Front propagation dynamics with exponentially-distributed hopping

Journal of Statistical Physics

Volumn 122, Issue 5, 2006, Pages 925-948

  Cohen, Elisheva ^a   Kessler, David A ^a  

^a BAR ILAN UNIVERSITY   (Israel)

Author keywords

Front propagation; Reaction diffusion

Indexed keywords

EID: 33645782934     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-005-9004-8     Document Type: Article

References (28)

1. A. I. Kolmogorov, I. Petrovsky, and N. Piscounov. Moscow Univ. Bull. Math. A1:1 (1937).
2. D. A. Kessler, I Koplik, and H. Levine. Adv. Phys. 37:255 (1988).
3. J.Mai, I. M. Sokolov, and A. Blumen. Phys. Rev. Lett. 77:4462 (1996).
4. R. A. Fisher. Annual Eugenics 7:355 (1937).
5. D. A. Kessler, Z. Ner, and L. M. Sander. Phys. Rev. E 58:107 (1998).
6. E. Brunei and B. Derrida. Phys. Rev. E 56:2597 (1997).
7. U. Ebert and W. van Saarloos. Phys. Rev. Lett. 80:1650 (1998).
8. L. Pechenik and H. Levine. Phys. Rev. E 59:3893 (1999).
9. E. Ben-Jacob, et al. Physica D 14:348 (1985).
10. E. Brener, H. Levine, and Y. Tu. Phys. Rev. Lett. 66:1978 (1991).
11. T. B. Kepler and A. S. Perelson. PNAS 92:8219 (1995).
12. Progress has also been made on proving that modelling the stochastic process by adding appropriate multiplicative noise to the mean-field reaction-diffusion equation introduces qualitative changes to the nature of the solution, in particular producing a reaction zone with compact support. See C. Mueller and R. B. Sowers. J. Funct. Anal. 128:439 (1995). See also
13. J. G. Conlon and C R. Doering, "On Travelling Waves for the Stochastic Fisher-Kolmogorov-Petrovsky-Piscunov Equation", (preprint) who obtain bounds on the front velocity.
14. D. A. Kessler and H. Levine., Nature 394:556 (1998).
15. E. Moro, Phys. Rev. Lett. 87:238303 (2001).
16. E. Cohen, D. A. Kessler, and H. Levine., Phys. Rev. Lett. 94:158302 (2005).
17. E. Cohen, D. A. Kessler, and H. Levine., in preparation.
18. Experimental propagation against a gradient appears in D. Giller, et al., Phys. Rev. B 63:220502(R) (2001).
19. M. Freidlin, in P. L. Hennequin, ed., Lecture Notes in Mathematics 1527 (Springer-Verlag, Berlin, 1992).
20. L. S. Tsimring, H. Levine and D. A. Kessler., Phys. Rev. Lett. 76:4440 (1996).
21. D. A. Kessler, D. Ridgway, H. Levine, and L. Tsimring., J. Stat. Phys. 87:519 (1997).
22. I. M. Rouzine, J. Wakeley, and J. M. Coffin., PNAS 100:587 (2003).
23. E. Cohen, D. A. Kessler and H. Levine., Phys. Rev. Lett. 94: 098102 (2005).
24. R. E. Snyder., Ecology 84:1333 (2003).
25. P. J. Gerrish and R. E. Lenski., Genetica 102/103:127 (1998).
26. For a study of Fisher dynamics with Lévy flight transport, without a consideration of cutoff/stochastic effects, see D. del-Castillo-Negrete, B. A. Carreras, and V E. Lynch., Phys. Rev. Lett. 91:018302(2003).
27. L. I. Slepyan., Sov. Phys. Dokl. 26:538 (1981).
28. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, (Springer, New York, 1999), Sec. 5.5.