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• W2782137657 abstract "Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions." @default.
• W2782137657 created "2018-01-12" @default.
• W2782137657 creator A5047565816 @default.
• W2782137657 creator A5061071237 @default.
• W2782137657 date "2018-07-01" @default.
• W2782137657 modified "2023-09-27" @default.
• W2782137657 title "Local causal states and discrete coherent structures" @default.
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• W2782137657 doi "https://doi.org/10.1063/1.5021130" @default.
• W2782137657 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/30070532" @default.
• W2782137657 hasPublicationYear "2018" @default.
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