Linear Boltzmann dynamics in a strip with large reflective obstacles: stationary state and residence time

TL;DR

This paper investigates how large reflective obstacles within a rectangular strip influence particle diffusion and residence time under linear Boltzmann dynamics, revealing non-monotonic effects based on obstacle size and placement.

Contribution

It introduces a detailed analysis of residence time behavior in a strip with reflective obstacles, highlighting non-intuitive effects on particle crossing times.

Findings

Residence time is non-monotonic with obstacle size and position.

Obstacles can reduce the time particles spend crossing the strip.

The study provides insights into diffusion processes with reflective barriers.

Abstract

The presence of obstacles modify the way in which particles diffuse. In cells, for instance, it is observed that, due to the presence of macromolecules playing the role of obstacles, the mean square displacement ofbiomolecules scales as a power law with exponent smaller than one. On the other hand, different situations in grain and pedestrian dynamics in which the presence of an obstacle accelerate the dynamics are known. We focus on the time, called residence time, needed by particles to cross a strip assuming that the dynamics inside the strip follows the linear Boltzmann dynamics. We find that the residence time is not monotonic with the sizeand the location of the obstacles, since the obstacle can force those particles that eventually cross the strip to spend a smaller time in the strip itself. We focus on the case of a rectangular strip with two open sides and two reflective sides and we consider reflective obstaclea into the strip.