Ornstein-Uhlenbeck Process on Three-Dimensional Comb under Stochastic Resetting

The Ornstein-Uhlenbeck (O-U) process with resetting is considered as the anomalous transport taking place on a three-dimensional comb. The three-dimensional comb is a comb inside a comb structure, consisting of backbones and fingers in the following geometrical correspondence x-backbone?y-fingers-backbone ?z-fingers. Realisation of the O-U process on the three-dimensional comb leads to anomalous (non-Markovian) diffusion. This specific anomalous transport in the presence of resets results in non-equilibrium stationary states. Explicit analytical expressions for the mean values and the mean squared displacements along all three directions of the comb are obtained and verified numerically. The marginal probability density functions for each direction are obtained numerically by Monte Carlo simulation of a random transport described by a system of coupled Langevin equations for the comb geometry.

Automated summary

This study investigates anomalous transport in a three-dimensional comb structure using the Ornstein-Uhlenbeck (O-U) process with resetting. The three-dimensional comb structure consists of backbones and fingers, with x-axis corresponding to the backbones and y-axis and z-axis corresponding to the fingers. Implementation of the O-U process on the comb structure leads to anomalous (non-Markovian) diffusion. This specific anomalous transport with resetting results in non-equilibrium stationary states. Analytical expressions for the mean values and mean squared displacements along all three directions of the comb are obtained and numerically verified. The marginal probability density functions for each direction are obtained through Monte Carlo simulation of a random transport described by a system of coupled Langevin equations for the comb geometry.