Stochastic resetting on comb-like structures

TL;DR

This paper investigates how stochastic resetting affects diffusion on a 3D comb structure, revealing diverse dynamics and transport behaviors depending on the resetting mechanism, including transport suppression and enhancement in different directions.

Contribution

It introduces and analyzes three distinct resetting mechanisms on a 3D comb, providing new insights into their effects on diffusion dynamics and stationary states.

Findings

Global resetting breaks transport in all directions.

Resetting to the backbone enhances main axis transport.

Resetting to fingers increases transport in backbone and main fingers.

Abstract

We study a diffusion process on a three-dimensional comb under stochastic resetting. We consider three different types of resetting: global resetting from any point in the comb to the initial position, resetting from a finger to the corresponding backbone and resetting from secondary fingers to the main fingers. The transient dynamics along the backbone in all three cases is different due to the different resetting mechanisms, finding a wide range of dynamics for the mean squared displacement. For the particular geometry studied herein, we compute the stationary solution and the mean square displacement and find that the global resetting breaks the transport in the three directions. Regarding the resetting to the backbone, the transport is broken in two directions but it is enhanced in the main axis. Finally, the resetting to the fingers enhances the transport in the backbone and the main fingers but reaches a steady value for the mean squared displacement in the secondary fingers.