Critical volume in diffusion through random media.

Abstract

It has been found, very generally, that there is a critical volume of the diffusion space, ${\mathrm{\ensuremath{\Omega}}}_{\mathit{c}}$, for a class of diffusions in random media, characterized by V(r) with a zero mean. If the size of the diffusion space is bigger than ${\mathrm{\ensuremath{\Omega}}}_{\mathit{c}}$, the total population increases with time. Otherwise, the total population decreases with time and will eventually vanish. An estimation of ${\mathrm{\ensuremath{\Omega}}}_{\mathit{c}}$ is obtained by a variation method.