42 research outputs found
Cohesive motion in one-dimensional flocking
A one-dimensional rule-based model for flocking, that combines velocity
alignment and long-range centering interactions, is presented and studied. The
induced cohesion in the collective motion of the self-propelled agents leads to
a unique group behaviour that contrasts with previous studies. Our results show
that the largest cluster of particles, in the condensed states, develops a mean
velocity slower than the preferred one in the absence of noise. For strong
noise, the system also develops a non-vanishing mean velocity, alternating its
direction of motion stochastically. This allows us to address the directional
switching phenomenon. The effects of different sources of stochasticity on the
system are also discussed.Comment: 24 pages, 11 figure
Self-organization in systems of self-propelled particles
We investigate a discrete model consisting of self-propelled particles that
obey simple interaction rules. We show that this model can self-organize and
exhibit coherent localized solutions in one- and in two-dimensions.In
one-dimension, the self-organized solution is a localized flock of finite
extent in which the density abruptly drops to zero at the edges.In
two-dimensions, we focus on the vortex solution in which the particles rotate
around a common center and show that this solution can be obtained from random
initial conditions, even in the absence of a confining boundary. Furthermore,
we develop a continuum version of our discrete model and demonstrate that the
agreement between the discrete and the continuum model is excellent.Comment: 4 pages, 5 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.
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
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
One-dimensional Particle Processes with Acceleration/Braking Asymmetry
The slow-to-start mechanism is known to play an important role in the
particular shape of the Fundamental diagram of traffic and to be associated to
hysteresis effects of traffic flow.We study this question in the context of
exclusion and queueing processes,by including an asymmetry between deceleration
and acceleration in the formulation of these processes. For exclusions
processes, this corresponds to a multi-class process with transition asymmetry
between different speed levels, while for queueing processes we consider
non-reversible stochastic dependency of the service rate w.r.t the number of
clients. The relationship between these 2 families of models is analyzed on the
ring geometry, along with their steady state properties. Spatial condensation
phenomena and metastability is observed, depending on the level of the
aforementioned asymmetry. In addition we provide a large deviation formulation
of the fundamental diagram (FD) which includes the level of fluctuations, in
the canonical ensemble when the stationary state is expressed as a product form
of such generalized queues.Comment: 28 pages, 8 figure
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