非平衡系における大自由度複雑力学系の理論的および数値実験的研究

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1. Self-similarity statistics of on-off intermittecncy :Right above the instability point where particular chaotic motion becomes unstabale, we found a new statistics associated with the strong temporal correlation. To analyze it, we constructed a thermodynamics formalism valid in the strong correlation region. It was found that the resulting statistical quantities agree with numerical experiments.2. Intermittency associated with the onset of convection in systems under modulational noise :We proposed a nonlinear stochastic model for on-off intermittent pattern evolution observed in nematic liquid crystal system under multiplicative stochastic noise. Carrying out numerical experiment, we analyzed statistical quantities in detail. Furhtermore, introducing thermal noise in an additive way, we studied the effect of thermal noise on the temporal pattern change.3. Universal statistics in turbulence :By carrying out numerical calculation of the OGY shell model of turbulence, velocity- and energy-dissipation-rate-stucture functions were studied from the self-similarity statistics viewpoint. We found a good agreement with the result so far proposed for structure functions. We succeeded in deriving the extended self-similarity statistical law experimentally found.4. Dynamic phase transition in Ising spin system under periodic external field :We elucidated that the dynamic phase transition (DPT) observed in Monte Carlo simulation of Ising spin system under periodic external field is associated with the symmetry change of periodic motions, and then approximately reconstructed the phase diagram in the frequency-amplitude space. Furthermore, deriving the reduced dynamics of local magnetizaton near DPT, we found that statistical quantities resulting from it agree with those of numerical experiment.