Activation through a narrow opening

SIAM Journal on Applied Mathematics

Volumn 68, Issue 1, 2007, Pages 98-108

  Singer, A ^a   Schuss, Z ^b  

^a YALE UNIVERSITY   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Exit problem; Mixed boundary value problem; Narrow escape; Stochastic differential equations

Indexed keywords

EXIT PROBLEM; MIXED BOUNDARY VALUE PROBLEMS; NARROW ESCAPE;

BOUNDARY VALUE PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; STOCHASTIC CONTROL SYSTEMS;

BROWNIAN MOVEMENT;

EID: 41849096685     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/060663477     Document Type: Article

References (24)

1. J. W. S. BARON RAYLEIGH, The Theory of Sound, Vol. 2, 2nd ed., Dover, New York, 1945.
2. W. D. COLLINS, On some dual series equations and their application to electrostatic problems for spheroidal caps, Proc. Cambridge Philos. Soc., 57 (1961), pp. 367-384.
3. W. D. COLLINS, Note on an electrified circular disk situated inside an earthed coaxial infinite hollow cylinder, Proc. Cambridge Philos. Soc., 57 (1961), pp. 623-627.
4. C. W. GARDINER, Handbook of Stochastic Methods, 2nd ed., Springer, New York, 1985.
5. I. V. GRIGORIEV, Y. A. MAKHNOVSKII, A. M. BEREZHKOVSKII, AND V. Y. ZITSERMAN, Kinetics of escape through a small hole, J. Chem. Phys., 116 (2002), pp. 9574-9577.
6. P. HÄNNGI, P. TALKNER, AND M. BORKOVEC, Reaction-rate theory: Fifty years after Kramers, Rev. Modern Phys., 62 (1990), pp. 251-341.
7. B. HILLE, Ionic Channels of Excitable Membranes, 2nd ed., Sinauer, Sunderland, MA, 1992.
8. D. HOLCMAN AND Z. SCHUSS, Escape through a small opening: Receptor trafficking in a synaptic membrane, J. Statist. Phys., 117 (2004), pp. 975-1014.
9. D. HOLCMAN AND Z. SCHUSS, Stochastic chemical reactions in microdomains, J. Chem. Phys., 122 (2005), 114710.
10. J. D. JACKSON, Classical Electrodynamics, 2nd ed., Wiley, New York, 1975.
11. T. KOLOKOLNIKOV, M. TITCOMBE, AND M. J. WARD, Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps, European J. Appl. Math., 16 (2005), pp. 161-200.
12. H. KRAMERS, Brownian motion in a field of force, Physica, 7 (1940), pp. 284-304.
13. A. I. LUR'E, Three-Dimensional Problems of the Theory of Elasticity, Interscience, New York, 1964.
14. B. J. MATKOWSKY AND Z. SCHUSS, Eigenvalues of the Fokker-Planck operator and the approach to equilibrium in potential fields, SIAM J. Appl. Math., 40 (1981), pp. 242-254.
15. B. J. MATKOWSKY, Z. SCHUSS, AND C. TIER, Uniform expansion of the transition rate in Kramers' problem, J. Statist. Phys., 35 (1984), pp. 443-456.
16. Z. SCHUSS, Theory and Applications of Stochastic Differential Equations, Wiley Ser. Probab. Stat., Wiley, New York, 1980.
17. A. SINGER, Z. SCHUSS, D. HOLCMAN, AND R. S. EISENBERG, Narrow escape, Part I, J. Stat. Phys., 122 (2006), pp. 437-463.
18. A. SINGER, Z. SCHUSS, AND D. HOLCMAN, Narrow escape, Part II: The circular disk, J. Stat. Phys., 122 (2006), pp. 465-489.
19. A. SINGER, Z. SCHUSS, AND D. HOLCMAN, Narrow escape, Part III: Non-smooth domains and Riemann surfaces, J. Stat. Phys., 122 (2006), pp. 491-509.
20. N. G. VAN KAMPEN, Stochastic Processes in Physics and Chemistry, 3rd ed., North-Holland, Amsterdam, 1992.
21. H. L. F. VON HELMHOLTZ, Theorie der Luftschwingungen in Röhren mit offenen Enden, Crelle, 57 (1860), pp. 1-72.
22. M. J. WARD AND J. B. KELLER, Strong localized perturbations of eigenvalue problems, SIAM J. Appl. Math., 53 (1993), pp. 770-798.
23. M. J. WARD, W. D. HENSHAW, AND J. B. KELLER, Summing logarithmic expansions for singularly perturbed eigenvalue problems, SIAM J. Appl. Math., 53 (1993), pp. 799-828.
24. M. J. WARD AND E. VAN DE VELDE, The onset of thermal runaway in partially insulated or cooled reactors, IMA J. Appl. Math., 48 (1992), pp. 53-85.