Microscopic field theory for structure formation in systems of self-propelled particles with generic torques

Abstract

We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques inducing self-rotation, as well as interparticle torques leading to, for instance, the local alignment of particles' orientations. Within this approach, although the functional form of the pairwise interactions does not need to be specified, one can directly map the parameters of the field theory onto the parameters of particle-based models. We perform a linear stability analysis of the homogeneous solution of the field equations and find both long-wavelength and short-wavelength instabilities. The former signals the emergence of a macroscopic structure, which we associate with motility-induced phase separation, while the second one signals the growth of a finite structure with a characteristic size. Intrinsic torques hinder phase separation, pushing the onset of the long-wavelength instability to higher activities. Further, they generate finite-sized structures with a characteristic size proportional to both the self-propulsion velocity and the inverse of the self-rotation frequency. Our results show that a general mechanism might explain why chirality tends to suppress motility-induced phase separation but instead promotes the formation of non-equilibrium patterns.

Chiral active matter

“…The spinodal-like instability shifts to higher values of v 0 (and ζ) as ω increases, showing how chirality opposes MIPS. Notably, for the short-wavelength instability, the characteristic length scales as ∝ v 0 , and, for large ω also as ∝ 1/ω [95]. Interestingly, this linear increase of the onset cluster size with the single-particle swimming radius ( ∝ v 0 /ω) is the same scaling law which occurs for CAPs with alignment interactions as we shall see below.…”

“…This is the key aspect of the theory leading to particle aggregation and eventually MIPS: particles block each other in the direction of self-propulsion, giving rise to a reduction of v ρ. The linear stability analysis of the homogeneous disordered solution of these field equations predicts a spinodal-like, long-wavelength instability [93][94][95]97], and a short-wavelength one [95], interpreted as the onset of MIPS in the first case, and the formation of structures with a characteristic (onset) length scale in the second case [95]. The spinodal-like instability shifts to higher values of v 0 (and ζ) as ω increases, showing how chirality opposes MIPS.…”

“…A question that has attracted a significant interest in the past few years is how MIPS is affected by chirality (i.e., ω = 0). Both studies based on particle-based simulations [29,93] and on the analysis of continuum equations [50,94,95] found that circular swimming (in 2D) tends to hinder MIPS. Remarkably, however, chirality also leads to a new phenomenon which does not occur for ω = 0: the emergence of finite dynamical clusters which counter-rotate with respect to the surrounding gas [29,93].…”

“…By explicitly coarse-graining the microscopic dynamics, eqs. ( 2), and performing a meanfield-like closure scheme [93][94][95]97], the following equations can be derived for a coarse-grained version of the microscopic density ρ( r, t) = i δ( r − r i ) and the polarization density w( r, t…”

Collective behavior of passive and active circle swimming particle mixtures

“…Thus, this is not a case of microphase separation which was observed in active systems with alignment interactions. [66][67][68]…”