Inverse Scattering Problems

逆散射问题

基本信息

批准号：
9803219
负责人：
Tuncay Aktosun
金额：
$ 7.55万
依托单位：
North Dakota State University Fargo
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1998
资助国家：
美国
起止时间：
1998-07-15 至 2001-11-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9803219&HistoricalAwards=false
关键词：
Inverse Scattering Problems

项目摘要

9803219AktosunIt is proposed to study certain inverse scattering problems arising in quantum mechanics and wave propagation. Such problems are governed by the Schroedinger equation, its variants, the wave equation and the telegraphy equation in the frequency domain. Using techniques related to Riemann-Hilbert problems, operator factorizations, and spectral analysis of differential operators, the aim is to recover coefficients appearing in the relevant differential equations in terms of a suitable set of scattering data. In addition to their practical importance in physics, engineering, and other applied fields, these inverse problems contribute mathematical techniques to various areas of mathematics such as nonlinear differential equations, integral equations, boundary value problems, and applied functional analysis.The inverse scattering problems under study are motivated by their important applications in many areas such as materials science, nondestructive testing, acoustic imaging, seismology, geophysics, and remote sensing. In materials science the solution of the inverse scattering problem amounts to determining surface and subsurface structure of materials by analyzing neutron beams scattered off the materials, for example, helping to understand bonding of polymer components. In quantum mechanics it corresponds to the determination of forces holding molecules, atoms, and subatomic particles together by analyzing colliding beams of particles. In remote sensing it helps to profile unknown targets by analyzing acoustic or electromagnetic waves scattered off such targets.

提出了9803219aktosunit，以研究量子力学和波传播中产生的某些反散射问题。此类问题受施罗丁格方程，其变体，波动方程和频域电报方程的控制。使用与差分运算符的Riemann-Hilbert问题，操作员分析和光谱分析有关的技术，其目的是根据适当的散射数据恢复相关微分方程中出现的系数。除了它们在物理，工程和其他应用领域中的实际重要性外，这些反问题还为数学的各个领域（例如非线性差分方程，积分方程，积分价值问题，边界价值问题和应用功能分析）促进了数学技术。感应。在材料科学中，反向散射问题的解决方案相当于通过分析散射从材料的中子梁分析的中子束来确定材料的表面和地下结构，例如，有助于了解聚合物成分的键合。在量子力学中，它对应于通过分析粒子的碰撞光束来确定持有分子，原子和亚原子颗粒的力。在遥感中，它通过分析散布在此类目标的声波或电磁波来介绍未知目标。