Steady states of active Brownian particles interacting with boundaries
Steady states of active Brownian particles interacting with boundaries
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DOI：
10.1088/1742-5468/ac42cf
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Caleb G. Wagner;M. Hagan;A. Baskaran
中科院分区：
文献类型：
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作者：
Caleb G. Wagner;M. Hagan;A. Baskaran
主动布朗粒子是耗散环境中自推进胶体的最小模型。实验和模拟表明，在存在边界和障碍物的情况下，活跃的布朗粒子系统接近非平凡的非平衡定态与有趣的现象，如在边界处的积累，棘轮效应，和远程耗尽相互作用。然而，对这些现象的理论分析已被证明是困难的。在这里，我们解决这个理论挑战的背景下，非相互作用的粒子在两个维度上，基于我们的分析的稳态Smoluchowski方程的单粒子分布函数。我们的主要结果是一个近似策略，连接Smoluchowski方程的渐近解的边界条件。我们测试这种近似对精确的解析解在二维平面几何形状，以及在圆形和椭圆形几何形状的数值解。我们发现，只要边界条件不变化太快，粒子轨迹的持久长度很好的协议。我们的研究结果是相关的特征长程流动和耗尽在这样的系统中的相互作用。特别是，我们的框架显示了这些行为是如何与打破边界上的详细平衡联系在一起的。
An active Brownian particle is a minimal model for a self-propelled colloid in a dissipative environment. Experiments and simulations show that, in the presence of boundaries and obstacles, active Brownian particle systems approach nontrivial nonequilibrium steady states with intriguing phenomenology, such as accumulation at boundaries, ratchet effects, and long-range depletion interactions. Nevertheless, theoretical analysis of these phenomena has proven difficult. Here, we address this theoretical challenge in the context of non-interacting particles in two dimensions, basing our analysis on the steady-state Smoluchowski equation for the one-particle distribution function. Our primary result is an approximation strategy that connects asymptotic solutions of the Smoluchowski equation to boundary conditions. We test this approximation against the exact analytic solution in a 2D planar geometry, as well as numerical solutions in circular and elliptic geometries. We find good agreement so long as the boundary conditions do not vary too rapidly with respect to the persistence length of particle trajectories. Our results are relevant for characterizing long-range flows and depletion interactions in such systems. In particular, our framework shows how such behaviors are connected to the breaking of detailed balance at the boundaries.