Scattering of Acoustic and Electromagnetic Waves by Small Impedance Bodies of Arbitrary Shape:Applications to Creating New Engineered Materials

Alexander G. Ramm

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The behavior of acoustic or electromagnetic waves reflecting off, and scattering from, intercepted bodies of any size and kind can make determinations about the materials of those bodies and help in better understanding how to manipulate such materials for desired characteristics. This book offers analytical formulas which allow you to calculate acoustic and electromagnetic waves, scattered by one and many small bodies of an arbitrary shape under various boundary conditions. Equations for the effective (self-consistent) field in media consisting of many small bodies are derived. These results and formulas are new and not available in the works of other authors. In particular, the theory developed in this book is different from the classical work of Rayleigh on scattering by small bodies: not only analytical formulas are derived for the waves scattered by small bodies of an arbitrary shape, but the amplitude of the scattered waves is much larger, of the order O(a 2-k), than in Rayleigh scattering, where the order of the scattered waves is O(a3). Moreover, the many-body scattering theory is developed and equations for the effective field in the medium in which many small particles are embedded are derived. Applications, including meta- materials with a desired refraction coefficient, are discussed.

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Alexander G. Ramm

Alexander G. Ramm is a Professor of Mathematics at Kansas State University.
He is a leading expert in Mathematical Physics (scattering theory, inverse scattering, wave propagation, theoretical numerical analysis, tomography). He consulted at Los Alamos National Laboratory and at major oil corporations. He is an editor of several journals, an invited plenary speaker at numerous major conferences, and is the author of more than 600 publications, including 13 monographs and editor of 3 books.