2012/04/30 by Robert Grossmann, R Großmann, Lutz Schimansky-Geier +3 · 63 citations
Physics and Astronomy · #Active matter #Advanced Thermodynamics and Statistical Mechanics #Brownian motion #Geometric Brownian motion #Kinetic energy #Micro and Nano Robotics #Moment (physics) #Perpendicular #Stochastic differential equation #Stochastic process #cond-mat.other #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1367-2630/14/7/073033
published in New Journal of Physics 14(7), 073033 (IOP Publishing) · 5 figures, 22 pages, submitted to New Journal of Physics
arxiv created 2012/05/01 · openalex publication_date 2012/07/13 · arxiv updated 2016/05/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider a model of active Brownian particles (ABPs) with velocity alignment in two spatial dimensions with passive and active fluctuations. Here, active fluctuations refers to purely non-equilibrium stochastic forces correlated with the heading of an individual active particle. In the simplest case studied here, they are assumed to be independent stochastic forces parallel (speed noise) and perpendicular (angular noise) to the velocity of the particle. On the other hand, passive fluctuations are defined by a noise vector independent of the direction of motion of a particle, and may account, for example, for thermal fluctuations. We derive a macroscopic description of the ABP gas with velocity-alignment interaction. Here, we start from the individual-based description in terms of stochastic differential equations (Langevin equations) and derive equations of motion for the coarse-grained kinetic variables (density, velocity and temperature) via a moment expansion of the corresponding probability density function. We focus here on the different impact of active and passive fluctuations on onset of collective motion and show how active fluctuations in the active Brownian dynamics can change the phase-transition behaviour of the system. In particular, we show that active angular fluctuations lead to an earlier breakdown of collective motion and to the emergence of a new bistable regime in the mean-field case.