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Volumn 63, Issue 2 I, 2001, Pages 0211031-0211036

Adaptation of autocatalytic fluctuations to diffusive noise

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CONTINUUM MECHANICS; DIFFUSION; LATTICE CONSTANTS; MATHEMATICAL MODELS; MOLECULAR DYNAMICS; PROBABILITY DISTRIBUTIONS;

EID: 4243971213     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.021103     Document Type: Article
Times cited : (32)

References (28)
  • 2
    • 33744842323 scopus 로고
    • See, e.g., J.D. Murray, Mathematical Biology (Springer-Verlag, New York, 1989); A. Okubo, Diffusion and Ecological Problems: Mathematical Models (Springer-Verlag, New York, 1980); R. Durrett and S. Levin, Theo. Popu. Bio. 46, 395 (1994).
    • (1994) Mathematical Biology Springer-Verlag, New York , vol.1989 , pp. 1980
    • See, E.G.1    Murray, J.D.2
  • 8
    • 0004018896 scopus 로고
    • edited by G. Deutsch, R. Zallen, and J. Adler Adam Hilger, Bristol
    • W. Kinzel, in Percolation Structure and Processes, edited by G. Deutsch, R. Zallen, and J. Adler (Adam Hilger, Bristol, 1983).
    • (1983) Percolation Structure and Processes
    • Kinzel In, W.1
  • 22
    • 0000453695 scopus 로고
    • our work here deals with the limit of 1/ω noise, which is not connected perturbatively to the uncorrelated (KPZ) limit.
    • Burger's system with correlated noise has been considered by E. Medina, T. Hvva, M. Kardar, and Y-C. Zhang, Phys. Rev. A 39, 3053 (1989); our work here deals with the limit of 1/ω noise, which is not connected perturbatively to the uncorrelated (KPZ) limit.
    • (1989) Phys. Rev. a , vol.39 , pp. 3053
    • Medina, E.1    Hvva, T.2    Kardar, M.3    Zhang, Y.-C.4
  • 25
    • 33744868822 scopus 로고    scopus 로고
    • note
    • Actually, all the states in the tail are localized for any dimensionality or disorder strength, and the first state to become active, with positive eigenvalue, is always localized. However, as we have noted before, taking into account the discrete nature of the reactants implies the extinction of any finite colony due to rare fluctuations, and the activation of the system takes place only as the time scale for this extinction of a single colony is comparable to the tunneling rate to neighboring oases. For the sake of simplicity, we assume that all the relevant eigenstates of L are localized.
  • 26
    • 33744845985 scopus 로고    scopus 로고
    • We may approximate the effect of reactant quantization by taking a lower cutoff for b(r), e.g., b(r) is given by Eq. (3) only for b>const and is zero elsewhere.
    • We may approximate the effect of reactant quantization by taking a lower cutoff for b(r), e.g., b(r) is given by Eq. (3) only for b>const and is zero elsewhere.
  • 27


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