Relevant bibliographies by topics / Spectral Fourier Method

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Spectral Fourier Method'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Spectral Fourier Method"

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Kawata, S., T. Noda, and S. Minami. "Spectral Searching by Fourier-Phase Correlation." Applied Spectroscopy 41, no. 7 (September 1987): 1176–82. http://dx.doi.org/10.1366/0003702874447536.

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A new idea of spectral library searching is proposed, in which only the phase components of Fourier transforms of both the sample and the reference spectra are used for spectral identification. Compared with the conventional methods, this method has essentially a very high discrimination ability for distinguishing between similar spectra and is very resistant to the peak-height variation and the peak-position shift due to the experimental conditions. The principle and the algorithm of this library search method are described, along with the experimental results for infrared absorption spectra. The results demonstrate that the proposed method gives much lower scores for wrong reference spectra than does the ordinary correlation method, and gives high scores for the sample spectra measured by the various slit widths of the spectrophotometer.
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Wang, Li-lian, and Ben-yu Guo. "Mixed Fourier–Jacobi spectral method." Journal of Mathematical Analysis and Applications 315, no. 1 (March 2006): 8–28. http://dx.doi.org/10.1016/j.jmaa.2005.09.088.

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Eskola, Sisko Maria, and Folke Stenman. "Interpolation of Spectral Data Using the Shift Theorem of the Discrete Fourier Transform." Applied Spectroscopy 51, no. 8 (August 1997): 1179–84. http://dx.doi.org/10.1366/0003702971941719.

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We present a method for interpolating discrete spectral data using the shift theorem of the discrete Fourier transform. The advantages of the method as compared to ordinary curve fitting and similar direct interpolation methods are that, being based on the discrete Fourier transform, our method is also very fast for large sample volumes if used with the fast Fourier transform (FFT) algorithm. In contrast to direct interpolation methods in spectral space, our method does not modify the modulus of the inverse Fourier transform of the shifted profile, so that the spectral content of the signal is preserved. The basis of the method also makes it suitable for analyzing hot-band structures in vibrational spectra. The method is illustrated with two examples.
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Pelz, Richard B. "Fourier spectral method on ensemble architectures." Computer Methods in Applied Mechanics and Engineering 89, no. 1-3 (August 1991): 529–42. http://dx.doi.org/10.1016/0045-7825(91)90058-e.

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Petibois, Cyril, Georges Cazorla, André Cassaigne, and Gérard Déléris. "Plasma Protein Contents Determined by Fourier-Transform Infrared Spectrometry." Clinical Chemistry 47, no. 4 (April 1, 2001): 730–38. http://dx.doi.org/10.1093/clinchem/47.4.730.

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Abstract Background: Fourier-transform infrared (FT-IR) spectrometry has been used to measure small molecules in plasma. We wished to extend this use to measurement of plasma proteins. Methods: We analyzed plasma proteins, glucose, lactate, and urea in 49 blood samples from 35 healthy subjects and 14 patients. For determining the concentration of each biomolecule, the method used the following steps: (a) The biomolecule was sought for which the correlation between spectral range areas of plasma FT-IR spectra and concentrations determined by comparison method was greatest. (b) The IR absorption of the biomolecule at the most characteristic spectral range was calculated by analyzing pure samples of known concentrations. (c) The plasma concentration of the biomolecule was determined using the FT-IR absorption of the pure compound and the integration value obtained for the plasma FT-IR spectra. (d) The spectral contribution of the biomolecule was subtracted from the plasma FT-IR spectra, and the resulting spectra were saved for further analyses. (e) The same method was then applied to determining the concentrations of other biomolecules by sequentially comparing the resulting FT-IR spectra. Results: Results agreed with those obtained by clinical methods for the following biomolecules when analyzed in the following order: albumin, glucose, fibrinogen, IgG2, lactate, IgG1, α1-antitrypsin, α2-macroglobulin, transferrin, apolipoprotein (Apo)-A1, urea, Apo-B, IgM, Apo-C3, IgA, IgG4, IgG3, IgD, haptoglobin, and α1-acid glycoprotein. Conclusion: FT-IR spectrometry is a useful tool for determining concentrations of several plasma biomolecules.
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Meek, R. A., and A. A. Vassiliou. "Characterizing three‐dimensional wavefields with high‐resolution spectra." GEOPHYSICS 57, no. 4 (April 1992): 522–31. http://dx.doi.org/10.1190/1.1443266.

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Three‐dimensional spectra (frequency‐x‐wavenumber‐y‐wavenumber or [Formula: see text] spectra) can be used to determine the frequency content, velocity, and direction of waves entering an array of receivers. This information is important in detecting aliasing problems, understanding coherent noise, designing arrays, and determining parameters for coherent noise filters. Because of the limited spatial dimensions of most arrays the discrete Fourier transform produces an estimate of the three‐dimensional (3-D) spectrum with severe wavenumber distortion. We extend a 2-D hybrid spectral estimation method to three dimensions by combining a temporal Fourier transform with a spatial 2-D maximum entropy spectral estimation technique. The method produces [Formula: see text] spectra with higher wavenumber resolution and less spectral distortion than corresponding 3-D Fourier spectra. The 2-D maximum entropy spectral estimation algorithm uses a sequence of Fourier transforms to extrapolate the estimated autocorrelation function of the data. We assume the wavenumber spectrum of the data comprises a sum of a few poles. Field and synthetic data are used to demonstrate how 3-D wavefields can be characterized with this method of spectral analysis. From these results we conclude that the method gives excellent wavenumber resolution but performs poorly in detecting small signals in the presence of high amplitude signals. We feel this limitation is not serious for characterizing strong amplitude coherent energy recorded by an array of receivers.
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Zhang, Lei, Weihua Ou Yang, Xuan Liu, and Haidong Qu. "Fourier Spectral Method for a Class of Nonlinear Schrödinger Models." Advances in Mathematical Physics 2021 (July 1, 2021): 1–11. http://dx.doi.org/10.1155/2021/9934858.

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In this paper, Fourier spectral method combined with modified fourth order exponential time-differencing Runge-Kutta is proposed to solve the nonlinear Schrödinger equation with a source term. The Fourier spectral method is applied to approximate the spatial direction, and fourth order exponential time-differencing Runge-Kutta method is used to discrete temporal direction. The proof of the conservation law of the mass and the energy for the semidiscrete and full-discrete Fourier spectral scheme is given. The error of the semidiscrete Fourier spectral scheme is analyzed in the proper Sobolev space. Finally, several numerical examples are presented to support our analysis.
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Yoon, Sungha, Darae Jeong, Chaeyoung Lee, Hyundong Kim, Sangkwon Kim, Hyun Geun Lee, and Junseok Kim. "Fourier-Spectral Method for the Phase-Field Equations." Mathematics 8, no. 8 (August 18, 2020): 1385. http://dx.doi.org/10.3390/math8081385.

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In this paper, we review the Fourier-spectral method for some phase-field models: Allen–Cahn (AC), Cahn–Hilliard (CH), Swift–Hohenberg (SH), phase-field crystal (PFC), and molecular beam epitaxy (MBE) growth. These equations are very important parabolic partial differential equations and are applicable to many interesting scientific problems. The AC equation is a reaction-diffusion equation modeling anti-phase domain coarsening dynamics. The CH equation models phase segregation of binary mixtures. The SH equation is a popular model for generating patterns in spatially extended dissipative systems. A classical PFC model is originally derived to investigate the dynamics of atomic-scale crystal growth. An isotropic symmetry MBE growth model is originally devised as a method for directly growing high purity epitaxial thin film of molecular beams evaporating on a heated substrate. The Fourier-spectral method is highly accurate and simple to implement. We present a detailed description of the method and explain its connection to MATLAB usage so that the interested readers can use the Fourier-spectral method for their research needs without difficulties. Several standard computational tests are done to demonstrate the performance of the method. Furthermore, we provide the MATLAB codes implementation in the Appendix A.
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Owolabi, Kolade M., and Ayodeji A. Adejola. "Fourier Spectral Method for Solving Fractional-order System." Universal Journal of Computational Mathematics 5, no. 3 (July 2017): 75–85. http://dx.doi.org/10.13189/ujcmj.2017.050304.

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Jiao, Yujian, Tianjun Wang, Xiandong Shi, and Wenjie Liu. "MIXED JACOBI-FOURIER SPECTRAL METHOD FOR FISHER EQUATION." Mathematical Modelling and Analysis 23, no. 2 (April 18, 2018): 240–61. http://dx.doi.org/10.3846/mma.2018.016.

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In this paper, we propose a mixed Jacobi-Fourier spectral method for solving the Fisher equation in a disc. Some mixed Jacobi-Fourier approximation results are established, which play important roles in numerical simulation of various problems defined in a disc. We use the generalized Jacobi approximation to simulate the singularity of solution at the regional center. This also simplifies the theoretical analysis and provides a sparse system. The stability and convergence of the proposed scheme are proved. Numerical results demonstrate the efficiency of this new algorithm and coincide well with the theoretical analysis.
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Dissertations / Theses on the topic "Spectral Fourier Method"

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Bolis, Alessandro. "Fourier spectral/hp element method : investigation of time-stepping and parallelisation strategies." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/25140.

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As computer hardware has evolved, the time required to perform numerical simulations has reduced, allowing investigations of a wide range of new problems. This thesis focuses on algorithm optimization, to minimize run-time, when solving the incompressible Navier-Stokes equations. Aspects affecting performance related to the discretisation and algorithm parallelization are investigated in the context of high-order methods. The roles played by numerical approximations and computational strategies are highlighted and it is recognized that a versatile implementation provides additional benefits, allowing an ad-hoc selection of techniques to fit the needs of heterogeneous computing environments. We initially describe the building blocks of a spectral/hp element and pure spectral method and how they can be encapsulated and combined to create a 3D discretisation, the Fourier spectral/hp element method. Time-stepping strategies are also described and encapsulated in a flexible framework based on the General Linear Method. After implementing and validating an incompressible Navier-Stokes solver, two canonical turbulent flows are analyzed. Afterward a 2D hyperbolic equation is considered to investigate the efficiency of low- and high-order methods when discretising the spatial and temporal derivatives. We perform parametric studies, monitoring accuracy and CPU-time for different numerical approximations. We identify optimal discretisations, demonstrating that high-order methods are the computationally fastest approach to attain a desired accuracy for this problem. Following the same philosophy, we investigate the benefits of using a hybrid parallel implementation. The message passing model is introduced to parallelize different kernels of an incompressible Navier-Stokes solver. Monitoring the parallel performance of these strategies the most efficient approach is highlighted. We also demonstrate that hybrid parallel solutions can be used to significantly extend the strong scalability limit and support greater parallelism.
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Akkineni, Dharma Teja. "A Fourier Spectral Method to Solve Linear and Non-Linear Differential Equations and its Applications." University of Akron / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1418994964.

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Mahmoud, Ali. "Analyseur de spectre à haute résolution : Apllication à la mesure des oscillateurs ultrastables." Besançon, 1989. http://www.theses.fr/1989BESA2004.

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Une methode de mesure par intercorrelation utilisant l'intercomparaison de trois oscillateurs deux a deux, permet de mesurer les fluctuations de phase ou de frequence des oscillateurs ultrastables. Nous presentons l'etude et la realisation d'un analyseur de spectre par correlation. Cet appareil permet d'analyser la fonction de correlation ou de calculer la densite spectrale de puissance du bruit de phase de l'oscillateur a mesurer
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Sadrinezhad, Arezoo. "Multiaxial Probabilistic Elastic-Plastic Constitutive Simulations of Soils." University of Akron / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1406637815.

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Miar, Yasin. "Improved Wideband Spectrum Sensing Methods for Cognitive Radio." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/23333.

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Abstract Cognitive Radio (CR) improves the efficiency of spectrum utilization by allowing non- licensed users to utilize bands when not occupied by licensed users. In this thesis, we address several challenges currently limiting the wide use of cognitive radios. These challenges include identification of unoccupied bands, energy consumption and other technical challenges. Improved accuracy edge detection techniques are developed for CR to mitigate both noise and estimation error variance effects. Next, a reduced complexity Simplified DFT (SDFT) is proposed for use in CR. Then, a sub-Nyquist rate A to D converter is introduced to reduce energy consumption. Finally, a novel multi-resolution PSD estimation based on expectation-maximization algorithm is introduced that can obtain a more accurate PSD within a specified sensing time.
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Jacob, Bruno Tadeu Pereira. "Modelagem matemática de esteiras em desenvolvimento temporal utilizando o método pseudoespectral de Fourier." Universidade Federal de Uberlândia, 2015. https://repositorio.ufu.br/handle/123456789/14997.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The present work is dedicated to perform the mathematical modeling and DNS and LES simulations of a three-dimensional, temporally evolving incompressible plane wake are performed, seeking to evidence differences in stability, transition and onset of both coherent and small scale structures, when the flow is subjected to random perturbations of different amplitudes. The perturbations are generated using the Random-Flow-Generator (RFG) technique, being imposed to the flow as initial conditions. The Navier-Stokes equations are solved in a prismatic domain, with periodic boundary conditions in all directions, using Fourier pseudospectral method. The invariants of the velocity gradient tensor, Q and R, are analyzed for random perturbations with magnitudes 10−3, 10−4 and 10−5, showing the onset of their characteristic teardrop correlation map. Moreover, maps of the second and third invariants of the rate-of-strain tensor, QS and RS, are shown, in order to evidence the differences in local flow strain and topological characteristics of the dissipation of kinetic energy. Isosurface plots of Q and QW, as well as vorticity contours are shown, allowing visual identification of the coherent structures and confirming patterns predicted by the invariant maps.
O presente trabalho se dedica a modelagem matemática e a simulações numéricas DNS e LES de uma esteira tridimensional, incompressível, em desenvolvimento temporal, buscando evidenciar diferenças na estabilidade, transição e no desenvolvimento de estruturas coerentes e de pequena escala, quando o escoamento é submetido a perturbações randômicas de diferentes amplitudes. As perturbações são geradas utilizando-se a técnica Random Flow Generator (RFG), sendo sobrepostas à condição inicial do escoamento. As equações de Navier-Stokes são resolvidas em um domínio prismático, com condições de contorno periódicas em todas as direções, utilizando-se o método pseudoespectral de Fourier. Os invariantes do tensor gradiente de velocidade, Q e R, são analisados para perturbações de magnitude 10−3, 10−4 and 10−5, mostrando a formação de uma correlação no formato de gota, característica da resolução das equações de Navier-Stokes. Além disso, são apresentados mapas do segundo e terceiro invariante do tensor taxa de deformação, QS e RS, a fim de evidenciar as diferenças locais no escoamento e as características topológicas na taxa de dissipação de energia cinética. Isosuperfícies de Q e QW, bem como contornos de vorticidade são apresentados, possibilitando a identificação visual das estruturas coerentes, e confirmando os padrões de estruturas previstos pelos mapas de invariância.
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Silva, Francisco EstÃnio da. "AnÃlise da Integridade Estrutural de CompÃsitos AtravÃs da CaracterizaÃÃo Fractal de Sinais de EmissÃo AcÃstica." Universidade Federal do CearÃ, 2002. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=7508.

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FundaÃÃo de Amparo à Pesquisa do Estado do CearÃ
Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
Neste trabalho analisou-se a integridade mecÃnica do material compÃsito constituÃdo por uma matriz polimÃrica, resina epoxi DER 331, e por fibra de vidro tipo âEâ como agente de reforÃo. Esta anÃlise foi realizada utilizando-se o ensaio de emissÃo acÃstica, com o objetivo de correlacionar as formas de onda dos sinais com os mecanismos de falhas associados aos esforÃos de traÃÃo e flexÃo aplicados a espÃcimes fabricados com tal material. Na anÃlise dos sinais como funÃÃo do tempo foram utilizados os mÃtodos de contagem de caixas, que fornece a dimensÃo fractal, e o do intervalo re-escalado de Hurst, sendo tambÃm utilizado o mÃtodo espectral de Fourier para a anÃlise no domÃnio da freqÃÃncia. Mostrou-se que os expoentes calculados pelos mÃtodos espectral de Fourier e re-escalado de Hurst estÃo correlacionados com a dimensÃo fractal obtida pelo mÃtodo de contagem de caixa, e satisfazem as relaÃÃes previstas pelas leis de escala. Os resultados mostraram tambÃm a existÃncia de duas regiÃes de escala distintas, sendo uma caracterizada pela persistÃncia do sinal e outra por um comportamento aleatÃrio caracterÃstica do ruÃdo presente. As dimensÃes fractais obtidas apresentaram-se independentes da taxa de aquisiÃÃo da forma da onda emitida indicando a propriedade de auto-similaridade dos sinais estudados, o que confirma a sua caracterÃstica fractal. Finalmente, Ã conjecturado uma correlaÃÃo entre o coeficiente de Hurst/dimensÃo fractal e as falhas mecÃnicas observadas.
In this work it is analysed the mechanical integrity of the composite material constituted of a polymeric matrix, epoxy resin DER 331, reinforced by glass fiber type E. This analysis has been done by using the acoustic emission testing with the aim to correlating the wave-form of the pulse with the flaw mechanisms associated to the tensile and bending loads applied to the samples. The analysis of the pulses as a function of time has been made by using box counting method, which provides the fractal dimension, and the rescaled Hurst analysis. The analysis in the frequency domain has been made by using the spectral Fourier method It has been shown that the exponents obtained from the spectral Fourier method and the rescaled Hurst analysis are correlated to the box counting fractal dimension, and satisfy the known relations obtained from the scaling laws. The results have also shown the existence of two scaling regions, characterized by the persistence of the pulse and by a random behaviour, respectively. The fractal dimensions have also been shown to be independent of time acquisition of the emitted pulse, and this indication of self-similarity confirms its fractal characteristics. Finally, it is conjectured a correlation between the Hurst coefficient/fractal dimension and the mechanical flaws observed.
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Mariano, Felipe Pamplona. "Simulação de escoamentos não-periódicos utilizando as metodologias pseudo-espectral e da fronteira imersa acopladas." Universidade Federal de Uberlândia, 2007. https://repositorio.ufu.br/handle/123456789/15021.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Modern engineering increasingly requires the comprehension of phenomena related to combustion, aeroacustics, turbulence transition, among others. For these purposes the Computational Fluids Dynamics (CFD) requires the used high order methods. One of these methods is the Fourier pseudo-spectral method, that provides an excellent numerical accuracy, and with the use of the Fast Fourier Transform algorithm (FFT), it presents a low computational cost in comparison to anothers high-order methods. Another important issue is the projection method of the pression term, which does not require the pressure computation from the Navier-Stokes equations. The procedure to calculate the pression field is usually the most onerous in classical methodologies. Nevertheless, the pseudo-spectral method can be only applied to periodic boundary flows, thus limiting its use. Aiming to solve this restriction, a new methodology is proposed at the present work, which has the objective of simulating nonperiodic flows using the Fourier pseudo-spectral method. For this purpose the immersed boundary method, that represents the boundary conditions through a force field imposed at Navier-Stokes equations is used. As a test to this new methodology, a classic problem of Computational Fluid Dynamics, The Lid Driven Cavity was simulated. The obtained results are promising and demonstrate the possibility to simulating non-periodic flows making use of the Fourier pseudo-spectral method.
Para compreender fenômenos relacionados à combustão, aeroacústica, transição a turbulência entre outros, a Dinâmica de Fluídos Computacional (CFD) utiliza os métodos de alta ordem. Um dos mais conhecidos é o método pseudo-espectral de Fourier, o qual alia: alta ordem de precisão na resolução das equações, com um baixo custo computacional. Este está ligado à utilização da FFT e do método da projeção do termo da pressão, o qual desvincula os cálculos da pressão da resolução das equações de Navier-Stokes. O procedimento de calcular o campo de pressão, normalmente é o mais oneroso nas metodologias convencionais. Apesar destas vantagens, o método pseudo-espectral de Fourier só pode ser utilizado para resolver problemas com condições de contorno periódicas, limitando o seu uso no campo da dinâmica de fluídos. Visando resolver essa restrição uma nova metodologia é proposta no presente trabalho, que tem como objetivo simular escoamentos não-periódicos utilizando o método pseudo-espectral de Fourier. Para isso, é utilizada a metodologia da Fronteira Imersa, a qual representa as condições de contorno de um escoamento através de um campo de força imposto nas equações de Navier-Stokes. Como teste, para essa nova metodologia, foi simulada uma cavidade com tampa deslizante (Lid Driven Cavity), problema clássico da mecânica de fluídos, que objetiva validar novas metodologias e códigos computacionais. Os resultados obtidos são promissores e demostram que é possível simular um escoamento não-periódico com o método pseudo-espectral de Fourier.
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Ismail, Atikah. "Fourier spectral methods for numerical modeling of ionospheric processes." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-03142009-040454/.

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Anhaouy, Pichmony. "Fourier spectral methods for solving the Korteweg-de Vries equation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ51284.pdf.

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Books on the topic "Spectral Fourier Method"

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Deville, M. O. Fourier analysis of finite element preconditioned collocation schemes. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1990.

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Deville, M. O. Fourier analysis of finite element preconditioned collocation schemes. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1990.

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Boyd, J. P. Chebyshev & Fourier spectral methods. Berlin: Springer-Verlag, 1989.

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Chebyshev and Fourier spectral methods. 2nd ed. Mineola, N.Y: Dover Publications, 2001.

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Boyd, John Philip. Chebyshev & Fourier Spectral Methods. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83876-7.

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Cai, Wei. On one-sided filters for spectral Fourier approximations of discontinuous functions. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1991.

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Cai, Wei. Non-oscillatory spectral Fourier methods for shock wave calculations. Hampton, Va: ICASE, 1988.

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Cai, Wei. Non-oscillatory spectral Fourier methods for shock wave calculations. Hampton, Va: ICASE, 1988.

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Mercier, Bertrand. An introduction to the numerical analysis of spectral methods. Berlin: Springer-Verlag, 1989.

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Tadmor, Eitan. Spectral methods for time dependent problems. Hampton, Va: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1990.

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Book chapters on the topic "Spectral Fourier Method"

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Peyret, Roger. "Fourier Method." In Spectral Methods for Incompressible Viscous Flow, 17–37. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-6557-1_3.

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Kundu, Sayani, Palaiahnakote Shivakumara, Anaica Grouver, Umapada Pal, Tong Lu, and Michael Blumenstein. "A New Forged Handwriting Detection Method Based on Fourier Spectral Density and Variation." In Lecture Notes in Computer Science, 136–50. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41404-7_10.

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Saha Ray, Santanu. "A Novel Approach with Time-Splitting Fourier Spectral Method for Riesz Fractional Differential Equations." In Nonlinear Differential Equations in Physics, 335–73. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-1656-6_8.

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Shen, Jie, Tao Tang, and Li-Lian Wang. "Fourier Spectral Methods for Periodic Problems." In Spectral Methods, 23–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-540-71041-7_2.

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Kido, Ken’iti. "Cross-Spectrum Method." In Digital Fourier Analysis: Advanced Techniques, 53–84. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1127-1_3.

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Khare, Kedar. "The Angular Spectrum Method." In Fourier Optics and Computational Imaging, 145–51. Chichester, UK: John Wiley & Sons, Ltd, 2015. http://dx.doi.org/10.1002/9781118900352.ch10.

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Benedetto, John J. "Some Mathematical Methods for Spectrum Estimation." In Fourier Techniques and Applications, 73–100. Boston, MA: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4613-2525-3_5.

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Iwaniec, Henryk. "Estimates for the Fourier coefficients of Maass forms." In Spectral Methods of Automorphic Forms, 107–20. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/gsm/053/10.

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Biner, S. Bulent. "Solving Phase-Field Models with Fourier Spectral Methods." In Programming Phase-Field Modeling, 99–168. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-41196-5_5.

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Jekeli, Christopher. "Fourier transforms of functions on the continuous domain." In Spectral Methods in Geodesy and Geophysics, 13–81. Boca Raton, FL : CRC Press, 2017. | "A science publishers book.": CRC Press, 2017. http://dx.doi.org/10.1201/9781315118659-2.

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Conference papers on the topic "Spectral Fourier Method"

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Schwartz, Eyal, and Stephen G. Lipson. "Spectroscopic interferometric method of revealing spectral features from extra-solar planets." In Fourier Transform Spectroscopy. Washington, D.C.: OSA, 2011. http://dx.doi.org/10.1364/fts.2011.jpdp4.

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Tanaka, S. "Application of Fourier transform method to spectral interferometry." In 17th Congress of the International Commission for Optics: Optics for Science and New Technology. SPIE, 1996. http://dx.doi.org/10.1117/12.2316234.

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Fu, Huankun, and Chaoqun Liu. "Modified Fourier Spectral Method for Non-periodic CFD." In 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2012. http://dx.doi.org/10.2514/6.2012-576.

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AMON, CRISTINA. "Spectral element-Fourier method for transitional flows in complex geometries." In 10th Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1991. http://dx.doi.org/10.2514/6.1991-1608.

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Cui, Deqi, Ningfang Liao, Ling Ma, Minyong Liang, and Yu Lin. "Spectral calibration method for all-reflected Fourier transform imaging spectrometer." In International Conference of Optical Instrument and Technology, edited by Shenghua Ye, Guangjun Zhang, and Jun Ni. SPIE, 2008. http://dx.doi.org/10.1117/12.806914.

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Diatroptov, Mikhail, Victor Panchelyuga, Maria Panchelyuga, and Olga Seraya. "On the universal spectrum of periods in the time series of temperature fluctuations in starlings and rats." In International Conference "Computing for Physics and Technology - CPT2020". Bryansk State Technical University, 2020. http://dx.doi.org/10.30987/conferencearticle_5fce2772b9b793.28915214.

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The paper considers a spectral analysis based on Fourier transform of the time series in the temperature fluctuations in the bodies of common starlings (Sturnus vulgaris) and rats (mature Wistar males). The spectra of the periods in the starlings and rats contain the same sets of harmonics, so on this basis we can tell about a common spectrum. Interesting to note that the spectrum coincides with a previously revealed spectrum of the periods, obtained with the use of local fractal analysis by the all permutations method in the course of studies of time series of the alpha decay rate fluctuations. Despite different methods of the experimental data processing used in this work (spectral analysis based on Fourier transform and local fractal analysis by the all permutations method), as well as different raw experimental data (the temperature fluctuations and alpha-decay rate fluctuations), the same spectrum of periods was obtained. On this basis, we can consider the spectrum of periods as universal one.
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Moore, Travis J., Darron P. Cundick, Matthew R. Jones, Dale R. Tree, R. Daniel Maynes, and Larry L. Baxter. "An Experimental Method for Making In Situ Spectral Emittance Measurements of Coal Ash Deposits." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-13215.

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An experimental procedure has been developed to make in situ spectral emittance measurements of coal ash deposits. Pulverized coal is injected into a down-fired, entrained-flow reactor. Ash accumulates on a probe placed in the reactor effluent. The spectral emittance of the ash layer is calculated using measurements of the surface temperature and the spectral emissive power of the deposit. Measurements of the spectral emissive power and the surface temperature are obtained using a Fourier transform infrared (FTIR) spectrometer. The methods used to extract the spectral emissive power and surface temperature from measured infrared spectra were validated using a blackbody radiator at known temperatures. The experimental procedure was then used to find the spectral emittance of a coal ash deposit formed under oxidizing conditions.
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Kobayashi, Marcelo, and Melike Nikbay. "On a Fourier Spectral Variational Asymptotic Method for Cellular Composite Structures." In 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-1543.

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Wu, Qiong, and Ji Wu. "Complex spectral Fourier-domain imaging method for Synthetic Aperture Microwave Radiometer." In 2010 Second IITA International Conference on Geoscience and Remote Sensing (IITA-GRS 2010). IEEE, 2010. http://dx.doi.org/10.1109/iita-grs.2010.5603093.

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Pitz, Diogo B., John W. Chew, Olaf Marxen, and Nicholas J. Hills. "Direct Numerical Simulation of Rotating Cavity Flows Using a Spectral Element-Fourier Method." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-56486.

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A high-order numerical method is employed to investigate flow in a rotor/stator cavity without heat transfer and buoyant flow in a rotor/rotor cavity. The numerical tool used employs a spectral element discretisation in two dimensions and a Fourier expansion in the remaining direction, which is periodic and corresponds to the azimuthal coordinate in cylindrical coordinates. The spectral element approximation uses a Galerkin method to discretise the governing equations, similarly to a finite element method, but employs high-order polynomials within each element to obtain spectral accuracy. A second-order, semi-implicit, stiffly stable algorithm is used for the time discretisation, and no subgrid modelling is included in the governing equations. Numerical results obtained for the rotor/stator cavity compare favourably with experimental results for Reynolds numbers up to Re1 = 106 in terms of velocities and Reynolds stresses. For the buoyancy-driven flow, the energy equation is coupled to the momentum equations via the Boussinesq approximation, which has been implemented in the code considering two different formulations. Numerical predictions of the Nusselt number obtained using the traditional Boussinesq approximation are considerably higher than available experimental data. Much better agreement is obtained when the extended Boussinesq approximation is employed. It is concluded that the numerical method employed has considerable potential for further investigations of rotating cavity flows.
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