Multi-affinity and multi-fractality in systems of chaotic elements with long-wave forcing |
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Authors: | H. Nakao Y. Kuramoto |
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Affiliation: | (1) Department of Physics, Graduate School of Sciences, Kyoto University, Kyoto 606-8502, Japan, JP |
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Abstract: | Multi-scaling properties in quasi-continuous arrays of chaotic maps driven by long-wave random force are studied. The spatial pattern of the amplitude X(x,t) is characterized by multi-affinity, while the field defined by its coarse-grained spatial derivative exhibits multi-fractality. The strong behavioral similarity of the X- and Y-fields respectively to the velocity and energy dissipation fields in fully-developed fluid turbulence is remarkable, still our system is unique in that the scaling exponents are parameter-dependent and exhibit nontrivial q-phase transitions. A theory based on a random multiplicative process is developed to explain the multi-affinity of the X-field, and some attempts are made towards the understanding of the multi-fractality of the Y-field. Received 16 November 1998 |
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Keywords: | PACS. 05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 47.53.+n Fractals |
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