This paper concerns the homogenization problem of a parabolic equation with large, timedependent, random potentials in high dimensions d ≥ 3. Depending on the competition between temporal and spatial mixing of the randomness, the homogenization procedure turns to be different. We characterize the difference by proving the corresponding weak convergence of Brownian motion in random scenery. When...

In this paper, we consider the derivation of the modified Wenzel’s and Cassie’s equations for wetting phenomena on rough surfaces from a three-dimensional phase field model. We derive an effective boundary condition by asymptotic two-scale homogenization technique when the size of the roughness is small. The modified Wenzel’s and Cassie’s equations for the apparent contact angles on the rough s...

In this paper, we prove an individual homogenization result for a class of almost periodic nonlinear parabolic operators. The spatial and temporal heterogeneities are almost periodic functions in the sense of Besicovitch. The latter allows discontinuities and suitable for many applications. First, we derive stability and comparison estimates for sequences of G-convergent nonlinear parabolic ope...

Aim Biotic homogenization describes the process by which species invasions and extinctions increase the genetic, taxonomic or functional similarity of two or more biotas over a specified time interval. The study of biotic homogenization is a young and rapidly emerging research area in the budding field of conservation biogeography, and this paper aims to synthesize our current knowledge of this...

For problems with strongly varying or discontinuous diiusion coeecients we present a method to compute coarse-scale operators and to approximately determine the eeective diiusion tensor on the coarse-scale level. The approach is based on techniques that are used in multigrid, such as matrix-dependent prolongations and the construction of coarse grid operators by means of the Galerkin approximat...

This article explores the use of a homogenization method inspired by the classical Irving-Kirkwood procedure in the continuous multiscale modeling of elastic solids within the context of the finite element method. This homogenization method gives rise to a broad range of allowable boundary conditions for the RVE, which, in turn, yield a rich spectrum of estimates of the macroscopic stress respo...

According to the direct homogenization theory of inhomogeneous material, a single medium homogenization constitutive model of the confined concrete in the steel box-concrete combined member has been established, and model parameters have been determined by the measured data of the bending test. By analyzing the theoretical ultimate strength and overall process curve, the results obtained is con...

For problems with strongly varying or discontinuous diiusion coeecients we present a method to compute coarse-scale operators and to approximately determine the eeective diiusion tensor on the coarse-scale level. The approach is based on techniques that are used in multigrid, such as matrix-dependent prolongations and the construction of coarse-grid operators by means of the Galerkin approximat...

The goal of this lecture is to show that homogenization is a very efficient tool in the modeling of complex phenomena in heterogeneous media. In the first lecture we considered a model problem of diffusion for which the homogenized operator was of the same type (still a diffusion equation). In this context, homogenization is really a matter of defining and computing effective diffusion tensors....

The present study was initiated to understand the effect of PLGA concentration, PVA concentration, internal-external phase ratio, homogenization speed, and homogenization time on mean particle size, zeta potential, and percentage drug encapsulation using fractional factorial design. Using PLGA (50-50) as the carrier, hyaluronidase loaded PLGA nanoparticles were prepared using double emulsion so...