| Research Abstract |
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.
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