1987 Fiscal Year Final Research Report Summary
Statistical Destribution on Symmetry Groups
| 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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| Keywords | Statistical distribution / crystal group / crystal structure / stochastic model / ランダムパッキング |
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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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Research Products
(11 results)
