Confined run and tumble particles with non-Markovian tumbling statistics
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| Format: | Preprint |
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2024
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| _version_ | 1866929304736104448 |
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| author | Farago, Oded Smith, Naftali R. |
| author_facet | Farago, Oded Smith, Naftali R. |
| contents | Confined active particles constitute simple, yet realistic, examples of systems that converge into a non-equilibrium steady state. We investigate a run-and-tumble particle in one spatial dimension, trapped by an external potential, with a given distribution $g(t)$ of waiting times between tumbling events whose mean value is equal to $τ$. Unless $g(t)$ is an exponential distribution (corresponding to a constant tumbling rate), the process is non-Markovian, which makes the analysis of the model particularly challenging. We use an analytical framework involving effective position-dependent tumbling rates, to develop a numerical method that yields the full steady-state distribution (SSD) of the particle's position. The method is very efficient and requires modest computing resources, including in the large-deviations and/or small-$τ$ regime, where the SSD can be related to the the large-deviation function, $s(x)$, via the scaling relation $P_{\rm st}(x)\sim e^{-s\left(x\right)/τ}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_01576 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Confined run and tumble particles with non-Markovian tumbling statistics Farago, Oded Smith, Naftali R. Statistical Mechanics Soft Condensed Matter Confined active particles constitute simple, yet realistic, examples of systems that converge into a non-equilibrium steady state. We investigate a run-and-tumble particle in one spatial dimension, trapped by an external potential, with a given distribution $g(t)$ of waiting times between tumbling events whose mean value is equal to $τ$. Unless $g(t)$ is an exponential distribution (corresponding to a constant tumbling rate), the process is non-Markovian, which makes the analysis of the model particularly challenging. We use an analytical framework involving effective position-dependent tumbling rates, to develop a numerical method that yields the full steady-state distribution (SSD) of the particle's position. The method is very efficient and requires modest computing resources, including in the large-deviations and/or small-$τ$ regime, where the SSD can be related to the the large-deviation function, $s(x)$, via the scaling relation $P_{\rm st}(x)\sim e^{-s\left(x\right)/τ}$. |
| title | Confined run and tumble particles with non-Markovian tumbling statistics |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2401.01576 |