Transient aging in fractional Brownian and Langevin-equation motion

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

Volumn 88, Issue 6, 2013, Pages

  Kursawe, Jochen ^a   Schulz, Johannes ^b   Metzler, Ralf ^a,c,d  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^c UNIVERSITY OF POTSDAM   (Germany)

^d TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

AGING PHENOMENA; ANALYTICAL EXPRESSIONS; ENSEMBLE AVERAGES; EXTERNAL CONFINEMENT; FRACTIONAL BROWNIAN MOTION; FRACTIONAL GAUSSIAN NOISE; MEAN SQUARED DISPLACEMENT; PARTICLE POSITION;

ELASTIC MODULI; RANDOM PROCESSES;

EQUATIONS OF MOTION;

EID: 84891679889     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.88.062124     Document Type: Article

References (63)

1. E. Barkai, Y. Garini, and R. Metzler, Phys. Today 10.1063/PT.3.1677 65 (8), 29 (2012).
2. I. M. Sokolov, Soft Matter 1744-683X 10.1039/c2sm25701g 8, 9043 (2012).
3. J. H. P. Schulz, E. Barkai, and R. Metzler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.110.020602 110, 020602 (2013).
4. Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.058101 101, 058101 (2008).
5. S. Burov, J.-H. Jeon, R. Metzler, and E. Barkai, Phys. Chem. Chem. Phys. PPCPFQ 1463-9076 10.1039/c0cp01879a 13, 1800 (2011).
6. E. W. Montroll and G. H. Weiss, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704269 6, 167 (1965);
7. H. Scher and E. W. Montroll, Phys. Rev. B 1098-0121 10.1103/PhysRevB.12. 2455 12, 2455 (1975).
8. J.-P. Bouchaud, J. Phys. I (Paris) 2, 1705 (1992);
9. G. Bel and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.240602 94, 240602 (2005); (Pubitemid 41636460)
10. A. Rebenshtok and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.210601 99, 210601 (2007). (Pubitemid 350137198)
11. A. Lubelski, I. M. Sokolov, and J. Klafter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.250602 100, 250602 (2008).
12. S. Burov, R. Metzler, and E. Barkai, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.1003693107 107, 13228 (2010).
13. T. Neusius, I. M. Sokolov, and J. C. Smith, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.011109 80, 011109 (2009).
14. J.-H. Jeon, V. Tejedor, S. Burov, E. Barkai, C. Selhuber-Unkel, K. Berg-Sørensen, L. Oddershede, and R. Metzler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.048103 106, 048103 (2011).
15. A. V. Weigel, B. Simon, M. M. Tamkun, and D. Krapf, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.1016325108 108, 6438 (2011).
16. S. M. A. Tabei, S. Burov, H. Y. Kim, A. Kuznetsov, T. Huynh, J. Jureller, L. H. Philipson, A. R. Dinner, and N. F. Scherer, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.1221962110 110, 4911 (2013).
17. M. Magdziarz, R. Metzler, W. Szczotka, and P. Zebrowski, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.051103 85, 051103 (2012);
18. V. Tejedor and R. Metzler, J. Phys. A 1751-8113 10.1088/1751-8113/43/8/ 082002 43, 082002 (2010).
19. M. A. Lomholt, L. Lizana, R. Metzler, and T. Ambjörnsson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.110.208301 110, 208301 (2013).
20. A. G. Cherstvy, A. V. Chechkin, and R. Metzler, New J. Phys. 10.1088/1367-2630/15/8/083039 15, 083039 (2013);
21. A. G. Cherstvy and R. Metzler, Phys. Chem. Chem. Phys. 10.1039/c3cp53056f 15, 20220 (2013).
22. G. Zumofen and J. Klafter, Physica D PDNPDT 0167-2789 10.1016/0167-2789(93)90105-A 69, 436 (1993);
23. D. Froemberg and E. Barkai, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.87.030104 87, 030104 (R) (2013);
24. A. Godec and R. Metzler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.110.020603 110, 020603 (2013).
25. E. Barkai and Y.-C. Cheng, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1559676 118, 6167 (2003);
26. E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90. 104101 90, 104101 (2003).
27. W. Deng and E. Barkai, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79. 011112 79, 011112 (2009).
28. J.-H. Jeon and R. Metzler, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.021103 81, 021103 (2010).
29. J.-H. Jeon and R. Metzler, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.021147 85, 021147 (2012).
30. F. Höfling and T. Franosch, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/76/4/046602 76, 046602 (2013).
31. I. Goychuk, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.046125 80, 046125 (2009);
32. I. Goychuk, Adv. Chem. Phys. 9781-1181 10.1002/9781118197714.ch5 150, 187 (2012).
33. J. Szymanski and M. Weiss, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.038102 103, 038102 (2009).
34. L. P. Sanders and T. Ambjörnsson, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.4707349 136, 175103 (2012);
35. L. Lizana, T. Ambjörnsson, A. Taloni, E. Barkai, and M. A. Lomholt, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.051118 81, 051118 (2010).
36. I. Bronstein, Y. Israel, E. Kepten, S. Mai, Y. Shav-Tal, E. Barkai, and Y. Garini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.018102 103, 018102 (2009);
37. K. Burnecki, E. Kepten, J. Janczura, I. Bronshtein, Y. Garini, and A. Weron, Biophys. J. BIOJAU 0006-3495 10.1016/j.bpj.2012.09.040 103, 1839 (2012).
38. S. C. Weber, A. J. Spakowitz, and J. A. Theriot, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.238102 104, 238102 (2010).
39. J.-H. Jeon, H. Martinez-Seara Monne, M. Javanainen, and R. Metzler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.109.188103 109, 188103 (2012);
40. G. R. Kneller, K. Baczynski, and M. Pasenkiewicz-Gierula, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3651800 135, 141105 (2011).
41. J.-H. Jeon, N. Leijnse, L. Oddershede, and R. Metzler, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/15/4/045011 15, 045011 (2013).
42. R. Kubo, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/29/1/306 29, 255 (1966).
43. B. B. Mandelbrot and J. W. van Ness, SIAM Rev. SIREAD 0036-1445 10.1137/1010093 10, 422 (1968).
44. G. Gripenberg and I. Norros, J. Appl. Probab. JPRBAM 0021-9002 10.2307/3215063 33, 400 (1996).
45. E. Lutz, Phys. Rev. E 1063-651X 10.1103/PhysRevE.64.051106 64, 051106 (2001).
46. S. C. Kou, Ann. Appl. Stat. 1932-6157 10.1214/07-AOAS149 2, 501 (2008).
47. W. Min, G. Luo, B. J. Cherayil, S. C. Kou, and X. S. Xie, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.198302 94, 198302 (2005). (Pubitemid 41493017)
48. R. Kupferman, J. Stat. Phys. JSTPBS 0022-4715 10.1023/B:JOSS.0000003113. 22621.f0 114, 291 (2004).
49. A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 26, 115 (1940).
50. A. Weron and M. Magdziarz, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/86/60010 86, 60010 (2009).
51. N. N. Pottier, Physica A PHYADX 0378-4371 10.1016/S0378-4371(02)01361-4 317, 371 (2003).
52. Higher Transcendental Functions, edited by H. Bateman and A. Erdélyi, Bateman Manuscript Project Vol. III (McGraw Hill, New York, 1955).
53. P. Siegle, I. Goychuk, and P. Hänggi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.100602 105, 100602 (2010).
54. P. Siegle, I. Goychuk, P. Talkner, and P. Hänggi, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.011136 81, 011136 (2010).
55. S. Burov and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.070601 100, 070601 (2008); (Pubitemid 351393590)
56. S. Burov and E. Barkai, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.031112 78, 031112 (2008).
57. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
58. O. Yu. Sliusarenko, V. Yu. Gonchar, A. V. Chechkin, I. M. Sokolov, and R. Metzler, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.041119 81, 041119 (2010).
59. K. Diethelm, N. J. Ford, and A. D. Freed, Nonlinear Dynam. NODYES 0924-090X 10.1023/A:1016592219341 29, 3 (2002). (Pubitemid 34945390)
60. A. B. Dieker, M.Sc. thesis, Vrije Universiteit Amsterdam, 2004.
61. A. B. Dieker and M. Mandjes, Probab. Eng. Inf. Sci. 17, 417 (2003).
62. J. R. M. Hosking, Water Resour. Res. WRERAQ 0043-1397 10.1029/WR020i012p01898 20, 1898 (1984).
63. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 2007).