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Based on a microscopic density functional theory we investigate the morphology of thin liquidlike wetting films adsorbed on substrates endowed with well-defined chemical heterogeneities. As paradigmatic cases we focus on a single chemical…

Soft Condensed Matter · Physics 2009-10-31 C. Bauer , S. Dietrich

This investigation develops basic methods for the multi-scale analysis for problems in thin porous layers. More precisely, we provide tools for the homogenization in case of "tangentially" periodic structures and dimensional reduction…

Analysis of PDEs · Mathematics 2021-12-02 Markus Gahn , Willi Jäger , Maria Neuss-Radu

We prove that certain nonlocal functionals defined on partitions made of measurable sets Gamma-converge to a local functional modeled on the perimeter in the sense of De Giorgi. Those nonlocal functionals involve generalized surface tension…

Analysis of PDEs · Mathematics 2025-06-26 Thomas Gabard , Vincent Millot

Paints and coatings often feature interfacial defects due to disturbances during the deposition process which, if they persist until solidification, worsen the product quality. In this article, we investigate the stability of a thin liquid…

Fluid Dynamics · Physics 2023-07-26 David Barreiro-Villaverde , Anne Gosset , Marcos Lema , Miguel Alfonso Mendez

Starting from 3D elasticity equations we derive the model of the homogenized von K\'arm\'an plate by means of $\Gamma$-convergence. This generalizes the recent results, where the material oscillations were assumed to be periodic.

Analysis of PDEs · Mathematics 2014-10-07 Igor Velcic

Artificial antiferromagnets and synthetic metamagnets have attracted much attention recently due to their potential for many different applications. Under some simplifying assumptions these systems can be modeled by thin Ising metamagnetic…

Statistical Mechanics · Physics 2011-10-18 Yen-Liang Chou , Michel Pleimling

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…

Analysis of PDEs · Mathematics 2015-08-21 Elisa Davoli , Irene Fonseca

Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…

Dynamical Systems · Mathematics 2025-04-08 A. J. Roberts

Given an image $u_0$, the aim of minimising the Mumford-Shah functional is to find a decomposition of the image domain into sub-domains and a piecewise smooth approximation $u$ of $u_0$ such that $u$ varies smoothly within each sub-domain.…

Optimization and Control · Mathematics 2023-09-06 Irene Fonseca , Lisa Maria Kreusser , Carola-Bibiane Schönlieb , Matthew Thorpe

We study the non-Euclidean (incompatible) elastic energy functionals in the description of prestressed thin films, at their singular limits ($\Gamma$-limits) as $h\to 0$ in the film's thickness $h$. Firstly, we extend the prior results…

Analysis of PDEs · Mathematics 2019-02-08 Marta Lewicka , Danka Lučić

The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of {\Gamma}-convergence, in the framework of finite plasticity. Denoting by {\epsilon} the thickness of the plate, we analyse the case where…

Analysis of PDEs · Mathematics 2019-02-20 Elisa Davoli

The aim of this work is to provide further insight into the qualitative behavior of mechanical systems that are well described by Lennard-Jones type interactions on an atomistic scale. By means of $\Gamma$-convergence techniques, we study…

Analysis of PDEs · Mathematics 2017-06-09 Mathias Schäffner , Anja Schlömerkemper

For many complex systems the interaction of different scales is among the most interesting and challenging features. It seems not very successful to extract the physical properties in different scale regimes by the existing approaches, such…

Fluid Dynamics · Physics 2015-05-14 L. P. Wang , Y. X. Huang

Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…

Numerical Analysis · Mathematics 2009-11-16 Bjorn Engquist , Henrik Holst , Olof Runborg

Inverse design of optical multilayer stacks seeks to infer layer materials, thicknesses, and ordering from a desired target spectrum. It is a long-standing challenge due to the large design space and non-unique solutions. We introduce…

We consider the family of non-local and non-convex functionals introduced by H. Brezis and H.-M. Nguyen in a recent paper. These functionals Gamma-converge to a multiple of the Sobolev norm or the total variation, depending on a summability…

Functional Analysis · Mathematics 2018-05-22 Clara Antonucci , Massimo Gobbino , Matteo Migliorini , Nicola Picenni

We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…

Probability · Mathematics 2021-04-21 Michael Röckner , Longjie Xie

The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…

Analysis of PDEs · Mathematics 2016-07-20 François Alouges , Giovanni Di Fratta

We study the limit behavior of Cahn--Hilliard-type functionals in which the derivative is replaced by higher-order fractional derivatives and modulated by an oscillating factor. Depending on the ratio between the oscillation scale and the…

Analysis of PDEs · Mathematics 2026-05-26 Fabrizio Caragiulo , Sergio Scalabrino , Edoardo Voglino

The sensitivity of thin-film materials and devices to defects motivates extensive research into the optimization of film morphology. This research could be accelerated by automated experiments that characterize the response of film…