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Journal articles on the topic 'Fourier decomposition'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Batyanovskii, A. V., V. A. Namiot, I. V. Filatov, V. G. Tumanyan, N. G. Esipova, and I. D. Volotovsky. "Fourier transformation in spherical systems as a tool of structural biology." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 4 (2020): 496–503. http://dx.doi.org/10.29235/1561-2430-2020-56-4-496-503.

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Applications of the most common adaptation of Fourier analysis in spherical coordinate systems used to solve a number of problems in structural biology, namely, flat wave decomposition (flat waves are represented as spherical functions decomposition), are herein considered. Arguments in favor of this decomposition are compared with other decompositions in superposition of special functions. A more general justification for the correctness of this decomposition is obtained than that existing today. A method for representing groups of atoms in the form of a Fourier object is proposed. It is also

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2

Batyanovskii, A. V., V. A. Namiot, I. V. Filatov, V. G. Tumanyan, N. G. Esipova, and I. D. Volotovsky. "Fourier transformation in spherical systems as a tool of structural biology." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 4 (2020): 496–503. http://dx.doi.org/10.29235/1561-2430-2020-56-4-496-503.

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Applications of the most common adaptation of Fourier analysis in spherical coordinate systems used to solve a number of problems in structural biology, namely, flat wave decomposition (flat waves are represented as spherical functions decomposition), are herein considered. Arguments in favor of this decomposition are compared with other decompositions in superposition of special functions. A more general justification for the correctness of this decomposition is obtained than that existing today. A method for representing groups of atoms in the form of a Fourier object is proposed. It is also

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3

Wang, Yanbo, and Tao Qian. "Adaptive Fourier decomposition in." Mathematical Methods in the Applied Sciences 42, no. 6 (2019): 2016–24. http://dx.doi.org/10.1002/mma.5494.

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4

ZHANG, LIMING, and HONG LI. "A NOVEL SIGNAL DECOMPOSITION APPROACH — ADAPTIVE FOURIER DECOMPOSITION." Advances in Adaptive Data Analysis 03, no. 03 (2011): 325–38. http://dx.doi.org/10.1142/s1793536911000702.

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This paper presents a novel signal decomposition approach — adaptive Fourier decomposition (AFD), which decomposes a given signal based on its physical characters. The algorithm is described in detail, that is based on recent theoretical studies on analytic instantaneous frequencies and stands as a realizable variation of the greedy algorithm. The principle of the algorithm gives rise to fast convergence in terms of energy. Effectiveness of the algorithm is evaluated by comparison experiments with the classical Fourier decomposition (FD) algorithm. The results are promising.

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5

Qian, Tao, Liming Zhang, and Zhixiong Li. "Algorithm of Adaptive Fourier Decomposition." IEEE Transactions on Signal Processing 59, no. 12 (2011): 5899–906. http://dx.doi.org/10.1109/tsp.2011.2168520.

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6

Kutay, M. Alper, Hakan Özaktaş, Haldun M. Ozaktas, and Orhan Arıkan. "The fractional Fourier domain decomposition." Signal Processing 77, no. 1 (1999): 105–9. http://dx.doi.org/10.1016/s0165-1684(99)00063-8.

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7

QIAN, TAO, and YANBO WANG. "REMARKS ON ADAPTIVE FOURIER DECOMPOSITION." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 01 (2013): 1350007. http://dx.doi.org/10.1142/s0219691313500070.

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This is a continuation of the study of adaptive Fourier decomposition (AFD).15 Under a mild condition not in terms of smoothness, a convergence rate is provided. We prove that the selection of the parameters corresponding to Fourier series in the average sense is optimal. We also present the transformation matrices between the adaptive rational orthogonal system and the related sequence of the shifted Cauchy kernels and their derivatives.

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8

Qian, Tao. "Two-dimensional adaptive Fourier decomposition." Mathematical Methods in the Applied Sciences 39, no. 10 (2016): 2431–48. http://dx.doi.org/10.1002/mma.3649.

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9

Hansen, L., and J. O. Petersen. "Fourier Decomposition Parameters for the Halo RR Lyrae Variables U and V Caeli." International Astronomical Union Colloquium 82 (1985): 272–75. http://dx.doi.org/10.1017/s0252921100109509.

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AbstractUBVRI light curves are obtained for the two halo RR Lyrae variables U Caeli with period 0.420 days (73 observations) and V Caeli with period 0.571 days (42 observations). It is shown that their light curve characteristics are very similar to those of field RR Lyrae stars.Fourier decompositions are studied for all five magnitudes and the resulting amplitude ratios and phase differences are discussed. The differences in the Fourier decomposition parameters between the five magnitudes are shown to be relatively small. Comparisons of the Fourier decomposition parameters for the two halo RR

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10

Kožar, Ivica, Željko Jeričević, and Tatjana Pecak. "Approximate modal analysis using Fourier decomposition." IOP Conference Series: Materials Science and Engineering 10 (June 1, 2010): 012119. http://dx.doi.org/10.1088/1757-899x/10/1/012119.

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11

Zhou, Yicong, Weijia Cao, Licheng Liu, Sos Agaian, and C. L. Philip Chen. "Fast Fourier transform using matrix decomposition." Information Sciences 291 (January 2015): 172–83. http://dx.doi.org/10.1016/j.ins.2014.08.022.

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12

Ma, LiQun, LiHao Feng, Chong Pan, Qi Gao, and JinJun Wang. "Fourier mode decomposition of PIV data." Science China Technological Sciences 58, no. 11 (2015): 1935–48. http://dx.doi.org/10.1007/s11431-015-5908-y.

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13

Gao, You, Min Ku, Tao Qian, and Jianzhong Wang. "FFT formulations of adaptive Fourier decomposition." Journal of Computational and Applied Mathematics 324 (November 2017): 204–15. http://dx.doi.org/10.1016/j.cam.2017.04.029.

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14

Wang, Ze, Feng Wan, Chi Man Wong, and Liming Zhang. "Adaptive Fourier decomposition based ECG denoising." Computers in Biology and Medicine 77 (October 2016): 195–205. http://dx.doi.org/10.1016/j.compbiomed.2016.08.013.

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15

Petersen, J. O. "On the Application of Fourier Decomposition Parameters." International Astronomical Union Colloquium 134 (1993): 157–58. http://dx.doi.org/10.1017/s0252921100014081.

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The application of Fourier decomposition parameters has revolutionized important areas of investigations of Cepheid type variables since the introduction of Fourier analysis in its modern form by Simon and Lee (1981).In the literature several different representations of the results of Fourier analysis have been utilized. In view of the growing interest for applications of Fourier decomposition it is important to use and publish Fourier data in an optimal way. Most studies until now have used amplitude ratios and phase differences derived from traditional light curves giving the light variatio

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16

DÜZ, Murat. "Solution of Lane-Emden Equation with Fourier Decomposition Method." Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi 17, no. 2 (2022): 247–60. http://dx.doi.org/10.29233/sdufeffd.978260.

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In this article, we tried to get the solution of a class of Lane Emden type equations by using the Fourier Decomposition Method. This method is obtained by using the Fourier transform and the Adomian Decomposition method (FADM) together.

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17

Lorsolo, Sylvie, and Altuğ Aksoy. "Wavenumber Analysis of Azimuthally Distributed Data: Assessing Maximum Allowable Gap Size." Monthly Weather Review 140, no. 6 (2012): 1945–56. http://dx.doi.org/10.1175/mwr-d-11-00219.1.

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Abstract Performing wavenumber decomposition on azimuthally distributed data such as those in tropical cyclones can be challenging when data gaps exist in the signal. In the literature, ad hoc approaches are found to determine maximum gap size beyond which not to perform Fourier decomposition. The goal of the present study is to provide a more objective and systematic method to choose the maximum gap size allowed to perform a Fourier analysis on observational data. A Monte Carlo–type experiment is conducted where signals of various wavenumber configurations are generated with gaps of varying s

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18

Wang, Wenlong, George A. McMechan, Chen Tang, and Fei Xie. "Up/down and P/S decompositions of elastic wavefields using complex seismic traces with applications to calculating Poynting vectors and angle-domain common-image gathers from reverse time migrations." GEOPHYSICS 81, no. 4 (2016): S181—S194. http://dx.doi.org/10.1190/geo2015-0456.1.

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Separations of up- and down-going as well as of P- and S-waves are often a part of processing of multicomponent recorded data and propagating wavefields. Most previous methods for separating up/down propagating wavefields are expensive because of the requirement to save time steps to perform Fourier transforms over time. An alternate approach for separation of up-and down-going waves, based on extrapolation of complex data traces is extended from acoustic to elastic, and combined with P- and S-wave decomposition by decoupled propagation. This preserves all the information in the original data

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19

GYONGYOSI, LASZLO, and SANDOR IMRE. "QUANTUM SINGULAR VALUE DECOMPOSITION BASED APPROXIMATION ALGORITHM." Journal of Circuits, Systems and Computers 19, no. 06 (2010): 1141–62. http://dx.doi.org/10.1142/s0218126610006797.

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Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. The proposed Quantum-SVD algorithm interpolates the non-uniform angles in the Fourier domain. The error of the Quantum-SVD approach is some orders lower than the error given by ordinary Quantum Fourier Transformation. Our Quantum-SVD algorithm is a fundamentally novel approach for the computation of the Quantum Fourier Transformation (QFT) of non-uniform states. The presented Quant

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20

Le Clainche, Soledad, and José M. Vega. "Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods." Complexity 2018 (December 12, 2018): 1–21. http://dx.doi.org/10.1155/2018/6920783.

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This article presents a review on two methods based on dynamic mode decomposition and its multiple applications, focusing on higher order dynamic mode decomposition (which provides a purely temporal Fourier-like decomposition) and spatiotemporal Koopman decomposition (which gives a spatiotemporal Fourier-like decomposition). These methods are purely data-driven, using either numerical or experimental data, and permit reconstructing the given data and identifying the temporal growth rates and frequencies involved in the dynamics and the spatial growth rates and wavenumbers in the case of the sp

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21

Elbi, Mehmet Dogan, and Aydin Kizilkaya. "Multicomponent signal analysis: Interwoven Fourier decomposition method." Digital Signal Processing 104 (September 2020): 102771. http://dx.doi.org/10.1016/j.dsp.2020.102771.

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22

Petersen, J. O. "On the application of Fourier decomposition parameters." Astrophysics and Space Science 210, no. 1-2 (1993): 157–58. http://dx.doi.org/10.1007/bf00657888.

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23

Niu, Qiang, and Lin-Zhang Lu. "Fourier analysis of frequency filtering decomposition preconditioners." Applied Mathematics and Computation 216, no. 6 (2010): 1805–18. http://dx.doi.org/10.1016/j.amc.2009.12.024.

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24

Cho, Z. H., K. J. Jung, and Y. M. Ro. "MR fourier transform arteriography using spectral decomposition." Magnetic Resonance in Medicine 16, no. 2 (1990): 226–37. http://dx.doi.org/10.1002/mrm.1910160204.

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25

Cabrel, Wouladje, Golden Tendekai Mumanikidzwa, Jianguo Shen, and Yutong Yan. "Enhanced Fourier Transform Using Wavelet Packet Decomposition." Journal of Sensor Technology 14, no. 01 (2024): 1–15. http://dx.doi.org/10.4236/jst.2024.141001.

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26

Shi, Ruonan, Jae-Hun Jung, and Ferdinand Schweser. "Two-dimensional local Fourier image reconstruction via domain decomposition Fourier continuation method." PLOS ONE 14, no. 1 (2019): e0197963. http://dx.doi.org/10.1371/journal.pone.0197963.

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27

Hrivnák, Jiří, Mariia Myronova, and Jiří Patera. "Central Splitting of A2 Discrete Fourier–Weyl Transforms." Symmetry 12, no. 11 (2020): 1828. http://dx.doi.org/10.3390/sym12111828.

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Two types of bivariate discrete weight lattice Fourier–Weyl transforms are related by the central splitting decomposition. The two-variable symmetric and antisymmetric Weyl orbit functions of the crystallographic reflection group A2 constitute the kernels of the considered transforms. The central splitting of any function carrying the data into a sum of components governed by the number of elements of the center of A2 is employed to reduce the original weight lattice Fourier–Weyl transform into the corresponding weight lattice splitting transforms. The weight lattice elements intersecting with

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28

Mendez, M. A., M. Balabane, and J. M. Buchlin. "Multi-scale proper orthogonal decomposition of complex fluid flows." Journal of Fluid Mechanics 870 (May 15, 2019): 988–1036. http://dx.doi.org/10.1017/jfm.2019.212.

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Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysi

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29

Kou, Kit Ian, and Hong Li. "Greedy adaptive decomposition of signals based on nonlinear Fourier atoms." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 03 (2016): 1650014. http://dx.doi.org/10.1142/s0219691316500144.

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This paper aims at adaptive decomposition of signals in terms of nonlinear Fourier atoms. Each nonlinear Fourier atom is analytic and mono-component. The algorithm is considered as an adaptive greedy procedure based on nonlinear Fourier atoms. The convergence results for the proposed algorithms show that it is suitable to approximate a signal by a linear combinations of nonlinear Fourier atoms. Experiments are presented to illustrate the proposed algorithm and theory.

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30

Nakajima, M. Y., Y. Kawano, and H. Sekigawa. "A new algorithm for producing quantum circuits using KAK decompositions." Quantum Information and Computation 6, no. 1 (2006): 67–80. http://dx.doi.org/10.26421/qic6.1-5.

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We provide a new algorithm that translates a unitary matrix into a quantum circuit according to the G=KAK theorem in Lie group theory. With our algorithm, any matrix decomposition corresponding to type-AIII KAK decompositions can be derived according to the given Cartan involution. Our algorithm contains, as its special cases, Cosine-Sine decomposition (CSD) and Khaneja-Glaser decomposition (KGD) in the sense that it derives the same quantum circuits as the ones obtained by them if we select suitable Cartan involutions and square root matrices. The selections of Cartan involutions for computin

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31

Hole, M. J., and L. C. Appel. "Fourier decomposition of magnetic perturbations in toroidal plasmas using singular value decomposition." Plasma Physics and Controlled Fusion 49, no. 12 (2007): 1971–88. http://dx.doi.org/10.1088/0741-3335/49/12/002.

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32

Avetisyan, Zhirayr G. "A unified mode decomposition method for physical fields in homogeneous cosmology." Reviews in Mathematical Physics 26, no. 03 (2014): 1430001. http://dx.doi.org/10.1142/s0129055x14300015.

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The methods of mode decomposition and Fourier analysis of classical and quantum fields on curved spacetimes previously available mainly for the scalar field on Friedman–Robertson–Walker (FRW) spacetimes are extended to arbitrary vector bundle fields on general spatially homogeneous spacetimes. This is done by developing a rigorous unified framework which incorporates mode decomposition, harmonic analysis and Fourier analysis. The limits of applicability and uniqueness of mode decomposition by separation of the time variable in the field equation are found. It is shown how mode decomposition ca

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33

Kulkarni, SS, AK Bewoor, and RB Ingle. "Vibration signature analysis of distributed defects in ball bearing using wavelet decomposition technique." Noise & Vibration Worldwide 48, no. 1-2 (2017): 7–18. http://dx.doi.org/10.1177/0957456517698318.

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The analysis of vibration signals acquired from a ball bearing with an extended type of distributed defects is carried out using wavelet decomposition technique. The influence of artificially generated defect and its location on outer and inner race of the ball bearing is observed using vibration data acquired from bearing housing. The comparison of diagnostic information from fast Fourier transform and time frequency decomposition method is made for inner and outer race of ball bearing with single as well as multiple extended defects. To decompose vibration signal acquired from bearing, db04

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34

Wang, Wenlong, Biaolong Hua, George A. McMechan, and Bertrand Duquet. "P- and S-decomposition in anisotropic media with localized low-rank approximations." GEOPHYSICS 83, no. 1 (2018): C13—C26. http://dx.doi.org/10.1190/geo2017-0138.1.

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We have developed a P- and S-wave decomposition algorithm based on windowed Fourier transforms and a localized low-rank approximation with improved scalability and efficiency for anisotropic wavefields. The model and wavefield are divided into rectangular blocks that do not have to be geologically constrained; low-rank approximations and P- and S-decomposition are performed separately in each block. An overlap-add method reduces artifacts at block boundaries caused by Fourier transforms at wavefield truncations; limited communication is required between blocks. Localization allows a lower rank

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35

Chen, Zhuo, and Bingting Zha. "Research on decomposition filter optimization algorithm of laser echo signal based on fractional fourier transform." Journal of Physics: Conference Series 2891, no. 4 (2024): 042001. https://doi.org/10.1088/1742-6596/2891/4/042001.

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Abstract For laser echo signal, a decomposition filter optimization algorithm based on fractional Fourier transform is proposed. Faced with the problem of effective signal loss caused by empirical mode decomposition algorithm, the signal component is further filtered by Fourier transform, and then the signal is reconstructed. The denoising algorithm can reduce the signal loss under the condition of effective denoising, and the numerical simulation test proves the effectiveness.

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36

Gaudard, Éric, Philippe Druault, Régis Marchiano, and François Van Herpe. "POD and Fourier analyses of a fluid-structure-acoustic interaction problem related to interior car noise." Mechanics & Industry 18, no. 2 (2017): 201. http://dx.doi.org/10.1051/meca/2016027.

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In order to approach a flow configuration revealing the aerodynamic noise contribution in the interior of road vehicles due to the A-pillar vortex, a numerical simulation of a Forward Facing Step (FFS) coupled with a vibrating structure is performed. This numerical study is based on a weak coupling of three solvers to compute (i) the flow field in interaction with the FFS, (ii) the vibration of the structure and (iii) the acoustic radiation in the open cavity. The purpose of this work is then to evaluate the ability of two different post-processing methods: Proper Orthogonal Decomposition and

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37

Heinig, Hans P. "Fourier operators on weighted Hardy spaces." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 1 (1987): 113–21. http://dx.doi.org/10.1017/s0305004100066457.

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AbstractIn this note we utilize the atomic decomposition of weighted Hardy spaces to prove weighted versions of Hardy's inequality for the Fourier transform with Muckenhoupt weight. The result extends to certain integral operators with homogeneous kernels of degree −1.

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38

Chou, Jung-Hua, and Raylin Wu. "Fourier Series With Spectral and Wave Number Decomposition." American Journal of Applied Sciences 1, no. 4 (2004): 258–60. http://dx.doi.org/10.3844/ajassp.2004.258.260.

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39

Wang, Ze, Chi Man Wong, Agostinho Rosa, Tao Qian, and Feng Wan. "Adaptive Fourier Decomposition for Multi-Channel Signal Analysis." IEEE Transactions on Signal Processing 70 (2022): 903–18. http://dx.doi.org/10.1109/tsp.2022.3143723.

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40

Cheng Liu, 刘诚, 金东永 Dug Young Kim, and 朱健强 Jianqiang Zhu. "Spatial Fourier-decomposition optical fluorescence tomography-theoretical investigation." Chinese Optics Letters 6, no. 9 (2008): 665–68. http://dx.doi.org/10.3788/col20080609.0665.

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41

Young, Leslie A. "RAPID COMPUTATION OF OCCULTATION LIGHTCURVES USING FOURIER DECOMPOSITION." Astronomical Journal 137, no. 2 (2009): 3398–403. http://dx.doi.org/10.1088/0004-6256/137/2/3398.

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42

Lu, Yufeng, Alireza Kasaeifard, Erdal Oruklu, and Jafar Saniie. "Fractional Fourier Transform for Ultrasonic Chirplet Signal Decomposition." Advances in Acoustics and Vibration 2012 (July 25, 2012): 1–13. http://dx.doi.org/10.1155/2012/480473.

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A fractional fourier transform (FrFT) based chirplet signal decomposition (FrFT-CSD) algorithm is proposed to analyze ultrasonic signals for NDE applications. Particularly, this method is utilized to isolate dominant chirplet echoes for successive steps in signal decomposition and parameter estimation. FrFT rotates the signal with an optimal transform order. The search of optimal transform order is conducted by determining the highest kurtosis value of the signal in the transformed domain. A simulation study reveals the relationship among the kurtosis, the transform order of FrFT, and the chir

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43

Wan, Qun, Li Hong Guo, Ding Wang, Lin Zou, and Ji Hao Yin. "Relationship between Discrete Fourier Transformation and Eigenvalue Decomposition." International Journal of Information and Education Technology 9, no. 1 (2019): 74–77. http://dx.doi.org/10.18178/ijiet.2019.9.1.1177.

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44

Moskalik, P., T. Krzyt, N. A. Gorynya, and N. N. Samus. "Accurate Fourier Decomposition of Cepheid Radial Velocity Curves." International Astronomical Union Colloquium 176 (2000): 233–34. http://dx.doi.org/10.1017/s0252921100057614.

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AbstractThe shapes of light curves and of radial velocity curves are two main predictions of the hydrodynamical models of Cepheids. Of the two, the velocity curves are more robust numerically and therefore, more suitable for comparison with the observations. In this report, we present accurate Fourier parameters for an extensive set of classical Cepheid velocity curves. Published radiative models reproduce the observations very well, with only small discrepancies present. We estimate the center of the ω2 = 2ω0 resonance to occur at Pr = 9.947 ± 0.051 day

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45

Qian, Tao, Jianzhong Wang, and Weixiong Mai. "An enhancement algorithm for cyclic adaptive Fourier decomposition." Applied and Computational Harmonic Analysis 47, no. 2 (2019): 516–25. http://dx.doi.org/10.1016/j.acha.2019.01.003.

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46

Li, Jingyu, Xuenan Yang, Tao Qian, and Qiwei Xie. "The adaptive Fourier decomposition for financial time series." Engineering Analysis with Boundary Elements 150 (May 2023): 139–53. http://dx.doi.org/10.1016/j.enganabound.2023.01.037.

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47

Guo, Kai, Jun Ma, Xin Xiong, Yuming Hu, and Xiang Li. "Fault Feature Extraction Method of Rolling Bearing Based on IAFD and TKEO." Journal of Sensors 2024 (February 15, 2024): 1–13. http://dx.doi.org/10.1155/2024/8551009.

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The study of bearing fault feature extraction using adaptive Fourier decomposition (AFD) holds significant practical importance. However, AFD is constrained by its reliance on prior knowledge for determining decomposition levels, which can result in either underdecomposition or overdecomposition based on a single indicator. Consequently, an improved adaptive Fourier decomposition (IAFD) is proposed. First, a combined weight index called SP is constructed, and the whale optimization algorithm is employed to optimize the SP weight parameter. Second, the IAFD decomposition levels can be adaptivel

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48

Zhang, Zhihua. "Fourier Expansions with Polynomial Terms for Random Processes." Journal of Function Spaces 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/763075.

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Based on calculus of random processes, we present a kind of Fourier expansions with simple polynomial terms via our decomposition method of random processes. Using our method, the expectations and variances of the corresponding coefficients decay fast and partial sum approximations attain the best approximation order. Moreover, since we remove boundary effect in our decomposition of random process, these coefficients can discover the instinct frequency information of this random process. Therefore, our method has an obvious advantage over traditional Fourier expansion. These results are also n

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49

Kinsella, Karen, James R. Markham, Chad M. Nelson, and Thomas R. Burkholder. "Thermal Decomposition Products of Fiberglass Composites: A Fourier Transform Infrared Analysis." Journal of Fire Sciences 15, no. 2 (1997): 108–25. http://dx.doi.org/10.1177/073490419701500203.

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Decomposition products of fiberglass composites used in construc tion were identified using Fourier transform infrared (FT-IR) spectroscopy. This bench-scale study concentrated on identification and quantification of toxic species. Identifying compounds evolved during thermal decomposition provides data to develop early fire detection systems as well as evaluate product fire safety performance. Material fire behavior depends on many factors. Ventila tion, radiant heat flux, and chemical composition are three factors that can be modeled. Physical observations of composites during thermal decomp

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50

Abdel Kareem, Waleed, Mahmoud Abdel Aty, and Zafer M. Asker. "Fourier Decomposition and Anisotropic Diffusion Filtering of Forced Turbulence." International Journal of Applied Mechanics 09, no. 08 (2017): 1750121. http://dx.doi.org/10.1142/s1758825117501216.

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The Fourier decomposition and the anisotropic diffusion filtering model are used to extract various flow field scales and their coherent and incoherent parts. The different flow field scales are identified using the Fourier decomposition. Three cutoff wavenumbers are chosen to extract large, medium and fine scale velocity fields, respectively. Then, the anisotropic diffusion model is applied against the obtained velocity fields for each scale to define the coherent and incoherent parts. The forced turbulent velocities are simulated using the lattice Boltzmann method with resolutions [Formula:

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