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Journal articles on the topic 'Harmonics functions'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Matsuoka, Osamu. "Molecular integrals over Laguerre Gaussian-type functions of real spherical harmonics." Canadian Journal of Chemistry 70, no. 2 (1992): 388–92. http://dx.doi.org/10.1139/v92-055.

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Molecular integrals are formulated over the Laguerre Gaussian-type functions (LGTF) of real spherical harmonics. They include the overlap integrals and the energy integrals of kinetic, nuclear attraction, and electron repulsion. For the nuclear-attraction integrals the formulations based on the point as well as the Gaussian nuclear charge distribution models are presented. Integral formulas over the LGTFs of real spherical harmonics are found a little more complicated than those of the LGTFs of complex spherical harmonics due to the summations over magnetic quantum numbers. Keywords: molecular

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2

Quintero, Niurka, José Cuesta, and Renato Alvarez-Nodarse. "Functionals of Harmonics Functions." Proceedings 2, no. 1 (2018): 17. http://dx.doi.org/10.3390/proceedings2010017.

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3

Singh, Saransh, Donald E. Boyce, Joel V. Bernier, and Nathan R. Barton. "Discrete spherical harmonic functions for texture representation and analysis." Journal of Applied Crystallography 53, no. 5 (2020): 1299–309. http://dx.doi.org/10.1107/s1600576720011097.

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A basis of discrete harmonic functions for efficient representation and analysis of crystallographic texture is presented. Discrete harmonics are a numerical representation of the harmonics on the sphere. A finite element formulation is utilized to calculate these orthonormal basis functions, which provides several advantageous features for quantitative texture analysis. These include high-precision numerical integration, a simple implementation of the non-negativity constraint and computational efficiency. Simple examples of pole figure and texture interpolation and of Fourier filtering using

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Foskolos, Georgios. "Measurement-Based Current-Harmonics Modeling of Aggregated Electric-Vehicle Loads Using Power-Exponential Functions." World Electric Vehicle Journal 11, no. 3 (2020): 51. http://dx.doi.org/10.3390/wevj11030051.

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This paper presents an aggregate current-harmonic load model using power exponential functions and built from actual measurement data during the individual charging of four different fully electric vehicles. The model is based on individual emitted current harmonics as a function of state of charge (SOC), and was used to deterministically simulate the simultaneous charging of six vehicles fed from the same bus. The aggregation of current harmonics up to the 11th was simulated in order to find the circumstances when maximal current-harmonic magnitude occurs, and the phase-angle location. The nu

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5

Juhas, Anamarija, and Ladislav A. Novak. "Maximally Flat Waveforms with Finite Number of Harmonics in Class-FPower Amplifiers." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/169590.

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In this paper general solution to the problem of finding maximally flat waveforms with finite number of harmonics (maximally flat trigonometric polynomials) is provided. Waveform coefficients are expressed in closed form as functions of harmonic orders. Two special cases of maximally flat waveforms (so-called maximally flat even harmonic and maximally flat odd harmonic waveforms), which proved to play an important role in class-Fand inverse class-Fpower amplifier (PA) operations, are also considered. For these two special types of waveforms, coefficients are expressed as functions of two param

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Kondratyuk, A. A. "SPHERICAL HARMONICS AND SUBHARMONIC FUNCTIONS." Mathematics of the USSR-Sbornik 53, no. 1 (1986): 147–67. http://dx.doi.org/10.1070/sm1986v053n01abeh002914.

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Gong, Mao Fa, Guo Liang Li, Wen Hua Xia, Qing Xue Liu, and Jing Jing Wang. "A New Method to Detect Harmonics and Inter-Harmonics Based on Hilbert Marginal Spectrum." Applied Mechanics and Materials 229-231 (November 2012): 1060–63. http://dx.doi.org/10.4028/www.scientific.net/amm.229-231.1060.

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Aiming at the problem that harmonic pollution is becoming more and more serious in power system, a new method to detect harmonics and inter-harmonics based on Hilbert marginal spectrum is proposed in this paper. Firstly, the original signal is decomposed into several Intrinsic Mode Functions through Empirical Mode Decomposition. Then Hilbert marginal spectrum is obtained through Hilbert Huang Transform. It contains the information of signal’s harmonics frequency and those amplitudes. Finally, both harmonics and inter-harmonics are detected by this method. Fourier transform lacks the ability of

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Zou, Wan Feng, and Lei Zhang. "An Active Power Filter Controller Based on Dual-DSPs in Low-Voltage Power System." Applied Mechanics and Materials 291-294 (February 2013): 2302–7. http://dx.doi.org/10.4028/www.scientific.net/amm.291-294.2302.

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To compensate harmonics from nonlinear load, the controller of Active Power Filter (APF) need to detect harmonic and generate compensation current in high speed. APF controller functions are divided into two parts: outside controller part and inside controller part. Inside controller part detect harmonic current and control the IGBT to generate grid harmonics current. Outside controller part detect common power parameters and generate signal of management in main circuit. An experiment circuit of APF Controller is established. Some experiments are presented here.

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9

NIKOLAEV, NIKOLAY Y., and HITOSHI IBA. "GENETIC PROGRAMMING OF POLYNOMIAL HARMONIC NETWORKS USING THE DISCRETE FOURIER TRANSFORM." International Journal of Neural Systems 12, no. 05 (2002): 399–410. http://dx.doi.org/10.1142/s0129065702001242.

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This paper presents a genetic programming system that evolves polynomial harmonic networks. These are multilayer feed-forward neural networks with polynomial activation functions. The novel hybrids assume that harmonics with non-multiple frequencies may enter as inputs the activation polynomials. The harmonics with non-multiple, irregular frequencies are derived analytically using the discrete Fourier transform. The polynomial harmonic networks have tree-structured topology which makes them especially suitable for evolutionary structural search. Empirical results show that this hybrid genetic

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Navascués, M. A. "Fractal Spherical Harmonics." International Journal of Analysis 2013 (May 13, 2013): 1–7. http://dx.doi.org/10.1155/2013/927368.

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This paper tackles the construction of fractal maps on the unit sphere. The functions defined are a generalization of the classical spherical harmonics. The methodology used involves an iterated function system and a linear and bounded operator of functions on the sphere. For a suitable choice of the coefficients of the system, one obtains classical maps on the sphere. The different values of the system parameters provide Bessel sequences, frames, and Riesz fractal bases for the Lebesgue space of the square integrable functions on the sphere. The Laplace series expansion is generalized to a su

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11

Zhukovsky, K. "Emission and tuning of harmonics in a planar two-frequency undulator with account for broadening." Laser and Particle Beams 34, no. 3 (2016): 447–56. http://dx.doi.org/10.1017/s0263034616000264.

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AbstractWe analyze the undulator radiation from planar bi-harmonic undulators with account for all principle losses in real devices. The exact analytical expressions for the UR spectrum, intensity, and the line shape are obtained in terms of special functions. The interplay of various broadening contribution is elucidated and their role is explored. Suspension and boost of certain harmonics by fine tuning the undulator parameters is demonstrated. The constant non-periodic magnetic constituents are studied to compensate the divergency of the electronic beam. The examples of harmonic generation

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12

Dunne, J. F. "Subharmonic-Response Computation and Stability Analysis for a Nonlinear Oscillator Using a Split-Frequency Harmonic Balance Method." Journal of Computational and Nonlinear Dynamics 1, no. 3 (2006): 221–29. http://dx.doi.org/10.1115/1.2198875.

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A split-frequency harmonic balance method (SF-HBM) is developed to obtain subharmonic responses of a nonlinear single-degree-of-freedom oscillator driven by periodic excitation. This method is capable of generating highly accurate periodic solutions involving a large number of solution harmonics. Responses at the excitation period, or corresponding multiples (such as period 2 and period 3), can be readily obtained with this method, either in isolation or as combinations. To achieve this, the oscillator equation error is first expressed in terms of two Mickens functions, where the assumed Fouri

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Dunkl, Charles F. "Symmetric functions andBN-invariant spherical harmonics." Journal of Physics A: Mathematical and General 35, no. 48 (2002): 10391–408. http://dx.doi.org/10.1088/0305-4470/35/48/312.

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Do, Van Dong, Thien Phu Le, and Alexis Beakou. "Operational modal analysis of mechanical systems using transmissibility functions in the presence of harmonics." Journal of Science and Technology in Civil Engineering (STCE) - NUCE 13, no. 3 (2019): 1–14. http://dx.doi.org/10.31814/stce.nuce2019-13(3)-01.

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Ambient vibration testing is a preferred technique for heath monitoring of civil engineering structures because of several advantages such as simple equipment, low cost, continuous use and real boundary conditions. However, the excitation not controlled and not measured, is always assumed as Gaussian white noise in the processing of ambient responses called operational modal analysis. In presence of harmonics due to rotating parts of machines or equipment inside the structures, e.g., fans or air-conditioners…, the white noise assumption is not verified and the response analysis becomes difficu

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Danes, Leandro, and Andrea Vacca. "A Tandem Axial-Piston Unit Based Strategy for the Reduction of Noise Sources in Hydraulic Systems." Energies 13, no. 20 (2020): 5377. http://dx.doi.org/10.3390/en13205377.

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This article presents a novel passive fluid borne noise source reduction strategy, based on tandem axial-piston unit indexing with the usage of symmetric lines. The strategy consists of setting the phase between the two synchronous units to accomplish destructive interference in targeted unit harmonics. A strategy capable of achieving destructive interference in all odd harmonics is investigated first analytically and then confirmed by a simulation study. Experiments on the proposed strategy confirmed its effectiveness at the first and third pump fundamental harmonics, and pressure ripple redu

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Schwanz, Daphne, Math Bollen, Oscar Lennerhag, and Anders Larsson. "Harmonic Transfers for Quantifying Propagation of Harmonics in Wind Power Plants." Energies 14, no. 18 (2021): 5798. http://dx.doi.org/10.3390/en14185798.

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In this paper, primary and secondary emissions in wind power plants are studied by using transfer admittance and current transfer functions between turbines and the public grid. The use of such transfer functions allows harmonic propagation studies without knowledge of the emission from individual turbines or the background voltage distortion. The transfer functions are calculated for one synthetic and one existing wind power plant, and results are discussed. Primary emission, secondary emission from other turbines and secondary emission from the public grid are shown to be of the same order o

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Zhukovsky, K. "Theoretical spectral analysis of FEL radiation from multi-harmonic undulators." Journal of Synchrotron Radiation 27, no. 6 (2020): 1648–61. http://dx.doi.org/10.1107/s1600577520012230.

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A theoretical study of the spontaneous and stimulated undulator radiation (UR) from electrons in undulators with multiple periods in both transversal directions is presented. Exact expressions are derived for the UR intensities in terms of the generalized Bessel and Airy functions, accounting for undulator field harmonics of arbitrary strength and for real parameters of the beams and installations. Theoretical results are verified with numerical and experimental data for SWISS-XFEL, PAL-XFEL, LEUTL, LCLS etc. The spectrum, UR line shape and width, and the harmonic evolution along the undulator

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18

Liu, Liyan, Carlos Lozano, and Dan Iredell. "Time–Space SST Variability in the Atlantic during 2013: Seasonal Cycle." Journal of Atmospheric and Oceanic Technology 32, no. 9 (2015): 1689–705. http://dx.doi.org/10.1175/jtech-d-15-0028.1.

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AbstractA 2-yr-long daily gridded field of sea surface temperature (SST) in the Atlantic centered for the year 2013 is projected onto orthogonal components: its mean, six harmonics of the year cycle, the slow-varying contribution, and the fast-varying contribution. The periodic function defined by the year harmonics, referred to here as the seasonal harmonic, contains most of the year variability in 2013. The seasonal harmonic is examined in its spatial and temporal distribution by describing the amplitude and phase of its maxima and minima, and other associated parameters. In the seasonal har

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Zhukovsky, Konstantin, and Igor Fedorov. "Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields." Symmetry 13, no. 1 (2021): 135. http://dx.doi.org/10.3390/sym13010135.

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In this work, the radiation from electrons in multi-periodic undulator fields with symmetric and asymmetric harmonics was analyzed using generalized Bessel functions formalism. The asymmetric, symmetric, and anti-symmetric periodic magnetic fields with harmonics were studied in order to get the enhanced radiation of the high harmonics of undulator radiation (UR). The effect on the spontaneous and stimulated UR was explored. The exact integral forms for the Bessel coefficients were obtained for undulators with general symmetric and asymmetric field harmonics. Spectral properties of the radiatio

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20

Volkmer, Hans. "Expansions of analytic functions in spherical harmonics." Complex Variables, Theory and Application: An International Journal 35, no. 3 (1998): 213–24. http://dx.doi.org/10.1080/17476939808815084.

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21

Nassim Kraimia, Mohamed, and Mohamed Boudour. "Harmonic interaction of a static Var compensator with AC power system containing multiple non-linear loads." Engineering review 40, no. 3 (2020): 21–31. http://dx.doi.org/10.30765/er.40.3.03.

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In this paper a study of the impact of the harmonics generated by a static Var compensator (SVC) is presented. The SVC is modeled, in the harmonic domain, as a coupled current source by using the complex Fourier transforms. Then, this model is converted to polar form to be integrated into the harmonic power flow program. This approach has been carried out on the IEEE 14 bus test power system, in order to show its effectiveness in evaluating the impact of harmonics, injected by the shunt compensating devices, and its interaction with the AC transmission system, in meshed power networks. Since t

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22

SHOJAEI, M. R., A. A. RAJABI, and H. HASANABADI. "HYPER-SPHERICAL HARMONICS AND ANHARMONICS IN m-DIMENSIONAL SPACE." International Journal of Modern Physics E 17, no. 06 (2008): 1125–30. http://dx.doi.org/10.1142/s0218301308010398.

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In quantum mechanics the hyper-spherical method is one of the most well-established and successful computational tools. The general theory of harmonic polynomials and hyper-spherical harmonics is of central importance in this paper. The interaction potential V is assumed to depend on the hyper-radius ρ only where ρ is the function of the Jacobi relative coordinate x1, x2,…, xn which are functions of the particles' relative positions.

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23

Beauchamp, James W. "Trombone Transfer Functions: Comparison Between Frequency-Swept Sine Wave and Human Performer Input." Archives of Acoustics 37, no. 4 (2012): 447–54. http://dx.doi.org/10.2478/v10168-012-0056-x.

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Abstract Source/filter models have frequently been used to model sound production of the vocal apparatus and musical instruments. Beginning in 1968, in an effort to measure the transfer function (i.e., transmission response or filter characteristic) of a trombone while being played by expert musicians, sound pressure signals from the mouthpiece and the trombone bell output were recorded in an anechoic room and then subjected to harmonic spectrum analysis. Output/input ratios of the signals’ harmonic amplitudes plotted vs. harmonic frequency then became points on the trombone’s transfer functio

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Kim, Yee-Joon, Marcia Grabowecky, Ken A. Paller, and Satoru Suzuki. "Differential Roles of Frequency-following and Frequency-doubling Visual Responses Revealed by Evoked Neural Harmonics." Journal of Cognitive Neuroscience 23, no. 8 (2011): 1875–86. http://dx.doi.org/10.1162/jocn.2010.21536.

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Frequency-following and frequency-doubling neurons are ubiquitous in both striate and extrastriate visual areas. However, responses from these two types of neural populations have not been effectively compared in humans because previous EEG studies have not successfully dissociated responses from these populations. We devised a light–dark flicker stimulus that unambiguously distinguished these responses as reflected in the first and second harmonics in the steady-state visual evoked potentials. These harmonics revealed the spatial and functional segregation of frequency-following (the first ha

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Cerejeiras, P., U. Kähler, and R. Lávička. "Generating Functions for Spherical Harmonics and Spherical Monogenics." Advances in Applied Clifford Algebras 24, no. 4 (2014): 995–1004. http://dx.doi.org/10.1007/s00006-014-0495-8.

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Vazquez, Jon, Jose Felix Miñambres, Miguel Angel Zorrozua, and Jorge Lázaro. "Phasor Estimation of Transient Electrical Signals Composed of Harmonics and Interharmonics." Energies 14, no. 16 (2021): 5166. http://dx.doi.org/10.3390/en14165166.

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Numerical relays have become essential tools for carrying out the protection and surveillance tasks of electrical power systems. These relays implement their functions from the phasors of the electrical network signals, estimated by digital processing using digital filters. Digital filters must meet certain requirements, such as providing a fast and effective response to increasingly complex transient signals made up of components that make the estimation process difficult. In addition to the decreasing exponential (decaying dc offset), harmonics, and signal noise, it must be added that the in

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Dray, Tevian. "A unified treatment of Wigner D functions, spin‐weighted spherical harmonics, and monopole harmonics." Journal of Mathematical Physics 27, no. 3 (1986): 781–92. http://dx.doi.org/10.1063/1.527183.

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Faham, M. A. A. M., and H. M. Nasir. "Weakly Orthogonal Spherical Harmonics in a Non-Polar Spherical Coordinates and its Application to Functions on Cubed-Sphere." Sultan Qaboos University Journal for Science [SQUJS] 17, no. 2 (2012): 200. http://dx.doi.org/10.24200/squjs.vol17iss2pp200-213.

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In a recent paper (Nasir, 2007), a set of weakly orthogonal and completely orthogonal spherical harmonics in a non-polar spherical coordinate system based on a cubed-sphere was constructed. In this work, we explore some linear relations between these two sets of spherical harmonics. Moreover, a power representation for the set of weakly orthogonal spherical harmonics corresponding to a mode is presented. We also determine the norm of the orthogonal spherical harmonics and hence the inner products for the weakly orthogonal spherical harmonics. As an immediate application of these properties, we

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Roxburgh, I. W., and S. V. Vorontsov. "Simulated Power Spectra of Solar-Type Oscillations Driven by an Elementary Excitation Source." International Astronomical Union Colloquium 155 (1995): 111–12. http://dx.doi.org/10.1017/s0252921100036861.

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AbstractWe consider the synthetic power spectra of multi-mode solar-type acoustic oscillations in stars, computed within a general framework of the linear response of the dynamical system to an arbitrary excitation force which is decomposed in spherical harmonics in space and harmonic functions in time. We discuss possible signatures in the observational data which might be used as diagnostics of the excitation source.

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Schaeben, H. "The de la Vallée Poussin Standard Orientation Density Function." Textures and Microstructures 33, no. 1-4 (1999): 365–73. http://dx.doi.org/10.1155/tsm.33.365.

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The de la Vallée Poussin standard orientation density function νκ(ω)=C(κ)cos⁡2κ(ω/2) is discussed with emphasis on the finiteness of its harmonic series expansion which, advantageously distinguishes it from other known standard functions. Given its halfwidth, the de la Vallée Poussin standard orientation density function allows, for example, to tabulate the degree of series expansion into harmonics required for its exact representation.

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31

DELBOURGO, R. "GRASSMANN WAVE FUNCTIONS AND INTRINSIC SPIN." International Journal of Modern Physics A 03, no. 03 (1988): 591–602. http://dx.doi.org/10.1142/s0217751x88000242.

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By associating spin angular momentum with Sp(2) transformations on two Grassmann coordinates, we show how one may formulate spinor wave functions in complete analogy to spherical harmonics for orbital momentum. The relativistic generalization requires a doubling of Grassmann coordinates and a connection may be established with the Dirac equation.

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Nortje, Caitlin R., Wil O. C. Ward, Bartosz P. Neuman, and Li Bai. "Spherical Harmonics for Surface Parametrisation and Remeshing." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/582870.

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This paper proposes a novel method for parametrisation and remeshing incomplete and irregular polygonal meshes. Spherical harmonics basis functions are used for parametrisation. This involves least squares fitting of spherical harmonics basis functions to the surface mesh. Tikhonov regularisation is then used to improve the parametrisation before remeshing the surface. Experiments show that the proposed techniques are effective for parametrising and remeshing polygonal meshes.

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Ramillien, Guillaume, Lucía Seoane, and José Darrozes. "An Innovative Slepian Approach to Invert GRACE KBRR for Localized Hydrological Information at the Sub-Basin Scale." Remote Sensing 13, no. 9 (2021): 1824. http://dx.doi.org/10.3390/rs13091824.

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GRACE spherical harmonics are well-adapted for representation of hydrological signals in river drainage basins of large size such as the Amazon or Mississippi basins. However, when one needs to study smaller drainage basins, one comes up against the low spatial resolution of the solutions in spherical harmonics. To overcome this limitation, we propose a new approach based on Slepian functions which can reduce the energy loss by integrating information in the spatial, spectral and time domains. Another advantage of these regionally-defined functions is the reduction of the problem dimensions co

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Solberg Eikrem, Kjersti. "Random Harmonic Functions in Growth Spaces and Bloch-type Spaces." Canadian Journal of Mathematics 66, no. 2 (2014): 284–302. http://dx.doi.org/10.4153/cjm-2013-029-7.

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Abstract. Let h∞v (D) and h∞v (B) be the spaces of harmonic functions in the unit disk and multidimensional unit ball admitting a two-sided radial majorant v(r). We consider functions v that fulfill a doubling condition. In the two-dimensional case letwhere ξ ={ξji} is a sequence of random subnormal variables and aji are real. In higher dimensions we consider series of spherical harmonics. We will obtain conditions on the coefficients aji that imply that u is in h∞v (B) almost surely. Our estimate improves previous results by Bennett, Stegenga, and Timoney, and we prove that the estimate is sh

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Moretti, Valter, and Davide Pastorello. "Generalized Complex Spherical Harmonics, Frame Functions, and Gleason Theorem." Annales Henri Poincaré 14, no. 5 (2012): 1435–43. http://dx.doi.org/10.1007/s00023-012-0220-x.

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Claessens, S. J. "New relations among associated Legendre functions and spherical harmonics." Journal of Geodesy 79, no. 6-7 (2005): 398–406. http://dx.doi.org/10.1007/s00190-005-0483-9.

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Liang, Ying Yu, Xing Tao Xu, Jian Zheng Liu, Yi Wang, and Qi Xun Yang. "A Shunt Active Filter Based on Voltage Detection for Harmonic Filtering and Resonance Suppression." Applied Mechanics and Materials 457-458 (October 2013): 1113–17. http://dx.doi.org/10.4028/www.scientific.net/amm.457-458.1113.

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In most occasions shunt APFs and capacitors used for power factor correction exist simultaneously in the distribution network for saving costs. Ideally, APFs are used for harmonics filtering and capacitors are used for power factor correction. However, traditional control methods of APF have potential risk of resonance, affecting the stability and the effect of harmonic compensation, if the detected current contains capacitive current. This paper proposes a new control method based on voltage detection of point of common Coupling(PCC). Theoretical analysis and simulation demonstrate the new co

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Selmi, Hassib, Mohamed Abdelwahed, Hatem Hamda, and Lassaad El Asmi. "The FMM-BEM Method for the 3D Particulate Stokes Flow." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/563603.

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This work introduces new functions based on the spherical harmonics and the solid harmonics which have been used to construct a multipole development for the 3D Stokes problem in order to reduce the operations costs in the BEM method. We show that the major properties of those functions are inherited from the solid harmonics. The contribution of this paper is the introduction of new formulas that serve to calculate the multipole moments and the transfer functions that are necessary for the schemes of orderO(NlogN). Moreover, new translation formulas are introduced to obtain anO(N)scheme. The e

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Sampath, Namratha, and P. V. S. S. A. Parimala. "D-STATCOM Control using SRFT Method for PQ Improvement in a PV System." Regular issue 10, no. 8 (2021): 113–19. http://dx.doi.org/10.35940/ijitee.h9261.0610821.

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The set of restrictions defined for a system's electrical characteristics so that the entire electrical system can function in the intended manner and without losses is known as power quality. Power quality issues such as transients, harmonics, voltage swell, sag, flicker, fluctuations, and power factor difficulties are becoming more common as power electronic devices become more widely used. The usage of a Distribution Static Compensator (D-STATCOM) to mitigate power quality issues is discussed in this study. In this case, D-STATCOM functions as a shunt active power filter to reduce harmonics

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Kim, Hyung Chul, Moon Seob Han, Hyun June Park, Dong Uk Jang, Gyung Suk Kil, and Nirmal Kumar Nair. "Consideration of Uncertainty in Diagnosis for Railway Arrester." Key Engineering Materials 321-323 (October 2006): 1507–12. http://dx.doi.org/10.4028/www.scientific.net/kem.321-323.1507.

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This paper presents a method for diagnosis of railway arrester considering uncertainty. Arresters, a protective device that prevents damage due to transient voltages, deteriorate due to the absorption of moisture, repetitive operation during over-voltages and manufacturing defects. Various diagnostic techniques are available for monitoring deterioration of arresters. The technique based on the amplitude of leakage current measures the root mean square or peak values of leakage current components. After measuring the total leakage current, harmonics of leakage current components are analyzed by

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Dwi Ade Saputra, G. A. M., I. Wayan Rinas, and I. Made Suartika. "Studi Analisis Pengaruh Filter Aktif Berbasis Fuzzy Logic Controller Untuk Mereduksi Harmonisa Akibat Beban Non Linier." Jurnal SPEKTRUM 6, no. 2 (2019): 24. http://dx.doi.org/10.24843/spektrum.2019.v06.i02.p04.

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Electrical equipment categorized as the nonlinear load will cause harmonics. Harmonic is a periodic distortion of the sine wave that can cause a negative impact on electronic equipment components. One way to improve power quality is to reduce harmonics using harmonic filters. In this study, an analysis of the system was carried out before adding a filter and after adding an active filter based on a fuzzy logic controller. The application of the fuzzy logic method on filters functions to reduce over switching in the inverter so that it can reach the lowest THDi value. THDi simulation results wh

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ERMANYUK, E. V., J. B. FLÓR, and B. VOISIN. "Spatial structure of first and higher harmonic internal waves from a horizontally oscillating sphere." Journal of Fluid Mechanics 671 (February 10, 2011): 364–83. http://dx.doi.org/10.1017/s0022112010005719.

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An experimental study is presented on the spatial structure of the internal wave field emitted by a horizontally oscillating sphere in a uniformly stratified fluid. The limits of linear theory and the nonlinear features of the waves are considered as functions of oscillation amplitude. Fourier decomposition is applied to separate first harmonic waves at the fundamental frequency and higher harmonic waves at multiples of this frequency. For low oscillation amplitude, of 10% of the sphere radius, only the first harmonic is significant and the agreement between linear theory and experiment is exc

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Chang, Gary W., Yu-Luh Lin, Yu-Jen Liu, Gary H. Sun, and Johnson T. Yu. "A Hybrid Approach for Time-Varying Harmonic and Interharmonic Detection Using Synchrosqueezing Wavelet Transform." Applied Sciences 11, no. 2 (2021): 752. http://dx.doi.org/10.3390/app11020752.

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With widespread non-linear loads and the increasing penetration of distributed generations in the power system, harmonic pollution has become a great concern. The causes of harmonic pollution not only include the integer harmonics, but also interharmonics, which exacerbate the complexity of harmonic analysis. In addition, the output variability of highly non-linear loads and renewables such as electric arc furnaces and photovoltaic solar or wind generation may lead to weakly time-varying harmonics and interharmonics in both frequency and magnitude. These features present challenges for accurat

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Medjber, Salim, Hacene Bekkar, Salah Menouar, and Jeong Ryeol Choi. "Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System." Advances in Mathematical Physics 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/3693572.

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The Schrödinger solutions for a three-dimensional central potential system whose Hamiltonian is composed of a time-dependent harmonic plus an inverse harmonic potential are investigated. Because of the time-dependence of parameters, we cannot solve the Schrödinger solutions relying only on the conventional method of separation of variables. To overcome this difficulty, special mathematical methods, which are the invariant operator method, the unitary transformation method, and the Nikiforov-Uvarov method, are used when we derive solutions of the Schrödinger equation for the system. In particul

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Schettino, Ala, Caruso, et al. "Experimental Study on B-Spline-Based Modulation Schemes Applied in Multilevel Inverters for Electric Drive Applications." Energies 12, no. 23 (2019): 4521. http://dx.doi.org/10.3390/en12234521.

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This work presents the design, simulation, and experimental validation of new B-Spline-based modulation techniques applied to a Multilevel Power Inverter (MPI), particularly focusing the attention on the harmonic content of the output voltages of the inverter. Simulation and experimental results are proposed and discussed, mainly describing the potential benefits, such as the increase of the multi-level operation of the converter, and drawbacks (low-order harmonics) related to the adoption of B-Spline functions for multilevel inverters applied in the field of electrical drives.

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Winch, D. E., and P. H. Roberts. "Derivatives of addition theorems for Legendre functions." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 37, no. 2 (1995): 212–34. http://dx.doi.org/10.1017/s0334270000007670.

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AbstractDifferentiation of the well-known addition theorem for Legendre polynomials produces results for sums over order m of products of various derivatives of associated Legendre functions. The same method is applied to the corresponding addition theorems for vector and tensor spherical harmonics. Results are also given for Chebyshev polynomials of the second kind, corresponding to ‘spin-weighted’ associated Legendre functions, as used in studies of distributions of rotations.

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Maintz, S., M. Esser, and R. Dronskowski. "Efficient Rotation of Local Basis Functions Using Real Spherical Harmonics." Acta Physica Polonica B 47, no. 4 (2016): 1165. http://dx.doi.org/10.5506/aphyspolb.47.1165.

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Han, Deokhwa, Ho Yun, and Changdon Kee. "Modeling of Ionospheric Delay for SBAS Using Spherical Harmonics Functions." TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation 7, no. 2 (2013): 205–9. http://dx.doi.org/10.12716/1001.07.02.07.

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Glomb, Katharina, Morten L. Kringelbach, Gustavo Deco, Patric Hagmann, Joel Pearson, and Selen Atasoy. "Functional harmonics reveal multi-dimensional basis functions underlying cortical organization." Cell Reports 36, no. 8 (2021): 109554. http://dx.doi.org/10.1016/j.celrep.2021.109554.

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Lang, Moritz, and Mikhail Shkolnikov. "Harmonic dynamics of the abelian sandpile." Proceedings of the National Academy of Sciences 116, no. 8 (2019): 2821–30. http://dx.doi.org/10.1073/pnas.1812015116.

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The abelian sandpile is a cellular automaton which serves as the archetypical model to study self-organized criticality, a phenomenon occurring in various biological, physical, and social processes. Its recurrent configurations form an abelian group, whose identity is a fractal composed of self-similar patches. Here, we analyze the evolution of the sandpile identity under harmonic fields of different orders. We show that this evolution corresponds to periodic cycles through the abelian group characterized by the smooth transformation and apparent conservation of the patches constituting the id

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