一维活性布朗粒子平均首达时间的渐近分析与模拟
Asymptotic analysis and simulation of mean first passage time for active Brownian particles in 1-D
AI总结：
本文研究了一维吸收边界条件下活性布朗粒子的平均首达时间，通过小Péclet数极限下的渐近分析推导出解析表达式，并揭示了起始取向偏置会导致MFPT关于区域中心不对称。
摘要：
活性布朗粒子（ABPs）是非平衡系统的一种模型，其中组成粒子除了布朗运动外还具有自推进特性。与已被充分研究的被动布朗粒子的平均首达时间（MFPT）相比，ABPs的MFPT研究尚不成熟。本文研究了在两端具有吸收边界条件的一维区域内ABPs的MFPT。为了揭示游动对MFPT的影响，我们在弱游动或小Péclet（Pe）数极限下进行了渐近分析。具体而言，我们推导了直至O(Pe$^2$)的存活概率和MFPT的解析表达式。我们探讨了起始位置和起始取向对MFPT的影响。分析表明，若起始取向偏向区域一侧，MFPT作为起始位置的函数会变得关于区域中心不对称。解析结果得到了完整PDE模型的数值解的证实。
英文摘要：
Active Brownian particles (ABPs) are a model for nonequilibrium systems in which the constituent particles are self-propelled in addition to their Brownian motion. Compared to the well-studied mean first passage time (MFPT) of passive Brownian particles, the MFPT of ABPs is much less developed. In this paper, we study the MFPT for ABPs in a 1-D domain with absorbing boundary conditions at both ends of the domain. To reveal the effect of swimming on the MFPT, we consider an asymptotic analysis in the weak-swimming or small Péclet (Pe) number limit. In particular, analytical expressions for the survival probability and the MFPT are developed up to O(Pe$^2$). We explore the effects of the starting positions and starting orientations on the MFPT. Our analysis shows that if the starting orientations are biased towards one side of the domain, the MFPT as a function of the starting position becomes asymmetric about the center of the domain. The analytical results were confirmed by the numerical solutions of the full PDE model.
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