Active Brownian particles: From individual to collective behavior
Single self-propelled particles as well as ensembles of self-propelled particles are examples of non-equilibrium states and a topic of the interdisciplinary research at the borderline between physics and biology. Interesting examples of self-moving objects come from biology, these are bacteria, eukaryots, amoeba, insects, fishes and animals etc. But also in physics self-moving objects are known, which are active colloids and moving spots in reaction-diffusion systems.
I will review various models of self-propelled particles from a viewpoint of statistical physics. Special attention is payed to the influence of noise on the dynamics of single particles and on the exhibition of spatial structures in groups of interacting moving particles. In detail, the determination of velocity distribution function, the calculation of diffusion coefficients and correlation functions, properties of swarms, the connection between the micro-dynamics of particles and the macro-dynamics of ensembles of particles, the response to external forces and many different examples are considered.
In the last part I will discuss active particles which exhibit a turbulent-like motion as was reported recently in experiments with bacteria. I will introduce a new nonlocal microscopic model which exhibits a large variety of different flows including a turbulent one.