On anomalous diffusion in a plasma in velocity space

The problem of anomalous diffusion in momentum space is considered for plasma-like systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in momentum space. The generalized Fokker-Planck equation for description of diffusion (in momentum space) of particles (ions, grains etc.) in a stochastic system of light particles (electrons, or electrons and ions, respectively) is applied to the evolution of the momentum particle distribution in a plasma. In a plasma the developed approach is also applicable to the diffusion of particles with an arbitrary mass relation, due to the small characteristic momentum transfer. The cases of an exponentially decreasing in momentum space (including the Boltzmann-like) kernel in the PT-function, as well as the more general kernels, which create the anomalous diffusion in velocity space due to the long tail in the PT-function, are considered. Effective friction and diffusion coefficients for plasma-like systems are found.Comment: 18 pages, no figure

Statistical Mechanics of Canonical-Dissipative Systems and Applications to Swarm Dynamics

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the take-up/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of non-equilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e. for active motion, (b) interactions between the particles based on global couplings. We derive analytical expressions for the non-equilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.Comment: 14 pages incl. 13 figures. v2: misprints in Eq. (40) corrected, ref. updated. For related work see also: http://summa.physik.hu-berlin.de/~frank/active.htm

The X-ray Luminosity Function of Nearby Rich and Poor Clusters of Galaxies: A Cosmological Probe

In this letter, we present a new determination of the local (z<0.09) X-ray luminosity function (XLF) using a large, statistical sample of 294 Abell clusters and the ROSAT All-Sky-Survey. Given our large sample size, we have reduced errors by a factor of two for L(X)(0.5-2keV)>10^43 ergs/sec. We combine our data with previous work in order to explore possible constraints imposed by the shape of the XLF on cosmological models. A set of currently viable cosmologies is used to construct theoretical XLFs assuming Lx is proportional to M^p and a sigma_8-Omega_0 constraint (from Viana & Liddle 1996) based on the local X-ray temperature function. We fit these models to our observed XLF and verify that the simplest adiabatic, analytic scaling relation (e.g. Kaiser 1986) disagrees strongly with observations. If we assume that clusters can be described by the pre-heated, constant core-entropy models of Evrard & Henry (1991) then the observed XLF is consistent only with 0.1 < Omega_0 < 0.4 if the energy per unit mass in galaxies is roughly equal to the gas energy (ie if beta=1). (abridged)Comment: 4 pages, 2 figures, accepted for publication in ApJ Letters. uses emulateapj.st

Reconstruction of a first-order phase transition from computer simulations of individual phases and subphases

We present a new method for investigating first-order phase transitions using Monte Carlo simulations. It relies on the multiple-histogram method and uses solely histograms of individual phases. In addition, we extend the method to include histograms of subphases. The free energy difference between phases, necessary for attributing the correct statistical weights to the histograms, is determined by a detour in control parameter space via auxiliary systems with short relaxation times. We apply this method to a recently introduced model for structure formation in polypeptides for which other methods fail.Comment: 13 pages in preprint mode, REVTeX, 2 Figures available from the authors ([email protected], [email protected]

The Dipole Anisotropy of the First All-Sky X-ray Cluster Sample

We combine the recently published CIZA galaxy cluster catalogue with the XBACs cluster sample to produce the first all-sky catalogue of X-ray clusters in order to examine the origins of the Local Group's peculiar velocity without the use of reconstruction methods to fill the traditional Zone of Avoidance. The advantages of this approach are (i) X-ray emitting clusters tend to trace the deepest potential wells and therefore have the greatest effect on the dynamics of the Local Group and (ii) our all-sky sample provides data for nearly a quarter of the sky that is largely incomplete in optical cluster catalogues. We find that the direction of the Local Group's peculiar velocity is well aligned with the CMB as early as the Great Attractor region 40 h^-1 Mpc away, but that the amplitude of its dipole motion is largely set between 140 and 160 h^-1 Mpc. Unlike previous studies using galaxy samples, we find that without Virgo included, roughly ~70% of our dipole signal comes from mass concentrations at large distances (>60 h^-1 Mpc) and does not flatten, indicating isotropy in the cluster distribution, until at least 160 h^-1 Mpc. We also present a detailed discussion of our dipole profile, linking observed features to the structures and superclusters that produce them. We find that most of the dipole signal can be attributed to the Shapley supercluster centered at about 150 h^-1 Mpc and a handful of very massive individual clusters, some of which are newly discovered and lie well in the Zone of Avoidance.Comment: 15 Pages, 9 Figures. Accepted by Ap

Can coarse-graining introduce long-range correlations in a symbolic sequence?

We present an exactly solvable mean-field-like theory of correlated ternary sequences which are actually systems with two independent parameters. Depending on the values of these parameters, the variance on the average number of any given symbol shows a linear or a superlinear dependence on the length of the sequence. We have shown that the available phase space of the system is made up a diffusive region surrounded by a superdiffusive region. Motivated by the fact that the diffusive portion of the phase space is larger than that for the binary, we have studied the mapping between these two. We have identified the region of the ternary phase space, particularly the diffusive part, that gets mapped into the superdiffusive regime of the binary. This exact mapping implies that long-range correlation found in a lower dimensional representative sequence may not, in general, correspond to the correlation properties of the original system.Comment: 10 pages including 1 figur

CIRS: Cluster Infall Regions in the Sloan Digital Sky Survey I. Infall Patterns and Mass Profiles

We use the Fourth Data Release of the Sloan Digital Sky Survey to test the ubiquity of infall patterns around galaxy clusters and measure cluster mass profiles to large radii. We match X-ray cluster catalogs with SDSS, search for infall patterns, and compute mass profiles for a complete sample of X-ray selected clusters. Very clean infall patterns are apparent in most of the clusters, with the fraction decreasing with increasing redshift due to shallower sampling. All 72 clusters in a well-defined sample limited by redshift (ensuring good sampling) and X-ray flux (excluding superpositions) show infall patterns sufficient to apply the caustic technique. This sample is by far the largest sample of cluster mass profiles extending to large radii to date. Similar to CAIRNS, cluster infall patterns are better defined in observations than in simulations. Further work is needed to determine the source of this difference. We use the infall patterns to compute mass profiles for 72 clusters and compare them to model profiles. Cluster scaling relations using caustic masses agree well with those using X-ray or virial mass estimates, confirming the reliability of the caustic technique. We confirm the conclusion of CAIRNS that cluster infall regions are well fit by NFW and Hernquist profiles and poorly fit by singular isothermal spheres. This much larger sample enables new comparisons of cluster properties with those in simulations. The shapes (specifically, NFW concentrations) of the mass profiles agree well with the predictions of simulations. The mass inside the turnaround radius is on average 2.19$\pm$0.18 times that within the virial radius. This ratio agrees well with recent predictions from simulations of the final masses of dark matter haloes.Comment: 34 pages, 24 figures, accepted for publication in AJ, full resolution version available at http://www.astro.yale.edu/krines

A Radio Survey of Seven Southern X-ray Luminous Clusters of Galaxies

The Australia Telescope Compact Array (ATCA) has been used at 1.38 and 2.38 GHz to survey seven southern Abell clusters of galaxies with high X-ray luminosities: A2746, A2837, A3126, A3216, A3230, A3827 and A3836. The clusters have also been surveyed at 0.843 GHz with the Molonglo Observatory Synthesis Telescope (MOST). We have listed a complete 1.38-GHz sample of 149 radio sources within the Abell circles centred on their X-ray centroids. We compare their identification fractions, emitted 1.38-GHz and optical powers, radio spectral indices and radial variation in projected source density with those of the radio-selected samples of Slee et al. (1998). We compare our fractional radio luminosity function with that of the radio-selected samples of Ledlow and Owen (1996) and Slee et al. (1998). Three significant differences are noted between X-ray and radio-selected samples of clusters; (1) the X-ray sample has an excess of flat-spectrum radio sources; (2) the fractional radio luminosity function for the FR I sources in the X-ray selected sample is much steeper, implying that fewer of their cluster galaxies become hosts for the stronger FR I radio galaxies; (3) a complete absence of FR II radio galaxies in the X-ray selected sample. The average excess projected density of radio sources near our cluster centres is approx. 5 times the background source density.Comment: 24 pages, 8 figures, plus 6 figures to be published online only; accepted to appear in MNRA

Hysteresis in the Mott Transition between Plasma and Insulating Gas

We show that hysteresis can occur in the transition between a neutral plasma and the insulating gas consisting of neutral pairs bound by Coulomb attraction. Since the transition depends sensitively on the screening length in the plasma, regions of bistability occur in density--temperature phase space. We present numerical results which indicate where these regions occur for systems such as spin-polarized hydrogen, positronium gas, and excitons in a semiconductor.Comment: 9 pages (Latex/RevTex), 6 postscript figures which are in compressed and uuencoded file, prepared using the utility "uufiles" and separately submitted. They should be automatically included with the text when it is downloaded. Figures also available in hard copy from the authors ([email protected]; [email protected]); paper submitted to Phys. Rev.

The Lensed Arc Production Efficiency of Galaxy Clusters: A Comparison of Matched Observed and Simulated Samples

We compare the statistical properties of giant gravitationally lensed arcs produced in matched simulated and observed cluster samples. The observed sample consists of 10 X-ray selected clusters at redshifts z ~ 0.2 imaged with HST by Smith et al. The simulated dataset is produced by lensing the Hubble Deep Field, which serves as a background source image, with 150 realizations (different projections and shifts) of five simulated z = 0.2 clusters from a LambdaCDM N-body simulation. The real and simulated clusters have similar masses, the real photometric redshift is used for each background source, and all the observational effects influencing arc detection in the real dataset, including light from cluster galaxies, are simulated in the artificial dataset. We develop, and apply to both datasets, an objective automatic arc-finding algorithm. We find consistent arc statistics in the real and in the simulated sample, with an average of ~ 1 detected giant (length to width ratio >= 10) arc per cluster and ~ 0.2 giant luminous (R<22.3 mag) arc per cluster. Thus, taking into account a realistic source population and observational effects, the clusters predicted by LambdaCDM have the same arc-production efficiency as the observed clusters. If, as suggested by other studies, there is a discrepancy between the predicted and the observed total number of arcs on the sky, it must be the result of differences between the redshift dependent cluster mass functions, and not due to differences in the lensing efficiency of the most massive clusters.Comment: 13 pages, Accepted by ApJ, High resolution version of the paper can be found at: ftp://wise3.tau.ac.il/pub/assafh/horesh_arcs_stat_2005.ps.gz, Arc-finding algorithm available at: http://wise-obs.tau.ac.il/~assafh/ ; A comment was added ; A missing x-axis label in Fig. 7 was adde