Related papers: Closed Form Fractional Integration and Differentia…
The pseudo-polar Fourier transform is a specialized non-equally spaced Fourier transform, which evaluates the Fourier transform on a near-polar grid, known as the pseudo-polar grid. The advantage of the pseudo-polar grid over other…
We analyse the performance of a communication link assisted by an intelligent reflective surface (IRS) positioned in the far field of both the source and the destination. A direct link between the transmitting and receiving devices is…
Magnetometers based on ensembles of nitrogen-vacancy centres are a promising platform for continuously sensing static and low-frequency magnetic fields. Their combination with phase-sensitive (lock-in) detection creates a highly versatile…
We present the Method Of Lines (MOL), which is based on the spectral collocation method, to solve space-fractional advection-diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which the…
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…
It remains an open problem to find the optimal configuration of phase shifts under the discrete constraint for intelligent reflecting surface (IRS) in polynomial time. The above problem is widely believed to be difficult because it is not…
We develop an effective computational tool for simulating the scattering of 1D waves by a composite layer architected in an otherwise homogeneous medium. The layer is designed as the union of segments cut from various mother periodic media,…
We introduce optical polarization-insensitive high pass filters based on total internal reflection of light at the interface of two dielectric media (1D) and Bragg reflection of a multilayer stack (2D) in transmission mode. The wavevectors…
The proximal extrapolated gradient method \cite{Malitsky18a} is an extension of the projected reflected gradient method \cite{Malitsky15}. Both methods were proposed for solving the classic variational inequalities. In this paper, we…
An opportunistic relay selection based on instantaneous knowledge of channels is considered to increase security against eavesdroppers. The closed-form expressions are derived for the average secrecy rates and the outage probability when…
Multi-soliton pulses, as special solutions of the Nonlinear Schroedinger Equation (NLSE), are potential candidates for optical fiber transmission where the information is modulated and recovered in the so-called nonlinear Fourier domain.…
We extend the hidden zeros and $2$-split of tree-level ${\rm Tr}(\phi^3)$ amplitudes to loop-level Feynman integrands, apart from some physically irrelevant scaleless integrals. Our method is based on a certain factorization mechanism that…
This paper addresses the numerical optimization of proportional-integral-derivative (PID) controllers for linear time-invariant systems with delays, where the derivative action is implemented using a low-pass filter. While performance…
This paper studies discretization of time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Most of the analysis in the literature has been performed on fully-discrete…
Sliced optimal transport reduces optimal transport on multi-dimensional domains to transport on the line. More precisely, sliced optimal transport is the concatenation of the well-known Radon transform and the cumulative density transform,…
Two ways of designing low-order discrete-time (i.e. digital) controls for low-order plant (i.e. process) models are considered in this tutorial. The first polynomial method finds the controller coefficients that place the poles of the…
We propose a scheme for manipulations of a variety of topological states in fractional optical systems through spiral modulation of the local refraction index. An analytical approximation, based on a truncated finite-mode system, and direct…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
We propose a new, simple model-independent method to extract information of near-threshold resonances, such as complex energies and residues. The method is based on the observation that the Green's function and the T-matrix can be…
We propose a method based on sinc series approximations for computing the Rayleigh-Sommerfeld and Fresnel diffraction integrals of optics. The diffraction integrals are given in terms of a convolution, and our proposed numerical approach is…