Intermediate scattering function of an anisotropic Brownian circle swimmer

Abstract

Microswimmers exhibit noisy circular motion due to asymmetric propulsion mechanisms, their chiral body shape, or by hydrodynamic couplings in the vicinity of surfaces. Here, we employ the Brownian circle swimmer model and characterize theoretically the dynamics in terms of the directly measurable intermediate scattering function. We derive the associated Fokker-Planck equation for the conditional probabilities and provide an exact solution in terms of generalizations of the Mathieu functions. Different spatiotemporal regimes are identified reflecting the bare translational diffusion at large wavenumbers, the persistent circular motion at intermediate wavenumbers and an enhanced effective diffusion at small wavenumbers. In particular, the circular motion of the particle manifests itself in characteristic oscillations at a plateau of the intermediate scattering function for wavenumbers probing the radius.

Random motion of a circle microswimmer in a random environment

“…The orientation itself changes in time by an angular drift Ω as well as by rotational diffusion [48,45,49] d dt…”

“…Then M is a measure of how many circles a microswimmer can complete before the orientation becomes randomized in diffusion time 1/D θ [48,49].…”

“…To provide an intuitive explanation for such a drastic difference we consider the mean-squared displacement of an active circle Brownian swimmer in free space [48,49,53] δr…”

“…Rather, the trajectories will be intrinsically curved, due to asymmetries in shape or the propulsion mechanism [45,46], or hydrodynamic coupling to walls [29,47]. If the angular drift is large compared to the rotational diffusion, many circles are completed before the orientation is randomized [48,49]. Currently, a complete study of transport amplification and suppression which includes both circular motion subject to noise and the wall-following mechanism, in a randomly distributed array of obstacles, is lacking.…”

Two-dimensional active motion

“…Even in the case of forward or reverse scattering, circular motion emerges as consequence of the skewness of the distribution. These statistical considerations allow to describe the motion of circular swimmers, which are ubiquitous in nature and have been observed in a variety of biological organisms and of artificially designed swimmers [32][33][34][35][36][37][38][39][40][41], and have been of theoretical interest leading to diverse models that describe their motion [25,[42][43][44][45][46][47][48].…”