Related papers: Characterization of two-scale gradient Young measu…

In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE$^2$ methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible…

In this paper a model for partial melts is constructed using two-scale homogenization theory. While this technique is well known to the mathematics and materials communities, it is relatively novel to problems in the solid Earth. This…

Given an approximate eigenvector, its (standard) Rayleigh quotient and harmonic Rayleigh quotient are two well-known approximations of the corresponding eigenvalue. We propose a new type of Rayleigh quotient, the homogeneous Rayleigh…

We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…

We study quantitative periodic homogenization of integral functionals in the context of non-linear elasticity. Under suitable assumptions on the energy densities (in particular frame indifference; minimality, non-degeneracy and smoothness…

We derive effective, parsimonious models from a heterogeneous second-gradient nonlinear elastic material taking into account chiral scale-size effects. Our classification of the effective equations depends on the hierarchy of four…

We propose a general approach to the higher-order homogenization of discrete elastic networks made up of linear elastic beams or springs in dimension 2 or 3. The network may be nearly (rather than exactly) periodic: its elastic and…

This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…

A multi-scale characterization of the field concentrations inside composite and polycrystalline media is developed. The analysis focuses on gradient fields associated with the intensive quantities given by the temperature and the electric…

We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…

Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions of a class of highly…

A geometrical interpretation of the $G$-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of…

A homogenization result for a family of integral energies is presented, where the fields are subjected to periodic first order oscillating differential constraints in divergence form. The work is based on the theory of A -quasiconvexity…

We employ Monte Carlo simulations to investigate the two-time density autocorrelation function for the two-dimensional Coulomb glass. We find that the nonequilibrium relaxation properties of this highly correlated disordered system can be…

In this article, we prove the existence of measure-valued solutions to the Ericksen-Leslie system equipped with the Oseen-Frank energy. We introduce the concept of generalized gradient Young measures. Via a Galerkin approximation, we show…

In this paper, we obtain some inequalities by using a kernel and an inequality which is a result of Young inequality. Besides we give some applications to special means.

Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…

Nonlinear Young integrals have been first introduced in [Catellier,Gubinelli, SPA 2016] and provide a natural generalisation of classical Young ones, but also a versatile tool in the pathwise study of regularisation by noise phenomena. We…

We study the homogenization of a class of non-local functionals featuring a rapidly oscillating periodic weight. By means of two-scale convergence, we explicitly evaluate the {\Gamma}-limit for constant target functions, revealing how the…

Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…