LEADER 06339nam 2200757 450 001 9910453391503321 005 20200520144314.0 010 $a1-60650-622-6 024 7 $a10.5643/9781606506226 035 $a(CKB)2550000001138960 035 $a(OCoLC)865580197 035 $a(CaPaEBR)ebrary10810845 035 $a(SSID)ssj0001140031 035 $a(PQKBManifestationID)11993249 035 $a(PQKBTitleCode)TC0001140031 035 $a(PQKBWorkID)11220330 035 $a(PQKB)11232779 035 $a(CaBNvSL)swl00402963 035 $a(MiAaPQ)EBC1495935 035 $a(Au-PeEL)EBL1495935 035 $a(CaPaEBR)ebr10810845 035 $a(CaONFJC)MIL538630 035 $a(OCoLC)861559782 035 $a(EXLCZ)992550000001138960 100 $a20180728d2013 uy 0 101 0 $aeng 135 $aurcn||||m|||a 181 $ctxt 182 $cc 183 $acr 200 10$aScattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes $eapplications to creating new engineered materials /$fAlexander G. Ramm 210 1$aNew York, New York :$cMomentum Press,$d[2013] 210 4$dİ2013 215 $a1 online resource (262 p.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-60650-621-8 311 $a1-306-07379-0 320 $aIncludes bibliographical references and index. 327 $aContents -- Preface -- Introduction -- 327 $a1. Scalar wave scattering by one small body of an arbitrary shape -- 1.1 Impedance bodies -- 1.2 Acoustically soft bodies (the Dirichlet boundary condition) -- 1.3 Acoustically hard bodies (the Neumann boundary condition) -- 1.4 The interface (transmission) boundary condition -- 1.5 Summary of the results -- 327 $a2. Scalar wave scattering by many small bodies of an arbitrary shape -- 2.1 Impedance bodies -- 2.2 The Dirichlet boundary condition -- 2.3 The Neumann boundary condition -- 2.4 The transmission boundary condition -- 2.5 Wave scattering in an inhomogeneous medium -- 2.6 Summary of the results -- 327 $a3. Creating materials with a desired refraction coefficient -- 3.1 Scalar wave scattering. Formula for the refraction coefficient -- 3.2 A recipe for creating materials with a desired refraction coefficient -- 3.3 A discussion of the practical implementation of the recipe -- 3.4 Summary of the results -- 327 $a4. Wave-focusing materials -- 4.1 What is a wave-focusing material? -- 4.2 Creating wave-focusing materials -- 4.3 Computational aspects of the problem -- 4.4 Open problems -- 4.5 Summary of the results -- 327 $a5. Electromagnetic wave scattering by a single small body of an arbitrary shape -- 5.1 The impedance boundary condition -- 5.2 Perfectly conducting bodies -- 5.3 Formulas for the scattered field in the case of EM wave scattering by one impedance small body of an arbitrary shape -- 5.4 Summary of the results -- 327 $a6. Many-body scattering problem in the case of small scatterers -- 6.1 Reduction of the problem to linear algebraic system -- 6.2 Derivation of the integral equation for the effective field -- 6.3 Summary of the results -- 327 $a7. Creating materials with a desired refraction coefficient -- 7.1 A formula for the refraction coefficient -- 7.2 Formula for the magnetic permeability -- 7.3 Summary of the results -- 327 $a8. Electromagnetic wave scattering by many nanowires -- 8.1 Statement of the problem -- 8.2 Asymptotic solution of the problem -- 8.3 Many-body scattering problem equation for the effective field -- 8.4 Physical properties of the limiting medium -- 8.5 Summary of the results -- 327 $a9. Heat transfer in a medium in which many small bodies are embedded -- 9.1 Introduction -- 9.2 Derivation of the equation for the limiting temperature -- 9.3 Various results -- 9.4 Summary of the results -- 327 $a10. Quantum-mechanical wave scattering by many potentials with small support -- 10.1 Problem formulation -- 10.2 Proofs -- 10.3 Summary of the results -- 327 $a11. Some results from the potential theory -- 11.1 Potentials of the simple and double layers -- 11.2 Replacement of the surface potentials -- 11.3 Asymptotic behavior of the solution to the Helmholtz equation under the impedance boundary condition -- 11.4 Some properties of the electrical capacitance -- 11.5 Summary of the results -- 327 $a12. Collocation method -- 12.1 Convergence of the collocation method -- 12.2 Collocation method and homogenization -- 12.3 Summary of the results -- 327 $a13. Some inverse problems related to small scatterers -- 13.1 Finding the position and size of a small body from the scattering data -- 13.2 Finding small subsurface inhomogeneities -- 13.3 Inverse radio measurements problem -- 13.4 Summary of the results -- 327 $aAppendix -- A1. Banach and Hilbert spaces -- A2. A result from perturbation theory -- A3. The Fredholm alternative -- Bibliographical notes -- Bibliography -- Index. 330 3 $aIn this book, mathematicians, engineers, physicists, and materials scientists will learn how to create material with a desired refraction coefficient. For example, how to create material with negative refraction or with desired wave-focusing properties. The methods for creating these materials are based on the many-body wave scattering theory developed by the author. The book offers new analytical formulas that allow one to calculate acoustic and electromagnetic waves, scattered by one and many small impedance bodies of an arbitrary shape under various boundary conditions. Equations for the effective (self-consistent) field in media consisting of many small impedance particles are derived. Numerical methods for solving many-body wave scattering problems are developed for small impedance scatterers. 606 $aWave-motion, Theory of 608 $aElectronic books. 615 0$aWave-motion, Theory of. 676 $a531.1133 700 $aRamm$b A. G$g(Alexander G.),$050066 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910453391503321 996 $aScattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes$91916292 997 $aUNINA