论文标题
活性布朗粒子的最可能路径
Most probable path of an active Brownian particle
论文作者
论文摘要
在这项研究中，我们研究了两个给定状态之间的二维平面上游离活性布朗颗粒（ABP）的过渡路径。使用OnSager-Machlup积分及其变异原理得出了连接这两个状态的最可能路径的极值条件。我们为这些极值条件提供明确的解决方案，并通过与摆在可能多个路径的摆式方程的类比来证明它们的非唯一性。摆锤类比还用于表征通过明确计算多个溶液的路径概率获得的全球最可能路径的形状。我们全面研究了ABP向正面的翻译过程，这是一个原型示例。有趣的是，数值和理论分析表明，最可能的路径的形状从i形到U形和$ \ ell $形状随着过渡过程的增加而变化。 Langevin模拟还确认了这种形状的转变。我们还讨论了在活动物质中罕见事件中评估过渡路径的进一步方法。
In this study, we investigate the transition path of a free active Brownian particle (ABP) on a two-dimensional plane between two given states. The extremum conditions for the most probable path connecting the two states are derived using the Onsager--Machlup integral and its variational principle. We provide explicit solutions to these extremum conditions and demonstrate their nonuniqueness through an analogy with the pendulum equation indicating possible multiple paths. The pendulum analogy is also employed to characterize the shape of the globally most probable path obtained by explicitly calculating the path probability for multiple solutions. We comprehensively examine a translation process of an ABP to the front as a prototypical example. Interestingly, the numerical and theoretical analyses reveal that the shape of the most probable path changes from an I to a U shape and to the $\ell$ shape with an increase in the transition process time. The Langevin simulation also confirms this shape transition. We also discuss further method applications for evaluating a transition path in rare events in active matter.
