Details

Autor(en) / Beteiligte

• Bénichou, O.
• Grebenkov, D. S.
• Hillairet, L.
• Phun, L.
• Voituriez, R.
• Zinsmeister, M.

Titel

Mean exit time for surface-mediated diffusion: spectral analysis and asymptotic behavior

Ist Teil von

• Analysis and mathematical physics, 2015-12, Vol.5 (4), p.321-362

Ort / Verlag

Basel: Springer Basel

Erscheinungsjahr

2015

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We consider a model of surface-mediated diffusion with alternating phases of bulk and surface diffusion for two geometries: the disk and rectangles. We develop a spectral approach to derive an exact formula for the mean exit time of a particle through a hole on the boundary. The spectral representation of the mean exit time through the eigenvalues of an appropriate self-adjoint operator is particularly well-suited to investigate the asymptotic behavior in the limit of large desorption rate λ . For a point-like target, we show that the mean exit time diverges as λ . For extended targets, we establish the asymptotic approach to a finite limit. In both cases, the mean exit time is shown to asymptotically increase as λ tends to infinity. That implies that the pure bulk diffusion is never an optimal search strategy. We also investigate the influence of rectangle elongation onto the mean exit time, in particular, the dependence of the critical ratio of bulk and surface diffusion coefficients on the rectangle aspect ratio. We show that the intermittent search strategy can significantly outperform pure surface diffusion for elongated rectangles.