局域共振谱理论及其应用（英文版）
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北京通州
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作者邓又军
出版社科学出版社
ISBN9787030775436
出版时间2024-03
装帧平装
纸张其他
定价168元
上书时间2024-11-07
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目录
Contents
1 Introduction and Preliminaries 1
1.1 Overview 1
1.2 Layer Potentials in Electro-Magnetic System 2
13 Layer Potentials in Elastic System 4
1.4 Bessel and Neumann Functions 6
2 Mathematical Theory of Plasmon/Polariton Resonances in Quasi-Static Regime 9
2.1 Maxwells Problem 9
2.1.1 Introduction to Plasmonic Resonances 9
2.1.2 Drudes Model for the Electric Permittivity and Magnetic Permeability 12
2.1.3 Boundary Integral Operators and Resolvent Estimates 15
2.1.4 Layer Potential Formulation 24
2.1.5 Derivation of the Asymptotic Formula 25
2.1.6 Numerical Ilustrations 46
2.1.7 Concluding Remarks 48
2.2 Elastic Problem 48
2.2.1 Layer Potential Techniques 51
2.2.2 Asymptotics for the Integral Operators 53
2.23 Far Field Expansion 57
2.2.5 Resolvent Analysis 67
2.2.6 Polariton Resonance for Elastic Nanoparticles 69
3 Anomalous Localized Resonances and Their Cloaking Effect 77
3.1 Elastostatic Problem 77
3.1.1 Mathematical Setup of Elastostatics Problem 77
3.1.2 Preliminaries on Layer Potentials 79
3.1.3 Spectral Analysis of N-P Operator in Spherical Geometry 81
3.1.4 Anomalous Localized Resonances and Their Cloaking Effect 90
3.1.5 Cloaking by Anomalous Localized Resonance on a Coated Structure in Two Dimensional Case 97
3.2 Electrostatic Problem 115
3.2.1 Background 115
3.2.2 Layer Potential Formulation and Spectral Theory of a Neumann Poincare -Type Operator 117
3.2.3 Analysis of Cloaking Due to Anomalous Localized Resonance 121
4 Localized Resonances for Anisotropic Geometry 129
4.1 Conductivity Problem 129
4.1.1 Some Auxiliary Results 130
4.1.2 Quantitative Analysis of the Electric Field 135
4.13 Application to Calderons Inverse Inclusion Problem 144
4.2 Helmholtz Problem 145
4.2.1 Asymptotic and Quantitative Analysis of the Scattering Field 150
4.2.2 Resonance Analysis of the Exterior Wave Field 169
4.2.3 Resonance Analysis of the Interior Wave Field 176
4.2.4 Conclusion 181
5 Localized Resonances Beyond the Quasi-Static Approximation 183
5.1 Spectral System of Neumann Poincare Operators in Helmoholtz System and Its Asymptotic Behavior 184
5.1.1 Layer Potential and Spectral Properties of Neumann Poincare Operator in R3 184
5.1.2 Asymptotic Behavior of Spectral System of Ncumann-Poincare Operator 187
5.1.3 Two Dimensional Case 191
5.2 Helmboltz System 196
5.2.1 Atypical Resonance and ALR Results in Three Dimensions 200
5.2.2 Spectral System of the N-P Operalor and IIs Application to Atypical Resonance in R3 210
5.2.3 Atypical Resonance and ALR Results in Two Dimensions 213
5.3 Maxwells Problem 219
5.3.1 Integral Formulation of the Maxwell System 220
5.3.2 Spectral Analysis of the Integral Operators 225
5.3.3 Atypical Resonance and Its Cloaking Effect 233
5.3.4 Invisibility Cloaking 240
5.4 Elastic Problem 248
5.4.1 Preliminaries 251
5.4.2 Spectrum System of the Neumann-Poincare Operator 257
5.4.3 Atypical Resonance Beyond the Quasi -Static 267
5.4.4 CALR Beyond the Quasi-Static Approximation 273
6 Interior Transmission Resonance 281
6.1 Introduction 281
6.2 Scalar Case (Helmholtz Equations) 285
6.2.1 Boundary-Localized Transmission Eigenstates 285
6.2.2 Super-Resolution Wave Imaing 311
6.2.3 Numerical Example 321
6.2.4 Pseudo Surface Plasmon Resonances and Potential 324
6.2.5 Concluding Remarks and Discussions 325
6.3 Vectorial Case (Maxwell Equations) 328
6.3.1 Background 328
6.3.2 Boundary-L ocalized Transmission Eigenmodes 329
6.3.3 Numerics 348
6.3.4 Application of Boundary-Localized Transmission Eigenfunctions: Artificial Mirage 351
6.4 Concluding Remarks 356
References 357
内容摘要
本书籍主要介绍作者近几年在局部共振（包括等离子激元/极化共振、不规则局部共振、有限频率局部共振、各向异性材料结构局部共振、内传输共振等）的数学理论及相关应用的研究成果以及国际其他相关的前沿研究成果。研究主要基于不同系统下面诺伊曼-庞加莱算子的谱分析进行开展，结合层势理论以及渐近分析方法，对相应场能进行相关理论分析。书籍将分为6章进行撰写，第一章为引言部分，主要包含一些基础理论：如调和函数相关性质，基本解，层势理论等。第二章到第六章分别介绍不同系统下发生等离子激元/极化共振、不规则局部共振、有限频率局部共振、各向异性材料结构局部共振、内传输共振的基本数学理论和相关应用。
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