Active Brownian particles

2012/02/11 by Paweł Romańczuk, Pawel Romanczuk, Markus Bär +4 · 1,141 citations
Environmental Science · Physics and Astronomy · #Active matter #Advanced Thermodynamics and Statistical Mechanics #Biological system #Biology #Brownian motion #Classical mechanics #Diffusion #Dynamics (music) #Ecosystem dynamics and resilience #Mechanics #Micro and Nano Robotics #Nonlinear system #Observable #Pattern formation #Physics #Simple (philosophy) #Statistical physics #Stochastic differential equation #Thermodynamics #cond-mat.other #cond-mat.soft #physics.bio-ph

paper · pdf · doi:10.1140/epjst/e2012-01529-y

published in The European Physical Journal Special Topics 202(1), 1-162 (Springer Science+Business Media) · 161 pages, Review, Eur Phys J Special-Topics, accepted

arxiv created 2012/02/11 · openalex publication_date 2012/03/01 · arxiv updated 2015/06/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

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.

Citations

• Statistical mechanics of canonical-dissipative systems and applications to swarm dynamics
• A user’s guide to PDE models for chemotaxis
• Phase transition in the collective migration of tissue cells: experiment and model
• Colloid Transport by Interfacial Forces
• Active behavior of the Cytoskeleton
• Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
• The dispersion of matter in turbulent flow through a pipe
• On the Theory of the Brownian Motion
• Collective motion of self-propelled particles interacting without cohesion
• THE EFFECTS OF SHAPE ON THE INTERACTION OF COLLOIDAL PARTICLES
• Model for chemotaxis
• Physics of chemoreception
• Self-Running Droplet: Emergence of Regular Motion from Nonequilibrium Noise
• Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen
• Noise-induced transition from translational to rotational motion of swarms
• Self-organization in systems of self-propelled particles
• Advantages of hopping on a zig-zag course
• Active nematics on a substrate: Giant number fluctuations and long-time tails
• Making sense of it all: bacterial chemotaxis
• ON THE ATTRACTORS OF TWO-DIMENSIONAL RAYLEIGH OSCILLATORS INCLUDING NOISE
• Persistent Cell Motion in the Absence of External Signals: A Search Strategy for Eukaryotic Cells
• Dynamics of a Brownian circle swimmer
• Building bridges: A study of coordination in projects
• LXXV. A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin
• Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion
• Ordering, metastability and phase transitions in two-dimensional systems
• Hydrodynamic Fluctuations and Instabilities in Ordered Suspensions of Self-Propelled Particles
• Fundamental aspects of quantum Brownian motion
• Dispersion of soluble matter in solvent flowing slowly through a tube
• Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen
• The random walk's guide to anomalous diffusion: a fractional dynamics approach
• The hydrodynamics of swimming microorganisms
• Transport, Collective Motion, and Brownian Motion
• The Mechanics and Statistics of Active Matter
• Random walk models in biology
• Fluid dynamics and noise in bacterial cell–cell and cell–surface scattering
• Self-Propelled Particles with Fluctuating Speed and Direction of Motion in Two Dimensions

Cited by

• Moment analysis of two-dimensional active Brownian run-and-tumble particles
• Collective dynamics of active Brownian particles in three spatial dimensions: A predictive field theory
• Coherent Motion of Monolayer Sheets under Confinement and Its Pathological Implications
• Emergent smectic order in simple active particle models
• Dynamics of a linear magnetic “microswimmer molecule”
• Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
• Cell Motion Alignment as a Polarity Memory Effect
• Entropy Production and Fluctuation Theorems for Active Matter
• Nonlinear friction in underdamped anharmonic stochastic oscillators
• Breakdown of effective temperature, power law interactions, and self-propulsion in a momentum-conserving active fluid
• Cell Decision Making through the Lens of Bayesian Learning
• Flocking from a quantum analogy: spin–orbit coupling in an active fluid
• Getting drowned in a swirl: Deformable bead-spring model microswimmers in external flow fields
• Synchronization and anchoring of two non-harmonic canonical-dissipative oscillators via Smorodinsky-Winternitz potentials
• Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation

Related

• Self-Organization, Active Brownian Dynamics, and Biological Applications
• Nonequilibrium statistical mechanics of swarms of driven particles
• Collective motion of Active Brownian Particles with polar alignment
• Active-Passive Brownian Particle in Two Dimensions
• Nonlinear Dynamics of Active Brownian Particles