17,044 research outputs found
Numerical Determination of the Distribution of Energies for the XY-model
We compute numerically the distribution of energies W(E,N) for the XY-model
with short-range and long-range interactions. We find that in both cases the
distribution can be fitted to the functional form: W(E,N) ~ exp(N f(E,N)), with
f(E,N) an intensive function of the energy.Comment: 4 pages, 1 figure. Submitted to Physica
Weakly Nonextensive Thermostatistics and the Ising Model with Long--range Interactions
We introduce a nonextensive entropic measure that grows like
, where is the size of the system under consideration. This kind
of nonextensivity arises in a natural way in some -body systems endowed with
long-range interactions described by interparticle potentials.
The power law (weakly nonextensive) behavior exhibited by is
intermediate between (1) the linear (extensive) regime characterizing the
standard Boltzmann-Gibbs entropy and the (2) the exponential law (strongly
nonextensive) behavior associated with the Tsallis generalized -entropies.
The functional is parametrized by the real number
in such a way that the standard logarithmic entropy is recovered when
>. We study the mathematical properties of the new entropy, showing that the
basic requirements for a well behaved entropy functional are verified, i.e.,
possesses the usual properties of positivity, equiprobability,
concavity and irreversibility and verifies Khinchin axioms except the one
related to additivity since is nonextensive. For , the
entropy becomes superadditive in the thermodynamic limit. The
present formalism is illustrated by a numerical study of the thermodynamic
scaling laws of a ferromagnetic Ising model with long-range interactions.Comment: LaTeX file, 20 pages, 7 figure
From particle segregation to the granular clock
Recently several authors studied the segregation of particles for a system
composed of mono-dispersed inelastic spheres contained in a box divided by a
wall in the middle. The system exhibited a symmetry breaking leading to an
overpopulation of particles in one side of the box. Here we study the
segregation of a mixture of particles composed of inelastic hard spheres and
fluidized by a vibrating wall. Our numerical simulations show a rich
phenomenology: horizontal segregation and periodic behavior. We also propose an
empirical system of ODEs representing the proportion of each type of particles
and the segregation flux of particles. These equations reproduce the major
features observed by the simulations.Comment: 10 page
Thermostatistics of extensive and non-extensive systems using generalized entropies
We describe in detail two numerical simulation methods valid to study systems
whose thermostatistics is described by generalized entropies, such as Tsallis.
The methods are useful for applications to non-trivial interacting systems with
a large number of degrees of freedom, and both short-range and long-range
interactions. The first method is quite general and it is based on the
numerical evaluation of the density of states with a given energy. The second
method is more specific for Tsallis thermostatistics and it is based on a
standard Monte Carlo Metropolis algorithm along with a numerical integration
procedure. We show here that both methods are robust and efficient. We present
results of the application of the methods to the one-dimensional Ising model
both in a short-range case and in a long-range (non-extensive) case. We show
that the thermodynamic potentials for different values of the system size N and
different values of the non-extensivity parameter q can be described by scaling
relations which are an extension of the ones holding for the Boltzmann-Gibbs
statistics (q=1). Finally, we discuss the differences in using standard or
non-standard mean value definitions in the Tsallis thermostatistics formalism
and present a microcanonical ensemble calculation approach of the averages.Comment: Submitted to Physica A. LaTeX format, 38 pages, 17 EPS figures.
IMEDEA-UIB, 07071 Palma de Mallorca, Spain, http://www.imedea.uib.e
Indices of the iterates of -homeomorphisms at Lyapunov stable fixed points
Given any positive sequence (\{c_n\}_{n \in {\Bbb N}}), we construct
orientation preserving homeomorphisms (f:{\Bbb R}^3 \to {\Bbb R}^3) such that
(Fix(f)=Per(f)=\{0\}), (0) is Lyapunov stable and (\limsup \frac{|i(f^m,
0)|}{c_m}= \infty). We will use our results to discuss and to point out some
strong differences with respect to the computation and behavior of the
sequences of the indices of planar homeomorphisms.Comment: 19 pages, 8 figure
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