Individual-based models for bacterial chemotaxis in the diffusion asymptoticsReport as inadecuate

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1 MICMAC - Methods and engineering of multiscale computing from atom to continuum Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech 2 Inria - Institut National de Recherche en Informatique et en Automatique 3 MATHERIALS - MATHematics for MatERIALS CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris 4 Department of Computer Science

Abstract : We discuss velocity-jump models for chemotaxis of bacteria with an internal state that allows the velocity jump rate to depend on the memory of the chemoattractant concentration along their path of motion. Using probabilistic techniques, we provide a pathwise result that shows that the considered process converges to an advection-diffusion process in the long-time diffusion limit. We also re-prove using the same approach that the same limiting equation arises for a related, simpler process with direct sensing of the chemoattractant gradient. Additionally, we propose a time discretization technique that retains these diffusion limits exactly, i.e., without error that depends on the time discretization. In the companion paper \cite{variance}, these results are used to construct a coupling technique that allows numerical simulation of the process with internal state with asymptotic variance reduction, in the sense that the variance vanishes in the diffusion limit.

Author: Mathias Rousset - Giovanni Samaey -



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