Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria.
Soft Matter. 2017 Sep 27;13(37):6396-6406. doi: 10.1039/c7sm00873b.
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.
微游泳者由于不对称的推进机制、手性体型或在表面附近的水动力耦合而表现出嘈杂的圆周运动。在这里，我们采用布朗圆泳者模型，并根据可直接测量的中间散射函数从理论上描述动力学。我们推导出关联的福克-普朗克方程用于条件概率，并以马蒂厄函数的推广形式提供精确解。不同的时空状态被识别出来，反映了在大波数下的裸平动扩散，在中波数下的持续圆周运动和在小波数下的增强的有效扩散。特别是，在探测半径的波数的中间散射函数的平台上，粒子的圆周运动表现出特征性的振荡。
