Phase separation of self-propelled disks with ferromagnetic and nematic alignment

Abstract

We present a comprehensive study of a model system of repulsive self-propelled disks in two dimensions with ferromagnetic and nematic velocity alignment interactions. We characterize the phase behavior of the system as a function of the alignment and self-propulsion strength, featuring orientational order for strong alignment and motility-induced phase separation (MIPS) at moderate alignment but high enough self-propulsion. We derive a microscopic theory for these systems yielding a closed set of hydrodynamic equations from which we perform a linear stability analysis of the homogenous disordered state. This analysis predicts MIPS in the presence of aligning torques. The nature of the continuum theory allows for an explicit quantitative comparison with particle-based simulations, which consistently shows that ferromagnetic alignment fosters phase separation, while nematic alignment does not alter either the nature or the location of the instability responsible for it. In the ferromagnetic case, such behavior is due to an increase of the imbalance of the number of particle collisions along different orientations, giving rise to the self-trapping of particles along their self-propulsion direction. On the contrary, the anisotropy of the pair correlation function, which encodes this self-trapping effect, is not significantly affected by nematic torques. Our work shows the predictive power of such microscopic theories to describe complex active matter systems with different interaction symmetries and sheds light on the impact of velocity-alignment interactions in motility-induced phase separation.

Impact of dipole-dipole interactions on motility-induced phase separation

“…It has been recently reported in numerical simulations of dipolar active Brownian particles that dipole-dipole interactions actually hinder MIPS [62]. This finding is in contrast with, e.g., Vicsek-like interactions [49,52,64], showing that details of the anisotropy play an important role. There is, however, so far no (coarse-grained) theory describing systems of self-propelled particles with dipolar interactions, which, due to their long-range nature and to the fact that they depend on both the orientation and spatial configuration of a pair of particles, pose a severe challenge for hydrodynamic theories.…”

“…Following [64], we here derive hydrodynamic equations based on a Fokker-Planck approach. We start from the N -body Smoluchowski equation, corresponding to the Langevin equations, Eqs.…”

“…On the contrary, MIPS is promoted by torques leading to autotaxis [63] and also in the presence of polar velocity-alignment in discoidal selfpropelled particles [49,52,64]. Further, MIPS remains essentially unaffected by nematic interactions between disks [64].…”

“…Recently, a line of research has specifically focused on understanding the impact of aligning mechanisms on the collective behavior of self-propelled particles [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64], paying special attention to the effect they have on MIPS. This has been tackled both in particle-resolved simulations [51,52,55,57,[60][61][62]64] and also by deriving coarse-grained descriptions [53,60,61,63,64], which often provide a deeper insight into the underlying mechanisms governing the system's phase behavior. It has been shown that the resulting impact of aligning interactions on MIPS depends very much on the origin and type of interactions, and resulting torques, considered.…”

“…In the case of 'steric' alignment due to collisions of elongated particles, the phase separation induced by motility disappears as soon as shape anisotropy sets in [51,55,60,61]. On the contrary, MIPS is promoted by torques leading to autotaxis [63] and also in the presence of polar velocity-alignment in discoidal selfpropelled particles [49,52,64]. Further, MIPS remains essentially unaffected by nematic interactions between disks [64].…”