Related papers: Homogenization Techniques for Periodic Structures
Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour…
Tilings based on the cut and project method are key model systems for the description of aperiodic solids. Typically, quantities of interest in crystallography involve averaging over large patches, and are well defined only in the…
In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this…
This chapter is a collection of techniques, warnings, facts and ideas that are sometimes regarded as theoretical curiosities in high-energy physics but have important consequences in condensed matter physics. In particular, we describe…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack…
Plasmonic gratings constitute a paradigmatic instance of the wide range of applications enabled by plasmonics. While subwavelength metal gratings find applications in optical biosensing and photovoltaics, atomically thin gratings achieved…
The relationship according to which one physical theory encompasses the domain of empirical validity of another is widely known as "reduction." Here it is argued that one popular methodology for showing that one theory reduces to another,…
In this work we examine the stability of some classes of integrals, and in particular with respect to homogenization. The prototypical case is the homogenization of quadratic energies with periodic coefficients perturbed by a term vanishing…
We derive, by means of Gamma-convergence, the equations of homogenized bending rod starting from $3D$ nonlinear elasticity equations. The main assumption is that the energy behaves like h^2 (after dividing by the order h^2 of vanishing…
This is the second part in a series of two papers that concern with the quantitative analysis of the electromagnetic field enhancement and anomalous diffraction by a periodic array of subwavelength slits. In this part, we explore the…
The optical characterization of dielectric periodic line-gratings for which the period of the grating is significantly larger than the probing wavelength is investigated experimentally, numerically, and analytically. The experimental…
The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase…
We introduce a homogenization approach to characterize the dynamical response of a generic dispersive spacetime crystal in the long-wavelength limit. The theory is applied to dispersive spacetime platforms with a travelling-wave modulation.…
We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half-space, and derive and implement a…
This article is the first part of a two-fold study, the objective of which is the theoretical analysis and numerical investigation of new approximate corrector problems in the context of stochastic homogenization. We present here three new…
For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is.…
A thermodynamically consistent mathematical model for hydrogen adsorption in metal hydrides is proposed. Beside hydrogen diffusion, the model accounts for phase transformation accompanied by hysteresis, swelling, temperature and heat…
This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…
Dielectric properties of material mixtures are of importance in diagnostics, characterization and design of systems in various engineering fields. In this Letter, we propose a peculiar dielectric mixture expression, which is based on the…