CHARACTERIZATION OF ASYMMETRIC FRAGMENTATION PATTERNS IN SPATIALLY EXTENDED SYSTEMS

R. R. Rosa (), A. S. Sharma () and J. A. Valdivia
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R. R. Rosa: Lab for Computing and Applied Mathematics (LAC), National Institute for Space Research-INPE, Brazil Cx. Postal 515, 12201-970, S. J. dos Campos, SP, Brazil
A. S. Sharma: Astronomy and Physics Departments, University of Maryland, College Park-MD, 20742-2421, USA
J. A. Valdivia: Astronomy and Physics Departments, University of Maryland, College Park-MD, 20742-2421, USA

International Journal of Modern Physics C (IJMPC), 1999, vol. 10, issue 01, 147-163

Abstract: Spatially extended systems yield complex patterns arising from the coupled dynamics of its different regions. In this paper we introduce a matrix computational operator,${\mathcal F}_{\mathcal A}$, for the characterization of asymmetric amplitude fragmentation in extended systems. For a given matrix of amplitudes this operation results in an asymmetric-triangulation field composed byLpoints andIstraight lines. The parameter(I-L)/Lis a new quantitative measure of the local complexity defined in terms of the asymmetry in the gradient field of the amplitudes. This asymmetric fragmentation parameter is a measure of the degree of structural complexity and characterizes the localized regions of a spatially extended system and symmetry breaking along the evolution of the system. For the case of a random field, in the real domain, which has total asymmetry, this asymmetric fragmentation parameter is expected to have the highest value and this is used to normalize the values for the other cases. Here, we present a detailed description of the operator${\mathcal F}_{\mathcal A}$and some of the fundamental conjectures that arises from its application in spatio-temporal asymmetric patterns.

Keywords: Spatio-Temporal complexity; Amplitude fragmentation; Extended systems; Symmetry breaking; Pattern dynamics (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1142/S0129183199000103

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