Collective motion of run-and-tumble particles drives aggregation in one-dimensional systems (original) (raw)

Aggregation of self-propelled particles with sensitivity to local order

Physical Review E

We study a system of self-propelled particles (SPPs) in which individual particles are allowed to switch between a fast aligning and a slow nonaligning state depending upon the degree of the alignment in the neighborhood. The switching is modeled using a threshold for the local order parameter. This additional attribute gives rise to a mixed phase, in contrast to the ordered phases found in clean SPP systems. As the threshold is increased from zero, we find the sudden appearance of clusters of nonaligners. Clusters of nonaligners coexist with moving clusters of aligners with continual coalescence and fragmentation. The behavior of the system with respect to the clustering of nonaligners appears to be very different for values of low and high global densities. In the low density regime, for an optimal value of the threshold, the largest cluster of nonaligners grows in size up to a maximum that varies logarithmically with the total number of particles. However, on further increasing the threshold the size decreases. In contrast, for the high density regime, an initial abrupt rise is followed by the appearance of a giant cluster of nonaligners. The latter growth can be characterized as a continuous percolation transition. In addition, we find that the speed differences between aligners and nonaligners is necessary for the segregation of aligners and nonaligners.

Collective motion of self-propelled particles interacting without cohesion

Physical Review E, 2008

We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and shown to be discontinuous (first-order like). The properties of the ordered, collectively moving phase are investigated. In a large domain of parameter space including the transition region, well-defined high-density and high-order propagating solitary structures are shown to dominate the dynamics. Far enough from the transition region, on the other hand, these objects are not present. A statistically-homogeneous ordered phase is then observed, which is characterized by anomalously-strong density fluctuations, superdiffusion, and strong intermittency.

Irreversible aggregation of interacting particles in one dimension

Physical Review E, 2005

We present a study of the aggregation of interacting particles in one dimension. This situation, for example, applies to atoms trapped along linear defects at the surface of a crystal. Simulations are performed with two lattice models. In the first model, the borders of atoms and islands interact in a vectorial manner via force monopoles. In the second model, each atom carries a dipole. These two models lead to qualitatively similar but quantitatively different behaviors. In both cases, the final average island size S f does not depend on the interactions in the limits of very low and very high coverages. For intermediate coverages, S f exhibits an asymmetric behavior as a function of the interaction strength: while it saturates for attractive interactions, it decreases for repulsive interactions. A class of mean-field models is designed, which allows one to retrieve the interaction dependence on the coverage dependence of the average island size with a good accuracy.

Ordering kinetics and steady state of self-propelled particles with random-bond disorder

Journal of Physics A: Mathematical and Theoretical

In this study, we introduce a minimal model for a collection of polar self-propelled particles (SPPs) on a two-dimensional substrate where each particle has a different ability to interact with its neighbors. The SPPs interact through a short-range alignment interaction and interaction strength of each particle is obtained from a uniform distribution. Moreover, the volume exclusion among the SPPs is taken care of by introducing a repulsive interaction among them. We characterise the ordered steady state and kinetics of the system for different strengths of the disorder. We find that the presence of the disorder does not destroy the usual long-range ordering in the system. To our surprise, we note that the density clustering is enhanced in the presence of the disorder. Moreover, the disorder leads to the formation of a random network of different interaction strengths, which makes the alignment weaker and it results in the slower dynamics. Hence, the disorder leads to more cohesion a...

The role of collective motion in examples of coarsening and self-assembly

Soft Matter, 2009

The simplest prescription for building a patterned structure from its constituents is to add particles, one at a time, to an appropriate template. However, self-organizing molecular and colloidal systems in nature can evolve in much more hierarchical ways. Specifically, constituents (or clusters of constituents) may aggregate to form clusters (or clusters of clusters) that serve as building blocks for later stages of assembly. Here we evaluate the character and consequences of such collective motion in a set of prototypical assembly processes. We do so using computer simulations in which a system's capacity for hierarchical dynamics can be controlled systematically. By explicitly allowing or suppressing collective motion, we quantify its effects. We find that coarsening within a two dimensional attractive lattice gas (and an analogous off-lattice model in three dimensions) is naturally dominated by collective motion over a broad range of temperatures and densities. Under such circumstances, cluster mobility inhibits the development of uniform coexisting phases, especially when macroscopic segregation is strongly favored by thermodynamics. By contrast, the assembly of model viral capsids is not frustrated but is instead facilitated by collective moves, which promote the orderly binding of intermediates consisting of several monomers.

Self-organization in systems of self-propelled particles

Physical Review E, 2000

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.

Kinetics of self-induced aggregation in Brownian particles

Physical Review E, 2007

We study a model of interacting random walkers that proposes a simple mechanism for the emergence of cooperation in group of individuals. Each individual, represented by a Brownian particle, experiences an interaction produced by the local unbalance in the spatial distribution of the other individuals. This interaction results in a nonlinear velocity driving the particle trajectories in the direction of the nearest more crowded regions; the competition among different aggregating centers generates nontrivial dynamical regimes. Our simulations show that for sufficiently low randomness, the system evolves through a coalescence behavior characterized by clusters of particles growing with a power law in time. In addition, the typical scaling properties of the general theory of stochastic aggregation processes are verified.

Position Distribution of Run-and-Tumble particles in Two-dimensions

arXiv: Statistical Mechanics, 2020

We study a set of Run-and-tumble particle (RTP) dynamics in two spatial dimensions. In the first case of the orientation {\theta} of the particle can assume a set of n possible discrete values while in the second case {\theta} is a continuous variable. We calculate exactly the marginal position distributions for n = 3,4 and the continuous case and show that in all the cases the RTP shows a cross-over from a ballistic to diffusive regime. The ballistic regime is a typical signature of the active nature of the systems and is characterized by non-trivial position distributions which depends on the specific model. We also show that, the signature of activity at long-times can be found in the atypical fluctuations which we also characterize by computing the large deviation functions explicitly.