We derive a cluster expansion for the electric susceptibility kernel of a dielectric suspension of spherically symmetric inclusions in a uniform background. This also leads to a cluster expansion for the effective dielectric constant. It is shown that the cluster integrals of any order are absolutely convergent, so that the dielectric constant is well defined and independent of the shape of the...

Starting from the tight-binding dielectric matrix in the random phase approximation we examine the collective modes and electron-hole excitations in a two-band electronic system. For long wavelengths (q → 0), for which most of the analysis is carried out, the properties of the collective modes are closely related to the symmetry of the atomic orbitals involved in the tight-binding states. In in...

The paper discusses the effort carried out at VNIIEF to consider the applicability of unstructured Lagrange meshes to multidimensional continuum mechanics problems with high shear strain and vortex flows. Three finite-difference numerical techniques for solving continuum mechanics problems on polyhedral unstructured Lagrange meshes are described. Examples of numerical calculations of benchmark ...

1. Basic Results in Continuum Mechanics 1.1. Kinematics 1.2. Stress Tensors and Balance of Momenta 1.3. Energy Balance Principle and Entropy Inequality 1.4. Fundamental Principles of Constitutive Models 2. Elastic and Hyperelastic Materials 2.1. Isotropic Hyperelastic Materials 2.2. Constitutive Models for Fiber-Reinforced Hyperelastic Materials 2.3. Examples of Numerical Applications 3. Elasto...