| Project/Area Number |
63540194
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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 |
Astronomy
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
INAGAKI Shogo Kyoto University, Fac. of Science, Dept. of Astronomy, Instructor, 理学部, 助手 (80115790)
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| Project Period (FY) |
1988 – 1989
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| Project Status |
Completed (Fiscal Year 1989)
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| Budget Amount *help |
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1989: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1988: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | Stellar Dynamics / Fokker-Planck equation / Variational Principle / Large Scale Structure of the Universe / 球状星団 / フォッカー・プランク方程式 |
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| Research Abstract |
Orbit-averaged Fokker-Planck equations are the fundamental evolution equation for collisional stellar dynamics. However, it is difficult to integrate the orbit-averaged Fokker-Planck equations when the number of the independent variables is equal or larger than two. Therefor, it is desirable to obtain approximate solutions. Variational Principles are useful to get such solutions. Since the orbit-averaged Fokker-Planck equations are nonlinear and non-self-adjoining, ordinary variational principles are out of use. We used the local potential proposed by Glansdorf and Prigogine and derived a variational principle.
In Itoh et al. (1988) we studied the gravitational clustering of galaxies when the initial distribution of galaxies is Poisson distribution. In this period of the research, we investigated the case when the initial distribution of galaxies has power laws. We find that b appearing in f(V) depend on the volume of the sample, V. The relation between b(V) and the two-particle correlation function is obtained analytically and the results of the simulations are in agreement with it.
We further investigated the effects of different mass components. For simplicity we adopted two component model where the mass of the less massive galaxy is m_1 and that of the massive galaxy is m_2. We find that f(N) derived by Saslaw and Hamilton (1984) is reproduced when m_2/m_1 < 10.
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