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Statistical-Physical Study for Chaos and Turbulence.

混沌和湍流的统计物理研究。

基本信息

批准号：
61540280
负责人：
MORI Hazime
金额：
$ 0.64万
依托单位：
Kyushu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1986
资助国家：
日本
起止时间：
1986 至 1987
项目状态：
已结题

项目摘要

" Oji Seminar on Non-Linear Non-Equilibrium Statistical Mechanics" was organized by Professor H. Mori and held at Kyoto in 1978 (see Prog. Theor. Phys. Suppl. No.64 (1978)). Since then the studies of nonlinear dynamics on the basis of dissipative dynamical systems were started and encouraged for Japanese scientists, particularly, physicists, mathematicians, biologists, chemists, engineers, geologists and even for socialists.Onset of trubulence or the scenario to chaos in dissipative dynamical systems is now known to be classified into a few types, which are the well-known period-doubling route, the collapse of a torus and the intermittency. Prominent properties of chaotic orbits are represented by several scaling laws for spatial and temporal scales and highly coherent behaviors or strong time correlations due to order in chaos.Our goal is to construct a statistical-dynamical paradigm for chaotic or turbulent motions which gives universal behaviors in nonlinear-nonequilibrium systems. Due to the above guiding priciples, we have performed successfully the following themes :1) Statistical-physical theory of global spectral structures of type I and III intermittent chaos and the intermittent chaos due to the collapse of period-3 windows.2) Dynamical theory of the spectra of singularities of strange attractors of chaos f(<alpha>).3) Spatial and temporal scaling properties of strange attractors and their representation by unstable periodic orbits.4) Characterization of local structures of chaotic attractors in terms of coarse-grained local expansion rates.5) Fluctuations of coarse-grained expansion rates and discontinuous transitions in their weighted averages for crises of sine-circle maps.6) Local structures of chaotic attractors at crises in the Henon and annulus maps.7) Anomalous dynamic scaling laws and time correlations of local expansion rates for intermittent chaos.

“王子非线性非平衡统计力学研讨会”由H。Mori和京都在1978年举行（见Prog. Theor. Phys.Suppl.No.64（1978））。从那时起，在耗散动力系统的基础上对非线性动力学的研究开始了，并受到了日本科学家，特别是物理学家、数学家、生物学家、化学家、工程师、地质学家，甚至社会学家的鼓励。耗散动力系统中湍流的发生或混沌的情况现在已知分为几种类型，即著名的倍周期途径，环面的坍缩和不对称性。混沌轨道的突出性质表现为空间和时间尺度的标度律以及混沌中的有序性所导致的高度相干行为或强时间相关性，我们的目标是构建一个混沌或湍流运动的动力学范式，给出非线性-非平衡系统的普遍行为。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）I型和III型阵发混沌以及周期3窗口坍塌引起的阵发混沌全局谱结构的统计物理理论; 2）混沌奇异吸引子奇异谱的动力学理论; <alpha>3）奇异吸引子的时空标度性质及其不稳定周期轨道表示; 4）混沌吸引子局部结构的粗-细-细-粗-粗-细-粗-粗5）正弦圆映射的粗粒度局部膨胀率的涨落及其加权平均值的不连续跃迁; 6）Henon和环面映射的混沌吸引子在临界点的局部结构; 7）间歇混沌的反常动力学标度律和局部膨胀率的时间相关性.