Inverse Scattering Problems and Applications

逆散射问题及应用

• 批准号: 0610494
• 负责人: Tuncay Aktosun
• 金额: --
• 依托单位: University of Texas at Arlington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2008-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0610494&HistoricalAwards=false
• 关键词: Inverse; Scattering; Problems; Applications

This research is to study various aspects of inverse scattering problems arising in wave propagation and in quantum mechanics and their applications. These include wave propagation in a nonhomogeneous and absorptive medium and the determination ofthe nonhomogeneities and absorptivity of the medium, X-ray reflectometry and the determination of material properties ofstratified thin films by probing them with X-rays, focusing of waves at target locations and the determination medium propertiesby using wave focusing, developing exact quadratures to analytically continue a reflection coefficient from an interval to larger domains and their numerical implementation, and solving inversescattering problems in order to recover functions with slower decay conditions at infinity.The inverse scattering problems investigated have important applications in manyareas such as materials science, nondestructive testing, acoustic imaging, and remote sensing. The principal aim is to determineproperties of a target in a remote fashion: send a wave onto thetarget, analyze the scattered wave, and infer the properties of thetarget from the scattering data. In addition to its practical importance in physical sciences, engineering, and other applied areas, the research will contribute mathematical techniques to various areas of mathematics and it will also help to train some graduate and undergraduate students in applied mathematics.

这项研究是研究在波传播和量子力学及其应用中引起的反散射问题的各个方面。 These include wave propagation in a nonhomogeneous and absorptive medium and the determination ofthe nonhomogeneities and absorptivity of the medium, X-ray reflectometry and the determination of material properties ofstratified thin films by probing them with X-rays, focusing of waves at target locations and the determination medium propertiesby using wave focusing, developing exact quadratures to analytically continue a reflection coefficient from an interval to larger域及其数值实施，并解决反截面的问题，以便在无穷大的衰减条件下恢复功能。所研究的反散射问题在材料科学，非破坏性测试，声学成像和遥感等许多人中都有重要应用。 主要目的是以遥远的方式确定目标的权限：将波浪发送到thetarget，分析散射波，并从散射数据中推断出thetarget的特性。 除了其在物理科学，工程和其他应用领域中的实际重要性外，该研究还将为数学的各个领域提供数学技术，还将有助于培训一些应用数学领域的研究生和本科生。