A narrow escape from splenectomy.

The Narrow Escape Problem

The narrow escape problem in diffusion theory is to calculate the mean first passage time of a diffusion process to a small target on the reflecting boundary of a bounded domain. The problem is equivalent to solving the mixed Dirichlet–Neumann boundary value problem for the Poisson equation with small Dirichlet and large Neumann parts. The mixed boundary value problem, which goes back to Lord R...

Narrow Escape, Part I

A Brownian particle with diffusion coefficient D is confined to a bounded domain by a reflecting boundary, except for a small absorbing window ∂ a . The mean time to absorption diverges as the window shrinks, thus rendering the calculation of the mean escape time a singular perturbation problem. In the three-dimensional case, we construct an asymptotic approximation when the window is an ellips...

The narrow escape problem revisited

The time needed for a particle to exit a confining domain through a small window, called the narrow escape time (NET), is a limiting factor of various processes, such as some biochemical reactions in cells. Obtaining an estimate of the mean NET for a given geometric environment is therefore a requisite step to quantify the reaction rate constant of such processes, which has raised a growing int...

4 Narrow Escape , Part I

A Brownian particle with diffusion coefficientD is confined to a bounded domain of volume V in R by a reflecting boundary, except for a small absorbing window. The mean time to absorption diverges as the window shrinks, thus rendering the calculation of the mean escape time a singular perturbation problem. We construct an asymptotic approximation for the case of an elliptical window of large se...

On the narrow escape problem