Collective motion in actively propelled particle systems is triggered on the
very local scale by nucleation of coherently moving units consisting of just a
handful of particles. These units grow and merge over time, ending up in a
long-range ordered, coherently-moving state. So far, there exists no bottom-up
understanding of how the microscopic dynamics and interactions between the
constituents are related to the system's ordering instability. In this paper,
we study a class of models for propelled colloids allowing an explicit
treatment of the microscopic details of the collision process. Specifically,
the model equations are Newtonian equations of motion with separate force terms
for particles' driving, dissipation and interaction forces. Focusing on dilute
particle systems, we analyze the binary scattering behavior for these models,
and determine-based on the microscopic dynamics-the corresponding
collision-rule, i.e., the mapping of pre-collisional velocities and impact
parameter on post-collisional velocities. By studying binary scattering we also
find that the considered models for active colloids share the same principle
for parallel alignment: the first incoming particle (with respect to the center
of collision) is aligned to the second particle as a result of the encounter.
This behavior is distinctively different to alignment in non-driven dissipative
gases. Moreover, the obtained collision rule lends itself as a starting point
to apply kinetic theory for propelled particle systems in order to determine
the phase boundary to a long-range ordered, coherently-moving state. The
microscopic origin of the collision rule offers the opportunity to
quantitatively scrutinize the predictions of kinetic theory for propelled
particle systems through direct comparison with multi-particle simulations.Comment: 19 pages, 12 figure
