2003 Fiscal Year Final Research Report Summary
Systematic study for self-organization phenomena based on mathematical informatics and statistical mechanics
| Project/Area Number |
13650062
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Chiba University |
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Principal Investigator |
MATSUBA Ikuo Chiba University, Faculty of Engineering, Professor, 工学部, 教授 (30251177)
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| Co-Investigator(Kenkyū-buntansha) |
SUYARI Hiroki Chiba University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (70246685)
KOSHIGOE Hideyuki Chiba University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (70110294)
KAWARADA Hideo Ryutsu Keizai University, Distribution and logistics, Professor, 流通情報学部, 教授 (90010793)
SUITO Hiroshi Okayama University, Faculty of Environmental Science and Technology, Associate Professor, 環境理工学部, 助教授 (10302530)
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| Project Period (FY) |
2001 – 2003
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| Keywords | Self-organization / Fractal / Self-similarity / Neural networks / Renormalization method |
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| Research Abstract |
It is a common feature of some physical systems consisting of a large number of coupled systems that a cascade of energy flow from large to small scales generates a scaling behavior, namely power-law behavior of some observable. Scaling is found in a wide range of systems, from geophysical to biological. A typical example is seismicity that is characterized by an energy transfer through a hierarchy stricture. One of recent research is to apply this idea to explain the observed scaling laws. We proposed the general model equation of threshold dynamics that exhibits self-similar properties. The commonly used dynamically driven Renormalization Group method is useful to analyze the scale invariance of the spatiotemporal structures produced by the operation of the updating algorithm. This method integrates the model in space and time in the analysis of the effect of coarse graining on the dynamics to produce the set of Renormalization group equations from which various characteristic exponents are obtained. A technically simpler, but nevertheless asymptotically exact, method where coarse graining is performed by updating the model with respect to time is used to study the self-similar behavior of the model to predict the characteristic exponents.
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