294 research outputs found
Spinodal Decomposition in Binary Gases
We carried out three-dimensional simulations, with about 1.4 million
particles, of phase segregation in a low density binary fluid mixture,
described mesoscopically by energy and momentum conserving Boltzmann-Vlasov
equations. Using a combination of Direct Simulation Monte Carlo(DSMC) for the
short range collisions and a version of Particle-In-Cell(PIC) evolution for the
smooth long range interaction, we found dynamical scaling after the ratio of
the interface thickness(whose shape is described approximately by a hyperbolic
tangent profile) to the domain size is less than ~0.1. The scaling length R(t)
grows at late times like t^alpha, with alpha=1 for critical quenches and
alpha=1/3 for off-critical ones. We also measured the variation of temperature,
total particle density and hydrodynamic velocity during the segregation
process.Comment: 11 pages, Revtex, 4 Postscript figures, submitted to PR
Slow Relaxation and Phase Space Properties of a Conservative System with Many Degrees of Freedom
We study the one-dimensional discrete model. We compare two
equilibrium properties by use of molecular dynamics simulations: the Lyapunov
spectrum and the time dependence of local correlation functions. Both
properties imply the existence of a dynamical crossover of the system at the
same temperature. This correlation holds for two rather different regimes of
the system - the displacive and intermediate coupling regimes. Our results
imply a deep connection between slowing down of relaxations and phase space
properties of complex systems.Comment: 14 pages, LaTeX, 10 Figures available upon request (SF), Phys. Rev.
E, accepted for publicatio
Clusters and Fluctuations at Mean-Field Critical Points and Spinodals
We show that the structure of the fluctuations close to spinodals and
mean-field critical points is qualitatively different than the structure close
to non-mean-field critical points. This difference has important implications
for many areas including the formation of glasses in supercooled liquids. In
particular, the divergence of the measured static structure function in
near-mean-field systems close to the glass transition is suppressed relative to
the mean-field prediction in systems for which a spatial symmetry is broken.Comment: 5 pages, 1 figur
Model for Glass Transition in a Binary fluid from a Mode Coupling approach
We consider the Mode Coupling Theory (MCT) of Glass transition for a Binary
fluid. The Equations of Nonlinear Fluctuating Hydrodynamics are obtained with a
proper choice of the slow variables corresponding to the conservation laws. The
resulting model equations are solved in the long time limit to locate the
dynamic transition. The transition point from our model is considerably higher
than predicted in existing MCT models for binary systems. This is in agreement
with what is seen in Computer Simulation of binary fluids. fluids.Comment: 9 Pages, 3 Figure
An Alternative Interpretation of Statistical Mechanics
In this paper I propose an interpretation of classical statistical mechanics that centers on taking seriously the idea that probability measures represent complete states of statistical mechanical systems. I show how this leads naturally to the idea that the stochasticity of statistical mechanics is associated directly with the observables of the theory rather than with the microstates (as traditional accounts would have it). The usual assumption that microstates are representationally significant in the theory is therefore dispensable, a consequence which suggests interesting possibilities for developing non-equilibrium statistical mechanics and investigating inter-theoretic answers to the foundational questions of statistical mechanics
Asymptotic laws for tagged-particle motion in glassy systems
Within the mode-coupling theory for structural relaxation in simple systems
the asymptotic laws and their leading-asymptotic correction formulas are
derived for the motion of a tagged particle near a glass-transition
singularity. These analytic results are compared with numerical ones of the
equations of motion evaluated for a tagged hard sphere moving in a hard-sphere
system. It is found that the long-time part of the two-step relaxation process
for the mean-squared displacement can be characterized by the -relaxation-scaling law and von Schweidler's power-law decay while the
critical-decay regime is dominated by the corrections to the leading power-law
behavior. For parameters of interest for the interpretations of experimental
data, the corrections to the leading asymptotic laws for the non-Gaussian
parameter are found to be so large that the leading asymptotic results are
altered qualitatively by the corrections. Results for the non-Gaussian
parameter are shown to follow qualitatively the findings reported in the
molecular-dynamics-simulations work by Kob and Andersen [Phys. Rev. E 51, 4626
(1995)]
Generalized entropy and temperature in nuclear multifragmentation
In the framework of a 2D Vlasov model, we study the time evolution of the
"coarse-grained" Generalized Entropy (GE) in a nuclear system which undergoes a
multifragmentation (MF) phase transition. We investigate the GE both for the
gas and the fragments (surface and bulk part respectively). We find that the
formation of the surface causes the growth of the GE during the process of
fragmentation. This quantity then characterizes the MF and confirms the crucial
role of deterministic chaos in filling the new available phase-space: at
variance with the exact time evolution, no entropy change is found when the
linear response is applied. Numerical simulations were used also to extract
information about final temperatures of the fragments. From a fitting of the
momentum distribution with a Fermi-Dirac function we extract the temperature of
the fragments at the end of the process. We calculate also the gas temperature
by averaging over the available phase space. The latter is a few times larger
than the former, indicating a gas not in equilibrium. Though the model is very
schematic, this fact seems to be very general and could explain the discrepancy
found in experimental data when using the slope of light particles spectra
instead of the double ratio of isotope yields method in order to extract the
nuclear caloric curve.Comment: 26 pages, 9 postscript figures included, Revtex, some figures and
part of text changed, version accepted for publication in PR
Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations
We reconsider the conceptual foundations of the renormalization-group (RG)
formalism, and prove some rigorous theorems on the regularity properties and
possible pathologies of the RG map. Regarding regularity, we show that the RG
map, defined on a suitable space of interactions (= formal Hamiltonians), is
always single-valued and Lipschitz continuous on its domain of definition. This
rules out a recently proposed scenario for the RG description of first-order
phase transitions. On the pathological side, we make rigorous some arguments of
Griffiths, Pearce and Israel, and prove in several cases that the renormalized
measure is not a Gibbs measure for any reasonable interaction. This means that
the RG map is ill-defined, and that the conventional RG description of
first-order phase transitions is not universally valid. For decimation or
Kadanoff transformations applied to the Ising model in dimension ,
these pathologies occur in a full neighborhood of the low-temperature part of the first-order
phase-transition surface. For block-averaging transformations applied to the
Ising model in dimension , the pathologies occur at low temperatures
for arbitrary magnetic-field strength. Pathologies may also occur in the
critical region for Ising models in dimension . We discuss in detail
the distinction between Gibbsian and non-Gibbsian measures, and give a rather
complete catalogue of the known examples. Finally, we discuss the heuristic and
numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also
ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.
Dynamics and transport near quantum-critical points
The physics of non-zero temperature dynamics and transport near
quantum-critical points is discussed by a detailed study of the O(N)-symmetric,
relativistic, quantum field theory of a N-component scalar field in spatial
dimensions. A great deal of insight is gained from a simple, exact solution of
the long-time dynamics for the N=1 d=1 case: this model describes the critical
point of the Ising chain in a transverse field, and the dynamics in all the
distinct, limiting, physical regions of its finite temperature phase diagram is
obtained. The N=3, d=1 model describes insulating, gapped, spin chain
compounds: the exact, low temperature value of the spin diffusivity is
computed, and compared with NMR experiments. The N=3, d=2,3 models describe
Heisenberg antiferromagnets with collinear N\'{e}el correlations, and
experimental realizations of quantum-critical behavior in these systems are
discussed. Finally, the N=2, d=2 model describes the superfluid-insulator
transition in lattice boson systems: the frequency and temperature dependence
of the the conductivity at the quantum-critical coupling is described and
implications for experiments in two-dimensional thin films and inversion layers
are noted.Comment: Lectures presented at the NATO Advanced Study Institute on "Dynamical
properties of unconventional magnetic systems", Geilo, Norway, April 2-12,
1997, edited by A. Skjeltorp and D. Sherrington, Kluwer Academic, to be
published. 46 page
Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions
We evaluate the virial coefficients B_k for k<=10 for hard spheres in
dimensions D=2,...,8. Virial coefficients with k even are found to be negative
when D>=5. This provides strong evidence that the leading singularity for the
virial series lies away from the positive real axis when D>=5. Further analysis
provides evidence that negative virial coefficients will be seen for some k>10
for D=4, and there is a distinct possibility that negative virial coefficients
will also eventually occur for D=3.Comment: 33 pages, 12 figure
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