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Analysis of various amounts charactering scattering phenomena for the elastic surface waves

弹性表面波散射现象的各种表征量分析

基本信息

批准号：
16540156
负责人：
KAWASHITA Mishio
金额：
$ 2.37万
依托单位：
Hiroshima University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
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/en/grant/KAKENHI-PROJECT-16540156/
关键词：
surface waves scattering theory Rayleigh wave Lax-Phillips scattering kernel

项目摘要

The aim of this research is analyzing the more detailed character of a surface wave based on the formulation of scattering theory to the surface wave by the research representatives of this research. One of the quantity which describes the scattering phenomena of elastic surface waves is in the component of the physical quantity called a "scattering kernel. " Existence of a scattering kernel is shown and the representation formula of it is obtained. The representation formula obtained above is represented by using the generalized eigenfunctions to a free system and a perturbed system. From this formula, the concrete representation of the part describing the scattering phenomena of an elastic surface wave among scattering kernels is obtained. By using this representation, how to interpret scattering of a surface wave as the scattering problem of the hyperbolic equation on an boundary surface is considered. The obtained results in this research are as follows:(1) The concrete representat … More ion linking directly to the phenomenon of propagation of surface waves is given.(2) An approximate solution of the Rayleigh wave for pulling out the information about the singularity of a scattering kernel is constructed.(3) Study for pulling out the information about singularities of the scattering kernel is performed by using the approximate solution. The similarity from a viewpoint of the influence which the singularity of waves has on a scattering kernel is shown among various scattering theories for hyperbolic equations.(4) In steps performing (3), oscillatory integrals of more complicated forms than those appeared in the previous work appeared. About this, more precise estimates than those in the previous works are obtained.The "representation formula of the scattering kernel" obtained in this research includes the contents which renew interpretation of the similar formulae obtained until now. Moreover, through analyzing (1)--(4), it become clear that analysis peculiar to scattering of an elastic surface wave is needed. Less

本研究的目的是在本研究的研究代表对表面波散射理论的阐述的基础上，对表面波的更详细的特性进行分析。描述弹性表面波散射现象的量之一是称为“散射核”的物理量的组成部分。“证明了散射核的存在性，并得到了散射核的表示公式.用广义本征函数表示自由系统和扰动系统的表示式。从这个公式出发，得到了散射核中描述弹性表面波散射现象的部分的具体表示。利用这种表示，考虑如何将表面波的散射解释为边界面上双曲方程的散射问题。本研究取得的主要成果如下：（1）具体表现为： ...更多信息离子直接链接到表面波的传播现象。(2)本文构造了一种瑞利波近似解，用以提取散射核奇异性的信息。(3)利用近似解进行了提取散射核奇异性信息的研究。从波的奇异性对散射核的影响的观点来看，在双曲方程的各种散射理论之间显示出相似性。(4)在进行（3）的步骤中，出现了比先前工作中出现的形式更复杂的振荡积分。关于这一点，我们得到了比以往工作更精确的估计，我们得到的“散射核表示公式”包含了对迄今为止得到的类似公式重新解释的内容。此外，通过分析（1）-（4），显然需要对弹性表面波的散射进行特有的分析。少