Homogenization of the one-dimensional wave equation

We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The novelty reported here is on the asymptotic behavior of high frequency waves and especially on the boundary conditions of the homogenized equation. Numerical simulations are reported

Periodic Homogenization of strongly nonlinear reaction-diffusion equations with large reaction terms

We study in this paper the periodic homogenization problem related to a strongly nonlinear reaction-diffusion equation. Owing to the large reaction term, the homogenized equation has a rather quite different form which puts together both the reaction and convection effects. We show in a special case that, the homogenized equation is exactly of a convection-diffusion type. The study relies on a suitable version of the well-known two-scale convergence method.Comment: 19 page

Effective macroscopic dynamics of stochastic partial differential equations in perforated domains

An effective macroscopic model for a stochastic microscopic system is derived. The original microscopic system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes or heterogeneities. The homogenized effective model is still a stochastic partial differential equation but defined on a unified domain without holes. The solutions of the microscopic model is shown to converge to those of the effective macroscopic model in probability distribution, as the size of holes diminishes to zero. Moreover, the long time effectivity of the macroscopic system in the sense of \emph{convergence in probability distribution}, and the effectivity of the macroscopic system in the sense of \emph{convergence in energy} are also proved

Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions

A microscopic heterogeneous system under random influence is considered. The randomness enters the system at physical boundary of small scale obstacles as well as at the interior of the physical medium. This system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes (obstacles or heterogeneities), together with random dynamical boundary conditions on the boundaries of these small holes. A homogenized macroscopic model for this microscopic heterogeneous stochastic system is derived. This homogenized effective model is a new stochastic partial differential equation defined on a unified domain without small holes, with static boundary condition only. In fact, the random dynamical boundary conditions are homogenized out, but the impact of random forces on the small holes' boundaries is quantified as an extra stochastic term in the homogenized stochastic partial differential equation. Moreover, the validity of the homogenized model is justified by showing that the solutions of the microscopic model converge to those of the effective macroscopic model in probability distribution, as the size of small holes diminishes to zero.Comment: Communications in Mathematical Physics, to appear, 200

Optical and photovoltaic properties of indium selenide thin films prepared by van der Waals epitaxy

Indium selenide thin films have been grown on p-type gallium selenide single crystal substrates by van der Waals epitaxy. The use of two crucibles in the growth process has resulted in indium selenide films with physical properties closer to these of bulk indium selenide than those prepared by other techniques. The optical properties of the films have been studied by electroabsorption measurements. The band gap and its temperature dependence are very close to those of indium selenide single crystals. The width of the fundamental transition, even if larger than that of the pure single crystal material, decreases monotonously with temperature. Exciton peaks are not observed even at low temperature, which reveals that these layers still contain a large defect concentration. The current–voltage characteristic of indium selenide thin film devices was measured under simulated AM2 conditions. The solar conversion efficiency of these devices is lower than 0.6%. The high concentration of defects reduces the diffusion length of minority carriers down to values round to 0.2 μ[email protected] ; [email protected]