Matched asymptotic analysis to solve the narrow escape problem in a domain with a long neck

• Published in: Journal of physics. A, Mathematical and theoretical Vol. 47; no. 50; pp. 505202 - 505219
• Main Author: Xiaofei Li
• Format: Journal Article
• Language: English
• Published: IOP Publishing 19.12.2014
• Subjects: asymptotic expansion; calcium diffusion; dendritic spine; mean first passage time; mixed boundary value problem; narrow escape problem; Neumann-Robin boundary model
• ISSN: 1751-8113; 1751-8121
• DOI: 10.1088/1751-8113/47/50/505202

In this study, we mainly consider the narrow escape problem (NEP) in a two-dimensional domain with a long neck, which is the two-dimensional analogue of a dendritic spine geometry. The NEP requires the computation of the mean escape time of a Brownian particle starting from the head until it exits from the end of the neck, where the particle is absorbed. We divide the domain into the neck part n and the head part h, with the common boundary . The escape time in h can be considered to be the time from the head to the end of the neck, while the escape time in n can be considered to be the time from the neck to the end of the neck. We compute the two exit times separately and match them by considering some boundary value problem with an impedance boundary condition on , which we refer to as the Neumann-Robin boundary model.