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Electromagnetic Heterostructures
Background and Calculation Methods
- 1st Edition - January 21, 2025
- Author: Christian Brosseau
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 3 3 5 4 0 - 2
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 3 3 5 4 1 - 9
Electromagnetic Properties of Heterostructures: Background and Calculation Methods covers the fundamental aspects of the electromagnetic properties of heterostructures and the th… Read more
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Request a sales quoteElectromagnetic Properties of Heterostructures: Background and Calculation Methods covers the fundamental aspects of the electromagnetic properties of heterostructures and the theoretical knowledge of the computational techniques needed to understand dielectric phenomena in quantitative and physical terms. The book re-establishes the conceptual foundations of the physics associated with numerical simulation tools of the Laplace or the Poisson equations and shows their immediate implementation. It is relevant for all practicing engineers and materials scientists who develop composite materials that are capable of handling specified technological requirements by utilizing their electromagnetic properties.
- Explains the basic concepts of the dielectric behavior of heterostructures and discusses how they relate to existing computational methods
- Covers the most widely used and efficient computational approaches, including effective medium and percolation theory
- Fills the gap between theoretical knowledge learned in the classroom and practical knowledge gleaned through extensive work in the lab
Early-career engineering and materials science researchers working with electromagnetic characteristics of composite materials
- Electromagnetic Heterostructures
- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- References
- Acknowledgments
- Part One: Elementary concepts and definitions
- 1 Maxwell’s equations and conventional classical electromagnetic theory
- Abstract
- Keywords
- 1.1 Electromagnetic field in matter
- 1.2 Boundary conditions for electromagnetic fields at (perfectly smooth) interfaces between any two dissimilar media
- 1.3 Use of vector and scalar potentials in Maxwell’s equations: Gauge invariance
- 1.4 Boundary-value problems: Dirichlet versus Neumann
- 1.5 Green’s theorems for Poisson’s and Laplace’s equations (potential theory)
- 1.6 Electrostatic energy for a linear isotropic dielectric media
- 1.7 Forces and torques in electromagnetic field and Maxwell stress tensor
- References
- 2 Polarization in a static electric field
- Abstract
- Keywords
- 2.1 Electrostatic field and potential of a uniformly polarized homogeneous sphere in an infinite dielectric
- 2.2 Onsager derivation for the polarizability of a spherical homogeneous particle
- 2.3 Homogeneous polarizable ellipsoid in a uniform external electric field
- 2.4 Clausius-Mossotti relationship, Lorentz’s method for the treatment of dipolar interaction, and the local field representation
- References
- 3 Polarization and permittivity in an alternating electric field
- Abstract
- Keywords
- 3.1 Harmonic time dependence
- 3.2 Drude-Lorentz model and frequency-dependent electronic (ionic) polarizability
- 3.3 Frequency-dependent orientation polarizability
- 3.4 Frequency-dependent permittivity due to interfacial polarization (Maxwell-Wagner-Sillars) effects
- 3.5 Summary of frequency-dependent dielectric responses
- 3.6 Causality relationships between the real and imaginary parts of the permittivity of passive materials
- 3.7 Some considerations on the deviations from the Debye model of dielectric relaxation
- References
- Part Two: Analytical approaches
- 4 Prelude: A historical examination
- Abstract
- Keyword
- 4.1 From Maxwell to Bruggeman and beyond
- 4.2 The effective medium (“coarsening”) approximation
- 4.3 Bounding methods
- 4.4 Percolation theory: Critical exponents, scaling, and universality
- 4.5 Computational electromagnetics
- 4.6 Concluding remarks
- References
- 5 Some preliminary definitions and considerations
- Abstract
- Keywords
- 5.1 The long-wavelength and quasistatic limits
- 5.2 The multiple scattering regime
- 5.3 The dilute limit and the electric dipole approximation
- 5.4 The topology of the embedded inclusions
- 5.5 Representative volume element
- References
- 6 Mixing laws for two-phase composite media
- Abstract
- Keywords
- 6.1 MG formalism: Commonsense view
- 6.2 Other empirical mixture formulae
- 6.3 Puzzles in the application of mixing laws
- References
- 7 Effective medium approximation: Its basis and formulation
- Abstract
- Keywords
- 7.1 Exact results
- 7.2 Bruggeman effective equation
- 7.3 Virial series
- 7.4 Landau and Lifshitz analysis
- 7.5 McLachlan’s generalized effective media (GEM) equation
- 7.6 Bergman-Milton spectral representation of the effective permittivity
- 7.7 Multiple-scattering theory with infinite order perturbation summation
- 7.8 Iterated homogenization and differential effective medium theories
- 7.9 Asymptotic homogenization method and multiscale analysis
- References
- 8 Bounds for the homogenization of dielectric composite materials
- Abstract
- Keyword
- 8.1 Wiener bounds
- 8.2 Hashin-Shtrikman bounds
- 8.3 Beran-Milton formalism
- 8.4 Bergman-Milton formalism
- 8.5 Bounds on the derivatives of the effective permittivity
- 8.6 Final remarks on bounds
- References
- 9 Percolation: Crossing the great divide of bulk heterogeneous matter
- Abstract
- Keywords
- 9.1 Electrical conductivity of conductor-insulator mixtures: Key experimental facts
- 9.2 Bond and site lattice percolation models
- 9.3 Continuum (off-lattice) percolation models
- 9.4 Percolation and transport properties
- 9.5 Anisotropic percolation
- References
- 10 Reciprocity relations and extensions
- Abstract
- Keywords
- 10.1 Reciprocity relations
- 10.2 Variational integral and Euler’s equation
- 10.3 Fourier expansion technique for media with regularly spaced inhomogeneities
- 10.4 Phase-field model of dielectric heterostructures in k-space
- 10.5 Nonlinear dielectric response of heterostructures
- 10.6 Effective permittivity from circuit theory
- References
- Part Three: Computational approaches
- 11 Some preliminary considerations: The problem in context
- Abstract
- Keywords
- References
- 12 Finite differences method
- Abstract
- Keyword
- References
- 13 Finite-difference time-domain propagation
- Abstract
- Keyword
- 13.1 Yee’s method
- 13.2 Application to computation of the effective permittivity of mixtures
- 13.3 Transmission line matrix method
- References
- 14 Finite element method
- Abstract
- Keywords
- 14.1 Nodal and edge elements
- 14.2 Galerkin’s method
- 14.3 Computational example
- References
- 15 Integral equation approaches
- Abstract
- Keyword
- 15.1 Integral formulation of electrostatics and Maxwell’s equations
- 15.2 Green’s functions and numerical integration
- 15.3 Application to effective permittivity calculation
- 15.4 The method of moments
- 15.5 A comparison between numerical methods
- References
- 16 Monte Carlo method
- Abstract
- Keyword
- 16.1 Introduction
- 16.2 Two-phase microstructure and representative surface element
- 16.3 Further computational details
- 16.4 Model of the effective permittivity and its basic equations
- References
- 17 Other selected methods
- Abstract
- Keywords
- 17.1 Genetic algorithms
- 17.2 Simulated annealing
- 17.3 Stochastic simulation using Boolean models and digital image-based models
- 17.4 Electromagnetic modeling using graphics processing unit
- References
- Appendix 1A Analogy between magnetism, thermal conduction, diffusion, flow in a porous medium, and electrostatics
- References
- Appendix 1B Maxwell stress tensor and electrostatic force acting on an isolated body in an electric field
- References
- Appendix 1C Electric dipole and polarizability
- References
- Appendix 1D Solving Laplace’s equation for the CS spherical model
- References
- Appendix 1E Electric modulus
- References
- Appendix 1F Mie theory, quasistatic approximation, and discrete dipole approximation for calculating the optical properties of particles
- References
- Appendix 2A Microstructure characterization and statistical descriptors
- References
- Appendix 2B Equivalence between the definition of the effective permittivity using the average, Eq. (7.7), and the energy density, Eq. (7.10)
- References
- Appendix 2C Selected mixing laws
- References
- Appendix 2D Herglotz function and sum rules
- References
- Appendix 2E Incremental MG formalism for homogenizing particulate composite media
- References
- Index
- No. of pages: 406
- Language: English
- Edition: 1
- Published: January 21, 2025
- Imprint: Woodhead Publishing
- Paperback ISBN: 9780443335402
- eBook ISBN: 9780443335419
CB
Christian Brosseau
Christian Brosseau is Professor of Physics at the Université de Bretagne Occidentale, Brest, France where he led the wave–matter interaction modelling and simulation group. His research interests include electromagnetic wave propagation in complex media, plasmonics, nanophysics, biological physics, and computational materials physics.
Affiliations and expertise
Professor of Physics, Université de Bretagne Occidentale, Brest, FranceRead Electromagnetic Heterostructures on ScienceDirect