论文标题
自发运动阈值附近的化学活性粒子的弱非线性动力学。 ii。与历史有关的运动
Weakly nonlinear dynamics of a chemically active particle near the threshold for spontaneous motion. II. History-dependent motion
论文作者
论文摘要
我们为自发运动阈值附近的各向同性化学活性粒子的慢速非稳态动力学开发了一个还原模型。在本系列第I部分中开发的稳定理论的基础上，我们将在粒子尺度上有效的弱非线性膨胀与在较大规模的不稳定远程区域中的前阶近似有效，在该区域中，粒子充当扩散浓度的移动点源。粒子速度的产生振幅方程包括一个术语，该项代表粒子在远程区域中醒目的相互作用的相互作用，这可以作为粒子运动历史上的时间积分表示，从而可以有效地模拟和理论分析三维不稳定的问题。为了说明如何使用该模型，我们研究了作用于粒子的弱力的影响，包括稳态的稳定性以及速度矢量如何对稳定的稳定性重新调整，而先前的轴对称和稳定模型都无法捕获。这种不稳定的公式也可以应用于第I部分研究的大多数其他扰动方案以及相互作用的活动粒子的动力学。
We develop a reduced model for the slow unsteady dynamics of an isotropic chemically active particle near the threshold for spontaneous motion. Building on the steady theory developed in part I of this series, we match a weakly nonlinear expansion valid on the particle scale with a leading-order approximation in a larger-scale unsteady remote region, where the particle acts as a moving point source of diffusing concentration. The resulting amplitude equation for the velocity of the particle includes a term representing the interaction of the particle with its own concentration wake in the remote region, which can be expressed as a time integral over the history of the particle motion, allowing efficient simulation and theoretical analysis of fully three-dimensional unsteady problems. To illustrate how to use the model, we study the effects of a weak force acting on the particle, including the stability of the steady states and how the velocity vector realigns towards the stable one, neither of which previous axisymmetric and steady models were able to capture. This unsteady formulation could also be applied to most of the other perturbation scenarios studied in part I as well as the dynamics of interacting active particles.
