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.

The topological index of a surface was previously introduced by the first author as the topological analogue of the index of an unstable minimal surface. Here we show that surfaces of arbitrarily high topological index exist. Consider a compact, connected, two sided surface S properly embedded in a compact, orientable 3-manifold M . The disk complex Γ(S) is the simplicial complex defined as fol...

We prove the Γ-convergence of the one-dimensional Allen-Cahn action functional in the sharp-interface limit. In previous work, a good lower bound was developed under the assumption of single multiplicity, but the bound deteriorated in the case of higher multiplicity interfaces. We develop an improved bound by working directly with the limiting energy measures.

We characterize the macroscopic effective mechanical behavior of a graphene sheet modeled by a hexagonal lattice with twoand three-point atomic interactions, using Γ-convergence.

We prove that the family of functionals (Iδ) defined by Iδ(g) = ∫∫ RN×RN |g(x)−g(y)|>δ δ |x− y|N+p dx dy, ∀ g ∈ L(R ), for p ≥ 1 and δ > 0, Γ-converges in L(R ), as δ goes to 0, when p ≥ 1. Hereafter | | denotes the Euclidean norm of R . We also introduce a characterization for BV functions which has some advantages in comparison with the classic one based on the notion of essential variation o...

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.

We consider a sequence of linear Dirichlet problems as follows

Objective(s): The effects of alpha linolenic acid (ALA) on tracheal responsiveness (TR), total protein (TP), phospholipase A2 (PLA2), immunoglobulin E (IgE), interleukin 4 (IL-4), interferon gamma (INF-γ) level and INF-γ/IL4 ratio in bronchoalveolar lavage fluid (BALF) of sensitized rats were examined.Materials and Methods: TR to methacholine and ovalbumin (OA), BALF levels of TP, PLA2 and IgE ...

Let Γ = Cay(G,S) be a Cayley digraph on a group G and let A = Aut(Γ). The Cayley index of Γ is |A : G|. It has previously been shown that, if p is a prime, G is a cyclic p-group and A contains a noncyclic regular subgroup, then the Cayley index of Γ is superexponential in p. We present evidence suggesting that cyclic groups are exceptional in this respect. Specifically, we establish the contras...