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 voltage on a single-turn loop inside an enclosure characterizes the enclosure shielding effectiveness against a lightning insult. In this paper, the maximum induced voltage on a single-turn loop inside an enclosure from lightning coupling to a metal enclosure wall is expressed in terms of two multiplicative factors: (A) the normalized enclosure wall peak penetration ratio (i.e., ratio of th...

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

─ This paper deals with an impact of receiving antenna placed in a metal enclosure on an electromagnetic field distribution within the enclosure, and thus on its shielding effectiveness. In an experimental setup, a frequently used tool for measuring the electromagnetic field level at certain points within the enclosure is a dipole antenna connected to a measuring instrument via a coaxial cable....

We study the minimum energy configuration of a uniform distribution of negative charge subject to Coulomb repulsive self-interaction and attractive interaction with a fixed positively charged domain. After having established existence and uniqueness of a minimizing configuration, we prove charge neutrality and the complete screening of the Coulomb potential exerted by the positive charge, and w...

where Ω is an open bounded set of R and W and V are two non-negative continuous functions vanishing at α, β and α, β, respectively. In the previous functional, we fix a = 2 − p and u is a scalar density function, Tu denotes its trace on ∂Ω, d(x, ∂Ω) stands for the distance function to the boundary ∂Ω. We show that the singular limit of the energies Fε leads to a coupled problem of bulk and surf...