Asymptotic analysis of the concentration difference due to diffusive fluxes across narrow windows

Speaker: Frédéric Paquin-Lefebvre

Date: Wed, Feb 9, 2022

Location: PIMS, University of British Columbia, Zoom, Online

Conference: Mathematical Biology Seminar

Subject: Mathematics, Mathematical Biology

Class: Scientific


How far inside a domain does a flux of Brownian particles perturb a background concentration when particles can escape through a neighboring window? What motivates this question is the dynamics of ions entering and exiting nanoregions of excitable cells through ionic membrane channels. Here this is explored using a simple diffusion model consisting of the Laplace's equation in a domain whose boundary is everywhere reflective except for a collection of narrow circular windows, where either flux or absorbing boundary conditions are prescribed. We derive asymptotic formulas revealing the role of the influx amplitude, the diffusion properties, and the geometry, on the concentration difference. Lastly, a length scale to estimate how deep inside a domain a local diffusion current can spread is introduced. This is joint work with David Holcman at ENS.