Power law statistics in the velocity fluctuations of Brownian particle in inhomogeneous media and driven by colored noise

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2015, Issue 2, 2015, Pages

  Kazakevicius R ^a   Ruseckas, J ^a  

^a VILNIUS UNIVERSITY   (Lithuania)

Author keywords

Brownian motion; memory effects (theory); stochastic processes (theory)

Indexed keywords

EID: 84923812641     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2015/02/P02021     Document Type: Article

References (70)

1. Franosch T, Grimm M, Belushkin M, Mor F M, Foffi G, Forró L and Jeney S 2011 Nature 478 85
2. Landau L D and Lifshits E M 1987 Fluid Mechanics, Course of Theoretical Physics vol 6 (Burlington: Butterworth-Heinemann)
3. Zhou X 2009 Phys. Rev. A 80 023818
4. Kim S, Park S H and Ryu C S 1998 Phys. Rev. E 58 7994
5. Lande R 1993 Am. Nat. 142 911
6. Kamenev A, Meerson B and Shklovskii B 2008 Phys. Rev. Lett. 101 268103
7. Wang Y, Lai Y and Zheng Z 2009 Phys. Rev. E 79 056210
8. Gammaitoni L, Hänggi and Marchesoni F 1998 Rev. Mod. Phys. 70 223
9. Nozaki D, Mar D J, Grigg P and Collins J J 1999 Phys. Rev. Lett. 82 2402
10. Ward L M and Greenwood P E 2007 Scholarpedia 2 1537
11. Weissman M B 1988 Rev. Mod. Phys. 60 537
12. Barabasi A L and Albert R 1999 Science 286 509
13. Gisiger T 2001 Biol. Rev. 76 161
14. Wagenmakers E J, Farrell S and Ratcliff R 2004 Psychon. Bull. Rev. 11 579
15. Szabo G and Fath G 2007 Phys. Rep. 446 97
16. Castellano C, Fortunato S and Loreto V 2009 Rev. Mod. Phys. 81 591
17. Balandin A A 2013 Nat. Nanotechnol. 8 549
18. Kogan S 2008 Electronic Noise and Fluctuations in Solids (Cambridge: Cambridge University Press)
19. Li M and Zhao W 2012 Math. Problems Eng. 2012 673648
20. Orlyanchik V, Weissman M B, Torija M A, Sharma M and Leighton C 2008 Phys. Rev. B 78 094430
21. Melkonyan S V 2010 Physica B 405 379
22. Marinari E, Parisi G, Ruelle D and Windey P 1983 Phys. Rev. Lett. 50 1223
23. Kaulakys B and Meškauskas T 1998 Phys. Rev. E 58 7013
24. Kaulakys B 1999 Phys. Lett. A 257 37
25. Kaulakys B, Gontis V and Alaburda M 2005 Phys. Rev. E 71 051105
26. Kaulakys B and Ruseckas J 2004 Phys. Rev. E 70 020101
27. Kaulakys B, Ruseckas J, Gontis V and Alaburda M 2006 Physica A 365 217
28. Ruseckas J, Kaulakys B and Gontis V 2011 Europhys. Lett. 96 60007
29. Gontis V, Ruseckas J and Kononovicius A 2010 Physica A 389 100-6
30. Mathiesen J, Angheluta L, Ahlgren P T H and Jensen M H 2013 Proc. Natl Acad. Sci. 110 17259
31. Hottovy S, Volpe G and Wehr J 2012 Europhys. Lett. 99 60002
32. Piazza R and Parola A 2008 J. Phys.: Condens. Matter 20 153102
33. Piazza R 2008 Soft Matter 4 1740
34. Ghosh A. W and Khare S V 2000 Phys. Rev. Lett. 84 5243
35. Kaulakys B and Alaburda M 2009 J. Stat. Mech. 2009 P02051
36. Kononovicius A and Gontis V 2012 Physica A 391 1309
37. Jeanblanc M, Yor M and Chesney M 2009 Mathematical Methods for Financial Markets (Berlin: Springer)
38. Turelli M 1977 Theor. Popul. Biol. 12 140-78
39. Smythe J, Moss F and McClintock P V E 1983 Phys. Rev. Lett. 51 1062
40. Gardiner C W 2004 Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Berlin: Springer)
41. Pesce G, McDaniel A, Hottovy S, Wehr J and Volpe G 2013 Nat. Commun. 4 2733
42. Ruseckas J and Kaulakys B 2014 J. Stat. Mech. P06005
43. Ruseckas J and Kaulakys B 2010 Phys. Rev. E 81 031105
44. Weron A, Burnecki K, Mercik S and Weron K 2005 Phys. Rev. E 71 016113
45. Kazakevičius R and Ruseckas J 2014 Physica A 411 95
46. Risken H 1989 The Fokker-Planck Equation, Methods of Solution and Applications (Berlin: Springer)
47. Sancho J M, San Miguel M and Dürr D 1982 J. Stat. Phys. 28 291
48. Beck C and Cohen E G D 2003 Physica A 322 267-75
49. Tsallis C and Souza A M C 2003 Phys. Rev. E 67 026106
50. Abe S, Beck C and Cohen E G D 2007 Phys. Rev. E 76 031102
51. Hahn M G, Jiang X and Umarov S 2010 J. Phys. A: Math. Theor. 43 165208
52. Beck C 2011 Phil. Trans. R. Soc. A 369 453
53. Wilk G and Włodarczyk Z 2000 Phys. Rev. Lett. 84 2770
54. Beck C 2001 Phys. Rev. Lett. 87 180601
55. Beck C, Cohen E G D and Swinney H L 2005 Phys. Rev. E 72 056133
56. Beck C, Cohen E G D and Rizzo S 2005 Europhys. News 36 189
57. Beck C 2007 Phys. Rev. Lett. 98 064502
58. Beck C 2006 Physica A 365 96
59. Sattin F and Salasnich L 2002 Phys. Rev. E 65 035106
60. Van der Straeten E and Beck C 2011 Chin. Sci. Bull. 56 3633
61. Wong E and Zakai M 1965 Ann. Math. Stat. 36 1560
62. Doob J L 1944 Ann. Math. Stat. 15 229
63. Hänggi P and Jung P 1995 Coloured Noise in Dynamical Systems (Advances in Chemical Physics vol 89) (Hoboken, NJ: Wiley) ch 4
64. Jung P and Hänggi P 1987 Phys. Rev. A 35 4464
65. Graham R and Schenzle A 1982 Phys. Rev. A 26 1676
66. Sigurgeirsson H and Stuart A M 2002 Phys. Fluids 14 4352
67. Kupferman R, Pavliotis G A and Stuart A M 2004 Phys. Rev. E 70 036120
68. Fox R F, Gatland I R, Roy R and Vemuri G 1988 Phys. Rev. A 38 5938
69. Milshtein G N and Tret'yakov M V 1994 J. Stat. Phys. 77 691
70. Kulasiri D 2002 Stochastic Dynamics: Modeling Solute Transport in Porous Media (Amsterdam: North-Holland)