Related papers: Heterogeneous thin films: Combining homogenization…
The introduced notion of locally-periodic two-scale convergence allows to average a wider range of microstructures, compared to the periodic one. The compactness theorem for the locally-periodic two-scale convergence and the…
Owing to additive manufacturing techniques, a structure at millimeter length scale (macroscale) can be produced by using a lattice substructure at micrometer length scale (microscale). Such a system is called a metamaterial at the…
Many numerical methods for multiscale differential equations require a scale separation between the larger and the smaller scales to achieve accuracy and computational efficiency. In the area of multiscale dynamical systems, so-called,…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
Plastic deformation of heterogeneous solid structures is often characterized by random intermittent local plastic events. On the mesoscale this feature can be represented by a spatially fluctuating local yield threshold. Here we study the…
We study a Phase-Field-Crystal model described by a free energy functional involving second order derivatives of the order parameter in a periodic setting and under a fixed mass constraint. We prove a $\Gamma$-convergence result in an…
Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a…
Advancement in manufacturing methods enable designing so called metamaterials with a tailor-made microstructure. Microstructure affects materials response within a length-scale, where we model this behavior by using the generalized…
While multiple time scales generally arise in the dynamics of disordered systems, we find multiple time scales in absence of disorder, in a simple model with hard local constraints. The dynamics of the model, which consists of local…
We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space $\R^N$. For such optimal control…
We prove the two-scale transformation method which allows rigorous homogenisation of problems defined on locally periodic domains by transformation on periodic domains. The idea to consider periodic substitute problems was originally…
Asymptotic homogenisation is used to systematically derive reduced-order macroscopic models of conductive behaviour in spirally-wound layered materials in which the layers have very different conductivities. The problem is motivated by the…
Two approaches to incorporate heterogeneity in discrete models are compared. In the first, standard approach, the heterogeneity is dictated by geometrical structure of the discrete system. In the second approach, the heterogeneity is…
In this paper we study the asymptotic behaviour of the solutions of some minimization problems for integral functionals with convex integrands, in two-dimensional domains with cracks, under perturbations of the cracks in the Hausdorff…
We propose a homogenized filter for multiscale signals, which allows us to reduce the dimension of the system. We prove that the nonlinear filter converges to our homogenized filter with rate $\sqrt{\varepsilon}$. This is achieved by a…
We numerically study dynamics and correlation length scales of a colloidal liquid in both quiescent and sheared conditions to further understand the origin of slow dynamics and dynamic heterogeneity in glass-forming systems. The simulation…
A multi-time probing of density fluctuations is introduced to investigate hidden time scales of heterogeneous dynamics in glass-forming liquids. Molecular dynamics simulations for simple glass-forming liquids are performed, and a three-time…
A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…
The existence of heterogeneity in the dynamics of supercooled liquids is believed to be one of the hallmarks of the glass transition. Intense research has been carried out in the past to understand the origin of this heterogeneity in…
The phenomenon of drag reduction by polymer additives had been studied in simulations on the basis of non-Newtonian fluid mechanical models that take into account the field of polymer extension (conformation tensor) and its interaction with…