CAREER: Time Reversal and Inverse Problems in Wave and Particle Propagation

Bal 研究者和他的学生们研究了波和粒子在非均匀介质中的传播以及相关的逆问题，更准确地说，他们分析了时间反演波的重聚焦和稳定性特性，这些特性可用于无损检测和无线通信。 他们还分析了光子在人体组织中的传播，以了解如何通过光子强度测量来成像这些组织的特性。 数值计算工具和软件的开发，以模拟上述的正问题和反问题。 调查员还开发了一个理论和numericalinverse问题的课程。 在许多应用中，很好地理解波和粒子在复杂介质中的传播是必要的：地震产生的地震波传播，破坏肾结石（碎石术）的声波传播，无线通信中的微波传播，或光学断层扫描中的光子传播，这是一种非常强大的成像技术，可以检测脑肿瘤和手指关节炎。 该工程师设计理论和数值工具来分析波和粒子的传播，并了解如何使用它来解决实际问题，如在特定环境中可以获得的最大通信容量，也就是光学断层扫描可以成像的最小尺寸的肿瘤。研究人员的主要目标是向未来几代本科生和研究生教授已经出现的新技术最近在应用医学界来解决这些问题。

Bal The investigator and his students study wave and particlepropagation in heterogeneous media and related inverse problems.More precisely, they analyze the refocusing and stabilityproperties of time reversed waves, which can be used innon-destructive testing and wireless communication. They alsoanalyze photon propagation in human tissues to understand how theproperties of these tissues can be imaged from photon intensitymeasurements. Numerical tools and software are developed tosimulate the aforementioned forward and inverse problems. Theinvestigator also develops a course on theoretical and numericalinverse problems. In many applications a good understanding of wave andparticle propagation in complicated media is necessary: seismicwave propagation generated by earthquakes, acoustic wavepropagation to destroy kidney stones (lithotripsy), microwavepropagation in wireless communication, or photon propagation inoptical tomography, a quite powerful imaging technique to detect,for instance, brain tumors and finger arthritis. The investigatordevises theoretical and numerical tools to analyze wave andparticle propagation and to understand how it can be used tosolve practical problems, such as the maximal capacity ofcommunication that can be obtained in a specific environment, orthe minimal size tumor that can be imaged in optical tomography.It is also a primary goal of the investigator to teach cominggenerations of undergraduate and graduate students the noveltechniques that have emerged recently in the applied mathematicalcommunity to address these problems.