Sergey Kanaun – författare

Heterogeneous Media: Local Fields, Effective Properties, and Wave Propagation outlines new computational methods for solving volume integral equation problems in heterogeneous media. The book starts by surveying the various numerical methods of analysis of static and dynamic fields in heterogeneous media, listing their strengths and weaknesses, before moving onto an introduction of static and dynamic green functions for homogeneous media. Volume and surface integral equations for fields in heterogenous media are discussed next, followed by an overview of explicit formulas for numerical calculations of volume and surface potentials.

The book then segues into Gaussian functions for discretization of volume integral equations for fields in heterogenous media, static problems for a homogeneous host medium with heterogeneous inclusions, volume integral equations for scattering problems, and concludes with a chapter outlining solutions to homogenization problems and calculations of effective properties of heterogeneous media. The book concludes with multiple appendices that feature the texts of basic programs for solving volume integral equations as written in Mathematica.

Outlines cutting-edge computational methods for solving volume integral equation problems in heterogeneous media Provides applied examples of approximation and other methods being employed Demonstrates calculation of composite material properties and the constitutive laws for averaged fields within them Covers static and dynamic 2D and 3D mechanical-mathematical models for heterogeneous media

Heterogeneous Media: Local Fields, Effective Properties, and Wave Propagation outlines new computational methods for solving volume integral equation problems in heterogeneous media. The book starts by surveying the various numerical methods of analysis of static and dynamic fields in heterogeneous media, listing their strengths and weaknesses, before moving onto an introduction of static and dynamic green functions for homogeneous media. Volume and surface integral equations for fields in heterogenous media are discussed next, followed by an overview of explicit formulas for numerical calculations of volume and surface potentials.The book then segues into Gaussian functions for discretization of volume integral equations for fields in heterogenous media, static problems for a homogeneous host medium with heterogeneous inclusions, volume integral equations for scattering problems, and concludes with a chapter outlining solutions to homogenization problems and calculations of effective properties of heterogeneous media. The book concludes with multiple appendices that feature the texts of basic programs for solving volume integral equations as written in Mathematica.- Outlines cutting-edge computational methods for solving volume integral equation problems in heterogeneous media- Provides applied examples of approximation and other methods being employed- Demonstrates calculation of composite material properties and the constitutive laws for averaged fields within them- Covers static and dynamic 2D and 3D mechanical-mathematical models for heterogeneous media

This book introduces new chapters that delve into the structure of electromagnetic and elastic fields in anisotropic media, the detailed solutions of the conductivity and elasticity problems for spherical radially transverse isotropic inclusions, the analysis of the neutral inclusion problem in static conductivity and elasticity, and the homogenization problem for polycrystalline materials. In the second edition of this book, readers will find a comprehensive update on the application of self-consistent methods in material science, reflecting the advancements in computational capabilities since its first publication. It also emphasizes the growing importance of numerical methods, which have expanded the applicability of self-consistent methods, and includes updated references to the latest research in the field since 2008.

This book introduces new chapters that delve into the structure of electromagnetic and elastic fields in anisotropic media, the detailed solutions of the conductivity and elasticity problems for spherical radially transverse isotropic inclusions, the analysis of the neutral inclusion problem in static conductivity and elasticity, and the homogenization problem for polycrystalline materials. In the second edition of this book, readers will find a comprehensive update on the application of self-consistent methods in material science, reflecting the advancements in computational capabilities since its first publication. It also emphasizes the growing importance of numerical methods, which have expanded the applicability of self-consistent methods, and includes updated references to the latest research in the field since 2008.

This second edition explores wave propagation in heterogeneous materials, focusing on electromagnetic and elastic waves in matrix composites and polycrystals under time-harmonic fields. Employing self-consistent methods, the book evaluates phase velocities and attenuation factors, comparing theoretical predictions with experimental data and simulations. Reflecting the shift in analytical practices due to advanced computational tools like Mathematica and MATLAB, this edition emphasizes detailed calculation algorithms over complex final formulas. Notable revisions include expanded coverage of scalar wave homogenization methods, streamlined chapters on wave propagation, and an appendix featuring specialized tensor computation codes.