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Journal articles on the topic 'Harmonic complexity'

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Published: 7 July 2024
Last updated: 7 July 2024

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1

Ghodake, Pravinkumar. "The complexity of harmonically scattered nonlinear waves from triangular, circular, and rectangular corners of the 2-D domain." Journal of the Acoustical Society of America 154, no. 4_supplement (October 1, 2023): A262. http://dx.doi.org/10.1121/10.0023468.

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Considering recent advancements in the nonlinear pulse-echo technique, understanding reflected nonlinear waves from inaccessible edges and surfaces becomes important. A unique geometrical model solved numerically using the finite element method is proposed and studied via extensive numerical experiments to gain insight into harmonically scattered waves from different shapes of the 2-D spaced corners considering the challenges of theoretical solutions that can capture the interplay between multiple phenomena. Tang et al. (2012), Kube (2017-18), and Achenbach and Wang (2017-18) studied the harmonic scattering of waves from nonlinear inclusions using analytical techniques. Linear longitudinal waves scattered from the triangular, circular, and rectangular-shaped free and fixed edges of the 2-D spaced corner show mode conversion and energy transfer between bulk wave modes at fundamental frequencies. The interaction of nonlinear ultrasonic waves with the edges makes things complex due to an interplay between harmonic generation, linear scattering, harmonic scattering, bulk wave mode conversion, and harmonic energy redistribution between all harmonics of the scattered longitudinal and transverse waves. This results in non-intuitive interesting responses. These studies are extended to explore one-way and two-way two-wave mixing of longitudinal waves and their interesting nonlinear effects. Phase difference introduced during harmonic scattering distinguishes the sensitivity of fundamental harmonics.
2

Abdullah, Muhammad, Tahir N. Malik, Ali Ahmed, Muhammad F. Nadeem, Irfan A. Khan, and Rui Bo. "A Novel Hybrid GWO-LS Estimator for Harmonic Estimation Problem in Time Varying Noisy Environment." Energies 14, no. 9 (May 1, 2021): 2587. http://dx.doi.org/10.3390/en14092587.

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The power quality of the Electrical Power System (EPS) is greatly affected by electrical harmonics. Hence, accurate and proper estimation of electrical harmonics is essential to design appropriate filters for mitigation of harmonics and their associated effects on the power quality of EPS. This paper presents a novel statistical (Least Square) and meta-heuristic (Grey wolf optimizer) based hybrid technique for accurate detection and estimation of electrical harmonics with minimum computational time. The non-linear part (phase and frequency) of harmonics is estimated using GWO, while the linear part (amplitude) is estimated using the LS method. Furthermore, harmonics having transients are also estimated using proposed harmonic estimators. The effectiveness of the proposed harmonic estimator is evaluated using various case studies. Comparing the proposed approach with other harmonic estimation techniques demonstrates that it has a minimum mean square error with less complexity and better computational efficiency.
3

Bernasconi, A. "Harmonic analysis and Boolean function complexity." Calcolo 35, no. 3 (November 1, 1998): 149–86. http://dx.doi.org/10.1007/s100920050014.

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4

Witek, Maria A. G., Tomas Matthews, Rebeka Bodak, Marta W. Blausz, Virginia Penhune, and Peter Vuust. "Musicians and non-musicians show different preference profiles for single chords of varying harmonic complexity." PLOS ONE 18, no. 2 (February 2, 2023): e0281057. http://dx.doi.org/10.1371/journal.pone.0281057.

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The inverted U hypothesis in music predicts that listeners prefer intermediate levels of complexity. However, the shape of the liking response to harmonic complexity and the effect of musicianship remains unclear. Here, we tested whether the relationship between liking and harmonic complexity in single chords shows an inverted U shape and whether this U shape is different for musicians and non-musicians. We recorded these groups’ liking ratings for four levels of harmonic complexity, indexed by their level of acoustic roughness, as well as several measures of inter-individual difference. Results showed that there is an inverted U-shaped relationship between harmonic complexity and liking in both musicians and non-musicians, but that the shape of the U is different for the two groups. Non-musicians’ U is more left-skewed, with peak liking for low harmonic complexity, while musicians’ U is more right-skewed, with highest ratings for medium and low complexity. Furthermore, musicians who showed greater liking for medium compared to low complexity chords reported higher levels of active musical engagement and higher levels of openness to experience. This suggests that a combination of practical musical experience and personality is reflected in musicians’ inverted U-shaped preference response to harmonic complexity in chords.
5

Williams, Lindsey R. "Effect of Music Training and Musical Complexity on Focus of Attention to Melody or Harmony." Journal of Research in Music Education 53, no. 3 (October 2005): 210–21. http://dx.doi.org/10.1177/002242940505300303.

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The purpose of this study was to investigate the relationships between music training and musical complexity and focus of attention to melody or harmony. Participants ( N= 192) were divided into four groups: university jazz majors ( n= 64), other university music majors ( n= 64), high school instrumentalists ( n= 32), and junior high instrumentalists ( n= 32). The musical complexity variable consisted of four levels of melodic complexity and four levels of harmonic complexity each paired for a total of 16 possible combinations all heard by each participant. Each trial consisted of a melodic complexity/harmonic complexity pairing performed by the same performer on jazz piano. Subjects indicated their overall perceived focus of attention for melody or harmony either during or immediately after they listened. A four-factor ANOVA was conducted with two between-subjects factors (order and music-training groups) and two within-subjects factors (melodic complexity and harmonic complexity). Significant differences were found for focus of attention for both melodic complexity and harmonic complexity. Significant interactions occurred between music training and focus of attention. Overall, data showed that as music training increases, so does harmonic focus of attention. March 11, 2005 October 4, 2005
6

Xu, Wanwan, Bin Wang, Jiang Liu, and Da Li. "An Improved Droop Control Strategy for Grid-Connected Inverter Applied in Grid Voltage Inter-Harmonics and Fundamental Frequency Fluctuation." Electronics 10, no. 15 (July 30, 2021): 1827. http://dx.doi.org/10.3390/electronics10151827.

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This paper presents a current suppression method based on a droop control strategy under distorted grid voltage with inter-harmonics and fundamental frequency fluctuation. In this proposed strategy, the current incomplete derivation controller is employed to decrease the negative impact caused by harmonic and inter-harmonic grid voltage. This method provides a good dynamic response and has low complexity against the inter-harmonics with unfixed fundamental frequency. Based on a mathematical model of the grid-connected inverter, we designed novel instantaneous frequency detection and feed-forward methods to suppress the grid fundamental frequency fluctuation impacts. Then the main parameters were analyzed. The simulation and experimental results verified the feasibility and effectiveness of the proposed method.
7

Yanagawa, Kazunori, Ayane Fujihira, Hideki Yamaguchi, and Nozomu Yoshizawa. "Describing the characteristics of light field in architectural spaces using spherical harmonic function." IOP Conference Series: Earth and Environmental Science 1099, no. 1 (November 1, 2022): 012014. http://dx.doi.org/10.1088/1755-1315/1099/1/012014.

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Abstract The direction, density, and diffusivity of light are important indicators of spatial characteristics in describing a three-dimensional light environment. Mury presented a method for describing, measuring, and visualizing the structure of light fields using spherical harmonics in terms of changes in the density and direction of light in three-dimensional space. We extended this study by using higher-order spherical harmonics, which would represent more diverse characteristics of the light environment. We also quantitatively described the light environment as numerical values and investigated the correspondence between these numerical values and human perceptual quantities. As a result, we confirmed that there is a certain degree of correspondence between the “complexity” quantified by the spherical harmonic and the “complexity” perceived by people when observing real space.
8

Shao, Kunming, Mingjian Zhao, Jiachun Zheng, Guangsen Zeng, Bin Li, Biyun Ma, and Zhaohui Wu. "A high-precision harmonic distortion measurement algorithm and its system design based on time-domain matrix operations." Journal of Physics: Conference Series 2290, no. 1 (June 1, 2022): 012109. http://dx.doi.org/10.1088/1742-6596/2290/1/012109.

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Abstract In this paper, a harmonic distortion measurement algorithm and its system design based on time-domain matrix operations are proposed, which can quickly calculate the harmonic amplitudes, phases and total harmonic distortion of a signal. To realize the calculation of harmonic signal parameters in the time domain, we proposed a method to convert the nonlinear function representing the signal into a linear function, constructed a matrix equation, and solved the equation by the row transformation method, which significantly reduced the complexity of the algorithm. Finally, based on the proposed algorithm, a system design was implemented by the digital signal processing theory, and the measurements showed that the system achieves an amplitude error of nearly 1% and a THD error of less than 0.3% when measuring the generated 10 kHz fundamental with 5-order harmonics. The system can be used to measure and calculate the amplitudes and THD of harmonic distortion signals with high precision.
9

Hadiprayitno, Kasidi. "Relasitas Lakuan Wayang dengan Iringan Gamelan Gagrag Yogyakarta." Dance and Theatre Review 4, no. 1 (June 13, 2021): 21–35. http://dx.doi.org/10.24821/dtr.v4i1.4923.

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ABSTRAKMaksud dari penulisan ini adalah mengadakan studi terhadap relasitas lakuan gerak wayang gaya pedalangan Yogyakarta dengan musik iringan wayang. Data diperoleh dari pengamatan dan survei pergelaran wayang yang diselenggarakan di Sasana Hinggil Dwi Abad Yogyakarta. Pendekatan masalah dengan metode deskriptif analitis, sedangkan untuk kepentingan pembahasan dengan menggunakan analisis estetika terutama estetika pewayangan. Berdasarkan analisis yang dilakukan, diketahui bahwa lakuan gerak wayang dengan iringan wayang membentuk jalinan harmonik. Gending iringan wayang meliputi bentuk gending ageng, ladrangan, ketawang, lancaran, playon dan sampak, sedangkan dari segi estetik memenuhi kesatuan atau keutuhan, kekuatan, dan kerumitan (unity, intencity, dan complexcity).Kata kuci: Pertunjukan wayang, relasi gerak wayang dan gamelan, struktur harmonik ABSTRACTThe purpose of this is to conduct a study of the behavior of Yogyakarta puppet style movements with puppet accompaniment music. Data obtained from observations and surveys of wayang performances held at Sasana Hinggil Dwi Abad Yogyakarta. Approach to the problem with the analytical descriptive method, while for the purpose of discussion using aesthetic analysis, especially puppet aesthetics. Based on the analysis carried out, it is known that the wayang movements with accompaniment form a harmonic structure. Puppet accompaniment gending includes the forms of gending ageng, ladrangan, ketawang, lancaran, playon and sampak, while in terms of aesthetics it takes care of unity or integrity, strength, and complexity (unity, intencity, and complexcity).Key word: Wayang performance, relation of movement and music, harmonic structure.
10

Hachemi, Glaoui, Harrouz Abdelkader, and Dehini Rachid. "Optimal Sizing of Passive Filters for Typical Industrial Power Systems." Applied Mechanics and Materials 905 (February 15, 2022): 65–77. http://dx.doi.org/10.4028/p-u37f6q.

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Because of The low complexity of passive filters (PF) compared to the active filter, their high efficiency, their ease of installation and their different topologies,theyremained the devices required in the power system. In order to minimize the harmonic distortion produced by the large industrial loads, harmonic filters should, therefore, be designed with the utmost rigor, because a poorly designed filter may amplify the undesired harmonics. The determination of the PFcomponents requires both adetailed study ofthe power system parameters, which influence the efficiency and economic viability of the harmonic compensation and the reactive power required by the load.This article studies the use of the Cuckoo optimization algorithm (COA), in order to designpassive filters with an improved power quality and reduced cost. The optimal filters are connected concurrently to the power system so that each individual Harmonic distortion respects the recommended limits. The results show that the optimized (PF) is effective, and has a lower cost.
11

Hernández-Gómez, Juan, J. Méndez-Bermúdez, José Rodríguez, and José M. Sigarreta. "Harmonic Index and Harmonic Polynomial on Graph Operations." Symmetry 10, no. 10 (October 1, 2018): 456. http://dx.doi.org/10.3390/sym10100456.

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Some years ago, the harmonic polynomial was introduced to study the harmonic topological index. Here, using this polynomial, we obtain several properties of the harmonic index of many classical symmetric operations of graphs: Cartesian product, corona product, join, Cartesian sum and lexicographic product. Some upper and lower bounds for the harmonic indices of these operations of graphs, in terms of related indices, are derived from known bounds on the integral of a product on nonnegative convex functions. Besides, we provide an algorithm that computes the harmonic polynomial with complexity O ( n 2 ) .
12

Abdollahi, Rohollah. "Harmonic reduction using a novel multipulse AC-DC converter." World Journal of Engineering 15, no. 4 (August 6, 2018): 520–30. http://dx.doi.org/10.1108/wje-11-2017-0353.

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Purpose For direct torque controlled induction motor drives, an effective solution to eliminate harmonics is the use of multipulse alternating current (AC)-direct current (DC) converters. Many researchers have used different configurations based on 24- and 30-pulse rectifications for improved power quality. However, the total harmonic distortion (THD) of AC mains current with these topology is more than 4 per cent when operating at a light load. For mitigating the THD problems observed in the input currents, Abdollahi propose 40-, 72- and 88-pulse AC-DC converters, while the power quality enhancement was the main concern. It is known that by increasing the number of pulses further results in reduction in current harmonics, but this is accompanied by an increase in cost and complexity. In this context, the purpose of this paper is to design a new delta/hexagon transformer based 36-pulse AC-DC converter for harmonic reduction without increasing the cost and complexity. Design/methodology/approach The proposed converter consists of two paralleled 18-pulse AC-DC converters involving a nine-phase shifted uncontrolled diode bridges with an interphase transformer circuit. Findings In this paper, the proposed scheme is simulated by matrix laboratory (MATLAB)/SIMULINK considering different loading scenarios. The simulation results show that the proposed scheme improves the power quality indices and satisfies the The Institute of Electrical and Electronics Engineers (IEEE)-519 requirements at the point of common coupling. Also, a laboratory prototype is implemented using the proposed design, and the experimental results confirm the simulation results under different loading conditions. Originality/value The proposed solution is a tradeoff among the pulse number, the transformer platform, the complexity of the scheme and the cost. The proposed scheme has an optimized configuration in this regard.
13

Nutku, Ferhat, K. D. Sen, and Ekrem Aydiner. "Complexity study of q-deformed quantum harmonic oscillator." Physica A: Statistical Mechanics and its Applications 533 (November 2019): 122041. http://dx.doi.org/10.1016/j.physa.2019.122041.

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14

Mukherjee, Neetik, and Amlan K. Roy. "Some complexity measures in confined isotropic harmonic oscillator." Journal of Mathematical Chemistry 57, no. 7 (June 15, 2019): 1806–21. http://dx.doi.org/10.1007/s10910-019-01039-8.

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15

Zhe, Cao, Sun Xiangwen, and Niu Xinwen. "Harmonic Frequency Estimation Algorithm Based on MSWF in Power System." Open Electrical & Electronic Engineering Journal 9, no. 1 (October 28, 2015): 524–29. http://dx.doi.org/10.2174/1874129001509010524.

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This paper pointed out the disadvantage of harmonic frequency estimation algorithm in current power system, presented the MUSIC (multiple signal classification)-based harmonic frequency estimation algorithm in power system, and analyzed the computational complexity of the MUSIC algorithm. In order to reduce the computational complexity of conventional MUSIC algorithm and to increase the real-time characteristic of harmonic frequency estimation algorithm, we combined the multi-stage wiener filter (MSWF) recursive algorithm and MUSIC algorithm so as to avoid the subspace decomposition process of the conventional MUSIC algorithm, thus realizing the purpose of significantly reducing the computational complexity of the MUSIC algorithm. Through theoretical analysis and simulation experiments, we find that the algorithm proposed in this paper is of excellent resolution characteristic, and less dependent on data volume.
16

CHENNAI, SALIM. "NOVEL SHUNT ACTIVE POWER FILTER BASED ON NINE-LEVEL NPC INVERTER USING MC-LSPWM MODULATION STRATEGY." REVUE ROUMAINE DES SCIENCES TECHNIQUES — SÉRIE ÉLECTROTECHNIQUE ET ÉNERGÉTIQUE 69, no. 1 (April 4, 2024): 21–26. http://dx.doi.org/10.59277/rrst-ee.2024.1.4.

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This paper presents a novel shunt active power filter (Shunt APF) system based on a nine-level neutral point clamped (NPC) inverter, which can reduce current harmonics under various nonlinear loads. These loads can introduce harmonic currents within the system, which causes excessive power losses and alters the voltage systems' characteristics. Today, multi-level inverters are more suitable for high-voltage applications; their advantages are low harmonic distortions, low switching losses, low electromagnetic interference, and low acoustic noise. The reference signals required to compensate harmonic currents use the synchronous detection method (SDM) with phase disposition sinusoidal pulse width modulation (PD-SPWM) control due to its low complexity and superior performance. The proposed shunt APF configuration simulation is evaluated using MATLAB-Simulink and SimPowerSystem environment with inductive and capacitive non-linear loads. The simulation results show the efficiency of the proposed shunt APF in terms of harmonic compensation and power quality improvement. The results of comparative studies with other less multi-level inverters confirm the superiority of the proposed shunt APF system.
17

Laurano, Christian, Sergio Toscani, and Michele Zanoni. "A Simple Method for Compensating Harmonic Distortion in Current Transformers: Experimental Validation." Sensors 21, no. 9 (April 21, 2021): 2907. http://dx.doi.org/10.3390/s21092907.

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Conventional current transformers (CTs) suffer from nonlinearities due to their ferromagnetic cores. On one hand, it is well-known that severe core saturation may occur because of large overcurrents or unidirectional transient components: this may substantially impact the operation of relays. On the other hand, weaker nonlinear effects are also present during regular working conditions. In particular, the spectral content of typical current waveforms is characterized by a strong fundamental term responsible for harmonic distortion affecting the frequency components at the secondary side. In turn, this has a significant impact on the accuracy that can be reached as long as current harmonics must be monitored. The target of this work is implementing a simple signal processing technique that allows compensating for this effect. The method, characterized by extremely low computational complexity, is first introduced and validated using numerical simulations. After this, it was tested experimentally to improve the harmonic measurement capability of inductive CTs. The achieved results highlight a noticeable reduction of errors at low-order harmonics over a wide range of primary current amplitudes. It is worth noting that the black-box approach makes the technique suitable also for compensating nonlinearities introduced by current transducers based on different operating principles. Thanks to this peculiarity and to the low computational complexity, the proposed method is suitable to be employed in power quality analyzers and merging units. In this way, high-accuracy monitoring of current harmonics in power systems can be achieved, opening the way to advanced power quality management and to the location of disturbing users.
18

Börjesson Axén, Jenny, Rudi Soares, Oskar Wallmark, Peter Thelin, Erika Widenkvist Zetterström, and Göran Lindbergh. "Short-Term Impact of AC Harmonics on Aging of NiMH Batteries for Grid Storage Applications." Materials 14, no. 5 (March 6, 2021): 1248. http://dx.doi.org/10.3390/ma14051248.

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Batteries in energy storage systems are exposed to electrical noise, such as alternating current (AC) harmonics. While there have been many studies investigating whether Lithium-ion batteries are affected by AC harmonics, such studies on Nickel Metal Hydride (NiMH) batteries are scarce. In this study a 10 Ah, 12 V NiMH battery was tested with three different harmonic current frequency overlays during a single charge/discharge cycle: 50 Hz, 100 Hz, and 1000 Hz. No effect on battery internal temperature or gas pressure was found, indicating that NiMH battery aging is not affected by the tested harmonic AC frequencies. This can reduce the cost of energy storage systems, as no extra filters are needed to safeguard the batteries. Instead, the capacitive properties of the batteries give the possibility to use the battery bank itself as a high pass filter, further reducing system complexity and cost.
19

Ghaffarian, Mohammad Saeid, Gholamreza Moradi, and Reza Zaker. "Harmonic Suppressed Slot Antennas Using Rectangular/Circular Defected Ground Structures." International Journal of Antennas and Propagation 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/721565.

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Two wide rectangle-shaped microstrip-fed 2.6-GHz slot antennas using defected ground structures (DGSs) with a low design complexity are proposed to achieve wideband harmonic suppression. To accomplish this, two rectangular DGSs (RDGSs) in the first antenna and two circular DGSs (CDGSs) in the second one with various dimensions are etched into the ground plane, which could have a wideband-stop characteristic. Simulated and measured reflection coefficients indicate that the two proposed structures effectively suppress the second and third harmonics up to 23 dB between 3.5 and 10.5 GHz with a maximum ripple of 2.4 dB. In addition, the radiation patterns and peak gains of the antennas can be suppressed at least 17 dB and 7.1 dBi, respectively, at the third harmonic frequency of 7.86 GHz.
20

Manoj, Vasupalli, Dr Prabodh Khampariya, and Dr Ramana Pilla. "Performance Evaluation of Fuzzy One Cycle Control Based Custom Power Device for Harmonic Mitigation." International Journal of Electrical and Electronics Research 10, no. 3 (September 30, 2022): 765–71. http://dx.doi.org/10.37391/ijeer.100358.

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Custom power devices (CPDs) provide better harmonic minimization when they are connected in parallel with the distribution network. Power switches have a hard impact on harmonic production in distribution networks, which leads to aging effects. Techniques used to control CPD’s provide full switching in various ways. A pulse width modulation (PWM) scheme requires a reference frame transformation that tracks source and load currents to produce a control signal. The voltage de-coupler is installed in the power device's current controllers to minimize fast current harmonics and remove complexity. One-cycle control (OCC) operates in dual boost converter mode and requires only source currents to produce a control signal. Minimum distortions are obtained by the output voltage feedback compensator. The proposed approach compares the performance of two methodologies based on total harmonic distortion (THD) analysis of the same grid voltage. The performance of the CPD using PI and fuzzy one-cycle control techniques is illustrated by simulation, which gives accurate results.
21

Busatto, Tatiano, Sarah K. Rönnberg, and Math H. J. Bollen. "Comparison of Models of Single-Phase Diode Bridge Rectifiers for Their Use in Harmonic Studies with Many Devices." Energies 15, no. 1 (December 22, 2021): 66. http://dx.doi.org/10.3390/en15010066.

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Harmonic modeling of low-voltage networks with many devices requires simple but accurate models. This paper investigates the advantages and drawbacks of such models to predict the current harmonics created by single-phase full-bridge rectifiers. An overview is given of the methods, limiting the focus to harmonic analysis. The error of each method, compared to an accurate numerical simulation model, is quantified in frequency and time domain considering realistic input scenarios, including background voltage distortion and different system impedances. The results of the comparison are used to discuss the applicability of the models depending on the harmonic studies scale and the required level of detail. It is concluded that all models have their applicability, but also limitations. From the simplest and fastest model, which does not require a numerical solution, to the more accurate one that allows discontinuous conduction mode to be included, the trade-off involves accuracy and computational complexity.
22

Martin, Cristina, Federico Barrero, Manuel R. Arahal, and Mario J. Duran. "Model-Based Predictive Current Controllers in Multiphase Drives Dealing with Natural Reduction of Harmonic Distortion." Energies 12, no. 9 (May 3, 2019): 1679. http://dx.doi.org/10.3390/en12091679.

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An important drawback in the application of model-based predictive controllers for multiphase systems is the relatively high harmonic content. Harmonics arise due to the fixed sampling-time nature and the absence of modulation methods in the control technique. Recent research works have proposed different procedures to overcome this disadvantage at the expense of increasing the complexity of the controller and, in most cases, the computational requirements. There are, however, natural ways to face this harmonic generation that have been barely explored in the scientific literature. These alternatives include the use of variable sampling times or the application of the observer theory, whose utility has been stated without excessively increasing the computational cost of the controller. This paper presents the basis of both methodologies, analyzing their interest as natural alternatives to mitigate the generation of harmonic components in modern electrical drives when using predictive controllers. A five-phase induction machine is used as a case example to experimentally validate the study and draw conclusions.
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Xiao, Linfu. "Distribution Network Mixed-harmonic Separation Method Based on Characteristic Vector." Journal of Physics: Conference Series 2589, no. 1 (September 1, 2023): 012040. http://dx.doi.org/10.1088/1742-6596/2589/1/012040.

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Abstract The threat of harmonic pollution has become increasingly serious with the rapid increase in the scale and complexity of distribution networks. However, the harmonic source variety of distribution networks and the phenomena about harmonic characteristics become vague after harmonic mixture because harmonic governance and responsibility division cause much inconvenience. To address this point, a distribution network mixed-harmonic separation method based on characteristic vector is developed in this study. This method realizes the division of the current working state, harmonic emission levels, and harmonic governance responsibility of each harmonic source by equivalent analysis and reverse thinking. The results are verified through an experiment.
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Yotter, Rachel A., Igor Nenadic, Gabriel Ziegler, Paul M. Thompson, and Christian Gaser. "Local cortical surface complexity maps from spherical harmonic reconstructions." NeuroImage 56, no. 3 (June 2011): 961–73. http://dx.doi.org/10.1016/j.neuroimage.2011.02.007.

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Mohaqeqi, Morteza, Mitra Nasri, Yang Xu, Anton Cervin, and Karl-Erik Årzén. "Optimal harmonic period assignment: complexity results and approximation algorithms." Real-Time Systems 54, no. 4 (April 6, 2018): 830–60. http://dx.doi.org/10.1007/s11241-018-9304-0.

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Fu, Haoyang, Qiang Zhou, Lei Zhu, Zhang Chen, Zhihu Wei, and Siyu Zeng. "A Five-Level RF-PWM Method with Third and Fifth Harmonic Elimination for All-Digital Transmitters." Electronics 11, no. 19 (October 10, 2022): 3257. http://dx.doi.org/10.3390/electronics11193257.

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An appropriate pulse-coding algorithm is the key to achieving an efficient switched-mode power amplification in all-digital transmitters. A five-level RF-PWM method with third and fifth harmonic elimination is proposed to relax the requirements of the filter and to reduce the control complexity of the SMPA for all-digital transmitters. By controlling the pulse width and the center position of three-level sub-pulses, third and fifth harmonic elimination is achieved. Meanwhile, the control complexity of the SMPA is reduced by the decrease in the output-signal-level number. Finally, the feasibility of the method is verified by simulation. For the 16QAM signal with a carrier frequency of 200 MHz, the proposed method can achieve third harmonic suppression of −46.24 dBc and fifth harmonic suppression of −54.05 dBc when coding efficiency reaches 77.51%.
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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 (January 14, 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 accurate assessment of associated power-quality (PQ) disturbances. To tackle such increasing time-varying PQ problems, a hybrid detection method using synchrosqueezing wavelet transform (SSWT) is proposed. The proposed method first obtains the proper parameter values for the mother wavelet according to numerical computations. The wavelet transform-based synchrosqueezing and a clustering method are applied to determine each frequency component of the waveform under assessment. The time-domain waveform and the associated magnitude of each frequency component is then reconstructed by the inverse SSWT operation. The novelty of the proposed method is that it can decompose the measured waveform containing both harmonics and interharmonics into intrinsic mode functions without the need for fundamental frequency detection. Compared to other time–frequency analysis methods, SSWT has better anti-noise and higher resolution of time–frequency curves; even the measured signal has close frequency components. Simulation results and actual measurement validations show that the proposed method is effective and relatively accurate in time-varying harmonic and interharmonic detection and is suitable for applications in power networks and microgrids that have high penetration of renewables or non-linear loads causing time-varying voltage or current waveforms.
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Blanchard, A., D. M. McFarland, L. A. Bergman, and A. F. Vakakis. "Damping-induced interplay between vibrations and waves in a forced non-dispersive elastic continuum with asymmetrically placed local attachments." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2176 (April 2015): 20140402. http://dx.doi.org/10.1098/rspa.2014.0402.

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We study the dynamics of a linear, uniform, undamped string under harmonic base excitation, with an attachment consisting of either a spring–dashpot system or a vibration absorber. Mode complexity caused by the local damping of the attachment can lead to coexistence of vibrations and waves in the string. We consider either identical harmonic base motions at both ends or harmonic base excitation at one end. In the case of double harmonic base excitation, it is possible to choose the parameters of the attachment, so that the mode complexity is maximal in one part of the string (leading to travelling waves and elimination of vibrations) and almost zero in the other part (with standing waves or vibration modes). Similarly, for single base excitation, we analytically predict the parameters of the attachment that maximize mode complexity and enhance the interplay of vibrations and travelling waves in the string. Under such conditions, the system acts as a passive vibration confinement device, with induced energy being transmitted through travelling waves to a region where it is confined in the form of standing waves. Our results can be used for predictive design and reveal an unexpected new application of the classical linear vibration absorber.
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García-Cabrera, Ana, Roberto Boyero-García, Óscar Zurrón-Cifuentes, Javier Serrano, Julio San Román, Carlos Hernández-García,, and Luis Plaja. "High-harmonic spectroscopy of solids driven by structured light." EPJ Web of Conferences 287 (2023): 11006. http://dx.doi.org/10.1051/epjconf/202328711006.

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Understanding high-order harmonic generation (HHG) from solid targets holds the key of potential technological innovations in the field of high-frequency coherent sources. Solids present optical nonlinearities at lower driving intensities, and harmonics can be efficiently emitted due to the increased electron density in comparison with the atomic and molecular counterparts. In addition, crystalline solids introduce a new complexity, as symmetries play a role in the anisotropic character of the optical response. An extraordinary playground is, therefore, the scenario in which solids are driven by vector beams, since crystal symmetries can be directly coupled with the topology of the driving laser beam. In this contribution we analyze the topological properties of the HHG radiation emitted by a single-layer graphene sheet driven by a vector beam. We show that the harmonic field is a complex combination of vortices, whose geometrical properties hold information about the details of the non-linear response of the crystal. We demonstrate, therefore, that the analysis of the topological structure of the harmonic field can be used as a spectroscopic measurement technique, paving the way of topological spectroscopy as a new strategy for the characterization of the optical response of macroscopic targets.
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Ligong, Sun Ligong, Sun Xiangwen, and Xiang Fei. "Harmonic Estimation Algorithm for Power System Based on Improved MUISC and Linear Neural Networks." Open Electrical & Electronic Engineering Journal 9, no. 1 (September 30, 2015): 445–51. http://dx.doi.org/10.2174/1874129001509010445.

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The paper proposes harmonic estimation algorithm for power system based on Multiple Signal Classification (MUSIC) and linear neural network because of the insufficiency of harmonic frequency estimation algorithm. The conventional MUSIC algorithm has the advantage of higher estimation accuracy, while the disadvantage is that the computational complexity is high and it cannot estimate the harmonic phase and amplitude. In the paper, a new harmonic estimation algorithm for power system is constructed with combining the MUSIC algorithm, the multistage Wiener filter (MSWF) and linear neural network. Theoretic analysis and simulation experiments show that the requirement to data is relatively low, and has good harmonic estimation accuracy and reliability.
31

Bhattacharyya, Arpan. "Circuit complexity and (some of) its applications." International Journal of Modern Physics E 30, no. 07 (July 2021): 2130005. http://dx.doi.org/10.1142/s0218301321300058.

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Motivated by recent interesting holographic results, several attempts have been made to study complexity (rather “Circuit Complexity”) for quantum field theories using Nielsen’s geometric method. Since then, it has found many interesting applications. We discuss some of its applications. In particular, we discuss whether circuit complexity can be used as a diagnostics of quantum chaos. We use a simple toy model, namely the Inverted Harmonic Oscillator (IHO), to establish our claim and discuss further applications in the context of quantum cosmology.
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Pal, Kuntal, Kunal Pal, Ankit Gill, and Tapobrata Sarkar. "Evolution of circuit complexity in a harmonic chain under multiple quenches." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 5 (May 1, 2023): 053108. http://dx.doi.org/10.1088/1742-5468/acd4b3.

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Abstract We study Nielsen’s circuit complexity in a periodic harmonic oscillator chain, under single and multiple quenches. This simple system is amenable to analytical computations and yet offers considerable insight into the dynamics of quantum information. For a single quench scenario, we highlight some important differences between our results that explicitly use the wavefunction, as compared to the recently proposed covariance matrix method and point out the consequences. In a multiple quench scenario, the complexity shows remarkably different behaviour compared to the other information theoretic measures, such as the entanglement entropy and the out of time ordered correlator. In particular, the latter is known to show signs of chaos in this integrable system, but our results indicate the contrary. We further show the presence of a ‘residual complexity,’ i.e. after two successive quenches, when the frequency returns to its initial value, the complexity has a non-zero lower limit. Further, applying a large number of successive quenches, the complexity of the time evolved state can be increased to a high value, which is not possible by applying a single quench. Finally, we show that this simplistic model exhibits the interesting phenomenon of ‘complexity crossover’ between two successive quenches performed at different times.
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Chen, Long, Wenhua Chen, Xiaofan Chen, Jiaming Chu, and Zhenghe Feng. "A Complexity-Reduced Harmonic-Cancellation Digital Predistortion for HF Transmitters." IEEE Microwave and Wireless Components Letters 31, no. 5 (May 2021): 529–32. http://dx.doi.org/10.1109/lmwc.2021.3069489.

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34

Rizzi, Romeo, Pritha Mahata, Luke Mathieson, and Pablo Moscato. "Hierarchical Clustering Using the Arithmetic-Harmonic Cut: Complexity and Experiments." PLoS ONE 5, no. 12 (December 2, 2010): e14067. http://dx.doi.org/10.1371/journal.pone.0014067.

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35

Madichetty, S., A. Dasgupta, and S. Jinka. "A New Harmonic Mitigation Scheme for MMC – An Experimental Approach." International Journal of Emerging Electric Power Systems 15, no. 3 (June 1, 2014): 299–311. http://dx.doi.org/10.1515/ijeeps-2014-0015.

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Abstract A multilevel converter has been brought into limelight in this article, however, particular attention has been provided to the form and function of modular multilevel converter (MMC) with new design, control and harmonic mitigation schemes. A new controller scheme has been proposed to mitigate the lower and higher order harmonics. The proposed scheme shows its effectiveness by theoretical calculations, verified by simulation and experimental results. Till date, research in this field is very limited with circulating currents and harmonics as the major problem. This article effectively addresses the problem with prototype 1 kVA implementation and attempts to make a detailed analysis with their functions in comprehensive manner with high-voltage DC application under different conditions. Also, the applicability of zero voltage switching at turn ON and zero current transition at turn OFF has been verified experimentally. The strategic conclusions on MMC have been made in order to make the system more robust in operation, less complexity in design and control.
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Xiangwen, Sun, Cao Zhe, and Tian Wei. "Harmonic Frequency Estimation Algorithm based on ESPRIT and MSWF in Power System." Open Electrical & Electronic Engineering Journal 9, no. 1 (October 28, 2015): 518–23. http://dx.doi.org/10.2174/1874129001509010518.

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This paper points out the deficiency in the current harmonic frequency estimation algorithm in power system. In order to improve the accuracy of detection and reduce the computational complexity, the study combined the ESPRIT algorithm with multistage Wiener filter (MSWF) recurrence to achieve fast estimation of harmonic frequency. Theoretical analysis and simulation experiment show that the algorithm had relatively low requirement for the amount of data, and demonstrated good frequency resolution characteristics and anti-jamming capability, which made it ideally suitable for harmonic analysis in power system.
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Xie, Yuzhe, Yanhua He, Xuntian Zhou, and Zhigang Zhang. "Investigation of the Feasibility of the Dynamic Equivalent Model of Large Photovoltaic Power Plants in a Harmonic Resonance Study." Electronics 12, no. 18 (September 5, 2023): 3746. http://dx.doi.org/10.3390/electronics12183746.

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In recent years, there have been several harmonic resonance accidents around the world that involve renewable energy power plants. The frequency scanning method is the most widely used technique in engineering practice to evaluate the severity of resonance due to its simple operation and clear physical meaning. However, when establishing electromagnetic transient simulation models and conducting frequency scans, a single generation unit or a few renewable generation units are usually used to represent the original power plant for the purpose of reducing model complexity and improving the simulation efficiency. Such a practice has been found to be effective in dynamic studies around the fundamental frequency. However, its feasibility in harmonic resonance studies has not yet been fully investigated. Because of this research gap, a feasibility study is conducted in this paper by using a real-life photovoltaic power plant. The detailed harmonic model of the plant is first established using the harmonic linearization method, and the equivalent harmonic model is then developed using the power loss conservation method. The feasibility of the equivalent model was investigated in detail, and the impact of the different impedance models on the resonance analysis was analyzed. The results indicate that the conventional dynamic equivalent model can effectively reflect the harmonic resonance characteristics of photovoltaic power plants. Furthermore, a more simplified model that ignores the inductance of the collector line is recommended in this paper to further reduce the modeling complexity.
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Jopri, M. H., A. R. Abdullah, T. Sutikno, M. Manap, M. R. Ab Ghani, and M. R. Yusoff. "A Critical Review of Time-frequency Distribution Analysis for Detection and Classification of Harmonic Signal in Power Distribution System." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 6 (December 1, 2018): 4603. http://dx.doi.org/10.11591/ijece.v8i6.pp4603-4618.

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<p>This paper presents a critical review of time-frequency distributions (TFDs) analysis for detection and classification of harmonic signal. 100 unique harmonic signals comprise of numerous characteristic are detected and classified by using spectrogram, Gabor transform and S-transform. The rulebased classifier and the threshold settings of the analysis are according to the IEEE Standard 1159 2009. The best TFD for harmonic signals detection and classification is selected through performance analysis with regards to the accuracy, computational complexity and memory size that been used during the analysis.</p>
39

Demerdziev, Kiril, and Vladimir Dimchev. "Analysis of Errors in Active Power and Energy Measurements Under Random Harmonic Distortion Conditions." Measurement Science Review 21, no. 6 (October 26, 2021): 168–79. http://dx.doi.org/10.2478/msr-2021-0023.

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Abstract As harmonic distortion of voltage and current is reality in the power system, the need for accurate measurement of electrical power and energy goes beyond the instruments’ specifications and calibration procedures regarding pure sine wave signals. Several international standards and recommendations provide test signals for examination of electricity meters under non-sinusoidal conditions, however, not all of the test signal parameters’ possible states are faithfully represented in those documents. Because the high order harmonics may possess random amplitudes and phase shifts in relation to components at fundamental frequency, it is important that the meter’s performance is verified with random waveforms as well. The non-linear dependence between the measured power/energy and the phase shifts, both between fundamental and harmonic components, provides additional complexity of such an analysis. Simple test signals, which are in accordance with the standards’ demands and propositions, are used for determination of the measurement error in case of different harmonic distortion parameter change. In order for a general error function for any measurement device to be determined, mathematical modelling, regarding the results from multiple tests, is performed. The mathematical model presents a strong dependence between a single component’s phase shifts and a meter’s error and it provides a systematization of all signal parameters’ influence on the measurement accuracy.
40

Istrate, Daniela, Deepak Amaripadath, Etienne Toutain, Robin Roche, and Fei Gao. "Traceable measurements of harmonic (2 to 150) kHz emissions in smart grids: uncertainty calculation." Journal of Sensors and Sensor Systems 9, no. 2 (November 10, 2020): 375–81. http://dx.doi.org/10.5194/jsss-9-375-2020.

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Abstract. The necessity of measuring harmonic emissions between 2 and 150 kHz is outlined by several standard committees and electrical utilities. This paper presents a measurement system and its traceable characterization designed to acquire and analyse voltages up to 230 V and currents up to 100 A with harmonics up to 150 kHz that may occur in smart grids. The uncertainty estimation is carried out and described in detail for both the fundamental and supraharmonics components. From a metrological point of view, ensuring the traceability of current measurements for frequencies higher than 100 kHz and dealing with the complexity of uncertainty determination are bottlenecks related to supraharmonics measurements that this paper proposes an approach to deal with.
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Butler, Gary C., Shin-Ichi Ando, and John S. Floras. "Fractal Component of Variability of Heart Rate and Systolic Blood Pressure in Congestive Heart Failure." Clinical Science 92, no. 6 (June 1, 1997): 543–50. http://dx.doi.org/10.1042/cs0920543.

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1. There is a substantial non-harmonic or fractal component to the variability of both heart rate and blood pressure in normal subjects. Heart rate is the more complex of these two signals, with respect to the slope, β, of the 1/fβ relationship. In congestive heart failure, heart rate spectral power is attenuated, but the fractal and harmonic components of heart rate and systolic blood pressure variability have not been characterized. 2. Two groups, each comprising 20 men, were studied during 15 min of supine rest and spontaneous respiration: one with functional class II—IV heart failure (age 52 ± 2 years; mean ± SEM) and a second group of healthy men (age 46 ± 2 years). 3. Total spectral power for heart rate was significantly reduced in heart failure (P < 0.02), whereas total spectral power for systolic blood pressure was similar in the two groups. In both heart failure and normal subjects, 65–80% of total spectral power in these two signals displayed fractal characteristics. 4. In heart failure, the slope of the 1/fβ relationship for heart rate was significantly steeper than in normal subjects (1.40 ± 0.08 compared with 1.14 ± 0.05; P < 0.05), indicating reduced complexity of the fractal component of heart rate variability. There was no significant difference in the 1/fβ slope for systolic blood pressure variability between these two groups, but the blood pressure signals were less complex than heart rate variations in both heart failure (2.31 ± 0.15; P < 0.006) and normal subjects (2.47 ± 0.15; P < 0.0001). 5. Parasympathetic nervous system activity, as estimated from heart rate variability was reduced (P < 0.01) in patients with heart failure, whereas trends towards increased sympathetic nervous system activity and decreased non-harmonic power were not significant. 6. The non-harmonic components of cardiac frequency are reduced in heart failure. Non-harmonic power is not attenuated, but the complexity of the heart rate signal is less than in subjects with normal ventricular function. A reduction in parasympathetic modulation appears to contribute to this loss of complexity of heart rate. Consequently, the heart rate signal comes to resemble that of blood pressure. In contrast, the variability and complexity of the systolic blood pressure signal is similar in heart failure and normal subjects. This reduced complexity of heart rate variability may have adverse implications for patients with heart failure.
42

Mariotto, S., and M. Sorbi. "Quench position reconstruction through harmonic field analysis in superconducting magnets." Superconductor Science and Technology 35, no. 1 (November 29, 2021): 015006. http://dx.doi.org/10.1088/1361-6668/ac39e8.

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Abstract The performances of superconducting magnets for particle accelerators are limited by instabilities or disturbances which lead to the transition of the superconducting material to the normal resistive state and the activation of the quench protection system to prevent damage to the magnet. To locate the position of the state transition, voltage taps or quench antennas are the most commonly used technologies for their reliability and accuracy. However, during the production phase of a magnet, the number of voltage taps is commonly reduced to simplify the construction process and quench antennas are generally used only for dipoles or quadrupoles to limit the antenna design complexity. To increase the accuracy in the reconstruction of the quench event position, a novel method, suitable for magnets with independent superconducting coils and quench protected without the use of quench heaters, is proposed in this paper. This method, based on standard magnetic measurement techniques for field harmonic analysis, can locate the position of the superconductor transition inside the magnet after the quench event when the magnet has been discharged. Analyzing the not allowed harmonics produced in the field quality at zero current, the position of the quenched coils can be retrieved for any magnet orders without increasing the complexity of the dedicated measurement technique.
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CABEZA, C., and M. ROSEN. "COMPLEXITY IN FARADAY EXPERIMENT WITH VISCOELASTIC FLUID." International Journal of Bifurcation and Chaos 17, no. 05 (May 2007): 1599–607. http://dx.doi.org/10.1142/s0218127407017938.

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A systematic experimental study of the Faraday instability in viscoelastic fluid is presented. We have used a shear thinning polymer solution in which the elastic effects are predominant within our work range. We have analyzed the dependence of the threshold instability as a function of the depth in layer. Depending on the fluid layer depth and the driving frequency, harmonic or subharmonic regimes are developed. We have focused our work on the subharmonic region and temporal and spatial behaviors were analyzed. In addition, we have used the onset acceleration to estimate the rheological properties of the fluid. These predictions are supported by experimental measurements.
44

Krishnamoorthy, Umapathi, Ushaa Pitchaikani, Eugen Rusu, and Hady H. Fayek. "Performance Analysis of Harmonic-Reduced Modified PUC Multi-Level Inverter Based on an MPC Algorithm." Inventions 8, no. 4 (July 13, 2023): 90. http://dx.doi.org/10.3390/inventions8040090.

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Renewable and distributed energy generation includes wind turbines, fuel cells, solar cells, and batteries. These distributed energy sources need special power converters in order to connect them to the grid and make the generated power available for public use. Solar energy is the most readily available energy source; hence, if utilized properly, it can power up both domestic and industrial loads. Solar cells produce DC power, and this should be converted to an AC source with the help of inverters. A multi-level inverter for an application is selected based on a trade-off between cost, complexity, losses, and total harmonic distortion (THD). A packed U-cell (PUC) topology is composed of power switches and voltage sources connected in a series-parallel fashion. This basic unit can be extended to a greater number of output voltage levels. The significance of this design is the reduced use of power switches, gate drivers, protection circuits, and capacitors. The converter presented in this paper is a 31-level topology switched by a variable switching frequency-based model predictive controller that helps in achieving optimal output with reduced harmonics to a great extent. The gate driver circuit is also optimized in terms of power consumption and size complexity. A comparison of the 9-level and the 31-level PUC inverters is carried out to study the impact of the number of levels on the total harmonic distortion. The simulation results depict that the total harmonic distortion (THD) for a nominal modulation index of 0.8 is 11.54% and 3.27% for the 9-level multi-level inverter (MLI) and the 31-level modified packed U-cell multi-level inverter (MPUC-MLI), respectively. The reduction in THD is attributed to the increased number of steps in the output when using the model predictive controller.
45

Layton, Anita T., Leon C. Moore, and Harold E. Layton. "Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats." American Journal of Physiology-Renal Physiology 291, no. 1 (July 2006): F79—F97. http://dx.doi.org/10.1152/ajprenal.00048.2005.

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Single-nephron proximal tubule pressure in spontaneously hypertensive rats (SHR) can exhibit highly irregular oscillations similar to deterministic chaos. We used a mathematical model of tubuloglomerular feedback (TGF) to investigate potential sources of the irregular oscillations and the corresponding complex power spectra in SHR. A bifurcation analysis of the TGF model equations, for nonzero thick ascending limb (TAL) NaCl permeability, was performed by finding roots of the characteristic equation, and numerical simulations of model solutions were conducted to assist in the interpretation of the analysis. These techniques revealed four parameter regions, consistent with TGF gain and delays in SHR, where multiple stable model solutions are possible: 1) a region having one stable, time-independent steady-state solution; 2) a region having one stable oscillatory solution only, of frequency f1; 3) a region having one stable oscillatory solution only, of frequency f2, which is approximately equal to 2 f1; and 4) a region having two possible stable oscillatory solutions, of frequencies f1 and f2. In addition, we conducted simulations in which TAL volume was assumed to vary as a function of time and simulations in which two or three nephrons were assumed to have coupled TGF systems. Four potential sources of spectral complexity in SHR were identified: 1) bifurcations that permit switching between different stable oscillatory modes, leading to multiple spectral peaks and their respective harmonic peaks; 2) sustained lability in delay parameters, leading to broadening of peaks and of their harmonics; 3) episodic, but abrupt, lability in delay parameters, leading to multiple peaks and their harmonics; and 4) coupling of small numbers of nephrons, leading to multiple peaks and their harmonics. We conclude that the TGF system in SHR may exhibit multistability and that the complex power spectra of the irregular TGF fluctuations in this strain may be explained by switching between multiple dynamic modes, temporal variation in TGF parameters, and nephron coupling.
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Ghodake, Pravinkumar R. "Finite element studies to understand reflection of nonlinear waves in a continuous functionally graded material." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A294. http://dx.doi.org/10.1121/10.0016325.

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The nonlinear pulse-echo ultrasonics technique is effective when only one side of pressure vessels mainly used in thermal and nuclear power plants is assessable. As another side is exposed to continuous thermal and nuclear damages, the early-stage damages accumulate as a function of position. Concluding experimental results from such a complex interaction of reflected nonlinear waves during pulse-echo testing is difficult. Obtaining analytical solutions to the reflected waves from a functionally graded nonlinear region with an extended linear part is challenging. This complexity in understanding is resolved through various computational studies presented in this article. The linear and exponential variation of nonlinear parameters, loss in elastic stiffness, and density of the damaged region are modeled by updating linear and nonlinear constitutive equations. The results demonstrate higher energy of reflected longitudinal harmonic waves (2f, 3f, 4f,….) from a fixed boundary than a free boundary. Amplitudes of higher harmonic responses as a function of the position are verified. Harmonically reflected higher harmonics are more sensitive to the spatial distribution of nonlinear parameters than the loss in linear elastic stiffness, whereas a significant change in the overall shapes of the pulses in time domains is observed. Self-wave mixing increases the number of higher harmonics.
47

Cosgrove, Michael S. "Writers and readers: deconvoluting the harmonic complexity of the histone code." Nature Structural & Molecular Biology 19, no. 8 (August 2012): 739–40. http://dx.doi.org/10.1038/nsmb.2350.

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48

Reed, Catherine L., Steven J. Cahn, Christopher Cory, and Jerzy P. Szaflarski. "Impaired perception of harmonic complexity in congenital amusia: A case study." Cognitive Neuropsychology 28, no. 5 (July 2011): 305–21. http://dx.doi.org/10.1080/02643294.2011.646972.

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49

Djebbar, Bachir, and Chahrazed Harrat. "Complexity of Separately Harmonic Function and Application to Arithmetical Entire Functions." International Journal of Open Problems in Computer Science and Mathematics 9, no. 1 (2016): 22–34. http://dx.doi.org/10.12816/0026352.

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50

Grolmusz, V. "Harmonic Analysis, Real Approximation, and the Communication Complexity of Boolean Functions." Algorithmica 23, no. 4 (April 1999): 341–53. http://dx.doi.org/10.1007/pl00009265.

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