Survival of a diffusing particle in an expanding cage
Abstract
We consider a Brownian particle, with diffusion constant D, moving inside an expanding d-dimensional sphere whose surface is an absorbing boundary for the particle. The sphere has initial radius L0 and expands at a constant rate c. We calculate the joint probability density, p(r,t|r0), that the particle survives until time t, and is at a distance r from the centre of the sphere, given that it started at a distance r0 from the centre.
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