Residence times and other functionals of reflected Brownian motion

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 76, Issue 4, 2007, Pages

  Grebenkov, D S ^a  

^a LABORATOIRE DE PHYSIQUE DE LA MATIÈRE CONDENSÉE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; FOURIER TRANSFORMS; FUNCTIONAL ANALYSIS; LAPLACE TRANSFORMS; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING;

COMBINATORIAL RELATIONS; LAPLACE OPERATOR EIGENBASIS; RESIDENCE TIMES;

BROWNIAN MOVEMENT;

EID: 35649003831     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.041139     Document Type: Article

References (52)

1. G. H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
2. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, England, 2001).
3. K. Allinger and A. Blumen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.442347 75, 2762 (1981).
4. A. Blumen and G. Zumofen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.442086 75, 892 (1981)
5. A. Blumen and G. Zumofen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.443410 76, 3713 (1982).
6. A. Szabo, J. Phys. Chem. JPCHAX 0022-3654 10.1021/j100356a011 93, 6929 (1989).
7. A. H. Gandjbakhche and G. H. Weiss, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.6958 61, 6958 (2000).
8. M. Kac, Trans. Am. Math. Soc. TAMTAM 0002-9947 10.1086/257878 65, 1 (1949).
9. M. Kac, in Proceedings of the Second Berkeley Symposium on Mathematical and Statistical Problems, edited by, J. Neyman, (University of California Press, Berkeley, 1951), pp. 189-215.
10. D. A. Darling and M. Kac, Trans. Am. Math. Soc. TAMTAM 0002-9947 10.2307/1992825 84, 444 (1957).
11. N. Agmon, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.448113 81, 3644 (1984).
12. A. M. Berezhkovskii, V. Zaloj, and N. Agmon, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.57.3937 57, 3937 (1998).
13. A. Dhar and S. N. Majumdar, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.6413 59, 6413 (1999).
14. L. Dagdug, A. M. Berezhkovskii, and G. H. Weiss, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.012901 66, 012901 (2002).
15. S. Blanco and R. Fournier, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00208-x 61, 168 (2003).
16. A. Mazzolo, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2004-10216-4 68, 350 (2004).
17. J. D. Noh and H. Rieger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.118701 92, 118701 (2004).
18. O. Benichou, M. Coppey, J. Klafter, M. Moreau, and G. Oshanin, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/33/001 38, 7205 (2005).
19. S. Majumdar, Curr. Sci. 89, 2076 (2005). 0011-3891
20. E. Barkai, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-006-9109-8 123, 883 (2006).
21. K. R. Brownstein and C. E. Tarr, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.19.2446 19 (6), 2446 (1979).
22. P. T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy (Clarendon, Oxford, 1991).
23. G. F. Froment and K. B. Bischoff, Chemical Reactor Analysis and Design (John Wiley & Sons, New York, 1990).
24. J. M. Thomas and W. J. Thomas, Principles and Practice of Heterogeneous Chemistry (VCH, Weinheim, 1997).
25. B. Sapoval, in Fractals and Disordered Systems, edited by, A. Bunde, and, S. Havlin, (Springer, Berlin, 1996), pp. 233-261.
26. E. R. Weibel, The Pathway for Oxygen. Structure and Function in the Mammalian Respiratory System (Harvard University Press, Cambridge, MA, 1984).
27. M. Felici, M. Filoche, C. Straus, T. Similowski, and B. Sapoval, Respir. Physiol. Neurobiol. 145, 279 (2005). 1569-9048
28. S. Condamin, O. Bénichou, and M. Moreau, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.260601 95, 260601 (2005)
29. S. Condamin, O. Bénichou, and M. Moreau, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.016127 72, 016127 (2005)
30. S. Condamin, O. Bénichou, and M. Moreau, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.021111 75, 021111 (2007).
31. O. Bénichou, M. Coppey, M. Moreau, P. H. Suet, and R. Voituriez, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2005-10001-y 70, 42 (2005).
32. O. V. Bychuk and B. O'Shaughnessy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.1795 74, 1795 (1995).
33. S. Stapf, R. Kimmich, and R.-O. Seitter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.2855 75, 2855 (1995).
34. P. E. Levitz, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/17/49/004 17, S4059 (2005).
35. P. Levitz, D. S. Grebenkov, M. Zinsmeister, K. Kolwankar, and B. Sapoval, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.180601 96, 180601 (2006).
36. M. Freidlin, Functional Integration and Partial Differential Equations (Princeton University Press, Princeton, NJ, 1985).
37. D. S. Grebenkov, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.79. 1077 79, 1077 (2007).
38. H. C. Torrey, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.104.563 104, 563 (1956).
39. A. Caprihan, L. Z. Wang, and E. Fukushima, J. Magn. Reson., Ser. A JMRAE2 1064-1858 10.1006/jmra.1996.0013 118, 94 (1996).
40. P. T. Callaghan, J. Magn. Reson. JMARF3 1090-7807 10.1006/jmre.1997.1233 129, 74 (1997).
41. A. V. Barzykin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58.14171 58, 14171 (1998)
42. A. V. Barzykin, J. Magn. Reson. JMARF3 1090-7807 10.1006/jmre.1999.1778 139, 342 (1999).
43. S. Axelrod and P. N. Sen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1356010 114, 6878 (2001).
44. H. Wilf, Generating Functionology, 2nd ed. (Academic, New York, 1993).
45. D. S. Grebenkov, in Focus on Probability Theory, edited by, L. R. Velle, (Nova Science Publishers, New York, 2006), pp. 135-169.
46. D. S. Grebenkov, Fractals FRACEG 0218-348X 10.1142/S0218348X06003209 14, 231 (2006).
47. B. Sapoval, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.3314 73, 3314 (1994).
48. D. S. Grebenkov, M. Filoche, and B. Sapoval, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.021103 73, 021103 (2006).
49. D. S. Grebenkov, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2539073 126, 104706 (2007).
50. D. S. Grebenkov, Diff. Fundam. 5, 1 (2007).
51. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Clarendon, Oxford, 1959).
52. J. Crank, The Mathematics of Diffusion, 2nd ed. (Clarendon, Oxford, 1975).