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

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

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

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 $q$ 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 $q=\exp{(-\beta/N)}$ where $N$ 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 $\beta_c$. The value of $\beta_c = 2 \pi \sqrt{3}$ 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 $\leq 1$ 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