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

1. 开关间歇的自相似统计：在特定混沌运动变得不稳定的不稳定点上方，我们发现了与强时间相关性相关的新统计。为了分析它，我们构造了一个在强相关区域有效的热力学形式。结果表明，所得的统计量与数值实验结果一致。调制噪声下系统中与对流开始相关的间歇性：我们提出了一个非线性随机模型，用于在乘性随机噪声下向列液晶系统中观察到的开-关间歇性模式演变。通过数值实验，对统计量进行了详细分析。在此基础上，以加性方式引入热噪声，研究了热噪声对时间格局变化的影响。紊流中的普遍统计：通过对紊流的OGY壳模型进行数值计算，从自相似统计的角度研究了速度-和耗能-率-结构函数。我们发现在结构函数上的结果与目前提出的结果很吻合。我们成功地推导了实验发现的扩展自相似统计定律。周期外场作用下Ising自旋系统的动态相变：阐明了周期外场作用下Ising自旋系统Monte Carlo模拟中观测到的动态相变（DPT）与周期运动的对称性变化有关，并在频幅空间中近似重建了相图。进一步推导了DPT附近局部磁化的约化动力学，得到的统计量与数值实验结果一致。

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.