Effective medium theory : principles and applications

1. Essentials 1.1 Lorentz field 1.2 Clausius-Mossotti 1.3 Maxwell-Garnett 1.4 Bruggeman 1.5 Green's functions formulation 1.6 Summary and equivalence 2. Rigorous results 2.1 Introduction 2.2 Variational bounds 2.3 The concentric shell model 2.4 Spectral representation 2.5 Exactly soluble models 2.6 Reciprocity theorems 3. Dynamical theory 3.1 Introduction 3.2 Review 3.3 Macroscopic electrodynamics 3.4 Quasi-static regime 3.5 Displacement current and wave scattering 3.6 Mie scattering 3.7 Dynamical effective medium theory 3.8 Open problems 4. Limitations and beyond 4.1 Introductory remarks 4.2 Higher order terms 4.3 Percolation and criticality 4.4 Mie resonances 4.5 Multiple scattering 4.6 Competing interactions 4.7 Two body effective medium 4.8 Non-equilibrium 5. Related theories 5.1 Comments 5.2 Coherent potential approximation 5.3 Feynman diagrams 5.4 Localization of light 5.5 Classical theory of liquids 5.6 Density functional theories 5.7 Hubbard model, CPA and DFT 5.8 Summary 6. EMT applications 6.1 Introduction 6.2 Electric and magnetic properties 6.3 Optical properties 6.4 Granular high Tc superconductors 6.5 Hydrodynamics of suspensions 6.6 Mechanical properties 6.7 Nonlinear composites 6.8 Conclusions Appendices A.1 Stationery properties of UP and UR A.2 Evaluation of the last term in equation (2.18)