Alexander G Ramm 
WAVE SCATTERING BY SMALL BODIES [EPUB ebook] 
Creating Materials with a Desired Refraction Coefficient and Other Applications

The book is a research monograph. An asymptotically exact solution of the many-body scattering problem is given under the assumption a ≪ d ≪ λ, where a is the characteristic size of a small particle, d is the smallest distance between particles and λ is the wavelength in the medium in which the particles are embedded. Scattering of scalar and electromagnetic waves is considered. Heat transfer theory in the medium in which many small bodies are embedded is developed. Quantum-mechanical theory of scattering by many potentials with small support is constructed.

On the basis of these theoretical results, important applications are presented. First, a method for creating materials with a desired refraction coefficient is given. Secondly, a method for creating wave-focusing materials is developed. Technological problems to be solved for practical usage of these applied results are discussed.

This book contains the contents of the author’s earlier monograph, published in 2013. New appendices, based on the author’s review papers published after 2013, are added.

Contents:

• Foreword


• Preface


• About the Author


• Introduction


• Scalar Wave Scattering by One Small Body of an Arbitrary Shape


• Scalar Wave Scattering by Many Small Bodies of an Arbitrary Shape


• Creating Materials with a Desired Refraction Coefficient


• Wave-Focusing Materials


• Electromagnetic Wave Scattering by a Single Small Body of an Arbitrary Shape


• Many-Body Scattering Problem in the Case of Small Scatterers


• Creating Materials with a Desired Refraction Coefficient


• Electromagnetic Wave Scattering by Many Nanowires


• Heat Transfer in a Medium in Which Many Small Bodies are Embedded


• Quantum-Mechanical Wave Scattering by Many Potentials with Small Support


• Some Results from the Potential Theory


• Collocation Method


• Some Inverse Problems Related to Small Scatterers


• Appendices

Readership: Mathematical physics and Physics graduate students and researchers interested in wave scattering. Engineers and materials scientists creating materials with desired refraction coefficient or wave focusing properties.

Key Features:

• Contains novel and interesting analytical (exact) results not found in other researchers’ work


• Author is a leading expert in scattering theory


• No other books have treated both acoustics and electromagnetic wave scattering together in one volume


• Contains clear recipes of applications in engineering, materials science and physics