| Project/Area Number |
61540171
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
ITOH Yoshiaki The Institute of Satistical Mathematics, 領域統計研究系, 教授 (60000212)
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| Project Period (FY) |
1986 – 1987
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| Project Status |
Completed (Fiscal Year 1987)
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| Budget Amount *help |
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1987: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1986: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | Statistical distribution / crystal group / crystal structure / stochastic model / ランダムパッキング / 幾何学的対称性 / 群論 / 点群 / 空間群 / 結晶 |
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| Research Abstract |
Group theory is successfully applied to analysis of crystal structure. The symmetry of a crystalline substance is represented by one of the 32 point groups In this note a stochastic model is introduced for the distribution of crystalline substances among the 32 point groups. Consider a point group x. and take possible symmetry operations.which can be added to the x. at random. Assume the number of operations is given by Poisson distribution. Add the operations to the x and we get a point group generated by the operations and the x. A simulation study is carried out by the model to compave the result with the data of the distribution of crystalline substances.
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