Encounter-based model of a run-and-tumble particle with stochastic resetting
File(s)
Published version
Author(s)
Bressloff, Paul C
Type
Journal Article
Abstract
In this paper we analyze the effects of stochastic resetting on an encounter-based model of an unbiased run-and-tumble particle (RTP) confined to the half-line [0, ∞) with a partially absorbing wall at x = 0. The RTP tumbles at a constant rate α between the velocity states ±v with v > 0. Absorption occurs when the number of collisions with the wall (discrete local time) exceeds a ran-
domly generated threshold̂ ℓ with probability distribution Ψ(ℓ). The extended RTP model has three state variables, namely, particle position X(t) ∈ [0, ∞), the velocity direction σ(t) ∈ {−1, 1}, and the discrete local time L(t) ∈ N. We
initially assume that only X(t) and σ(t) reset at a Poisson rate r, whereas L(t) is not changed. This implies that resetting is not governed by a renewal process.
We use the stochastic calculus of jump processes to derive an evolution equation for the joint probability distribution of the triplet (X(t), σ(t), L(t)). This is then
used to calculate the mean first passage time (MFPT) by performing a discrete Laplace transform of the evolution equation with respect to the local time. We thus find that the MFPT’s only dependence on the distribution Ψ is via the mean local time threshold. We also identify parameter regimes in which the MFPT is a unimodal function of both the resetting and tumbling rates. Finally, we consider conditions under which resetting is given by a renewal process and show how the MFPT in the presence of local time resetting depends on the full statistics of Ψ.
domly generated threshold̂ ℓ with probability distribution Ψ(ℓ). The extended RTP model has three state variables, namely, particle position X(t) ∈ [0, ∞), the velocity direction σ(t) ∈ {−1, 1}, and the discrete local time L(t) ∈ N. We
initially assume that only X(t) and σ(t) reset at a Poisson rate r, whereas L(t) is not changed. This implies that resetting is not governed by a renewal process.
We use the stochastic calculus of jump processes to derive an evolution equation for the joint probability distribution of the triplet (X(t), σ(t), L(t)). This is then
used to calculate the mean first passage time (MFPT) by performing a discrete Laplace transform of the evolution equation with respect to the local time. We thus find that the MFPT’s only dependence on the distribution Ψ is via the mean local time threshold. We also identify parameter regimes in which the MFPT is a unimodal function of both the resetting and tumbling rates. Finally, we consider conditions under which resetting is given by a renewal process and show how the MFPT in the presence of local time resetting depends on the full statistics of Ψ.
Date Issued
2025-03-24
Date Acceptance
2025-03-12
Citation
Journal of Physics A: Mathematical and Theoretical, 2025, 58 (12)
ISSN
1751-8113
Publisher
IOP Publishing
Journal / Book Title
Journal of Physics A: Mathematical and Theoretical
Volume
58
Issue
12
Copyright Statement
© 2025 The Author(s). Published by IOP Publishing Ltd. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
License URL
Publication Status
Published
Article Number
ARTN 125002
Date Publish Online
2025-03-20