narrow escape

The narrow escape problem is a ubiquitous problem in biology, biophysics and cellular biology.
The mathematical formulation is the following: 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 diverges as the window shrinks, thus rendering the calculation a singular perturbation problem.When escape is even more stringent due to severe geometrical restrictions at the place of escape, the narrow escape problem becomes the dire strait problem.The narrow escape problem was proposed in the context of biology and biophysics by D. Holcman and Z. Schuss, and later on with A.Singer and led to the narrow escape theory in applied mathematics and computational biology.

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