A particle-field approach bridges phase separation and collective motion in active matter

Abstract

Whereas self-propelled hard discs undergo motility-induced phase separation, self-propelled rods exhibit a variety of nonequilibrium phenomena, including clustering, collective motion, and spatio-temporal chaos. In this work, we present a theoretical framework representing active particles by continuum fields. This concept combines the simplicity of alignment-based models, enabling analytical studies, and realistic models that incorporate the shape of self-propelled objects explicitly. By varying particle shape from circular to ellipsoidal, we show how nonequilibrium stresses acting among self-propelled rods destabilize motility-induced phase separation and facilitate orientational ordering, thereby connecting the realms of scalar and vectorial active matter. Though the interaction potential is strictly apolar, both, polar and nematic order may emerge and even coexist. Accordingly, the symmetry of ordered states is a dynamical property in active matter. The presented framework may represent various systems including bacterial colonies, cytoskeletal extracts, or shaken granular media.

Active nematic order and dynamic lane formation of microtubules driven by membrane-bound diffusing motors

“…At even higher activity, the lanes become dynamic, since motilityinduced patterns are expected to be transient, and chaotic instabilities are also a generic feature of active nematic systems (15). Such transitions into lanes and chaotic dynamics of the lanes have also been reported in agent-based simulations of polar rods with nematic alignment (34,(36)(37)(38) and predicted by hydrodynamic models (39)(40)(41).…”

Collective motion of cells modeled as ring polymers

“…While many models of cells’ collective behavior do not explicitly account for their elongation 10,20,43 or for a static elongation, 23,24,26,42 spatiotemporal variability in cell deformation requires models that explicitly account for cell deformation. Phase field models have the advantage of readily accounting for cell deformation.…”

Pattern formation and polarity sorting of driven actin filaments on lipid membranes

“…As orientation mismatches are unstable, particles end up aligning and this leads to flocking behavior rather than to phase separation ( 5 , 20 – 25 ). This latter case, in which strong steric constraints dominate binary interactions but alignment is still present, is poorly understood, and how modeling has to be extended to account for the emergent collective behavior of elongated, flexible agents with volume exclusion also remains still under debate ( 26 – 30 ). This is partly due to the lack of microscopic experimental systems allowing to explore this regime.…”