-
2
-
-
33744842323
-
-
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
-
-
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
-
15
-
-
0343827125
-
-
edited by D. Reguera, J. M. G. Vilar and J.M. Rubi Springer, Berlin
-
K.A. Dahmen, D.R. Nelson, and N.M. Shnerb, in Statistical Mechanics of Biocomplexity, edited by D. Reguera, J. M. G. Vilar and J.M. Rubi (Springer, Berlin, 1999).
-
(1999)
Statistical Mechanics of Biocomplexity
-
-
Dahmen, K.A.1
Nelson, D.R.2
Shnerb, N.M.3
-
22
-
-
0000453695
-
-
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
-
23
-
-
0034641717
-
-
N.M. Shnerb, Y. Louzoun, E. Bettelheim, and S. Solomon, Proc. Natl. Acad. Sci. 97, 10322 (2000).
-
(2000)
Proc. Natl. Acad. Sci.
, vol.97
, pp. 10322
-
-
Shnerb, N.M.1
Louzoun, Y.2
Bettelheim, E.3
Solomon, S.4
-
25
-
-
33744868822
-
-
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
-
-
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
-
-
36149049574
-
-
M. Doi, J. Phys. A 9, 1465 (1976);
-
(1976)
J. Phys. a
, vol.9
, pp. 1465
-
-
Doi, M.1
|