A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation (η) added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, |v a | = 0) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous since |v a | is found to scale as (η c − η) β with β ≃ 0.45.-------

Bacterial colonies must often cope with unfavourable environmental conditions. To do so, they have developed sophisticated modes of cooperative behaviour. It has been found that such behaviour can cause bacterial colonies to exhibit complex growth patterns similar to those observed during non-equilibrium growth processes in non-living systems; some of the qualitative features of the latter may be invoked to account for the complex patterns of bacterial growth. Here we show that a simple model of bacterial growth can reproduce the salient features of the observed growth patterns. The model incorporates random walkers, representing aggregates of bacteria, which move in response to gradients in nutrient concentration and communicate with each other by means of chemotactic 'feedback'. These simple features allow the colony to respond efficiently to adverse growth conditions, and generate self-organization over a wide range of length scales.

Collective cell motility is an important aspect of several developmental and pathophysiological processes. Despite its importance, the mechanisms that allow cells to be both motile and adhere to one another are poorly understood. In this study we establish statistical properties of the random streaming behavior of endothelial monolayer cultures. To understand the reported empirical findings, we expand the widely used cellular Potts model to include active cell motility. For spontaneous directed motility we assume a positive feedback between cell displacements and cell polarity. The resulting model is studied with computer simulations, and is shown to exhibit behavior compatible with experimental findings. In particular, in monolayer cultures both the speed and persistence of cell motion decreases, transient cell chains move together as groups, and velocity correlations extend over several cell diameters. As active cell motility is ubiquitous both in vitro and in vivo, our model is expected to be a generally applicable representation of cellular behavior.

We demonstrate that a system of self-propelled particles exhibits spontaneous symmetry breaking and self-organization in one dimension, in contrast with previous analytical predictions. To explain this surprising result we derive a new continuum theory that can account for the development of the symmetry broken state and belongs to the same universality class as the discrete self-propelled particle model. [S0031-9007(98)07911-3] PACS numbers: 64.60.Cn, 05.60.CdThe transport properties of systems consisting of selfpropelled particles (SPP) have generated much attention lately [1][2][3][4][5][6]. This interest has been largely motivated by analogous processes taking place in numerous biological phenomena (e.g., bacterial migration on surfaces [7], flocking of birds, fish, quadrupeds [8], correlated motion of ants [9] and pedestrians [10]), as well as in various other systems, including driven granular materials [11,12] and traffic models [13]. The models describing these phenomena are distinctively nonequilibrium, exhibiting kinetic phase transitions and self-organization, and are of particular interest from the point of view of modern statistical mechanics [14].In the simplest version of the SPP model [1]-introduced to study collective biological motion-each particle's velocity is set to a fixed magnitude, y 0 . The interaction with the neighboring particles changes only the direction of motion: the particles tend to align their orientation to the local average velocity. Numerical simulations in 2D provided evidence of a second order phase transition [15] between an ordered phase in which the mean velocity of the entire system, ͗y͘, is nonzero and a disordered phase with ͗y͘ 0, as the strength of the noise is increased or the density of the particles decreased.This SPP model is similar to the XY model of classical magnetic spins because the velocity of the particles, such as the local spin of the XY model, has fixed length and continuous rotational symmetry. In the y 0 0 and low noise limit the model reduces exactly to a Monte Carlo dynamics of the XY model. Since the XY model does not exhibit a long-range ordered phase at temperatures T . 0 [16], the ordered state observed in [1] is surprising. To explain this discrepancy, Toner and Tu (TT) [3] proposed a continuum theory that included in a self-consistent way the nonequilibrium effects as well. They have shown that their model is different from the XY model for d , 4 and found an ordered phase in d 2 [17]. While TT provided the first theoretical demonstration of the ordered phase in 2D SPP models, the nonlinearity responsible for the longrange order in their continuum model is absent for d 1.Here we demonstrate that a kinetic phase transition and ordering takes place in 1D as well; i.e., the discrete U ! 2U symmetry breaks spontaneously. This result is as surprising as breaking of the rotational symmetry in 2D. This nonequilibrium phenomenon was not foreseen by the existing analytical approaches, which motivated us to introduce a new continuum theory describing ...