Statistical-Physical Study for Global Spectral Structures of Intermittent Chaos and Its Spatio-Temporal Scaling Properties.

间歇混沌全局谱结构及其时空尺度特性的统计物理研究。

基本信息

批准号：
63540276
负责人：
OKAMOTO Hisao
金额：
$ 1.28万
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：
1988
资助国家：
日本
起止时间：
1988 至 1990
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 (one of the investigators of the present project) 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 turbulence or the scenario to chaos in dissiparatieve 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) Characterization of local structures of chaotic attractors in terms of coarse-grained local expansion rates, and its spectrum psi (LAMBDA) and q-phase transition.3) Long-time correlations due to memory effect of critical orbits and its critical scaling laws of local expansion rate spectrum.4) Advective diffusion and mixing of particles in Hamiltonian dynamical systems.5) Energy dissipation and its fluctuations in chaotic dynamical systems.

H. Mori教授（本项目的研究人员之一）组织了“非线性非平衡统计力学的OJI研讨会”，并于1978年在京都举行（参见Prog。Theas。Phys。Suppl。Suppl。No.64（1978））。从那时起，对日本科学家的启动和鼓励了非线性动力学的研究，特别是物理学家，数学家，生物学家，生物学家，化学家，工程师，工程师，地质学家，甚至针对社会主义者。湍流或对散发性动态系统中的混乱的场景，众所周知，这是典型的典范，这些途径是典型的典范间歇性。混乱轨道的突出特性由几种定标定律用于空间和时间尺度，高度相干行为或由于混乱中的顺序而引起的较强的时间相关性。我们的目标是为混乱或湍流构建统计 - 动态范式，以使非线性 - 非线性 - 非线性 - 非核核定系统中的普遍行为在内。由于上述指导定价，我们已经成功执行了以下主题：1）I型和III型全球光谱结构的统计 - 物理理论，以及III的间歇性混乱和间歇性混乱，因为周期3 Windows的崩溃而引起的混乱量。由于临界轨道的记忆效应及其局部膨胀速率谱的临界缩放定律而引起的长期相关性。4）对哈密顿动力学系统中颗粒的对流扩散和混合。5）能量耗散及其在混乱的动力学系统中的波动。