The inverse backscattering problem and the inverse fixed angle scattering problem
逆后向散射问题和逆固定角散射问题
基本信息
- 批准号:2307800
- 负责人:
- 金额:$ 13.24万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2023
- 资助国家:美国
- 起止时间:2023-07-01 至 2026-06-30
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
The main goal of this project is to study the recovery of acoustic properties of a medium, such as the earth, by probing the medium with sound waves mechanically generated on the boundary of the medium and measuring the medium response on the boundary. This question will be studied theoretically with a focus on the recovery of the acoustic property from the data coming from a small number of experiments. This results of this study will provide insight in a variety of settings, including the exploration of the subsurface of other planets as well as medical imaging settings, where it may not be possible to generate acoustic waves at many different locations in the medium or measure the medium response at many different locations.The project will focus on two specific problems - the potential recovery backscattering problem for the constant velocity wave equation and the fixed angle velocity recovery problem for the non-constant velocity wave equation. The backscattering problem measurements are equivalent to certain measurements for the ultra-hyperbolic equation with potential, so the corresponding coefficient recovery problem for the ultra-hyperbolic equation will be studied by an adaptation of the Bukhgeim-Klibanov method. The fixed angle velocity recovery problem will be studied by an adaptation of the Bukhgeim-Klibanov method used to study the fixed angle potential recovery problem, with new techniques devised to overcome the difficulties associated with the unknown velocity affecting the structure of the solution of the differential equation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
本项目的主要目的是通过在介质的边界上机械产生的声波探测介质并测量边界上的介质响应来研究恢复介质(例如地球)的声学特性。这个问题将在理论上进行研究,重点是从来自少量实验的数据中恢复声学特性。本研究的结果将为各种环境提供见解,包括探索其他行星的地下以及医学成像环境,在这些地方,可能无法在介质的多个不同位置产生声波,或在多个不同位置测量介质的响应。该项目将集中于两个具体问题:常速度波动方程的势恢复后向散射问题和非常速度波动方程的固定角速度恢复问题。后向散射问题的测量结果等价于超双曲型方程的某些测量结果,因此超双曲型方程的相应系数恢复问题将通过Bukhgeim-Klibanov方法的一个改进来研究。固定角速度恢复问题将通过用于研究固定角势恢复问题的Bukhgeim-Klibanov方法的修改来研究,该奖项反映了NSF的法定使命,并被认为值得通过使用基金会的知识产权进行评估来支持。优点和更广泛的影响审查标准。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Rakesh Rakesh其他文献
Innovative Approaches for Characterizing Chlorantraniliprole and Its Metabolites in Soil, Water and Plants
表征土壤、水和植物中氯虫苯甲酰胺及其代谢物的创新方法
- DOI:
- 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
Rakesh Rakesh;H. Inani - 通讯作者:
H. Inani
Smart Systems and IoT: Innovations in Computing
智能系统和物联网:计算创新
- DOI:
10.1007/978-981-13-8406-6 - 发表时间:
2020 - 期刊:
- 影响因子:0
- 作者:
Arun K. Somani;Rajveer Singh;Ankit Mundra;S. Srivastava;Vivek Kumar Verma;.. .. .. .. .. D. Kumar;Nehal Patel;Radhika Patel;Jenny Kasudiya;Ankit Bhavsar;Harshal A. Arolkar;Tigilu Mitiku;M. S. Manshahia;Rutba Mufti;Kartike Khatri;Sumit Bhardwaj;Punit Gupta;Pankaj Kumar;Sidhartha Barui;Deepanwita Das;Mangala N. Sumedh;Sneha Srinivasan;S. Basavaraju;Nidhi Gangrade;Nirmal Choudhary;K. K. Bharadwaj;Abdul Rehman;Nitin Khan;Rakesh Rakesh;Matam;Dinesh Siddhant Goswami;Singh Shekhawat;Neetu Faujdar;Nitin Rakesh;P. Rohatgi;Karan Gupta;G. Chauhan;Y. Meena;Nidhi Gupta;Deepak Vaswani;Kuldeep Singh;Sakar Gupta;Sunita Gupta;Amit Deepak Soni;Kumar Behera;Dheeraj Sharma;M. Aslam;Shivendra Yadav;Nirav Bhatt;Amit Thakkar;Nikita Bhatt;Purvi Prajapati;Neeru Meena;Buddha Singh;Laxmi Chaudhary;Deepak Kumar - 通讯作者:
Deepak Kumar
Rakesh Rakesh的其他文献
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{{ truncateString('Rakesh Rakesh', 18)}}的其他基金
Inverse Problems for the Wave Equation
波动方程的反问题
- 批准号:
1615616 - 财政年份:2016
- 资助金额:
$ 13.24万 - 项目类别:
Standard Grant
Formally determined inverse problems for hyperbolic PDEs
双曲偏微分方程的正式确定的反问题
- 批准号:
1312708 - 财政年份:2013
- 资助金额:
$ 13.24万 - 项目类别:
Standard Grant
Inversion from Time Domain Backscattering Data for the Wave Equation
时域后向散射数据反演波动方程
- 批准号:
0907909 - 财政年份:2009
- 资助金额:
$ 13.24万 - 项目类别:
Standard Grant
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