Noisy Wavefront Propagation in the Fisher-Kolmogorov-Petrovsky-Piscounov Equation

AIP Conference Proceedings

Volumn 665, Issue , 2003, Pages 523-530

  Doering, Charles R ^a   Mueller, Carl ^b   Smereka, Peter ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

^b UNIVERSITY OF ROCHESTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

WAVEFRONTS;

FRONT PROPAGATION; KOLMOGOROV; STOCHASTICS; WAVEFRONT PROPAGATION;

STOCHASTIC SYSTEMS;

EID: 29144445554     PISSN: 0094243X     EISSN: 15517616     Source Type: Conference Proceeding    
DOI: 10.1063/1.1584929     Document Type: Conference Paper

References (24)

1. R. A. FISHER, The wave of advance of advantageous genes, Annals of Eugenics 7, 353 (1937).
2. A. KOLMOGOROV, I. PETROVSKY, AND N. PISCOUNOV, Etude de l'equation de la diffusion avec croissance de la quantité de matière et son application a un probleme biologique, Moscow University Bulletin of Mathematics 1, 1 (1937).
3. J. A. MURRAY, Mathematical Biology (Springer-Verlag, Berlin, 1998).
4. M. BRAMSON, Convergence of Solutions of the Kolmogorov Equations to Traveling waves, Memoirs of the American Mathematical Society 44 (1983).
5. U. EBERT AND W. VAN SAARLOOS, Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts, Physica D 146, 1 (2000).
6. N. G. VAN KAMPEN, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
7. E. BRUNET AND B. DERRIDA, Shift in the velocity of a front due to a cutoff, Physical Review E 56, 2597 (1997).
8. D. A. KESSLER, Z. NER, AND L. M. SANDER, Front propagation: Precursors, cutoffs and structural stability, Physical Review E 58, 107 (1998).
9. L. PECHENIK AND H. LEVINE, Interfacial velocity corrections due to multiplicative noise, Physical Review E 59, 3893 (1999).
10. E. BRUNET AND B. DERRIDA, Effect of microscopic noise on front propagation, Journal of Statis_tical Physics 103, 269 (2001).
11. D. PANJA, Surprising Aspects of Fluctuating "Pulled" Fronts, UPoN 2002 (this volume).
12. C. MUELLER AND R. TRIBE, Stochastic PDEs arising from the long range contact and long range voter processes, Probability Theory & Related Fields 102, 519 (1995).
13. C. MUELLER AND R. B. SOWERS, Random travelling waves for the KPP equation with noise, Journal of Functional Analysis 128, 439 (1995).
14. J. XIN, Front propagation in heterogeneous media, SIAM Review 42, 161 (2000).
15. T.M. LIGGETT, Interacting Particle Systems (Springer-Verlag, Berlin, 1985).
16. T. SHIGA AND K. UCHIYAMA, Stationary states and the stability of the stepping stone model involving mutation and selection, Probability Theory & Related Fields 73, 87 (1986).
17. C. R. DOERING, C. MUELLER AND P. SMEREKA, Physica A (submitted, 2002).
18. M. A. BURSCHKA, C. R. DOERING, AND D. BEN AVRAHAM, Statics and Dynamics of a Diffusion_Limited Reaction: Anomalous Kinetics, Nonequilibrium Self-Ordering, and a Dynamic Transition, Journal of Statistical Physics 60, 695 (1990).
19. C. R. DOERING, M. A. BURSCHKA, AND W. HORSTHEMKE, Fluctuations and correlations in a diffusion-reaction systems: Exact hydrodynamics, Journal of Statistical Physics 65, 953 (1991).
20. D. BEN AVRAHAM, Fisher waves in the diffusion-limited coalescence process A Physics Letters A 247, 53 (1998).
21. J. RIORDAN, C. DOERING, AND D. BEN-AVRAHAM, Fluctuations and stability of Fisher waves, Physical Review Letters 75, 565 (1995).
22. G. TRIPATHY AND W. VAN SAARLOOS, Fluctuation and relaxation properties of pulled fronts: A scenario for nonstandard Kardar-Parisi-Zhang scaling, Physical Review Letters 85, 3556 (2000).
23. G. TRIPATHY, A. ROCCO, J. CASADEMUNT, AND W. VAN SAARLOOS, The universality class of fluctuating pulled fronts, Physical Review Letters 86, 5215 (2001).
24. E. MORO, Internal fluctuations effects on Fisher waves, Physical Review Letters 87, 238303.1-4 (2001