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Closed-loop adaptive optics systems which use minimum mean square error wavefront reconstruction require the computation of pseudo open loop wavefront slopes. These techniques incorporate a knowledge of atmospheric statistics which must…
We demonstrate a phenomenon of condensation of the Fourier transform $\widehat{f}$ of a function $f$ defined on the real line $\mathbb{R}$ which decreases rapidly on one half of the line. For instance, we prove that if $f$ is…
Abstract Purpose The complex signal decay during the transient FLASH MRI readout can lead to artifacts in magnitude and phase images. We show that target-driven optimization of individual rf flip angles and phases can realize near-ideal…
Direct phase-resolved simulations are performed to investigate the propagation and scattering of nonlinear ocean waves in fragmented sea ice. The numerical model solves the full time-dependent equations for nonlinear potential flow coupled…
We study the spectrum of one dimensional integral operators in bounded real intervals of length $2L$, for value of $L$ large. The integral operators are obtained by linearizing a non local evolution equation for a non conserved order…
We consider radially symmetric capillary surfaces that are described by bounded generating curves. We use the arc-length representation of the differential equations for these surfaces to allow for vertical points and inflection points…
An operator theoretic approach to orthogonal rational functions on the unit circle with poles in its exterior is presented in this paper. This approach is based on the identification of a suitable matrix representation of the multiplication…
Calculating dynamical diffraction patterns for X-ray topography and similar x-ray scattering-imaging techniques require the numerical integration of the Takagi-Taupin equations. This is usually performed with a simple second order finite…
The Singularity Expansion Method Parameter Optimizer -- SEMPO -- is a toolbox to extract the complex poles, zeros and residues of an arbitrary response function acquired along the real frequency axis. SEMPO allows to determine this full set…
The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate…
Dynamical potentials appear in many advanced electronic-structure methods, including self-energies from many-body perturbation theory, dynamical mean-field theory, electronic-transport formulations, and many embedding approaches. Here, we…
A convenient way to represent a nonlinear input-output system in control theory is via a Chen-Fliess functional expansion or Fliess operator. The general goal of this paper is to describe how to approximate Fliess operators with iterated…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…
Phase curve of an open loop system is flat in nature if the derivative of phase with respect to frequency is zero. With a flat phase curve, the corresponding closed-loop system exhibits an iso-damped property i.e. maintains constant…
The steady, asymmetric and two-dimensional flow of viscous, incompressible micropolar fluid through a rectangular channel with a splitter (parallel to walls) was formulated and simulated numerically. The plane Poiseuille flow was considered…
This paper proposes a novel, rigorous and simple Fourier-transformation approach to study resonances in a perfectly conducting slab with finite number of subwavelength slits of width $h\ll 1$. Since regions outside the slits are variable…
Rotatable intelligent reflecting surface (IRS) introduces a new spatial degree of freedom (DoF) by dynamically adjusting orientations without the need of changing its elements' positions in real time. To unleash the full potential of…
This paper focuses on studying orthogonal and non-orthogonal multiple access in intelligent reflecting surface (IRS)-aided systems. Unlike most prior works assuming continuous phase shifts, we employ the practical setup where only a finite…
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…
Linear (spectro) polarimetry is usually performed using separate photon flux measurements after spatial or temporal polarization modulation. Such classical polarimeters are limited in sensitivity and accuracy by systematic effects and…