Related papers: Loss of polyconvexity by homogenization: a new exa…
This work is a follow-up to our previous work "A numerical approach related to defect-type theories for some weakly random problems in homogenization" (preprint available on this archive). It extends and complements, both theoretically and…
The purpose of the present paper is to show few examples of nonlinear PDEs (mostly with strong geometric features) for which there is a hidden convex structure. This is not only a matter of curiosity. Once the convex structure is…
We consider a partially hinged composite plate problem and we investigate qualitative properties, e.g. symmetry and monotonicity, of the eigenfunction corresponding to the density minimizing the first eigenvalue. The analysis is performed…
We obtain the gauge invariant energy eigenvalues and degeneracies together with rotationally symmetric wavefunctions of a particle moving on 2D noncommutative plane subjected to homogeneous magnetic field $B$ and harmonic potential. This…
Motivated by partition regularity problems of homogeneous quadratic equations, we prove multiple recurrence and convergence results for multiplicative measure preserving actions with iterates given by rational sequences involving…
Spectral asymptotics of linear periodic elliptic operators with indefinite (sign-changing) density function is investigated in perforated domains with the two-scale convergence method. The limiting behavior of positive and negative…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
The focus in this paper is on elliptic homogenization of a certain kind of possibly non-periodic problems. A non-periodic and two-dimensional example is studied, where we numerically illustrate the homogenized matrix.
Symmetric quasiconvexity plays a key role for energy minimization in geometrically linear elasticity theory. Due to the complexity of this notion, a common approach is to retreat to necessary and sufficient conditions that are easier to…
In this paper we determine, in dimension three, the effective conductivities of non periodic high-contrast two-phase cylindrical composites, placed in a constant magnetic field, without any assumption on the geometry of their cross…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
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…
We study the homogenisation of geometrically nonlinear elastic composites with high contrast. The composites we analyse consist of a perforated matrix material, which we call the "stiff" material, and a "soft" material that fills the pores.…
We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…
A multiscale asymptotic homogenization method for periodic microstructured materials in presence of thermoelasticity with periodic spatially dependent one relaxation time is introduced. The asymptotic expansions of the micro-displacement…
In this paper we discuss a couple of observations related to polynomial convexity. More precisely, (i) We observe that the union of finitely many disjoint closed balls with centres in $\cup_{\theta\in[0,\pi/2]}e^{i\theta}V$ is polynomially…
For a class of linear elliptic equations of general type with rapidly oscillating coefficients, we use the sigma-convergence method to prove the homogenization result and a corrector-type result. In the case of asymptotic periodic…
We consider the homogenization of a model of reactive flows through periodic porous media involving a single solute which can be absorbed and desorbed on the pore boundaries. This is a system of two convection-diffusion equations, one in…
We show that in the framework of CAT(0) spaces, any convex combination of two mappings which are firmly nonexpansive -- or which satisfy the more general property $(P_2)$ -- is asymptotically regular, conditional on its fixed point set…
Multiscale periodic homogenization is extended to an Orlicz-Sobolev setting. It is shown by the reiteraded periodic two-scale convergence method that the sequence of minimizers of a class of highly oscillatory minimizations problems…