Propagation of Electromagnetic Waves in Non-Homogeneous Media

We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell partial differential equations.     

A multi-scale theory of swelling porous media: I. Application to one-dimensional consolidation

A theory is developed which describes flow in multi-scale, saturated swelling media. To upscale information, both the hybrid theory of mixtures and the homogenization technique are employed. In particular, a model is formulated in which vicinal water (water adsorbed to the solid phase) is treated as a separate phase from bulk (non-vicinal) water. A new form of Darcy's law governing the flow of both vicinal and bulk water is derived which involves an interaction potential to account for the swelling nature of the system. The theory is applied to the classical one-dimensional consolidation problem of Terzaghi and to verify Low's empirical, exponential, swelling result for clay at the macroscale.     

Negative Poisson's ratios in composites with star-shaped inclusions: a numerical homogenization approach

Summary Materials with specific microstructural characteristics and composite structures are able to exhibit negative Poisson's ratio. This result has been proved for continuum materials by analytical methods in previous works of the first author, among others [1]. Furthermore, it also has been shown to be valid for certain mechanisms involving beams or rigid levers, springs or sliding collars frameworks and, in general, composites with voids having a nonconvex microstructure.Recently microstructures optimally designed by the homogenization approach have been verified. For microstructures composed of beams, it has been postulated that nonconvex shapes with re-entrant corners are responsible for this effect [2]. In this paper, it is numerically shown that mainly the shape of the re-entrant corner of a non-convex, star-shaped, microstructure influences the apparent (phenomenological) Poisson's ratio. The same is valid for continua with voids or for composities with irregular shapes of inclusions, even if the individual constituents are quite usual materials. Elements of the numerical homogenization theory are reviewed and used for the numerical investigation. Accepted for publication 10 September 1996     

Dynamic mechanical characterization and optimization of particle-reinforced W-Ni-Fe composites

A visco-plastic rate-dependent homogenization theory for particle-reinforced composites was derived and the equivalent elastic constants and the equivalent visco-plastic parameters of these composites were obtained. A framework of homogenization theory for particle-reinforced W-Ni-Fe composites, a kind of tungsten alloy, was established. Based on the homogenization theory and a fixed-point iteration method, a unit cell model with typical microstructures of the composite was established by using dynamic anal...     

Worst scenario method in homogenization. Linear case

The paper deals with homogenization of a linear elliptic boundary problem with a specific class of uncertain coefficients describing composite materials with periodic structure. Instead of stochastic approach to the problem, we use the worst scenario method due to Hlaváček (method of reliable solution). A few criterion functionals are introduced. We focus on the range of the homogenized coefficients from knowledge of the ranges of individual components in the composite, on the values of generalized gradient in the places where these components change and on the average of homogenized solution in some critical subdomain. This research was supported by grant No. 201/03/0570 of the Grant Agency of the Czech Republic.     

On Boundary-Value Problems for the Laplacian in Bounded Domains with Micro Inhomogeneous Structure of the Boundaries

We consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized （limit） problems depending on the ratio of small parameters, which characterize the diameter of parts of the boundary with different types of boundary conditions. Also we study the respective spectral problem of this type.     

On the structural and optical properties investigation of annealed Zn nanorods in the oxygen flux

Zn nano rods were produced on glass substrates using oblique angle deposition method at different deposition angles. For oxidation, the samples were placed in a furnace under oxygen flux. AFM and FESEM images were used to morphology analysis of the structures. The results showed that with increasing the angle of deposition, the grain size decreases and the porosity of the structures increases. XRD pattern and XPS depth profile analysis were used to crystallography and oxide thickness investigations, respectively. The XRD results confirmed oxide phase formation, and the XPS results analyzed the oxide layer thickness. The result showed that as the deposition angle of the nanorods increases, the thickness of the oxide layer increases. The reason for the increase in the thickness of the oxide layer with increasing deposition angle was investigated and attributed to the increase in the porosity of the thin films. The optical spectra of the structures for p polarized light at 10° incident light angle were obtained using single beam spectrophotometer in the 300 nm to 1000 nm wavelengths. The results showed that the formed structures although annealed in oxygen flux, tend to behave like metal. To calculate the optical constant of the structures, the reverse homogenization theory was used and the void fraction and complex refractive index of the structures were obtained. Finally, by calculating permittivity and optical conductivity of the structures, their changes with the deposition angle were investigated.     

Homogeneous films by inverse pulsed laser deposition

Recently, we proposed an alternative arrangement to traditional on- or off-axis PLD geometries, termed inverse PLD (IPLD) that is capable of producing films of improved surface morphology. Two configurations of this new target-substrate arrangement were developed, namely static and co-rotating IPLD. In the static IPLD configuration, the substrate is stationary with respect to the ablated spot; while in the co-rotating IPLD configuration the substrate is fixed to the target surface and rotates simultaneously with the target, hence offering an appealingly simple approach to homogenize film properties.Here we report the growth of CN_x and Ti films, simultaneously deposited in the co-rotating and static IPLD arrangements. The homogeneity of the co-rotating films is described by a thickness inhomogeneity index, which allows for the comparison of films of different lateral dimension. A semi-analytical, semi-numerical model is proposed to derive the radial variation of the growth rate of co-rotating IPLD films from the lateral growth rate distributions measured along the symmetry axes of static IPLD films. The laterally averaged growth rate, LAGR is used to describe how the ambient pressure affects growth in the 0.5-50 Pa domain. As an example, the absolute error between the measured and calculated radial growth rate variation, obtained at 5 Pa, was less than 3%, while the LAGR of CN_x layers grown by co-rotating IPLD was predicted with 20% accuracy.