Löwen Hartmut
Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany.
Phys Rev E. 2019 Jun;99(6-1):062608. doi: 10.1103/PhysRevE.99.062608.
Typically the motion of self-propelled active particles is described in a quiescent environment establishing an inertial frame of reference. Here we assume that friction, self-propulsion, and fluctuations occur relative to a noninertial frame and thereby the active Brownian motion model is generalized to noninertial frames. First, analytical solutions are presented for the overdamped case, both for linear swimmers and for circle swimmers. For a frame rotating with constant angular velocity ("carousel"), the resulting noise-free trajectories in the static laboratory frame are trochoids if these are circles in the rotating frame. For systems governed by inertia, such as vibrated granulates or active complex plasmas, centrifugal and Coriolis forces become relevant. For both linear and circling self-propulsion, these forces lead to out-spiraling trajectories which for long times approach a spira mirabilis. This implies that a self-propelled particle will typically leave a rotating carousel. A navigation strategy is proposed to avoid this expulsion, by adjusting the self-propulsion direction at will. For a particle, initially quiescent in the rotating frame, it is shown that this strategy only works if the initial distance to the rotation center is smaller than a critical radius R_{c} which scales with the self-propulsion velocity. Possible experiments to verify the theoretical predictions are discussed.
通常，自驱动活性粒子的运动是在建立惯性参考系的静止环境中进行描述的。在此，我们假设摩擦、自推进和涨落是相对于非惯性参考系发生的，从而将活性布朗运动模型推广到非惯性参考系。首先，给出了过阻尼情况下线性游动者和圆周游动者的解析解。对于以恒定角速度旋转的框架（“旋转木马”），如果在旋转框架中这些是圆，那么在静态实验室框架中得到的无噪声轨迹就是次摆线。对于受惯性支配的系统，如振动颗粒或活性复杂等离子体，离心力和科里奥利力变得重要。对于线性和圆周自推进，这些力都会导致向外螺旋的轨迹，长时间后会趋近于等角螺线。这意味着自驱动粒子通常会离开旋转的旋转木马。提出了一种导航策略来避免这种排斥，即随意调整自推进方向。对于在旋转框架中最初静止的粒子，结果表明只有当初始到旋转中心的距离小于一个与自推进速度成比例的临界半径(R_{c})时，该策略才有效。讨论了验证理论预测的可能实验。
