Mean first-passage time to a small absorbing target in an elongated planar domain
Denis S. Grebenkov, Alexei T. Skvortsov
Abstract
Abstract We derive an approximate but fully explicit formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape in a general elongated domain in the plane. Our approximation combines conformal mapping, boundary homogenisation, and Fick–Jacobs equation to express the MFPT in terms of diffusivity and geometric parameters. A systematic comparison with a numerical solution of the original problem validates its accuracy when the starting point is not too close to the target. This is a practical tool for a rapid estimation of the MFPT for various applications in chemical physics and biology.
Topics & Concepts
PhysicsFirst-hitting-time modelConformal mapThermal diffusivityDomain (mathematical analysis)PlanarBoundary (topology)Plane (geometry)Mathematical analysisBoundary value problemPoint (geometry)Statistical physicsGeometryQuantum mechanicsMathematicsComputer scienceComputer graphics (images)Diffusion and Search DynamicsDNA and Nucleic Acid ChemistryBacterial Genetics and Biotechnology