Inverse Scattering Problems in Locally Perturbed Periodic Layers
Inverse scattering problems arise from many real-life applications, such as non-destructive testing, medical imaging, geophysical protesting,... An inverse scattering problem typically aims to determine some information about a scattering object or an inhomogeneous medium from some knowledge about the waves that are scattered by that object or medium.
This talk will briefly introduce an inverse scattering problem in general and inverse scattering problems in a locally perturbed periodic domain with an unknown background. Some open questions and projects will be discussed.
This project focuses on modeling soft matter systems using methods that include modeling, discrete element simulations, network analysis using computational topology methods, and machine learning. The considered setups are typical for big-data problems involving large amounts of dynamic data. The plan is to use various mathematical methods to simplify these data sets, focusing on extracting physical mechanisms governing the behavior of underlying systems. The systems of interest include porous media flow, as well as wet and dry granular systems that are of relevance to a number of soft matter systems, such as suspensions, including active matter ones, among others. The part of the project at NJIT focuses on modeling and simulations and will be carried out in close collaboration with the groups focusing on physical experiments.
The presentation will provide an overview of various approaches being used, as well as of specific problems that have been explored recently. In addition, we will briefly discuss a few other projects that are currently considered by Complex Flow and Soft Matter Group members; more information about current and past projects can be found on the group page, cfsm.njit.edu.