Encounter-based model of a run-and-tumble particle

Abstract

In this paper we extend the encounter-based model of diffusion-mediated surface absorption to the case of an unbiased run-and-tumble particle (RTP) confined to a finite interval $[0,L]$ and switching between two constant velocity states $\pm v$ at a rate $\alpha$. The encounter-based formalism is motivated by the observation that various surface-based reactions are better modeled in terms of a reactivity that is a function of the amount of time that a particle spends in a neighborhood of an absorbing surface, which is specified by a functional known as the boundary local time. The effects of surface reactions are taken into account by identifying the first passage time (FPT) for absorption with the event that the local time crosses some random threshold $\hat{\ell }$. In the case of a Brownian particle, the local time $\ell (t)$ is a continuous non-decreasing function of the time $t$. Taking $\Psi (\ell )\equiv \P [\hat{\ell }>\ell ]$ to be an exponential distribution, $Ψ[\ell]=\e^{-κ_0\ell}$, is equivalent to imposing a Robin boundary condition with a constant rate of absorption ${\kappa }_0$. One major difference in the encounter-based model of an RTP is that the boundary local time $\ell (t)$ is a now a discrete random variable that counts the number of collisions of the RTP with the boundary. Given this modification, we show that in the case of a geometric distribution $\Psi (\ell )=z^{\ell }$, $z=1/(1+{\kappa }_0/v)$, we recover the RTP analog of the Robin boundary condition. This allows us to solve the boundary value problem (BVP) for the joint probability density for particle position and the local time, and thus incorporate more general models of absorption based on non-geometric distributions $\Psi (\ell )$.

arXiv comment20 pages, 4 figures

References in corpus (19)

• Run and tumble particle under resetting: a renewal approach
• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• Run-and-tumble particle in one-dimensional confining potential: Steady state, relaxation and first passage properties
• Paradigm shift in diffusion-mediated surface phenomena
• Universal survival probability for a $d$-dimensional run-and-tumble particle
• First-passage time of run-and-tumble particles
• Run-and-tumble particles in two-dimensions : Marginal position distributions
• A First-Order Dynamical Transition in the displacement distribution of a Driven Run-and-Tumble Particle
• Run-and-Tumble particles in Two-dimensions under Stochastic Resetting
• Confined run-and-tumble swimmers in one dimension
• Stationary superstatistics distributions of trapped run-and-tumble particles
• Active processes in one dimension
• Generalised `Arcsine' laws for run-and-tumble particle in one dimension
• Non-crossing run-and-tumble particles on a line
• Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces
• Occupation time of a run-and-tumble particle with resetting
• Diffusion-mediated surface reactions and stochastic resetting
• Ramifications of disorder on active particles in one dimension
• Local time for run and tumble particle

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• Asymptotic analysis and simulation of mean first passage time for active Brownian particles in 1-D
• Trapping of an active Brownian particle at a partially absorbing wall
• Active particle in a harmonic trap driven by a resetting noise: an approach via Kesten variables
• Persistent and anti-Persistent Motion in Bounded and Unbounded Space: Resolution of the First-Passage Problem
• Anomalous random flights and time-fractional run-and-tumble equations