72,584 research outputs found
Conserved mass models with stickiness and chipping
We study a chipping model in one dimensional periodic lattice with continuous
mass, where a fixed fraction of the mass is chipped off from a site and
distributed randomly among the departure site and its neighbours; the remaining
mass sticks to the site. In the asymmetric version, the chipped off mass is
distributed among the site and the right neighbour, whereas in the symmetric
version the redistribution occurs among the two neighbours. The steady state
mass distribution of the model is obtained using a perturbation method for both
parallel and random sequential updates. In most cases, this perturbation theory
provides a steady state distribution with reasonable accuracy.Comment: 17 pages, 4 eps figure
Phase Transition in the ABC Model
Recent studies have shown that one-dimensional driven systems can exhibit
phase separation even if the dynamics is governed by local rules. The ABC
model, which comprises three particle species that diffuse asymmetrically
around a ring, shows anomalous coarsening into a phase separated steady state.
In the limiting case in which the dynamics is symmetric and the parameter
describing the asymmetry tends to one, no phase separation occurs and the
steady state of the system is disordered. In the present work we consider the
weak asymmetry regime where is the system size and
study how the disordered state is approached. In the case of equal densities,
we find that the system exhibits a second order phase transition at some
nonzero .
The value of and the optimal profiles can be
obtained by writing the exact large deviation functional. For nonequal
densities, we write down mean field equations and analyze some of their
predictions.Comment: 18 pages, 3 figure
Effects of Confinement on Critical Adsorption: Absence of Critical Depletion for Fluids in Slit Pores
The adsorption of a near-critical fluid confined in a slit pore is
investigated by means of density functional theory and by Monte Carlo
simulation for a Lennard-Jones fluid. Our work was stimulated by recent
experiments for SF_6 adsorbed in a mesoporous glass which showed the striking
phenomenon of critical depletion, i.e. the adsorption excess "Gamma" first
increases but then decreases very rapidly to negative values as the bulk
critical temperature T_c is approached from above along near-critical
isochores. By contrast, our density functional and simulation results, for a
range of strongly attractive wall-fluid potentials, show Gamma monotonically
increasing and eventually saturating as the temperature is lowered towards T_c
along both the critical (rho=rho_c) and sub-critical isochores (rho<\rho_c).
Such behaviour results from the increasingly slow decay of the density profile
away from the walls, into the middle of the slit, as T->T_c. For rho < rho_c we
find that in the fluid the effective bulk field, which is negative and which
favours desorption, is insufficient to dominate the effects of the surface
fields which favour adsorption. We compare this situation with earlier results
for the lattice gas model with a constant (negative) bulk field where critical
depletion was found. Qualitatively different behaviour of the density profiles
and adsorption is found in simulations for intermediate and weakly attractive
wall-fluid potentials but in no case do we observe the critical depletion found
in experiments. We conclude that the latter cannot be accounted for by a single
pore model.Comment: 21 pages Revtex. Submitted to Phys. Rev.
Pair-factorized steady states on arbitrary graphs
Stochastic mass transport models are usually described by specifying hopping
rates of particles between sites of a given lattice, and the goal is to predict
the existence and properties of the steady state. Here we ask the reverse
question: given a stationary state that factorizes over links (pairs of sites)
of an arbitrary connected graph, what are possible hopping rates that converge
to this state? We define a class of hopping functions which lead to the same
steady state and guarantee current conservation but may differ by the induced
current strength. For the special case of anisotropic hopping in two dimensions
we discuss some aspects of the phase structure. We also show how this case can
be traced back to an effective zero-range process in one dimension which is
solvable for a large class of hopping functions.Comment: IOP style, 9 pages, 1 figur
Spontaneous Symmetry Breaking in a Non-Conserving Two-Species Driven Model
A two species particle model on an open chain with dynamics which is
non-conserving in the bulk is introduced. The dynamical rules which define the
model obey a symmetry between the two species. The model exhibits a rich
behavior which includes spontaneous symmetry breaking and localized shocks. The
phase diagram in several regions of parameter space is calculated within
mean-field approximation, and compared with Monte-Carlo simulations. In the
limit where fluctuations in the number of particles in the system are taken to
zero, an exact solution is obtained. We present and analyze a physical picture
which serves to explain the different phases of the model
Symmetry breaking through a sequence of transitions in a driven diffusive system
In this work we study a two species driven diffusive system with open
boundaries that exhibits spontaneous symmetry breaking in one dimension. In a
symmetry broken state the currents of the two species are not equal, although
the dynamics is symmetric. A mean field theory predicts a sequence of two
transitions from a strongly symmetry broken state through an intermediate
symmetry broken state to a symmetric state. However, a recent numerical study
has questioned the existence of the intermediate state and instead suggested a
single discontinuous transition. In this work we present an extensive numerical
study that supports the existence of the intermediate phase but shows that this
phase and the transition to the symmetric phase are qualitatively different
from the mean-field predictions.Comment: 19 pages, 12 figure
Effects of weak surface fields on the density profiles and adsorption of a confined fluid near bulk criticality
The density profile and Gibbs adsorption of a near-critical fluid confined
between two identical planar walls is studied by means of
Monte Carlo simulation and by density functional theory for a Lennard-Jones
fluid. By reducing the strength of wall-fluid interactions relative to
fluid-fluid interactions we observe a crossover from behaviour characteristic
of the normal surface universality class, strong critical adsorption, to
behaviour characteristic of a 'neutral' wall. The crossover is reminiscent of
that which occurs near the ordinary surface transition in Ising films subject
to vanishing surface fields. For the 'neutral' wall the density profile, away
from the walls, is almost constant throughout the slit capillary and gives rise
to an adsorption that is constant along the critical isochore. The same
'neutral' wall yields a line of capillary coexistence that is almost identical
to the bulk coexistence line. In the crossover regime we observe features in
the density profile similar to those found in the magnetisation profile of the
critical Ising film subject to weak surface fields, namely two smooth maxima,
located away from the walls, which merge into a single maximum at midpoint as
the strength of the wall-fluid interaction is reduced or as the distance
between walls is decreased. We discuss similarities and differences between the
surface critical behaviour of fluids and of Ising magnets.Comment: 34 pages, 10 figures, submitted to the Journ. Chem. Phy
Condensation Transitions in Two Species Zero-Range Process
We study condensation transitions in the steady state of a zero-range process
with two species of particles. The steady state is exactly soluble -- it is
given by a factorised form provided the dynamics satisfy certain constraints --
and we exploit this to derive the phase diagram for a quite general choice of
dynamics. This phase diagram contains a variety of new mechanisms of condensate
formation, and a novel phase in which the condensate of one of the particle
species is sustained by a `weak' condensate of particles of the other species.
We also demonstrate how a single particle of one of the species (which plays
the role of a defect particle) can induce Bose-Einstein condensation above a
critical density of particles of the other species.Comment: 17 pages, 4 Postscript figure
Exact solution of the zero-range process: fundamental diagram of the corresponding exclusion process
In this paper, we propose a general way of computing expectation values in
the zero-range process, using an exact form of the partition function. As an
example, we provide the fundamental diagram (the flux-density plot) of the
asymmetric exclusion process corresponding to the zero-range process.We express
the partition function for the steady state by the Lauricella hypergeometric
function, and thereby have two exact fundamental diagrams each for the parallel
and random sequential update rules. Meanwhile, from the viewpoint of
equilibrium statistical mechanics, we work within the canonical ensemble but
the result obtained is certainly in agreement with previous works done in the
grand canonical ensemble.Comment: 12 pages, 2 figure
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