Computer simulations of active Brownian particles
Date issued
Authors
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
License
Abstract
In recent years, active particles have received significant attention. Their defining property to convert (free) energy into some form of directed motion inherently drives them out of equilibrium. For interacting particles, this driving leads to a variety of collective behaviors. Active Brownian particles are a simplified model system that allows to study such collective behavior by numerical simulation or analytic theory. They extend the overdamped dynamics of nearly hard disks by introducing an additional self-propulsion velocity. At sufficient propulsion strength, active Brownian particles show a motility induced phase separation, a phenomenon known from other active systems in both experiment and theory. This phase separation closely resembles a gas-liquid transition in equilibrium, which raises the question how far concepts of equilibrium statistical physics and thermodynamics can be applied to this system far from equilibrium.
In this thesis, we study said analogy by employing large-scale computer simulations. Through the application of methods known from equilibrium physics, we extract precise, finite-size independent estimates for the phase boundaries. Furthermore, we examine the influence that other parameters, namely anisotropic particle shapes and the dimensionality of the system, have on the position of the phase boundaries, also known as binodal lines. Additionally, we study a proposed definition of an active pressure, that extends the concept of pressure for active Brownian particles. We verify the thermodynamical intensiveness of this active pressure, supporting its validity. Nonetheless, we also find limits for the analogy to equilibrium physics, as the resulting interfacial tension in the phase separated state turns out to be negative. Finally, the main part of the thesis is dedicated to finding the position of the critical point using a subsystem distribution method. By improving this scheme known from equilibrium, we determine the critical point to be at critical Peclet number 40(2) and critical packing fraction 0.597(3). Based on this estimate for the position of the critical point, we find critical exponents by studying different scaling laws close to the critical point. The extracted exponents for order parameter, susceptibility, and correlation length indicate that active Brownian particles do not follow 2D Ising universality, thus raising the question of the existence of an active universality class far from equilibrium.