829 research outputs found
Remarks on NonHamiltonian Statistical Mechanics: Lyapunov Exponents and Phase-Space Dimensionality Loss
The dissipation associated with nonequilibrium flow processes is reflected by
the formation of strange attractor distributions in phase space. The
information dimension of these attractors is less than that of the equilibrium
phase space, corresponding to the extreme rarity of nonequilibrium states. Here
we take advantage of a simple model for heat conduction to demonstrate that the
nonequilibrium dimensionality loss can definitely exceed the number of
phase-space dimensions required to thermostat an otherwise Hamiltonian system.Comment: 5 pages, 2 figures, minor typos correcte
Harmonic oscillators in the Nos\'e - Hoover thermostat
We study the dynamics of an ensemble of non-interacting harmonic oscillators
in a nonlinear dissipative environment described by the Nos\'e - Hoover model.
Using numerical simulation we find the histogram for total energy, which agrees
with the analysis of the Nos\'e - Hoover equations effected with the method of
averaging. The histogram does not correspond to Gibbs' canonical distribution.
We have found oscillations at frequency proportional to ,
the dissipative parameter of thermostat and the characteristic
mass of particle, about the stationary state corresponding to equilibrium. The
oscillations could have an important bearing upon the analysis of simulating
molecular dynamics in the Nos\'e - Hoover thermostat.Comment: 7 pages, 4 figure
Soft disks in a narrow channel
The pressure components of "soft" disks in a two dimensional narrow channel
are analyzed in the dilute gas regime using the Mayer cluster expansion and
molecular dynamics. Channels with either periodic or reflecting boundaries are
considered. It is found that when the two-body potential, u(r), is singular at
some distance r_0, the dependence of the pressure components on the channel
width exhibits a singularity at one or more channel widths which are simply
related to r_0. In channels with periodic boundary conditions and for
potentials which are discontinuous at r_0, the transverse and longitudinal
pressure components exhibit a 1/2 and 3/2 singularity, respectively. Continuous
potentials with a power law singularity result in weaker singularities of the
pressure components. In channels with reflecting boundary conditions the
singularities are found to be weaker than those corresponding to periodic
boundaries
Anomalous diffusion as a signature of collapsing phase in two dimensional self-gravitating systems
A two dimensional self-gravitating Hamiltonian model made by
fully-coupled classical particles exhibits a transition from a collapsing phase
(CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical
point of view, the two phases are characterized by two distinct single-particle
motions : namely, superdiffusive in the CP and ballistic in the HP. Anomalous
diffusion is observed up to a time that increases linearly with .
Therefore, the finite particle number acts like a white noise source for the
system, inhibiting anomalous transport at longer times.Comment: 10 pages, Revtex - 3 Figs - Submitted to Physical Review
Lyapunov instability for a periodic Lorentz gas thermostated by deterministic scattering
In recent work a deterministic and time-reversible boundary thermostat called
thermostating by deterministic scattering has been introduced for the periodic
Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the
nonlinear properties of this new dynamical system by numerically calculating
its Lyapunov exponents. Based on a revised method for computing Lyapunov
exponents, which employs periodic orthonormalization with a constraint, we
present results for the Lyapunov exponents and related quantities in
equilibrium and nonequilibrium. Finally, we check whether we obtain the same
relations between quantities characterizing the microscopic chaotic dynamics
and quantities characterizing macroscopic transport as obtained for
conventional deterministic and time-reversible bulk thermostats.Comment: 18 pages (revtex), 7 figures (postscript
The modalities of Iranian soft power: from cultural diplomacy to soft war
Through exploring Iran's public diplomacy at the international level, this article demonstrates how the Islamic Republic's motives should not only be contextualised within the oft-sensationalised, material or âhardâ aspects of its foreign policy, but also within the desire to project its cultural reach through âsofterâ means. Iran's utilisation of culturally defined foreign policy objectives and actions demonstrates its understanding of soft power's potentialities. This article explores the ways in which Iran's public diplomacy is used to promote its soft power and craft its, at times, shifting image on the world stage
Effect of angular momentum on equilibrium properties of a self-gravitating system
The microcanonical properties of a two dimensional system of N classical
particles interacting via a smoothed Newtonian potential as a function of the
total energy E and the total angular momentum L are discussed. In order to
estimate suitable observables a numerical method based on an importance
sampling algorithm is presented. The entropy surface shows a negative specific
heat region at fixed L for all L. Observables probing the average mass
distribution are used to understand the link between thermostatistical
properties and the spatial distribution of particles. In order to define a
phase in non-extensive system we introduce a more general observable than the
one proposed by Gross and Votyakov [Eur. Phys. J. B:15, 115 (2000)]: the sign
of the largest eigenvalue of the entropy surface curvature. At large E the
gravitational system is in a homogeneous gas phase. At low E there are several
collapse phases; at L=0 there is a single cluster phase and for L>0 there are
several phases with 2 clusters. All these pure phases are separated by first
order phase transition regions. The signal of critical behaviour emerges at
different points of the parameter space (E,L). We also discuss the ensemble
introduced in a recent pre-print by Klinko & Miller; this ensemble is the
canonical analogue of the one at constant energy and constant angular momentum.
We show that a huge loss of informations appears if we treat the system as a
function of intensive parameters: besides the known non-equivalence at first
order phase transitions, there exit in the microcanonical ensemble some values
of the temperature and the angular velocity for which the corresponding
canonical ensemble does not exist, i.e. the partition sum diverges.Comment: 17 pages, 11 figures, submitted to Phys. Rev.
Critical evaluation of platelet size as a prognostic biomarker in colorectal cancer across multiple treatment settings: a retrospective cohort study
A vortex description of the first-order phase transition in type-I superconductors
Using both analytical arguments and detailed numerical evidence we show that
the first order transition in the type-I 2D Abelian Higgs model can be
understood in terms of the statistical mechanics of vortices, which behave in
this regime as an ensemble of attractive particles. The well-known
instabilities of such ensembles are shown to be connected to the process of
phase nucleation. By characterizing the equation of state for the vortex
ensemble we show that the temperature for the onset of a clustering instability
is in qualitative agreement with the critical temperature. Below this point the
vortex ensemble collapses to a single cluster, which is a non-extensive phase,
and disappears in the absence of net topological charge. The vortex description
provides a detailed mechanism for the first order transition, which applies at
arbitrarily weak type-I and is gauge invariant unlike the usual field-theoretic
considerations, which rely on asymptotically large gauge coupling.Comment: 4 pages, 6 figures, uses RevTex. Additional references added, some
small corrections to the tex
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