We study the motion of an active Brownian particle (ABP) using overdamped Langevin dynamics on a two-dimensional substrate with periodic array of obstacles and in a quasi-one-dimensional corrugated channel comprised of periodically arrayed obstacles. The periodic arrangement of the obstacles enhances the persistent motion of the ABP in comparison to its motion in the free space. Persistent motion increases with the activity of the ABP. We note that the periodic arrangement induces directionality in ABP motion at late time, and it increases with the size of the obstacles. We also note that the ABP exhibits a super-diffusive dynamics in the corrugated channel. The transport property is independent of the shape of the channel; rather it depends on the packing fraction of the obstacles in the system. However, the ABP shows the usual diffusive dynamics in the quasi-one-dimensional channel with flat boundary.
We study the disorder-to-order transition in a collection of polar self-propelled particles interacting through a distance dependent alignment interaction. Strength of the interaction, a d (0<a<1) decays with metric distance d between particle pair, and the interaction is short range. At a=1.0, our model reduces to the famous Vicsek model. For all a>0, the system shows a transition from a disordered to an ordered state as a function of noise strength. We calculate the critical noise strength, η c (a) for different a and compare it with the mean-field result. Nature of the disorder-to-order transition continuously changes from discontinuous to continuous with decreasing a. We numerically estimate tri-critical point a TCP at which the nature of transition changes from discontinuous to continuous. The density phase separation is large for a close to unity, and it decays with decreasing a. We also write the coarse-grained hydrodynamic equations of motion for general a, and find that the homogeneous ordered state is unstable to small perturbation as a approaches to 1. The instability in the homogeneous ordered state is consistent with the large density phase separation for a close to unity.
A collection of self-propelled particles (SPPs) shows coherent motion and exhibits a true long range ordered (LRO) state in two dimensions. Various studies show that the presence of spatial inhomogeneities can destroy the usual long range ordering in the system. However, effects of inhomogeneity due to the intrinsic properties of the particles are barely addressed. In this paper we consider a collection of polar SPPs moving with inhomogeneous speed (IS) on a two dimensional substrate, which can arise due to varying physical strength of the individual particle. To our surprise the IS not only preserves the usual long range ordering present in the homogeneous speed models, but also induces faster ordering in the system. Furthermore, The response of the flock to an external perturbation is also faster, compared to Vicsek like model systems, due to the frequent update of neighbors of each SPP in the presence of the IS. Therefore, our study shows that the IS can help in faster information transfer in the moving flock.
We model a binary mixture of passive and active Brownian particles in two dimensions using the effective interaction between passive particles in the active bath. The activity of active particles and the size ratio of two types of particles are two control parameters in the system. The effective interaction is calculated from the average force on two particles generated by the active particles. The effective interaction can be attractive or repulsive, depending on the system parameters. The passive particles form four distinct structural orders for different system parameters viz; homogeneous structures (HS), disordered cluster (DC), ordered cluster (OC), and crystalline structure (CS). The change in structure is dictated by the change in nature of the effective interaction. We further confirm the four structures using full microscopic simulation of active and passive mixture. Our study is useful to understand the different collective behaviour in non-equilibrium systems.
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