Statistical Physical Study for Mixing, Trasport and Dissipation due to Chaos in Non-Equilibrium Open Systems

非平衡开放系统中混沌引起的混合、传输和耗散的统计物理研究

• 批准号: 03640339
• 负责人: OKAMOTO Hisao
• 金额: $ 1.02万
• 依托单位: Kochi University (1993)Kyushu University (1991-1992)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1991
• 资助国家: 日本
• 起止时间: 1991 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03640339/
• 关键词: chaos; fluctuations; nonequilibrium open systems; mixing in chaos; transport in chaos; 2-dimensional Rossby wave; eddy viscosity coefficient; エネルギ-散逸と揺らぎ; 奇妙なアトラクタ-

Due the progress of a computer technology, several properties of nonlinear-nonequilibrium systems are clarified. Since then the studies of nonlinear dynamics on the bases of dissipative dynamical systems were started and encouraged for Japanese scientists, particularly, physicists, mathematicians, biologists, chemists, engineers, geologists and even for socialists. Prominent properties of chaotic orbits are represented by (A) several scaling laws for spatial and temporal scales and (B) highly coherent behaviors or strong time correlations due to order in chaos.Our goal is to construct a statistical-dynamical theory for mixing, transport and disippation due to chaos in non-equilibrium open systems. Due to the above guiding principles, we have performed successfully the following themes :1) Energy dissipation and its fluctuations in chaotic dynamical systems.2) Momentum diffusion in 2-dimensional maps amd Hamiltonian dynamical systems.3) Advective diffusion and mixing of particles in Hamiltonian dynamical systems.4) Characterization and its crossover effect of local structures of chaotic attractors in terms of coarse-graining in variable spatio-temporal scales.5) Scale dependence of the fractal dimension of spatio-temporal fluctuation in atomospheric flow.6) Statistical-physical theory of eddy viscosity coefficient for two-dimensional inviscid barotropic fluid.

由于计算机技术的进步，非线性非平衡系统的一些性质得到了澄清。从那时起，基于耗散动力系统的非线性动力学研究开始了，并鼓励日本科学家，特别是物理学家，数学家，生物学家，化学家，工程师，地质学家，甚至社会主义者。混沌轨道的突出性质表现为（A）空间和时间尺度的几个标度律和（B）混沌中的有序性所导致的高度相干行为或强时间关联。基于上述指导思想，我们成功地完成了以下几个方面的工作：1）混沌动力系统中的能量耗散及其涨落; 2）二维映射和Hamilton动力系统中的动量扩散; 3）Hamilton动力系统中的粒子对流扩散和混合; 4）混沌吸引子的局部结构在不同时空尺度下的粗粒化表征及其交叉效应; 5）大气流时空涨落分维的尺度依赖性; 6）二维无粘正压流体涡动粘性系数的统计物理理论。

项目成果

栢原 孝浩: "Estimating the Corrrelation Dimension and the Largest Lyapunov Exponent from the FGGE IIIb Data" Mem.Fac.Sci.Kochi University.(Information Science). 15. 143-151 (1994)

Takahiro Kayahara：“根据 FGGE IIIb 数据估计相关维数和最大 Lyapunov 指数”Mem.Fac.Sci.Kochi University.（信息科学）15. 143-151 (1994)。

岩山隆寛 Takahiro IWAYAMA: "Generalized Langevin Equation for Two-Dimensional Inviscid Barotropic Vorticity." Progress of Theoretical Physics. 90. 343-351 (1993)

Takahiro IWAYAMA：“二维无粘正压涡度的广义朗之万方程。理论物理学进展”90。343-351（1993）

Takahiro KAYAHARA(柏原 孝浩): "Estimation of the Correlation Dimension and the Largest Lyapunov Exponent from the FGGE IIIb Data."

Takahiro KAYAHARA：“根据 FGGE IIIb 数据估计相关维数和最大 Lyapunov 指数。”

大内 克哉: "Advective Diffusion of Particles in Rayleigh-Benard Convection" Progress of Theoretical Physics. 85. 687-691 (1991)

Katsuya Ouchi：“瑞利-贝纳德对流中粒子的平流扩散”理论物理进展 85. 687-691 (1991)。

大内 克哉: "Anomalous Diffusion and Mixing in an Oscillating Rayleigh-Benard Flow" Progress of Theoretical Physics. 88. 467-484 (1992)

Katsuya Ouchi：“振荡瑞利-贝纳德流中的反常扩散和混合”理论物理进展 88. 467-484 (1992)。