ArticlePhysical review. E, Statistical, nonlinear, and soft matter physics2010
Extended narrow escape problem: boundary homogenization-based analysis.
Article in Physical review. E, Statistical, nonlinear, and soft matter physics, 2010. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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Who cites it
3 citing papers in PubMed.
- Experimentally Probing the Effect of Confinement Geometry on Lipid Diffusion.The journal of physical chemistry. B · 2024Article
- Trapping of diffusing particles by striped cylindrical surfaces. Boundary homogenization approach.The Journal of chemical physics · 2015Article
- Diffusion in periodic two-dimensional channels formed by overlapping circles: comparison of analytical and numerical results.The Journal of chemical physics · 2011Article
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2 authors.
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Abstract
Diffusion of particles in confined domains with absorbing spots on the otherwise reflecting boundaries is ubiquitous in nature and technology. Because of nonuniform boundary conditions, the problem of finding the mean first passage time (MFPT) of the particle to one of the spots is extremely complicated. We show how the difficulties can be overcome by means of boundary homogenization when the domain is a circular disk whose boundary contains n nonoverlapping identical absorbing arcs, which may occupy an arbitrary fraction of the boundary. We find the MFPT as a function of the fraction of the boundary occupied by the arcs (i) for n evenly spaced arcs and (ii) for two arcs arbitrarily located on the boundary. As the arc length tends to zero, our approximate solution reduces to the known asymptotic formula for the MFPT rigorously derived in studies devoted of the narrow escape problem.
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