Truncation effects in superdiffusive front propagation with Lévy flights

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

Volumn 79, Issue 3, 2009, Pages

  Del Castillo Negrete, D ^a  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC REGIMES; CONSTANT VELOCITIES; DIFFUSION CONSTANTS; DIFFUSION OPERATORS; EXPONENTIAL CONVERGENCES; EXPONENTIAL TAILS; FISHER-KOLMOGOROV EQUATIONS; FRACTIONAL DERIVATIVES; FRONT PROPAGATION; FRONT VELOCITIES; GAUSSIAN; INITIAL CONDITIONS; LENGTH-SCALE; REACTION-DIFFUSION SYSTEMS; TRUNCATION EFFECTS;

ASYMPTOTIC ANALYSIS; BOUNDARY LAYER FLOW; COMPUTATIONAL COMPLEXITY; DIFFUSION; GROWTH KINETICS; MATHEMATICAL OPERATORS; SIGNAL ENCODING;

REACTION KINETICS;

EID: 65349151299     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.031120     Document Type: Article

References (34)

1. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993). 10.1103/RevModPhys.65.851
2. J. D. Murray, Mathematical Biology (Springer-Verlag, New York, 1989).
3. R. Metzler and J. Klafter, J. Phys. A 37, R161 (2004). 10.1088/0305-4470/37/31/R01
4. J. P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990). 10.1016/0370-1573(90)90099-N
5. Anomalous Transport. Foundations and Applications, edited by, R. Klages, G. Radons and, I. M. Sokolov, (Wiley-VCH Verlag, Weinheim, 2008).
6. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000). 10.1016/S0370- 1573(00)00070-3
7. D. H. Zanette, Phys. Rev. E 55, 1181 (1997). 10.1103/PhysRevE.55.1181
8. B. I. Henry and S. L. Wearne, Physica A 276, 448 (2000). 10.1016/S0378-4371(99)00469-0
9. R. Mancinelli, D. Vergni, and A. Vulpiani, Europhys. Lett. 60, 532 (2002). 10.1209/epl/i2002-00251-7
10. D. del-Castillo-Negrete, B. A. Carreras, and V. E. Lynch, Phys. Rev. Lett. 91, 018302 (2003). 10.1103/PhysRevLett.91.018302
11. A. Torcini and S. Lepri, Phys. Rev. E 55, R3805 (1997). 10.1103/PhysRevE.55.R3805
12. R. K. Saxena, A. M. Mathai, and H. J. Haubold, Astrophys. Space Sci. 305, 289 (2006). 10.1007/s10509-006-9189-6
13. D. Hernandez, R. Barrio, and C. Varea, Phys. Rev. E 74, 046116 (2006). 10.1103/PhysRevE.74.046116
14. I. M. Sokolov, M. G. W. Schmidt, and F. Sagues, Phys. Rev. E 73, 031102 (2006). 10.1103/PhysRevE.73.031102
15. D. Brockmann and L. Hufnagel, Phys. Rev. Lett. 98, 178301 (2007). 10.1103/PhysRevLett.98.178301
16. T. A. M. Langlands, B. I. Henry, and S. L. Wearne, J. Phys.: Condens. Matter 19, 065115 (2007). 10.1088/0953-8984/19/6/065115
17. A. A. Golovin, B. J. Matkowsky, and V. A. Volpert, SIAM J. Appl. Math. 69, 251 (2008). 10.1137/070703454
18. Y. Nec, A. A. Nepomnyashchy, and A. A. Golovin, Europhys. Lett. 82, 58003 (2008). 10.1209/0295-5075/82/58003
19. R. N. Mantegna and H. E. Stanley, Phys. Rev. Lett. 73, 2946 (1994). 10.1103/PhysRevLett.73.2946
20. I. Koponen, Phys. Rev. E 52, 1197 (1995). 10.1103/PhysRevE.52.1197
21. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1966), Vol. 2, Chap., p. 525.
22. M. F. Shlesinger, Phys. Rev. Lett. 74, 4959 (1995). 10.1103/PhysRevLett. 74.4959
23. A. Cartea and D. del-Castillo-Negrete, Phys. Rev. E 76, 041105 (2007). 10.1103/PhysRevE.76.041105
24. I. M. Sokolov, A. V. Chechkin, and J. Klafter, Physica A 336, 245 (2004). 10.1016/j.physa.2003.12.044
25. I. Podlubny, Fractional Differential Equations (Academic, San Diego, 1999).
26. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives (Gordon and Breach, Amsterdam, 1993).
27. G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes (Chapman & Hall, New York, 1994).
28. F. Mainardi, Y. Luchko, and G. Pagnini, Fractional Calculus Appl. Anal. 4, 153 (2001).
29. D. del-Castillo-Negrete, Phys. Plasmas 13, 082308 (2006). 10.1063/1.2336114
30. V. Lynch, B. A. Carreras, D. del-Castillo-Negrete, K. M. Ferreira-Mejias, and H. R. Hicks, J. Comput. Phys. 192, 406 (2003). 10.1016/j.jcp.2003.07.008
31. D. del-Castillo-Negrete and B. A. Carreras, Phys. Plasmas 9, 118 (2002); 10.1063/1.1421076
32. X. Garbet, Y. Sarazin, F. Imbeaux, P. Ghendrih, C. Bourdelle, O. D. Gurcan, and P. H. Diamond, Phys. Plasmas 14, 122305 (2007). 10.1063/1.2824375
33. D. del-Castillo-Negrete, in Turbulent Transport in Fusion Plasmas: First ITER International Summer School, edited by, S. Benkadda AIP Conf. Proc. No. 1013 (AIP, Melville, NY, 2008).
34. R. Jha, P. K. Kaw, D. R. Kulkami, J. C. Parikh, and the ADITYA Team, Phys. Plasmas 10, 699 (2003). 10.1063/1.1541607