Abstract
We formulate a model of self-propelled hard disks whose dynamics is governed by mutually coupled vectors for velocity and body orientation. Numerical integration at low densities reveals that the expected transition from isotropic to aligned collective motion is present. However, the transition at the Landau mean-field level is strongly first-order, while it is continuous in the Vicsek model. We show that this difference is rooted in the completely opposite effect that individual scattering events have on alignment. We argue that such differences will generically hold for systems of self-propelled particles with repulsive short-ranged interactions. We obtain these results by matching the numerical results to the framework of Boltzmann theory, based on the statistics of binary scattering properties, always assuming that the system is small enough to stay homogeneous. We further show that the presence of noise in the dynamics can change the nature of the transition from discontinuous to continuous.
Highlights
Self-propelled particles borrow energy from their environment and convert it to translational motion
Most theoretical knowledge about such active matter and its transitions has been developed for Vicsek-like models: point particles travel at a speed which is constant to represent self-propulsion, and their direction changes according to interaction rules which comprise both explicit alignment and noise, to account for external or internal perturbations
In this paper, (i) we formulate a model of active liquid, made of self-propelled hard disks which interact through elastic collisions.‡ As we shall see, the key ingredient of the model is the mutual coupling of the positional and orientational degrees of freedom in the dynamics of each particle
Summary
Self-propelled particles borrow energy from their environment and convert it to translational motion. In this paper, (i) we formulate a model of active liquid, made of self-propelled hard disks which interact through elastic collisions.‡ As we shall see, the key ingredient of the model is the mutual coupling of the positional and orientational degrees of freedom in the dynamics of each particle. We argue that this coupling is generically present in. (iv) We scrutinize the very peculiar dynamics of a single collision between two self propelled disks and explain the specific shape of the scattering function that was obtained numerically This result explains how self-propulsion intrinsically generates effective alignment, requiring from the interaction only to be repulsive
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