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.开关间歇性的自相似统计量：就在特定混沌运动变得不稳定的不稳定点上方，我们发现了一个与强时间相关性相关的新统计量。为了分析它，我们构造了一个在强关联区有效的热力学公式。结果表明，所得的统计量与数值实验结果相吻合。调制噪声下系统中与对流开始有关的间歇性：我们提出了一个乘性随机噪声下向列相液晶系统中观察到的开关间歇性图案演化的非线性随机模型。通过数值实验，对统计量进行了详细的分析。在此基础上，以加性的方式引入热噪声，研究了热噪声对时间图样变化的影响。湍流中的普适统计：通过对OGY壳体湍流模型进行数值计算，从自相似统计的观点研究了速度和能量耗散率结构函数。我们发现与目前提出的结构函数的结果有很好的一致性。成功地推导出了实验发现的扩展自相似统计定律。周期外场下伊辛自旋系统的动态相变：我们阐明了周期外场下伊辛自旋系统的蒙特卡罗模拟中观察到的动态相变(DPT)与周期运动的对称性变化有关，并在频率-幅度空间中近似重建了相图。此外，通过推导DPT附近的局域磁化约化动力学，我们发现由此得到的统计量与数值实验的结果一致。

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.