Order-disorder transition in repulsive self-propelled particle systems

Abstract

We study the collective dynamics of repulsive self-propelled particles. The particles are governed by coupled equations of motion that include polar self-propulsion, damping of velocity and of polarity, repulsive particle-particle interaction, and deterministic dynamics. Particle dynamics simulations show that the collective coherent motion with large density fluctuations spontaneously emerges from a disordered, isotropic state. In the parameter region where the rotational damping of polarity is strong, the systems undergoes an abrupt shift to the absorbing ordered state after a waiting period in the metastable disordered state. In order to obtain a simple understanding of the mechanism underlying the collective behavior, we analyze binary particle scattering process. We show that this approach correctly predicts the order-disorder transition at dilute limit. The same approach is expanded for finite densities, although it disagrees with the result from many-particle simulations due to many-body correlations and density fluctuations.

Modeling the influence of noise and interaction strength on the collective motion of interactive particles

“…Using this model, Hanke et al [12] examined the collective behavior of active repulsive particles and reported an ordered state observed at certain parameters region. In another study, Hiraoka et al [13] employed a simple model for repulsive self-propelled particles applicable to various systems of different length scales. They showed that the coherent collective motion with large density fluctuation spontaneously appeared from a disordered, isotropic state.…”

Cell Motion Alignment as a Polarity Memory Effect

“…In the self-propelled disk, the damping parameter γ is a control parameter of the motion alignment [22,23]. Naively, the dependence on γ = |dR/dt|/aτ p in our model is evaluable from the τ p dependence.…”

“…In these cases, the direct aligning-interaction is not necessary at least for this alignment. Especially for the disks, the polarity memory recording the past motion aligns the subsequent motion through collisions even with rotation-symmetric excluded volume [22,23,24,25].…”

“…Secondarily, we give the method to identify the motion alignment in our examination. Refer to the previous work [17,23], we define the motion alignment by finite values of the order parameter of p m ,…”

“…3(a), the direction of motion after the 1st collision is maintained until the 2nd collision, because the 2nd collision typically occurs in the cell movement length of l d . Owing to the polarity memory effect, cells align their motion in the common direction through the 1st and 2nd collisions [22,23]. This aligning repeats in the following collisions and finally results in the motion alignment over all cells.…”