Kramers-like escape driven by fractional Gaussian noise

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

Volumn 81, Issue 4, 2010, Pages

  Sliusarenko, Oleksii Yu ^a   Gonchar, Vsevolod Yu ^a   Chechkin, Aleksei V ^a,b   Sokolov, Igor M ^c   Metzler, Ralf ^d  

^a KHARKOV INSTITUTE OF PHYSICS AND TECHNOLOGY   (Ukraine)

^b TEL AVIV UNIVERSITY   (Israel)

^c HUMBOLDT UNIVERSITY   (Germany)

^d TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL CALCULATION; ESCAPE TIME; EXPONENTIAL DISTRIBUTIONS; FIRST-PASSAGE; FRACTIONAL GAUSSIAN NOISE; HURST EXPONENTS; PARTICLE DIFFUSIVITY; POTENTIAL WELLS; TEST PARTICLES;

NUMERICAL ANALYSIS;

GAUSSIAN NOISE (ELECTRONIC);

EID: 77951596339     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.041119     Document Type: Article

References (96)

1. Y. G. Sinai, Theory Probab. Appl. 27, 256 (1982). 10.1137/1127028
2. J. Dräger and J. Klafter, Phys. Rev. Lett. 84, 5998 (2000). 10.1103/PhysRevLett.84.5998
3. V. Tejedor and R. Metzler, J. Phys. A 43, 082002 (2010). 10.1088/1751-8113/43/8/082002
4. L. F. Richardson, Proc. R. Soc. London, Ser. A 110, 709 (1926). 10.1098/rspa.1926.0043
5. G. Boffetta and I. M. Sokolov, Phys. Rev. Lett. 88, 094501 (2002). 10.1103/PhysRevLett.88.094501
6. J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990). 10.1016/0370-1573(90)90099-N
7. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000) 10.1016/S0370- 1573(00)00070-3
8. R. Metzler and J. Klafter, J. Phys. A 37, R161 (2004). 10.1088/0305-4470/37/31/R01
9. H. Scher and E. W. Montroll, Phys. Rev. B 12, 2455 (1975). 10.1103/PhysRevB.12.2455
10. G. Pfister and H. Scher, Adv. Phys. 27, 747 (1978) 10.1080/ 00018737800101474
11. Q. Gu, E. A. Schiff, S. Grebner, F. Wang, and R. Schwarz, Phys. Rev. Lett. 76, 3196 (1996). 10.1103/PhysRevLett.76.3196
12. H. Scher, G. Margolin, R. Metzler, J. Klafter, and B. Berkowitz, Geophys. Res. Lett. 29, 1061 (2002) 10.1029/2001GL014123
13. B. Berkowitz, A. Cortis, M. Dentz, and H. Scher, Rev. Geophys. 44, RG2003 (2006). 10.1029/2005RG000178
14. A. Klemm, R. Metzler, and R. Kimmich, Phys. Rev. E 65, 021112 (2002) 10.1103/PhysRevE.65.021112
15. S. Havlin and D. ben-Avraham, Adv. Phys. 36, 695 (1987). 10.1080/00018738700101072
16. A. Caspi, R. Granek, and M. Elbaum, Phys. Rev. Lett. 85, 5655 (2000) 10.1103/PhysRevLett.85.5655
17. I. M. Tolić-Nørrelykke, E. L. Munteanu, G. Thon, L. Oddershede, and K. Berg-Sørensen, Phys. Rev. Lett. 93, 078102 (2004) 10.1103/PhysRevLett.93.078102
18. I. Golding and E. C. Cox, Phys. Rev. Lett. 96, 098102 (2006) 10.1103/PhysRevLett.96.098102
19. H. Yang, Science 302, 262 (2003) 10.1126/science.1086911
20. M. Weiss, M. Elsner, F. Kartberg, and T. Nilsson, Biophys. J. 87, 3518 (2004) 10.1529/biophysj.104.044263
21. G. Seisenberger, Science 294, 1929 (2001). 10.1126/science.1064103
22. I. Y. Wong, M. L. Gardel, D. R. Reichman, E. R. Weeks, M. T. Valentine, A. R. Bausch, and D. A. Weitz, Phys. Rev. Lett. 92, 178101 (2004) 10.1103/PhysRevLett.92.178101
23. W. Pan, L. Filobelo, N. D. Q. Pham, O. Galkin, V. V. Uzunova, and P. G. Vekilov, Phys. Rev. Lett. 102, 058101 (2009) 10.1103/PhysRevLett.102.058101
24. D. Banks and C. Fradin, Biophys. J. 89, 2960 (2005). 10.1529/biophysj. 104.051078
25. A. Caspi, R. Granek, and M. Elbaum, Phys. Rev. E 66, 011916 (2002). 10.1103/PhysRevE.66.011916
26. G. Matheron and G. de Marsily, Water Resour. Res. 16, 901 (1980). 10.1029/WR016i005p00901
27. T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993). 10.1103/PhysRevLett.71.3975
28. S. Stapf, R. Kimmich, and R.-O. Seitter, Phys. Rev. Lett. 75, 2855 (1995) 10.1103/PhysRevLett.75.2855
29. O. V. Bychuk and B. O'Shaugnessy, J. Chem. Phys. 101, 772 (1994) 10.1063/1.468132
30. A. V. Chechkin, I. M. Zaid, M. A. Lomholt, I. M. Sokolov, and R. Metzler, Phys. Rev. E 79, 040105 (R) (2009). 10.1103/PhysRevE.79.040105
31. A. Einstein, Investigations on the Theory of Brownian Movement (Dover, New York, 1956).
32. J. Klafter, A. Blumen, and M. F. Shlesinger, Phys. Rev. A 35, 3081 (1987). 10.1103/PhysRevA.35.3081
33. R. Metzler and J. Klafter, Chem. Phys. Lett. 321, 238 (2000). 10.1016/S0009-2614(00)00374-2
34. P. D. Ditlevsen, Phys. Rev. E 60, 172 (1999). 10.1103/PhysRevE.60.172
35. A. V. Chechkin, V. Yu. Gonchar, J. Klafter, and R. Metzler, Europhys. Lett. 72, 348 (2005) 10.1209/epl/i2005-10265-1
36. A. V. Chechkin, O. Yu. Sliusarenko, R. Metzler, and J. Klafter, Phys. Rev. E 75, 041101 (2007). 10.1103/PhysRevE.75.041101
37. P. Imkeller and I. Pavlyukevich, J. Phys. A 39, L237 (2006). 10.1088/0305-4470/39/15/L01
38. S. Havlin and D. ben-Avraham, Adv. Phys. 51 187 (2002). 10.1080/00018730110116353
39. L. Acedo and S. B. Yuste, Phys. Rev. E 66, 011110 (2002). 10.1103/PhysRevE.66.011110
40. S. Condamin, O. Bénichou, V. Tejedor, R. Voituriez, and J. Klafter, Nature (London) 450, 77 (2007). 10.1038/nature06201
41. A. N. Kolmogorov, Dokl. Acad. Sci. USSR 26, 115 (1940).
42. B. B. Mandelbrot and J. W. van Ness, SIAM Rev. 10, 422 (1968) 10.1137/1010093
43. compare also B. B. Mandelbrot, Phys. Scr. 32, 257 (1985). 10.1088/0031-8949/32/4/001
44. A. Yaglom, Correlation Theory of Stationary and Related Random Functions (Springer, Berlin, 1987).
45. H. Qian, in Processes with Long-Range Correlations, edited by, G. Rangarajan, and, M. Z. Ding,, Lecture Notes in Physics Vol. 621 (Springer, New York, 2003), pp. 22-33. 10.1007/3-540-44832-2-2
46. D. Panja, J. Stat Mech.: Theory Exp. (2010), L02001. 10.1088/1742-5468/ 2010/02/L02001
47. L. Lizana and T. Ambjörnsson, Phys. Rev. Lett. 100, 200601 (2008) 10.1103/PhysRevLett.100.200601
48. L. Lizana and T. Ambjörnsson, Phys. Rev. E 80, 051103 (2009). 10.1103/PhysRevE.80.051103
49. G. Guigas and M. Weiss, Biophys. J. 94, 90 (2008) 10.1529/biophysj.107. 117044
50. J. Szymanski and M. Weiss, Phys. Rev. Lett. 103, 038102 (2009) 10.1103/PhysRevLett.103.038102
51. V. Tejedor, O. Bénichou, R. Voituriez, R. Jungmann, F. Simmel, C. Selhuber, L. Oddershede, and R. Metzler, Biophys J. 98, 1364 (2010). 10.1016/j.bpj.2009.12.4282
52. H. E. Hurst, Trans. Am. Soc. Civ. Eng. 116, 400 (1951).
53. T. N. Palmer, G. J. Shutts, R. Hagedorn, F. J. Doblas-Reyes, T. Jung, and M. Leutbecher, Annu. Rev. Earth Planet Sci. 33, 163 (2005). 10.1146/annurev.earth.33.092203.122552
54. I. Simonsen, Physica A 322, 597 (2003) 10.1016/S0378-4371(02)01938-6
55. N. E. Frangos, S. D. Vrontos, and A. N. Yannacopoulos Appl. Stoch., Models Bus. Ind. 23, 403 (2007). 10.1002/asmb.680
56. T. Mikosch, S. Rednick, H. Rootzén, and A. Stegemann, Ann. Appl. Probab. 12, 23 (2002). 10.1214/aoap/1015961155
57. K. E. Bassler, G. H. Gunaratne, and J. L. McCauley, Physica A 369, 343 (2006) 10.1016/j.physa.2006.01.081
58. J. L. McCauley, G. H. Gunaratne, and K. E. Bassler, Physica A 379, 1 (2007). 10.1016/j.physa.2006.12.028
59. M. Ding and W. Yang, Phys. Rev. E 52, 207 (1995) 10.1103/PhysRevE.52.207
60. J. Krug, H. Kallabis, S. N. Majumdar, S. J. Cornell, A. J. Bray, and C. Sire, Phys. Rev. E 56, 2702 (1997) 10.1103/PhysRevE.56.2702
61. G. M. Molchan, Commun. Math. Phys. 205, 97 (1999). 10.1007/s002200050669
62. S. Burov and E. Barkai, Phys. Rev. Lett. 100, 070601 (2008). 10.1103/PhysRevLett.100.070601
63. H. A. Kramers, Physica A 7, 284 (1940).
64. P. Hänggi and P. Jung, Adv. Chem. Phys. 89, 239 (1995). 10.1002/9780470141489.ch4
65. P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990). 10.1103/RevModPhys.62.251
66. E. Barkai and R. Silbey, Phys. Rev. Lett. 102, 050602 (2009). 10.1103/PhysRevLett.102.050602
67. A. Romero, J. M. Sancho, and K. Lindenberg, Fluct. Noise Lett. 2, L79 (2002). 10.1142/S0219477502000658
68. I. Goychuk and P. Hänggi, Phys. Rev. Lett. 99, 200601 (2007) 10.1103/PhysRevLett.99.200601
69. compare also I. Goychuk, Phys. Rev. E 80, 046125 (2009). 10.1103/PhysRevE.80.046125
70. Yu. L. Klimontovich, Turbulent Motion and the Structure of Chaos: A New Approach to the Statistical Theory of Open Systems (Kluwer, Dordrecht, The Netherlands, 1992).
71. S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943). 10.1103/RevModPhys.15.1
72. H. Risken, The Fokker-Planck Equation (Springer-Verlag, Berlin, 1989).
73. B. S. Lowen, Methodol. Comput. Appl. Probab. 1, 445 (1999). 10.1023/A:1010027211901
74. A. V. Chechkin and V. Yu. Gonchar, Chaos, Solitons Fractals 12, 391 (2001). 10.1016/S0960-0779(99)00183-6
75. D. Slepian, Bell Syst. Tech. J. 41, 463 (1962).
76. S. O. Rice, Bell Syst. Tech. J. 23, 282 (1944)
77. S. O. Rice, Bell Syst. Tech. J. 24, 46 (1945)
78. S. O. Rice, in Noise and Stochastic Processes, edited by, N. Wax, (Dover, New York, 1954).
79. R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New York, 1967), Vol. II.
80. G. Wilemski and M. Fixman, J. Chem. Phys. 60, 866 (1974) 10.1063/1.1681162
81. G. Wilemski and M. Fixman, J. Chem. Phys. 60, 878 (1974). 10.1063/1.1681163
82. A. Szabo, K. Schulten, and Z. Schulten, J. Chem. Phys. 72, 4350 (1980). 10.1063/1.439715
83. T. Verechtchaguina, I. M. Sokolov, and L. Schimansky-Geier, Phys. Rev. E 73, 031108 (2006). 10.1103/PhysRevE.73.031108
84. I. M. Sokolov, Phys. Rev. Lett. 90, 080601 (2003). 10.1103/PhysRevLett. 90.080601
85. S. Redner, A Guide to First Passage Processes (Cambridge University Press, Cambridge, UK, 2001). 10.1017/CBO9780511606014
86. B. D. Hughes, Random Walks and Random Environments. Vol. 1: Random Walks (Clarendon, Oxford, UK, 1995) Chap..
87. A. E. Likthman and C. M. Marques, Europhys. Lett. 75, 971 (2006). 10.1209/epl/i2006-10206-6
88. W. H. Deng and E. Barkai, Phys. Rev. E 79, 011112 (2009) 10.1103/PhysRevE.79.011112
89. J.-H. Jeon and R. Metzler, Phys. Rev. E 81, 021103 (2010). 10.1103/PhysRevE.81.021103
90. A. Lubelski, I. M. Sokolov, and J. Klafter, Phys. Rev. Lett. 100, 250602 (2008) 10.1103/PhysRevLett.100.250602
91. Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008) 10.1103/PhysRevLett.101.058101
92. R. Metzler, V. Tejedor, J.-H. Jeon, Y. He, W. Deng, S. Burov, and E. Barkai, Acta Phys. Pol. B 40, 1315 (2009)
93. T. Neusius, I. M. Sokolov, and J. C. Smith, Phys. Rev. E 80, 011109 (2009) 10.1103/PhysRevE.80.011109
94. S. Burov, R. Metzler, and E. Barkai, e-print arXiv:1003.3182.
95. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1972).
96. F. W. J. Olver, Asymptotics and Special Functions (Academic, New York, 1974).