"Active systems fractal dynamics"
D.I. Iudin (Radiophysical Research Institute, Nizhny Novgorod)
Abstract:
We consider dynamic percolation effects on the base of a cellular automaton model on tree-dimensional lattice. Each site of the lattice is related to a time-dependent scalar that characterises potential of the point. We consider three random-growth models: the simplest one, when random additions with a normal distribution are added to the potentials at the lattice sites at each step of model time; the second, when along with random additions we add an external bias field; and the last and most complicated case, when potential relief looks like generalised Brownian landscape. In every case, each site, independently of its neighbours, undergoes Brownian motion in the space of potential values. The potential difference growth is limited by some critical value. As soon as this critical value is reached for any two neighbouring sites on the lattice, breakdown between the sites takes place and the lattice bond between the sites becomes a conductor. We assume that such a fine scale spark discharge can initiate breakdowns of the neighbouring lattice bonds ("infect" the neighbours), if the potential difference between the cells exceeds some activation level, which is less than critical one. The process manifests itself as a self-maintaining chain reaction and can be considered as a self-organized critical phenomenon. Then we consider thunderstorm activity problem on the base of the model developed. Our principal aim is to raise the idea that preliminary stage of lightning discharge is closely related to the fine electrical structure of a thundercloud, which has been detected practically in all in-situ experiments. Dissipative beam-plasma instability provides physical basis for this structure and generates small-scale electric cells with a scale 1 - 10 m . Short-living electric discharges appear at first in these cells. Interaction of neighbouring cells leads to formation of dynamical chains of microdischarges, which reveal percolation-like behaviour in the wide range of model parameters. Even a weak macroscopic electric field modifies drastically the structure and dynamical features of the conducting percolation cluster. The important new effect in this situation is a large-scale electric current, which flows through the conducting cluster and redistributes the large-scale electric charge. We show that fractal dynamics of electrical microdischarges in a thundercloud can serve as the basis for explanation of main features of a lightning flash on its preliminary stage. We consider dynamical modification of Hack’s and Horton’s lows.