Actively propelled particles undergoing dissipative collisions areknown to develop a state of spatially distributed coherently moving clusters.For densities larger than a characteristic value, clusters grow in time and forma stationary well-ordered state of coherent macroscopic motion. In this workwe address two questions. (i) What is the role of the particles’ aspect ratio inthe context of cluster formation, and does the particle shape affect the system’sbehavior on hydrodynamic scales? (ii) To what extent does particle conservationinfluence pattern formation? To answer these questions we suggest a simplekinetic model permitting us to depict some of the interaction properties betweenfreely moving particles and particles integrated in clusters. To this end, weintroduce two particle species: single and cluster particles. Specifically, weaccount for coalescence of clusters from single particles, assembly of singleparticles on existing clusters, collisions between clusters and cluster disassembly.Coarse graining our kinetic model, (i) we demonstrate that particle shape (i.e.aspect ratio) shifts the scale of the transition density, but does not impact theinstabilities at the ordering threshold and (ii) we show that the validity of particleconservation determines the existence of a longitudinal instability, which tends to amplify density heterogeneities locally, and in turn triggers a wave patternwith wave vectors parallel to the axis of macroscopic order. If the system is incontact with a particle reservoir, this instability vanishes due to a compensationof density heterogeneities.
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