Fokker–Plank System for Movement of Micro-organism Population in Confined Environment - Sorbonne Université
Journal Articles Journal of Statistical Physics Year : 2021

Fokker–Plank System for Movement of Micro-organism Population in Confined Environment

Abstract

We consider self-propelled particles confined between two parallel plates, moving with a constant velocity while their moving direction changes by rotational diffusion. The probability distribution of such microorganisms in confined environment is singular because particles accumulate at the boundaries. This leads us to distinguish between the probability distribution densities in the bulk and in the boundaries. They satisfy a degenerate Fokker-Planck system and we propose boundary conditions that take into account the switching between free-moving and boundary-contacting particles. Relative entropy property, a priori estimates and the convergence to an unique steady state are established. The steady states of both the PDE and individual based stochastic models are compared numerically.
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Dates and versions

hal-03278860 , version 1 (06-07-2021)

Identifiers

Cite

Jingyi Fu, Benoît Perthame, Min Tang. Fokker–Plank System for Movement of Micro-organism Population in Confined Environment. Journal of Statistical Physics, 2021, 184 (1), ⟨10.1007/s10955-021-02760-y⟩. ⟨hal-03278860⟩
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