Direct Methods For Inverse Scattering With Time Dependent And Reduced Data
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Direct Methods for Inverse Scattering with Time Dependent and Reduced Data
This thesis is focused on the motion of acoustic waves through penetrable media, and the use of such waves to reconstruct material properties of the fluid through which the waves are moving. The reconstruction methods developed in this thesis fall under the category of qualitative inversion methods and, as such, are fast and mathematically justified. Unlike in typical qualitative methods, however, these new methods require only small amounts of scattered field data to be collected. In particular, we demonstrate that with both far field time harmonic data and near field time dependent data, the location of weakly scattering point obstacles can be reconstructed with reduced data collection requirements compared to typical qualitative schemes. We give full mathematical justification for the time harmonic method and partial justification for the time dependent method. We also analyze the transmission eigenvalue problem for weakly scattering media, proving that, under this assumption, transmission eigenvalues are discrete and can sometimes have complex part which grows without bound. Finally, we introduce a fast method for simulating time harmonic and time dependent acoustic wave scattering and apply this method to optimization schemes for reconstructing penetrable media based on scattered field data.
Scattering Theory And Biomedical Engineering Modelling And Applications - Proceedings Of The 4th International Workshop
This book addresses issues of scattering theory and biomedical engineering, as well as methodological approaches and tools from related scientific areas such as applied mathematics, mechanics, numerical analysis, and signal and image processing.
Applications of Differential Equations in Engineering and Mechanics
This second of two comprehensive reference texts on differential equations continues coverage of the essential material students they are likely to encounter in solving engineering and mechanics problems across the field - alongside a preliminary volume on theory. This book covers a very broad range of problems, including beams and columns, plates, shells, structural dynamics, catenary and cable suspension bridge, nonlinear buckling, transports and waves in fluids, geophysical fluid flows, nonlinear waves and solitons, Maxwell equations, Schrodinger equations, celestial mechanics and fracture mechanics and dynamics. The focus is on the mathematical technique for solving the differential equations involved. All readers who are concerned with and interested in engineering mechanics problems, climate change, and nanotechnology will find topics covered in this book providing valuable information and mathematics background for their multi-disciplinary research and education.