Asymptotic analysis and simulation of mean first passage time for active Brownian particles in 1-D

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 (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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• Siegmund duality for physicists: a bridge between spatial and first-passage properties of continuous and discrete time stochastic processes
• Target search by active particles
• Boundary layers, transport and universal distribution in boundary driven active systems