Sprenger Alexander R, Jahanshahi Soudeh, Ivlev Alexei V, Löwen Hartmut
Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany.
Max-Planck-Institut für Extraterrestrische Physik, 85748 Garching, Germany.
Phys Rev E. 2021 Apr;103(4-1):042601. doi: 10.1103/PhysRevE.103.042601.
Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics, which involve inertia, friction, and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation are manifold, ranging from minirockets (which are self-propelled by burning their own mass), to dust particles in plasma (which lose mass by evaporating material), to walkers with expiring activity. Here we present analytical solutions for several dynamical correlation functions, such as mean-square displacement and orientational and velocity autocorrelation functions. If the parameters exhibit a slow power law in time, we obtain anomalous superdiffusion with a nontrivial dynamical exponent. Finally, we constitute the "Langevin rocket" model by including orientational fluctuations in the traditional Tsiolkovsky rocket equation. We calculate the mean reach of the Langevin rocket and discuss different mass ejection strategies to maximize it. Our results can be tested in experiments on macroscopic robotic or living particles or in self-propelled mesoscopic objects moving in media of low viscosity, such as complex plasma.
许多自行推进的物体足够大，能够表现出惯性效应，但仍会受到环境波动的影响。相应的基本运动方程由主动朗之万动力学支配，该动力学涉及惯性、摩擦以及平移和取向自由度的随机噪声，这些自由度通过沿粒子取向的自推进相互耦合。在本文中，我们将主动朗之万模型推广到随时间变化的参数，并明确讨论了随时间变化的惯性对非手性和手性粒子的影响。这种情况的实例多种多样，从微型火箭（通过燃烧自身质量自行推进）到等离子体中的尘埃粒子（通过蒸发物质而质量损失），再到活性逐渐消失的行走器。在这里，我们给出了几个动力学相关函数的解析解，如均方位移、取向和速度自相关函数。如果参数随时间呈现缓慢的幂律关系，我们会得到具有非平凡动力学指数的反常超扩散。最后，我们通过在传统齐奥尔科夫斯基火箭方程中纳入取向涨落，构建了“朗之万火箭”模型。我们计算了朗之万火箭的平均射程，并讨论了不同的质量喷射策略以使其最大化。我们的结果可以在宏观机器人或活体粒子的实验中进行测试，或者在低粘度介质（如复杂等离子体）中运动的自推进介观物体的实验中进行测试。
