Crossover from ballistic transport to normal diffusion: a kinetic view
Analysis of PDEs
2025-01-07 v1
Abstract
The crossover between dispersion patterns has been frequently observed in various systems. Inspired by the pathway-based kinetic model for E. coli chemotaxis that accounts for the intracellular adaptation process and noise, we propose a kinetic model that can exhibit a crossover from ballistic transport to normal diffusion at the population level. At the particle level, this framework aligns with a stochastic individual-based model. Using numerical simulations and rigorous asymptotic analysis, we demonstrate this crossover both analytically and computationally. Notably, under suitable scaling, the model reveals two distinct limits in which the macroscopic densities exhibit either ballistic transport or normal diffusion.
Cite
@article{arxiv.2501.02240,
title = {Crossover from ballistic transport to normal diffusion: a kinetic view},
author = {Zhe Xue and Weiran Sun and Zhennan Zhou and Min Tang},
journal= {arXiv preprint arXiv:2501.02240},
year = {2025}
}