| Dedication | p. v |
| Acknowledgments | p. vii |
| Preface | p. ix |
| Introductory Examples of Homogenization Method | p. 1 |
| Long Waves in a Layered Elastic Medium | p. 1 |
| Short Waves in a Weakly Stratified Elastic Medium | p. 6 |
| Dispersion of Passive Solute in Pipe Flow | p. 10 |
| Scale Estimates | p. 11 |
| Multiple-Scale Analysis | p. 12 |
| Dispersion Coefficient for Steady Flow | p. 17 |
| Dispersion Coefficient for Oscillatory Flow | p. 18 |
| Typical Procedure of Homogenization Analysis | p. 19 |
| References | p. 20 |
| Diffusion in a Composite | p. 23 |
| Basic Equations for Two Components in Perfect Contact | p. 23 |
| Effective Equation on the Macroscale | p. 24 |
| Effective Boundary Condition | p. 29 |
| Symmetry and Positiveness of Effective Conductivity | p. 33 |
| Laminated Composites | p. 35 |
| Bounds for Effective Conductivity | p. 38 |
| First Variational Principle and the Upper Bound | p. 38 |
| Dual Variational Principle and the Lower Bound | p. 41 |
| Hashin-Shtrikman Bounds | p. 44 |
| Results and Implications | p. 44 |
| Derivation of Hashin-Shtrikman Bounds | p. 46 |
| Other Approximate Results for Dilute Inclusions | p. 50 |
| Thermal Resistance at the Interface | p. 52 |
| Laminated Composites with Thermal Resistance | p. 58 |
| Effective Coefficients | p. 58 |
| Application to Thermal Barrier Coatings | p. 61 |
| Bounds for the Effective Conductivity | p. 63 |
| Variational Principles and Bounds | p. 63 |
| Application to a Particulate Composite | p. 66 |
| Chemical Transport in Aggregated Soil | p. 70 |
| Heat Transfer in a Two-Slab System | p. 79 |
| References | p. 82 |
| Seepage in Rigid Porous Media | p. 85 |
| Equations for Seepage Flow and Darcy's Law | p. 85 |
| Uniqueness of the Cell Boundary-Value Problem | p. 90 |
| Symmetry and Positiveness of Hydraulic Conductivity | p. 91 |
| Numerical Computation of the Permeability Tensor | p. 92 |
| Seepage of a Compressible Fluid | p. 96 |
| Two-Dimensional Flow Through a Three-Dimensional Matrix | p. 99 |
| Governing Equations | p. 100 |
| Homogenization | p. 103 |
| Numerical Results | p. 107 |
| Porous Media with Three Scales | p. 109 |
| Effective Equations | p. 110 |
| Properties of Hydraulic Conductivity | p. 113 |
| Macropermeability of a Laminated Medium | p. 114 |
| Brinkman's Modification of Darcy's Law | p. 118 |
| Effects of Weak Fluid Inertia | p. 123 |
| Spatial Averaging Theorem | p. 130 |
| References | p. 132 |
| Dispersion in Periodic Media or Flows | p. 135 |
| Passive Solute in a Two-Scale Seepage Flow | p. 135 |
| The Solute Transport Equation and Scale Estimates | p. 136 |
| Macroscale Transport Equation | p. 138 |
| Numerical Computation of Dispersivity | p. 145 |
| Macrodispersion in a Three-Scale Porous Medium | p. 149 |
| From Micro- to Mesoscale | p. 151 |
| Mass Transport Equation on the Macroscale | p. 152 |
| Second-Order Seepage Velocity | p. 156 |
| Dispersion and Transport in a Wave Boundary Layer Above the Seabed | p. 158 |
| Depth-Integrated Transport Equation in the Boundary Layer | p. 159 |
| Effective Convection Velocity | p. 164 |
| Correlation Coefficients $$$ and Dispersivity Tensor | p. 166 |
| Dispersion Under a Standing Wave in a Lake | p. 169 |
| Derivation of Convection-Dispersion Equation | p. 173 |
| An Alternate Form of Macrodispersion Tensor | p. 175 |
| References | p. 176 |
| Heterogeneous Elastic Materials | p. 179 |
| Effective Equations on the Macroscale | p. 180 |
| The Effective Elastic Coefficients | p. 184 |
| Application to Fiber-Reinforced Composite | p. 185 |
| Elastic Panels with Periodic Microstructure | p. 186 |
| Order Estimates | p. 189 |
| Two-Scale Analysis and Effective Equations | p. 190 |
| Homogeneous Plate - A Limiting Case | p. 196 |
| Variational Principles and Bounds for the Elastic Moduli | p. 199 |
| First Variational Principle and the Upper Bound | p. 199 |
| Second Variational Principle and the Lower Bound | p. 201 |
| Hashin-Shtrikman Bounds | p. 203 |
| Partially Cohesive Composites | p. 208 |
| Effective Equations on the Macroscale | p. 210 |
| Variational Principles | p. 212 |
| Bounds for Particulate Composites | p. 219 |
| Size Effects for Particulate Composites | p. 226 |
| Critical Radii for Particulate Composites | p. 227 |
| Properties of a Tensor of Fourth Rank | p. 234 |
| References | p. 235 |
| Deformable Porous Media | p. 239 |
| Basic Equations for Fluid and Solid Phases | p. 240 |
| Scale Estimates | p. 242 |
| Quasi-Static Poroelasticity | p. 242 |
| Dynamic Poroelasticity | p. 244 |
| Multiple-Scale Expansions | p. 246 |
| Averaged Total Momentum of the Composite | p. 248 |
| Averaged Mass Conservation of Fluid Phase | p. 251 |
| Averaged Fluid Momentum | p. 252 |
| Quasi-Static Case | p. 252 |
| Dynamic Case | p. 253 |
| Time-Harmonic Motion | p. 254 |
| Properties of the Effective Coefficients | p. 257 |
| Three Identities for General Media | p. 257 |
| Homogeneous and Isotropic Grains | p. 259 |
| Computed Elastic Coefficients | p. 262 |
| Boundary-Layer Approximation for Macroscale Problems | p. 263 |
| The Outer Approximation | p. 264 |
| Boundary-Layer Correction | p. 267 |
| Plane Rayleigh Wave in a Poroelastic Half Space | p. 272 |
| Properties of the Compliance Tensor | p. 274 |
| Variational Principle for the Elastostatic Problem in a Cell | p. 275 |
| References | p. 276 |
| Wave Propagation in Inhomogeneous Media | p. 279 |
| Long Wave Through a Compact Cylinder Array | p. 279 |
| Bragg Scattering of Short Waves by a Cylinder Array | p. 286 |
| Envelope Equations | p. 287 |
| Dispersion Relation for a Detuned Wave Train | p. 291 |
| Scattering by a Finite Strip of Periodic Cylinders | p. 292 |
| Sound Propagation in a Bubbly Liquid | p. 294 |
| Scale and Order Estimates | p. 295 |
| Near Field of a Spherical Bubble | p. 296 |
| The Intermediate Field | p. 298 |
| The Macroscale Equation | p. 300 |
| One-Dimensional Sound Through a Weakly Random Medium | p. 302 |
| Weakly Nonlinear Dispersive Waves in a Random Medium | p. 306 |
| Envelope Equation | p. 306 |
| Modulational Instability | p. 311 |
| Harmonic Generation in Random Media | p. 312 |
| Long Waves in Shallow Water | p. 313 |
| Harmonic Amplitudes | p. 315 |
| Gaussian Disorder | p. 319 |
| References | p. 321 |
| Additional References on Homogenization Theory | p. 325 |
| Subject Index | p. 327 |
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