| Project/Area Number |
63540276
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物性一般（含極低温･固体物性に対する理論）
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| Research Institution | Kyushu University |
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Principal Investigator |
OKAMOTO Hisao Kyushu University, Fac. of Sci., Assoc. Professor, 理学部, 助教授 (50037222)
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| Co-Investigator(Kenkyū-buntansha) |
MORI Hazime Kyushu Kyoritsu University, Fac. of Tech., Professor, 工学部, 教授 (90037143)
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| Project Period (FY) |
1988 – 1990
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| Project Status |
Completed (Fiscal Year 1990)
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| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1990: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1989: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1988: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | Chaos, / Intermittent chaos, / Power spectrum, / Coarse-grained local expansion rates, / Anomalous scaling laws, / q-phase transition of chaotic attractors, / Statistical-thermodynamical formalism, / Energy dissipation and its fluctuations in chaos. / カオス / 間歇性カオス / パワ-スペクトル / 粗視化の統計測 / カオスの動的構造関数の統計熱力学形式 / カオスにおけるqー相転移 / 微分方程式系のカオス / エネルギ-散逸とその揺らぎ / カオスにおけるq-相転移 / カオスの粗視化された局所的軌道拡大率 / パワースペクトル / 微分方程式系のカオス。 |
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| Research Abstract |
"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.
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