Order statistics of Rosenstock's trapping problem in disordered media

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

Volumn 68, Issue 3 2, 2003, Pages 361341-361349

  Yuste, S B ^a   Acedo, L ^a  

^a UNIVERSITY OF EXTREMADURA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

AGGLOMERATION; APPROXIMATION THEORY; COLLOIDS; CRYSTAL LATTICES; DIFFUSION; FRACTALS; PERCOLATION (SOLID STATE); PROBLEM SOLVING; STATISTICAL METHODS;

ORDER STATISTICS; RANDOM WALK THEORY;

RANDOM PROCESSES;

EID: 0242579527     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (57)

1. J.R. Beeler, Phys. Rev. 134, 1396 (1964); E.W. Montroll, J. Phys. Soc. Jpn. Suppl. 26, 6 (1969); E.W. Montroll, J. Math. Phys. 10, 753 (1969); J.K. Anlauf, Phys. Rev. Lett. 52, 1845 (1984).
2. J.R. Beeler, Phys. Rev. 134, 1396 (1964); E.W. Montroll, J. Phys. Soc. Jpn. Suppl. 26, 6 (1969); E.W. Montroll, J. Math. Phys. 10, 753 (1969); J.K. Anlauf, Phys. Rev. Lett. 52, 1845 (1984).
3. J.R. Beeler, Phys. Rev. 134, 1396 (1964); E.W. Montroll, J. Phys. Soc. Jpn. Suppl. 26, 6 (1969); E.W. Montroll, J. Math. Phys. 10, 753 (1969); J.K. Anlauf, Phys. Rev. Lett. 52, 1845 (1984).
4. J.R. Beeler, Phys. Rev. 134, 1396 (1964); E.W. Montroll, J. Phys. Soc. Jpn. Suppl. 26, 6 (1969); E.W. Montroll, J. Math. Phys. 10, 753 (1969); J.K. Anlauf, Phys. Rev. Lett. 52, 1845 (1984).
5. A. Blumen, J. Klafter, and G. Zumofen, Optical Spectroscopy of Glasses, edited by I. Zschokke (Reidel, Dordrecht, 1986).
6. B.H. Hughes, Random Walks and Random Environments (Clarendon Press, Oxford, 1995), Vols. 1 and 2.
7. S. Havlin and D. Ben-Avraham, Adv. Phys. 36, 695 (1987).
8. F. den Hollander and G.H. Weiss, Contemporary Problems in Statistical Physics, edited by G.H. Weiss (SIAM, Philadelphia, 1994), pp. 147-203.
9. J.R. Beeler, Phys. Rev. 134, 1396 (1964).
10. H.B. Rosenstock, Phys. Rev. 187, 1166 (1969).
11. P. Damask and P. Dienes, Point Defects in Metals (Gordon and Breach, New York, 1964).
12. G. Oshanin, S. Nechaev, A.M. Cazabat, and M. Moreau, Phys. Rev. E 58, 6134 (1998); S. Nechaev, G. Oshanin, and A. Blumen, J. Stat. Phys. 98, 281 (2000).
13. G. Oshanin, S. Nechaev, A.M. Cazabat, and M. Moreau, Phys. Rev. E 58, 6134 (1998); S. Nechaev, G. Oshanin, and A. Blumen, J. Stat. Phys. 98, 281 (2000).
14. H. Miyagawa, Y. Hiwatari, B. Bernu, and J.P. Hansen, J. Chem. Phys. 88, 3879 (1988); T. Odagaki, J. Matsui, and Y. Hiwatari, Phys. Rev. E 49, 3150 (1994).
15. H. Miyagawa, Y. Hiwatari, B. Bernu, and J.P. Hansen, J. Chem. Phys. 88, 3879 (1988); T. Odagaki, J. Matsui, and Y. Hiwatari, Phys. Rev. E 49, 3150 (1994).
16. P.L. Krapivsky and S. Redner, J. Phys. A 29, 5347 (1996); S. Redner and P.L. Krapivsky, Am. J. Phys. 67, 1277 (1999).
17. P.L. Krapivsky and S. Redner, J. Phys. A 29, 5347 (1996); S. Redner and P.L. Krapivsky, Am. J. Phys. 67, 1277 (1999).
18. S.B. Yuste and L. Acedo, Physica A 297, 321 (2001).
19. S.B. Yuste and L. Acedo, Phys. Rev. E 64, 061107 (2001).
20. For reviews, see T. Bache, W.E. Moerner, M. Orrit, and U.P. Wild, Single-Molecule Optical Detection, Imaging and Spectroscopy (VCH, Weinheim, 1996); X.S. Xie and J.K. Trautman, Annu. Rev. Phys. Chem. 49, 441 (1998); Science 283, 1667 (1999).
21. For reviews, see T. Bache, W.E. Moerner, M. Orrit, and U.P. Wild, Single-Molecule Optical Detection, Imaging and Spectroscopy (VCH, Weinheim, 1996); X.S. Xie and J.K. Trautman, Annu. Rev. Phys. Chem. 49, 441 (1998); Science 283, 1667 (1999).
22. For reviews, see T. Bache, W.E. Moerner, M. Orrit, and U.P. Wild, Single-Molecule Optical Detection, Imaging and Spectroscopy (VCH, Weinheim, 1996); X.S. Xie and J.K. Trautman, Annu. Rev. Phys. Chem. 49, 441 (1998); Science 283, 1667 (1999).
23. M.T. Valentine, P.D. Kaplan, D. Thota, J.C. Crocker, T. Gisler, R.K. Prud'homme, M. Beck, and D.A. Weitz, Phys. Rev. E 64, 061506 (2001).
24. Fractals in Science, edited by A. Bunde and S. Havlin (Springer-Verlag, Berlin, 1994); Fractals and Disordered Systems, edited by A. Bunde and S. Havlin (Springer-Verlag, Berlin, 1996).
25. Fractals in Science, edited by A. Bunde and S. Havlin (Springer-Verlag, Berlin, 1994); Fractals and Disordered Systems, edited by A. Bunde and S. Havlin (Springer-Verlag, Berlin, 1996).
26. P. Pfeifer, F. Ehrburger-Dolle, T.P. Rieker, M.T. González, W.P. Hoffman, M. Molina-Sabio, F. Rodríguez-Reinoso, P.W. Schmidt, and D.I. Voss, Phys. Rev. Lett. 88, 115502 (2002).
27. A. Blumen, J. Klafter, and G. Zumofen, Phys. Rev. B 28, 6112 (1983).
28. H. Larralde, P. Trunfio, S. Havlin, H.E. Stanley, and G.H. Weiss, Phys. Rev. A 45, 7128 (1992).
29. L. Acedo and S.B. Yuste, Phys. Rev. E 63, 011105 (2001); e-print cond-mat/0003446.
30. K. Lindenberg, V. Seshadri, K.E. Shuler, and G.H. Weiss, J. Stat. Phys. 23, 11 (1980).
31. G.H. Weiss, K.E. Shuler, and K. Lindenberg, J. Stat. Phys. 31, 255 (1983).
32. S.B. Yuste and K. Lindenberg, J. Stat. Phys. 85, 501 (1996); S.B. Yuste, Phys. Rev. Lett. 79, 3565 (1997); Phys. Rev. E 57, 6327 (1998); S.B. Yuste and L. Acedo, J. Phys. A 33, 507 (2000); S.B. Yuste, L. Acedo, and K. Lindenberg, Phys. Rev. E 64, 052102 (2001).
33. S.B. Yuste and K. Lindenberg, J. Stat. Phys. 85, 501 (1996); S.B. Yuste, Phys. Rev. Lett. 79, 3565 (1997); Phys. Rev. E 57, 6327 (1998); S.B. Yuste and L. Acedo, J. Phys. A 33, 507 (2000); S.B. Yuste, L. Acedo, and K. Lindenberg, Phys. Rev. E 64, 052102 (2001).
34. S.B. Yuste and K. Lindenberg, J. Stat. Phys. 85, 501 (1996); S.B. Yuste, Phys. Rev. Lett. 79, 3565 (1997); Phys. Rev. E 57, 6327 (1998); S.B. Yuste and L. Acedo, J. Phys. A 33, 507 (2000); S.B. Yuste, L. Acedo, and K. Lindenberg, Phys. Rev. E 64, 052102 (2001).
35. S.B. Yuste and K. Lindenberg, J. Stat. Phys. 85, 501 (1996); S.B. Yuste, Phys. Rev. Lett. 79, 3565 (1997); Phys. Rev. E 57, 6327 (1998); S.B. Yuste and L. Acedo, J. Phys. A 33, 507 (2000); S.B. Yuste, L. Acedo, and K. Lindenberg, Phys. Rev. E 64, 052102 (2001).
36. S.B. Yuste and K. Lindenberg, J. Stat. Phys. 85, 501 (1996); S.B. Yuste, Phys. Rev. Lett. 79, 3565 (1997); Phys. Rev. E 57, 6327 (1998); S.B. Yuste and L. Acedo, J. Phys. A 33, 507 (2000); S.B. Yuste, L. Acedo, and K. Lindenberg, Phys. Rev. E 64, 052102 (2001).
37. J. Dräger and J. Klafter, Phys. Rev. E 60, 6503 (1999).
38. O. Benichou, M. Coppey, J. Klafter, M. Moreau, and G. Oshanin, J. Phys. A 36, 7225 (2003).
39. P.G. de Gennes, Recherche 7, 919 (1976).
40. H. Larralde, P. Trunfio, S. Havlin, H.E. Stanley, and G.H. Weiss, Nature (London) 355, 423 (1992); G.H. Weiss, I. Dayan, S. Havlin, J.E. Kiefer, H. Larralde, H.E. Stanley and P. Trunfio, Physica A 191, 479 (1992); A.M. Berezhkovskii, J. Stat. Phys. 76, 1089 (1994); G.M. Sastry and N. Agmon, J. Chem. Phys. 104, 3022 (1996).
41. H. Larralde, P. Trunfio, S. Havlin, H.E. Stanley, and G.H. Weiss, Nature (London) 355, 423 (1992); G.H. Weiss, I. Dayan, S. Havlin, J.E. Kiefer, H. Larralde, H.E. Stanley and P. Trunfio, Physica A 191, 479 (1992); A.M. Berezhkovskii, J. Stat. Phys. 76, 1089 (1994); G.M. Sastry and N. Agmon, J. Chem. Phys. 104, 3022 (1996).
42. H. Larralde, P. Trunfio, S. Havlin, H.E. Stanley, and G.H. Weiss, Nature (London) 355, 423 (1992); G.H. Weiss, I. Dayan, S. Havlin, J.E. Kiefer, H. Larralde, H.E. Stanley and P. Trunfio, Physica A 191, 479 (1992); A.M. Berezhkovskii, J. Stat. Phys. 76, 1089 (1994); G.M. Sastry and N. Agmon, J. Chem. Phys. 104, 3022 (1996).
43. H. Larralde, P. Trunfio, S. Havlin, H.E. Stanley, and G.H. Weiss, Nature (London) 355, 423 (1992); G.H. Weiss, I. Dayan, S. Havlin, J.E. Kiefer, H. Larralde, H.E. Stanley and P. Trunfio, Physica A 191, 479 (1992); A.M. Berezhkovskii, J. Stat. Phys. 76, 1089 (1994); G.M. Sastry and N. Agmon, J. Chem. Phys. 104, 3022 (1996).
44. S.B. Yuste and L. Acedo, Phys. Rev. E 60, R3459 (1999); 61, 2340 (2000).
45. S.B. Yuste and L. Acedo, Phys. Rev. E 60, R3459 (1999); 61, 2340 (2000).
46. L. Acedo and S.B. Yuste, in Recent Research Developments in Statistical Physics (Transworld Research Network, Trivandrum, 2002), Vol. 2.
47. R. Rammal and G. Toulouse, J. Phys. (France) Lett. 44, (1983).
48. G. Zumofen and A. Blumen, Chem. Phys. Lett. 83, 372 (1981).
49. G.H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
50. Handbook of Mathematical Functions, edited by M. Abramowitz and I. Stegun (Dover, New York, 1972).
51. D.V. Donsker and S.R.S. Varadhan, Commun. Pure Appl. Math. 28, 525 (1975); A.A. Ovchinnikov and Y.B. Zeldovich, Chem. Phys. 28, 215 (1978); P. Grassberger and I. Procaccia, J. Chem. Phys. 77, 6281 (1982); R.F. Kayser and J.B. Hubbard, Phys. Rev. Lett. 51, 79 (1983).
52. D.V. Donsker and S.R.S. Varadhan, Commun. Pure Appl. Math. 28, 525 (1975); A.A. Ovchinnikov and Y.B. Zeldovich, Chem. Phys. 28, 215 (1978); P. Grassberger and I. Procaccia, J. Chem. Phys. 77, 6281 (1982); R.F. Kayser and J.B. Hubbard, Phys. Rev. Lett. 51, 79 (1983).
53. D.V. Donsker and S.R.S. Varadhan, Commun. Pure Appl. Math. 28, 525 (1975); A.A. Ovchinnikov and Y.B. Zeldovich, Chem. Phys. 28, 215 (1978); P. Grassberger and I. Procaccia, J. Chem. Phys. 77, 6281 (1982); R.F. Kayser and J.B. Hubbard, Phys. Rev. Lett. 51, 79 (1983).
54. D.V. Donsker and S.R.S. Varadhan, Commun. Pure Appl. Math. 28, 525 (1975); A.A. Ovchinnikov and Y.B. Zeldovich, Chem. Phys. 28, 215 (1978); P. Grassberger and I. Procaccia, J. Chem. Phys. 77, 6281 (1982); R.F. Kayser and J.B. Hubbard, Phys. Rev. Lett. 51, 79 (1983).
55. G.T. Barkema, P. Biswas, and H. van Beijeren, Phys. Rev. Lett. 87, 170601 (2001).
56. L.K. Gallos, P. Argyrakis, and K.W. Kehr, Phys. Rev. E 63, 021104 (2001).
57. Y. Shapir, J. Phys. (France) Lett. 45, L-895 (1984).