Asymptotic Analysis and Simulation of Mean First Passage Time for Active Brownian Particles in 1-D

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-05-17 DOI:10.1137/23m1593917

Sarafa A. Iyaniwura, Zhiwei Peng

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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1079-1095, June 2024.
Abstract. 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 ([math]) number limit. In particular, analytical expressions for the survival probability and the MFPT are developed up to [math]. 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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一维活动布朗粒子平均首次通过时间的渐近分析与模拟

SIAM 应用数学杂志》第 84 卷第 3 期第 1079-1095 页，2024 年 6 月。摘要主动布朗粒子（ABPs）是一种非平衡系统模型，其中的组成粒子除了布朗运动外还具有自推进力。与研究较多的被动布朗粒子的平均首次通过时间（MFPT）相比，ABPs的MFPT研究要少得多。在本文中，我们研究了 ABPs 在一维域中的平均首次通过时间，该域的两端具有吸收边界条件。为了揭示游动对 MFPT 的影响，我们考虑了弱游动或小 Péclet （[math]）数极限的渐近分析。其中，生存概率和 MFPT 的分析表达式已发展到 [math]。我们探讨了起始位置和起始方向对 MFPT 的影响。我们的分析表明，如果起始方向偏向域的一侧，则 MFPT 作为起始位置的函数会变得与域中心不对称。分析结果得到了完整 PDE 模型数值解的证实。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.