Felix Faisant 1 Benjamin Besga 1 Artyom Petrosyan 1 Sergio Ciliberto 1 Satya N. Majumdar 2 Satya Majumdar 2
Felix Faisant, Benjamin Besga, Artyom Petrosyan, Sergio Ciliberto, Satya N. Majumdar, et al.. Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: experiments, theory and numerical tests. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2021, 2021 (11), pp.113203. ⟨10.1088/1742-5468/ac2cc7⟩. ⟨hal-03480548⟩
Abstract We experimentally, numerically and theoretically study the optimal mean time needed by a Brownian particle, freely diffusing either in one or two dimensions, to reach, within a tolerance radius R tol , a target at a distance L from an initial position in the presence of resetting. The reset position is Gaussian distributed with width σ . We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full first-passage probability distribution that displays spectacular spikes immediately after each resetting time for close targets. We study the optimal mean first-passage time as a function of the resetting period/rate for different target distances (values of the ratios b = L / σ ) and target size ( a = R tol / L ). We find an interesting phase transition at a critical value of b , both in one and two dimensions. The details of the calculations as well as the experimental setup and limitations are discussed.
- 1. Phys-ENS – Laboratoire de Physique de l’ENS Lyon
- 2. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques