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Journal articles on the topic 'Helmholtz Model'

Author: Grafiati

Published: 6 September 2023

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1

Tang, H., and S. Zhong. "A static compressible flow model of synthetic jet actuators." Aeronautical Journal 111, no. 1121 (2007): 421–31. http://dx.doi.org/10.1017/s0001924000004681.

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Abstract In this paper, a simple static compressible flow model for circular synthetic jet actuators is described. It is used to undertake a systematic computational investigation of the effect of changing actuator geometrical and operating parameters on the magnitude of peak jet velocity at the orifice exit of an actuator whose diaphragm displacement and frequency are allowed to vary independently. It is found that, depending on the flow conditions inside the orifice duct, the actuator may operate in two distinct regimes, i.e. the Helmholtz resonance regime and the viscous flow regime. In the

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2

Liu, Xin, Yuanyu Yu, Jiujiang Wang, Sio Hang Pun, Mang I. Vai, and Peng Un Mak. "An Analytical Model for Bandwidth Enhancement of Air-Coupled Unsealed Helmholtz Structural CMUTs." Journal of Sensors 2019 (April 17, 2019): 1–16. http://dx.doi.org/10.1155/2019/3896965.

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Capacitive micromachined ultrasonic transducers (CMUTs) were reported to own high potential in air-coupled ultrasonic applications such as noncontact nondestructive examination and gas flow measurement. The unsealed CMUTs which utilized the squeeze film effect were reported to overcome the narrow output pressure bandwidth of the conventional sealed CMUTs in air operation. This kind of unsealed CMUTs can also be regarded as Helmholtz resonators. In this work, we present the air-coupled unsealed Helmholtz structural CMUTs which utilize both the squeeze film effect and the Helmholtz resonant effe

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3

Sosnov, Valeriy. "Analysis of Control Problems for 2-D Model of Sound Scattering." Applied Mechanics and Materials 770 (June 2015): 531–34. http://dx.doi.org/10.4028/www.scientific.net/amm.770.531.

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In this paper control problems for 2-D Helmholtz equation are formulated and investigated. These problems are associated with developing technology of acoustic cloaking. Helmholtz equation is considered in an unbounded domain with the impedance boundary condition. The role of control in control problems under study is played by surface impedance.

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4

Feng, Guo-Hua, and Wen-Sheng Chen. "Piezoelectric Micromachined Ultrasonic Transducer-Integrated Helmholtz Resonator with Microliter-Sized Volume-Tunable Cavity." Sensors 22, no. 19 (2022): 7471. http://dx.doi.org/10.3390/s22197471.

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In this study, a piezoelectric micromachined ultrasonic transducer (PMUT) is integrated with a microliter-sized volume-tunable Helmholtz resonator. The passive Helmholtz resonator is constructed using an SU8 photolithography-defined square opening plate as the neck portion, a 3D-printed hollow structure with a threaded insert nut, and a precision set screw to form the volume-controllable cavity of the Helmholtz resonator. The fabricated piezoelectric films acted as ultrasonic actuators attached to the surface of the neck SU8 plate. Experimental results show that the sound pressure level (SPL)

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5

Dayan, Peter, Geoffrey E. Hinton, Radford M. Neal, and Richard S. Zemel. "The Helmholtz Machine." Neural Computation 7, no. 5 (1995): 889–904. http://dx.doi.org/10.1162/neco.1995.7.5.889.

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Discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning. One fruitful approach is to build a parameterized stochastic generative model, independent draws from which are likely to produce the patterns. For all but the simplest generative models, each pattern can be generated in exponentially many ways. It is thus intractable to adjust the parameters to maximize the probability of the observed patterns. We describe a way of finessing this combinatorial explosion by maximizing an easily computed lower bound on the probability of the observ

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6

Megasari, M. "Dual Reciprocity Boundary Element Method untuk Menyelesaikan Masalah Infiltrasi Stasioner pada Saluran Datar Periodik." Journal of Mathematics Computations and Statistics 4, no. 1 (2021): 30. http://dx.doi.org/10.35580/jmathcos.v4i1.20447.

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Abstrak. Penelitian ini membahas tentang penyelesaian masalah infiltrasi stasioner dari saluran datar dengan Dual Reciprocity Boundary Element Method (DRBEM). Persamaan pembangun untuk masalah ini adalah persamaan Richard. Menggunakan transformasi Kirchhoff dan relasi eksponensial konduktifitas hidrolik, persamaan Richard ditransformasi ke dalam persamaan infiltrasi stasioner dalam Matric Flux Potential (MFP). Persamaan infiltrasi dalam MFP selanjutnya diubah ke dalam persamaan Helmholtz termodifikasi. Model matematika infiltrasi stasioner pada saluran datar berbentuk Masalah Syarat batas Helm

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7

Wang, Jianguo, Philip Rubini, Qin Qin, and Brian Houston. "A Model to Predict Acoustic Resonant Frequencies of Distributed Helmholtz Resonators on Gas Turbine Engines." Applied Sciences 9, no. 7 (2019): 1419. http://dx.doi.org/10.3390/app9071419.

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Helmholtz resonators, traditionally designed as a narrow neck backed by a cavity, are widely applied to attenuate combustion instabilities in gas turbine engines. The use of multiple small holes with an equivalent open area to that of a single neck has been found to be able to significantly improve the noise damping bandwidth. This type of resonator is often referred to as “distributed Helmholtz resonator”. When multiple holes are employed, interactions between acoustic radiations from neighboring holes changes the resonance frequency of the resonator. In this work, the resonance frequencies f

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8

Matveev, Konstantin I. "Thermoacoustically controlled Helmholtz resonators." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 11 (2013): 2563–68. http://dx.doi.org/10.1177/0954406213477569.

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Helmholtz resonators and their modifications are commonly applied for suppressing unwanted sound, including acoustic oscillations in chambers of propulsion and power systems. Sound absorption characteristics of Helmholtz resonators can be enhanced and controlled with a use of thermal stratification in porous insets inside resonators. A simplified lumped-element model for thermoacoustically augmented Helmholtz resonators is developed in this article. Sample calculations illustrate effects of temperature gradients, porosity, positions of porous insets, and locations of resonators inside chambers

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9

Hersh, A. S., B. E. Walker, and J. W. Celano. "Helmholtz Resonator Impedance Model, Part 1: Nonlinear Behavior." AIAA Journal 41, no. 5 (2003): 795–808. http://dx.doi.org/10.2514/2.2041.

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10

El-Sayed, Salah M., and Doǧan Kaya. "Comparing numerical methods for Helmholtz equation model problem." Applied Mathematics and Computation 150, no. 3 (2004): 763–73. http://dx.doi.org/10.1016/s0096-3003(03)00305-9.

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11

Suchenek, M., and L. J. Opalski. "Accuracy Improvement of a Photoacoustic Helmholtz Cell Model." Acta Physica Polonica A 125, no. 5 (2014): 1132–37. http://dx.doi.org/10.12693/aphyspola.125.1132.

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12

Guo, Li Shuai, Xing Rong Zheng, and Zhi Rong Wu. "The Chemistry Model of Ion-Ion Interaction Energy of Full Ionized Hydrogen Plasma." Advanced Materials Research 989-994 (July 2014): 779–82. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.779.

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The ion-ion interaction contribution to the Helmholtz free energy is one of thermodynamic properties which discribing full ionized hydrogen plasma. Based quantum statistical theory and its simulation results to construct the free energy model of statistical mechanics, it is great significant to understand the properties of full ionized hydrogen plasma under high temperatures and pressures. Using Fortran program, we calculated the isotherms with some sensitive parameters, making comparison between our results and the formers. We find that former formula proposed by Chabrier appears variation at

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13

SZE, K. Y., Q. H. ZHANG, and G. H. LIU. "MULTI-FIELD THREE-NODE TRIANGULAR FINITE ELEMENT MODEL FOR HELMHOLTZ PROBLEM." Journal of Computational Acoustics 19, no. 03 (2011): 317–44. http://dx.doi.org/10.1142/s0218396x11004353.

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In this paper, four three-node triangular finite element models which can readily be incorporated into the standard finite element program framework are devised via a multi-field variational functional for the bounded plane Helmholtz problem. In the models, boundary and domain fields are independently assumed. The former is constructed by nodal interpolation and the latter comprises nonsingular solutions of the Helmholtz equation. The equality of the two fields are enforced along the element boundary. Among the four devised models, the most accurate one is 1/3 to 1/2 less erroneous than the co

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14

Liu, Haitao. "Acoustic performance analysis of Helmholtz resonators with conical necks and its application." Noise Control Engineering Journal 67, no. 3 (2019): 155–67. http://dx.doi.org/10.3397/1/376714.

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The acoustic properties of the Helmholtz resonators with conical necks, which have broad acoustic attenuation band performance in the low frequency range, are investigated in this study. In order to investigate its wide-band acoustic attenuation mechanism, three-dimensional finite element models for the Helmholtz resonators with different necks are built respectively. The acoustic performance prediction model based on the one-dimensional analytical approach with acoustic length corrections is built to calculate the transmission loss results more efficiently, and the formula for calculating the

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15

Griffin, Steve, Steven A. Lane, and Steve Huybrechts. "Coupled Helmholtz Resonators for Acoustic Attenuation." Journal of Vibration and Acoustics 123, no. 1 (2000): 11–17. http://dx.doi.org/10.1115/1.1320812.

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Helmholtz resonators are used in a variety of applications to reduce the transmission of unwanted sound. This work demonstrates that mechanically coupled resonators can be used to design a particular transmission loss response, provide a wider bandwidth of attenuation, and adapt the transmission loss characteristics of a structure to attenuate disturbances of varying frequency. An analytical model is developed for a single, coupled resonator system mounted on a one-dimensional duct. Experiments are conducted on a similar system that uses a thin membrane to couple the resonator volumes. A simpl

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16

Salomatov, V. N. "Klein‐Gordon and Schrödinger equations for a free particle in the rest frame." Physics Essays 33, no. 1 (2020): 10–12. http://dx.doi.org/10.4006/0836-1398-33.1.10.

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A system of two equations is found that has solutions which coincide with the solutions of the Klein‐Gordon equation in the rest frame. This system includes the Schrödinger equation for a free neutral spinless particle. Using the Schrödinger equation as an additional condition for solving the Klein‐Gordon equation in the rest frame leads to two Helmholtz equations. Helmholtz equations can be solved by specifying a particle model and boundary conditions. One of the Helmholtz equations leads to discreteness of the rest masses of relativistic particles.

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17

Aoki, Koichi Jeremiah, Ridong He, and Jingyuan Chen. "Parallel Combination of Inner Capacitance and Ionic Capacitance, Apparently Inconsistent with Stern’s Model." Electrochem 2, no. 1 (2021): 71–82. http://dx.doi.org/10.3390/electrochem2010007.

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A double layer capacitance (DLC) has mainly been brought about in the Helmholtz layer rather than in the diffuse layer, as was demonstrated with the invariance of DLC to salt concentration, c, less than 0.5 M (M = mol dm−3). The DLC measured here increased with concentrations of KCl and HCl solutions as high as 1 M at a platinum electrode by the ac impedance method. It was represented as a sum of the Helmholtz capacitance and the ionic one which had 0.7 power of the concentrations. The simple addition implies that the Helmholtz contribution and the ionic one should be represented by a parallel

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18

Bi, Rong, Zheng Shi Liu, Kai Ming Li, Jun Chen, and Yong Wang. "Helmholtz Resonator with Extended Neck and Absorbing Material." Applied Mechanics and Materials 141 (November 2011): 308–12. http://dx.doi.org/10.4028/www.scientific.net/amm.141.308.

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The acoustic attenuation of Helmholtz resonator including an extended neck and sound–absorbing materials is investigated in current study. A two-dimensional analytical method based on mode matching method is developed to determine the Transmission loss (TL) of a piston-driven model of Helmholtz resonator. The resonance frequency and Transmission loss predicted from this method show reasonable agreements with published experimental results. Finally, this method is used to examine the effect of length of extended neck, extended neck with/without absorbing material and acoustic properties of soun

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19

Raymond, Jean-Pierre, and Muthusamy Vanninathan. "Exact controllability in fluid – solid structure: The Helmholtz model." ESAIM: Control, Optimisation and Calculus of Variations 11, no. 2 (2005): 180–203. http://dx.doi.org/10.1051/cocv:2005006.

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20

Singh, Deepesh K., and Sjoerd W. Rienstra. "Nonlinear asymptotic impedance model for a Helmholtz resonator liner." Journal of Sound and Vibration 333, no. 15 (2014): 3536–49. http://dx.doi.org/10.1016/j.jsv.2014.03.013.

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21

Estela-Uribe, J. F. "A Helmholtz energy model for liquefied natural gas systems." Fluid Phase Equilibria 246, no. 1-2 (2006): 64–70. http://dx.doi.org/10.1016/j.fluid.2006.05.017.

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22

Popov, Igor. "Model of Point-Like Window for Electromagnetic Helmholtz Resonator." Zeitschrift für Analysis und ihre Anwendungen 32, no. 2 (2013): 155–62. http://dx.doi.org/10.4171/zaa/1478.

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23

Sze, K. Y., and Y. K. Cheung. "A hybrid-Trefftz finite element model for Helmholtz problem." Communications in Numerical Methods in Engineering 24, no. 12 (2008): 2047–60. http://dx.doi.org/10.1002/cnm.1094.

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24

Zubair, Hisham bin, Bram Reps, and Wim Vanroose. "A Preconditioned Iterative Solver for the Scattering Solutions of the Schrödinger Equation." Communications in Computational Physics 11, no. 2 (2012): 415–34. http://dx.doi.org/10.4208/cicp.121209.180910s.

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AbstractThe Schrödinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics. We demonstrate how simple transformations of the Schrödinger equation leads to a coupled linear system, whereby each diagonal block is a high frequency Helmholtz problem. Based on this model, we derive indefinite Helmholtz model problems with strongly varying wavenumbers. We employ the iterative approach for their solution. In particular, we develop a preconditioner that has its spectrum restricted to a quadrant (of the complex plane) thereby making it easily inver

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25

Gysling, D. L., G. S. Copeland, D. C. McCormick, and W. M. Proscia. "Combustion System Damping Augmentation With Helmholtz Resonators." Journal of Engineering for Gas Turbines and Power 122, no. 2 (1999): 269–74. http://dx.doi.org/10.1115/1.483205.

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This paper describes an analytical and experimental investigation to enhance combustion system operability using side branch resonators. First, a simplified model of the combustion system dynamics is developed in which the large amplitude pressure oscillations encountered at the operability limit are viewed as limit cycle oscillations of an initially linear instability. Under this assumption, increasing the damping of the small amplitude combustion system dynamics will increase combustor operability. The model is then modified to include side branch resonators. The parameters describing the si

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26

Askes, Harm, Juha Hartikainen, Kari Kolari, Reijo Kouhia, Timo Saksala, and Jani Vilppo. "On the Kachanov-Rabotnov continuum damage model." Rakenteiden Mekaniikka 53, no. 2 (2020): 125–44. http://dx.doi.org/10.23998/rm.82528.

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In this paper two partially complementary formulations of the simple phenomenological Kachanov-Rabotnov continuum damage constitutive model are presented. The models are based on a consistent thermodynamic formulation using proper expressions for the Helmholtz free energy or its complementary form of the dissipation potential. Basic features of the models are discussed and the behaviour in tensile test and creep problems is demonstrated.

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27

Bartłomiej Chrobak, Łukasz, and Mirosław Andrzej Maliński. "Comparison of the CRLC Models Describing the Helmholtz Type Cells for the Nondestructive Photoacoustic Spectroscopy." Metrology and Measurement Systems 21, no. 3 (2014): 545–52. http://dx.doi.org/10.2478/mms-2014-0046.

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Abstract The photoacoustic cell is the heart of the nondestructive photoacoustic method. This article presents a new simple lumped-components CRLC model of the Helmholtz type photoacoustic cell. This model has been compared with the well known literature models describing the Helmholtz type cells for photoacoustic spectroscopy. Experimental amplitude and phase frequency data obtained for the two photoacoustic cells have been presented and interpreted in a series of models. Results of the fitting of theoretical curves, obtained in these models, to the experimental data have been shown and discu

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28

Schwarz, R. B. "Helmholtz vibrations in bowed strings." Journal of the Acoustical Society of America 151, no. 4 (2022): 2461–73. http://dx.doi.org/10.1121/10.0010159.

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For almost 160 years, it has been known that Helmholtz oscillations, unique to vibrating strings in bowed instruments (violin, cello, etc.), have two distinct regimes: “slip” and “stick.” During the slip regime, the force at the bow-string interaction is attributed to friction between the sliding bow hair and the vibrating string, with a friction coefficient that decreases with increasing relative velocity. Yet the hair-string interaction during the stick regime is less understood. We propose that the interaction force during the stick regime is proportional to the product of the longitudinal

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29

Gou, J. N., Y. B. Sun, and R. H. Zeng. "An analytical model for the Kelvin–Helmholtz instability in solids." International Journal of Mechanical Sciences 222 (May 2022): 107252. http://dx.doi.org/10.1016/j.ijmecsci.2022.107252.

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30

Luminari, Nicola, Christophe Airiau, and Alessandro Bottaro. "Drag-model sensitivity of Kelvin-Helmholtz waves in canopy flows." Physics of Fluids 28, no. 12 (2016): 124103. http://dx.doi.org/10.1063/1.4971789.

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31

Huttunen, T., M. Malinen, J. P. Kaipio, P. J. White, and K. Hynynen. "A full-wave Helmholtz model for continuous-wave ultrasound transmission." IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 52, no. 3 (2005): 397–409. http://dx.doi.org/10.1109/tuffc.2005.1417262.

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32

Yan, Qiliang, Honglai Liu, and Ying Hu. "Analytical expressions of Helmholtz function of mixing for Ising model." Fluid Phase Equilibria 218, no. 1 (2004): 157–61. http://dx.doi.org/10.1016/j.fluid.2003.12.006.

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33

Suchenek, Mariusz. "Model of the Photoacoustic Helmholtz Resonator with Conical-Ended Duct." International Journal of Thermophysics 35, no. 12 (2014): 2279–86. http://dx.doi.org/10.1007/s10765-014-1562-z.

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34

Nagem, Raymond, Guido Sandri, David Uminsky, and C. Eugene Wayne. "Generalized Helmholtz–Kirchhoff Model for Two-Dimensional Distributed Vortex Motion." SIAM Journal on Applied Dynamical Systems 8, no. 1 (2009): 160–79. http://dx.doi.org/10.1137/080715056.

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35

Heinen, Stephen, Arvind Chandna, Devashish Singh, and Scott Watamaniuk. "Marrying Helmholtz and Hering: A hybrid model of binocular control." Journal of Vision 22, no. 14 (2022): 4171. http://dx.doi.org/10.1167/jov.22.14.4171.

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36

Allaire, G., C. Conca, and M. Vanninathan. "Spectral asymptotics of the Helmholtz model in fluid-solid structures." International Journal for Numerical Methods in Engineering 46, no. 9 (1999): 1463–504. http://dx.doi.org/10.1002/(sici)1097-0207(19991130)46:9<1463::aid-nme708>3.0.co;2-9.

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37

Huang, WJ, Y. Yang, and MR Luo. "Verification of the CAM15u colour appearance model and the QUGR glare model." Lighting Research & Technology 51, no. 1 (2017): 24–36. http://dx.doi.org/10.1177/1477153517734402.

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A psychophysical experiment was carried out to evaluate the glare, brightness, whiteness and hue composition of a glare source made by a multiple-channel LED lighting system. About 80 stimuli were produced to cover a large colour gamut at two luminance levels, 280 and 2400 cd/m2, respectively. The results were used to verify the earlier CAM15u colour appearance model and the QUGR glare model. A revised model, CAM15uz, is refined from CAM15u by adding an effect of hue to the prediction of brightness caused by the Helmholtz–Kohlrausch effect. In addition, a new hue composition scale is establish

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38

Gil, Paweł, Joanna Wilk, and Michał Korzeniowski. "Helmholtz Resonance Frequency of the Synthetic Jet Actuator." Applied Sciences 11, no. 12 (2021): 5666. http://dx.doi.org/10.3390/app11125666.

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This paper presents the results of experimental investigations of 108 geometrical configurations of a loudspeaker-driven synthetic jet (SJ) actuator. The considered cases of the SJ actuator were characterized by a high coupling ratio. The experiment was performed to determine the impact of geometry on the Helmholtz resonance frequency. Geometrical parameters of the orifice diameter, orifice length, and cavity volume were changed within a wide range. The dependences of electrical and flow parameters that characterized the synthetic jet actuators as a function of the excitation frequency were al

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39

Roberty, Nilson C., and Marcelo L. S. Rainha. "Moving Heat Source Reconstruction from the Cauchy Boundary Data." Mathematical Problems in Engineering 2010 (2010): 1–22. http://dx.doi.org/10.1155/2010/987545.

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We consider the problem of reconstruction of an unknown characteristic transient thermal source inside a domain. By introducing the definition of an extended dirichlet-to-Neumann map in the time-space cylinder and the adoption of the anisotropic Sobolev-Hilbert spaces, we can treat the problem with methods similar to those used in the analysis of the stationary source reconstruction problem. Further, the finite differenceθscheme applied to the transient heat conduction equation leads to a model based on a sequence of modified Helmholtz equation solutions. For each modified Helmholtz equation t

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40

Duduchava, Roland, and Medea Tsaava. "Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain." Georgian Mathematical Journal 27, no. 2 (2020): 211–31. http://dx.doi.org/10.1515/gmj-2019-2031.

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AbstractThe purpose of the present research is to investigate model mixed boundary value problems (BVPs) for the Helmholtz equation in a planar angular domain {\Omega_{\alpha}\subset\mathbb{R}^{2}} of magnitude α. These problems are considered in a non-classical setting when a solution is sought in the Bessel potential spaces {\mathbb{H}^{s}_{p}(\Omega_{\alpha})}, {s>\frac{1}{p}}, {1<p<\infty}. The investigation is carried out using the potential method by reducing the problems to an equivalent boundary integral equation (BIE) in the Sobolev–Slobodečkii space on a semi-infinite axis {

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41

Dmitriev, S. P., V. E. Kurochkin, and B. P. Sharfarets. "ON THE IMPROVEMENT OF THE MATHEMATICAL MODEL OF THE ELECTROACOUSTIC TRANSDUCER UNDER THE CONDITION OF A THIN DOUBLE LAYER IN THE POROUS STRUCTURE OF THE TRANSDUCER BODY." NAUCHNOE PRIBOROSTROENIE 31, no. 2 (2021): 44–51. http://dx.doi.org/10.18358/np-31-2-i4451.

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In the approximation of a thin double layer, simple dependences of the acoustic fields excited in an electrokinetic electroacoustic transducer on the velocity of the Helmholtz—Smolukhovsky osmotic movement are obtained. From the dependencies it follows that in the absence of losses, when the nonlinearity of the fluid motion equation does not yet affect and there is no turbulent mode of fluid motion in the transducer body, the magnitudes of the amplitudes of the acoustic velocity and pressure linearly depend on the magnitude of the Helmholtz—Smolukhovsky electroosmotic motion velocity.

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42

Saide Sarıgül, A. "Boundary Element Modeling of Sound Attenuation in Acoustically Lined Curved Pipes." Journal of Theoretical and Computational Acoustics 27, no. 03 (2019): 1850046. http://dx.doi.org/10.1142/s2591728518500469.

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The results of a modeling study for the numerical solution of the interior surface Helmholtz integral for acoustically lined curved pipes with rectangular cross-section are presented. The solution of the Helmholtz integral equation is calculated by using the boundary element method (BEM). The sound attenuation spectra of different possible models with regard to the lining on the boundaries are compared with the analytical solution. The acoustic behavior of different models is discussed and the features of the model that gives more accurate results are presented.

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43

Chiu, Min-Chie. "Noise Elimination of a Multi-tone Broadband Noise with Hybrid Helmholtz Mufflers Using a Simulated Annealing Method." Archives of Acoustics 37, no. 4 (2012): 489–98. http://dx.doi.org/10.2478/v10168-012-0061-0.

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Abstract Noise control is essential in an enclosed machine room where the noise level has to comply with the occupational safety and health act. In order to overcome a pure tone noise with a high peak value that is harmful to human hearing, a traditional reactive muffler has been used. However, the traditional method for designing a reactive muffler has proven to be time-consuming and insufficient. In order to efficiently reduce the peak noise level, interest in shape optimization of a Helmholtz muffler is coming to the forefront. Helmholtz mufflers that deal with a pure tone have been adequat

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44

Riku, Isamu, Masashi Ueda, Tomoki Sawada, and Koji Mimura. "A Nonaffine Molecular Chain Network Model for Elastomeric Gel." Key Engineering Materials 774 (August 2018): 203–9. http://dx.doi.org/10.4028/www.scientific.net/kem.774.203.

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Submerged in a solvent-containing environment and subject to applied forces, a nonaffine molecular chain network absorbs the solvent and deforms, forming an elastomeric gel. The Helmholtz free energy of the gel is separated into the contribution due to stretching the nonaffine molecular chain network and that due to mixing the polymer and the solvent. The effect of the nonaffine movement of the molecular chain on the deformation behavior of the gel is discussed.

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45

Reitz, Rolf D., and Jennifer C. Beale. "MODELING SPRAY ATOMIZATION WITH THE KELVIN-HELMHOLTZ/RAYLEIGH-TAYLOR HYBRID MODEL." Atomization and Sprays 9, no. 6 (1999): 623–50. http://dx.doi.org/10.1615/atomizspr.v9.i6.40.

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46

Rienstra, Sjoerd W., and Deepesh Kumar Singh. "Nonlinear Asymptotic Impedance Model for a Helmholtz Resonator of Finite Depth." AIAA Journal 56, no. 5 (2018): 1792–802. http://dx.doi.org/10.2514/1.j055882.

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Vorobiev, A. M., and I. Yu Popov. "Model of quantum dot and resonant states for the Helmholtz resonator." Journal of Physics: Conference Series 643 (November 2, 2015): 012097. http://dx.doi.org/10.1088/1742-6596/643/1/012097.

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Margolis, Stephen B. "Stability of acoustic oscillations in a model helmholtz-type pulse combustor." Symposium (International) on Combustion 24, no. 1 (1992): 19–27. http://dx.doi.org/10.1016/s0082-0784(06)80007-x.

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Estela-Uribe, J. F. "An improved Helmholtz energy model for air and the related systems." Fluid Phase Equilibria 287, no. 2 (2010): 95–105. http://dx.doi.org/10.1016/j.fluid.2009.09.017.

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Li-Feng, Wang, Ye Wen-Hua, Fan Zheng-Feng, Xue Chuang, and Li Ying-Jun. "A Weakly Nonlinear Model for Kelvin–Helmholtz Instability in Incompressible Fluids." Chinese Physics Letters 26, no. 7 (2009): 074704. http://dx.doi.org/10.1088/0256-307x/26/7/074704.

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