Discrete double-porosity models for spin systems

We consider spin systems between a finite number $N$ of "species" or "phases" partitioning a cubic lattice $\mathbb{Z}^d$. We suppose that interactions between points of the same phase are coercive, while between point of different phases (or, possibly, between points of an additional "weak phase") are of lower order. Following a discrete-to-continuum approach we characterize the limit as a continuum energy defined on $N$-tuples of sets (corresponding to the $N$ strong phases) composed of a surface part, taking into account homogenization at the interface of each strong phase, and a bulk part which describes the combined effect of lower-order terms, weak interactions between phases, and possible oscillations in the weak phase.Comment: arXiv admin note: text overlap with arXiv:1406.175

Homogenization of multivalued monotone operators with variable growth exponent

We consider the Dirichlet problem for an elliptic multivalued maximal monotone operator A(epsilon) satisfying growth estimates of power type with a variable exponent. This exponent p epsilon (x) and also the symbol of the operator A epsilon oscillate with a small period epsilon with respect to the space variable x. We prove a homogenization result for this problem

Homogenization of some quasi-linear elliptic equations with gradient constraints

We prove a homogenization formula for quasi-linear elliptic equations with gradient constraints on a disperse set, within the framework of monotonic operator theory and compensated compactness methods

An extension theorem from connected sets and homogenization of non-local functionals

We study the asymptotic behaviour of convolution-type functionals defined on general periodic domains by proving an extension theore

Lagrange multipliers and transport densities

In this paper we consider a stationary variational inequality with nonconstant gradient constraint and we prove the existence of solution of a Lagrange multiplier, assuming that the bounded open not necessarily convex set O has a smooth boundary. If the gradient constraint g is sufficiently smooth and satisfies ?g 2 =0 and the source term belongs to L 8 (O), we are able to prove that the Lagrange multiplier belongs to L q (O), for 1 0 of our problem has a subsequence that converges weakly to (? 0 ,u 0 ), which solves the transport equation.FCTO -Fuel Cell Technologies Office(UID/MAT/00013/2013)info:eu-repo/semantics/publishedVersio

A variational approach to the local character of G-closure: the convex case

This article is devoted to characterize all possible effective behaviors of composite materials by means of periodic homogenization. This is known as a $G$-closure problem. Under convexity and $p$-growth conditions ($p>1$), it is proved that all such possible effective energy densities obtained by a $\Gamma$-convergence analysis, can be locally recovered by the pointwise limit of a sequence of periodic homogenized energy densities with prescribed volume fractions. A weaker locality result is also provided without any kind of convexity assumption and the zero level set of effective energy densities is characterized in terms of Young measures. A similar result is given for cell integrands which enables to propose new counter-examples to the validity of the cell formula in the nonconvex case and to the continuity of the determinant with respect to the two-scale convergence.Comment: 24 pages, 1 figur

On the Filter Narrowing Issues in Elastic Optical Networks

This paper describes the problematic filter narrowing effect in the context of next-generation elastic optical networks. First, three possible scenarios are introduced: the transition from an actual fixed-grid to a flexigrid network, the generic full flexi-grid network, and a proposal for a filterless optical network. Next, we investigate different transmission techniques and evaluate the penalty introduced by the filtering effect when considering Nyquist wavelength division multiplexing, single side-band direct-detection orthogonal frequency division multiplexing, and symbol-rate variable dual polarization quadrature amplitude modulation. Also, different approaches to compensate for the filter narrowing effect are discussed. Results show that the specific needs per each scenario can be fulfilled by the aforementioned technologies and techniques or a combination of them, when balancing performance, network reach, and cost