Active Brownian particles From individual to collective stochastic dynamics

• Published in: The European physical journal. ST, Special topics Vol. 202; no. 1; pp. 1 - 162
• Main Authors: Romanczuk, P., Bär, M., Ebeling, W., Lindner, B., Schimansky-Geier, L.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-03-2012; EDP Sciences
• Subjects: Atomic; Brownian motion; Classical and Continuum Physics; Condensed Matter Physics; Exact sciences and technology; Fluctuation phenomena, random processes, noise, and brownian motion; Materials Science; Measurement Science and Instrumentation; Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Review; Statistical physics, thermodynamics, and nonlinear dynamical systems; Noise Intensity; European Physical Journal Special Topic; Collective Motion; Cluster Size Distribution; Active Particle; Brownian motion; Markov process; Stochastic model; Fluctuations; Friction; Angular variation; Shot noise; Spatiotemporal phenomena; Diffusion coefficient; Non linear effect; Statistical mechanics
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjst/e2012-01529-y

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.