Anomalous transport equations and their application to fractal walking

Physica A: Statistical Mechanics and its Applications

Volumn 255, Issue 1-2, 1998, Pages 65-92

  Uchaikin, Vladimir V ^a  

^a ULYANOVSK STATE UNIVERSITY   (Russian Federation)

Author keywords

Anomalous diffusion; Fractals; Stable laws; Transport equation

Indexed keywords

DIFFUSION; EQUATIONS OF MOTION; FRACTALS; NUMERICAL ANALYSIS;

FRACTAL WALKING;

STATISTICAL MECHANICS;

EID: 0032099840     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00047-8     Document Type: Article

References (27)

1. B. Davison, Neutron Transport Theory, Clarendon Press, Oxford, 1947.
2. K.M. Case, P.F. Zweifel, Linear Transport Theory, Addison-Wesley, Reading, MA, 1967.
3. E. Wigner, in: Nuclear Reactor Theory, Proc. Symp. in Applied Mathematics, vol. XI, Providence, RI, 1961.
4. M.V. Maslennikov, Axiomatic Model of Particles Transport Phenomena, Nauka, Moscow, 1989.
5. J.-P. Bouchaud, A. Georges, Phys. Rep. 195 (1990) 127.
6. M.B. Isichenko, Rev. Mod. Phys. 64 (1992) 961.
7. B.J. West, W. Deering, Phys Rep. 246 (1994) 1.
8. B.B. Mandelbrot, Fractals, Forms, Chance and Dimension, Freeman, San Francisco, 1977.
9. V. Seshadri, B.J. West, Proc. Natl. Acad. Sci. USA 79 (1982) 4501.
10. R.R. Nigmatullin, Phys. Stat. Sol. (b) 123 (1984) 739.
11. T.F. Nonnenmacher, D.J.F. Nonnenmacher, Acta Phys. Hung. 66 (1989) 145.
12. B.J. West, J. Opt. Soc. Am. A 7 (1990) 1074.
13. V.V. Afanasiev, R.Z. Sagdeev, G.M. Zaslavsky, Chaos 1 (2) (1991) 143.
14. W. Feller, An Introduction to Probability Theory, vol. 2, Wiley, New York, 1971.
15. D.R. Cox, Renewal Theory, Chapman & Hall, London, 1982.
16. J. Spanier, E. Gelbard, Monte Carlo Principles and Neutron Transport Problems, Addison-Wesley, Reading, MA, 1968.
17. K.V. Chukbar, Zh. Eksp. Teor. Fiz. 108 (1995) 1875.
18. J. Klafter, A. Blumen, M.F. Shlesinger, Phys. Rev. A 35 (1987) 3081.
19. A. Compte, Phys. Rev. E 53 (1996) 4191.
20. A. Compte, D. Jou, Y. Katayama, J. Phys. A: Math. Gen. 30 (1997) 1023.
21. E.W. Montroll, G.H. Weiss, J. Math. Phys. 6 (1965) 167.
22. A.S. Monin, A.M. Yaglom, Statistical Fluid Mechanics, vol. I, MIT, Cambridge, MA, 1971.
23. W. Wyss, J. Math. Phys. 27 (1986) 2782.
24. W.G. Glöckle, T.F. Nonnenmacher, J. Stat. Phys. 71 (1993) 741.
25. B.J. West, P. Grigolini, R. Metzler, T.F. Nonnenmacher, Phys. Rev. E 55 (1997) 99.
26. M.F. Shlesinger, J. Klafter, Y.M. Wong, J. Stat. Phys. 27 (1982) 499.
27. V.M. Zolotarev, One-dimensional Stable Distributions, American Mathematical Society, Providence, RI, 1986.