Ordering Mechanisms in Dynamical Systems

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9412416 This grant is supported jointly by the Materials Theory Program in the Division of Materials Research and the Mathematical Physics Activity in the Physics Division. The theoretical research concerns several different mechanisms that may play a role in generating spatial or temporal order in systems governed by simple dynamical rules. The emphases are on controlling chaos in high- frequency systems and spatiotemporally complex systems and on coherent global oscillations and self-organized critical correlations in slowly driven dynamical systems. Immediate goals include a more complete understanding of a novel technique for controlling chaos using continuous feedback, the development of tests for detecting this type of control mechanism in natural systems, and the analysis of simple models of sandpiles that exhibit global oscillations and novel forms of self-organized critical behavior. %%% This theoretical research is in the general area of nonlinear science and is jointly supported by the Physics and Materials Research Divisions. The work focuses on a class of problems which are governed by simple local rules. The work may impact the design of individual semiconductor laser devices, the design of feedback mechanisms for inducing coherence in arrays of such lasers or arrays of Josephson junctions, and better methods for characterizing the instabilities observed in natural dynamical systems ranging from cardiac chaos to avalanches in granular materials.