Role of particle conservation in self-propelled particle systems
Actively propelled particles undergoing dissipative collisions are
known to develop a state of spatially distributed coherently moving clusters.
For densities larger than a characteristic value, clusters grow in time and form
a stationary well-ordered state of coherent macroscopic motion. In this work
we address two questions. (i) What is the role of the particles’ aspect ratio in
the context of cluster formation, and does the particle shape affect the system’s
behavior on hydrodynamic scales? (ii) To what extent does particle conservation
influence pattern formation? To answer these questions we suggest a simple
kinetic model permitting us to depict some of the interaction properties between
freely moving particles and particles integrated in clusters. To this end, we
introduce two particle species: single and cluster particles. Specifically, we
account for coalescence of clusters from single particles, assembly of single
particles 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 the
instabilities at the ordering threshold and (ii) we show that the validity of particle
conservation determines the existence of a longitudinal instability, which tends to amplify density heterogeneities locally, and in turn triggers a wave pattern
with wave vectors parallel to the axis of macroscopic order. If the system is in
contact with a particle reservoir, this instability vanishes due to a compensation
of density heterogeneities.
