Related papers: Closed Form Fractional Integration and Differentia…
Traditionally, the diffraction of a scalar wave satisfying Helmholtz equation through an aperture on an otherwise black screen can be solved approximately by Kirchhoff's integral over the aperture. Rubinowicz, on the other hand, was able to…
Guided wave dispersion is commonly assessed by Fourier analysis of the field along a line, resulting in frequency-wavenumber dispersion curves. In anisotropic plates, a point source can generate multiple dispersion branches pertaining to…
The resonant excitation of an electromagnetic guided mode of a slab structure by exterior radiation results in anomalous scattering behavior, including sharp energy-transmission anomalies and field amplification around the frequency of the…
We propose an optimization algorithm to compute the optimal sensor locations in experimental design in the formulation of Bayesian inverse problems, where the parameter-to-observable mapping is described through an integral equation and its…
In this paper, we explore spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis.Our approach involves utilizing the integral periodic zeros set of Fourier transform to characterize…
The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schroedinger equation including fractional one- or two-dimensional diffraction…
In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are…
The perfectly matched layers (PMLs), as a boundary termination over an unbounded spatial domain, are widely used in numerical simulations of wave propagation problems. Given a set of discretization parameters, a procedure to select the PML…
A simple procedure for the design of recursive digital filters with an infinite impulse response (IIR) and non-recursive digital filters with a finite impulse response (FIR) is described. The fixed-lag smoothing filters are designed to…
A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. A key aspect of this approach is that it…
Modulation is the key element of the comprehensive two-dimensional gas chromatography separation. Forward fill/flush flow modulation is cost effective, robust and suitable for analysis of a wide range of samples. Even though this modulation…
An interferometer has been used to measure the surface profile of generic object. Frequency scanning interferometry has been employed to provide unambiguous phase readings, to suppress etalon fringes, and to supersede phase-shifting. The…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
Monotone inclusions have wide applications in solving various convex optimization problems arising in signal and image processing, machine learning, and medical image reconstruction. In this paper, we propose a new splitting algorithm for…
The exact Green function for the scalar wave equation in a plane with any set of perfectly reflecting straight mirrors, which may be joined to form corners, is given as a diffraction scattering series. Instances would be slit diffraction in…
A finite element-based modal formulation of diffraction of a plane wave by an absorbing photonic crystal slab of arbitrary geometry is developed for photovoltaic applications. The semi-analytic approach allows efficient and accurate…
We show the effectiveness of automatic differentiation in efficiently and correctly computing and controlling the spectrum of implicitly linear operators, a rich family of layer types including all standard convolutional and dense layers.…
The solution of the Lippman-Schwinger (L-S) integral equation is equivalent to the the solution of the Schroedinger equation. A new numerical algorithm for solving the L-S equation is described in simple terms, and its high accuracy is…
We consider numerical approximations of spectral fractional Laplace-Beltrami problems on closed surfaces. The proposed numerical algorithms rely on their Balakrishnan integral representation and consist of a sinc quadrature coupled with…
This article presents proposals for the design of reduced-order controllers for high-dimensional dynamical systems. The objective is to develop efficient control strategies that ensure stability and robustness with reduced computational…