Wave Scattering by Small Bodies of Arbitrary Shapes

This 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 constructured 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; Appendix A: Optimal with Respect to Accuracy Algorithms for Calculation of Multidimensional Weakly Singular Integrals and Applications to Calculation of Capacitances of Conductors of Arbitrary Shapes