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Narrow escape problem
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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:
: dX_t=\sqrt \, dB_t+\fracF(x)dt
where D is the diffusion coefficient of the particle, \gamma is the friction coefficient
per unit of mass, F(x) the force per unit of mass, and B_t is a Brownian motion.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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