Study on fractal dimension of diffusion-limited aggregation in n-Euclidian space

n欧几里得空间中扩散限制聚集的分形维数研究

• 批准号: 15540373
• 负责人: HONJO Haruo
• 金额: $ 2.11万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540373/
• 关键词: diffusion-limited aggregation; fractal; non-linear and non-equilibrium phenomena; dissipative structure; Tsallis thermodynamics; pattern formation

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.

1.在DLA尺寸较小的情况下，粘附概率近似为高斯分布。随着DLA的增加，粘附概率变得不对称，并且具有长尾，而不是明显的正态分布。2.冻结区粘附概率服从泊松分布，活动区粘附概率服从正态分布。每一个随机步行者的粘附概率可以看作是一个幂律，但指数约为7，这在物理上太大了;此外，我们可以用Tsallis概率来拟合粘附概率，但q值与1相差很小（q = 1. 02）。这种与1的微小差异意味着概率几乎是高斯的，我们推测这种微小的差异可能在DLA动力学中是至关重要的。5.提出了一种新的方法，如何用一维序列来表示包含DLA的团簇随时间的增长。我们可以理解集群的所有动力学，并从序列中拓扑地创建集群。用一维序列表示DLA，并分析其分形性质。我们需要更多的时间来讨论它，因为DLA本质上是一个随机过程。

项目成果

S.Miyazaki: "Statistic properties of the radial growth probability distribution for diffusion-limited aggregation"Proceedings of the 5nd Cross Straits Symposium on Materials, Energy and Environmental Sciences. CSS5. 141-141 (2003)

S.Miyazaki：“扩散限制聚集的径向生长概率分布的统计特性”第五届海峡两岸材料、能源与环境科学研讨会论文集。

Dendritic side-branching with anisotropic viscous fingering

具有各向异性粘性指法的树突侧枝

• 发表时间: 2005
• 期刊: J.Crystal Growth 275・211(in press)
• 作者: Eiko Matsushita;K.Ozawa;T.Honda
• 通讯作者: T.Honda

Asymptotic function for multigrowth surfaces using power-law noise.

使用幂律噪声的多重生长曲面的渐近函数。

• 发表时间: 2003
• 期刊: Phys.Rev.E 67
• 作者: H.Katsuragi;H.Honjo
• 通讯作者: H.Honjo

Statistic properties of the radial growth probability distribution for diffusion-limited aggregation.

扩散限制聚合的径向增长概率分布的统计特性。

• 发表时间: 2003
• 期刊: Proc.of the 5^<th> Cross Straits Symposium on Materials, Energy and Environmental Sciences 141
• 作者: S.Miyazaki;H.Honjo;H.Katsuragi
• 通讯作者: H.Katsuragi

Classification of KPZQ and BDP Models by Multiaffine Analysis

通过多重仿射分析对 KPZQ 和 BDP 模型进行分类

• 发表时间: 2004
• 期刊: J.Phys.Soc.Jpn. 73・11
• 作者: H.Katsuragi