1987 Fiscal Year Final Research Report Summary
Statistical-Physical Study for Chaos and Turbulence.
| Project/Area Number |
61540280
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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 |
物理学一般
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| Research Institution | Kyushu University |
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Principal Investigator |
MORI Hazime Kyushu University, Faculty of Science ; Professor, 理学部, 教授 (90037143)
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| Co-Investigator(Kenkyū-buntansha) |
OKAMOTO Hisao Kyushu University, Faculty of Science ; Associate Prof., 理学部, 助教授 (50037222)
YOSHIDA Takeshi Kyushu University, Faculty of Science ; Assistant, 理学部, 助手 (10037187)
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| Project Period (FY) |
1986 – 1987
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| Keywords | Chaos / Intermittent chaos / Power spectrum / Strange attractor / Spectra of singularities of chaotic attractors / カオスにおけるq-相転移 |
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| Research Abstract |
" 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.
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