Related papers: Nonuniform grids for Brillouin zone integration an…
In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tessellation, which induces a natural dual map to…
We present a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone. It provides an efficient method of computing (spin) Hall conductances without specifying…
Adaptive rational interpolation has been designed in the context of image processing as a new nonlinear technique that avoids the Gibbs phenomenon when we approximate a discontinuous function. In this work, we present a generalization to…
A mixed basis approach based on density functional theory is extended to one-dimensional(1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the…
The introduction of a twist between two layers of two-dimensional materials has opened up a new and exciting field of research known as twistronics. In these systems, the phonon dispersions show significant renormalization and enhanced…
The optical nonlinear effects can provide different advanced electromagnetic functionalities, such as wave mixing and phase conjugation, which can be applied in a variety of new applications. However, these effects usually suffer from…
Metamaterials derive their unconventional properties from engineered microstructures, with periodic lattices providing a versatile framework for modeling wave propagation. Dispersion relations, obtained from Bloch-Floquet theory, govern how…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
A grid-overlay finite difference method is proposed for the numerical approximation of the fractional Laplacian on arbitrary bounded domains. The method uses an unstructured simplicial mesh and an overlay uniform grid for the underlying…
In this paper, we propose a trigonometric-interpolation approach for solutions of second order nonlinear ODEs with mixed boundary conditions. The method interpolates secondary derivative $y''$ of a target solution $y$ by a trigonometric…
Cavity optomechanical systems enable coherent photon-phonon interactions essential for quantum technologies, yet high-performance devices have been limited to suspended structures. Here, we overcome this limitation by demonstrating cavity…
Topological phases of matter have revolutionised the fundamental understanding of band theory and hold great promise for next-generation technologies such as low-power electronics or quantum computers. Single-gap topologies have been…
The paper studies oscillations of graphene plates under the hypothesis that deformations are much more than the thickness of plate. In this most realistic case the oscillations are described by the system of nonlinear partial differential…
An effective solution to the problem of Hermite $G^1$ interpolation with a clothoid curve is provided. At the beginning the problem is naturally formulated as a system of nonlinear equations with multiple solutions that is generally…
In energy system analysis, coupling models with mismatched spatial resolutions is a significant challenge. A common solution is assigning weights to high-resolution geographic units for aggregation, but traditional models are limited by…
In this manuscript, we analyze the expansions of functions in orthogonal polynomials associated with a general weight function in a multidimensional setting. Such orthogonal polynomials can be obtained by Gram-Schmidt orthogonalization.…
Strong acousto-optic interaction in silicon-based waveguides generally requires releasing of the silicon core to avoid mechanical leakage into the underlying silica substrate. This complicates fabrication, limits thermalization, reduces the…
Hourglass dispersion is generally believed to be solely protected by nonsymmorphic symmetries, because these symmetries can introduce high-dimensional projective representations. Here, based on symmetry arguments, we propose that the…
We consider functions $f$ of two real variables, given as trigonometric functions over a finite set $F$ of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle $\frac{2k\pi}{M}$ for some integer $M$.…
This paper presents phononic band-structure calculation results obtained using a mixed variational formulation for 1-, and 2-dimensional unit cells. The formulation itself is presented in a form which is equally applicable to 3-dimensiomal…