Stochastic processes crossing from ballistic to fractional diffusion with memory: Exact results

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

Volumn 81, Issue 3, 2010, Pages

  Ilyin, Valery ^a   Procaccia, Itamar ^a   Zagorodny, Anatoly ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b BOGOLYUBOV INSTITUTE FOR THEORETICAL PHYSICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTICS; BALLISTIC REGIME; CLASSICAL PROBLEMS; CONTINUOUS FUNCTIONS; DIFFUSION EQUATIONS; DIFFUSION PROCESS; EXACT RESULTS; FRACTIONAL DIFFUSION; GENERAL SOLUTIONS; MEMORY KERNELS; NON-MARKOVIAN; STOCHASTIC PROCESS; SUBDIFFUSION; SUPERDIFFUSION;

BALLISTICS; DISTRIBUTION FUNCTIONS; RANDOM PROCESSES;

DIFFUSION;

EID: 77950148203     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.030105     Document Type: Article

References (19)

1. H. E. Hurst, Trans. Am. Soc. Civ. Eng. 116, 770 (1951).
2. B. B. Mandelbrot and J. W. van Ness, SIAM Rev. 10, 422 (1968). 10.1137/1010093
3. B. Rinn, W. Dietriech, and P. Maass, Philos. Mag. B 77, 1283 (1998). 10.1080/13642819808205021
4. A. Klemm, H.-P. Müller, and R. Kimmich, Physica A 266, 242 (1999). 10.1016/S0378-4371(98)00599-8
5. F. Klammler and R. Kimmich, Croat. Chem. Acta 65, 455 (1992).
6. E. Fischer, R. Kimmich, U. Beginn, M. Möller, and N. Fatkullin, Phys. Rev. E 59, 4079 (1999). 10.1103/PhysRevE.59.4079
7. M. Porto, A. Bunde, S. Havlin, and H. E. Roman, Phys. Rev. E 56, 1667 (1997). 10.1103/PhysRevE.56.1667
8. O. Cardoso and P. Tabeling, Europhys. Lett. 7, 225 (1988). 10.1209/0295-5075/7/3/007
9. E. R. Weeks and H. L. Swinney, Phys. Rev. E 57, 4915 (1998). 10.1103/PhysRevE.57.4915
10. W. D. Luedtke and U. Landman, Phys. Rev. Lett. 82, 3835 (1999). 10.1103/PhysRevLett.82.3835
11. L. F. Richardson, Proc. R. Soc. London, Ser. A 110, 709 (1926). 10.1098/rspa.1926.0043
12. J. Bodurka, R.-O. Seitter, R. Kimmich, and A. Gutsze, J. Chem. Phys. 107, 5621 (1997). 10.1063/1.474237
13. S. Schaufler, W. P. Schleich, and V. P. Yakovlev, Phys. Rev. Lett. 83, 3162 (1999). 10.1103/PhysRevLett.83.3162
14. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000). 10.1016/S0370- 1573(00)00070-3
15. V. M. Kenkre and R. S. Knox, Phys. Rev. B 9, 5279 (1974). 10.1103/PhysRevB.9.5279
16. I. M. Sokolov, Phys. Rev. E 66, 041101 (2002). 10.1103/PhysRevE.66.041101
17. B. van der Pol and H. Bremmer, Operational Calculus (Cambridge University Press, Cambrige, 1964).
18. D. G. Duffy, ACM Trans. Math. Softw. 19, 333 (1993). 10.1145/155743. 155788
19. R. C. Ball, S. Havlin, and G. H. Weiss, J. Phys. A 20, 4055 (1987). 10.1088/0305-4470/20/12/052