✦ LIBER ✦

Discrete models of growth and dynamical percolation in chemistry

✍ Scribed by Simon J. Fraser

Publisher: John Wiley and Sons
Year: 1987
Tongue: English
Weight: 830 KB
Volume: 8
Category: Article
ISSN: 0192-8651
DOI: 10.1002/jcc.540080420

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✦ Synopsis

Space-time lattice (cellular automaton) models of pattern formation and growth are described. Suitable local rules for automaton evolution represent the spreading of wave fronts of activity in an excitable medium. A random distribution of seeds produces expanding rings that fuse and are annihilated. The seeding density, p A , is used as a scaling parameter to give unique, reduced dynamics in an arbitrary dimensiop d . For d = 2, in this (continuum) picture, the rings fuse globally (percolate) at a critical instant, t , = 0.45. For the unscaled time evolution, dynamical percolation is examined in the pa x t plane. A swath of these percolating states is found. On the "explosion" boundary of this swath the percolation cluster just forms; on the "implosion" boundary it breaks up. Using a small-sample method the fractal dimension of the critical (boundary) cluster is estimated to be 1.9 (+0.01). Also percolation for continuously emitting seeds, which produce 'rdiscs'' of activity, is related to ring evolution.

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