Related papers: Basics of averaging of the Maxwell equations for b…
Volume or statistical averaging of the microscopic Maxwell equations (MEs), i.e. transition from microscopic MEs to their macroscopic counterparts, is one of the main steps in electrodynamics of materials. In spite of the fundamental…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
Scattering of electromagnetic (EM) waves by many small particles (bodies) embedded in a homogeneous medium is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for…
An analytical model for homogenization of Metamaterials (MM) with interacting Metaatoms (MA) is developed based on multipole approach for bulk media. The interaction is assumed to be near field type. i.e. no retardation in lateral direction…
Implementations of the Bruggeman and Maxwell Garnett homogenization formalisms were developed to estimate the relative permittivity dyadic of a homogenized composite material (HCM), namely $\underline{\underline{\epsilon}}^{\rm HCM}$,…
Computational models in cardiac electrophysiology are notorious for long runtimes, restricting the numbers of nodes and mesh elements in the numerical discretisations used for their solution. This makes it particularly challenging to…
We consider a linearly thermoelastic composite medium,which consists of a homogeneous matrix containing a statistically inhomogeneous random set of inclusions, when the concentration of the inclusions is a function of the coordinates…
Diffusion is the macroscopic manifestation of disordered molecular motion. Mathematically, diffusion equations are partial differential equations describing the fluid-like large-scale dynamics of parcels of molecules. Spatially…
In this paper we suggest a simple analytical method for description of electromagnetic properties of a geometrically regular two-dimensional subwavelength arrays (metasurfaces) formed by particles with randomly fluctuating polarizabilities.…
A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the…
The relation between microscopic and macroscopic entities in the generally covariant theories is considered, and it is argued that a sensible definition of the macroscopic averages requires a restriction of the allowed transformations of…
Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This…
We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability $\mu (\mathbf{r}) $ and permittivity $% \epsilon (\mathbf{r}) $ to study the wave propagation. The general form of the wave equation is derived…
Here, we present an overview of a first principles homogenization theory of periodic metamaterials. It is shown that in a rather general context it is possible to formally introduce effective parameters that describe the time evolution of…
A close examination of the Maxwell-Lorentz theory of electrodynamics reveals that polarization and magnetization of material media need not be treated as local averages over small volumes - volumes that nevertheless contain a large number…
A rigorous homogenization theory of metamaterials -- artificial periodic structures judiciously designed to control the propagation of electromagnetic waves -- is developed. All coarse-grained fields are unambiguously defined and effective…
A multifield asymptotic homogenization technique for periodic thermo-diffusive elastic materials is provided in the present study. Field equations for the first-order equivalent medium are derived and overall constitutive tensors are…
This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is prohibitively expensive as it requires resolving the…
The methods of macroscopic averaging used to derive the macroscopic Maxwell equations from electron theory are methodologically incorrect and lead in some cases to a substantial error. For instance, these methods do not take into account…
The well-known Hill's averaging theorems for stresses and strains as well as the so-called Hill-Mandel principle of macrohomogeneity are essential ingredients for the coupling and the consistency between the micro and macro scales in…