Diffusion–Advection Equations on a Comb: Resetting and Random Search

Abstract

This review addresses issues of various drift–diffusion and inhomogeneous advection problems with and without resetting on comblike structures. Both a Brownian diffusion search with drift and an inhomogeneous advection search on the comb structures are analyzed. The analytical results are verified by numerical simulations in terms of coupled Langevin equations for the comb structure. The subordination approach is one of the main technical methods used here, and we demonstrated how it can be effective in the study of various random search problems with and without resetting.

Keywords

• diffusion–advection equation
• stochastic resetting
• comb structure
• random search
• first arrival time density
• efficiency