Formation of fractal structures and the development of its simulation algorithms

分形结构的形成及其模拟算法的发展

• 批准号: 16360044
• 负责人: NAKAYAMA Tsuneyoshi
• 金额: $ 9.22万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16360044/
• 关键词: eigenvalue analysis; numerical algorithm; fractal strucutures; pattern formation; critical phenomena

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.

由于其普遍性和普遍性，对其形成的研究引起了物理学家的极大关注。要揭示分形图形成的物理起源，在计算机模拟等传统方法方面并不成功。这个课题有许多悬而未决的问题。本研究的目的是通过采用全新的数值方法来揭示分形图形成的物理根源。我们的目标是(1)自由地处理10^7×107个矩阵和(2)将我们的数值算法应用于量子和经典的分形结构。与其他传统方法不同，我们的方法是将本征值问题映射到晶格振动问题。通过应用这种方法，我们成功地为我们的课题获得了新的结果。

项目成果

Optical nonlinearity enhancement of graded metallic films

• DOI: 10.1063/1.1769086
• 发表时间: 2004-05
• 期刊: Applied Physics Letters
• 影响因子: 4
• 作者: Jintang Huang;Kin Wah Yu

Dispersion and transitions of dipolar plasmon modes in graded plasmonic waveguides

• DOI: 10.1063/1.2396905
• 发表时间: 2006-10
• 期刊: Applied Physics Letters
• 影响因子: 4
• 作者: J. Xiao;K. Yakubo;K. Yu

Harmonic vibrational excitations in garded elastic networks : Transition from phonons to gradons

守卫弹性网络中的谐波振动激发：从声子到格子的转变

• 发表时间: 2006
• 期刊: Physical Review B 73・22
• 作者: M. Mimura;et. al.;H.Yamamoto;Y.Hayasaki;H.Yamamoto;S.Matsumoto;Y.Hayasaki;早崎芳夫;早崎芳夫;J.J.Xiao;J.J.Xiao;J.J.Xiao;J.J.Xiao
• 通讯作者: J.J.Xiao

Optical nonlinearity of colloidal crystals

• DOI: 10.1063/1.2008359
• 发表时间: 2005-08
• 期刊: Applied Physics Letters
• 影响因子: 4
• 作者: Jintang Huang;K. Yu

Giant enhancement of optical nonlinearity in multilayer metallic films

• DOI: 10.1063/1.2175477
• 发表时间: 2006-03
• 期刊: Journal of Applied Physics
• 影响因子: 3.2
• 作者: Jiping Huang;L. Dong;K. Yu