Overshooting and undershooting subordination scenario for fractional two-power-law relaxation responses

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

Volumn 81, Issue 4, 2010, Pages

  Weron, Karina ^a   Jurlewicz, Agnieszka ^a   Magdziarz, Marcin ^a   Weron, Aleksander ^a   Trzmiel, Justyna ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ANOMALOUS DIFFUSION; COUNTING PROCESS; COUPLED CONTINUOUS-TIME RANDOM WALK; DIFFUSION PROCESS; MIXED CRYSTALS; NONEXPONENTIAL RELAXATION; OVERSHOOTING AND UNDERSHOOTING; POWER LAW RELAXATION; RELAXATION BEHAVIORS;

TELLURIUM COMPOUNDS;

GALLIUM;

EID: 77951526089     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.041123     Document Type: Article

References (38)

1. A. K. Jonscher, Dielectric Relaxation in Solids (Chelsea Dielectrics Press, London, 1983).
2. S. Havriliak, Jr. and S. J. Havriliak, J. Non-Cryst. Solids 172-174, 297 (1994). 10.1016/0022-3093(94)90448-0
3. A. K. Jonscher, Universal Relaxation Law (Chelsea Dielectrics Press, London, 1996).
4. Y. P. Kalmykov, W. T. Coffey, D. S. F. Crothers, and S. V. Titov, Phys. Rev. E 70, 041103 (2004). 10.1103/PhysRevE.70.041103
5. K. Weron, A. Jurlewicz, and M. Magdziarz, Acta Phys. Pol. B 36, 1855 (2005).
6. A. Jurlewicz, K. Weron, and M. Teuerle, Phys. Rev. E 78, 011103 (2008). 10.1103/PhysRevE.78.011103
7. J. Trzmiel, K. Weron, and E. Placzek-Popko, J. Appl. Phys. 103, 114902 (2008). 10.1063/1.2936984
8. J. Trzmiel, K. Weron, J. Janczura, and E. Placzek-Popko, J. Phys.: Condens. Matter 21, 345801 (2009). 10.1088/0953-8984/21/34/345801
9. I. M. Sokolov, Phys. Rev. E 63, 011104 (2000) 10.1103/PhysRevE.63.011104
10. I. M. Sokolov, Phys. Rev. E 66, 041101 (2002). 10.1103/PhysRevE.66.041101
11. M. M. Meerschaert and H.-P. Scheffler, J. Appl. Probab. 41, 623 (2004). 10.1239/jap/1091543414
12. M. M. Meerschaert, D. A. Benson, H.-P. Scheffler, and P. Becker-Kern, Phys. Rev. E 66, 060102 (R) (2002). 10.1103/PhysRevE.66.060102
13. M. M. Meerschaert and E. Scalas, Physica A 370, 114 (2006). 10.1016/j.physa.2006.04.034
14. A. Piryatinska, A. I. Saichev, and W. A. Woyczynski, Physica A 349, 375 (2005). 10.1016/j.physa.2004.11.003
15. I. M. Sokolov and J. Klafter, Phys. Rev. Lett. 97, 140602 (2006). 10.1103/PhysRevLett.97.140602
16. M. Magdziarz and K. Weron, Physica A 367, 1 (2006). 10.1016/j.physa.2005. 12.011
17. M. Magdziarz, A. Weron, and K. Weron, Phys. Rev. E 75, 016708 (2007). 10.1103/PhysRevE.75.016708
18. A. Lubelski, I. M. Sokolov, and J. Klafter, Phys. Rev. Lett. 100, 250602 (2008). 10.1103/PhysRevLett.100.250602
19. M. Magdziarz, A. Weron, and J. Klafter, Phys. Rev. Lett. 101, 210601 (2008). 10.1103/PhysRevLett.101.210601
20. R. Metzler, E. Barkai, and J. Klafter, Phys. Rev. Lett. 82, 3563 (1999). 10.1103/PhysRevLett.82.3563
21. K. Weron and M. Kotulski, Physica A 232, 180 (1996). 10.1016/0378- 4371(96)00209-9
22. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000). 10.1016/S0370- 1573(00)00070-3
23. E. Gudowska-Nowak, K. Bochenek, A. Jurlewicz, and K. Weron, Phys. Rev. E 72, 061101 (2005). 10.1103/PhysRevE.72.061101
24. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957). 10.1143/JPSJ.12.570
25. R. H. Cole, J. Chem. Phys. 42, 637 (1965). 10.1063/1.1695984
26. A. Jurlewicz, Diss. Math. 431, 1 (2005). 10.4064/dm431-0-1
27. M. O. Vlad, Phys. Rev. A 45, 3600 (1992). 10.1103/PhysRevA.45.3600
28. M. O. Vlad and M. C. Mackey, Phys. Rev. E 51, 3104 (1995). 10.1103/PhysRevE.51.3104
29. T. G. Dewey, Fractals in Molecular Biophysics (Oxford University Press, Oxford, 1997).
30. V. M. Zolotarev, One-Dimensional Stable Distributions (American Mathematical Society, Providence, 1986).
31. I. Eliazar and J. Klafter, Physica A 336, 219 (2004). 10.1016/j.physa.2003.12.032
32. T. Koren, M. A. Lomholt, A. V. Chechkin, J. Klafter, and R. Metzler, Phys. Rev. Lett. 99, 160602 (2007). 10.1103/PhysRevLett.99.160602
33. J. V. Bertelsen and A. Lindgård, J. Polym. Sci., Polym. Phys. Ed. 12, 1707 (1974). 10.1002/pol.1974.180120815
34. A. Jurlewicz, Appl. Math. (Warsaw, Poland) 30, 325 (2003). 10.4064/am30-3-7
35. R. Gorenflo and F. Mainardi, in Fractals and Fractional Calculus in Continuum Mechanics, edited by, A. Carpinteri, and, F. Mainardi, (Springer-Verlag, New York, 1997), pp. 223-276.
36. D. Fulger, E. Scalas, and G. Germano, Phys. Rev. E 77, 021122 (2008). 10.1103/PhysRevE.77.021122
37. W. Paul and J. Baschnagel, Stochastic Processes from Physics to Finance (Springer-Verlag, Berlin, 1999).
38. B. J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators (Springer-Verlag, New York, 2003).