The interface scattering law for run-and-tumble kinetic models
Abstract
For microorganisms with run-and-tumble motility, kinetic models provide a well-established description of transport in smoothly varying environments. Sharp signal changes, however, can induce asymmetric interface responses. A motivating example is the response to dark-light boundaries: cells moving into the light largely maintain their direction, whereas those entering the dark are effectively scattered back. Through an interface-layer analysis of pathway-based kinetic equations, we formally derive effective interface conditions for the limiting run-and-tumble model. These velocity-nonlocal conditions capture non-adiabatic scattering near signal discontinuities, linking intracellular sensory dynamics to transport across sharp environmental boundaries. For a two-velocity model, they reduce to an explicit transmission matrix. We assess the interface law numerically using biologically motivated parameters for E. coli chemotaxis.
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BibTeX
@misc{lei2026interface,
title = {{The interface scattering law for run-and-tumble kinetic models}},
author = {Shicong Lei and Jiangyan Liang and Weiran Sun and Min Tang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07409},
eprint = {2611.07409},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07409},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The interface scattering law for run-and-tumble kinetic models
AU - Shicong Lei
AU - Jiangyan Liang
AU - Weiran Sun
AU - Min Tang
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07409
UR - https://arxiv.org/abs/2611.07409
AB - For microorganisms with run-and-tumble motility, kinetic models provide a well-established description of transport in smoothly varying environments. Sharp signal changes, however, can induce asymmetric interface responses. A motivating example is the response to dark-light boundaries: cells moving into the light largely maintain their direction, whereas those entering the dark are effectively scattered back. Through an interface-layer analysis of pathway-based kinetic equations, we formally derive effective interface conditions for the limiting run-and-tumble model. These velocity-nonlocal conditions capture non-adiabatic scattering near signal discontinuities, linking intracellular sensory dynamics to transport across sharp environmental boundaries. For a two-velocity model, they reduce to an explicit transmission matrix. We assess the interface law numerically using biologically motivated parameters for E. coli chemotaxis.
ER -