First-passage times to anisotropic partially reactive targets

Adrien Chaigneau (1) , Denis S Grebenkov (1)

1 LPMC - Laboratoire de physique de la matière condensée

We investigate restricted diffusion in a bounded domain towards a small partially reactive target in three-and higher-dimensional spaces. We propose a simple explicit approximation for the principal eigenvalue of the Laplace operator with mixed Robin-Neumann boundary conditions. This approximation involves the harmonic capacity and the surface area of the target, the volume of the confining domain, the diffusion coefficient and the reactivity. The accuracy of the approximation is checked by using a finite-elements method. The proposed approximation determines also the mean first-reaction time, the long-time decay of the survival probability, and the overall reaction rate on that target. We identify the relevant length scale of the target, which determines its trapping capacity, and investigate its relation to the target shape. In particular, we study the effect of target anisotropy on the principal eigenvalue by computing the harmonic capacity of prolate and oblate spheroids in various space dimensions. Some implications of these results in chemical physics and biophysics are briefly discussed.

Mots clés: restricted diffusion; target; sink; spheroids; first-passage time; principal eigenvalue; mixed boundary condition; capacity; Laplace operator; trapping constant

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]

Adrien Chaigneau, Denis S Grebenkov. First-passage times to anisotropic partially reactive targets. Physical Review E , 2022, 105 (5), pp.054146. ⟨10.1103/PhysRevE.105.054146⟩. ⟨hal-03805574⟩