The Narrow Escape Problem--A Short Review of Recent Results

摘要: The narrow escape problem in diffusion theory, which goes back to Lord Rayleigh, is calculate the mean first passage time, also called time (NET), of a Brownian particle small absorbing window on otherwise reflecting boundary bounded domain. renewed interest NET due its relevance molecular biology and biophysics. often represents target cellular membrane, such as protein channel, for ions, receptor neurotransmitter molecules neuronal synapse, neck spine, calcium so on. leading order singularity Neumann function regular domain strongly depends geometric properties boundary. It can give smaller contribution than part absorption flux through when it located near cusp. We review here recent results dependence thus reveal geometrical features that modulate flux. This indicates possible way code information physiologically.