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In this work, we propose multicontinuum splitting schemes for the wave equation with a high-contrast coefficient, extending our previous research on multiscale flow problems. The proposed approach consists of two main parts: decomposing the…
This paper presents a method for computing two-dimensional constant mean curvature surfaces. The method in question uses the variational aspect of the problem to implement an efficient algorithm. In principle it is a flow like method in…
We compare two high order finite-difference methods that solve the elastic wave equation in two dimensional domains with curved boundaries and material discontinuities. Two numerical experiments are designed with focus on wave boundary…
We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…
In the realm of signal processing, frequency and spectrum detection are fundamental tasks that can be computationally intensive. This project leverages the power of FPGAs to perform wavelet analysis on an input signal. The goal is to detect…
This paper focuses on improved edge model based on Curvelet coefficients analysis. Curvelet transform is a powerful tool for multiresolution representation of object with anisotropic edge. Curvelet coefficients contributions have been…
There are many research works and methods about change point detection in the literature. However, there are only a few that provide inference for such change points after being estimated. This work mainly focuses on a statistical analysis…
Quantum interference is shown to deliver a means of regulating the diffraction pattern of a thermal atomic beam interacting with two standing wave electric fields. Parameters have been identified to enhance the diffraction probability of…
In this letter, the wavelet transform is used to decompose the classical linearly polarized plane light wave into a series of discrete Morlet wavelets. It is found that the energy of the light wave can be discrete, associated with its…
A method is given for finding small inhomogeneities from surface scattering data. The method consists in localization of the positions and finding the intensities of these small inhomogeneities. The case of acoustic wave scattering is…
An innovative interference-based method for detecting degenerate index states of polarization singularity is presented here. Index degeneracy occurs when different combinations of spin and orbital angular momentum states are superposed to…
This article presents novel proof methods for estimating interpolation errors, predicated on the understanding that one has already studied foundational error analysis using the finite element method.
Imaging of surface adsorbed molecules is investigated as a novel detection method for matter wave interferometry with fluorescent particles. Mechanically magnified fluorescence imaging turns out to be an excellent tool for recording quantum…
This paper describes the application of the adaptive whitening filter and the wavelet transform used to detect the abrupt changes in the signals recorded during disturbances in the electrical power network in South Africa. Main focus has…
We proposed a novel approach to coherent imaging of dynamic samples. The inter-frame similarity of the sample's local structures is found to be a powerful constraint in phasing a sequence of diffraction patterns. We devised a new image…
The profile of suspended silicon nitride thin films patterned with one-dimensional subwavelength grating structures is investigated using Atomic Force Microscopy. We first show that the results of the profilometry can be used as input to…
I derive in this paper theoretical expressions for biases on fringe contrast and fringe visibility phase for optical interferometers whose polarizing properties can be described by beam rotation, retardance, and diattenuation. The nature of…
In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…
We analyze the stability of an inverse problem for determining the time-dependent matrix potential appearing in the Dirichlet initial-boundary value problem for the wave equation in an unbounded cylindrical waveguide. The observation is…
Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed…