26 research outputs found
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
Jamming transition in a homogeneous one-dimensional system: the Bus Route Model
We present a driven diffusive model which we call the Bus Route Model. The
model is defined on a one-dimensional lattice, with each lattice site having
two binary variables, one of which is conserved (``buses'') and one of which is
non-conserved (``passengers''). The buses are driven in a preferred direction
and are slowed down by the presence of passengers who arrive with rate lambda.
We study the model by simulation, heuristic argument and a mean-field theory.
All these approaches provide strong evidence of a transition between an
inhomogeneous ``jammed'' phase (where the buses bunch together) and a
homogeneous phase as the bus density is increased. However, we argue that a
strict phase transition is present only in the limit lambda -> 0. For small
lambda, we argue that the transition is replaced by an abrupt crossover which
is exponentially sharp in 1/lambda. We also study the coarsening of gaps
between buses in the jammed regime. An alternative interpretation of the model
is given in which the spaces between ``buses'' and the buses themselves are
interchanged. This describes a system of particles whose mobility decreases the
longer they have been stationary and could provide a model for, say, the flow
of a gelling or sticky material along a pipe.Comment: 17 pages Revtex, 20 figures, submitted to Phys. Rev.
Cluster formation and anomalous fundamental diagram in an ant trail model
A recently proposed stochastic cellular automaton model ({\it J. Phys. A 35,
L573 (2002)}), motivated by the motions of ants in a trail, is investigated in
detail in this paper. The flux of ants in this model is sensitive to the
probability of evaporation of pheromone, and the average speed of the ants
varies non-monotonically with their density. This remarkable property is
analyzed here using phenomenological and microscopic approximations thereby
elucidating the nature of the spatio-temporal organization of the ants. We find
that the observations can be understood by the formation of loose clusters,
i.e. space regions of enhanced, but not maximal, density.Comment: 11 pages, REVTEX, with 11 embedded EPS file
Zero-range process with open boundaries
We calculate the exact stationary distribution of the one-dimensional
zero-range process with open boundaries for arbitrary bulk and boundary hopping
rates. When such a distribution exists, the steady state has no correlations
between sites and is uniquely characterized by a space-dependent fugacity which
is a function of the boundary rates and the hopping asymmetry. For strong
boundary drive the system has no stationary distribution. In systems which on a
ring geometry allow for a condensation transition, a condensate develops at one
or both boundary sites. On all other sites the particle distribution approaches
a product measure with the finite critical density \rho_c. In systems which do
not support condensation on a ring, strong boundary drive leads to a condensate
at the boundary. However, in this case the local particle density in the
interior exhibits a complex algebraic growth in time. We calculate the bulk and
boundary growth exponents as a function of the system parameters
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
First- and second-order phase transitions in a driven lattice gas with nearest-neighbor exclusion
A lattice gas with infinite repulsion between particles separated by
lattice spacing, and nearest-neighbor hopping dynamics, is subject to a drive
favoring movement along one axis of the square lattice. The equilibrium (zero
drive) transition to a phase with sublattice ordering, known to be continuous,
shifts to lower density, and becomes discontinuous for large bias. In the
ordered nonequilibrium steady state, both the particle and order-parameter
densities are nonuniform, with a large fraction of the particles occupying a
jammed strip oriented along the drive. The relaxation exhibits features
reminiscent of models of granular and glassy materials.Comment: 8 pages, 5 figures; results due to bad random number generator
corrected; significantly revised conclusion
Spontaneous pulsing states in an active particle system
International audienc
Complex Dynamics of Bus, Tram and Elevator Delays in Transportation System
It is necessary and important to operate buses and trams on time. The bus
schedule is closely related to the dynamic motion of buses. In this part, we
introduce the nonlinear maps for describing the dynamics of shuttle buses in
the transportation system. The complex motion of the buses is explained by the
nonlinear-map models. The transportation system of shuttle buses without
passing is similar to that of the trams. The transport of elevators is also
similar to that of shuttle buses with freely passing. The complex dynamics of a
single bus is described in terms of the piecewise map, the delayed map, the
extended circle map and the combined map. The dynamics of a few buses is
described by the model of freely passing buses, the model of no passing buses,
and the model of increase or decrease of buses. The nonlinear-map models are
useful to make an accurate estimate of the arrival time in the bus
transportation
Schizophrenia: do all roads lead to dopamine or is this where they start? Evidence from two epidemiologically informed developmental rodent models
The idea that there is some sort of abnormality in dopamine (DA) signalling is one of the more enduring hypotheses in schizophrenia research. Opinion leaders have published recent perspectives on the aetiology of this disorder with provocative titles such as ‘Risk factors for schizophrenia—all roads lead to dopamine' or ‘The dopamine hypothesis of schizophrenia—the final common pathway'. Perhaps, the other most enduring idea about schizophrenia is that it is a neurodevelopmental disorder. Those of us that model schizophrenia developmental risk-factor epidemiology in animals in an attempt to understand how this may translate to abnormal brain function have consistently shown that as adults these animals display behavioural, cognitive and pharmacological abnormalities consistent with aberrant DA signalling. The burning question remains how can in utero exposure to specific (environmental) insults induce persistent abnormalities in DA signalling in the adult? In this review, we summarize convergent evidence from two well-described developmental animal models, namely maternal immune activation and developmental vitamin D deficiency that begin to address this question. The adult offspring resulting from these two models consistently reveal locomotor abnormalities in response to DA-releasing or -blocking drugs. Additionally, as adults these animals have DA-related attentional and/or sensorimotor gating deficits. These findings are consistent with many other developmental animal models. However, the authors of this perspective have recently refocused their attention on very early aspects of DA ontogeny and describe reductions in genes that induce or specify dopaminergic phenotype in the embryonic brain and early changes in DA turnover suggesting that the origins of these behavioural abnormalities in adults may be traced to early alterations in DA ontogeny. Whether the convergent findings from these two models can be extended to other developmental animal models for this disease is at present unknown as such early brain alterations are rarely examined. Although it is premature to conclude that such mechanisms could be operating in other developmental animal models for schizophrenia, our convergent data have led us to propose that rather than all roads leading to DA, perhaps, this may be where they start