Use Of Spectral Methods Research Articles

Features of Recording Energy Parameters of Acoustic Emission Signals from Materials

The acoustic emission method is used as a means of analyzing the state of materials and structures, non-destructive testing and diagnosing them during operation. An important advantage over other methods is that it reacts only to the development of truly dangerous defects and is capable of monitoring large volumes and surfaces without scanning them. The article presents the results of the development of methods and algorithms designed to analyze the energy characteristics of acoustic signals. The use of spectral methods is justified.

The Use of Spectral Methods for the “Ensemble” Assessment of Synthesis Dynamics of the Arabinogalactan-Stabilized Selenium Nanoparticles

The Use of Spectral Methods for the “Ensemble” Assessment of Synthesis Dynamics of the Arabinogalactan-Stabilized Selenium Nanoparticles

Numerical Solutions of the Multi-Space Fractional-Order Coupled Korteweg–De Vries Equation with Several Different Kernels

In this article, the authors propose to investigate the numerical solutions of several fractional-order models of the multi-space coupled Korteweg–De Vries equation involving many different kernels. In order to transform these models into a set or system of differential equations, various properties of the first-kind Chebyshev polynomial are used in this study. The main objective of the present study is to apply the spectral collocation approach for the multi-space fractional-order coupled Korteweg–De Vries equation with different kernels. We use finite differences to numerically solve these differential equations by reducing them to algebraic equations. The Newton (or, more precisely, the Newton–Raphson) method is then used to solve these resulting algebraic equations. By calculating the error involved in our approach, the precision of the numerical solution is verified. The use of spectral methods, which provide excellent accuracy and exponential convergence for issues with smooth solutions, is shown to be a benefit of the current study.

Approximation of Differential Operators with Boundary Conditions

The use of spectral methods for solution of boundary value problems is very effective but involves great technical difficulties associated with the implementation of the boundary conditions. There exist several methods of such an implementation, but they are either very cumbersome or require a preliminary analysis of the problem and its reduction to an integral form. We propose a universal means of implementation of the boundary conditions for linear differential operators on a finite interval, which is very simple in its realization. The use of the rational arithmetic allows to assess the effectiveness of this method without interference of the round-off errors. We apply this approach for computation of rational approximations for some fundamental constants. We obtained approximations that in a number of cases are better than those that are given by convergents of regular continued fractions of these constants.

Spectroscopic neutron imaging for resolving hydrogen dynamics changes in battery electrolytes

We present the use of spectroscopic neutron imaging (SNI), a bridge between imaging and scattering techniques, for analyzing battery electrolytes. The scattering information of CHn–based organic solvents and electrolytes was mapped in a two-dimensional space through time-of-flight neutron imaging, which exploits the wavelength-dependent properties of hydrogen atoms. The results show partial solidification and concertation change of electrolyte as a function of temperature. Our investigation demonstrates a novel approach to tracking real-time physical and chemical changes in H-containing compounds, by which limitations of new electrolyte mixtures and additives can be evaluated. The sensitivity of SNI to hydrogen in CHn functional groups extends the use of spectral methods to inspect electrolytes in Li-ion batteries and organic solvents for relevant applications beyond electrochemical systems.

Spectral Methods in Nonlinear Optics Equations for Non-Uniform Grids Using an Accelerated NFFT Scheme

In this work, we propose the use of non-homogeneous grids in 1D and 2D for the study of various nonlinear physical equations using spectral methods. As is well known, the use of spectral methods allow a faster resolution of the problem via the application of the ubiquitous Fast Fourier Transform (FFT) algorithm. We will center our investigation on the search of fast and accurate schemes to solve the spectral operators in the Fourier space. In particular, we will use the Conjugate Gradient (CG) iterative method, with a preconditioning matrix to accelerate the inversion process of the non-uniform Fast Fourier Transform (NFFT). As it will be shown, the results obtained are in good agreement with the expected values.

Loading classification proposal for fatigue design of automotive chassis-parts: A relevant process for variable amplitude and multi-input load cases

It is essential for car manufacturers to ensure their vehicle robustness under a daily usage. As no detailed method nor standard prevails, each manufacturer is expected to setup its own methodology for safety parts life-assessment. The early stages of a renewed methodology are proposed in this study. This is based on proving-grounds measurements analysis to quantify the impact of various loads. The method, developed from the load measured at the vehicle wheels, considers the multi-input load case and its variable amplitude content. Measured time-series are analyzed and partitioned into two main categories depending on the time-correlation between the load axes. The driver-induced loads, Driven-Road, (DR) loads, are separated from the effects of random road conditions, Random-Road, (RR) loads. Then, for partition validation, a suitable life quantification method is applied in parallel to the two types of loading. On one hand, an assumption based on strong physical meaning eases the Rainflow Counting method application on the DR load. On the other hand, the use of spectral methods is explored to handle the random loads. This paper details the partition process of the time-series and each of the subsequent validation steps of the method to apply such a partition. Such a validation is performed via a comparison of the pseudo-damage between a referenced signal and the one issued from the partition.

Application of reflectance spectroscopy to identify maize genotypes and aflatoxin levels in single kernels

Spectroscopy is a rapid, non-destructive, and low-cost analytical technique that has the potential to complement more resource-intensive analytical methods. We explored the use of spectral methods to differentiate maize genotypes and assess aflatoxin (AF) contamination in maize kernels. We compared the performance of two instruments: a research-grade ultraviolet-visible-near infrared (UV-Vis-NIR) spectrometer that measures reflectance from 304 -1,085 nm, and a miniaturised NIR spectrometer that measures reflectance from 740-1,070 nm. Both systems were used to predict AF levels in maize kernels from a single genotype and across 10 genotypes, and to predict genotype for the latter. A partial least square discriminant analysis model was trained on 70% of the kernels and tested on the remaining 30%. The classification accuracy for 10 maize genotypes was 71-72% using the UV-Vis-NIR instrument on 1,170 kernels, and 65-66% using the NIR device on 740 kernels. The classification accuracy for 247 AF-contaminated kernels of a single genotype using the UV-Vis-NIR instrument was 71, 82, and 92% for AF thresholds of 20, 100, and 1000 μg/kg, respectively. Using the same spectrometer on 872 kernels from 10 genotypes, AF classification accuracy was 67, 90, and 95% in validation sets for AF thresholds of 20, 100, and 1000 μg/kg, respectively. The UV-Vis-NIR instrument and the NIR device had similar classification accuracies for AF thresholds of 100 and 1000 μg/kg, whereas the NIR device had higher accuracy for the AF threshold of 20 μg/kg. Reflectance spectroscopy outperformed visual sorting and the bright greenish yellow fluorescence test in identifying AF levels. Applying spectral analysis to estimate mycotoxin levels and to identify maize genotypes could contribute to regional toxin surveillance and action efforts. Further, using AF-associated spectral features for grain sorting can reduce AF exposure.

A new mixed Boltzmann-BGK model for mixtures solved with an IMEX finite volume scheme on unstructured meshes

In this work, we consider a novel model for a binary mixture of inert gases. The model, which preserves the structure of the original Boltzmann equations, combines integro-differential collision operators with BGK relaxation terms in each kinetic equation: the first involving only collisions among particles of the same species, while the second ones taking into account the inter–species interactions. We prove consistency of the model: conservation properties, positivity of all temperatures, H-theorem and convergence to a global equilibrium in the shape of a global Maxwell distribution. We also derive hydrodynamic equations under different collisional regimes. In a second part, to numerically solve the governing equations, we introduce a class of time and space high order finite volume schemes that are able to capture the behaviors of the different hydrodynamic limit models: the classical Euler equations as well as the multi-velocities and temperatures Euler system. The methods work by integrating the distribution functions over arbitrarily shaped and closed control volumes in 2D using Central Weighted ENO (CWENO) techniques and make use of spectral methods for the approximation of the Boltzmann integrals with high order Implicit-Explicit (IMEX) Runge Kutta schemes. For these methods, we prove accuracy and preservation of the discrete asymptotic states. In the numerical section we first show that the methods indeed possess the theoretical order of accuracy for different regimes and second we analyse their capacity in solving different two dimensional problems arising in kinetic theory. To speed up the computational time, all simulations are run with MPI parallelization on 64 cores, thus showing the potentiality of the proposed methods to be used for HPC (High Performance Computing) on massively parallel architectures.

Optimal Control of Pitch and Rotational Velocity for a Cyclorotor Wave Energy Device

The development of optimal control strategies for cyclorotor wave energy converters (WECs) is at an early stage. In this paper, we present new methods and solutions for optimal pitch and/or rotational velocity control strategies for different configurations of cyclorotor-based WECs, in both monochromatic and panchromatic waves. The cyclorotor is modelled with the use of an approximate two-dimensional mathematical model, where hydrofoils are approximated as point source vortices in potential waves. The goal of the developed control strategy is to determine the optimal velocity profile, and/or pitch angle variations, for maximum energy conversion, in terms of generated mechanical shaft power. The solutions, obtained with the use of spectral methods, show a clear benefit in using a variable velocity for cyclorotors with either one or two hydrofoils, in monochromatic waves, with a typical increase in energy capture of 30-40%, while the optimal pitching did not significantly increase the value of the absorbed wave energy. We also present control results for panchromatic waves, assuming all the properties of incoming wave packages, within a 10 s time interval, are known. The obtained solutions have shown significant benefit in joint optimal pitch and velocity control, especially in the case of panchromatic waves. It has been also shown that successful implementation of cyclorotor control strategies requires optimal configuration of the static characteristics of the cyclorotor. In conclusion, we discuss the optimal control benefits and highlight problems which must be solved for further successful development of these control strategies.

Numerical solutions of space-fractional diffusion equations via the exponential decay kernel

<abstract><p>The main object of this paper is to investigate the spectral collocation method for three new models of space fractional Fisher equations based on the exponential decay kernel, for which properties of Chebyshev polynomials are utilized to reduce these models to a set of differential equations. We then numerically solve these differential equations using finite differences, with the resulting algebraic equations solved using Newton 's method. The accuracy of the numerical solution is verified by computing the residual error function. Additionally, the numerical results are compared with other results obtained using the power law kernel and the Mittag-Leffler kernel. The advantage of the present work stems from the use of spectral methods, which have high accuracy and exponential convergence for problems with smooth solutions. The numerical solutions based on Chebyshev polynomials are in remarkably good agreement with numerical solutions obtained using the power law and the Mittag-Leffler kernels. Mathematica was used to obtain the numerical solutions.</p></abstract>

Approximation of differential operators with boundary conditions

The use of spectral methods for solution of boundary value problems is very effective but involves great technical difficulties associated with the implementation of the boundary conditions. There exist several methods of such an implementation, but they are either very cumbersome or require a preliminary analysis of the problem and its reduction to an integral form. We propose a universal means of implementation of the boundary conditions for linear differential operators on a finite interval, which is very simple in its realization. The use of the rational arithmetic allows to assess the effectiveness of this method without interference of the round-off errors. We apply this approach for computation of rational approximations for some fundamental constants. We obtained approximations that in a number of cases are better than those that are given by convergents of regular continued fractions of these constants.

Use of Spectral Transforms for Analysis of Power Consumption of Local Object

The paper is devoted to the use and comparative analysis of discrete spectral transforms of Fourier, Hartley, Wilenkin-Crestenson and transform at the oriented basis (OB). These methods are considered for analysis of discrete time dependence of electrical energy consumption in local objects like MicroGrid. The prediction of electrical power consumption in such object is quite actual task. One of the ways to solve it is use of spectral and wavelet analysis methods. The non-stationary character of power consumption time dependence curve needs to fulfill preliminary stage of smoothing. This is why wavelet analysis could be effectively used here – as a result of its use we obtain smoothed and compressed version of initial signal (so called “trend”). And the core of wavelet is defined by the type of basic function. These could be, in particular, basic functions of spectral transforms. This is why it was decided to compare different spectral methods – Fourier, Hartley, Wilenkin-Krestenson, and spectral transform at oriented basis.Comparison of spectral methods was carried out according to the following criteria: number of computational operations, simplicity and accuracy of calculations. The amplitude-frequency and phase-frequency spectra of the investigated signal for different spectral methods are considered. The process of finding the spectrum for the above methods was considered for the interval from 0 to 26. The interval was chosen based on demands of the transform at oriented basis where it’s necessary to provide the lengths of initial discrete function dividable to 3 (N=33=27). For the rest methods the interval could be changes accordingly. Thus it gives more objective assessment of the use of spectral methods for the analysis of power consumption of a local object. During the analysis of different spectral methods it was taken into account that Fourier and Wilenkin-Crestenson transforms operate with complex values of the spectra, while Hartley and OB-transforms deal with the real numbers. At the same time, Wilenkin-Crestenson and OB-transforms operate with the number presented in m-ary counting system. It should be noted that the transition to the m-ary system makes it possible to significantly simplify the calculation process at the interval of determination for the Wilenkin-Crestenson method. The Hartley transform differs from the Fourier transform because it operates only with real values, that leads to significant decreasing of the values of basic function and therefore simplifies and accelerates the calculation of the spectrum. It was shown that, in contrast to the Fourier transform, the transform at the oriented basis is asymmetrical, that is, for direct conversion, the angle of inclination of the transformation axis is possible. Comparisons of the considered methods were made on the basis of the values of the required amount of memory for the operation and storage of the program for the calculation of the spectra, as well as the time of performing mathematical operations for the calculation of the spectra of the daily power consumption function. In this way, the transform at the oriented basis is most effective for simplifying and speeding up the calculations. Given that the analysis of fractional power consumption is advisable to perform at a sampling interval of less than one hour, the advantage of this method becomes indisputable, thus showing that the method at the oriented basis is the most appropriate among the considered ones, because with a certain set of parameters allows to accelerate significantly spectrum for analyzing the power consumption signal.

Features of the use of spectral methods for the determination of boron in natural waters

Features of the use of spectral methods for the determination of boron in natural waters

Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. approximations

Considered here are systems of partial differential equations arising in internal wave theory. The systems are asymptotic models describing the two-way propagation of long-crested interfacial waves in the Benjamin-Ono and the Intermediate Long-Wave regimes. Of particular interest will be solitary-wave solutions of these systems. Several methods of numerically approximating these solitary waves are put forward and their performance compared. The output of these schemes is then used to better understand some of the fundamental properties of these solitary waves. The spatial structure of the systems of equations is non-local, like that of their one-dimensional, unidirectional relatives, the Benjamin-Ono and the Intermediate Long-Wave equations. As the non-local aspect is comprised of Fourier multiplier operators, this suggests the use of spectral methods for the discretization in space. Three iterative methods are proposed and implemented for approximating traveling-wave solutions. In addition to Newton-type and Petviashvili iterations, an interesting wrinkle on the usual Petviashvili method is put forward which appears to offer advantages over the other two techniques. The performance of these methods is checked in several ways, including using the approximations they generate as initial data in time-dependent codes for obtaining solutions of the Cauchy problem. Attention is then turned to determining speed versus amplitude relations of these families of waves and their dependence upon parameters in the models. There are also provided comparisons between the unidirectional and bidirectional solitary waves. It deserves remark that while small-amplitude solitary-wave solutions of these systems are known to exist, our results suggest the amplitude restriction in the theory is artificial.

Synthesis and in Vitro Antimicrobial Activity Screening of New 3-Acetyl-2,5-disubstituted-1,3,4-oxadiazoline Derivatives.

Thirteen new 3-acetyl-2,5-disubstituted-1,3,4-oxadiazoline derivatives were synthesized from corresponding hydrazide-hydrazones of isonicotinic acid in the reaction with acetic anhydride. The obtained compounds were identified with the use of spectral methods (IR, 1 H-NMR, 13 C-NMR, MS). In vitro antimicrobial activity screening of synthesized compounds against a panel of bacteria and fungi revealed interesting antibacterial and antifungal activity of tested 1,3,4-oxadiazoline derivatives, which is comparable to that of commonly used antimicrobial agents.

Application of spectral analysis for differentiation between metals using signals from eddy-current transducers

The authors theoretically and experimentally substantiated the use of the spectral method for processing a signal of the vortex-current metal detector for dichotomous differentiation between metals. Results of experimental research that prove the possibility of using spectral analysis for differentiation between metals were presented. The vortex-current method for detection of hidden metal objects was analyzed. It was indicated that amplitude of output VCD signal is determined by electric conductivity of material of a hidden object and its magnetic permeability. It was shown that the spectral density of a signal can be an informative feature. The authors designed and fabricated a mockup of the vortex-current device, the special features of which include modularity, which, if necessary, makes it possible to replace quickly each of the modules. The developed algorithm of normalization of signals allows an operator to choose freely a scan mode and compare correctly VCD signals with reference signals. Research results show that it is possible to distinguish easily between the spectra of ferrous metals and those of non-ferrous metals. Spectral methods can be applied both for dichotomous analysis of hidden metal objects and for analysis of the type of metal in the subgroup of non-ferrous metals under condition of using highly sensitive spectroanalyzers with measurement error not exceeding 1 %. It was shown that advantage of the spectral method for analysis of signals of vortex-current transducer is identification of hidden objects by type of metal. The use of spectral methods for detection of hidden metals offers a new property – distant analysis of composition of detected metal objects.

Self-gravitating scalar breathers with a negative cosmological constant

Breather-type (time-periodic and spatially localized) solutions with spherical symmetry are investigated in a massless scalar field theory coupled to Einstein's gravity with cosmological constant in $d$ spatial dimensions imposing anti--de Sitter (AdS) asymptotics on space-time. Using a code constructed with the Kadath library that enables the use of spectral methods, the phase space of breather solutions is explored in detail for $d=3$ and $d=4$. It is found that there are discrete families of solutions indexed by an integer and by their frequency. Using a time evolution code these AdS breathers are found to be stable for up to a critical central density, in analogy to boson stars. Using an analytical perturbative expansion small amplitude breathers are worked out for arbitrary dimensions $d$.

Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes

A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics, convenient exploitation of the residual diffeomorphism freedom, and use of spectral methods for discretizing and solving the resulting differential equations. Relevant issues and choices leading to this approach are discussed in detail. Three examples, motivated by applications to non-equilibrium dynamics in strongly coupled gauge theories, are discussed as instructive test cases. These are gravitational descriptions of homogeneous isotropization, collisions of planar shocks, and turbulent fluid flows in two spatial dimensions.

General relativistic neutrino transport using spectral methods

We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, θ, ϕ, ϵ, Θ, Φ), and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (θ, ϕ, Θ, Φ), and is fully energy-dependent. This approach is implemented in a spherical shell, using either Chebyshev polynomials or Fourier series as decomposition bases. It is here restricted to simplified collision terms (isoenergetic scattering) and to the case of a static fluid. We finish this paper by presenting test results using basic configurations, including general relativistic ones in the Schwarzschild metric, in order to demonstrate the convergence properties, the conservation of particle number and correct treatment of some general relativistic effects of our code. The use of spectral methods enables to run our test cases in a six-dimensional setting on a single processor.