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

• 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

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-关混沌运动的自相似统计：在特定混沌运动变得不稳定的不稳定点之上，我们发现了与强时间相关性相关的新统计。为了分析它，我们建立了一个热力学形式有效的强关联区域。结果表明，所得的统计量与数值实验结果一致.调制噪声下系统中对流发生的间歇性：我们提出了一个非线性随机模型，描述了在乘性随机噪声下液晶系统中观察到的开-关间歇性模式演化。通过数值实验，对统计量进行了详细分析。进一步，以叠加的方式引入热噪声，研究了热噪声对时间模式变化的影响.湍流中的普适统计：通过对OGY湍流壳模型的数值计算，从自相似统计的观点研究了速度-耗散率-结构函数和能量-耗散率-结构函数。我们发现一个很好的协议与迄今为止提出的结构功能的结果。我们成功地推导出了实验发现的扩展的自相似统计规律.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自旋系统的Monte Carlo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-振幅空间近似重构了相图。进一步推导了DPT附近局域磁化的约化动力学，发现由此得到的统计量与数值实验结果一致。

项目成果

藤坂博一: "カオス変調下の間欠性現象"応用物理. 9巻,1号. 28-39 (1999)

Hirokazu Fujisaka：“混沌调制下的间歇现象”应用物理学，第 9 卷，第 1. 28-39 期（1999 年）。

茨木他分担執筆: "数理工学のすすめ"現代数学社. 139 (1999)

茨木等人合着：《数学工程推荐》Gendai Majutsusha 139 (1999)。

H.Fujisaka,S.Grossmann: "Scaling hypothesis leading to extended self-similarity in tubulence"Phys.Res.E. vol.63 No.2. 026305-1-8 (2001)

H.Fujisaka、S.Grossmann：“标度假说导致管状管中扩展的自相似性”Phys.Res.E。

T.Tao and H.Fujisaka: "Modeling Chaotic Evolution with Nonlinear Langevin Dynamics"Prog.Theor.Phys.. vol.104, No.5. 925-941 (2000)

T.Tao 和 H.Fujisaka：“用非线性朗之万动力学模拟混沌演化”Prog.Theor.Phys.. vol.104，No.5。

H.Fujisaka,S.Grossmann: "Scaling hypothesis leading to extended self-similarity in turbulence"Phys.Rev.E. Vol.63 No.2. 026305-1-8 (2001)

H.Fujisaka、S.Grossmann：“标度假设导致湍流中扩展的自相似性”Phys.Rev.E。