Population growth in random media - II. Wavefront propagation

Greven A, den Hollander F (1991)

Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 1991


Publisher: Springer Verlag (Germany)

Book Volume: 65

Pages Range: 1147-1154

Journal Issue: 5/6

DOI: 10.1007/BF01049603


In this second part of a two-part presentation, we continue with the model introduced in Part I. In this part, the initial configuration has one particle at each site to the left of 0 and no particle elsewhere. The expected number of particles observed at a site moving at speed τ≥ has an exponential growth rate (speed-τ growth rate) that is computed explicitly. The result reveals two characteristic wavefront speeds: τ, the speed of the front of zero growth (rightmost particle), and τ, the speed of the front of maximal growth. The latter speed exhibits a phase transition, changing from zero to positive as the drift in the migration crosses a threshold. The qualitative shape of the growth rate as a function of τ changes as well. In particular, below the threshold there appears a linear piece, which corresponds to the system exhibiting an intermittency effect. © 1991 Plenum Publishing Corporation.

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Greven, A., & den Hollander, F. (1991). Population growth in random media - II. Wavefront propagation. Journal of Statistical Physics, 65(5/6), 1147-1154. https://doi.org/10.1007/BF01049603


Greven, Andreas, and Frank den Hollander. "Population growth in random media - II. Wavefront propagation." Journal of Statistical Physics 65.5/6 (1991): 1147-1154.

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