Cellular automata models of natural complex systems - Batac, Rene C.
We present a simple mathematical tool that captures the global dynamics of complex systems based only on the local interactions. Our model is a cellular automata (CA), a finite lattice of cells whose evolution is governed by the state of the local neighborhood. The simplicity of the technique rests on the fact that the evolution of each cell state is governed by a single rule, unlike agent-based techniques in which the agents have a certain level of judgment and gets to decide on how to behave. Moreover, the flexibility of the model is emphasized in its ability to incorporate the inhomogeneity inherent in many-particle complex systems, a property not accounted for in techniques that model the system as a continuum. We apply the technique to granular materials to give insight into the stability of granular media, and know the possible mitigation measures for the hazards associated with them. Table-top experiments probing repose angeles θ of mixed granular media confirm the CA prediction of the existence of a supra-maximal mixture repose angles, or θmix > {θ1, θ2), for binary mixtures. From the model, we determine the two conditions needed to achieve stability: (1) the particle size ratio Rsmall/Rbig → 0; and (2) the bigger particle is in volume packin fraction. CA and experiment results show good agreement on mean and standard deviation, showing the capability of the model to describe the complexity of the system. The model also predicts existence of vertical slopes, a phenomenon observed in nature but is unexplained by continuum techniques. For large-scale systems, we modify the known sand-pile model of landslides in natural sloped formations to include the gradual slope degradation, and observe, among others, a good correspondence between frequency-size distributions of avalanche events for the model and actual landslide survey data.
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Keywords: Cellular automata