Parametric ordering of complex systems

Cellular automata (CA) dynamics are ordered in terms of two global parameters, computable {\sl a priori} from the description of rules. While one of them (activity) has been used before, the second one is new; it estimates the average sensitivity of rules to small configurational changes. For two well-known families of rules, the Wolfram complexity Classes cluster satisfactorily. The observed simultaneous occurrence of sharp and smooth transitions from ordered to disordered dynamics in CA can be explained with the two-parameter diagram

Transport Phenomena at a Critical Point -- Thermal Conduction in the Creutz Cellular Automaton --

Nature of energy transport around a critical point is studied in the Creutz cellular automaton. Fourier heat law is confirmed to hold in this model by a direct measurement of heat flow under a temperature gradient. The thermal conductivity is carefully investigated near the phase transition by the use of the Kubo formula. As the result, the thermal conductivity is found to take a finite value at the critical point contrary to some previous works. Equal-time correlation of the heat flow is also analyzed by a mean-field type approximation to investigate the temperature dependence of thermal conductivity. A variant of the Creutz cellular automaton called the Q2R is also investigated and similar results are obtained.Comment: 27 pages including 14figure