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Narrow escape problem : ウィキペディア英語版 | Narrow escape problem
The narrow escape problem is a ubiquitous problem in biology, biophysics and cellular biology. The 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. == Formulation == The motion of a particle is described by the Smoluchowski limit of the Langevin equation: : where is the diffusion coefficient of the particle, is the friction coefficient per unit of mass, the force per unit of mass, and is a Brownian motion.
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