Spectral algorithms for vector elliptic equations in a spherical gap

2 - NUMERICAL INTEGRATION ALGORITHMS

Accurate modelling of the accumulation region of a double barrier resonant tunnelling diode

In this paper, noise estimation based on series expansion of orthogonal functions is proposed. The proposed method searches speechless frequency regions and estimates the noise spectrum from the searched speechless frequency regions. The proposed method can adapt to changing of noise power without estimation delay. Experimental results show that the proposed method provides a good performance against time-varying noise.

CHAPTER 16 - APPLICATION OF EXPANSIONS IN ORTHOGONAL FUNCTIONS TO THE ANALYSIS OF SHELLS

There are quantum algorithms for finding a function f satisfying a set of conditions, such as solving partial differential equations, and these achieve exponential quantum speedup compared to existing classical methods, especially when the number d of the variables of f is large. In general, however, these algorithms output the quantum state which encodes f in the amplitudes, and reading out the values of f as classical data from such a state can be so time-consuming that the quantum speedup is ruined. In this study, we propose a general method for this function readout task. Based on the function approximation by a combination of tensor network and orthogonal function expansion, we present a quantum circuit and its optimization procedure to obtain an approximating function of f that has a polynomial number of degrees of freedom with respect to d and is efficiently evaluable on a classical computer. We also conducted a numerical experiment to approximate a finance-motivated function to demonstrate that our method works.

In many areas of signal, system, and control theory, orthogonal functions play an important role in issues of analysis and design. In this paper, it is shown that there exist orthogonal functions that, in a natural way, are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l/sub 2sup n/. To this end, use is made of balanced realizations of inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion, i.e., to obtain a good approximation by retaining only a finite number of expansion coefficients. Consequences for identification of expansion coefficients are analyzed, and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The electromagnetically driven magnetised spherical Couette flow is studied experimentally, theoretically and numerically in the laminar regime. The working fluid, Galinstan, is contained in the spherical gap between two concentric spheres at rest. The electromagnetic stirring is primarily generated due to the interaction of a direct current, which is injected through two ring-shaped electrodes located at the equatorial zone of each sphere, and a dipolar magnetic field produced by a permanent magnet located inside the inner sphere. The flows were explored experimentally for a Reynolds number ranging from 450 to 2230 and a Hartmann number of 240. Ultrasound Doppler velocimetry and particle image velocimetry were used to characterise the flow. For low Reynolds numbers, given the symmetry of the problem, a one-dimensional analytic solution is obtained in the equatorial plane from the magnetohydrodynamic equations. The analytical solution reproduces the main characteristics of the flow. In addition, a full three-dimensional numerical model is able to reproduce both the analytical solution and the experimental measurements. To the best knowledge of the authors, this is the first time experimental results of the magnetised spherical Couette flow have been reported with electromagnetic forcing using a liquid metal as the working media.

The main objective of this paper is to describe a class of functional series expansions, known as Fliess operators, which admit inputs from a ball in an L p space as well as Poisson random processes. Conditions are given under which these functional series expansions converge absolutely in the mean. Then, it is shown that a continuous-time switched input-affine nonlinear system with a Poisson switching signal can be represented as a Fliess operator and that for certain cases a closed form solution can be obtained in terms of Poisson integrals.

A Multidomain Spectral Method for Scalar and Vectorial Poisson Equations with Noncompact Sources

Sound-pressure level (SPL) calculations are made along individual ray paths for one-dimensional, depth-dependent, speeds of sound using an enhanced version of the recursive ray acoustics (RRA) algorithm. The SPL calculations are valid (i.e., finite) at turning points and focal points and do not require the use of Airy functions. The SPL calculations include the effects of frequency-dependent volume attenuation and frequency-dependent attenuation due to surface and bottom reflections. The ocean surface and bottom are treated as boundaries between viscous fluid media. Although the ocean surface is modeled as a planar boundary, the bathymetry is an arbitrary function of horizontal range. Sound speed versus depth and bathymetric data are represented by orthogonal function expansions. Computer simulation results from preliminary test cases are presented. [Work supported by NAVSEA.]

Two methods for extending the definition of reactive power beyond the sinusoidal steady state are presented. Reactive power concepts are created that can be useful in the state-space analysis of nonlinear or nonperiodic systems. All definitions and results are given purely in the time domain without using Fourier analysis or other orthogonal function expansions. >

Magnetic Resonance Imaging techniques such as spectroscopic and echo-planar imaging require a highly uniform main magnetic field, B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> for achieving acceptable diagnostic image quality. In this work a patient-specific, non-iterating and fast gradient shimming method for applying field correction in the imaging plane is described. It requires two gradient-echo images acquired at readout time difference which is a multiple of the fat-water separation frequency of the scanner for 1H protons. A simple phase unwrapping method is applied on the computed B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> field map to correct for the inherent modulo $2\pi$ phase wrappings. The three linear terms in the orthogonal basis function expansion of the field map are used for estimating the linear shim. Field correction terms are estimated via a magnitude image weighted least squares method. The technique is suitable for linear field shimming of diametric spherical volume centered at the magnet isocenter and could be incorporated into scanners that do not have shimming system.

Matrix decomposition RBF algorithm for solving 3D elliptic problems

Orthogonal functions have many useful properties and can be used for different purposes in machine learning. One of the main applications of the orthogonal functions is producing powerful kernel functions for the support vector machine algorithm. Maybe the simplest orthogonal function that can be used for producing kernel functions is the Chebyshev polynomials. In this chapter, after reviewing some essential properties of Chebyshev polynomials and fractional Chebyshev functions, various Chebyshev kernel functions are presented, and fractional Chebyshev kernel functions are introduced. Finally, the performance of the various Chebyshev kernel functions is illustrated on two sample datasets.

Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the [formula omitted] symmetry group; Interpolation within a squircle, Part I