698 research outputs found
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
Consensus Formation in Multi-state Majority and Plurality Models
We study consensus formation in interacting systems that evolve by
multi-state majority rule and by plurality rule. In an update event, a group of
G agents (with G odd), each endowed with an s-state spin variable, is
specified. For majority rule, all group members adopt the local majority state;
for plurality rule the group adopts the local plurality state. This update is
repeated until a final consensus state is generally reached. In the mean field
limit, the consensus time for an N-spin system increases as ln N for both
majority and plurality rule, with an amplitude that depends on s and G. For
finite spatial dimensions, domains undergo diffusive coarsening in majority
rule when s or G is small. For larger s and G, opinions spread ballistically
from the few groups with an initial local majority. For plurality rule, there
is always diffusive domain coarsening toward consensus.Comment: 8 pages, 11 figures, 2-column revtex4 format. Updated version: small
changes in response to referee comments. For publication in J Phys
Two species coagulation approach to consensus by group level interactions
We explore the self-organization dynamics of a set of entities by considering
the interactions that affect the different subgroups conforming the whole. To
this end, we employ the widespread example of coagulation kinetics, and
characterize which interaction types lead to consensus formation and which do
not, as well as the corresponding different macroscopic patterns. The crucial
technical point is extending the usual one species coagulation dynamics to the
two species one. This is achieved by means of introducing explicitly solvable
kernels which have a clear physical meaning. The corresponding solutions are
calculated in the long time limit, in which consensus may or may not be
reached. The lack of consensus is characterized by means of scaling limits of
the solutions. The possible applications of our results to some topics in which
consensus reaching is fundamental, like collective animal motion and opinion
spreading dynamics, are also outlined
Statistics of opinion domains of the majority-vote model on a square lattice
The existence of juxtaposed regions of distinct cultures in spite of the fact
that people's beliefs have a tendency to become more similar to each other's as
the individuals interact repeatedly is a puzzling phenomenon in the social
sciences. Here we study an extreme version of the frequency-dependent bias
model of social influence in which an individual adopts the opinion shared by
the majority of the members of its extended neighborhood, which includes the
individual itself. This is a variant of the majority-vote model in which the
individual retains its opinion in case there is a tie among the neighbors'
opinions. We assume that the individuals are fixed in the sites of a square
lattice of linear size and that they interact with their nearest neighbors
only.
Within a mean-field framework, we derive the equations of motion for the
density of individuals adopting a particular opinion in the single-site and
pair approximations. Although the single-site approximation predicts a single
opinion domain that takes over the entire lattice, the pair approximation
yields a qualitatively correct picture with the coexistence of different
opinion domains and a strong dependence on the initial conditions. Extensive
Monte Carlo simulations indicate the existence of a rich distribution of
opinion domains or clusters, the number of which grows with whereas the
size of the largest cluster grows with . The analysis of the sizes of
the opinion domains shows that they obey a power-law distribution for not too
large sizes but that they are exponentially distributed in the limit of very
large clusters. In addition, similarly to other well-known social influence
model -- Axelrod's model -- we found that these opinion domains are unstable to
the effect of a thermal-like noise
Spatial correlations of the 1D KPZ surface on a flat substrate
We study the spatial correlations of the one-dimensional KPZ surface for the
flat initial condition. It is shown that the multi-point joint distribution for
the height is given by a Fredholm determinant, with its kernel in the scaling
limit explicitly obtained. This may also describe the dynamics of the largest
eigenvalue in the GOE Dyson's Brownian motion model. Our analysis is based on a
reformulation of the determinantal Green's function for the totally ASEP in
terms of a vicious walk problem.Comment: 11 pages, 2 figure
Exact probability function for bulk density and current in the asymmetric exclusion process
We examine the asymmetric simple exclusion process with open boundaries, a
paradigm of driven diffusive systems, having a nonequilibrium steady state
transition. We provide a full derivation and expanded discussion and digression
on results previously reported briefly in M. Depken and R. Stinchcombe, Phys.
Rev. Lett. {\bf 93}, 040602, (2004). In particular we derive an exact form for
the joint probability function for the bulk density and current, both for
finite systems, and also in the thermodynamic limit. The resulting distribution
is non-Gaussian, and while the fluctuations in the current are continuous at
the continuous phase transitions, the density fluctuations are discontinuous.
The derivations are done by using the standard operator algebraic techniques,
and by introducing a modified version of the original operator algebra. As a
byproduct of these considerations we also arrive at a novel and very simple way
of calculating the normalization constant appearing in the standard treatment
with the operator algebra. Like the partition function in equilibrium systems,
this normalization constant is shown to completely characterize the
fluctuations, albeit in a very different manner.Comment: 10 pages, 4 figure
Majority Rule Dynamics in Finite Dimensions
We investigate the long-time behavior of a majority rule opinion dynamics
model in finite spatial dimensions. Each site of the system is endowed with a
two-state spin variable that evolves by majority rule. In a single update
event, a group of spins with a fixed (odd) size is specified and all members of
the group adopt the local majority state. Repeated application of this update
step leads to a coarsening mosaic of spin domains and ultimate consensus in a
finite system. The approach to consensus is governed by two disparate time
scales, with the longer time scale arising from realizations in which spins
organize into coherent single-opinion bands. The consequences of this
geometrical organization on the long-time kinetics are explored.Comment: 8 pages, 2-column revtex format, 11 figures. Version 2: minor changes
in response to referee comments and typos corrected; final version for PR
Conventions spreading in open-ended systems
We introduce a simple open-ended model that describes the emergence of a
shared vocabulary. The ordering transition toward consensus is generated only
by an agreement mechanism. This interaction defines a finite and small number
of states, despite each individual having the ability to invent an unlimited
number of new words. The existence of a phase transition is studied by
analyzing the convergence times, the cognitive efforts of the agents and the
scaling behavior in memory and timeComment: 11 pages, 5 figure
Symmetric Exclusion Process with a Localized Source
We investigate the growth of the total number of particles in a symmetric
exclusion process driven by a localized source. The average total number of
particles entering an initially empty system grows with time as t^{1/2} in one
dimension, t/log(t) in two dimensions, and linearly in higher dimensions. In
one and two dimensions, the leading asymptotic behaviors for the average total
number of particles are independent on the intensity of the source. We also
discuss fluctuations of the total number of particles and determine the
asymptotic growth of the variance in one dimension.Comment: 7 pages; small corrections, references added, final versio
Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation
We investigate saturation effects in susceptible-infected-susceptible (SIS)
models of the spread of epidemics in heterogeneous populations. The structure
of interactions in the population is represented by networks with connectivity
distribution ,including scale-free(SF) networks with power law
distributions . Considering cases where the transmission
of infection between nodes depends on their connectivity, we introduce a
saturation function which reduces the infection transmission rate
across an edge going from a node with high connectivity . A mean
field approximation with the neglect of degree-degree correlation then leads to
a finite threshold for SF networks with . We
also find, in this approximation, the fraction of infected individuals among
those with degree for close to . We investigate via
computer simulation the contact process on a heterogeneous regular lattice and
compare the results with those obtained from mean field theory with and without
neglect of degree-degree correlations.Comment: 6 figure
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