Correlated continuous-time random walks in external force fields

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

Volumn 85, Issue 5, 2012, Pages

  Magdziarz, Marcin ^a   Metzler, Ralf ^b,c   Szczotka, Wladyslaw ^d   Zebrowski, Piotr ^d  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b UNIVERSITY OF POTSDAM   (Germany)

^c TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

^d UNIVERSITY OF WROC AW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ANOMALOUS DIFFUSION; CONTINUOUS TIME RANDOM WALKS; CONTINUOUS-TIME RANDOM WALK; EINSTEIN RELATIONS; ERGODICITY; EXTERNAL FORCE FIELD; FORCE FIELDS; HARMONIC POTENTIAL; LANGEVIN EQUATION; MODEL PARAMETERS; POWER-LAW; RELAXATION DYNAMICS; STATIONARY SOLUTIONS; STRETCHED EXPONENTIAL; WAITING-TIME;

CONDENSED MATTER PHYSICS; PHYSICS;

DIFFERENTIAL EQUATIONS;

EID: 84861917468     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.051103     Document Type: Article

References (47)

1. R. Metzler and J. Klafter, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3 339, 1 (2000);
2. R. Metzler and J. Klafter, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/37/31/R01 37, R161 (2004). (Pubitemid 39063557)
3. H. Scher and E. W. Montroll, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.12.2455 12, 2455 (1975).
4. H. Scher, Geophys. Rev. Lett. GPRLAJ 0094-8276 10.1029/2001GL014123 29, 1061 (2002);
5. B. Berkowitz, A. Cortis, M. Dentz, and H. Scher, Rev. Geophys. REGEEP 8755-1209 10.1029/2005RG000178 44, RG2003 (2006). (Pubitemid 46044201)
6. A. Klemm, R. Metzler, and R. Kimmich, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.65.021112 65, 021112 (2002). (Pubitemid 40619370)
7. S. S. Rogers, C. V. D. Walle, and T. A. Waigh, Langmuir LANGD5 0743-7463 10.1021/la802442d 24, 13549 (2008).
8. I. Golding and E. C. Cox, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.098102 96, 098102 (2006); (Pubitemid 43385256)
9. S. C. Weber, A. J. Spakowitz, and J. A. Theriot, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.238102 104, 238102 (2010);
10. J.-H. Jeon, V. Tejedor, S. Burov, E. Barkai, C. Selhuber-Unkel, K. Berg-Sorensen, L. Oddershede, and R. Metzler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.048103 106, 048103 (2011);
11. 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).
12. H. Risken, The Fokker-Planck Equation (Springer-Verlag, Berlin, 1989).
13. W. T. Coffey, Y. P. Kalmykov, and J. T. Waldron, The Langevin Equation (World Scientific, Singapore, 2004).
14. E. W. Montroll and G. H. Weiss, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704269 6, 167 (1965).
15. R. Metzler, E. Barkai, and J. Klafter, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.82.3563 82, 3563 (1999);
16. R. Metzler, E. Barkai, and J. Klafter, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i1999-00279-7 46, 431 (1999);
17. E. Barkai, R. Metzler, and J. Klafter, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.132 61, 132 (2000).
18. H. C. Fogedby, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.50.1657 50, 1657 (1994);
19. A. Stanislavsky, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.67.021111 67, 021111 (2003);
20. M. Magdziarz, A. Weron, and K. Weron, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.016708 75, 016708 (2007); (Pubitemid 46174720)
21. S. Eule, R. Friedrich, F. Jenko, and D. Kleinhans, J. Phys. Chem. B JPCBFK 1520-6106 10.1021/jp072173h 111, 11474 (2007). (Pubitemid 47598330)
22. A. N. Kolmogorov, Dokl. Acad. Sci. USSR 26, 115 (1940);
23. B. B. Mandelbrot and J. W. Van Ness, SIAM Rev. SIREAD 0036-1445 10.1137/1010093 10, 422 (1968).
24. S. Havlin and D. ben-Avraham, Adv. Phys. ADPHAH 0001-8732 10.1080/00018738700101072 36, 695 (1987).
25. R. Nathan, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0800375105 105, 19052 (2008).
26. C. Song, T. Koren, P. Wang, and A. L. Barabási, Nature Physics 1745-2473 10.1038/nphys1760 6, 818 (2010).
27. E. Scalas, Physica A PHYADX 0378-4371 10.1016/j.physa.2005.11.024 362, 225 (2006). (Pubitemid 43234049)
28. P. Manneville, Instabilities, Chaos and Turbulence (Imperial College Press, London, 2010).
29. B. B. Mandelbrot, Fractals and Scaling in Finance (Springer, Berlin, 1997).
30. G. M. Molchan, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s002200050669 205, 97 (1999);
31. J.-H. Jeon, A. V. Chechkin, and R. Metzler, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/94/20008 94, 20008 (2011).
32. V. Tejedor and R. Metzler, J. Phys. A 1751-8113 10.1088/1751-8113/43/8/ 082002 43, 082002 (2010).
33. Note that two alternative approaches to correlated diffusion processes were introduced by M. M. Meerschaert, E. Nane, and Y. Xiao, Stat. Probab. Lett. 0167-7152 10.1016/j.spl.2009.01.007 79, 1194 (2009);
34. A. V. Chechkin, M. Hofmann, and I. M. Sokolov, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.031112 80, 031112 (2009).
35. 0 were assigned a finite initial waiting time.
36. M. Magdziarz, R. Metzler, W. Szczotka, and P. Zebrowski, J. Stat. Mech. 10.1088/1742-5468/2012/04/P04010 (2012) P04010.
37. L. Takács, Ann. Appl. Probab. 1050-5164 10.1214/aoap/1177005514 3, 186 (1993).
38. Normal diffusion is only recovered for δ -correlated waiting times [20].
39. B. V. Popović, Comm. Statist. Theor. Meth. CSTMDC 0361-0926 10.1080/03610926.2010.521287 41, 166 (2012).
40. A. Rebenshtok and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.210601 99, 210601 (2007); (Pubitemid 350137198)
41. G. Bel and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.240602 94, 240602 (2005). (Pubitemid 41636460)
42. A. Lubelski, I. M. Sokolov, and J. Klafter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.250602 100, 250602 (2008);
43. Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.058101 101, 058101 (2008);
44. S. Burov, J.-H. Jeon, R. Metzler, and E. Barkai, Phys. Chem. Chem. Phys. PPCPFQ 1463-9076 10.1039/c0cp01879a 13, 1800 (2011).
45. I. M. Sokolov and J. Klafter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.140602 97, 140602 (2006). (Pubitemid 44522395)
46. A. Weron, M. Magdziarz, and K. Weron, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.036704 77, 036704 (2008). (Pubitemid 351465387)
47. M. Magdziarz, A. Weron, and J. Klafter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.210601 101, 210601 (2008).