The Resource Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials, Alexander G. Ramm, (electronic resource)
Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials, Alexander G. Ramm, (electronic resource)
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The item Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials, Alexander G. Ramm, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of MissouriSt. Louis Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials, Alexander G. Ramm, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of MissouriSt. Louis Libraries.
This item is available to borrow from 1 library branch.
 Summary

 In 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 wavefocusing properties. The methods for creating these materials are based on the manybody 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 (selfconsistent) field in media consisting of many small impedance particles are derived. Numerical methods for solving manybody wave scattering problems are developed for small impedance scatterers
 In 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 wavefocusing properties. The methods for creating these materials are based on the manybody 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 (selfconsistent) field in media consisting of many small impedance particles are derived. Numerical methods for solving manybody wave scattering problems are developed for small impedance scatterers
 Language
 eng
 Contents

 Contents  Preface  Introduction 
 1. 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 
 2. 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 
 3. 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 
 4. Wavefocusing materials  4.1 What is a wavefocusing material?  4.2 Creating wavefocusing materials  4.3 Computational aspects of the problem  4.4 Open problems  4.5 Summary of the results 
 5. 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 
 6. Manybody 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 
 7. 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 
 8. Electromagnetic wave scattering by many nanowires  8.1 Statement of the problem  8.2 Asymptotic solution of the problem  8.3 Manybody scattering problem equation for the effective field  8.4 Physical properties of the limiting medium  8.5 Summary of the results 
 9. 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 
 10. Quantummechanical wave scattering by many potentials with small support  10.1 Problem formulation  10.2 Proofs  10.3 Summary of the results 
 11. 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 
 12. Collocation method  12.1 Convergence of the collocation method  12.2 Collocation method and homogenization  12.3 Summary of the results 
 13. 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 
 Appendix  A1. Banach and Hilbert spaces  A2. A result from perturbation theory  A3. The Fredholm alternative  Bibliographical notes  Bibliography  Index
 Contents  Preface  Introduction 
 1. 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 
 2. 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 
 3. 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 
 4. Wavefocusing materials  4.1 What is a wavefocusing material?  4.2 Creating wavefocusing materials  4.3 Computational aspects of the problem  4.4 Open problems  4.5 Summary of the results 
 5. 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 
 6. Manybody 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 
 7. 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 
 8. Electromagnetic wave scattering by many nanowires  8.1 Statement of the problem  8.2 Asymptotic solution of the problem  8.3 Manybody scattering problem equation for the effective field  8.4 Physical properties of the limiting medium  8.5 Summary of the results 
 9. 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 
 10. Quantummechanical wave scattering by many potentials with small support  10.1 Problem formulation  10.2 Proofs  10.3 Summary of the results 
 11. 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 
 12. Collocation method  12.1 Convergence of the collocation method  12.2 Collocation method and homogenization  12.3 Summary of the results 
 13. 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 
 Appendix  A1. Banach and Hilbert spaces  A2. A result from perturbation theory  A3. The Fredholm alternative  Bibliographical notes  Bibliography  Index
 Isbn
 9781606506226
 Label
 Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials
 Title
 Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes
 Title remainder
 applications to creating new engineered materials
 Statement of responsibility
 Alexander G. Ramm
 Subject

 Acoustic waves
 Electromagnetic waves  Scattering
 Scattering (Physics)
 Soundwaves  Scattering
 creating materials with a desired refraction coefficient
 eave scattering
 Acoustic impedance
 inverse problems
 metamaterials
 nanowires
 radio measurements
 small impedance bodies of an arbitrary shape
 wave scattering by small impedance bodies of arbitrary shapes
 electromagnetic eaves
 Language
 eng
 Summary

 In 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 wavefocusing properties. The methods for creating these materials are based on the manybody 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 (selfconsistent) field in media consisting of many small impedance particles are derived. Numerical methods for solving manybody wave scattering problems are developed for small impedance scatterers
 In 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 wavefocusing properties. The methods for creating these materials are based on the manybody 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 (selfconsistent) field in media consisting of many small impedance particles are derived. Numerical methods for solving manybody wave scattering problems are developed for small impedance scatterers
 Cataloging source
 CaBNVSL
 http://library.link/vocab/creatorName
 Ramm, A. G.
 Dewey number
 534.2
 LC call number
 QC243.3.S3
 LC item number
 R257 2013
 http://library.link/vocab/subjectName

 Soundwaves
 Electromagnetic waves
 Scattering (Physics)
 Acoustic impedance
 Label
 Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials, Alexander G. Ramm, (electronic resource)
 Bibliography note
 Includes bibliographical references (pages 229238) and index
 Contents

 Contents  Preface  Introduction 
 1. 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 
 2. 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 
 3. 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 
 4. Wavefocusing materials  4.1 What is a wavefocusing material?  4.2 Creating wavefocusing materials  4.3 Computational aspects of the problem  4.4 Open problems  4.5 Summary of the results 
 5. 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 
 6. Manybody 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 
 7. 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 
 8. Electromagnetic wave scattering by many nanowires  8.1 Statement of the problem  8.2 Asymptotic solution of the problem  8.3 Manybody scattering problem equation for the effective field  8.4 Physical properties of the limiting medium  8.5 Summary of the results 
 9. 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 
 10. Quantummechanical wave scattering by many potentials with small support  10.1 Problem formulation  10.2 Proofs  10.3 Summary of the results 
 11. 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 
 12. Collocation method  12.1 Convergence of the collocation method  12.2 Collocation method and homogenization  12.3 Summary of the results 
 13. 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 
 Appendix  A1. Banach and Hilbert spaces  A2. A result from perturbation theory  A3. The Fredholm alternative  Bibliographical notes  Bibliography  Index
 Contents  Preface  Introduction 
 1. 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 
 2. 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 
 3. 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 
 4. Wavefocusing materials  4.1 What is a wavefocusing material?  4.2 Creating wavefocusing materials  4.3 Computational aspects of the problem  4.4 Open problems  4.5 Summary of the results 
 5. 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 
 6. Manybody 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 
 7. 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 
 8. Electromagnetic wave scattering by many nanowires  8.1 Statement of the problem  8.2 Asymptotic solution of the problem  8.3 Manybody scattering problem equation for the effective field  8.4 Physical properties of the limiting medium  8.5 Summary of the results 
 9. 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 
 10. Quantummechanical wave scattering by many potentials with small support  10.1 Problem formulation  10.2 Proofs  10.3 Summary of the results 
 11. 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 
 12. Collocation method  12.1 Convergence of the collocation method  12.2 Collocation method and homogenization  12.3 Summary of the results 
 13. 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 
 Appendix  A1. Banach and Hilbert spaces  A2. A result from perturbation theory  A3. The Fredholm alternative  Bibliographical notes  Bibliography  Index
 Control code
 OCM1bookssj0001140031
 Dimensions
 unknown
 Isbn
 9781606506226
 Isbn Type
 (ebook)
 Other control number
 10.5643/9781606506226
 Specific material designation
 remote
 System control number
 (WaSeSS)bookssj0001140031
 System details

 Mode of access: World Wide Web
 System requirements: Adobe Acrobat reader
 Label
 Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials, Alexander G. Ramm, (electronic resource)
 Bibliography note
 Includes bibliographical references (pages 229238) and index
 Contents

 Contents  Preface  Introduction 
 1. 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 
 2. 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 
 3. 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 
 4. Wavefocusing materials  4.1 What is a wavefocusing material?  4.2 Creating wavefocusing materials  4.3 Computational aspects of the problem  4.4 Open problems  4.5 Summary of the results 
 5. 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 
 6. Manybody 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 
 7. 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 
 8. Electromagnetic wave scattering by many nanowires  8.1 Statement of the problem  8.2 Asymptotic solution of the problem  8.3 Manybody scattering problem equation for the effective field  8.4 Physical properties of the limiting medium  8.5 Summary of the results 
 9. 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 
 10. Quantummechanical wave scattering by many potentials with small support  10.1 Problem formulation  10.2 Proofs  10.3 Summary of the results 
 11. 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 
 12. Collocation method  12.1 Convergence of the collocation method  12.2 Collocation method and homogenization  12.3 Summary of the results 
 13. 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 
 Appendix  A1. Banach and Hilbert spaces  A2. A result from perturbation theory  A3. The Fredholm alternative  Bibliographical notes  Bibliography  Index
 Contents  Preface  Introduction 
 1. 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 
 2. 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 
 3. 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 
 4. Wavefocusing materials  4.1 What is a wavefocusing material?  4.2 Creating wavefocusing materials  4.3 Computational aspects of the problem  4.4 Open problems  4.5 Summary of the results 
 5. 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 
 6. Manybody 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 
 7. 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 
 8. Electromagnetic wave scattering by many nanowires  8.1 Statement of the problem  8.2 Asymptotic solution of the problem  8.3 Manybody scattering problem equation for the effective field  8.4 Physical properties of the limiting medium  8.5 Summary of the results 
 9. 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 
 10. Quantummechanical wave scattering by many potentials with small support  10.1 Problem formulation  10.2 Proofs  10.3 Summary of the results 
 11. 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 
 12. Collocation method  12.1 Convergence of the collocation method  12.2 Collocation method and homogenization  12.3 Summary of the results 
 13. 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 
 Appendix  A1. Banach and Hilbert spaces  A2. A result from perturbation theory  A3. The Fredholm alternative  Bibliographical notes  Bibliography  Index
 Control code
 OCM1bookssj0001140031
 Dimensions
 unknown
 Isbn
 9781606506226
 Isbn Type
 (ebook)
 Other control number
 10.5643/9781606506226
 Specific material designation
 remote
 System control number
 (WaSeSS)bookssj0001140031
 System details

 Mode of access: World Wide Web
 System requirements: Adobe Acrobat reader
Subject
 Acoustic waves
 Electromagnetic waves  Scattering
 Scattering (Physics)
 Soundwaves  Scattering
 creating materials with a desired refraction coefficient
 eave scattering
 Acoustic impedance
 inverse problems
 metamaterials
 nanowires
 radio measurements
 small impedance bodies of an arbitrary shape
 wave scattering by small impedance bodies of arbitrary shapes
 electromagnetic eaves
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