Structure of the active Fokker-Planck equation.

Abstract

This paper solves in one and two dimensions the steady noninteractive active Fokker-Planck (FP) equation and finds that its velocity distribution admits, under limiting cases, a dual behavior. Briefly, when the inertial relaxation time is smaller than the orientation time, the active FP equation admits a bimodal shape, whereas the inverse condition is seen to admit a Gaussian one. Once the velocity distribution functions are available, they are used to find their effect on the system's transport properties, such as its mean-square speed. In the process, a useful mathematical identity for the first kind Bessel function as a sum of bimodal exponential functions is spotted.