相关论文: Multiscale analysis and homogenization of nonlocal…
We analyze integral representation and $\Gamma$-convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component…
In the context of finite elasticity, we propose plate models describing the spontaneous bending of nematic elastomer thin films due to variations along the thickness of the nematic order parameters. Reduced energy functionals are deduced…
We investigate the behavior of the solution to an elliptic diffraction problem in the union of a smooth set $\Omega$ and a thin layer $\Sigma$ locally described by $\varepsilon h$, where $h$ is a positive function defined on the boundary…
We study the asymptotic behaviour of a gradient system in a regime in which the driving energy becomes singular. For this system gradient-system convergence concepts are ineffective. We characterize the limiting behaviour in a different…
We discuss the $\Gamma$-convergence, under the appropriate scaling, of the energy functional $$ \|u\|_{H^s(\Omega)}^2+\int_\Omega W(u)dx,$$ with $s \in (0,1)$, where $\|u\|_{H^s(\Omega)}$ denotes the total contribution from $\Omega$ in 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.…
In this paper we study the derivation of nonlinear bending models for prestrained elastic plates from three-dimensional non-linear elasticity via homogenization and dimension reduction. We compare effective models obtained by either…
This paper investigates the homogenization, dimension reduction, and linearization of a composite plate subjected to external loading within the framework of non-linear elasticity problem. The total elastic energy of the problem is of order…
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…
For thin films of superfluid adsorbed on a disordered substrate, we derive the equation of motion for a vortex in the presence of a random potential within a mean field (Hartree) description of the condensate. The compressible nature of the…
This paper deals with a nonlinear degenerate parabolic equation of order $\alpha$ between 2 and 4 which is a kind of fractional version of the Thin Film Equation. Actually, this one corresponds to the limit value $\alpha=4$ while the Porous…
In this paper, we deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations. We restrict our analysis to the case of a cylindrical symmetry for the crystal in exam, so that the mathematical formulation…
We prove that that for nonlinear elastic energies with strong enough energetic control of the outer distortion of admissible deformations, almost everywhere global invertibility as constraint can be obtained in the $\Gamma$-limit of the…
We provide a novel sharp-interface analysis via Gamma-convergence for a non-local and non-homogeneous diffuse-interface model for phase transitions, featuring an interplay between a non-local interaction kernel and a spatially dependent…
The interplay between multiscale homogenization and dimension reduction for nonlinear elastic thin plates is analyzed in the case in which the scaling of the energy corresponds to Kirchhoff's nonlinear bending theory for plates. Different…
We study pattern formation for a variational model displaying competition between a local term penalizing interfaces and a non-local term favoring oscillations. By means of a $\Gamma$--convergence analysis, we show that as the parameter J…
We derive a homogenized mechanical model of a masonry-type structure constituted by a periodic assemblage of blocks with interposed mortar joints. The energy functionals in the model under investigation consist in (i) a linear elastic…
This paper is an extension of the result by Christowiak and Kreisbeck (2017), which addresses the Gamma-convergence approach to a homogenization problem for composite materials consisting of two distinct types of parallel layers. In…
We demonstrate that the elasticity of jammed solids is nonlocal. By forcing frictionless soft sphere packings at varying wavelength, we directly access their transverse and longitudinal compliances without resorting to curve fitting. The…
Based on a microscopic density functional theory we calculate the internal structure of the three-phase contact line between liquid, vapor, and a confining wall as well as the morphology of liquid wetting films on a substrate exhibiting a…