Front Dynamics in Reaction-Diffusion Systems with Levy Flights: A Fractional Diffusion Approach

Physical Review Letters

Volumn 91, Issue 1, 2003, Pages

  del Castillo Negrete, D ^a   Carreras, B A ^a   Lynch, V E ^a  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DIFFUSION; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION; REACTION KINETICS;

FRACTIONAL DIFFUSION; LEVY FLIGHTS; REACTION DIFFUSION SYSTEMS;

DYNAMICS;

EID: 0043210605     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.91.018302     Document Type: Article

References (22)

1. J.D. Murray, Mathematical Biology (Springer-Verlag, New York, 1989);
2. M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys.10.1103/RevModPhys.65.851 65, 851 (1993).
3. J.P. Bouchaud and A. Georges, Phys. Rep.10.1016/0370-1573(90)90099-N 195, 127 (1990).
4. D. del-Castillo-Negrete and B.A. Carreras, Phys. Plasmas10.1063/1.1421076 9, 118 (2002);
5. D. del-Castillo-Negrete, B.A. Carreras, and V. Lynch, Physica (Amsterdam)10.1016/S0167-2789(02)00494-3 168D–169D, 45–60 (2002).
6. K.W. Gentle et al, Phys. Plasmas10.1063/1.871252 2, 2292 (1995).
7. B.A. Carreras, V.E. Lynch, and G.M. Zaslavsky, Phys. Plasmas10.1063/1.1416180 8, 5096 (2001).
8. D. del-Castillo-Negrete, Phys. Plasmas10.1063/1.873988 7, 1702 (2000).
9. G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes (Chapman & Hall, New York, 1994).
10. T.H. Solomon, E.R. Weeks, and H.L. Swinney, Phys. Rev. Lett.10.1103/PhysRevLett.71.3975 71, 3975 (1993);
11. D. del-Castillo-Negrete, Phys. FluidsPHFLE610.1063/1.869585 10, 576 (1998).
12. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
13. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000).
14. R. Hilfer, Application of Fractional Calculus in Physics (World Scientific, Singapore, 2000);
15. I.M. Sokolov, J. Klafter, and A. Blumen, Phys. Today 55, 48 (2002).
16. B.I. Henry and S.L. Wearne, Physica (Amsterdam)10.1016/S0378-4371(99)00469-0 276A, 448 (2000).
17. D.H. Zanette, Phys. Rev. EPLEEE810.1103/PhysRevE.55.1181 55, 1181 (1997).
18. R. Mancinelli, D. Vergni, and A. Vulpiani, Europhys. Lett. 60, 532–538 (2002).
19. A.I. Saichev and G.M. Zaslavsky, Chaos10.1063/1.166272 7, 753 (1997);
20. A.S. Chaves, Phys. Lett. A10.1016/S0375-9601(97)00947-X 239, 13–16 (1998);
21. P. Paradisi, R. Cesari, F. Mainardi, and F. Tampieri, Physica (Amsterdam)10.1016/S0378-4371(00)00491-X 293A, 130–142 (2001).
22. W. van Saarloos, Phys. Rev. A10.1103/PhysRevA.37.211 37, 211 (1988).