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.
该项目的主要目标是通过在介质边界上用机械产生的声波探测介质并测量边界上的介质响应,来研究介质(如地球)的声学性质的恢复。这个问题将从理论上进行研究,重点是从少量实验数据中恢复声学性质。这项研究的结果将在各种环境中提供洞察力,包括对其他行星次表面的探索以及医学成像环境,在这些环境中,可能无法在介质中的许多不同位置产生声波或在许多不同位置测量介质响应。该项目将专注于两个具体问题--恒速波动方程的潜在恢复后向散射问题和非恒定速度波动方程的定角速度恢复问题。对于具有位势的超双曲型方程,后向散射问题的量测与某些量测是等价的,因此我们将采用Bukhgeim-Klibanov方法来研究超双曲型方程相应的系数恢复问题。固定角度速度恢复问题将通过采用Bukhgeim-Klibanov方法来研究,该方法用于研究固定角度潜在恢复问题,并设计了新技术来克服与未知速度影响微分方程解结构相关的困难。该奖项反映了NSF的法定使命,并通过使用基金会的智力优势和更广泛的影响审查标准进行评估,被认为值得支持。
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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