Velocity Distribution and Diffusion of an Athermal Inertial Run-and-Tumble Particle in a Shear-Thinning Medium
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| Format: | Preprint |
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2025
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| author | Mondal, Sayantan Das, Prasenjit |
| author_facet | Mondal, Sayantan Das, Prasenjit |
| contents | We study the dynamics of an athermal inertial active particle moving in a shear-thinning medium in $d=1$. The viscosity of the medium is modeled using a Coulomb-tanh function, while the activity is represented by an asymmetric dichotomous noise with strengths $-Δ$ and $μΔ$, transitioning between these states at a rate $λ$. Starting from the Fokker-Planck~(FP) equation for the time-dependent probability distributions $P(v,-Δ,t)$ and $P(v,μΔ,t)$ of the particle's velocity $v$ at time $t$, moving under the influence of active forces $-Δ$ and $μΔ$ respectively, we analytically derive the steady-state velocity distribution function $P_s(v)$, explicitly dependent on $μ$. Also, we obtain a quadrature expression for the effective diffusion coefficient $D_e$ for the symmetric active force case~($μ=1$). For a given $Δ$ and $μ$, we show that $P_s(v)$ exhibits multiple transitions as $λ$ is varied. Subsequently, we numerically compute $P_s(v)$, the mean-squared velocity $\langle v^2\rangle(t)$, and the diffusion coefficient $D_e$ by solving the particle's equation of motion, all of which show excellent agreement with the analytical results in the steady-state. Finally, we examine the universal nature of the transitions in $P_s(v)$ by considering an alternative functional form of medium's viscosity that also capture the shear-thinning behavior. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_11683 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Velocity Distribution and Diffusion of an Athermal Inertial Run-and-Tumble Particle in a Shear-Thinning Medium Mondal, Sayantan Das, Prasenjit Statistical Mechanics Soft Condensed Matter We study the dynamics of an athermal inertial active particle moving in a shear-thinning medium in $d=1$. The viscosity of the medium is modeled using a Coulomb-tanh function, while the activity is represented by an asymmetric dichotomous noise with strengths $-Δ$ and $μΔ$, transitioning between these states at a rate $λ$. Starting from the Fokker-Planck~(FP) equation for the time-dependent probability distributions $P(v,-Δ,t)$ and $P(v,μΔ,t)$ of the particle's velocity $v$ at time $t$, moving under the influence of active forces $-Δ$ and $μΔ$ respectively, we analytically derive the steady-state velocity distribution function $P_s(v)$, explicitly dependent on $μ$. Also, we obtain a quadrature expression for the effective diffusion coefficient $D_e$ for the symmetric active force case~($μ=1$). For a given $Δ$ and $μ$, we show that $P_s(v)$ exhibits multiple transitions as $λ$ is varied. Subsequently, we numerically compute $P_s(v)$, the mean-squared velocity $\langle v^2\rangle(t)$, and the diffusion coefficient $D_e$ by solving the particle's equation of motion, all of which show excellent agreement with the analytical results in the steady-state. Finally, we examine the universal nature of the transitions in $P_s(v)$ by considering an alternative functional form of medium's viscosity that also capture the shear-thinning behavior. |
| title | Velocity Distribution and Diffusion of an Athermal Inertial Run-and-Tumble Particle in a Shear-Thinning Medium |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2504.11683 |