Microencapsulation of flavors is the technology of converting liquid flavor materials into easy-to-handle solids. It also provides protection against degradation reactions and prevents the loss of volatiles compounds. The capsule wall material along with the emulsion properties (i.e. viscosity and droplets size) and the drying process conditions are some of the responsible factors for the flavo...

Weconsider linear divergence-form scalar elliptic equations and vectorial equations for elasticitywith rough (L∞( ), ⊂ Rd ) coefficientsa(x) that, in particular, model media with non-separated scales and high contrast in material properties. While the homogenization of PDEs with periodic or ergodic coefficients and well separated scales is now well understood, we consider here the most general ...

We consider divergence-form scalar elliptic equations and vectorial equations for elasticity with rough (L ∞ (Ω), Ω ⊂ R d) coefficients a(x) that, in particular, model media with non-separated scales and high contrast in material properties. While the homogenization of PDEs with periodic or ergodic coefficients and well separated scales is now well understood, we consider here the most general ...

We introduce a new geometric approach for the homogenization and inverse homogenization of the divergence form elliptic operator with rough conductivity coefficients σ(x) in dimension two. We show that conductivity coefficients are in one-to-one correspondence with divergence-free matrices and convex functions s(x) over the domain Ω. Although homogenization is a non-linear and non-injective ope...

The interplay between multiscale homogenization and dimension reduction for nonlinear elastic thin plates is analyzed in the case in which the scaling of the energy corresponds to Kirchhoff’s nonlinear bending theory for plates. Different limit models are deduced depending on the relative ratio between the thickness parameter h and the two homogenization scales ε and ε.

We present a simple example of toughening mechanism in the homogenization of composites with soft inclusions, produced by crack deflection at microscopic level. We show that the mechanism is connected to the irreversibility of the crack process. Because of that it cannot be detected through the standard homogenization tool of the Γ-convergence.

This paper deals with homogenization of diffusion processes in a locally stationary random environment. Roughly speaking, such an environment possesses two evolution scales: both a fast microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims at giving a macroscopic approximation that takes into account the microscopic heterogeneities.

We are concerned with homogenization of stochastic differential equations (SDE) with stationary coefficients driven by Poisson random measures and Brownian motions in the critical case, that is when the limiting equation admits both a Brownian part as well as a pure jump part. We state an annealed convergence theorem. This problem is deeply connected with homogenization of integral partial diff...

Using the tool of two-scale convergence, we provide a rigorous mathematical setting for the homogenization result obtained by Fleck and Willis (J. Mech. Phys. Solids, 2004) concerning the effective plastic behaviour of a strain gradient composite material. Moreover, moving from deformation theory to flow theory, we prove a convergence result for the homogenization of quasistatic evolutions in t...

In this paper we obtain Meyers type (Lp+ε -) estimates for approximate solutions of nonlinear parabolic equations. This research is motivated by a numerical homogenization of these type of equations [?]. Using derived estimates we show the convergence of numerical solutions obtained from numerical homogenization methods.