1995 Fiscal Year Final Research Report Summary
Theory on Dynamics of Growing Surfaces with Self-Affinity
| Project/Area Number |
06835009
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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 |
非線形科学
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| Research Institution | Shinshu University |
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Principal Investigator |
HONDA Katsuya Faculty of Science, Professor, 理学部, 教授 (50109302)
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| Co-Investigator(Kenkyū-buntansha) |
MITSUI Takemoto Graduate School of Human Informatics, Nagoya University, Professor, 大学院人間情報研究科, 教授 (50027380)
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| Project Period (FY) |
1994 – 1995
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| Keywords | Self-Affine Fractal / Stochastic Differential Equation / Scaling Law / Rough Surface |
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| Research Abstract |
Growing rough surfaces with self-affine symmetry are widely seen in nature and technological fields. We are interesting in such a fact that the height fluctuation of surface satisfies a scaling law with respect to time and space. The purpose of this project is to obtain the scaling exponents as functions of substrate dimensionality d. We expect that there are universality classes even in growth phenomena far from equlibrium states, as known in critical phenomena. The first theoretical breakthrough has been brought by Kardar, Parisi and Zhang (KPZ) by introducing a stochastic differential equation. Although this equation has a very simple form, it has been a very difficult problem to derive the scaling exponents from a theoretical point of view. We pointed out that the white-noise assumption in the KPZ equation is not valid for d>2. In the linearized version, we proved that the assumption cannot be accepted to obtain a finite width of surfaces, and the surfaces should be smooth for d>2.
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