in the present investigation surface modification of silica nanoparticles by alumina was carried out by sol-gel process. fourier transform infrared (ftir) and x-ray fluorescence (xrf) confirmed the synthesis of silica and the surface modification as alumina is anchored to silica surface. field emission scanning electron microscopy (fesem) and transmission electron microscopy (tem) investigation...

We characterize the macroscopic effective mechanical behavior of a graphene sheet modeled by a hexagonal lattice of elastic bars, using Γ-convergence.

We introduce new definitions of convergence, based on adding stability criteria to Γ-convergence, that are suitable in many cases for studying convergence of local minimizers.

We study the Γ-convergence of the power-law functionals

Porous alumina films had been fabricated by anodizing from aluminum films after an electropolishing procedure. Alumina stripes without pores can be distinguished on the surface of the porous alumina films. The width of the alumina stripes increases proportionally with the anodizing voltage. And the pores tend to be initiated close to the alumina stripes. These phenomena can be ascribed to the e...

In this paper we study the asymptotic behaviour via Γ-convergence of some integral functionals Fε which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals Fε are defined in particular classes of functions with bounded deformation while the limit problem is set in the usual framework of Sobolev spaces or BD(Ω). We also construct an exam...

We study homogenization by Γ-convergence of functionals of type Z Ω W “ x ε ,∇φ(x) ” dx, where Ω ⊂ RN is a bounded open set, φ ∈ W 1,p(Ω; Rm) and p > 1, when the 1-periodic integrand W : RN ×Mm×N → [0, +∞] is not of p-polynomial growth. Our homogenization technique can be applied when m = N and W has a singular behavior of type W (x, ξ) → +∞ as detξ → 0. However, our technique is not consistent...

We study homogenization by Γ-convergence, with respect to the L1-strong convergence, of periodic multiple integrals in W 1,∞ when the integrand can take infinite values outside of a convex bounded open set of matrices.