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Benson, D. J. A. "Finite volume solution of Stokes and Navier-Stokes equations." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302883.
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Langman, Philip J. "When is a Stokes line not a Stokes line?" Thesis, University of Southampton, 2005. https://eprints.soton.ac.uk/336279/.
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During the course of a Stokes phenomenon, an asymptotic expansion can change its form as a further series, prefactored by an exponentially small term and a Stokes multiplier, appears in the representation. The initially exponentially small contribution may nevertheless grow to dominate the behaviour for other values of the asymptotic or associated parameters. We introduce the concept of a higer order Stokes phenomenon, at which a Stokes multiplier itself can change value. We show that the higher order Stokes phenomenon can be used to explain the apparent sudden birth of Stokes lines at regular points, why some Stokes lines are irrelevant to a given problem and why it is indespensible to the proper derivation of expansions that involve three or more possible asymptotic contributions. We provide an example of how the higher order Stokes phenomenon can have important effects on the large time behaviour of linear partial differential equations. Subsequently we apply these techniques to Burgers equation, a non-linear partial differential equation developed to model turbulent fluId flow. We find that the higher order Stokes phenomenon plays a major, yet very subtle role in the smoothed shock wave formation of this equation.
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Allaire, Grégoire. "Homogénéisation des équations de Stokes et de Navier-Stokes." Paris 6, 1989. http://www.theses.fr/1989PA066010.
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On étudie l'homogénéisation des équations de Stokes et Navier-Stokes avec une condition aux limites de Dirichlet dans un domaine contenant de petits obstacles, qui sont d'abord supposes répartis aux noeuds d'un réseau régulier périodique. On démontre la convergence du procédé d'homogénéisation lorsque le pas du réseau tend vers zéro. On étudie le probleme homogénéisé suivant la taille des obstacles
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Barb, Jessica Gaus. "Biochemical, Genetic, and Cytogenetic Studies of Stokesia laevis (Stokes Aster)." NCSU, 2007. http://www.lib.ncsu.edu/theses/available/etd-11302007-145604/.
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Stokesia laevis (J. Hill) Greene is a herbaceous perennial with blue, lavender, violet, albescent, pale yellow or pale pink flowers. All cultivars are diploid (2n=2x=14) except for ?Omega Skyrocket, a tetraploid (2n=4x=28) cultivar selected from a wild population. Anthocyanidin and copigment aglycones extracted from floral tissue were characterized using high-performance liquid chromatography. Results indicated that blue, lavender, violet and albescent flowers contained petunidin, though albescent flowers contained a substantially smaller amount. Pale pink flowers were found to contain only cyanidin. Anthocyanidins and carotenoids were not present in pale yellow flowers. All flowers contained the flavone luteolin. Genetic analyses suggested that at least three genes (A, P, Y) each with two alleles control flower color: A permits normal synthesis of anthocyanins and other flavonoids, a reduces synthesis and/or prevents the accumulation of anthocyanins and other flavonoids; Y permits normal synthesis of anthocyanins, y completely blocks synthesis of anthocyanins; P produces petunidin, p produces cyanidin. All three genes are completely dominant, and yy is epistatic to A and P. We provide a model for flavonoid biosynthesis in Stokesia. Study of karyotypes and meiotic behavior of diploid cultivars and ?Omega Skyrocket? suggest that ?Omega Skyrocket? is an autotetraploid form of Stokesia. The karyotype of ?Omega Skyrocket? was almost indistinguishable from the average diploid karyotype. Meiotic pairing in diploids was normal (i.e. 100% bivalents); no meiotic irregularities such as laggards/bridges were observed and disjunction was equal (7:7). Meiotic pairing in ?Omega Skyrocket? demonstrated a high frequency (60%) of quadrivalent formation, though later stages of meiosis were regular with balanced disjunction (14:14). Meiosis in synthetic autotetraploids and triploids from crosses of diploid cultivars × ?Omega Skyrocket? included univalents, bivalents, trivalents, quadrivalents, 5-valents; abnormalities (i.e. laggards, unequal and/or premature disjunction, chromosome bridging, chromosome stickiness) were observed. Nuclear 2C DNA content for diploids and synthetic tetraploids was 20.3 pg and 39.9 pg. Nuclear 2C DNA content for ?Omega Skyrocket? was 37.3 pg (i.e. 8.2% less than twice the 2C DNA content of diploids), indicating that genomic downsizing has likely occurred in this cultivar. Differences in chromosome symmetry between the diploid and tetraploid karyotypes and the reduction in nuclear DNA content observed in ?Omega Skyrocket? both suggest that some divergence has occurred between ?Omega Skyrocket? and its diploid progenitor. A crossability study was conducted to determine the ploidy level and the frequency of progeny produced by interploid and intraploid crosses of Stokesia. A high percentage (70%) of progeny were aneuploids (i.e. 2x-1 to 6x+3) with the total percentage of aneuploids ranging from 92% to 94% in 2x × 3x, 3x × 2x, 3x × 3x, 3x × 4x and 4x × 3x crosses. Progeny (94%) from 2x × 2x crosses were diploids, and progeny (81%) from 2x × 4x and 4x × 2x crosses were triploids and 3x±1 aneuploids. Progeny from crosses of synthetic tetraploids were mostly tetraploids (16%) and tetraploid aneuploids (69%). Unreduced gamete production was estimated to be 0.7% to 1.4%. Reciprocal crosses of identical 2x and 4x parents produced viable progeny, demonstrating that a triploid block is not present in this species. Triploid fertility was higher than expected; crosses using triploids produced seed 38% of the time with an average seed set of ~2 seeds/inflorescence. Fertility of synthetic tetraploids was reduced relative to their progenitor diploids; pollen viability was reduced by 36% and the percentage of inflorescences producing seed and average seed set/inflorescence were reduced by ~50%. Pollen size was positively correlated with ploidy level (i.e. DNA content).
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Lewis, Mary L. Haynos. "Near-infrared stokes and anti-stokes Raman spectrometry of explosives." Full text available online (restricted access), 2003. http://images.lib.monash.edu.au/ts/theses/lewis.pdf.
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Barrère, Jean. "Modélisation des écoulements de Stokes et Navier-Stokes en milieux poreux." Bordeaux 1, 1990. http://www.theses.fr/1990BOR10516.
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On etudie le passage d'ecoulements microscopiques a l'echelle du pore, regis par les equations de stokes et de navier-stokes, aux ecoulements macroscopiques dans un milieu poreux, regis par la loi de darcy. Les principaux points d'etudes sont: le passage en revue des theories de prise de moyenne et l'etablissement de l'equivalence de celles-ci et la theorie d'homogeneisation dans le cas de milieux periodiques, la determination numerique par une methode aux differences finies, de tenseurs de permeabilite dans des milieux periodiques anisotropes tridimensionnels, l'etude numerique, par une methode aux elements finis, des non-linearites en regime de navier-stokes dans un treillis de cylindres. La loi macroscopique d'ecoulement obtenue fait intervenir une expression cubique de la vitesse de filtration
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Montoya, Zambrano Cristhian David. "Inverse source problems and controllability for the stokes and navier-stokes equations." Tesis, Universidad de Chile, 2016. http://repositorio.uchile.cl/handle/2250/141346.
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Doctor en Ciencias de la Ingeniería, Mención Modelación MatemáticaThis thesis is focused on the Navier{Stokes system for incompressible uids with either Dirichlet or nonlinear Navier{slip boundary conditions. For these systems, we exploit some ideas in the context of the control theory and inverse source problems. The thesis is divided in three parts. In the rst part, we deal with the local null controllability for the Navier{Stokes system with nonlinear Navier{slip conditions, where the internal controls have one vanishing component. The novelty of the boundary conditions and the new estimates with respect to the pressure term, has allowed us to extend previous results on controllability for the Navier{ Stokes system. The main ingredients to build our result are the following: a new regularity result for the linearized system around the origin, and a suitable Carleman inequality for the adjoint system associated to the linearized system. Finally, xed point arguments are used in order to conclude the proof. In the second part, we deal with an inverse source problem for the N- dimensional Stokes system from local and missing velocity measurements. More precisely, our main result establishes a reconstruction formula for the source F(x; t) = (t)f(x) from local observations of N ����� 1 components of the velocity. We consider that f(x) is an unknown vectorial function, meanwhile (t) is known. As a consequence, the uniqueness is achieved for f(x) in a suitable Sobolev space. The main tools are the following: connection between null controllability and inverse problems throughout a result on null controllability for the N- dimensional Stokes system with N ����� 1 scalar controls, spectral analysis of the Stokes operator and Volterra integral equations. We also implement this result and present several numerical experiments that show the feasibility of the proposed recovering formula. Finally, the last chapter of the thesis presents a partial result of stability for the Stokes system when we consider a source F(x; t) = R(x; t)g(x), where R(x; t) is a known vectorial function and g(x) is unknown. This result involves the Bukhgeim-Klibanov method for solving inverse problems and some topics in degenerate Sobolev spaces.
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Bochev, Pavel B. "Least squares finite element methods for the Stokes and Navier-Stokes equations." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06062008-165910/.
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FREJ, Milena Lima. "Fotoluminescência Stokes e anti-Stokes em vidros calcogenetos (Ga10Ge25S65) dopados com Er³+." Universidade Federal de Pernambuco, 2010. https://repositorio.ufpe.br/handle/123456789/6928.
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Previous issue date: 2010Conselho Nacional de Desenvolvimento Científico e Tecnológico
Neste trabalho, mostramos propriedades de fotoluminescência Stokes e anti - Stokes de vidros calcogenetos de composição Ga10Ge25S65 dopados com Er3+, a uma concentração de 0,1% em massa. Como fontes de excitação, foram utilizados lasers pulsados emitindo em 980 nm e 532 nm, em ressonância com as transições 4I15/2 →4I11/2 e 4I15/2 → 2H11/2, respectivamente, dos íons de Er3+. Os experimentos foram realizados à temperatura ambiente. Forças de oscilador foram obtidas através do espectro de absorção da amostra e utilizando a teoria de Judd-Ofelt. Probabilidades de transição de dipolo elétrico forçado, seções de choque e tempos de vida foram determinados. Bandas de emissão foram observadas do azul ao infravermelho próximo, e a dependência da amplitude dos sinais com a intensidade do laser foi analisada. Os resultados permitiram a identificação dos mecanismos que levam aos sinais fotoluminescentes como sendo absorção sequencial de dois fótons, com a excitação em 980 nm, e absorção de um único fóton com a excitação em 532 nm. A dinâmica dos estados envolvidos foi estudada através de equações de taxa para suas densidades de população e utilizando o modelo de Inokuti-Hirayama para transferência de energia entre íons. A caracterização dos processos de transferência de energia mostrou que a principal interação entre os íons é do tipo dipolo-dipolo
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BORDIGNON, ALEX LAIER. "NAVIER-STOKES EM GPU." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2006. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=8928@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORNesse trabalho, mostramos como simular um fluido em duas dimensões em um domÃnio com fronteiras arbitrárias. Nosso trabalho é baseado no esquema stable fluids desenvolvido por Joe Stam. A implementação é feita na GPU (Graphics Processing Unit), permitindo velocidade de interação com o fluido. Fazemos uso da linguagem Cg (C for Graphics), desenvolvida pela companhia NVidia. Nossas principais contribuições são o tratamento das múltiplas fronteiras, onde aplicamos interpolação bilinear para atingir melhores resultados, armazenamento das condições de fronteira usa apenas um canal de textura, e o uso de confinamento de vorticidade.
In this work we show how to simulate fluids in two dimensions in a domain with arbitrary bondaries. Our work is based on the stable fluid scheme developed by Jo Stam. The implementation is done in GPU (Graphics Processinfg Unit), thus allowing fluid interaction speed. We use the language Cg (C for Graphics) developed by the company Nvídia. Our main contributions are the treatment of domains with multiple boundaries, where we apply bilinear interpolation to obtain better results, the storage of the bondaty conditions in a unique texturre channel, and the use of vorticity confinement.
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Alliot, Frédéric. "Etude des équations stationnaires de Stokes et Navier-Stokes dans des domaines extérieurs." Phd thesis, Ecole des Ponts ParisTech, 1998. http://tel.archives-ouvertes.fr/tel-00005589.
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Nous étudions quelques problème mathémathiques posées par la modélisation d'écoulements de fluides visqueux incompressibles autour d'un obstacle borné, dans l'approximation stationnaire et pour un fluide au repos à l'infini. On dispose alors de modèles classiques avec les systèmes d'équations aux délivrées partielles de Stockes (linéaire) et de Navir-Stokes (non-linéaire), ici posés dans de domaines extérieurs. La prémière partie est consacrée au problème de Stokes. On y discute l'existance et l'unicité des solutions avec une croissance ou une décroissance donnée à l'infini grâce à l'utilisation d'espaces de Sobolev avec poids. Nous étudions aussi, dans le même cadre fonctionnel, quelques propriétés des champs de vecteurs à divergence nulle. Les résultats sont établis tout d'abord dans l'espace entier, puis dans un domaine extérieur. Le seconde partie est dédiée aux équations stationnaires de Navier-Stokes dans les domaines estérieurs. Nous y prouverons, en dimensions trois, des résultats de régularité des solutions faibles de ce problème qui permettent de vérifier la condition de repos à l'infini. En dimension deux, on détaille les propriétés asymptotiques d'une famille de solutions vérifiant certaines conditions de symétrie. Grâce à approche différente basée sur le théorème de point de Banach, nous obtenons, en dimention trois et pour des données suffisamment petites, l'existence et l'unicité d'une solution qui décroît rapidement et établissons un développement asymptotique de celle-ci.
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ALLIOT, FREDERIC. "Etude des équations stationnaires de Stokes et Navier-Stokes dans des domaines extérieurs." Marne-la-vallée, ENPC, 1998. http://www.theses.fr/1998ENPC9824.
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Nous étudions quelques problèmes mathématiques poses par la modélisation d'écoulements de fluides visqueux incompressibles autour d'un obstacle borne, dans l'approximation stationnaire et pour un fluide au repos à l'infini. On dispose alors de modèles classiques avec les systèmes d'équations aux dérivées partielles de stokes (linéaire) et de Navier-stokes (non-linéaire), ici poses dans des domaines extérieurs. La première partie est consacrée au problème de stokes. On y discute l'existence et l'unicité des solutions avec une croissance ou une décroissance donnée à l'infini grâce à l'utilisation d'espaces de Skobelev avec poids. Nous obtenons dans certains cas des developpements asymptotiques des solutions. Nous etudions aussi, dans le meme cadre fonctionnel, quelques proprietes des champs de vecteurs a divergence nulle. Les resultats sont etablis tout d'abord dans l'espace entier, puis dans un domaine exterieur. La seconde partie est dediee aux equations stationnaires de navier-stokes dans des domaines exterieurs. Nous y prouvons, en dimension trois, des resultats de regularite des solutions faibles de ce probleme qui permettent de verifier la condition de repos a l'infini. En dimension deux, on detaille les proprietes asymptotiques d'une famille de solutions verifiant certaines conditions de symetrie. Grace a une approche differente basee sur le theoreme de point fixe de banach, nous obtenons, en dimension trois et pour des donnees suffisamment petites, l'existence et l'unicite d'une solution qui decroit rapidement et etablissons un developpement asymptotique de celle-ci.
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Shen, Jie. "Résolution numérique des équations de Stokes et Navier-Stokes par les méthodes spectrales." Paris 11, 1987. http://www.theses.fr/1987PA112221.
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Nous présentons des méthodes spectrales pour la résolution des équations de Stokes et de Navier-Stokes. D'abord, nous construisons un solveur rapide de Helmholtz, basé sur la méthode de Tchebychev-Tau, qui sera fréquemment utilisé par la suite. Ensuite, nous considérons deux méthodes pour l'approximation du problème de Stokes: l'une est de type Uzawa; l'autre est appelée la méthode de la matrice d'influence. Divers résultats théoriques et numériques sont présentés. Enfin, nous proposons deux schémas pour l'approximation des équations de NavierStokes d'évolution. Nous montrons que ces deux schémas sont tous deux inconditionnellement stables et convergentsWe present spectral methods for solving Stokes et Navier-Stokes equations. First of all, we construct a fast Helmholtz solver, based on Chebychev-Tau method, which we will use frequently later. Then, we consider two methods for the approximation of Stokes problem : one is based on the Uzawa algorithm, the other is called the influence matrix method. Several theoritical and numerical results are presented. Finally, we propose two schemes for the approximation of Navier-Stokes equations. We prove that both schemes are unconditionary stable and convergent
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Manz, Thomas. "Stimulierte Stokes- und Anti-Stokes-Raman-Streuung mit Bessel-Bündeln in Aceton und Wasserstoff." [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975789325.
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Rejaiba, Ahmed. "Equations de Stokes et de Navier-Stokes avec des conditions aux limites de Navier." Thesis, Pau, 2014. http://www.theses.fr/2014PAUU3050/document.
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Résumé : Cette thèse est consacrée à l'étude des équations de Stokes et de Navier-Stokes avec des conditions aux limites de Navier dans un ouvert borné de . Le manuscrit ici est composé de trois chapitres. Dans le premier, nous considérons les équations de Stokes stationnaires avec des conditions aux limites de Navier. Nous démontrons l'existence, l'unicité et la régularité de la solution d'abord dans un cadre hilbertien puis dans le cadre de la théorie . Nous traitons aussi le cas de solutions très faibles. Dans le deuxième chapitre, nous nous intéressons aux équations de Navier-Stokes avec la condition de Navier. Sous certaines hypothèses sur les données, nous démontrons l'existence de solution faible dans , avec en utilisant un théorème du point fixe appliqué à un problème d'Oseen. Nous démontrons examinons ensuite les questions de régularité des solutions en particulier dans . Dans le dernier chapitre, nous étudions le problème d'évolution de Stokes avec la condition de Navier. La résolution de ce problème se fait au moyen de la théorie des semi-groupes analytiques qui jouent un rôle important pour établir l'existence et l'unicité de la solution dans le cas homogène. Nous traitons le cas du problème non homogène par le biais des puissances imaginaires de l'opérateur de StokesThis thesis is devoted to the study of the Stokes equations and Navier-Stokes equations with Navier boundary conditions in a bounded domain of . The work contains three chapters: In the first chapter, we consider the stationary Stokes equations with Navier boundary condition. We show the existence, uniqueness and regularity of the solution in the Hilbert case and in the -theory. We prove also the case of very weak solutions. In the second chapter, we focus on the Navier-Stokes equations with the Navier boundary condition. We show the existence of the weak solution in , with by a fixed point theorem over the Oseen equation. We show also the existence of the strong solution in . In chapter three, we study the evolution Stokes problem with Navier boundary condition. For this, we apply the analytic semi-groups theory, which plays a crucial role in the study of existence and uniqueness of solution in the case of the homogeneous evolution problem. We treat the case of non-homogeneous problem through imaginary powers of the Stokes operator
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Shen, Jie. "Résolution numérique des équations de Stokes et de Navier-Stokes par les méthodes spectrales." Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb376099439.
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Nilsson, Jonas. "Initial-boundary-value problems for the Stokes and Navier-Stokes equations on staggered grids /." Uppsala : Acta universitatis Upsaliensis, 2000. http://catalogue.bnf.fr/ark:/12148/cb392870516.
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Mulligan, P. G. "Asymptotics and the Stokes phenomenon." Thesis, Queen's University Belfast, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.397876.
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Wu, Xuesong. "Nonlinear instability of Stokes-layers." Thesis, Imperial College London, 1992. http://hdl.handle.net/10044/1/59202.
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The Stokes-layer generated by a sinusoidally oscillating flat plate in an infinite fluid is an important prototype of unsteady flows, and is known to be susceptible to high-frequency instability. According to linear theory (Tromans, 1977; Cowley, 1987), small disturbances can grow exponentially over part of a period and become neutral at some time. The present study considers nonlinear effects on the instability under a high-Reynolds-number assumption, i.e. R ^ 1. It is shown that in the vicinity of the neutral time, the small disturbances evolve from a linear stage to a nonlinear stage due to enhanced nonlinear interactions inside the critical layers - the neighbourhood of a level at which the phase velocity of the disturbance is equal to the basic flow velocity. Specifically, we have studied the evolution of a two-dimensional wave, a pair of oblique waves and a resonant triad of waves. The temporal-spatial modulation of near-planar waves is also considered. For a two-dimensional disturbance, it is shown that the evolution is controlled by nonlinear eff'ects once the linear growth rate has decreased from order one to 0(6?), where e is the magnitude of the disturbance. The amplitude equation turns out to be an integro-differential one of Hickernell type (Hickernell 1984). We study the amplitude equation by series-extension and numerical methods. For the inviscid case, i.e. e >> the solutions always develop a finite-time singularity. When viscosity is included, i.e. e ~ R~^, it is found that (a) viscosity generally delays the finite-time singularity, and (b) if viscosity is sufficiently large the singularity can be completely eliminated, with the result that the wave evolves to an equilibrium state, confirming the findings of Goldstein Sz Leib (1989). In particular, for the present problem it is found that for disturbances with wavenumbers in the range [0.6, 1.3], a finite-time singularity always occurs, no matter how large the scaled viscosity parameter is. If e < C i.e. the disturbance is relatively small, the amplitude equation can be reduced to a classical Stuart-Landau equation by taking a limit of the integro-differential equation. The stability of the equilibria is also studied. For the case where the disturbance consists of a pair of oblique waves, the non-linear evolution stage comes at a much earlier time, namely when linear growth rate is ), and it then evolves over a much faster time scale 0(e~3), as in Goldstein & Choi (1989). Mathematically this is due to a pole type of singularity in the outer solution for the streamwise and spanwise velocities, which is much stronger than the branch-point singularity associated with Uyy{yc) ^ 0. We show that for the disturbances with order-one spanwise wavenumbers, the amplitude equation is the same as that of Goldstein & Choi(1989), although Uyy{yc) = 0 in their case. However, we point out that when three-dimensionality is relatively weak, the fact that Uyy{yc) 7^ 0 in our problem does bring in a difference. Moreover, we obtain an amplitude equation for the case when viscosity effects are important in the leading order equations of the critical layers, thus extend the analysis of Goldstein & Choi (1989). At least under the inviscid hmit, the solution of the amplitude equation can develop a finite-time singularity, corresponding to the finite-distance singularity of Goldstein & Choi (1989). In addition, it is noted that the nonlinear interaction of waves can generate strong vortices of the same magnitude as the waves. We suggest that these vortices may be identified as those observed in experiments, and may have relevance to the streaky structure in a turbulent boundary layer. For the case when three waves form a resonant-triad, we show that when the amplitude of the planar and the obhque waves are C)(c3) and 0(e) respectively, a mutual interaction takes place and the disturbances are governed by a coupled integro-differential equation system. These amplitude equations are significantly different from those of Raetz (1959), Craik (1971), Smith & Stewart (1987) in two important aspects. Firstly the local growth rate depends on the the whole history of the evolution, unlike a conventional resonant triad, where the local growth rate depends only on the instantaneous amplitudes of the disturbances (see Goldstein & Lee, 1990). Secondly the back reaction of the obhque waves on the 2-D wave is accounted for by two cubic terms and one quartic term rather than by one quadratic term. The amplitudes of the two-dimensional and the three-dimensional waves can exhibit a finite-time singularity, the structure for which is proposed. The evolution equations obtained in our study are shown to be valid until the magnitude of the disturbance becomes order one; thus they provide a full description of the development of resonant-triad waves from their linear small amplitude stage towards the fully-nonhnear order-one-amplitude stage. For the temporal-spatial modulation case, i.e. the case when the amplitude of the disturbance is a slowly-varying function of spanwise position as well as of time, it is shown that the development of the disturbance is controlled by critical-layer nonlinearity when its linear growth rate decreases to 0(es). Nonlinear interactions influence the evolution by producing a streamwise vortex and cross-flow distortion. The modulation equation turns out to be an integro-payimZ-differential one contain-ing hi story-dependent nonlinear terms. A novel feature of the amplitude equation is that the derivatives with respect to space, including the highest derivative, appear in the nonlinear terms. These terms are associated with three-dimensionality, and hence represent vortex stretching and tilting effects. The possible properties of the amplitude equation are discussed. It is shown that a localized singularity may occur in a finite time. This provides a possible explanation for the focusing of streamwise vorticity and the formation of streaks. The finite-time singularity, which can occurs in all the four cases studied, suggests that explosive growth is induced by critical-layer nonlinear effects. Hence an initially small disturbance is further amplified by nonlinear effects; moreover this nonlinear growth can prevent the disturbance evolving into an equilibrium state as implied by linear theory. We suggest that this nonlinear blow-up of high-frequency disturbances is related to the bursting phenomena observed in experiments, and can lead to transition to turbulence.
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Jörgenfelt, Erik. "Stokes' Theorem on Smooth Manifolds." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-125404.
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A proof of Stokes' theorem on smooth manifolds is given, complete with prerequisite results in tensor algebra and differential geometry. The essay assumes familiarity with multi-variable calculus and linear algebra, as well as a basic understanding of point-set topology. Stokes' theorem is then applied to the conservation of energy-momentum in general relativity under the existence of so called Killing vectors.Stokes sats för släta mångfalder bevisas, komplett med nödvändiga resultat från tensoralgebran och differentialgeometrin. Uppsatsen förutsätter förtrogenhet med flervariabelanalys och linjär algebra, samt en grundläggande förståelse för allmän topologi. Stokes sats appliceras sedan till bevarande av energi-momentum i allmän relativitetsteori under existensen av so kallade Killingvektorer.
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Cannone, Marco. "Ondelettes, paraproduits et Navier-Stokes." Paris 9, 1994. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1994PA090016.
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Dans cette thèse nous donnons quelques théorèmes d'existence et unicité de solutions mild du problème de Cauchy associe aux équations de Navier-Stokes. Dans la première partie, inspirés par une approche en ondelettes établie par P. Federbush, nous utilisons la décomposition de Littlewood-Paley pour en déduire un théorème d'existence et unicité locale de solutions mild à valeurs dans un espace de Banach abstrait de distributions. Nombreux exemples de tels espaces seront fournis, comme ceux de Lebesgue, Sobolev, Morrey-Campanato et Besov. La deuxième partie de la thèse est consacrée aux solutions globales mild dans des espaces de Banach dont la norme est invariante par les dilatations normalisées. En particulier, nous généralisons un résultat classique du a t. Kato en faisant remarquer que le temps de vie de sa solution globale est, en effet, donne par une norme Besov plus faible que celle usuelle de Lebesgue ne le laissait prévoir. Enfin, nous montrons comment utiliser lesdits espaces de Besov pour en déduire un théorème d'existence et unicité de solutions auto-similaires pour les équations de Navier-Stokes
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Mallinger, François. "Couplage adaptatif Boltzmann Navier-Stokes." Paris 9, 1996. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1996PA090042.
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Nous étudions les écoulements externes en régime semi raréfié à grands nombre de mach. Pour ce faire, nous proposons une stratégie de décomposition de domaine couplant les modèles Boltzmann et Navier-Stokes. Le couplage est réalisé par le biais de conditions aux limites. Les domaines de calcul Boltzmann et Navier-Stokes sont déterminés de manière automatique par un critère analysant la validité de la solution Navier-Stokes. Nous proposons donc un algorithme de couplage adaptatif qui prend en compte d'une part la détermination automatique des domaines, et d'autre part un algorithme de marche en temps pour le couplage des modèles. Le couplage adaptatif résulte d'une interprétation cinétique des équations de Navier-Stokes. Pour le généraliser, nous étudions la transition entre régimes microscopiques (Boltzmann) and macroscopiques (Navier-Stokes) pour des gaz diatomiques, en étendant la démarche initiale de grad. Enfin nous donnons une justification mathématique du couplage Boltzmann Navier-StokesWe study external flows for semirarefied régimes at high mach number. We propose a domain décomposition strategy coupling Boltzmann and Navier-Stokes models. The coupling is done by boundary conditions. The Boltzmann and Navier-Stokes computational domains are defined automatically thanks to a critérium analysing the validity of the numerical Navier-Stokes solution. We propose therefore an adaptative coupling algorithm taking into account both the automatic définition of the computation domains and a time marching algorithm to couple the models. The whole strategy results from the transition between the microscopie model (Boltzmann) and the macroscopie model (Navier-Stokes). In order to generalize this adaptative coupling, we study this connection for diatomic gases. Finally, we justify the coupled problem from a mathematical view point
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Jones, Julia Craven. "Infrared Hyperspectral Imaging Stokes Polarimeter." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/145409.
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This work presents the design, development, and testing of a field portable imaging spectropolarimeter that operates over the short-wavelength and middle-wavelength portion of the infrared spectrum. The sensor includes a pair of sapphire Wollaston prisms and several high order retarders to produce the first infrared implementation of an imaging Fourier transform spectropolarimeter, providing for the measurement of the complete spectropolarimetric datacube over the passband. The Wollaston prisms serve as a birefringent interferometer with reduced sensitivity to vibration when compared to an unequal path interferometer, such as a Michelson. Polarimetric data are acquired through the use of channeled spectropolarimetry to modulate the spectrum with the Stokes parameter information. The collected interferogram is Fourier filtered and reconstructed to recover the spatially and spectrally varying Stokes vector data across the image.The intent of this dissertation is to provide the reader with a detailed understanding of the steps involved in the development of this infrared hyperspectral imaging polarimeter (IHIP) instrument. First, Chapter 1 provides an overview of the fundamental concepts relevant to this research. These include imaging spectrometers, polarimeters, and spectropolarimeters. A detailed discussion of channeled spectropolarimetry, including a historical study of previous implementations, is also presented. Next a few of the design alternatives that are possible for this work are outlined and discussed in Chapter 2. The configuration that was selected for the IHIP is then presented in detail, including the optical layout, design, and operation. Chapter 3 then presents an artifact reduction technique (ART) that was developed to improve the IHIP's spectropolarimetric reconstructions by reducing errors associated with non-band-limited spectral features. ART is experimentally verified in the infrared using a commercial Fourier transform spectrometer in combination with Yttrium Vanadate as well as Cadmium Sulfide retarders.The remainder of this dissertation then details the testing and analysis of the IHIP instrument. Implementation of ART with the IHIP as well as the employed calibration techniques are described in Chapter 4. Complete calibration of the IHIP includes three distinct processes to provide radiometric, spectral, and polarimetric calibration. With the instrument assembled and calibrated, results and error analyses are presented in Chapter 5. Spectropolarimetric results are obtained in the laboratory as well as outdoors to test the IHIP's real world functionality. The performance of the instrument is also assessed, including experimental measurement of signal-to-noise ratio (SNR), and an analysis of the potential sources of systematic error (such as retarder misalignment and finite polarizer extinction ratio). Chapter 6 presents the design and experimental results for a variable Wollaston prism that can be added to the IHIP to vary the fringe contrast across the field of view. Finally, Chapter 7 includes brief closing remarks summarizing this work and a few observations which may be useful for future infrared imaging Fourier transform channeled spectropolarimeter instruments.
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Kudenov, Michael W. "Infrared Stokes Polarimetry and Spectropolarimetry." Diss., The University of Arizona, 2009. http://hdl.handle.net/10150/193729.
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In this work, three methods of measuring the polarization state of light in the thermal infrared (3-12 microns) are modeled, simulated, calibrated and experimentally verified in the laboratory. The first utilizes the method of channeled spectropolarimetry (CP) to encode the Stokes polarization parameters onto the optical power spectrum. This channeled spectral technique is implemented with the use of two Yttrium Vanadate (YVO4) crystal retarders. A basic mathematical model for the system is presented, showing that all the Stokes parameters are directly present in the interferogram. Theoretical results are compared with real data from the system, an improved model is provided to simulate the effects of absorption within the crystal, and a modified calibration technique is introduced to account for this absorption. Lastly, effects due to interferometer instabilities on the reconstructions, including nonuniform sampling and interferogram translations, are investigated and techniques are employed to mitigate them.Second is the method of prismatic imaging polarimetry (PIP), which can be envisioned as the monochromatic application of channeled spectropolarimetry. Unlike CP, PIP encodes the 2-dimensional Stokes parameters in a scene onto spatial carrier frequencies. However, the calibration techniques derived in the infrared for CP are extremely similar to that of the PIP. Consequently, the PIP technique is implemented with a set of four YVO4 crystal prisms. A mathematical model for the polarimeter is presented in which diattenuation due to Fresnel effects and dichroism in the crystal are included. An improved polarimetric calibration technique is introduced to remove the diattenuation effects, along with the relative radiometric calibration required for the BPIP operating with a thermal background and large detector offsets. Data demonstrating emission polarization are presented from various blackbodies, which are compared to data from our Fourier transform infrared spectropolarimeter. Additionally, limitations in the PIP technique with regards to the spectral bandwidth and F/# of the imaging system are analyzed. A model able to predict the carrier frequency's fringe visibility is produced and experimentally verified, further reinforcing the PIP's limitations.The last technique is significantly different from CP or PIP and involves the simulation and calibration of a thermal infrared division of amplitude imaging Stokes polarimeter. For the first time, application of microbolometer focal plane array (FPA) technology to polarimetry is demonstrated. The sensor utilizes a wire-grid beamsplitter with imaging systems positioned at each output to analyze two orthogonal linear polarization states simultaneously. Combined with a form birefringent wave plate, the system is capable of snapshot imaging polarimetry in any one Stokes vector (S1, S2 or S3). Radiometric and polarimetric calibration procedures for the instrument are provided and the reduction matrices from the calibration are compared to rigorous coupled wave analysis (RCWA) and raytracing simulations. The design and optimization of the sensor's wire-grid beam splitter and wave plate are presented, along with their corresponding prescriptions. Polarimetric calibration error due to the spectrally broadband nature of the instrument is also overviewed. Image registration techniques for the sensor are discussed and data from the instrument are presented, demonstrating a microbolometer's ability to measure the small intensity variations corresponding to polarized emission in natural environments.
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Igreja, Iury Higor Aguiar da. "Métodos de elementos finitos híbridos estabilizados para escoamentos de Stokes, Darcy e Stokes-Darcy acoplados." Laboratório Nacional de Computação Científica, 2015. https://tede.lncc.br/handle/tede/225.
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
In this thesis we propose stabilized hybrid finite elemento formulations to the Stokes and Darcy problems that preserve main properties of the Galerkin discontinuous methods associated with these problems. Moreover, combining these formulations we propose a stabilized hybrid finite element method for the Stokes-Darcy coupled problem. Lagrange multipliers are introduced to weakly impose continuity at the element interfaces giving rise to a global system involving only degrees-of-freedom associated with the multipliers. Knowing the multipliers, the quantities of interest are obtained from local problems that are solved at the element level. Different choices for the multipliers are evaluated for the Stokes and Darcy problems separately and for the Stokes-Darcy coupled problem. With proper choice of multipliers, Beavers-Joseph and Beavers-Joseph-Saffman interface conditions are naturally imposed. Through stabilization techniques hybrid finite element methods are generated with great flexibility in the choice of approximation spaces allowing, for example, the same order of approximations for all variables (velocity, pressure and multiplier). To validate the formulations of the Stokes, Darcy and Stokes-Darcy coupled problems several numerical experiments are performed to illustrate the flexibility and robustness of the proposed formulations and show optimal convergence rates.
Nesta tese propomos formula ções de elementos finitos híbridas estabilizadas para os problemas de Stokes e de Darcy que preservam as principais propriedades dos métodos de Galerkin descontínuo associados a estes problemas. Além disso, combinando estas formulações propomos um método de elementos finitos híbrido estabilizado para o problema de Stokes-Darcy acoplado. Multiplicadores de Lagrange são introduzidos para impor fracamente a continuidade nas interfaces dos elementos dando origem há um sistema global que envolve apenas graus de liberdade associados aos multiplicadores. Conhecidos os multiplicadores, as variáveis de interesse são obtidas através dos problemas locais que são resolvidos em nível de elemento. Diferentes escolhas para os multiplicadores são avaliadas para os problemas de Stokes e de Darcy isoladamente e para o problema acoplado Stokes-Darcy. Com uma adequada escolha dos multiplicadores, as condi ções de interface de Beavers-Joseph e Beavers-Joseph-Saffman são impostas naturalmente. Através de técnicas de estabiliza ção são gerados métodos de elementos finitos híbridos com grande flexibilidade na escolha dos espa os de aproxima ção. Permitindo-se, por exemplo, o uso de aproxima ções de mesma ordem para todas as variáveis (velocidade, pressão e multiplicador). Para validar as formula ções do problema de Stokes, de Darcy e de Stokes-Darcy acoplado são realizados vários experimentos numéricos que ilustram a flexibilidade e robustez das formula ›es propostas e mostram taxas ótimas de convergê ncia.
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Gipouloux, Olivier. "Contribution numérique à l'homogenéisation des équations de Stokes et de Navier-Stokes en milieux poreux." Bordeaux 1, 1992. http://www.theses.fr/1992BOR10534.
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On etudie le regime macroscopique d'un ecoulement incompressible d'un fluide newtonien en milieu poreux periodique a partir de son comportement au niveau du pore. On considere d'abord que l'ecoulement est regi localement par les equations de stokes. On etablit un parallele entre les theories de prise de moyenne et de l'homogeneisation. On construit ensuite un solveur vectoriel des equations de stockes et on homogeneise numeriquement differentes situations d'ecoulement en milieu poreux. On considere enfin que l'ecoulement est regi par les equations de navier-stokes et on etudie le comportement non lineaire de la loi de darcy en fonction du nombre de reynolds
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Landmann, Björn. "A parallel discontinuous Galerkin code for the Navier-Stokes and Reynolds-averaged Navier-Stokes equations." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-35199.
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Landmann, Björn. "A parallel discontinuous Galerkin code for the Navier-Stokes and Reynolds averaged Navier-Stokes equations." München Verl. Dr. Hut, 2007. http://d-nb.info/988422433/04.
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Sahin, Pinar. "Navier-stokes Calculations Over Swept Wings." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12607618/index.pdf.
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In this study, the non-equilibrium Johnson and King Turbulence Model (JK model) is implemented in a three-dimensional, Navier-Stokes flow solver. The main program is a structured Euler/Navier-Stokes flow solver in which spatial discretization is accomplished by a finite volume formulation and a multigrid technique is used as a convergence accelerator. The aim is the validation of this in-house developed CFD (Computational Fluid Dynamics) tool with this enhanced enlarged capability in order to obtain a reliable flow solver that can solve flows over swept wings accurately. Various test cases were evaluated against reference solutions in order to demonstrate the accuracy of the newly implemented JK turbulence model. The selected test cases are NACA 0012 airfoil, ONERA M6 wing, DLR-F4 wing and two wings taken from the 3rd Drag Prediction Workshop. The solutions were analyzed and discussed in detail. The results show appreciably good agreement with the experimental data including force coefficients and surface pressure distributions.
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Shuttleworth, Robert. "Block preconditioning the Navier-Stokes equations." College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/7002.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2007.Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Gwilliam, Catherine Sarah. "Parallel algorithms for Navier-Stokes modelling." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357478.
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Lysov, Vyacheslav. "From Petrov-Einstein to Navier-Stokes." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11656.
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The fluid/gravity correspondence relates solutions of the incompressible Navier-Stokes equation to metrics which solve the Einstein equations. We propose propose two possible approaches to establish this correspondence: perturbative expansion for shear modes and large mean curvature expansion for algebraically special metrics.Physics
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Batycky, Richard Panko. "Inhomogeneous Stokes flow through porous media." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/36640.
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Neklyudov, Mikhail. "Navier-Stokes equations and vector advection." Thesis, University of York, 2006. http://etheses.whiterose.ac.uk/11011/.
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Warrilow, Ian Mark. "Some sedimentation problems in Stokes flow." Thesis, University of Surrey, 1989. http://epubs.surrey.ac.uk/848546/.
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This thesis explores a number of hydrodynamic sedimentation problems in which the fluid motion is governed by the quasi-steady Stokes approximation. In Chapter Two potential-theoretic methods are used to solve the axisymmetric sedimentation problem of a small slowly rotating and translating particle moving through a fluid-filled circular pore of finite length. In such an approach the velocity and pressure fields, governing the fluid motion, are expressed in terms of relevant harmonic functions, a method which is also applicable to linear elasticity. To give the motivation behind the selection of these harmonics and the analytic methods used, Chapter One discusses two electrostatic problems possessing analogous boundary conditions. In both chapters each problem is reduced to the solution of coupled infinite systems of linear equations and solved by truncation to coupled finite sets. The numerical solutions of these equations are then used to compute approximations to the resistive torque and drag experienced by the sedimenting particle. Chapter Three is divided into two parts. Part I treats the application of the method of subareas to some model electrostatic problems. In Part II we utilize the Oseen integral representation of solutions of the Stokes equations to develop a boundary-integral method for the study of further sedimentation problems. The method involves the discretization of the linear integral equations of the first kind, whose unknowns comprise boundary-stress components, using the method of subareas, thus reducing the integral equations to a system of linear equations. Problems solved using this method include the axial translation of a small particle towards a rigid square plate, an investigation of the flow field development for an axially translating small body moving through a hollow and constricted circular cylinder of finite length, the broadside motion of a circular disk through a circular cylinder and an investigation of a curious phenomenon, known as 'overshooting', in the developing axial velocity profile within a finite-length circular cylinder, given certain inlet and outlet velocity profiles.
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Patni, Kavita. "Damped Navier-Stokes equation in 2D." Thesis, University of Surrey, 2016. http://epubs.surrey.ac.uk/809731/.
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The main object to study in this thesis is the so-called damped and driven Navier-Stokes equations. These equations differ from the classical Navier-Stokes system by the presence of the extra damping term which is greater than zero, which is often referred to as the Ekman damping term and models the bottom friction in two-dimensional oceanic models.
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Lustri, Christopher Jessy. "Exponential asymptotics with multiple stokes lines." Thesis, Queensland University of Technology, 2009. https://eprints.qut.edu.au/33237/1/Christopher_Lustri_Thesis.pdf.
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When asymptotic series methods are applied in order to solve problems that arise in applied mathematics in the limit that some parameter becomes small, they are unable to demonstrate behaviour that occurs on a scale that is exponentially small compared to the algebraic terms of the asymptotic series. There are many examples of physical systems where behaviour on this scale has important effects and, as such, a range of techniques known as exponential asymptotic techniques were developed that may be used to examinine behaviour on this exponentially small scale. Many problems in applied mathematics may be represented by behaviour within the complex plane, which may subsequently be examined using asymptotic methods. These problems frequently demonstrate behaviour known as Stokes phenomenon, which involves the rapid switches of behaviour on an exponentially small scale in the neighbourhood of some curve known as a Stokes line. Exponential asymptotic techniques have been applied in order to obtain an expression for this exponentially small switching behaviour in the solutions to orginary and partial differential equations. The problem of potential flow over a submerged obstacle has been previously considered in this manner by Chapman & Vanden-Broeck (2006). By representing the problem in the complex plane and applying an exponential asymptotic technique, they were able to detect the switching, and subsequent behaviour, of exponentially small waves on the free surface of the flow in the limit of small Froude number, specifically considering the case of flow over a step with one Stokes line present in the complex plane. We consider an extension of this work to flow configurations with multiple Stokes lines, such as flow over an inclined step, or flow over a bump or trench. The resultant expressions are analysed, and demonstrate interesting implications, such as the presence of exponentially sub-subdominant intermediate waves and the possibility of trapped surface waves for flow over a bump or trench. We then consider the effect of multiple Stokes lines in higher order equations, particu- larly investigating the behaviour of higher-order Stokes lines in the solutions to partial differential equations. These higher-order Stokes lines switch off the ordinary Stokes lines themselves, adding a layer of complexity to the overall Stokes structure of the solution. Specifically, we consider the different approaches taken by Howls et al. (2004) and Chap- man & Mortimer (2005) in applying exponential asymptotic techniques to determine the higher-order Stokes phenomenon behaviour in the solution to a particular partial differ- ential equation.
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Seloula, Nour El Houda. "Mathematical analysis and numerical approximation of the Stokes and Navier-Stokes equations with non standard boundary conditions." Pau, 2010. http://www.theses.fr/2010PAUU3030.
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Les travaux de la thèse portent sur la résolution des équations de Stokes, d'abord avec des conditions au bord portant sur la composante normale du champ de vitesse et la composante tangentielle du tourbillon, ensuite avec des conditions au bord portant sur la pression et la composante tangentielle du champ de vitesse. Dans chaque cas nous démontrons l'existence, l'unicité et la régularité de la solution. Nous traitons aussi le cas de solutions très faibles, par dualité. Le cadre fonctionnel que nous avons choisi est celui des espaces de Banach du type H(div) et H(rot) ou l'intersection des deux, basés sur l'espace Lp, avec 1 < p < 1. En particulier, on se place dans des domaines non simplement connexes, avec des frontières non connexes. Nous nous intéressons en premier lieu à l'obtention d'inégalités de Sobolev pour des champs de vecteurs u 2 Lp(). Dans un second temps, nous établissons des résultats d'existence pour les potentiels vecteurs avec diverses conditions aux limites. Ceci nous permet d'abord d'effectuer des décompositions de type Helmholtz et ensuite de démontrer des conditions Inf-Sup lorsque la forme bilinéaire est un produit de rotationnels. Ces conditions aux limites font que l'équation de la pression est indépendante des autres variables. C'est la raison pour laquelle nous sommes naturellement conduit à étudier les problèmes elliptiques qui se traduisent par les systèmes de Stokes sans la pression. La résolution de ces problèmes se fait au moyen des Conditions Inf-Sup qui jouent un rôle clef pour établir l'existence et l'unicité de solutions. Nous donnons une applications aux systèmes de Navier-Stokes, où on obtient l'existence d'une solution en effectuant un point fixe autour du problème d'Oseen. Enfin, deux méthodes numériques sont proposées pour approcher le problème de Stokes. Nous analysons d'abord une méthode de Nitsche et puis une méthode de Galerkin discontinu. Quelques résultats numériques de convergence sont décrits qui sont parfaitement cohérents avec l'analyseThis work of thesis deals with the solving of the Stokes problem, first with boundary conditions on the normal component of the velocity field and the tangential component of the vorticity, next with boundary conditions on the pressure and the tangential component of the velocity field. In each case, we give existence, uniqueness and regularity of solutions. The case of very weak solutions is also treated by using a duality argument. The functional framework that we have choosed is that of Banach spaces of type H(div) and H(rot) or their intersection based on the space Lp, with 1 < p < 1. In particular, we suppose that is multiply connected and that the boundary R is not connexe. We are interested in a first time by some Sobolev inequality for vector fields u 2 Lp(). In a second time, we give some results concerning vector potentials with different boundary conditions. This allow to establish Helmholtz decompositions and Inf-Sup condition when the bilinear form is a rotational product. Due to these non standard boundary conditions, the pressure is decoupled from the system. It is the reason whay we are naturally reduced to solving elliptic problems which are the Stokes equations without the pressure term. For this, we use the Inf-Sup conditions, which plays a crutial role in the existence and uniqueness of solutions. We give an application to the Navier-Stokes equations where the proof of solutions is obtained by applying a fixed point theorem over the Oseen equations. Finally, two numerical methods are proposed inorder to approximate the Stokes problem. First, by means of the Nitsche method and next by means of the iscontinuous Galerkin method. Some numerical results of convergence verifying the theoretical predictions are given
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Albanez, Débora Aparecida Francisco 1984. "Continuous data assimilation for Navier-Stokes-alpha model = Assimilação contínua de dados para o modelo Navier-Stokes-alpha." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306185.
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Orientadores: Milton da Costa Lopes Filho, Helena Judith Nussenzveig LopesTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Motivados pela existênca de um número finito de parâmetros determinantes (graus de liberdade), tais como modos, nós e médias espaciais locais para sistemas dinâmicos dissipativos, principalmente as equações de Navier-Stokes, apresentamos nesta tese um novo algoritmo de assimilação contínua de dados para o modelo tridimensional das equações Navier-Stokes-alpha, o qual consiste na introdução de um tipo geral de operador interpolante de aproximação (construído a partir de medições observacionais) dentro das equações de Navier-Stokes-alpha. O principal resultado garante condições sob a resolução espacial de dimensão finita dos dados coletados, suficientes para que a solução aproximada, construída a partir desses dados coletados, convirja para a referente solução que não conhecemos (realidade física) no tempo. Essas condições são dadas em termos de alguns parâmetros físicos, tais como a viscosidade cinemática, o tamanho do domínio e o termo de força
Abstract: Motivated by the presence of the finite number of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages for dissipative dynamical systems, specially Navier-Stokes equations, we present in this thesis a new continuous data assimilation algorithm for the three-dimensional Navier-Stokes-alpha model, which consists of introducing a general type of approximation interpolation operator, (that is constructed from observational measurements), into the Navier-Stokes-alpha equations. The main result provides conditions on the finite-dimensional spatial resolution of the collected data, sufficient to guarantee that the approximating solution, that is obtained from these collected data, converges to the unkwown reference solution (physical reality) over time. These conditions are given in terms of some physical parameters, such as kinematic viscosity, the size of the domain and the forcing term
Doutorado
Matematica
Doutora em Matemática
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Bwemba, René-Joël. "Resolution numerique des formulations omega-psi des equations de stokes et de navier-stokes incompressibles par methode spectrale." Nice, 1994. http://www.theses.fr/1994NICE4727.
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Le travail presente dans cette these constitue une contribution a l'etude des formulations tourbillon-fonction de courant et tourbillon-potentiel vecteur des equations de stokes et de navier-stokes incompressibles. Les methodes numeriques utilisees sont des methodes pseudo-spectrales. La premiere partie est relative aux equations en formulation tourbillon-fonction de courant. Dans le cas 2d cartesien avec une direction de periodicite, on etudie la stabilite numerique des -schemas utilises pour la resolution de ces equations. Dans le cas 2d sans direction de periodicite on etudie la matrice d'influence permettant de definir des conditions aux limites sur le tourbillon, lorsque l'on utilise une methode de collocation tchebychev-tchebychev. La seconde partie concerne les problemes 3d et la formulation tourbillon-potentiel vecteur. La resolution numerique, dans une geometrie cartesienne 3d a deux directions de periodicite, est faite au moyen d'une methode spectrale de type fourier-fourier-tchebychev. Une technique de matrice d'influence est utilisee pour definir des conditions aux limites sur les composantes tangentielles du tourbillon. Enfin, pour la prise en compte des conditions aux limites, une methode de penalisation est introduite et adaptee a la resolution du probleme de stokes
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Wong, Ian Kai. "Numerical study of stokes' second flow problem." Thesis, University of Macau, 2011. http://umaclib3.umac.mo/record=b2550664.
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Tryggeson, Henrik. "Analytical vortex solutions to Navier-Stokes equation." Doctoral thesis, Växjö universitet, Matematiska och systemtekniska institutionen, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1282.
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Fluid dynamics considers the physics of liquids and gases. This is a branch of classical physics and is totally based on Newton's laws of motion. Nevertheless, the equation of fluid motion, Navier-Stokes equation, becomes very complicated to solve even for very simple configurations. This thesis treats mainly analytical vortex solutions to Navier-Stokes equations. Vorticity is usually concentrated to smaller regions of the flow, sometimes isolated objects, called vortices. If one are able to describe vortex structures exactly, important information about the flow properties are obtained. Initially, the modeling of a conical vortex geometry is considered. The results are compared with wind-tunnel measurements, which have been analyzed in detail. The conical vortex is a very interesting phenomenaon for building engineers because it is responsible for very low pressures on buildings with flat roofs. Secondly, a suggested analytical solution to Navier-Stokes equation for internal flows is presented. This is based on physical argumentation concerning the vorticity production at solid boundaries. Also, to obtain the desired result, Navier-Stokes equation is reformulated and integrated. In addition, a model for required information of vorticity production at boundaries is proposed. The last part of the thesis concerns the examples of vortex models in 2-D and 3-D. In both cases, analysis of the Navier-Stokes equation, leads to the opportunity to construct linear solutions. The 2-D studies are, by the use of diffusive elementary vortices, describing experimentally observed vortex statistics and turbulent energy spectrums in stratified systems and in soapfilms. Finally, in the 3-D analysis, three examples of recent experimentally observed vortex objects are reproduced theoretically. First, coherent structures in a pipe flow is modeled. These vortex structures in the pipe are of interest since they appear for Re in the range where transition to turbulence is expected. The second example considers the motion in a viscous vortex ring. The model, with diffusive properties, describes the experimentally measured velocity field as well as the turbulent energy spectrum. Finally, a streched spiral vortex is analysed. A rather general vortex model that has many degrees of freedom is proposed, which also may be applied in other configurations.
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Inubushi, Masanobu. "Covariant Lyapunov Analysis of Navier-Stokes Turbulence." 京都大学 (Kyoto University), 2013. http://hdl.handle.net/2433/175095.
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Fonteneau, Estelle. "Marianne Preindlsberger Stokes : les années de formation." Thesis, Paris 4, 2012. http://www.theses.fr/2012PA040193.
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Cette thèse dépeint le contexte artistique dans lequel Marianne Stokes évolue des années 1880 au tournant du siècle suivant. Une étude approfondie a été menée, qui permet de retracer ses premières années d’études d’art à Munich et à Paris, puis au sein de plusieurs colonies d’artistes en France, au Danemark et en Angleterre. Afin de restituer le milieu créatif de Marianne Stokes, des textes et des manuels d’histoire de l’art ancien et actuel furent étudiés. D’autres recherches furent entreprises, appuyées sur la correspondance d’artistes camarades de Marianne Stokes, et sur l’étude de leur accueil critique en France et en Angleterre. Des publications de l’époque sont au centre de ces recherches : autobiographie, narration de voyage, et correspondance. Cette thèse comprend aussi des études comparatives de toiles de Mariannes Stokes avec celles de plusieurs de ses contemporains.Nous cherchons à démontrer que l’art de Marianne Stokes est difficilement réductible à un mouvement artistique en particulier, mais présente les qualités de nombreux styles : naturalisme, impressionnisme, symbolisme, décoratif. Evoluant parmi ces nombreux courants artistiques, l’art de Marianne Stokes possède un certain silence, un sentiment de piété qui est la ligne directrice de son œuvreThis dissertation recreates the evolution of Marianne Stokes’ art within the context of her artistic milieu from 1880 to the turn of the century. These studies concern first her early school years in Munich and Paris, and then her years among artist colonies in France, Denmark and England. Stokes’ paintings are compared to those of her contemporaries within the artist colonies. Contemporary texts, such as travel journals, biographies, letters and press articles, are used to accurately reconstruct the artist’s milieu. This thesis demonstrates that Marianne Stokes’ body of work cannot be reduced to a specific artistic movement; instead, the style of her paintings ranges from naturalist, decorative, and impressionist to symbolist. Nevertheless, the paintings of Marianne Stokes maintain one distinctive trait; they express a certain silence, an articulation of the artist’s personal piety
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Wang, Yanping. "Adaptive integral equation methods for Stokes flow." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0020/MQ51499.pdf.
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Labbé, Julie. "Résolution itérative du problème tridimensionnel de Stokes." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ57870.pdf.
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Al-Jaboori, Mustafa Ali Hussain. "Navier-Stokes equations on the β-plane." Thesis, Durham University, 2012. http://etheses.dur.ac.uk/5582/.
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Mathematical analysis has been undertaken for the vorticity formulation of the two dimensional Navier–Stokes equation on the β-plane with periodic boundary conditions. This equation describes the flow of fluid near the equator of the Earth. The long time behaviour of the solution of this equation is investigated and we show that, given a sufficiently regular forcing, the solution of the equation is nearly zonal. We use this result to show that, for sufficiently large β, the global attractor of this system reduces to a point. Another result can be obtained if we assume that the forcing is time-independent and sufficiently smooth. If the forcing lies in some Gevrey space, the slow manifold of the Navier–Stokes equation on the β-plane can be approximated with O(εn/2) accuracy for arbitrary n = 0, 1, · · · , as well as with exponential accuracy.
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Smith, Brett. "Coherent Anti-Stokes Raman Scattering Miniaturized Microscope." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/24281.
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Microscopy techniques have been developed and refined over multiple decades, but innovation around single photon modalities has slowed. The advancement of the utility of information acquired, and minimum resolution available is seemingly reaching an asymptote. The fusion of light microscopy and well-studied nonlinear processes has broken through this barrier and enabled the collection of vast amounts of additional information beyond the topographical information relayed by traditional microscopes. Through nonlinear imaging modalities, chemical information can also be extracted from tissue. Nonlinear microscopy also can beat the resolution limit caused by diffraction, and offers up three-dimensional capabilities. The power of nonlinear imaging has been demonstrated by countless research groups, solidifying it as a major player in biomedical imaging.
The value of a nonlinear imaging system could be enhanced if a reduction in size would permit the insertion into bodily cavities, as has been demonstrated by linear imaging endoscopes. The miniaturization of single photon imaging devices has led to significant advancements in diagnostics and treatment in the medical field. Much more information can be extracted from a patient if the tissue can be imaged in vivo, a capability that traditional, bulky, table top microscopes cannot offer. The development of new technologies in optics has enabled the miniaturization of many critical components of standard microscopes. It is possible to combine nonlinear techniques with these miniaturized elements into a portable, hand held microscope that can be applied to various facets of the biomedical field.
The research demonstrated in this thesis is based on the selection, testing and assembly of several miniaturized optical components for use as a nonlinear imaging device. This thesis is the first demonstration of a fibre delivered, microelectromechanical systems mirror with miniaturized optics housed in a portable, hand held package. Specifically, it is designed for coherent anti-Stokes Raman scattering, second harmonic generation, and two-photon excitation fluorescence imaging. Depending on the modality being exploited, different chemical information can be extracted from the sample being imaged. This miniaturized microscope can be applied to diagnostics and treatments of spinal cord diseases and injuries, atherosclerosis research, cancer tumour identification and a plethora of other biomedical applications. The device that will be revealed in the upcoming text is validated by demonstrating all designed-for nonlinear modalities, and later will be used to perform serialized imaging of myelin of a single specimen over time.
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Ngom, Evrad Marie Diokel. "Contrôle frontière des équations de Navier-Stokes." Phd thesis, Université Claude Bernard - Lyon I, 2014. http://tel.archives-ouvertes.fr/tel-01064942.
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Cette thèse est consacrée à l'étude de problèmes de stabilisation exponentielle par retour d'état ou "feedback" des équations de Navier-Stokes dans un domaine borné Ω ⊂ Rd, d = 2 ou 3. Le cas d'un contrôle localisé sur la frontière du domaine est considéré. Le contrôle s'exprime en fonction du champ de vitesse à l'aide d'une loi de feedback non-linéaire. Celle-ci est fournie grâce aux techniques d'estimation a priori via la procédure de Faedo-Galerkin laquelle consiste à construire une suite de solutions approchées en utilisant une base de Galerkin adéquate. Cette loi de feedback assure la décroissance exponentielle de l'énergie du problème discret correspondant et grâce au résultat de compacité, nous passons à la limite dans le système satisfait par les solutions approchées. Le chapitre 1 étudie le problème de stabilisation des équations de Navier- Stokes autour d'un état stationnaire donné, tandis que le chapitre 2 examine le problème de stabilisation autour d'un état non-stationnaire prescrit. Le chapitre 3 est consacré à l'étude de la stabilisation du problème de Navier-Stokes avec des conditions aux bords mixtes (Dirichlet- Neumann) autour d'un état d'équilibre donné. Enfin, nous présentons dans le chapitre 4, des résultats numériques dans le cas d'un écoulement autour d'un obstacle circulaire
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Haddon, E. W. "Numerical studies of the Navier-Stokes equations." Thesis, University of East Anglia, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.377745.
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