Spelling suggestions: "subject:"chebyshev"" "subject:"tchebyshev""
61 |
Maximum Rate of Growth of Enstrophy in the Navier-Stokes System on 2D Bounded DomainsSliwiak, Adam January 2017 (has links)
One of the key open problems in the field of theoretical fluid mechanics concerns the possibility of the singularity formation in solutions of the 3D Navier-Stokes system in finite time. This phenomenon is associated with the behaviour of the enstrophy, which is an L2 norm of the vorticity and must become unbounded if such a singularity occurs. Although there is no blow-up in the 2D Navier-Stokes equation, we would like to investigate how much enstrophy can a planar incompressible flow in a bounded domain produce given certain initial enstrophy. We address this issue by formulating an optimization problem in which the time derivative of the enstrophy serves as the objective functional and solve it using tools of the optimization theory and calculus of variations. We propose an efficient computational approach which is based on the iterative steepest-ascent procedure. In addition, we introduce an easy-to-implement method of computing the gradient of the objective functional. Finally, we present computational results addressing the key question of this project and provide numerical evidence that the maximum enstrophy growth exhibits the scaling dE/dt ~ C*E*E for C>0 and very small E. All computations are performed using the Chebyshev spectral method. / Thesis / Master of Science (MSc) / For many decades, scientists have been investigating fundamental aspects of the Navier-Stokes equation, a central mathematical model arising in fluid mechanics. Although the equation is widely used by engineers to describe numerous flow phenomena, it is still an open question whether the Navier-Stokes system always admits physically meaningful solutions. To address this issue, we want to explore its mathematical aspects deeper by analyzing the behaviour of the enstrophy, which is a quantity associated with the vorticity of the flow and a convenient measure of the regularity of the solution. In this study, we consider a planar and incompressible flow bounded by solid walls. Using basic tools of mathematical analysis and optimization theory, we propose a computational method enabling us to find out how much enstrophy can such a flow produce instantaneously. We present numerical evidence that this instantaneous growth of enstrophy has a well-defined asymptotic behavior, which is consistent with physical assumptions.
|
62 |
Solution of non-linear partial differential equations with the Chebyshev Spectral methodEldred, Lloyd B. 21 November 2012 (has links)
The Spectral method is a powerful numerical technique for solving engineering differential equations. The method is a specialization of the method of weighted residuals. Trial functions that are easily and exactly differentiable are used. Often the functions used also satisfy an orthogonality equation, which can improve the efficiency of the approximation. Generally, the entire domain is modeled, but multiple sub-domains may be used.
A Chebyshev-Collocation Spectral method is used to solve a variety of ordinary and partial differential equations. The Chebyshev Polynomial series follows a well established recursion relation for calculation of the polynomials and their derivatives. Two different schemes are studied for formulation of the problems, a Fast Fourier Transform approach, and a matrix multiplication approach. First, the one-dimensional ordinary differential equation representing the deflection of a tapered bar under its own weight is studied. Next, the two dimensional Poisson's equation is examined. Lastly, a two dimensional, highly non-linear, two parameter Bratu's equation is solved.
Each problem's results are compared to results from other methods or published data. Accuracy is very good, with a significant improvement in computer time. / Master of Science
|
63 |
Solution de C. Hyltén-Cavallius pour un problème de P. Turán concernant des polynômesTinawi, Félix January 2008 (has links)
Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.
|
64 |
Análise do comportamento dinâmico de ponte de concreto por meio de filtragem de sinais GPS / Analysis of the dynamic behavior of concrete bridges by GPS signals filteringOliveira, José Venâncio Marra 06 September 2018 (has links)
Esta pesquisa propôs uma contribuição aos procedimentos de inspeção de pontes por meio de um plano de monitoramento de curta duração do comportamento dinâmico do tabuleiro de pontes rodoviárias de concreto com a utilização de receptores GPS de 100 Hz associado à diversas técnicas de filtragem de sinais. O estudo foi conduzido em uma ponte em serviço localizada na rodovia Fernão Dias (BR-381). O procedimento de inspeção proposto baseou-se no uso de dois sinais de satélites GPS, por meio da aplicação do Método Residual de Fase (MRF), e da análise temporal dos resíduos da dupla diferença de fase a partir da Fast Fourier Transform (FFT), Continuous Wavelet Transform (CWT), Passa-Faixa Chebyshev do Tipo I. A descrição do comportamento dinâmico do tabuleiro do vão central da ponte se deu por meio da extração dos valores de frequência e amplitude das deflexões verticais a partir dos dados GPS filtrados (resíduos), em três períodos de amostragem de 1 minuto. Os valores de frequência variaram de 0,5 Hz a 8 Hz nos três períodos de amostragens e também nos filtros FFT, CWT e Passa-Faixa Chebyshev do Tipo I. Os valores de amplitude de deslocamento vertical máximo ficaram em torno de 6 mm. Estes valores coincidiram com os valores de frequência e amplitude de deslocamento vertical registrados pela instrumentação clássica com acelerômetros, transdutores de deslocamento vertical, modelagem por elementos finitos e prova de carga estática e dinâmica realizadas sobre tabuleiro do vão central da ponte instrumentado. Por fim, pode-se afirmar que os procedimentos propostos, além de poderem ser utilizados como uma etapa preliminar de inspeção de tabuleiro de pontes rígidas possibilitaram a detecção de deslocamentos dinâmicos verticais milimétricos e suas frequências de vibração. / This research proposed a contribution for bridge inspection procedures at of a short-term monitoring plan of the dynamic behavior of the concrete road bridge with the use of 100 Hz GPS receivers associated with various signal filtering techniques. The study was conducted in the service bridge located on the highway Fernão Dias (BR-381). The procedure inspection proposed was based on the use of two satellite GPS signals, by applying the Phase Residual Method (PRM), and the temporal analysis of the residuals of the double difference phase from the Fast Fourier Transform (FFT), Continuous Wavelet Transform (CWT), Type I Chebyshev Band-Pass. The dynamic behavior of the central span of the bridge was described by extracting the frequency and amplitude values of the vertical deflections from the filtered GPS data (residues), in three sampling periods of 1 minute. The frequency values found ranged from 0.5 Hz to 8 Hz in the three sampling periods as well as in the FFT, CWT and Chebyshev Type I Band-Pass filters. The maximum vertical displacement peak values were around 6 mm. These values coincided with the vertical displacement and amplitude values recorded by the classical instrumentation with accelerometers, vertical displacement transducers, finite element modeling and static and dynamic load test performed on the central span deck of the instrumented bridge. Finally, it could affirm that the procedures proposed, besides being able to be used as a preliminary step of inspection of the rigid bridge\'s deck enabled the detection of millimetric vertical dynamic displacements and their frequencies of vibration.
|
65 |
Combinações lineares de polinômios de Chebyshev e polinômios auto-recíprocos /Hancco Suni, Mijael January 2019 (has links)
Orientador: Vanessa Avansini Botta Pirani / Resumo: O presente trabalho tem como objetivo principal estudar o comportamento dos zeros de alguns tipos de polinômios auto-recíprocos gerados a partir de polinômios quaseortogonais de Chebyshev de ordens um e dois. Os zeros dos polinômios auto-recíprocos que construímos estão ligados aos zeros de polinômios quase-ortogonais. Os polinômios quaseortogonais podem ser obtidos a partir de uma sequência de polinômios ortogonais. Neste trabalho, usaremos os polinômios de Chebyshev para obter polinômios quase-ortogonais e usaremos resultados sobre o comportamento de zeros desses polinômios para obter informações sobre o comportamento dos zeros de polinômios auto-recíprocos. / Abstract: The main objective of this work is to study the behavior of the zeros of some classes of self-reciprocal polynomials related to Chebyshev quasi-orthogonal polynomials of order one and two. The zeros of self-reciprocal polynomials are linked to the zeros of quasiorthogonal polynomials, which can be obtained from a sequence of orthogonal polynomials. In this work we use the Chebyshev polynomials to obtain classes of quasi-orthogonal polynomials and from results on the behavior of their zeros, we obtain information about the zeros of some classes of self-reciprocal polynomials. / Mestre
|
66 |
Solution de C. Hyltén-Cavallius pour un problème de P. Turán concernant des polynômesTinawi, Félix January 2008 (has links)
Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal
|
67 |
Fast, exact and stable reconstruction of multivariate algebraic polynomials in Chebyshev formPotts, Daniel, Volkmer, Toni 16 February 2015 (has links) (PDF)
We describe a fast method for the evaluation of an arbitrary high-dimensional multivariate algebraic polynomial in Chebyshev form at the nodes of an arbitrary rank-1 Chebyshev lattice. Our main focus is on conditions on rank-1 Chebyshev lattices allowing for the exact reconstruction of such polynomials from samples along such lattices and we present an algorithm for constructing suitable rank-1 Chebyshev lattices based on a component-by-component approach. Moreover, we give a method for the fast, exact and stable reconstruction.
|
68 |
Análise da estabilidade de sistemas dinâmicos periódicos usando Teoria de SinhaMesquita, Amábile Jeovana Neiris [UNESP] 11 June 2007 (has links) (PDF)
Made available in DSpace on 2014-06-11T19:27:08Z (GMT). No. of bitstreams: 0
Previous issue date: 2007-06-11Bitstream added on 2014-06-13T20:55:46Z : No. of bitstreams: 1
mesquita_ajn_me_sjrp.pdf: 655612 bytes, checksum: cb512103d01edb2f09f992e6cca22bdc (MD5) / Neste trabalho estuda-se alguns sistemas dinâmicos utilizando um novo método para aproximar a matriz de transição de estados (STM) para sistemas periódicos no tempo. Este método é baseado na transformação de Lyapunov-Floquet (L-F), e utiliza a expansão polinomial de Chebyshev para aproximar o termo periódico. O método iterativo de Picard é usado para aproximar a STM. Os multiplicadores de Floquet, determinados através deste método, permitem construir o diagrama de estabilidade do sistema dinâmico. Esta técnica é aplicada para analisar a estabilidade e os pontos de bifurcação do sistema dinâmico formado por um pêndulo elástico com excitação vertical periódica no suporte. Além dessa aplicação, é analisada também a equação de Mathieu e a estabilidade do sistema dinâmico constituído por partículas carregadas e imersas em um campo magnético perturbado. / In this work some dynamic systems are studied using a new method to approach state transition matrix (STM) for time-periodic systems. This method is based on Lyapunov- Floquet transformation (transformation L-F) and uses the Chebyshev polynomial expansion to approach the periodical term. The Picard iterative method is used to approach the STM. The Floquet multipliers determined through this method, allow to draw the stability diagram of the dynamic system. This technique is applied to analyze the stability and bifurcation points of the dynamic system formed by an elastic pendulum with periodic vertical excitation on support. Besides this application, the Mathieu equation is analyzed and also the stability of the dynamical system constituted by charged particle in a perturbed magnetic field is discussed.
|
69 |
Fórmula de valoração racional (RVF) e variabilidade no tempo das taxas de retorno de ativos no BrasilRipamonti, Alexandre 22 August 2011 (has links)
Made available in DSpace on 2016-03-15T19:30:48Z (GMT). No. of bitstreams: 1
Alexandre Ripamonti.pdf: 1715355 bytes, checksum: bafe49730ceb2c3f261ef6a51ffb5f5c (MD5)
Previous issue date: 2011-08-22 / Fundo Mackenzie de Pesquisa / Rational valuation formula and time varying cointegration are the main thesis´ concepts, under the Muth´s (MUTH, 1961) rational expectations and theory of price movements as underlying theory, and also testing the null of time invariant error correction mechanisms and another one of inequality of fundamental value and share´s price. The data were obtained from Brazilian listed companies for 1986 to 2010 and also from 1871 to 2010 US stock market. The Johansen´s maximum likelihood and trace models, combined to Chebyshev time polynomials, as proposed by Bierens and Martins (2010) were used in order to test the null. The finds have shown first null rejection and no rejection for the second null. These finds are consistent to Bierens e Martins (BIERENS e MARTINS, 2010) and non-consistent with Muth (MUTH, 1961) / A presente tese aborda os conceitos de fórmula de valoração racional e cointegração variante no tempo para, sob o referencial da teoria das expectativas racionais e de movimentação de preços de Muth (MUTH, 1961), supor a variabilidade das taxas de retorno de ativos no mercado brasileiro, no período de 1986 a 2010, testando as hipóteses nulas de mecanismos de correção de erros dos vetores de cointegração constantes no tempo e de desigualdade entre valor fundamental e preço da ação. Foram coletados dados de preços e dividendos de ações componentes da carteira teórica do IBOVESPA de janeiro de 1986 a outubro de 2010. Além disso, também aplicamos os modelos propostos aos dados norte-americanos de preço e dividendos de 1871 a 2010, disponibilizados por Shiller. Os dados foram analisados através das técnicas de séries temporais e os coeficientes estimados através da técnica de máxima verossimilhança, especificamente com os modelos de cointegração de Johansen combinados com os polinômios temporais de Chebyshev, como proposto por Bierens e Martins (2010). Os resultados indicam a rejeição da hipótese nula de constância dos vetores de cointegração e, ainda, a não rejeição da hipótese nula de desigualdade entre valor fundamental e preço da ação para todas as séries temporais analisadas. Tais resultados são consistentes com os obtidos por Bierens e Martins (BIERENS e MARTINS, 2010) e não consistentes com a teoria das expectativas racionais de Muth (MUTH, 1961).
|
70 |
Análise do comportamento dinâmico de ponte de concreto por meio de filtragem de sinais GPS / Analysis of the dynamic behavior of concrete bridges by GPS signals filteringJosé Venâncio Marra Oliveira 06 September 2018 (has links)
Esta pesquisa propôs uma contribuição aos procedimentos de inspeção de pontes por meio de um plano de monitoramento de curta duração do comportamento dinâmico do tabuleiro de pontes rodoviárias de concreto com a utilização de receptores GPS de 100 Hz associado à diversas técnicas de filtragem de sinais. O estudo foi conduzido em uma ponte em serviço localizada na rodovia Fernão Dias (BR-381). O procedimento de inspeção proposto baseou-se no uso de dois sinais de satélites GPS, por meio da aplicação do Método Residual de Fase (MRF), e da análise temporal dos resíduos da dupla diferença de fase a partir da Fast Fourier Transform (FFT), Continuous Wavelet Transform (CWT), Passa-Faixa Chebyshev do Tipo I. A descrição do comportamento dinâmico do tabuleiro do vão central da ponte se deu por meio da extração dos valores de frequência e amplitude das deflexões verticais a partir dos dados GPS filtrados (resíduos), em três períodos de amostragem de 1 minuto. Os valores de frequência variaram de 0,5 Hz a 8 Hz nos três períodos de amostragens e também nos filtros FFT, CWT e Passa-Faixa Chebyshev do Tipo I. Os valores de amplitude de deslocamento vertical máximo ficaram em torno de 6 mm. Estes valores coincidiram com os valores de frequência e amplitude de deslocamento vertical registrados pela instrumentação clássica com acelerômetros, transdutores de deslocamento vertical, modelagem por elementos finitos e prova de carga estática e dinâmica realizadas sobre tabuleiro do vão central da ponte instrumentado. Por fim, pode-se afirmar que os procedimentos propostos, além de poderem ser utilizados como uma etapa preliminar de inspeção de tabuleiro de pontes rígidas possibilitaram a detecção de deslocamentos dinâmicos verticais milimétricos e suas frequências de vibração. / This research proposed a contribution for bridge inspection procedures at of a short-term monitoring plan of the dynamic behavior of the concrete road bridge with the use of 100 Hz GPS receivers associated with various signal filtering techniques. The study was conducted in the service bridge located on the highway Fernão Dias (BR-381). The procedure inspection proposed was based on the use of two satellite GPS signals, by applying the Phase Residual Method (PRM), and the temporal analysis of the residuals of the double difference phase from the Fast Fourier Transform (FFT), Continuous Wavelet Transform (CWT), Type I Chebyshev Band-Pass. The dynamic behavior of the central span of the bridge was described by extracting the frequency and amplitude values of the vertical deflections from the filtered GPS data (residues), in three sampling periods of 1 minute. The frequency values found ranged from 0.5 Hz to 8 Hz in the three sampling periods as well as in the FFT, CWT and Chebyshev Type I Band-Pass filters. The maximum vertical displacement peak values were around 6 mm. These values coincided with the vertical displacement and amplitude values recorded by the classical instrumentation with accelerometers, vertical displacement transducers, finite element modeling and static and dynamic load test performed on the central span deck of the instrumented bridge. Finally, it could affirm that the procedures proposed, besides being able to be used as a preliminary step of inspection of the rigid bridge\'s deck enabled the detection of millimetric vertical dynamic displacements and their frequencies of vibration.
|
Page generated in 0.0933 seconds