Ramm A.G. Wave Scattering By Small Bodies Of Arbitrary Shapes

World Scientific Publishing, 2005, 293 pages, ISBN: 9812561862This book presents analytical formulas which allow one to calculate the S-matrix for the acoustic and electromagnetic wave scattering by small bodies or arbitrary shapes with arbitrary accuracy. Equations for the self-consistent field in media consisting of many small bodies are derived. Applications of these results to ultrasound mammography and electrical engineering are considered.The above formulas are not available in the works of other authors. Their derivation is based on a mathematical theory for solving integral equations of electrostatics, magnetostatics, and other static fields. These equations are at a simple characteristic value. Convergent iterative processes are constructed for stable solution of these equations. The theory completes the classical work of Rayleigh on scattering by small bodies by providing analytical formulas for polarizability tensors for bodies of arbitrary shapes.Basic Problems
Iterative Processes for Solving Fredholm's Integral Equations for Static Problems
Calculating Electric Capacitance
Numerical Examples
Calculating Polarizability Tensors
Iterative Methods: Mathematical Results
Wave Scattering by Small Bodies
Fredholm Alternative and a Characterization of Fredholm Operators
Boundary-Value Problems in Rough Domains
Low Frequency Asymptotics
Finding Small Inhomogeneities from Scattering Data
Modified Rayleigh Conjecture and Applications