Narrow escape problem
Singular perturbation problem dealing with confinement of Brownian particles / From Wikipedia, the free encyclopedia
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The narrow escape problem[1][2] 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.[3][4][5][6][7][8][9]
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.[10][11]
The narrow escape problem was proposed in the context of biology and biophysics by D. Holcman and Z. Schuss,[12] and later on with A.Singer and led to the narrow escape theory in applied mathematics and computational biology.[13][14][15]