Multiforms, dyadics, and electromagnetic media / / Ismo V. Lindell

• Autore: Lindell Ismo V.
• Pubblicazione: Hoboken, New Jersey : , : IEEE Press/Wiley, [2015]; [Piscataqay, New Jersey] : , : IEEE Xplore, , [2015]
• Descrizione fisica: 1 online resource (416 p.)
• Disciplina: 537.01/515
• Soggetto topico: Electromagnetism - Mathematics; Electromagnetism - Mathematical models
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Preface xi -- 1 Multivectors and Multiforms 1 -- 1.1 Vectors and One-Forms, 1 -- 1.1.1 Bar Product | 1 -- 1.1.2 Basis Expansions 2 -- 1.2 Bivectors and Two-Forms, 3 -- 1.2.1 Wedge Product ∧ 3 -- 1.2.2 Basis Expansions 4 -- 1.2.3 Bar Product 5 -- 1.2.4 Contraction Products ⌋ and ⌊ 6 -- 1.2.5 Decomposition of Vectors and One-Forms 8 -- 1.3 Multivectors and Multiforms, 8 -- 1.3.1 Basis of Multivectors 9 -- 1.3.2 Bar Product of Multivectors and Multiforms 10 -- 1.3.3 Contraction of Trivectors and Three-Forms 11 -- 1.3.4 Contraction of Quadrivectors and Four-Forms 12 -- 1.3.5 Construction of Reciprocal Basis 13 -- 1.3.6 Contraction of Quintivector 14 -- 1.3.7 Generalized Bac-Cab Rules 14 -- 1.4 Some Properties of Bivectors and Two-Forms, 16 -- 1.4.1 Bivector Invariant 16 -- 1.4.2 Natural Dot Product 17 -- 1.4.3 Bivector as Mapping 17 -- Problems, 18 -- 2 Dyadics 21 -- 2.1 Mapping Vectors and One-Forms, 21 -- 2.1.1 Dyadics 21 -- 2.1.2 Double-Bar Product || 23 -- 2.1.3 Metric Dyadics 24 -- 2.2 Mapping Multivectors and Multiforms, 25 -- 2.2.1 Bidyadics 25 -- 2.2.2 Double-Wedge Product ∧∧ -- 2.2.3 Double-Wedge Powers 28 -- 2.2.4 Double Contractions ⌊⌊ and ⌋⌋ 30 -- 2.2.5 Natural Dot Product for Bidyadics 31 -- 2.3 Dyadic Identities, 32 -- 2.3.1 Contraction Identities 32 -- 2.3.2 Special Cases 33 -- 2.3.3 More General Rules 35 -- 2.3.4 Cayley / Hamilton Equation 36 -- 2.3.5 Inverse Dyadics 36 -- 2.4 Rank of Dyadics, 39 -- 2.5 Eigenproblems, 41 -- 2.5.1 Eigenvectors and Eigen One-Forms 41 -- 2.5.2 Reduced Cayley / Hamilton Equations 42 -- 2.5.3 Construction of Eigenvectors 43 -- 2.6 Metric Dyadics, 45 -- 2.6.1 Symmetric Dyadics 46 -- 2.6.2 Antisymmetric Dyadics 47 -- 2.6.3 Inverse Rules for Metric Dyadics 48 -- Problems, 49 -- 3 Bidyadics 53 -- 3.1 Cayley / Hamilton Equation, 54 -- 3.1.1 Coefficient Functions 55 -- 3.1.2 Determinant of a Bidyadic 57 -- 3.1.3 Antisymmetric Bidyadic 57 -- 3.2 Bidyadic Eigenproblem, 58 -- 3.2.1 Eigenbidyadic C- 60 -- 3.2.2 Eigenbidyadic C+ 60 -- 3.3 Hehl / Obukhov Decomposition, 61. ; 3.4 Example: Simple Antisymmetric Bidyadic, 64 -- 3.5 Inverse Rules for Bidyadics, 66 -- 3.5.1 Skewon Bidyadic 67 -- 3.5.2 Extended Bidyadics 70 -- 3.5.3 3D Expansions 73 -- Problems, 74 -- 4 Special Dyadics and Bidyadics 79 -- 4.1 Orthogonality Conditions, 79 -- 4.1.1 Orthogonality of Dyadics 79 -- 4.1.2 Orthogonality of Bidyadics 81 -- 4.2 Nilpotent Dyadics and Bidyadics, 81 -- 4.3 Projection Dyadics and Bidyadics, 83 -- 4.4 Unipotent Dyadics and Bidyadics, 85 -- 4.5 Almost-Complex Dyadics, 87 -- 4.5.1 Two-Dimensional AC Dyadics 89 -- 4.5.2 Four-Dimensional AC Dyadics 89 -- 4.6 Almost-Complex Bidyadics, 91 -- 4.7 Modified Closure Relation, 93 -- 4.7.1 Equivalent Conditions 94 -- 4.7.2 Solutions 94 -- 4.7.3 Testing the Two Solutions 96 -- Problems, 98 -- 5 Electromagnetic Fields 101 -- 5.1 Field Equations, 101 -- 5.1.1 Differentiation Operator 101 -- 5.1.2 Maxwell Equations 103 -- 5.1.3 Potential One-Form 105 -- 5.2 Medium Equations, 106 -- 5.2.1 Medium Bidyadics 106 -- 5.2.2 Potential Equation 107 -- 5.2.3 Expansions of Medium Bidyadics 107 -- 5.2.4 Gibbsian Representation 109 -- 5.3 Basic Classes of Media, 110 -- 5.3.1 Hehl / Obukhov Decomposition 110 -- 5.3.2 3D Expansions 112 -- 5.3.3 Simple Principal Medium 114 -- 5.4 Interfaces and Boundaries, 117 -- 5.4.1 Interface Conditions 117 -- 5.4.2 Boundary Conditions 119 -- 5.5 Power and Energy, 123 -- 5.5.1 Bilinear Invariants 123 -- 5.5.2 The Stress / Energy Dyadic 125 -- 5.5.3 Differentiation Rule 127 -- 5.6 Plane Waves, 128 -- 5.6.1 Basic Equations 128 -- 5.6.2 Dispersion Equation 130 -- 5.6.3 Special Cases 132 -- 5.6.4 Plane-Wave Fields 132 -- 5.6.5 Simple Principal Medium 134 -- 5.6.6 Handedness of Plane Wave 135 -- Problems, 136 -- 6 Transformation of Fields and Media 141 -- 6.1 Affine Transformation, 141 -- 6.1.1 Transformation of Fields 141 -- 6.1.2 Transformation of Media 142 -- 6.1.3 Dispersion Equation 144 -- 6.1.4 Simple Principal Medium 145 -- 6.2 Duality Transformation, 145 -- 6.2.1 Transformation of Fields 146. ; 6.2.2 Involutionary Duality Transformation 147 -- 6.2.3 Transformation of Media 149 -- 6.3 Transformation of Boundary Conditions, 150 -- 6.3.1 Simple Principal Medium 152 -- 6.3.2 Plane Wave 152 -- 6.4 Reciprocity Transformation, 153 -- 6.4.1 Medium Transformation 153 -- 6.4.2 Reciprocity Conditions 155 -- 6.4.3 Field Relations 157 -- 6.4.4 Time-Harmonic Fields 158 -- 6.5 Conformal Transformation, 159 -- 6.5.1 Properties of the Conformal Transformation 160 -- 6.5.2 Field Transformation 164 -- 6.5.3 Medium Transformation 165 -- Problems, 166 -- 7 Basic Classes of Electromagnetic Media 169 -- 7.1 Gibbsian Isotropy, 169 -- 7.1.1 Gibbsian Isotropic Medium 169 -- 7.1.2 Gibbsian Bi-isotropic Medium 170 -- 7.1.3 Decomposition of GBI Medium 171 -- 7.1.4 Affine Transformation 173 -- 7.1.5 Eigenfields in GBI Medium 174 -- 7.1.6 Plane Wave in GBI Medium 176 -- 7.2 The Axion Medium, 178 -- 7.2.1 Perfect Electromagnetic Conductor 179 -- 7.2.2 PEMC as Limiting Case of GBI Medium 180 -- 7.2.3 PEMC Boundary Problems 181 -- 7.3 Skewon / Axion Media, 182 -- 7.3.1 Plane Wave in Skewon / Axion Medium 184 -- 7.3.2 Gibbsian Representation 185 -- 7.3.3 Boundary Conditions 187 -- 7.4 Extended Skewon / Axion Media, 192 -- Problems, 194 -- 8 Quadratic Media 197 -- 8.1 P Media and Q Media, 197 -- 8.2 Transformations, 200 -- 8.3 Spatial Expansions, 201 -- 8.3.1 Spatial Expansion of Q Media 201 -- 8.3.2 Spatial Expansion of P Media 203 -- 8.3.3 Relation Between P Media and Q Media 204 -- 8.4 Plane Waves, 205 -- 8.4.1 Plane Waves in Q Media 205 -- 8.4.2 Plane Waves in P Media 207 -- 8.4.3 P Medium as Boundary Material 208 -- 8.5 P-Axion and Q-Axion Media, 209 -- 8.6 Extended Q Media, 211 -- 8.6.1 Gibbsian Representation 211 -- 8.6.2 Field Decomposition 214 -- 8.6.3 Transformations 215 -- 8.6.4 Plane Waves in Extended Q Media 215 -- 8.7 Extended P Media, 218 -- 8.7.1 Medium Conditions 218 -- 8.7.2 Plane Waves in Extended P Media 219 -- 8.7.3 Field Conditions 220 -- Problems, 221 -- 9 Media Defined by Bidyadic Equations 225. ; 9.1 Quadratic Equation, 226 -- 9.1.1 SD Media 227 -- 9.1.2 Eigenexpansions 228 -- 9.1.3 Duality Transformation 229 -- 9.1.4 3D Representations 231 -- 9.1.5 SDN Media 234 -- 9.2 Cubic Equation, 235 -- 9.2.1 CU Media 235 -- 9.2.2 Eigenexpansions 236 -- 9.2.3 Examples of CU Media 238 -- 9.3 Bi-Quadratic Equation, 240 -- 9.3.1 BQ Media 241 -- 9.3.2 Eigenexpansions 242 -- 9.3.3 3D Representation 244 -- 9.3.4 Special Case 245 -- Problems, 246 -- 10 Media Defined by Plane-Wave Properties 249 -- 10.1 Media with No Dispersion Equation (NDE Media), 249 -- 10.1.1 Two Cases of Solutions 250 -- 10.1.2 Plane-Wave Fields in NDE Media 255 -- 10.1.3 Other Possible NDE Media 257 -- 10.2 Decomposable Media, 259 -- 10.2.1 Special Cases 259 -- 10.2.2 DC-Medium Subclasses 263 -- 10.2.3 Plane-Wave Properties 267 -- Problems, 269 -- Appendix A Solutions to Problems 273 -- Appendix B Transformation to Gibbsian Formalism 369 -- Appendix C Multivector and Dyadic Identities 375 -- References 389 -- Index 395.
• Sommario/riassunto: Internationally recognized authority on Differential Forms, Ismo V. Lindell, presents the tools for analyzing electromagnetic problems with special attention on electromagnetic media. The tools are applicable in basic studies of metamaterials and metasurfaces. This book deals with electromagnetic equations in terms of differential forms and exterior calculus (multivectors, multiforms and dyadics), allowing a coordinate-free way of doing analytic work. Also, applying four-dimensional formalism equations and expressions can be handled in a more compact form than through the conventional three-dimensional formalism. The content focuses on electromagnetic media by defining medium classes in several different ways and analyzing wave propagation in them. This book also deals with generation of boundary surfaces in terms of special medium interfaces. The introductory material on various types of dyadics is extended to include an appendix of operational rules ready for application. . Presents the tools for analyzing electromagnetic problems with special attention on electromagnetic media . Includes solutions to end of chapter problems within the appendix . Written by an internationally recognized expert on Differential Forms Multiforms, Dyadics and Electromagnetic Media is mainly focused on applying the formalism to the analysis of electromagnetic media as inspired by the ongoing engineering interest in constructing novel metamaterials and metaboundaries. Ismo V. Lindell is a Professor Emeritus in the Department of Radio Science and Engineering, in the School of Electrical Engineering at the Aalto University, Finland. Dr. Lindell has received many honors in the course of his career, including his recognition as an IEEE Fellow in 1990 for his contributions to electromagnetic theory and for the development of education in electromagnetics in Finland. Dr. Lindell has authored or co-authored 3 books in English, authored or co-authored 10 books in Finnish, and published several hundred articles in professional journals, conference proceedings, and contributed chapters to other books.
• Titolo autorizzato: Multiforms, dyadics, and electromagnetic media
• ISBN: 1-119-05239-4; 1-119-05238-6; 1-119-05240-8
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910813439503321
• Lo trovi qui: Univ. Federico II
• Serie: IEEE Press series on electromagnetic wave theory