ABSTRACT
Active Brownian particles are one particle systems described by stochastic differential equations (Langevin equations) which are driven by a nonlinear deterministic force. The interaction of the particles is described by a self consistent field. An ensemble of these particles far from equilibrium shows a complex behavior and pattern formation. The self consistent field is described by a reaction diffusion equation. These equations analyzed numerically. The stationary distribution of the velocities of the particles is derived by the corresponding Fokker Planck equation. For a macroscopic description we use a hydrodynamic approach to interpret the numerical results and to understand the behavior of nonlinear systems far from equilibrium.
