Matched asymptotic analysis to solve the narrow escape problem in a domain with a long neck
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 f...
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| Published in | Journal of physics. A, Mathematical and theoretical Vol. 47; no. 50; pp. 505202 - 505219 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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IOP Publishing
19.12.2014
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Xiaofei Li |
| Author_xml | – sequence: 1 surname: Xiaofei Li fullname: Xiaofei Li email: xiaofeili@inha.edu organization: Department of Mathematics , Inha University, Incheon 402-751, Korea |
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| Cites_doi | 10.1063/1.2746840 10.1137/090775257 10.1137/090752511 10.1063/1.3160546 10.1016/j.ceca.2005.01.015 10.1088/1751-8113/41/15/155001 10.1007/s10955-004-5712-8 10.1103/PhysRevE.76.021922 10.1007/s10955-005-8026-6 10.1007/s10955-005-8028-4 10.1016/j.matpur.2011.09.011 10.1137/100782620 10.1073/pnas.0706599104 10.1186/2190-8567-1-10 10.1529/biophysj.103.035972 10.1103/PhysRevE.78.051111 10.1016/j.physleta.2008.02.076 10.1063/1.3081633 10.1016/j.conb.2012.03.003 10.1016/j.crma.2010.11.024 |
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| SubjectTerms | asymptotic expansion calcium diffusion dendritic spine mean first passage time mixed boundary value problem narrow escape problem Neumann-Robin boundary model |
| Title | Matched asymptotic analysis to solve the narrow escape problem in a domain with a long neck |
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