Related papers: A Framework for FFT-based Homogenization on Anisot…
Reducing parameter spaces via exploiting symmetries has greatly accelerated and increased the quality of electronic-structure calculations. Unfortunately, many of the traditional methods fail when the global crystal symmetry is broken, even…
The purpose of this work is two-fold. First, we introduce an efficient homogenization-based approach to perform topology optimization of coated structures with orthotropic infill material. By making use of the relaxed design space, we can…
De-homogenization is becoming an effective method to significantly expedite the design of high-resolution multiscale structures, but existing methods have thus far been confined to simple static compliance minimization. There are two…
We carry out the homogenization of time-harmonic Maxwell's equations in a periodic, layered structure made of two-dimensional (2D) metallic sheets immersed in a heterogeneous and in principle anisotropic dielectric medium. In this setting,…
The envelope function method traditionally employs a single basis set which, in practice, relates to a single material because the $k\cdot p$ matrix elements are generally only known in a particular basis. In this work, we defined a basis…
The accurate and efficient computation of the electromagnetic response of objects made from artificial materials is crucial for designing photonic functionalities and interpreting experiments. Advanced fabrication techniques can nowadays…
Efficient numerical characterization is a key problem in composite material analysis. To follow accuracy improvement in image tomography, memory efficient methods of numerical characterization have been developed. Among them, an FFT based…
The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development…
We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…
Computational micromechanics and homogenization require the solution of the mechanical equilibrium of a periodic cell that comprises a (generally complex) microstructure. Techniques that apply the Fast Fourier Transform have attracted much…
This work combines three paradigms of image processing: i) the total variation approach to denoising, ii) the superior structure of hexagonal lattices, and iii) fast and exact graph cut optimization techniques. Although isotropic in theory,…
A special class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions are analyzed via the inverse scattering method (ISM). Using the dressing method we construct two classes…
Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present a new algorithm for…
We present a Fourier-based approach for high-dimensional function approximation. To this end, we analyze the truncated ANOVA (analysis of variance) decomposition and learn the anisotropic smoothness properties of the target function from…
The homogenization of auxetic cellular solids having periodic hexachiral and tetrachiral microstructure is dealt with two different techniques. The first approach is based on the representation of the cellular solid as a beam-lattice to be…
We study the effects of anisotropic hopping amplitudes on quantum phases of ultracold fermions in optical lattices described by the repulsive Fermi-Hubbard model. In particular, using dynamical mean-field theory (DMFT) we investigate the…
FFT-based solvers introduced in the 1990s for the numerical homogenization of heterogeneous elastic materials have been extended to a wide range of physical properties. In parallel, alternative algorithms and modified discrete Green…
The focus of this paper is on the analysis of the Conjugate Gradient method applied to a non-symmetric system of linear equations, arising from a Fast Fourier Transform-based homogenization method due to (Moulinec and Suquet, 1994).…
Two-dimensional materials on metallic surfaces or stacked one on top of the other can form a variety of moir\'e superstructures depending on the possible parameter and symmetry mismatch and misorientation angle. In most cases, such as…
Honeycomb-like microstructures have been shown to exhibit local elastic buckling under compression, with three possible geometric buckling modes, or pattern transformations. The individual pattern transformations, and consequently also…