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

由于计算机技术的进步，非线性非平衡系统的一些性质被阐明。从那时起，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，甚至社会主义者开始并鼓励基于耗散动力系统的非线性动力学研究。混沌轨道的突出特性由（A）空间和时间尺度的几个标度定律和（B）由于混沌中的秩序而导致的高度相干行为或强时间相关性来代表。我们的目标是构建一种统计动力学理论，用于非平衡开放系统中由于混沌而引起的混合、传输和耗散。由于上述指导原则，我们成功地完成了以下主题：1）混沌动力系统中的能量耗散及其波动。2）二维映射和哈密顿动力系统中的动量扩散。3）哈密顿动力系统中粒子的平流扩散和混合。4）可变时空尺度上粗粒化混沌吸引子局部结构的表征及其交叉效应。5）分形维数的尺度依赖性大气流动的时空涨落。6)二维无粘正压流体涡粘系数的统计物理理论。

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.