Related papers: A Constructive Approach to the Finite Wavelet Fram…
This document summarizes the main concepts of the finite element (FE) theory and constitutive relations as implemented in the open-source code phase-field multiphysics materials simulator PHIMATS https://github.com/ahcomat/PHIMATS. PHIMATS…
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory…
The concept of quasi-affine frame in Euclidean spaces was introduced to obtain translation invariance of the discrete wavelet transform. We extend this concept to a local field $K$ of positive characteristic. We show that the affine system…
Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few…
Calculations of the photonic band structure, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals by using the finite element method (FEM) are reported. The…
We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame members are obtained by maximizing their concentration in…
Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. This article gives an overview over some well known results about the continuous and discrete wavelet transforms and…
In affine formation control problems, the construction of the framework with universal rigidity and affine localizability is a critical prerequisite, but it has not yet been well addressed, especially when additional agents join the…
In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
A method for automatic computation of parameter derivatives of numerically computed light scattering signals is demonstrated. The finite-element based method is validated in a numerical convergence study, and it is applied to investigate…
In this paper, we present a mixed Generalized Multiscale Finite Element Method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis…
We present a novel formulation for calculating the transversal flexoelectric coefficient of nanostructures at finite deformations from first principles. Specifically, we introduce the concept of \emph{radial polarization} to make the…
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the…
In this work, we derive a generic overcomplete frame thresholding scheme based on risk minimization. Overcomplete frames being favored for analysis tasks such as classification, regression or anomaly detection, we provide a way to leverage…
The use of covariant projection finite elements in the efficient 3-D vector finite element analysis of wave guide is presented.
Continuing the ideas from our previous paper, we construct Parseval frames of weighted exponential functions for self-affine measures.
A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over the volume of the ball in three dimensions is described. Such methods are necessary in many areas of Applied…
This note provides new methods for constructing quadratic nonresidues in finite fields of characteristic p. It will be shown that there is an effective deterministic polynomial time algorithm for constructing quadratic nonresidues in finite…