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

非平衡系统中大自由度复杂动力系统的理论与数值实验研究

基本信息

批准号：
11837009
负责人：
FUJISAKA Hirokazu
金额：
$ 2.11万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11837009/
关键词：
Ising spin system under oscillating field Dynamic phase transition Electrohydrodynamic convection On-off intermittency Intermittency in turbulence Statistical theory of turbulence Self-similarity in turbulence 振動磁場下の相転移電磁流体力学的対流不安定

项目摘要

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.

1。开关间歇性的自相似性统计：高于不稳定点的不稳定点，使特定的混乱运动变得不稳定，我们发现了与强时间相关性相关的新统计数据。为了分析它，我们在强相关区域中构建了有效的热力学形式主义。发现所得的统计量与数值实验一致。2。与调节噪声下系统中对流的发作相关的间歇性：我们提出了一个非线性随机模型，用于在乘法随机噪声下观察到在列液晶系统中观察到的开关间歇性模式演化。进行数值实验，我们详细分析了统计量。 furhtermore，以增材方式引入热噪声，我们研究了热噪声对时间模式变化的影响3。湍流中的普遍统计数据：通过从自相似性统计观点进行湍流，速度和能量 - 散射速率 - 降低函数的数值计算，速度和能量 - 散射速率降低函数。我们发现迄今为止为结构功能提出的结果一个很好的一致性。我们成功地得出了实验发现的扩展自相似性统计法。4。在周期性外场下的Ising自旋系统中的动态相变：我们阐明了在周期性外部场下的Ising Spin系统中观察到的动态相变（DPT）与周期性运动的对称变化有关，然后大约重建了频率空间中的相图。此外，通过得出DPT附近局部磁石的动力学减少，我们发现由此产生的统计量与数值实验的统计数量一致。