| Project/Area Number |
60460007
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Astronomy
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| Research Institution | Univeristy of Tokyo |
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Principal Investigator |
UNNO Wasaburo University of Tokyo, Faculty of Science, Professor Emeritus, 理学部, 教授 (30011414)
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| Co-Investigator(Kenkyū-buntansha) |
SAIO Hideyuki University of Tokyo, Faculty of Science, Assistant, 理学部, 助手 (10162174)
SHIBAHASHI Hiromoto University of Tokyo, Faculty of Science, Assistant, 理学部, 助手 (30126081)
KONDO Masa-Aki Sensyu University, Faculty of Commerce, Assistant Professor, 商学部, 助教授 (60012457)
OSAKI Yoji University of Tokyo, Faculty of Science, Professor, 理学部, 教授 (30011547)
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| Project Period (FY) |
1985 – 1986
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| Project Status |
Completed (Fiscal Year 1986)
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| Budget Amount *help |
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 1986: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1985: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | Chaos / X-ray stars / convection / nonlinear dynamics / 脈動 |
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| Research Abstract |
1. In order to detect astrophysical chaotic phenomena, we analyzed non-periodic X-ray data of Cyg X-1 obtained from the satellite 'TENMA'. By testing various parameters, we found that its fractal dimension as the attractor in the reconstructed phase space is about five. We found the largest Lyapunov exponent of the attractor is positive. This result supports the dimension analysis and is indicative that a chaotic phenomenon manifests itself in the X-ray data of Cyg X-1.
2. Three dimensional Boussinesq convection has been numerically simulated and analyzed using the method of the dynamical system theory. When the Rayleigh number Ra=2・ <10^4> , a non-periodic solution and a periodic one have been obtained in the Prandtle number Pr=1 and Pr=3, respectively. The periodic solution with Pr=3 has a roll structure. We found in the case of Pr=1 that the vertical vorticity plays an important role and the dimension of the non-periodic attractor in the reconstructed phase space is 3.3 with two positive Lyapunov exponents. This result indicates the existence of low dimensional chaos in fluid systems.
3. From the viewpoint of nonlinear dynamics, we have constructed a general theory of geosphere-biosphere problems, especially in the <CO_2> problem. Human population, average surface temperature of the earth and <CO_2> content are taken as the independent variables. The solar radiation is considered as given. Linear interaction components of these variables are specified by considering the known effects (such as the blanketting effect of <CO_2> ), but the nonlinear interaction terms are not specified. The form of nonlinear interaction terms in this system is determined by following the instruction that a linear operator governs the form of nonlinear terms. Numerical experiments show that the chaotic variations caused by the periodic agitation of the solar radiation appear in some cases. But it is too early to conclude anything about the <CO_2> problem.
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