , heuristically , the negative weight could cancel out the @xmath42 term in . the jacobi polynomials with negative indexes have been used in spectral approximation on other domains in @xcite . one of our main results is an explicitly constructed mutually orthogonal polynomial basis for @xmath43 , which could be used as the building blocks for the spectral - galerkin method . for @xmath44 , its @xmath10-th best polynomial approximation is given by the @xmath10-th partial sum of its fourier orthogonal expansion on the ball . for @xmath45 , we shall prove that the best approximating polynomials to @xmath46 are @xmath47 , the partial sums of the fourier orthogonal expansion in @xmath14 equipped with the inner product @xmath48 , which can be expressed explicitly in terms of the mutually orthogonal polynomials that we constructed . for the @xmath16 with @xmath49 , the best approximating polynomial is not explicitly known , but we are able to show that a near - best approximating polynomial , denoted by @xmath50 and defined via a smooth cut - off function @xmath51 , satisfies our sharp estimate in @xmath16 . both @xmath47 and @xmath52 are given by explicit formulas that can be easily computed numerically ( see section 4 ) . our main result on approximation in the sobolev space is the following : let @xmath53 . for any @xmath54 , @xmath55 , @xmath56 , there is a constant @xmath57 independent of @xmath46 and @xmath10 , such that @xmath58 where @xmath52 can be taken as @xmath59 for @xmath60 . more precise results of this nature are stated in section 4.1 below . to illustrate the application of this result in the spectral approximation , we will consider two examples , the helmholtz equation and the biharmonic equation on the unit ball , and demonstrate how our results on approximation in the sobolev space can be used to error estimates in the spectral - galerkin method . furthermore , we provide numerical examples for these equations for @xmath61 and @xmath62 , which further illustrate our findings . the paper is written with readers in both approximation theory community and spectral method community in mind . the problem of is originated and studied in the spectral method , which is closely tied to the problem of characterizing best approximation that has been a central theme and studied intensely in approximation theory . our approach uses a mixed bag of tools , developed in both approximation theory and spectral methods . it is our hope that this paper will stimulate further collaboration between the two communities . the paper is organized as follows . in the next section we present background materials , orthogonal polynomials on the unit ball , fourier orthogonal expansions , and recent results on approximation on the unit ball . the orthogonal structure of the sobolev space is developed in section 3 . the main results on approximation by polynomials in the sobolev space are stated and proved in section 4 . finally , in section 5 , we discuss applications of our main results in the spectral - galerkin methods and present our numerical examples . to keep the presentation fluent , we leave technical details of extending orthogonal bases to negative indexes and proving equivalence of norms in the sobolev space to appendix a and appendix b , respectively .

spectral approximation by polynomials on the unit ball is studied in the frame of the sobolev spaces , . the main results give sharp estimates on the order of approximation by polynomials in the sobolev spaces and explicit construction of approximating polynomials . one major effort lies in understanding the structure of orthogonal polynomials with respect to an inner product of the sobolev space . as an application , a direct and efficient spectral - galerkin method based on our orthogonal polynomials is proposed for the second and the fourth order elliptic equations on the unit ball , its optimal error estimates are explicitly derived for both procedures in the sobolev spaces and , finally , numerical examples are presented to illustrate the theoretic results .

spectral approximation by polynomials on the unit ball is studied in the frame of the sobolev spaces , . the main results give sharp estimates on the order of approximation by polynomials in the sobolev spaces and explicit construction of approximating polynomials . one major effort lies in understanding the structure of orthogonal polynomials with respect to an inner product of the sobolev space . as an application , a direct and efficient spectral - galerkin method based on our orthogonal polynomials is proposed for the second and the fourth order elliptic equations on the unit ball , its optimal error estimates are explicitly derived for both procedures in the sobolev spaces and , finally , numerical examples are presented to illustrate the theoretic results .

astro-ph0007354

i

the cold dark matter plus cosmological constant model ( @xmath0cdm ) appears to be remarkably successful in describing cosmology on scales much larger than a mpc ( e.g. bahcall , ostriker , perlmutter & steinhardt 1999 ) . however recent observations on smaller scales find @xmath0cdm wanting : @xmath0cdm predicts dwarf galaxy halos ( e.g. moore et al . 1999 ) that are denser and more concentrated than observed ( dalcanton & bernstein 2000 ; firmani et al . the persistence of bars in galaxies like our own , suggests that the dark matter is not centrally concentrated ( sellwood 2000 ) . in addition , the intensively studied cl0024 + 1654 is nearly spherical ( colley , tyson & turner 1996 ; tyson , kochanski & dellantonio 1998 ) , at odds with @xmath0cdm predictions of triaxial systems . spergel & steinhardt ( 2000 ) have recently suggested that these and other discrepancies ( see for example dav@xmath1 , spergel , steinhardt & wandelt 2000 ; wandelt et al . 2000 and references therein ) could be resolved if cold dark matter were weakly self interacting with a large scattering cross - section ( sidm ) . several authors ( burkert 2000 ; yoshida , springel , white & tormen 2000 ; dav@xmath1 et al . 2000 ) have since undertaken n - body simulations of halos with self interactions in the regime suggested by spergel & steinhardt ( 2000 ) . these works find that sidm halos produce flatter , smoother and more spherical cores than their @xmath0cdm counterparts . we are interested in the statistics of multiple imaging due to a generalized nfw profile ( zhao 1996 ) which may be used to describe both cdm and sidm halos . we concentrate our efforts on lensing by clusters of galaxies , since single galaxies contain a significant mass in baryons , distributed to produce a flat rotation curve . this makes sidm in galaxies difficult to probe using gravitational lensing . conversely , clusters of galaxies have a much larger mass to light ratio , and baryons which are less centrally concentrated ( particularly in the absence of a central dominant galaxy ) . we assume spherically symmetric profiles and concentrate on the statistics of the optical depth to multiple imaging . the total magnification , and the maximum image splitting are also considered . in secs . [ darkmatter ] and [ lensing ] we discuss the properties of dark matter halos and introduce the formalism for computing the lensing statistics of the zhao profile . in secs . [ results ] , [ degeneracy ] and [ implications ] we discuss the statistics obtained , contrast the parameter degeneracies present in the lens statistics and in profile fitting , and present some implications for sidm cluster halos . in sec . [ halodist ] we discuss the important implications for lens statistics of the distribution of halo profile - parameters . we also discuss two potentially important caveats which turn out not to effect our conclusions : we discuss magnification bias ( sec . [ amp_dist_bias ] ) , and give a preliminary account of the effect of massive central galaxies on the multiple imaging rate ( sec . [ galaxies ] ) . throughout the paper we have assumed a standard @xmath2 , @xmath3 and @xmath4 filled beam cosmology .

a generalized form of the navarro , frenk and white profile ( zhao profile ) may be used to describe these halos . in this paper we examine gravitational lensing statistics for this class of model . we find that lensing statistics based on profile parameters obtained from fits out to the virial radius are dependent on the minimization scheme adopted , and may be seriously in error .

strong lensing is a powerful probe of the distribution of matter in the cores of clusters of galaxies . recent studies suggest that the cold dark matter model predicts cores that are denser than those observed in galaxies , groups and clusters . one possible resolution of the discrepancy is that the dark matter has strong interactions ( sidm ) , which leads to lower central densities . a generalized form of the navarro , frenk and white profile ( zhao profile ) may be used to describe these halos . in this paper we examine gravitational lensing statistics for this class of model . the optical depth to multiple imaging is a very sensitive function of the profile parameters in the range of interest for sidm halos around clusters of galaxies . less concentrated profiles , which result from larger self - interaction cross - sections , can produce many fewer lensed pairs . furthermore , profiles that result in a small optical depth exhibit reduced typical splittings , but produce multiple images that are more highly magnified . however the resulting increased magnification bias does not alter our conclusions . we find that lensing statistics based on profile parameters obtained from fits out to the virial radius are dependent on the minimization scheme adopted , and may be seriously in error . however , profile fits weighted towards the core region have parameter degeneracies that are approximately equivalent to those for strong lensing cross - sections . lensing statistics provide a powerful test for sidm . more realistic and observationally oriented calculations remain to be done , however larger self - interaction cross - sections may well be ruled out by the very existence of strong lenses on galaxy cluster scales . the inclusion of centrally dominant cluster galaxies should boost the cross - section to multiple imaging . however our preliminary calculations suggest that the additional multiple imaging rate is small with respect to the differences in multiple imaging rate for different halo profiles . in future statistical studies , it will be important to properly account for the scatter among halo profiles since the optical depth to multiple imaging is dominated by the most concentrated members of a cluster population .

astro-ph0007354

c

we have calculated the differential and total optical depths to multiple imaging , the average image splitting and the total magnification for a constant co - moving number density of unevolving generalized nfw ( zhao ) profile cluster mass gravitational lenses . we find that the number of expected strongly lensed quasars is a very sensitive function of the profile parameters . profiles whose central density is low either due to a shallow central cusp , or to a scale radius that is a reasonable fraction of the virial radius have cross - sections to multiple imaging that are reduced by a significant factor . moreover , the separation of multiple images is reduced ( by a factor of a few ) , although the total magnification is significantly enhanced . we find that the resulting magnification bias does not alter our conclusions . the zhao profile exhibits degeneracies between profile parameters with respect to lensing statistics . similarly , profile fits have parameter degeneracies which are a function of the minimization quantity adopted . if the properties of a profile core are accurately reproduced by an approximately degenerate profile , then the parameter degeneracies are nearly equivalent to those obtained from strong lensing statistics . however , a profile that attempts to fit the entire halo will introduce serious uncertainty into the inferred lensing rates ( up to an order of magnitude ) . this is particularly true in the region of parameter space where both @xmath23 and @xmath22 are small and will be an important consideration for detailed calculations of the lensing rate for sidm halos based on parametric results from n - body simulations . the lensing rate is a powerful probe of sidm in clusters of galaxies , particularly in the absence of a centrally dominant galaxy . we have obtained profile parameters for halos around clusters of galaxies by fitting zhao profiles to the simulations of yoshida , springel , white & tormen ( 2000 ) . we find that the optical depth to multiple imaging seriously constrains the sidm self - interaction cross - section . in particular , an interaction cross - section of @xmath178 is rarely capable of producing multiple images during its evolution . in the most highly concentrated phases , a halo composed of interacting dark matter with this cross - section has a rate of multiple imaging 1 to 2 orders of magnitude lower than the corresponding typical cdm halo . preliminary calculations show that centrally dominant galaxies increase the multiple imaging cross - section , but that the increase is small with respect to the variation in cross - section among different profiles . the presence of centrally dominant galaxies should not therefore inhibit the use of the multiple imaging rate as a probe of sidm . an important result from this study , with implications for cluster lensing studies is that the scatter in cdm / sidm profile parameters obtained from n - body studies describe a very large range of optical depth . the lensing statistics will therefore be dominated by the more concentrated members of the population , rather than by the typical halo . as a result , an estimate of the distribution of halo profiles must be included in future studies of cluster lensing statistics . the authors would like to thank romeel dav@xmath1 , bartosz pindor and daniel mortlock for helpful and stimulating discussions . we would also like to thank the anonymous referee whose comments led to the improvement of this work . this research was supported by nsf grant ast98 - 02802 to elt . jsbw acknowledges the support of an australian postgraduate award and a melbourne university overseas research experience award . avila - reese , v. , firmani , c. , donghia , e. , hernandez , x. , 2000 , in `` the seventh texas - mexico conference on astrophysics : flows , blows , and glows '' ( april 2000 ) , eds . w. lee & s. torres - peimbert , revmexaa ( serie deconferencias ) cccccccccccccc & & & & & & & + & & & & & & & + & & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 + & 0.5&&0.000&0.008&0.174&&na & 26.52&46.64&&na & 75.41&18.46 + @xmath22&1.0&&0.001&0.199&0.918&&11.56&43.06&57.13&&100.1&16.11&8.105 + & 1.5&&0.226&1.715&4.263&&34.91&57.79&68.71&&12.33&5.732&3.861 + cccccccccccccc & & & & & & & + & & & & & & & + & & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 + & 0.5&&na & 5.53 & 2.50 & & na & 35.57&7.35 & & na & 282.1&27.45 + @xmath22&1.0&&6.27 & 2.53 & 1.89 & & 45.32&7.50 & 4.13 & & 398.1&27.91&11.18 + & 1.5&&2.32 & 1.68 & 1.45 & & 6.24 & 3.22 & 2.38 & & 20.50&7.54 & 4.62 + cccccccccccccc & & & & & & & + & & & & & & & + & & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 + & 0.5&&na & 3.76 & 1.70 & & na & 13.34&2.76 & & na & 49.51&4.82 + @xmath22&1.0&&4.27 & 1.73 & 1.29 & & 16.99&2.81 & 1.55 & & 69.88&4.90 & 1.96 + & 1.5&&1.57 & 1.15 & 0.99 & & 2.34 & 1.20 & 0.89 & & 3.60 & 1.32 & 0.81 + cccccccccccccc & & & & & & & + & & & & & & & + & & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 + & 0.5&&na & 4.94 & 2.35 & & na & 29.23&6.55 & & na & 227.5&24.00 + @xmath22&1.0&&5.94 & 2.36 & 1.56 & & 41.98&6.59 & 2.97 & & 364.7&24.12&7.90 + & 1.5&&1.96 & 2.22 & 0.91 & & 4.61 & 1.87 & 1.10 & & 14.76&4.25 & 2.13 + cccccccccccccc & & & & & & & + & & & & & & & + & & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 + & 0.5&&na & 6.73 & 3.20 & & na & 30.90&6.93 & & na & 101.7&10.74 + @xmath22&1.0&&8.10 & 3.21 & 2.13 & & 43.84&6.96 & 3.14 & & 163.1&10.79&3.53 + & 1.5&&2.67 & 1.66 & 1.24 & & 4.88 & 1.98 & 1.16 & & 6.60 & 1.90 & 0.95 + cccccccccccccc & & & & & & & + & & & & & & & + & & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 + & 0.5&&0.000&0.030&0.296&&0.000&0.107&0.480&&0.000&0.396&0.839 + @xmath22&1.0&&0.004&0.344&1.184&&0.017&0.559&1.423&&0.070&0.975&1.799 + & 1.5&&0.355&1.972&4.220&&0.529&2.058&3.794&&0.814&2.264&3.453 + cccccccccccccc & & & & & & & + & & & & & & & + & & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 + & 0.5&&0.000&0.054&0.557&&0.000&0.247&1.206&&0.000&0.814&1.869 + @xmath22&1.0&&0.008&0.639&1.955&&0.044&1.385&2.883&&0.163&2.147&3.240 + & 1.5&&0.603&2.847&5.286&&1.103&3.396&4.945&&1.492&3.259&4.050 + cccccccccc & & & & & + & & & & & + & & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 + & 0.5&&0.008&0.026&0.233&&0.008&0.015&0.188 + @xmath22&1.0&&0.014&0.266&1.054&&0.010&0.217&0.952 + & 1.5&&0.306&1.916&4.581&&0.257&1.778&4.364 + cccccccccc & & & & & + & & & & & + & & & 5.0 & 12.5 & 20.0 & & 5.0 & 12.5 & 20.0 + & 0.5 & & na&3.250&1.339 & & na&1.875&1.080 + @xmath22&1.0&&14.00&1.337&1.148&&10.00&1.090&1.037 + & 1.5&&1.354&1.117&1.075&&1.137&1.037&1.024 +

strong lensing is a powerful probe of the distribution of matter in the cores of clusters of galaxies . however the resulting increased magnification bias does not alter our conclusions . however our preliminary calculations suggest that the additional multiple imaging rate is small with respect to the differences in multiple imaging rate for different halo profiles . in future statistical studies

strong lensing is a powerful probe of the distribution of matter in the cores of clusters of galaxies . recent studies suggest that the cold dark matter model predicts cores that are denser than those observed in galaxies , groups and clusters . one possible resolution of the discrepancy is that the dark matter has strong interactions ( sidm ) , which leads to lower central densities . a generalized form of the navarro , frenk and white profile ( zhao profile ) may be used to describe these halos . in this paper we examine gravitational lensing statistics for this class of model . the optical depth to multiple imaging is a very sensitive function of the profile parameters in the range of interest for sidm halos around clusters of galaxies . less concentrated profiles , which result from larger self - interaction cross - sections , can produce many fewer lensed pairs . furthermore , profiles that result in a small optical depth exhibit reduced typical splittings , but produce multiple images that are more highly magnified . however the resulting increased magnification bias does not alter our conclusions . we find that lensing statistics based on profile parameters obtained from fits out to the virial radius are dependent on the minimization scheme adopted , and may be seriously in error . however , profile fits weighted towards the core region have parameter degeneracies that are approximately equivalent to those for strong lensing cross - sections . lensing statistics provide a powerful test for sidm . more realistic and observationally oriented calculations remain to be done , however larger self - interaction cross - sections may well be ruled out by the very existence of strong lenses on galaxy cluster scales . the inclusion of centrally dominant cluster galaxies should boost the cross - section to multiple imaging . however our preliminary calculations suggest that the additional multiple imaging rate is small with respect to the differences in multiple imaging rate for different halo profiles . in future statistical studies , it will be important to properly account for the scatter among halo profiles since the optical depth to multiple imaging is dominated by the most concentrated members of a cluster population .

1111.4959

i

a. b. migdal s contribution to modern theoretical physics is very impressive . his endowment in and deep understanding of different domains of physics , including the nuclear and many - body physics , based on fermi - liquid approach , is outstanding . in migdal seminal papers a solid base for studying strongly interacting fermi systems and phase transitions occurring in them has been established @xcite . migdal s daring ideas of phase transitions related to @xmath0 condensation in nuclei and neutron stars @xcite inspired a theory of fermion condensation that has permitted to construct a new class of fermi liquids , new quasiparticles and new type of merging of single - particle levels of both finite and infinite fermi systems like nuclear , atomic and solid state systems @xcite . the new class of fermi liquids is represented by strongly correlated fermi systems where enormous number of experimental facts are collected . understanding the physics of these systems stimulates intensive studies of the possible manifestation of fermion condensation in other areas , as it has happened in the case of metal superconductivity , whose ideas were successfully used in describing atomic nuclei @xcite and in a possible explanation of the origin of the mass of elementary particles . therefore , we expect that the ideas associated with the new fermion condensation quantum phase transition @xcite in one area of research stimulates intensive studies of the possible manifestation of such a transition in other areas . strongly correlated fermi systems represented by heavy fermion ( hf ) metals and quasi - two - dimensional @xmath1he are among the most intriguing , best experimentally studied and fundamental systems in physics , which until very recently have lacked theoretical explanations @xcite . these are also a field never far from applications in synthesis of novel materials for cryogenics , rare earth magnets and applied superconductivity . the properties of these materials differ dramatically from those of ordinary fermi systems @xcite . their behavior is so unusual that the traditional landau quasiparticles paradigm does not apply to it . the paradigm states that the properties is determined by quasiparticles whose dispersion is characterized by the effective mass @xmath2 which is independent of temperature @xmath3 , the number density @xmath4 , magnetic field @xmath5 and other external parameters . the above systems are , however , in defiance of theoretical understanding . the ideas based on the concepts ( like kondo lattice involving quantum and thermal fluctuations at a quantum critical point ( qcp ) have been used to explain the unusual physics of these systems known as non - fermi liquid ( nfl ) behavior . alas , being suggested to describe one property , these approaches fail to explain the others . this means a real crisis in theory suggesting that there is a hidden fundamental law of nature , which remains to be recognized . it is widely believed that utterly new concepts are required to describe the underlying physics . there is a fundamental question : how many concepts do we need to describe the above physical mechanisms ? this can not be answered on purely experimental or theoretical grounds . rather , we have to use both of them . for instance , in the case of metals with heavy fermions , the strong correlation of electrons leads to a renormalization of the effective mass of quasiparticles , which may exceed the ordinary , `` bare '' , mass by several orders of magnitude or even become infinitely large at temperatures @xmath6 . moreover , the effective mass strongly depends on the temperature , pressure , or applied magnetic field . such metals exhibit nfl behavior and unusual power laws of the temperature dependence of the thermodynamic properties at low temperatures . the landau theory of the fermi liquid has remarkable results in describing a multitude of properties of the electron liquid in ordinary metals , fermi liquids of the @xmath1he type and nuclear liquid @xcite . the theory is based on the assumption that elementary excitations determine the physics at low temperatures . these excitations behave as quasiparticles , have a certain effective mass , and , judging by their basic properties , belong to the class of quasiparticles of a weakly interacting fermi gas . hence , the effective mass @xmath2 is independent of the temperature , pressure , and magnetic field strength and is a parameter of the theory . the landau fermi liquid ( lfl ) theory fails to explain the results of experimental observations related to the dependence of @xmath2 on the temperature @xmath3 , magnetic field @xmath5 , pressure , etc . ; this has led to the conclusion that quasiparticles do not survive in strongly correlated fermi systems and that the heavy electron does not retain its identity as a quasiparticle excitation , see e.g. @xcite . the unusual properties and nfl behavior observed in high-@xmath7 superconductors , hf metals and 2d fermi systems are assumed to be determined by various magnetic quantum phase transitions @xcite . indeed , when reasoning by analogy with respect to the second order phase transitions , one can assume that a phase transition responsible for the nfl behavior taking place up to lowest accessible temperatures is located at @xmath8 . since a quantum phase transition occurs at @xmath8 , the control parameters are the composition , electron ( hole ) number density @xmath4 , pressure , magnetic field strength @xmath5 , etc . a quantum phase transition occurs at a quantum critical point , which separates the ordered phase that emerges as a result of quantum phase transition from the disordered phase . it is usually assumed that magnetic ( e.g. , ferromagnetic and antiferromagnetic ) quantum phase transitions are responsible for the nfl behavior . the critical point of such a phase transition can be shifted to absolute zero by varying the above parameters . universal behavior can be expected only if the system under consideration is very close to a quantum critical point , e.g. , when the correlation length is much longer than the microscopic length scale , and critical quantum and thermal fluctuations determine the anomalous contribution to the thermodynamic functions of strongly correlated fermi system . quantum phase transitions of this type are so widespread @xcite that we call them ordinary quantum phase transitions @xcite . in this case , the physics of the phenomenon is determined by thermal and quantum fluctuations of the critical state , while quasiparticle excitations are destroyed by these fluctuations . conventional arguments that quasiparticles in strongly correlated fermi liquids `` get heavy and die '' at a quantum critical point commonly employ the well - known formula based on the assumptions that the @xmath9-factor ( the quasiparticle weight in the single - particle state ) vanishes at the points of second - order phase transitions @xcite . however , it has been shown that this scenario is problematic @xcite . the fluctuations in the order parameter developing an infinite correlation length and the absence of quasiparticle excitations are considered as the main reason for the nfl behavior of heavy - fermion metals , 2d fermion systems and high-@xmath7 superconductors @xcite . this approach faces certain difficulties , however . critical behavior in experiments with metals containing heavy fermions is observed at high temperatures comparable to the effective fermi temperature @xmath10 . for instance , the thermal expansion coefficient @xmath11 , which is a linear function of temperature for normal lfl , @xmath12 , demonstrates the @xmath13 temperature dependence in measurements involving ceni@xmath14ge@xmath14 as the temperature varies by two orders of magnitude ( as it decreases from 6 k to at least 50 mk ) @xcite . such behavior can hardly be explained within the framework of the critical point fluctuation theory . obviously , such a situation is possible only as @xmath6 , when the critical fluctuations make the leading contribution to the entropy and when the correlation length is much longer than the microscopic length scale . at a certain temperature @xmath10 , this macroscopically large correlation length must be destroyed by ordinary thermal fluctuations and the corresponding universal behavior must disappear . in the rest of this paper , we show that the fermion condensation quantum phase transition ( fcqpt ) @xcite is indeed responsible for the observed fascinating nfl behavior of strongly correlated fermi systems and quasiparticles survive both high temperatures and high magnetic fields . in section [ ehq ] , we give a detailed consideration of experimental evidences in favor of existence of quasiparticles , and formulate both a scaling behavior of strongly correlated fermi systems and the extended quasiparticle paradigm . then in section [ flfc1 ] , we consider the properties of landau fermi liquid . in section [ pom_m ] we demonstrate that the landau equation for the effective is not a phenomenological one and can be derived using the methods of density functional theory . thus , we establish the extended quasiparticle paradigm . fcqpt and a phase diagram of heavy fermion system located in the vicinity of fcqpt are investigated in section [ flfc ] . we propose that the phase diagram of systems located near fcqpt are strongly influenced by control parameters such as a chemical pressure , pressure or magnetic field . we find that under the application of the chemical pressure ( positive / negative ) qcp is destroyed or converted into a quantum critical line , correspondingly . in section [ hmf ] we establish that heavy fermion quasiparticles do exist in a very wide range of both temperatures @xmath3 and magnetic fields @xmath5 . finally , in section [ sum ] our results are summarized and discussed .

strongly correlated fermi systems are among the most intriguing , best experimentally studied and fundamental systems in physics . there is , however , lack of theoretical understanding in this field of physics . the ideas based on the concepts like kondo lattice and involving quantum and thermal fluctuations at a quantum critical point have been used to explain the unusual physics . alas , being suggested to describe one property , these approaches fail to explain the others . this means a real crisis in theory suggesting that there is a hidden fundamental law of nature . migdal quasiparticles , while the basic properties and the scaling behavior of the strongly correlated systems can be described within the framework of the fermion condensation quantum phase transition ( fcqpt ) .

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