Correlation of Fractional Derivative Structure and Fractal Structure of High Polymer Materials

高分子材料分数阶导数结构与分形结构的相关性

• 批准号: 13450095
• 负责人: SHIMIZU Nobuyuki
• 金额: $ 9.34万
• 依托单位: Iwaki Meisei University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13450095/
• 关键词: high polymer material; fractal geometry; fractional derivative; net density; SEM picture; viscoelastic material; nonlinearity; fractional diffusion equation; 分数解微分

The correlation of the fractional derivative structure and the fractal geometry in viscoelastic materials is tried to be found from the theoretical and experimental approaches. The detailed study points are1. Experiments for establishing fractional derivative model for viscoelastic material,2. Dynamical test for acrylic rubber,3. Observation of the structure of viscoelastic body by the electric microscope,4. Clarification of the contacting point between fractional, derivative model and fractal geometry.and the following detailed results are obtained;・Numerical solution of fractional diffusion equation with source point,・Some relations of fracture phenomenon and fractal model,・Relation of the density and the fractional derivative parameters of acrylic rubber,・Nonlear behavior of viscoelastic material by the actuation experiment.

试图从理论和实验方法中发现粘弹性材料中分数导数结构和分形几何的相关性。具体研究要点是1．建立粘弹性材料分数阶导数模型的实验，2．丙烯酸酯橡胶的动态试验，3．电镜观察粘弹性体结构；4．阐明了分数、导数模型和分形几何之间的接触点，得到了以下详细结果：·带源点的分数扩散方程的数值解，·断裂现象与分形模型的一些关系，·丙烯酸橡胶的密度与分数阶导数参数的关系，·通过驱动实验研究粘弹性材料的非线性行为。

项目成果

M.Fukunaga: "A Difference Method for Initial Value Problems of Ordinary Fractional Differential Equations"Int.J.Appl.Math. 8. 127-147 (2002)

M.Fukunaga：“普通分数阶微分方程初值问题的差分法”Int.J.Appl.Math。

T.Morita: "Lattice Green's Function, Elliptic Integral, and Wavelet"Journal of the Korean Physical Society. Vol.40. 1015-1017 (2002)

T.Morita：“格格林函数、椭圆积分和小波”韩国物理学会杂志。

M.Fukunaga: "A Difference Method for Initial Value Problems of Fractional Wave Diffusion Equations"Int.J.Appl.Math. 8. 449-468 (2002)

M.Fukunaga：“分数波扩散方程初值问题的差分法”Int.J.Appl.Math。

T.Morita: "Lattice Green's Function, Elliptic Integral, and Wavelet"Journal of the Korean Physical Society. 40. 1015-1017 (2002)

T.Morita：“格格林函数、椭圆积分和小波”韩国物理学会杂志。

H.Nasuno: "Experimental Veriticaion of Finite Element Formulation for Viscoelastic Body Described by Fractional Differential Operator."JSME. Vol.69, No.682(C). 29-35 (2003)

H.Nasuno：“分数阶微分算子描述的粘弹性体有限元公式的实验验证。”JSME。