Escape from the potential well: Competition between long jumps and long waiting times

Journal of Chemical Physics

Volumn 133, Issue 24, 2010, Pages

  Dybiec, Bartomiej ^a  

^a JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC PROPERTIES; FIRST-PASSAGE-TIME DENSITY; FRACTIONAL DIFFUSION EQUATION; JUMP LENGTH; POTENTIAL WELLS; POWER LAW; POWER LAW DISTRIBUTION; SURVIVAL PROBABILITIES; WAITING TIME;

ASYMPTOTIC ANALYSIS; COMPETITION; NUMERICAL METHODS;

PROBABILITY DISTRIBUTIONS;

EID: 78650922890     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3511722     Document Type: Article

References (71)

1. H. A. Kramers, Physica (Utrecht) 7, 284 (1940). 10.1016/S0031-8914(40) 90098-2
2. A. Janicki and A. Weron, Simulation and Chaotic Behavior of -stable Stochastic Processes (Marcel Dekker, New York, 1994); J. P. Nolan, Stable Distributions-Models for Heavy Tailed Data Stable Distributions-Models for Heavy Tailed Data (Birkhuser, Boston, in press), Chapter 1 online at http://academic2.american.edu/~jpnolan.
3. A. V. Chechkin, V. Y. Gonchar, J. Klafter, and R. Metzler, Adv. Chem. Phys. 133, 439 (2006).
4. A. A. Dubkov, B. Spagnolo, and V. V. Uchaikin, Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, 2649 (2008). 10.1142/S0218127408021877
5. A. V. Chechkin, V. Y. Gonchar, J. Klafter, and R. Metzler, Europhys. Lett. 72, 348 (2005). 10.1209/epl/i2005-10265-1 (Pubitemid 41595892)
6. B. Dybiec, E. Gudowska-Nowak, and P. Hnggi, Phys. Rev. E 75, 021109 (2007). 10.1103/PhysRevE.75.021109
7. A. V. Chechkin, O. Y. Sliusarenko, R. Metzler, and J. Klafter, Phys. Rev. E 75, 041101 (2007). 10.1103/PhysRevE.75.041101 (Pubitemid 46526896)
8. I. Eliazar and J. Klafter, Physica A 336, 219 (2004). 10.1016/j.physa.2003.12.032
9. P. Imkeller and I. Pavlyukevich, J. Phys. A 39, L237 (2006). 10.1088/0305-4470/39/15/L01 (Pubitemid 43501264)
10. Lvy Flights and Related Topics in Physics, edited by, M. F. Shlesinger, G. M. Zaslavsky, and, J. Frisch, (Springer Verlag, Berlin, 1995)
11. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000); 10.1016/S0370- 1573(00)00070-3
12. R. Metzler and J. Klafter, J. Phys. A: Math. Gen. 37, R161 (2004). 10.1088/0305-4470/37/31/R01 (Pubitemid 39063557)
13. T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993); 10.1103/PhysRevLett.71.3975
14. T. H. Solomon, E. R. Weeks, and H. L. Swinney, Physica D 76, 70 (1994). 10.1016/0167-2789(94)90251-8
15. I. M. Sokolov, J. Mai, and A. Blumen, Phys. Rev. Lett. 79, 857 (1997); 10.1103/PhysRevLett.79.857
16. M. A. Lomholt, T. Ambjrnsson, and R. Metzler, Phys. Rev. Lett. 95, 260603 (2005); 10.1103/PhysRevLett.95.260603 (Pubitemid 43061524)
17. V. V. Belik and D. Brockmann, New J. Phys. 9, 54 (2007). 10.1088/1367-2630/9/3/054 (Pubitemid 46417521)
18. A. M. Edwards, R. A. Phillips, N. W. Watkins, M. P. Freeman, E. J. Murphy, V. Afanasyev, S. V. Buldyrev, M. G. E. da Luz, E. P. Raposo, H. E. Stanley, and G. M. Viswanathan, Nature (London) 449, 1044 (2007); 10.1038/nature06199 (Pubitemid 350017586)
19. A. M. Reynolds and C. J. Rhodes, Ecology 90, 877 (2009). 10.1890/08-0153.1
20. R. Metzler and J. Klafter, Chem. Phys. Lett. 321, 238 (2000). 10.1016/S0009-2614(00)00374-2
21. G. Zumofen and J. Klafter, Phys. Rev. E 51, 1818 (1995). 10.1103/PhysRevE.51.1818
22. R. Klages, G. Radons, and I. M. Sokolov, Anomalous Transport: Foundations and Applications (Wiley, Weinheim, 2008).
23. B. Dybiec and E. Gudowska-Nowak, Phys. Rev. E 80, 061122 (2009). 10.1103/PhysRevE.80.061122
24. B. Ai and Y. He, J. Chem. Phys. 132, 094504 (2010). 10.1063/1.3327842
25. A. Lubelski and J. Klafter, J. Phys. Chem. B 112, 12740 (2008); 10.1021/jp800242b
26. Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008); 10.1103/PhysRevLett.101.058101
27. R. Metzler, V. Tejedor, J. H. Jeon, Y. He, W. H. Deng, S. Burov, and E. Barkai, Acta Phys. Pol. B 40, 1315 (2009); 10.1131/PhysRevE.80.061122
28. I. Bronstein, Y. Israel, E. Kepten, S. Mai, Y. Shav-Tal, E. Barkai, and Y. Garini, Phys. Rev. Lett. 103, 018102 (2009). 10.1103/PhysRevLett.103.018102
29. D. Brockmann and I. M. Sokolov, Chem. Phys. 284, 409 (2002). 10.1016/S0301-0104(02)00671-7
30. R. Metzler, E. Barkai, and J. Klafter, Europhys. Lett. 46, 431 (1999). 10.1209/epl/i1999-00279-7
31. I. Podlubny, Fractional Differential Equations (Academic, San Diego, 1999).
32. E. Pollak, J. Chem. Phys. 85, 865 (1986). 10.1063/1.451294
33. P. Hnggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990). 10.1103/RevModPhys.62.251
34. S. K. Banik, J. R. Chaudhuri, and D. S. Ray, J. Chem. Phys. 112, 8330 (2000). 10.1063/1.481439
35. H. C. Fogedby, Phys Rev. E 50, 1657 (1994); 10.1103/PhysRevE.50.1657
36. A. Compte, Phys. Rev. Lett 73, 2517 (1994); 10.1103/PhysRevLett.73.2517
37. A. Compte, Phys. Rev. E 53, 4191 (1996). 10.1103/PhysRevE.53.4191
38. V. V. Yanovsky, A. V. Chechkin, D. Schertzer, and A. V. Tur, Physica A 282, 13 (2000); 10.1016/S0378-4371(99)00565-8
39. D. Schertzer, M. Larchevque, J. Duan, V. V. Yanowsky, and S. Lovejoy, J. Math. Phys. 42, 200 (2001). 10.1063/1.1318734
40. M. F. Shlesinger, J. Klafter, and Y. M. Wong, J. Stat. Phys. 27, 499 (1982). 10.1007/BF01011089
41. H. Risken, The Fokker-Planck Equation. Methods of Solution and Application (Springer Verlag, Berlin, 1984).
42. J. Klafter, A. Blumen, and M. F. Shlesinger, Phys. Rev. A 35, 3081 (1987). 10.1103/PhysRevA.35.3081
43. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and Natural Sciences (Springer Verlag, Berlin, 2009).
44. P. D. Ditlevsen, Phys. Rev. E 60, 172 (1999). 10.1103/PhysRevE.60.172
45. M. Magdziarz and A. Weron, Phys. Rev. E 75, 056702 (2007). 10.1103/PhysRevE.75.056702 (Pubitemid 47138566)
46. M. Magdziarz, A. Weron, and K. Weron, Phys. Rev. E 75, 016708 (2007). 10.1103/PhysRevE.75.016708 (Pubitemid 46174720)
47. E. Heinsalu, M. Patriarca, I. Goychuk, G. Schmid, and P. Hnggi, Phys. Rev. E 73, 046133 (2006). 10.1103/PhysRevE.73.046133 (Pubitemid 43672781)
48. D. Fulger, E. Scalas, and G. Germano, Phys. Rev. E 77, 021122 (2008). 10.1103/PhysRevE.77.021122 (Pubitemid 351366235)
49. B. Dybiec, E. Gudowska-Nowak, and P. Hnggi, Phys. Rev. E 73, 046104 (2006); 10.1103/PhysRevE.73.046104
50. A. Zoia, A. Rosso, and M. Kardar, Phys. Rev. E 76, 021116 (2007). 10.1103/PhysRevE.76.021116 (Pubitemid 47311842)
51. I. M. Sokolov, Phys. Rev. E 66, 041101 (2002); 10.1103/PhysRevE.66.041101 (Pubitemid 40606155)
52. Phys. Rev. E, 63, 056111 (2001); 10.1103/PhysRevE.63.056111
53. E. Barkai, Phys. Rev. E 63, 046118 (2001). 10.1103/PhysRevE.63.046118
54. B. Dybiec, J. Stat. Mech. P01011 (2010). 10.1088/1742-5468/2010/01/ P01011
55. A. Janicki, Numerical and Statistical Approximation of Stochastic Differential Equations with Non-Gaussian Measures (Hugo Steinhaus Centre for Stochastic Methods, Wrocaw, 1996).
56. B. Dybiec and E. Gudowska-Nowak, Fluct. Noise Lett. 4, L273 (2004). 10.1142/S0219477504001872 (Pubitemid 40111624)
57. A. V. Chechkin, R. Metzler, V. Y. Gonchar, J. Klafter, and L. V. Tanatarov, J. Phys. A: Math. Gen. 36, L537 (2003); 10.1088/0305-4470/36/41/L01 (Pubitemid 37331371)
58. I. M. Sokolov and R. Metzler, J. Phys. A: Math. Gen. 37, L609 (2004). 10.1088/0305-4470/37/46/L02 (Pubitemid 39594065)
59. T. Koren, M. A. Lomholt, A. V. Chechkin, J. Klafter, and R. Metzler, Phys. Rev. Lett. 99, 160602 (2007); 10.1103/PhysRevLett.99.160602 (Pubitemid 47613344)
60. T. Koren, A. V. Chechkin, and J. Klafter, Physica A 379, 10 (2007). 10.1016/j.physa.2006.12.039 (Pubitemid 46453054)
61. I. M. Sokolov, J. Klafter, and A. Blumen, Phys. Today 55, 48 (2002). 10.1063/1.1535007
62. B. Dybiec, J. Stat. Mech.: Theory Exp. 2010, P03019.
63. S. B. Yuste and K. Lindenberg, Phys. Rev. E 69, 033101 (2004). 10.1103/PhysRevE.69.033101
64. D. del Castillo-Negrete, V. Y. Gonchar, and A. V. Chechkin, Physica A 387, 6693 (2008); 10.1016/j.physa.2008.08.034
65. B. Dybiec, E. Gudowska-Nowak, and I. M. Sokolov, Phys. Rev. E 78, 011117 (2008); 10.1103/PhysRevE.78.011117
66. B. Dybiec, Phys. Rev. E 78, 061120 (2008). 10.1103/PhysRevE.78.061120
67. C. R. Doering and J. C. Gadoua, Phys. Rev. Lett. 69, 2318 (1992). 10.1103/PhysRevLett.69.2318
68. V. Balakrishnan, Physica A 132, 569 (1985). 10.1016/0378-4371(85)90028-
69. G. Rangarajan and M. Ding, Phys. Lett. A 273, 322 (2000). 10.1016/S0375-9601(00)00518-1
70. T. Koren, J. Klafter, and M. Magdziarz, Phys. Rev. E 76, 031129 (2007). 10.1103/PhysRevE.76.031129 (Pubitemid 47507693)
71. B. Dybiec and E. Gudowska-Nowak, Europhys. Lett. 88, 10003 (2009). 10.1209/0295-5075/88/10003