Brownian motion diverges as the window shrinks, thus rendering the calculation a singular perturbation problem. Brownian motion Brownian motion or pedesis (from "leaping") is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the fast-moving molecules in the fluid. This pattern of motion typically alternates random fluctuations in a particle's position inside a fluid sub-domain with a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such fluid there exists no
Brownian motion "x", 1 ≤ "i" ≤ "m", is given by ½Δ, where Δ is the Laplace–Beltrami operator given in local coordinates by where ["g"] = ["g"] in the sense of the inverse of a square matrix. The narrow escape problem is a ubiquitous problem in biology, biophysics and cellular biology which has the following formulation: a Brownian particle (ion, molecule, or protein) is confined to a bounded domain (a compartment or a cell) by a reflecting boundary, except for a small window through which it can escape. The narrow escape problem is that of calculating the mean escape time. This time