Mean first-passage time to a small absorbing target in three-dimensional elongated domains

Denis S Grebenkov (1) , Alexei Skvortsov

1 LPMC - Laboratoire de physique de la matière condensée

We derive an approximate formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape inside an elongated domain of a slowly varying axisymmetric profile. For this purpose, the original Poisson equation in three dimensions is reduced an effective one-dimensional problem on an interval with a semi-permeable semi-absorbing membrane. The approximate formula captures correctly the dependence of the MFPT on the distance to the target, the radial profile of the domain, and the size and the shape of the target. This approximation is validated by Monte Carlo simulations.

Mots clés: numbers: 02.50.-r; 05.40.-a; 02.70.Rr; 05.10.Gg Mean first-passage time; homogenisation; reactivity; elongated domains; anisotropy

Domaines: Physique mathématique [math-ph]; Matière Condensée [cond-mat]; Mécanique statistique [cond-mat.stat-mech]; Biophysique [physics.bio-ph]; Chimie-Physique [physics.chem-ph]; Physique Numérique [physics.comp-ph]; Analyse de données, Statistiques et Probabilités [physics.data-an]

Denis S Grebenkov, Alexei Skvortsov. Mean first-passage time to a small absorbing target in three-dimensional elongated domains. Physical Review E , 2022, 105 (5), pp.054107. ⟨10.1103/PhysRevE.105.054107⟩. ⟨hal-03805573⟩