Collection of polar self-propelled particles with a modified alignment interaction

Abstract

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, ad (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, ηc(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 aTCP 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.