2004 Fiscal Year Final Research Report Summary
Study on fractal dimension of diffusion-limited aggregation in n-Euclidian space
| Project/Area Number |
15540373
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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 |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | KYUSHU UNIVERSITY |
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Principal Investigator |
HONJO Haruo Kyushu University, Interdisciplinary Graduate School of Engineering Sciences, Applied science for Electronics and Materials, Professor, 大学院・総合理工学研究院, 教授 (00181545)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAGUCHI Hidetsugu Kyushu University, Interdisciplinary Graduate School of Engineering Sciences, Applied science for Electronics and Materials, Assistant Professor, 大学院・総合理工学研究院, 助教授 (90192591)
KATSURAGI Hiroaki Kyushu University, Interdisciplinary Graduate School of Engineering Sciences, Applied science for Electronics and Materials, Research Associate, 大学院・総合理工学研究院, 助手 (30346853)
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| Project Period (FY) |
2003 – 2004
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| Keywords | diffusion-limited aggregation / fractal / non-linear and non-equilibrium phenomena / dissipative structure / Tsallis thermodynamics / pattern formation |
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| Research Abstract |
1.In the case that DLA size is small, the sticking probability to DLA seems to be Gaussian. As the DLA grows, however, the sticking probability becomes asymmetric and has a long tail, and is not a Gaussian apparently.
2.The sticking probability is a Poisson distribution in frozen zone and is Gaussian in active zone. The boundary between the frozen zone and the active zone is closer to the center than usually discussed.
3.The sticking probability per one random walker can be regarded as a power law, however, the index is about 7, which is too large physically.
4.Furthermore, we can fit the sticking probability as Tsallis probability, however, the value of q differs from unity just a little (q〜1.02). This small discrepancy from unity means that the probability is almost Gaussian, and we conjecture that the small discrepancy may be crucial in DLA dynamics.
5.We propose a new method how to represent a time dependent growth of cluster including DLA with one-dimensional sequence. We can understand all of the dynamics of the cluster and create the cluster topologically from the sequence. We represent a Vicsek fractal by the sequence and discuss the fractal dimension from the sequence.
6.We represent DLA by the one-dimensional sequence and try to analyze the fractal character. We need more time to discuss it because DLA is essentially random process.
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