Encounter-based model of a run-and-tumble particle with stochastic resetting
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916639794003968 |
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| author | Bressloff, Paul C |
| author_facet | Bressloff, Paul C |
| contents | 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 $[0,\infty)$ with a partially absorbing wall at $x=0$. The RTP tumbles at a constant rate $α$ between the velocity states $\pm v$ with $v>0$. Absorption occurs when the number of collisions with the wall (discrete local time) exceeds a randomly generated threshold $\widehat{\ell}$ with probability distribution $Ψ(\ell)$. The extended RTP model has three state variables, namely, particle position $X(t)\in [0,\infty)$, the velocity direction $σ(t)\in\{-1, 1\}$, and the discrete local time $L(t)\in {\mathbb N}$. 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 $Ψ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Encounter-based model of a run-and-tumble particle with stochastic resetting Bressloff, Paul C Statistical Mechanics Quantitative Methods 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 $[0,\infty)$ with a partially absorbing wall at $x=0$. The RTP tumbles at a constant rate $α$ between the velocity states $\pm v$ with $v>0$. Absorption occurs when the number of collisions with the wall (discrete local time) exceeds a randomly generated threshold $\widehat{\ell}$ with probability distribution $Ψ(\ell)$. The extended RTP model has three state variables, namely, particle position $X(t)\in [0,\infty)$, the velocity direction $σ(t)\in\{-1, 1\}$, and the discrete local time $L(t)\in {\mathbb N}$. 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 $Ψ$. |
| title | Encounter-based model of a run-and-tumble particle with stochastic resetting |
| topic | Statistical Mechanics Quantitative Methods |
| url | https://arxiv.org/abs/2503.01304 |