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.