Two-time scale subordination in physical processes with long-term memory

Annals of Physics

Volumn 323, Issue 3, 2008, Pages 643-653

  Stanislavsky, Aleksander ^a   Weron, Karina ^b  

^a INSTITUTE OF RADIO ASTRONOMY   (Ukraine)

^b WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

02.50. r; 02.50.Ey; 82.40. g; Anomalous diffusion; Continuous medium with memory; Nonexponential relaxation; Subordination; Trapping reaction

Indexed keywords

EID: 39749088801     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2007.04.011     Document Type: Article

References (30)

1. Toussaint D., and Wilczek F. J. Chem. Phys. 78 (1983) 2642-2647
2. Bramson M., and Lebowitz J.L. Phys. Rev. Lett. 61 (1988) 2397-2400
3. ben Avraham D., and Havlin S. Diffusion and Reactions in Fractals and Disordered Systems (2000), Cambridge University Press, Cambridge
4. Sung J., Barkai E., Silbey R.J., and Lee S. J. Chem. Phys. 116 6 (2002) 2338-2341
5. Moreau M., Oshanin G., Bénichou O., and Coppey M. Phys. Rev. E 67 (2003) 045104R
6. Bray A.J., Majumdar S.N., and Blythe R.A. Phys. Rev. E 67 (2003) 060102
7. Yuste S.B., and Lindenberg K. Phys. Rev. E 72 (2005) 061103
8. Yuste S.B., and Lindenberg K. Proc. SPIE 5845 (2005) 27-39
9. Klafter J., Blumen A., and Zumofen G. J. Stat. Phys. 36 (1984) 561-577
10. Metzler R., and Klafter J. Phys. Rep. 339 (2000) 1-77
11. Schneider W.R., and Wyss W. J. Math. Phys. 30 (1989) 134-144
12. Podlubny I. Fractional Differential Equations (1999), Academic Press, San Diego
13. Meerschaert M.M., and Scheffler H.-P. J. Appl. Probab. 41 (2004) 623-638
14. Stanislavsky A.A. Theor. Math. Phys. 138 3 (2004) 418-431
15. Sokolov I.M. Phys. Rev. E 63 (2000) 011104
16. Stanislavsky A.A. Acta Phys. Polon. B 34 7 (2003) 3649-3660
17. Magdziarz M., and Weron K. Physica A 367 (2006) 1-6
18. Magdziarz M., and Weron K. Acta Phys. Polon. B 37 5 (2006) 1617-1624
19. Z.B. Djordjeviover(c, ̌), Scaling observation in the trapping reaction, in: Fractals in Physics, Proceeding of Sixth Trieste International Symposium, L. Pietronero, E. Tossati, (Eds.), North-Holland, Amsterdam, 1986, pp. 581-585.
20. Dybiec B., Gudowska-Nowak E., and Hanggi P. Phys. Rev. E 73 (2006) 046104
21. Heinsalu E., Patriarca M., Goychuk I., Schmid G., and Hanggi P. Phys. Rev. E 73 (2006) 046133
22. Magdziarz M., Weron A., and Weron K. Phys. Rev. E 75 (2006) 016708
23. Piryatinska A., Saichev A.I., and Woyczynski W.A. Physica A 349 (2005) 375-420
24. Majumdar S.N., and Cornell S.J. Phys. Rev. E 57 (1998) 3757-3766
25. Landay L.D., and Lifshitz E.M. Fluid Mechanics (1997), Butterworth-Heinemann, Oxford
26. M.B. Vinogradova, O.V. Rudenko, A.P. Sukhorukov, Wave Theory, Fiziko-matematicheskaya literatura, Moscow, 1990, pp. 87-90.
27. Bagley R.L., and Torvik P.J. J. Rheol. 27 3 (1983) 201-210
28. Torvik P.J., and Bagley R.L. J. Appl. Mech. 51 (1984) 294-298
29. A.M. Nakhushev, Fractional calculus and its application, Fiziko-matema-ticheskaya literatura, Moscow, 2005, pp. 189-193.
30. Stanislavsky A.A. Phys. Rev. E 67 (2003) 021111