2006 Fiscal Year Final Research Report Summary
Formation of fractal structures and the development of its simulation algorithms
| Project/Area Number |
16360044
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | Hokkaido University |
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Principal Investigator |
NAKAYAMA Tsuneyoshi Hokkaido University, Grad.School of Eng., Professor, 大学院工学研究科, 教授 (80002236)
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| Co-Investigator(Kenkyū-buntansha) |
YAKUBO Kousuke Hokkaido University, Grad.School of Engineering, Asso.Prof, 大学院工学研究科, 助教授 (40200480)
SHIMA Hiroyuki Hokkaido University, Grad School of Engineering, Inst., 大学院工学研究科, 助手 (40312392)
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| Project Period (FY) |
2004 – 2006
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| Keywords | eigenvalue analysis / numerical algorithm / fractal strucutures / pattern formation / critical phenomena |
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| Research Abstract |
The research on the formation of fractal patterns attracts much attention of physicists according to its universality and generality. To reveal the physical origin of the formation of fractal patterns, it has not been successful in terms of convertional approaches such as computer simulations. There has been numerous unsolved problems for this subject. The goal of the present research is to reveal the the physical origin of fractal pattern formation by means of employing quite new numerical techniques. Our goal is (1) to handle freely 10^7×10^7 matrices and (2) to apply our numerical algorithm to quantum and classical fractal structures. Our method is unique, different from other conventional methods, to map the eigenvalue problem to the problem of lattice vibrations. By applying this method, we have succeeded to obtain new results for our subject.
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