937 research outputs found
Noise driven dynamic phase transition in a a one dimensional Ising-like model
The dynamical evolution of a recently introduced one dimensional model in
\cite{biswas-sen} (henceforth referred to as model I), has been made stochastic
by introducing a parameter such that corresponds to the
Ising model and to the original model I. The equilibrium
behaviour for any value of is identical: a homogeneous state. We
argue, from the behaviour of the dynamical exponent ,that for any , the system belongs to the dynamical class of model I indicating a
dynamic phase transition at . On the other hand, the persistence
probabilities in a system of spins saturate at a value , where remains constant for all supporting the existence of the dynamic phase transition at .
The scaling function shows a crossover behaviour with for and for
.Comment: 4 pages, 5 figures, accepted version in Physical Review
The contact process in heterogeneous and weakly-disordered systems
The critical behavior of the contact process (CP) in heterogeneous periodic
and weakly-disordered environments is investigated using the supercritical
series expansion and Monte Carlo (MC) simulations. Phase-separation lines and
critical exponents (from series expansion) and (from MC
simulations) are calculated. A general analytical expression for the locus of
critical points is suggested for the weak-disorder limit and confirmed by the
series expansion analysis and the MC simulations. Our results for the critical
exponents show that the CP in heterogeneous environments remains in the
directed percolation (DP) universality class, while for environments with
quenched disorder, the data are compatible with the scenario of continuously
changing critical exponents.Comment: 5 pages, 3 figure
Site-bond representation and self-duality for totalistic probabilistic cellular automata
We study the one-dimensional two-state totalistic probabilistic cellular
automata (TPCA) having an absorbing state with long-range interactions, which
can be considered as a natural extension of the Domany-Kinzel model. We
establish the conditions for existence of a site-bond representation and
self-dual property. Moreover we present an expression of a set-to-set
connectedness between two sets, a matrix expression for a condition of the
self-duality, and a convergence theorem for the TPCA.Comment: 11 pages, minor corrections, journal reference adde
Spreading of families in cyclic predator-prey models
We study the spreading of families in two-dimensional multispecies
predator-prey systems, in which species cyclically dominate each other. In each
time step randomly chosen individuals invade one of the nearest sites of the
square lattice eliminating their prey. Initially all individuals get a
family-name which will be carried on by their descendants. Monte Carlo
simulations show that the systems with several species (N=3,4,5) are
asymptotically approaching the behavior of the voter model, i.e., the survival
probability of families, the mean-size of families and the mean-square distance
of descendants from their ancestor exhibit the same scaling behavior. The
scaling behavior of the survival probability of families has a logarithmic
correction. In case of the voter model this correction depends on the number of
species, while cyclic predator-prey models behave like the voter model with
infinite species. It is found that changing the rates of invasions does not
change this asymptotic behavior. As an application a three-species system with
a fourth species intruder is also discussed.Comment: to be published in PR
Multi-shocks in asymmetric simple exclusions processes: Insights from fixed-point analysis of the boundary-layers
The boundary-induced phase transitions in an asymmetric simple exclusion
process with inter-particle repulsion and bulk non-conservation are analyzed
through the fixed points of the boundary layers. This system is known to have
phases in which particle density profiles have different kinds of shocks. We
show how this boundary-layer fixed-point method allows us to gain physical
insights on the nature of the phases and also to obtain several quantitative
results on the density profiles especially on the nature of the boundary-layers
and shocks.Comment: 12 pages, 8 figure
Revisiting the effect of external fields in Axelrod's model of social dynamics
The study of the effects of spatially uniform fields on the steady-state
properties of Axelrod's model has yielded plenty of controversial results. Here
we re-examine the impact of this type of field for a selection of parameters
such that the field-free steady state of the model is heterogeneous or
multicultural. Analyses of both one and two-dimensional versions of Axelrod's
model indicate that, contrary to previous claims in the literature, the steady
state remains heterogeneous regardless of the value of the field strength.
Turning on the field leads to a discontinuous decrease on the number of
cultural domains, which we argue is due to the instability of zero-field
heterogeneous absorbing configurations. We find, however, that spatially
nonuniform fields that implement a consensus rule among the neighborhood of the
agents enforces homogenization. Although the overall effects of the fields are
essentially the same irrespective of the dimensionality of the model, we argue
that the dimensionality has a significant impact on the stability of the
field-free homogeneous steady state
Classical diffusion of N interacting particles in one dimension: General results and asymptotic laws
I consider the coupled one-dimensional diffusion of a cluster of N classical
particles with contact repulsion. General expressions are given for the
probability distributions, allowing to obtain the transport coefficients. In
the limit of large N, and within a gaussian approximation, the diffusion
constant is found to behave as N^{-1} for the central particle and as (\ln
N)^{-1} for the edge ones. Absolute correlations between the edge particles
increase as (\ln N)^{2}. The asymptotic one-body distribution is obtained and
discussed in relation of the statistics of extreme events.Comment: 6 pages, 2 eps figure
Absorbing-state phase transitions on percolating lattices
We study nonequilibrium phase transitions of reaction-diffusion systems
defined on randomly diluted lattices, focusing on the transition across the
lattice percolation threshold. To develop a theory for this transition, we
combine classical percolation theory with the properties of the supercritical
nonequilibrium system on a finite-size cluster. In the case of the contact
process, the interplay between geometric criticality due to percolation and
dynamical fluctuations of the nonequilibrium system leads to a new universality
class. The critical point is characterized by ultraslow activated dynamical
scaling and accompanied by strong Griffiths singularities. To confirm the
universality of this exotic scaling scenario we also study the generalized
contact process with several (symmetric) absorbing states, and we support our
theory by extensive Monte-Carlo simulations.Comment: 11 pages, 10 eps figures included, final version as publishe
Spatial Scaling in Model Plant Communities
We present an analytically tractable variant of the voter model that provides
a quantitatively accurate description of beta-diversity (two-point correlation
function) in two tropical forests. The model exhibits novel scaling behavior
that leads to links between ecological measures such as relative species
abundance and the species area relationship.Comment: 10 pages, 3 figure
Evolutionary dynamics on degree-heterogeneous graphs
The evolution of two species with different fitness is investigated on
degree-heterogeneous graphs. The population evolves either by one individual
dying and being replaced by the offspring of a random neighbor (voter model
(VM) dynamics) or by an individual giving birth to an offspring that takes over
a random neighbor node (invasion process (IP) dynamics). The fixation
probability for one species to take over a population of N individuals depends
crucially on the dynamics and on the local environment. Starting with a single
fitter mutant at a node of degree k, the fixation probability is proportional
to k for VM dynamics and to 1/k for IP dynamics.Comment: 4 pages, 4 figures, 2 column revtex4 format. Revisions in response to
referee comments for publication in PRL. The version on arxiv.org has one
more figure than the published PR
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