Diffusion with Resetting Inside a Circle

Abstract

We study the Brownian motion of a particle in a bounded circular 2-dimensional domain, in search for a stationary target on the boundary of the domain. The process switches between two modes: one where it performs a two-dimensional diffusion inside the circle and one where it travels along the one-dimensional boundary. During the diffusion, the Brownian particle resets to its initial position with a constant rate $r$. The Fokker-Planck formalism allows us to calculate the mean time to absorption (MTA) as well as the optimal resetting rate for which the MTA is minimized. From the derived analytical results the parameter regions where resetting reduces the search time can be specified. We also provide a numerical method for the verification of our results.

arXiv comment11 pages, 10 figures

References in corpus (27)

• Diffusion with Stochastic Resetting
• Intermittent search strategies
• Diffusion with Optimal Resetting
• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• Diffusion in a potential landscape with stochastic resetting
• Diffusion with resetting in arbitrary spatial dimension
• Random walks with preferential relocations to places visited in the past and their application to biology
• Fluctuating interfaces subject to stochastic resetting
• First-passage times for random walks in bounded domains
• Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics
• Boosting search by rare events
• Mean first-passage times of non-Markovian random walkers in confinement
• Stochastic thermodynamics of resetting
• Optimal reaction time for surface-mediated diffusion
• Stochastic multiplicative processes with reset events
• Monotonous continuous-time random walks with drift and stochastic reset events
• Restart could optimize the probability of success in a Bernoulli trial
• Searching fast for a target on a DNA without falling to traps
• Phase transitions in optimal search times: how random walkers should combine resetting and flight scales
• Effect of Partial Absorption on Diffusion with Resetting
• Long time scaling behaviour for diffusion with resetting and memory
• Mean first passage time of active Brownian particle in one dimension
• Interacting Brownian Motion with Resetting
• Phase transitions in large deviations of reset processes
• Resetting of fluctuating interfaces at power-law times
• Optimal potentials for diffusive search strategies

Cited by in corpus (32)

• Stochastic Resetting and Applications
• First passage under stochastic resetting in an interval
• Stochastic resetting: A (very) brief review
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Random walks on networks with stochastic resetting
• First passage under restart with branching
• Symmetric Exclusion Process under Stochastic Resetting
• Diffusion with stochastic resetting is invariant to return speed
• Run-and-Tumble particles in Two-dimensions under Stochastic Resetting
• Invariants of motion with stochastic resetting and space-time coupled returns
• Stochastic resetting in underdamped Brownian motion
• Stochastic resetting in interacting particle systems: A review
• Stochastic resetting by a random amplitude
• First passage in the presence of stochastic resetting and a potential barrier
• Comparison of two models of tethered motion
• Diffusion with Local Resetting and Exclusion
• Synchronization in the Kuramoto model in presence of stochastic resetting
• Controlling particle currents with evaporation and resetting from an interval
• Discrete space-time resetting model: Application to first-passage and transmission statistics
• First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry
• Robust random search with scale-free stochastic resetting
• Active Brownian Particles in a Circular Disk with an Absorbing Boundary
• Zero-current Nonequilibrium State in Symmetric Exclusion Process with Dichotomous Stochastic Resetting
• Non-linear diffusion with stochastic resetting
• Role of dimensions in first passage of a diffusing particle under stochastic resetting and attractive bias
• Biased random walk on random networks in presence of stochastic resetting: Exact results
• First passage in discrete-time absorbing Markov chains under stochastic resetting
• Comparing the roles of time overhead and spatial dimensions on optimal resetting rate vanishing transitions, in Brownian processes with potential bias and stochastic resetting
• Random resetting in search problems
• Unified approach to reset processes and application to coupling between process and reset
• Ising Model with Power Law Resetting
• Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Finite Rectangular Domain with Absorbing Boundary Conditions