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Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to solve. To obtain a reasonable solution, a mesh size that is much smaller than the reciprocal of the wavenumber is typically required (known as the…
For a required payload, the existing reversible data hiding (RDH) methods always expect to reduce the embedding distortion as much as possible, such as by utilizing a well-designed predictor, taking into account the carrier-content…
This research thesis presents a novel higher-order spectral element method (SEM) formulated in cylindrical coordinates for analyzing electromagnetic fields in waveguides filled with complex anisotropic media. In this study, we consider a…
We describe a lattice-based crystallographic approximation for the analysis of distorted crystal structures via Electron Backscatter Diffraction (EBSD) in the scanning electron microscope. EBSD patterns are closely linked to local lattice…
We solve the problem of sparse signal deconvolution in the context of seismic reflectivity inversion, which pertains to high-resolution recovery of the subsurface reflection coefficients. Our formulation employs a nonuniform, non-convex…
The process of differential deposition is currently applied at the ESRF in order to correct figure errors of x-ray optics substrates, prior to multilayer deposition. The substrate is moved at a controlled speed in front of a sputtering…
We have carried out powder x-ray diffraction and dielectric studies on the lead free solid solution (1-x)SrTiO3-xBi(Zn1/2Ti1/2)O3 ((1-x)ST-xBZT) with x=0.05, 0.10, 0.15, 0.20, 0.30 and 0.50 to explore the ferroelectric and piezoelectric…
This paper presents a novel method for solving the 2D advection-diffusion equation using fixed-depth symbolic regression and symbolic differentiation without expression trees. The method is applied to two cases with distinct initial and…
Accurate measurement of light wavelength is critical for applications in spectroscopy, optical communication, and semiconductor manufacturing, ensuring precision and consistency of sensing, high-speed data transmission and device…
It is expensive to compute residual diffusivity in chaotic in-compressible flows by solving advection-diffusion equation due to the formation of sharp internal layers in the advection dominated regime. Proper orthogonal decomposition (POD)…
This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of…
Fluorescence microscopy is a critical tool across various disciplines, from materials science to biomedical research, yet it is limited by the diffraction limit of resolution. Advanced super-resolution techniques such as localization…
In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed method first performs the spatial discretization of the model…
This paper proposes an extra gradient Anderson-accelerated algorithm for solving pseudomonotone variational inequalities, which uses the extra gradient scheme with line search to guarantee the global convergence and Anderson acceleration to…
We present a computational framework for two-scale asymptotic homogenization to determine the intrinsic magnetic permeability of composites. To this end, considering linear magnetostatics, both vector and scalar potential formulations are…
This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front…
Deep clustering is a deep neural network-based speech separation algorithm that first trains the mixed component of signals with high-dimensional embeddings, and then uses a clustering algorithm to separate each mixture of sources. In this…
We present a computational methodology for obtaining rotationally symmetric sets of points satisfying discrete geometric constraints, and demonstrate its applicability by discovering new solutions to some well-known problems in…
We consider the problem of direction finding using partly calibrated arrays, a distributed subarray with position errors between subarrays. The key challenge is to enhance angular resolution in the presence of position errors. To achieve…
This study focuses on the application of ultra sonic diffrac tion tomography to noncircular 2D-cylindri - cal ob jects im mersed in an in fi nite fluid. The dis torted Born it er a tive method used to solve the in verse scat ter ing prob…