Distribution Functions and Moments of Harmonically Trapped Inertial Run-and-Tumble Particles in a Shear-Thickening Medium
Abstract
We study the dynamics of an athermal inertial active particle confined in a harmonic potential and moving through shear-thickening media in one dimension. The activity is modeled using a symmetric dichotomous noise of strength Σ and flipping rate λ, which mimics a run-and-tumble particle. The shear-thickening response of the medium is incorporated through a velocity-dependent viscous force of the form g(v) ∼ tan(v). Starting from the Fokker-Planck equations corresponding to the particle's dynamics, we numerically compute the time-dependent joint probability density function f(x,v,t) using a finite-volume upwind scheme. Next, we numerically solve the particle's equations of motion to obtain the steady-state position Ps(x) and velocity Ws(v) distributions and compare them with the marginal distributions obtained from f(x,v,t) at sufficiently large t. The two approaches show excellent agreement. Both Ps(x) and Ws(v) exhibit several intriguing transitions as λ is varied, and they eventually approach Gaussian-like profiles at sufficiently large λ. Our study of the time-dependent position-velocity correlation, ⟨ xv ⟩(t), shows that larger values of λ lead to faster relaxation to the steady state when all other parameters are held constant.
Versions
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BibTeX
@misc{howlader2026distribution,
title = {{Distribution Functions and Moments of Harmonically Trapped Inertial Run-and-Tumble Particles in a Shear-Thickening Medium}},
author = {Subhanker Howlader and Prasenjit Das},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21650},
eprint = {2610.21650},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21650},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Distribution Functions and Moments of Harmonically Trapped Inertial Run-and-Tumble Particles in a Shear-Thickening Medium
AU - Subhanker Howlader
AU - Prasenjit Das
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21650
UR - https://arxiv.org/abs/2610.21650
AB - We study the dynamics of an athermal inertial active particle confined in a harmonic potential and moving through shear-thickening media in one dimension. The activity is modeled using a symmetric dichotomous noise of strength Σ and flipping rate λ, which mimics a run-and-tumble particle. The shear-thickening response of the medium is incorporated through a velocity-dependent viscous force of the form g(v) ∼ tan(v). Starting from the Fokker-Planck equations corresponding to the particle's dynamics, we numerically compute the time-dependent joint probability density function f(x,v,t) using a finite-volume upwind scheme. Next, we numerically solve the particle's equations of motion to obtain the steady-state position P_s(x) and velocity W_s(v) distributions and compare them with the marginal distributions obtained from f(x,v,t) at sufficiently large t. The two approaches show excellent agreement. Both P_s(x) and W_s(v) exhibit several intriguing transitions as λ is varied, and they eventually approach Gaussian-like profiles at sufficiently large λ. Our study of the time-dependent position-velocity correlation, ⟨ xv ⟩(t), shows that larger values of λ lead to faster relaxation to the steady state when all other parameters are held constant.
ER -