Role of particle conservation in self-propelled particle systems
Actively propelled particles undergoing dissipative collisions are\nknown to develop a state of spatially distributed coherently moving clusters.\nFor densities larger than a characteristic value, clusters grow in time and form\na stationary well-ordered state of coherent macroscopic motion. In this work\nwe address two questions. (i) What is the role of the particles\u2019 aspect ratio in\nthe context of cluster formation, and does the particle shape affect the system\u2019s\nbehavior on hydrodynamic scales? (ii) To what extent does particle conservation\ninfluence pattern formation? To answer these questions we suggest a simple\nkinetic model permitting us to depict some of the interaction properties between\nfreely moving particles and particles integrated in clusters. To this end, we\nintroduce two particle species: single and cluster particles. Specifically, we\naccount for coalescence of clusters from single particles, assembly of single\nparticles on existing clusters, collisions between clusters and cluster disassembly.\nCoarse graining our kinetic model, (i) we demonstrate that particle shape (i.e.\naspect ratio) shifts the scale of the transition density, but does not impact the\ninstabilities at the ordering threshold and (ii) we show that the validity of particle\nconservation determines the existence of a longitudinal instability, which tends to amplify density heterogeneities locally, and in turn triggers a wave pattern\nwith wave vectors parallel to the axis of macroscopic order. If the system is in\ncontact with a particle reservoir, this instability vanishes due to a compensation\nof density heterogeneities.