To see the other types of publications on this topic, follow the link: Euler Equation.
Dissertations / Theses on the topic 'Euler Equation'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Euler Equation.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Eti, Neslihan Pashaev Oktay. "Classical And Quantum Euler Equation/." [s.l.]: [s.n.], 2007. http://library.iyte.edu.tr/tezler/master/matematik/T000610.pdf.
Full text
2
Voss, Alexander. "Exact Riemann solution for the Euler equations with nonconvex and nonsmooth equation of state." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=976791641.
Full text
3
Edwards, M. G. "Moving element methods with emphasis on the Euler equations." Thesis, University of Reading, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378193.
Full text
4
Im, Jeong Sook. "Comparison of the Korteweg-de Vries (KdV) equation with the Euler equations with irrotational initial conditions." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1281472399.
Full text
5
Roberts, Thomas Wesley. "Euler equation computations for the flow over a hovering helicopter rotor." Thesis, Massachusetts Institute of Technology, 1987. http://hdl.handle.net/1721.1/14907.
Full textAbstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1987.MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO.
Bibliography: leaves 227-233.
by Thomas Wesley Roberts.
Ph.D.
6
Modiano, David. "Adaptive mesh Euler equation computation of vortex breakdown in delta wing flow." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/49895.
Full text
7
Nishiyama, Shinichi. "Testing the life cycle/permanent income model : the Cross-Euler equation approach." Connect to resource, 2002. http://rave.ohiolink.edu/etdc/view.cgi?acc%5Fnum=osu1261399905.
Full text
8
Papadopoulos, George. "Semi-global symplectic invariants of the Euler top." Thesis, The University of Sydney, 2013. http://hdl.handle.net/2123/9221.
Full textAbstract:
The semi-global symplectic invariants were introduced by Dufour et. al. as a means of verifying equivalence of integrable systems in one degree of freedom. In the main part of the thesis we explicitly compute the semi-global symplectic invariants near the hyperbolic equilibrium point of the Euler top, otherwise known as the rigid body. As an interim step, the Birkhoff normal form of the Hamiltonian at this point is computed using Lie series. The Picard-Fuchs ODE for the action near the hyperbolic equilibrium is derived. Using the method of Frobenius on the Picard-Fuchs equation we show that the Birkhoff normal form can also be found by inverting the Frobenius series of the regular action integral. Composition of the regular action integral with the singular action integral leads to the symplectic invariant. To our knowledge this is the first time that such invariants near a hyperbolic point have been computed explicitly using the Picard-Fuchs equation. Finally we discuss the convergence of these invariants using both analytical and numerical arguments, as well as explore the possibility of equivalence with the pendulum.
9
Cichowlas, Cyril. "Equation d' Euler tronquée : de la dynamique des singularités complexes à la relaxation turbulente." Paris 6, 2005. https://tel.archives-ouvertes.fr/tel-00070819.
Full text
10
Sarria, Alejandro. "Blow-up of Solutions to the Generalized Inviscid Proudman-Johnson Equation." ScholarWorks@UNO, 2012. http://scholarworks.uno.edu/td/1555.
Full textAbstract:
The generalized inviscid Proudman-Johnson equation serves as a model for n-dimensional incompressible Euler flow, gas dynamics, high-frequency waves in shallow waters, and orientation of waves in a massive director field of a nematic liquid crystal. Furthermore, the equation also serves as a tool for studying the role that the natural fluid processes of convection and stretching play in the formation of spontaneous singularities, or of their absence.
In this work, we study blow-up, and blow-up properties, in solutions to the generalized, inviscid Proudman-Johnson equation endowed with periodic or Dirichlet boundary conditions. More particularly,regularity of solutions in an Lp setting will be measured via a direct approach which involves the derivation of representation formulae for solutions to the problem. For a real parameter lambda, several classes of initial data are considered. These include the class of smooth functions with either zero or nonzero mean, a family of piecewise constant functions, and a large class of initial data with a bounded derivative that is, at least, continuous almost everywhere and satisfies Holder-type estimates near particular locations in the domain. Amongst other results, our analysis will indicate that for appropriate values of the parameter, the curvature of the data in a neighborhood of these locations is responsible for an eventual breakdown of solutions, or their persistence for all time. Additionally, we will establish a nontrivial connection between the qualitative properties of L-infinity blow-up in ux, and its Lp regularity. Finally, for smooth and non-smooth initial data, a special emphasis is made on the study of regularity of stagnation point-form solutions to the two and three dimensional incompressible Euler equations subject to periodic or Dirichlet boundary conditions.
11
Helin, Mikael. "Inverse Parameter Estimation using Hamilton-Jacobi Equations." Thesis, KTH, Numerisk analys, NA, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-123092.
Full textAbstract:
Inthis degree project, a solution on a coarse grid is recovered by fitting apartial differential equation to a few known data points. The PDE to consideris the heat equation and the Dupire’s equation with their synthetic data,including synthetic data from the Black-Scholes formula. The approach to fit aPDE is by optimal control to derive discrete approximations to regularized Hamiltoncharacteristic equations to which discrete stepping schemes, and parameters forsmoothness, are examined. By non-parametric numerical implementation thedervied method is tested and then a few suggestions on possible improvementsare givenI detta examensarbete återskapas en lösning på ett glest rutnät genom att anpassa en partiell differentialekvation till några givna datapunkter. De partiella differentialekvationer med deras motsvarande syntetiska data som betraktas är värmeledningsekvationen och Dupires ekvation inklusive syntetiska data från Black-Scholes formel. Tillvägagångssättet att anpassa en PDE är att med hjälp av optimal styrning härleda diskreta approximationer på ett system av regulariserade Hamilton karakteristiska ekvationer till vilka olika diskreta stegmetoder och parametrar för släthet undersöks. Med en icke-parametrisk numerisk implementation prövas den härledda metoden och slutligen föreslås möjliga förbättringar till metoden.
12
Jahnke, Max Reinhold. "A equação de Euler e a análise assintótica de Gevrey." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-07022014-205830/.
Full textAbstract:
Neste trabalho, introduzimos a noção de desenvolvimento assintótico em classes de Gevrey e mostramos como o conceito clássico de convergência de séries de potências pode ser generalizado para englobar o caso em que o raio de convergência é nulo. Essa técnica pode ser útil em situações em que é necessário trabalhar com séries formais, como no estudo de Equações Diferenciais. Caracterizamos o conjunto das funções holomorfas que admitem desenvolvimento assintótico e, em cada classe de Gevrey, definimos uma aplicação que associa uma função a uma série formal. Determinamos sob quais condições tal aplicação é sobrejetora e sob quais ela é injetora, possibilitando a ampliação do conceito de convergência e as aplicações da teoria. Além disso, mostramos como essa técnica pode ser usada para obter resultados em equações diferenciais. Para isso, fazemos uma breve introdução de Equações Diferenciais com uma variável complexa e introduzimos o conceito de Polígono de Newton, ferramenta que permite obter a classe de Gevrey de uma solução formal. Finalmente, encontramos condições para que a soma de uma solução formal de uma equação diferencial seja uma solução clássica.In this work, we introduce the notion of Gevrey asymptotic expansion and we show how the classical concept of a convergent power series can be generalized to include the case in which the radius of convergence is zero. This technique can be useful in situations where it is necessary to work with formal power series, as in the study of Differential Equations. We characterize the set of holomorphic functions which admit Gevrey asymptotic expansion and we define in each Gevrey class a map that associates to function in the class a formal series. We determine under which conditions such a map is surjective and under which it is injective, allowing the extension of the concept of convergence and applications of the theory. Furthermore, we show how this technique can be used to obtain results in Differential Equations. For this, we briefly recall the theory of Differential Equations in one complex variable and we introduce the concept of the Newton Polygon, a tool that allows us to find the Gevrey class of a formal solution. Finally, we find suficient conditions for the sum of a formal solution of a differential equation to be a classical solution.
13
Shimizu, Yuuki. "Point vortex dynamics in background fields on surfaces." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263431.
Full text
14
Pirilla, Patrick Brian. "On the Trajectories of Particles in Solitary Waves." Youngstown State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1311100628.
Full text
15
Maciel, Saulo Ferreira. "Desenvolvimento de ferramenta computacional de alta ordem para a solução de problemas de propagação acústica." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/3/3150/tde-26062014-110754/.
Full textAbstract:
O desenvolvimento de uma ferramenta de Dinâmica de Fluidos Computacional que utiliza Método de Elementos Finitos baseada na discretização de Galerkin descontínuo é apresentado neste trabalho com objetivo de resolver a equação de Euler linearizada para escoamento compressível em duas dimensões usando malhas estruturadas e não estruturadas. Procuramos utilizar esta ferramenta como um propagador de ondas sonoras para estudar fenômenos aeroacústicos. O problema de Riemann presente no fluxo convectivo da equação de Euler é tratado com um método upwind HLL e para o avanço da solução no tempo é usado o método de Runge-Kutta explícito de 4 estágios com segunda ordem de precisão. A eficiência computacional, a convergência do método e a precisão são testadas através de simulações de escoamentos já apresentadas na literatura. A taxa de convergência para altas ordens de aproximação é assintótica que é um resultado compatível com a formulação Galerkin descontínuo.The development of a Computation Fluid Dynamic Tool based on the Finite Element Method with discontinuous Galerkin discretization is presented in this work. The aim of this study is to solve the compressible linearized Euler\'s equation in two dimensions on structured and non structured meshes. This tool has been used as a means to study aeroacoustics phenomena. The Riemann\'s problem presented on a convective flow in Euler\'s equation is tackled by a HLL\'s method and the time integration being used is the four-stage Runge-Kutta explicit method with second order of accuracy. The computational efficiency, the convergence of the method and the accuracy are tested by comparing our results for flow simulations with those that are available in the literature. The convergence rate to high approximation order is asymptotic and it shows a result which is compatible with a discontinuous Galerkin formulation.
16
Jawahar, P. "A High-Resolution Procedure For Euler And Navier-Stokes Computations On Unstructured Grids." Thesis, Indian Institute of Science, 2000. https://etd.iisc.ac.in/handle/2005/226.
Full textAbstract:
A finite-volume procedure, comprising a gradient-reconstruction technique and a multidimensional limiter, has been proposed for upwind algorithms on unstructured grids. The high-resolution strategy, with its inherent dependence on a wide computational stencil, does not suffer from a catastrophic loss of accuracy on a grid with poor connectivity as reported recently is the case with many unstructured-grid limiting procedures. The continuously-differentiable limiter is shown to be effective for strong discontinuities, even on a grid which is composed of highly-distorted triangles, without adversely affecting convergence to steady state. Numerical experiments involving transient computations of two-dimensional scalar convection to steady-state solutions of Euler and Navier-Stokes equations demonstrate the capabilities of the new procedure.
17
Jawahar, P. "A High-Resolution Procedure For Euler And Navier-Stokes Computations On Unstructured Grids." Thesis, Indian Institute of Science, 2000. http://hdl.handle.net/2005/226.
Full textAbstract:
A finite-volume procedure, comprising a gradient-reconstruction technique and a multidimensional limiter, has been proposed for upwind algorithms on unstructured grids. The high-resolution strategy, with its inherent dependence on a wide computational stencil, does not suffer from a catastrophic loss of accuracy on a grid with poor connectivity as reported recently is the case with many unstructured-grid limiting procedures. The continuously-differentiable limiter is shown to be effective for strong discontinuities, even on a grid which is composed of highly-distorted triangles, without adversely affecting convergence to steady state. Numerical experiments involving transient computations of two-dimensional scalar convection to steady-state solutions of Euler and Navier-Stokes equations demonstrate the capabilities of the new procedure.
18
Chittabathini, Kumaraswamy. "Investigation of the inverse cascade process in wall-bounded logarithmic flow as a solution of the Euler equation." Thesis, University of Edinburgh, 2008. http://hdl.handle.net/1842/27787.
Full textAbstract:
Wall-bounded shear flows (WBSF) can be regarded as turbulent, organized coherent structures and occur in many different circumstances. The self-similarity of statistical characteristics of turbulence at different heights in the log layer of WBSF might reflect coherent structures which are also self-similar. McNaughton suggested that these coherent structures are in the form of 'Theodorsen ejection amplifier' (TEA) patterns. The TEA model of the structure of turbulence may be responsible for the formation of the three-dimensional inverse cascade process in log layers over smooth walls. The inverse cascade can serve as an efficient mechanism of energy transfer from small to large scales and enables us to understand the dynamics of large-scale coherent structures in the near-wall region. As far as the author is aware, no previous research has been conducted into the existence of a 3-D inverse cascade in WBSF. The objective of the thesis is to investigate numerically an upscale cascade process that has been hypothesized as a basic element of WBSF, and to examine an inverse cascade of this kind as a valid solution of the Euler equations. Initially, the numerical experiments were performed using the commercial Computational Fluid Dynamics (CFD) FLUENT 6.0 software, to reproduce the 'ejection amplifier' cycle (TEA structure) found by McNaughton and Bluendell (2002). In the numerical experiments, fluid was injected from the wall into the base of an ideal, ffictionless logarithmic flow while an equal volume of fluid was removed by suction along two flanking slots. This arrangement is known to create hairpin vortices in physical experiments. The FLUENT simulation results followed the subsequent formation of a hairpin eddy which induced a second, larger ejection from within its arc. The limited computing resources did not allow the FLUENT simulations to be followed far enough to examine possibility of any subsequent hairpins and ejections, so the feasibility of the TEA cascade was not firmly established. Research-oriented Large-Eddy Simulation (LES) code has been used to examine the inverse cascade process, and to overcome the computational limitations of the FLUENT solver. Several numerical experiments have been done using the LES code. The flow velocity data obtained from the simulations have been used to study the formation and growth of hairpin vortices and ejections, and their regeneration into 'ejection amplifier' structures. A comparison has been made between the CFD FLUENT predictions and initial LES run results so as to validate the LES solver. The results of the initial LES experiment reproduced the formation of the primary hairpin vortex (PHV), but did not reproduce the formation of primary a 'ejection amplifier' cycle. This is because the injection parameters and the spatial resolution were influencing primary hairpin development. The possibility of an upscale cascade of 'ejection amplifier' structure formation has been investigated by changing the injection/suction velocity, size and location in both low and high resolution domains. Fifteen LES simulation runs have been done, in which sets of variables and parameters have been systematically varied. The results obtained from all the LES runs showed that the injected disturbance developed into a primary hairpin vortex. When the slot was near the inflow boundary of the simulation domain, the low resolution runs did not indicate the formation of a primary 'ejection amplifier' cycle from the primary hairpin vortex development. These results suggest that the frequency of hairpin generation decreases with decreasing injection velocity. When the disturbance was injected at the center of the low resolution domain, development of the primary hairpin vortex was not affected by the inflow boundary. However, because of the large injection velocity and large slot the primary hairpin vortex also did not evolve into a primary 'ejection amplifier' cycle. The low resolution simulations done using a small slot with large injection velocity showed that the primary hairpin vortex developed into a primary 'ejection amplifier' cycle, but its development was discontinued because of the small injection. All the high resolution runs that were done using a large slot and a high injection velocity showed the formation of a primary 'ejection amplifier' cycle. The high resolution runs that were done using different injection periods also showed the formation of primary 'ejection amplifier' cycles. However, none of the simulations developed fully into an inverse cascade of ejection amplifier structures. In general, these results suggested that the TEA structure formation depends on the injection parameters (injection velocity, injection size, injection duration and injection location) and resolution. The injected disturbances are able to generate TEA structures, but have not been able to generate upscale cascades of TEA structures in log flow. This suggests that the present LES is not able to establish the 3-D inverse cascade process in wall-bounded log flow.
19
PHAN, THI MY DUYEN. "Finite volume method for one-dimensional Euler equations and application to multi-fluid problem." Doctoral thesis, Gran Sasso Science Institute, 2021. http://hdl.handle.net/20.500.12571/23332.
Full textAbstract:
This thesis is about studying the finite volume method for hyperbolic conservation laws system. Starting from the one dimensional Euler equations, we rewrite them from the form in Eulerian coordinates into the form in the Lagrangian coordinates. This technique transforms a moving grid in Eulerian co- ordinates into a fixed grid in Lagrangian coordinates, thus allowing easier imple- mentation of boundary conditions.
The thesis consists of three parts:
• piston problem,
• multi-fluid models,
• asymptotic behavior of Euler equations.
In the first part, we consider the piston problem in the paper where the authors Yoshinori Inoue and Takeru Yano study the nonlinear propagation of plane waves radiated into a semi-infinite space filled with a perfect gas, by the sinusoidal motion of an infinite plate. They use the Euler equations in Eulerian coordinates describing the conservation of mass, momentum, and energy then approximate the solution. From this idea, we consider the waves propagating into a semi- infinite tube, which is filled with a perfect gas, closed by a piston on one end and extending along the x-axis at infinity. We use the mass Lagrangian coordinates to obtain the Euler equations rewritten in Lagrangian coordinates and reproduce the results following the piston problem in Yano's paper. The goal is to perform the computation in a finite computational domain, and to develop non-reflecting boundary conditions to impose on the right boundary. In order to reduce the impact of the reflected wave, we propose to combine the Burgers equation in few additional cells of the computational domain. The numerical error caused by the reflected wave is reduced by an order of magnitude by using this approach.
In the second part, we consider the tube filled periodically by a large number of pairs of two immiscible fluids. We use Roe’s solver, which is described in Munz's paper, in Lagrangian coordinates, to study the motion of multi-fluid problem and then compare this detailed numerical solution with two isentropic homogeneous models. The first one is a 2 × 2 isentropic system and the second model is a 3 × 3 system which takes into account some turbulent effects. The goal is to check which homogenized model gives better prediction. We study two cases according to the ratio of densities of the two fluids: moderate ratio and large ratio. For each case, we perform the test with smooth and discontinuous initial condition in pressure and velocity. For the problem with smooth initial conditions before the shock formation, the detailed numerical solutions and the numerical results of the two isentropic homogeneous models are in very good agreement. After the shock formation, the detailed numerical solution is strongly oscillatory and we have to use the average values, namely smoothed numerical solution, for the comparison with the two models. We observe the difference between the predictions of the two models. For moderate density ratio the 2×2 model gives a better prediction of the shock position, while for large density ratio, the turbulent 3×3 model is in better agreement with a smoothed out version of the detailed numerical solution compared with the simple 2 × 2 model.
In the third part, we study long time behavior of the solutions to the Euler equations by using two different numerical methods: the second order finite volume method in Lagrangian coordinates adopted in the previous chapters, and a high order finite volume method in Eulerian coordinate. In particular, the latter is based on WENO (Weighted Essentially Non-Oscillatory) reconstruction. Then we perform the comparison of the numerical solutions obtained at a final time, when pressure and velocity profiles are almost flat.
20
Artale, Valeria. "Level-Set Ghost Fluid Methods for Free Boundary Problems in Incompressible Euler and Navier-Stokes Equations." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1106.
Full textAbstract:
The present work is devoted to the study of free boundary problems for Euler and Navier-Stokes equations in primitive variables. The goal of the present work is to elaborate a methodology for numerical modeling of all kinds of incompressible viscous fluids, having in mind possible application to deep water, lava flow simulation and crust formation.
Our approach could be essentially divided in three fundamental components: finite difference for spatial approximation, second order accurate method for temporal discretization and level set methods for boundary representation.
The domain is discretized by a regular Cartesian grid. The boundary is described by level set methods. In this context the boundary is seen as a zero level set of a specific function. Navier-Stokes equations is solved starting from Semi-Lagrangian methods, achieving second order accuracy in time and space. Resolution of Navier-Stokes equations allows a Poisson problem for pressure as an intermediate step. This is solved by multigrid methods. The velocity and the pressure are computed by solving a single implicit system solved iteratively.
21
Picard, Thierry. "Modelisation eulerienne-lagrangienne de la combustion d'ergols dans un moteur de fusee biliquide." Paris, ENMP, 1987. http://www.theses.fr/1987ENMP0035.
Full textAbstract:
Modelisation d'un ecoulement gazeux turbulent dans lequel des gouttes d'ergols se vaporisent et brulent. Une etude parametrique sur une chambre bidimensionnelle, puis une simulation d'une chambre reelle
22
Said, Ayman. "Sur le flot de l’équation d’Euler à surface libre." Thesis, université Paris-Saclay, 2021. https://tel.archives-ouvertes.fr/tel-03267703.
Full textAbstract:
L'équation d'Euler à surface libre décrit l'évolution de l'interface séparant l'air d'un fluide parfait irrotationnel. C'est un système de deux équations couplées : l'équation d'Euler à l'intérieur du domaine et une équation cinématique qui décrit les déformations du domaine. Les 4 travaux qui constituent le corps de cette thèse peuvent être divisés en trois sujets connectés au problème de Cauchy du système des water waves. Dans le prolongement des travaux de [2, 4, 5, 7], où les auteurs ont montré que le problème de Cauchy pour le système des water waves est bien posé et que le flot est continu sur des espaces de Sobolev suffisamment réguliers, nous montrons :- Dans [60] que le système des water waves avec ou sans tension de surface estquasi-linéaire au sens le plus fort du terme, c'est-à-dire que le flow n'est pas uniformément continu. De plus, dans le cas avec tension de surface, nous montrons que pour avoir une estimation Lipschitz sur le flot, il faut au moins une perte de $frac{1}{2}$ dérivée. Plus généralement, pour l'équation de Burgers avec terme dispersif de la forme $partial_x |D|^{alpha-1},alphain ]1,2[$, nous montrons qu'il faut au moins une perte de $2-alpha$ dérivées pour assurer un contrôle Lipschitz sur le flot.- Dans [61], nous montrons que les résultats obtenus dans [60] sont effectivement optimaux, c'est-à-dire que pour l'équation de Burgers avec un terme dispersif $partial_x |D|^{alpha-1},alphain ]1,2[$ le flot est effectivement Lipschitz de $H^s$ à $H^{s-2+alpha}$ pour des données initiales périodiques de moyenne nulle. Pour le système des water waves avec tension de surface en deux dimensions d'espace, nous montrons qu'après re-normalisation, le flot est bien Lipschitz au prix d'une perte de $frac{1}{2}$ dérivés. Afin de démontrer les résultats dans [61], nous avons développé une généralisation para-différentielle d'une transformation de jauge complexe de type Cole-Hopf introduite pour la première fois par T. Tao pour l'équation de Benjamin-Ono. Dans [62], nous l'utilisons pour améliorer les résultats connus sur une conjecture numérique due à Saut et Klein dans [45] sur l'équation de Burgers dispersive. Ce qui, à la connaissance de l'auteur, est la première fois que la transformation de jauge est mise en œuvre à cette fin pour $alpha in ]1,2[$. Afin de démontrer les différents résultats dans [60, 61, 62], nous avons étudié et affiné différents résultats connus en calcul paradifférentiel. Plus précisément, dans [59], nous améliorons certaines estimations sur l'opérateur de paracomposition introduit par Alinhac, nous donnons une preuve du changement de variables dans le calcul paradifférentiel et enfin nous étudions comment le support du cut-off fréquentiel varie après la composition d'opérateurs para-différentielsThe Euler equation with free boundary, i.e the water waves system,describes the evolution of the interface between air and a perfect irrotational fluid.It is a system of two coupled equations : the Euler equation in the interior of thedomain and a kinematic equation describing the deformation of the domain. The four works that constitute the body of this thesis can be divided into three connected subjects on the Cauchy problem of the water waves system.In the continuation of the works in [2, 4, 5, 7] where the Cauchy problem forthe water waves system is shown to be well-posed and the flow map continuouson sufficiently regular Sobolev spaces we show :-In [60] that the water waves system with and without surface tension isquasi-linear in the strongest sense, i.e the flow map is not uniformly continuous.Moreover in the case with surface tension we show that in orderto have Lipschitz estimate on the flow map at least a loss of $frac{1}{2}$ derivative. More generally for the Burgers equation augmented by a dispersiveterm of the form $partial_x |D|^{alpha-1},alphain ]1,2[$, we show that at least a loss of $2-alpha$ derivative is needed to ensure Lipschitz control on the flow.-In [61] we show that the results obtained in [60] are indeed optimal, that isfor the Burgers equation augmented with a dispersive term $partial_x |D|^{alpha-1},alphain ]1,2[$ the flow map is indeed Lipschitz from $H^s$ to $H^{s-2+alpha}$ for periodic data with 0 mean value. For the water waves system with surface tensionin two space dimension we show that after suitable re-normalisation that the flow map is Lipschitz under $frac{1}{2}$ loss of derivative. In order to prove the results in [61] we developed a paradifferential generalisationof a complex Cole-Hopf type gauge transform first introduced by T. Taofor the Benjamin-Ono equation. In [62] we use this to improve upon knownresults on a numerical conjecture by Saut and Klein [45] on the dispersiveBurgers equation, which to the author’s knowledge is the first time the gaugetransform was implemented to that end for $alpha in ]1,2[$. In order to prove the different results in [60, 61, 62] we needed to study andrefine different known results in paradifferential calculus. More precisely in [59],we improve some estimates on the paracomposition operator introduced byAlinhac, give a proof of the change of variables in paradifferential operatorsand finally study the frequency cut-off after composition of paradifferentialoperators
23
Greenberg, Neil Louis. "Estimation of diastolic intraventricular pressure gradients using color Doppler M-mode echocardiographic spatiotemporal velocity distributions and the one dimensional Euler equation /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487944660931866.
Full text
24
Cruz, Christian Bueno. "LOGARITMOS DE NÚMEROS NEGATIVOS." UNIVERSIDADE ESTADUAL DE PONTA GROSSA, 2015. http://tede2.uepg.br/jspui/handle/prefix/1500.
Full textAbstract:
Made available in DSpace on 2017-07-21T20:56:27Z (GMT). No. of bitstreams: 1
Christian Bueno Cruz.pdf: 2632425 bytes, checksum: f57aafbd2d12b91ce6244542abec1d03 (MD5)
Previous issue date: 2015-03-20The great importance in the history of mathematics, concerning the study of logarithms, is consensual, both because the purpose for which they were created and because of their various applications. When this content is taught in high school, its definition and its basic properties to the positive real numbers are presented, but logarithms for negative numbers are not addressed. This work has as main objective the depth study of obtaining the logarithms for negative numbers: historical context, properties, exceptions and particularities, complex numbers and a study of the Euler equation. With the derived results of this study it is expected to provide input to obtain a methodology for teaching this subject, even superficially, in high school.
A grande importância na história da matemática no que concerne ao estudo dos logaritmos é consensual, tanto pela finalidade com que foram criados bem como devido às suas diversas aplicações. Quando este conteúdo é ensinado no ensino médio, são apresentadas sua definição e suas propriedades básicas para os números reais positivos, porém logaritmos para números negativos não são abordados. Este trabalho tem por objetivo principal o estudo aprofundado da obtenção dos logaritmos para números negativos: contextualização histórica, propriedades, exceções e particularidades, números complexos e um estudo sobre a equação de Euler. Com os resultados derivados do presente trabalho, espera-se fornecer subsídios para a obtenção de uma metodologia para o ensino de tal assunto, mesmo que superficialmente, no ensino médio.
25
Habeck, Daniel. "Kontaktprobleme in der nichtlinearen Elastizitätstheorie." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1217340286742-02578.
Full textAbstract:
Es werden Kontaktprobleme im Rahmen der nichtlinearen Elastizitätstheorie mit Mitteln der Variationsrechnung behandelt. Dabei liegt das Hauptaugenmerk auf der Untersuchung des Selbstkontakts eines nichtlinear elastischen Körpers. Unter Verwendung einer geeigneten Lagrangeschen Multiplikatorenregel wird eine notwendige Bedingung für Minimierer hergeleitet. Weiterhin werden Ergebnisse für den Kontakt zweier elastischer Körper formuliert.
26
Kumar, Chaman. "Explicit numerical schemes of SDEs driven by Lévy noise with super-linear coeffcients and their application to delay equations." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/15946.
Full textAbstract:
We investigate an explicit tamed Euler scheme of stochastic differential equation with random coefficients driven by Lévy noise, which has super-linear drift coefficient. The strong convergence property of the tamed Euler scheme is proved when drift coefficient satisfies one-sided local Lipschitz condition whereas diffusion and jump coefficients satisfy local Lipschitz conditions. A rate of convergence for the tamed Euler scheme is recovered when local Lipschitz conditions are replaced by global Lipschitz conditions and drift satisfies polynomial Lipschitz condition. These findings are consistent with those of the classical Euler scheme. New methodologies are developed to overcome challenges arising due to the jumps and the randomness of the coefficients. Moreover, as an application of these findings, a tamed Euler scheme is proposed for the stochastic delay differential equation driven by Lévy noise with drift coefficient that grows super-linearly in both delay and non-delay variables. The strong convergence property of the tamed Euler scheme for such SDDE driven by Lévy noise is studied and rate of convergence is shown to be consistent with that of the classical Euler scheme. Finally, an explicit tamed Milstein scheme with rate of convergence arbitrarily close to one is developed to approximate the stochastic differential equation driven by Lévy noise (without random coefficients) that has super-linearly growing drift coefficient.
27
BONFANTI, GIOVANNI. "Progresses on some classical problems of the calculus of variations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2012. http://hdl.handle.net/10281/28223.
Full textAbstract:
Some theorems about the validity of the Euler-Lagrange equation are proved. In particular, Lagrangians without regularity hypothesis or without growth assumptions are considered. Moreover, a result about the non-occurrence of the Lavrentiev phenomenon in the scalar case is proved.
28
Bianchi, Luigi Amedeo. "Dyadic models of turbulence on trees." Doctoral thesis, Scuola Normale Superiore, 2013. http://hdl.handle.net/11384/85691.
Full text
29
Prestipino, Marco. "Stability of boundary layers in magnetohydrodynamics." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC227.
Full textAbstract:
Dans cette thèse nous prouvons la stabilité de certains systèmes d'EDP issus de la magnétohydrodynamique et obtenus grâce à des développements de type couche limite.Nous commençons par discuter les conditions aux bords les plus appropriées pour le système MHD dans un contexte géophysique. Nous obtenons un résultat d'existence de solutions à la Leray pour de telles conditions. Ensuite, nous effectuons une analyse des couches limites sur l'équation adimensionnée, en identifiant les différents modèles asymptotiques selon les régimes d'intérêt.Nous étudions le caractère bien ou mal posé de chacun de ces modèles, dans des cadres linéarisé ou complètement non-linéaire. Nous montrons en particulier le caractère stabilisant d'un champ magnétique tangentiel à la paroi.Finalement, nous illustrons avec des simulations numériques la stabilité ou l'instabilité pour certains des modèles introduitsIn this thesis we establish the stability of some PDE systems derived from magnetohydrodynamics and obtained through some boundary layer developments.We begin discussing the most appropriate boundary conditions for the MHD system in a geophysics context. We obtain an existence result of Leray solutions for this complete system. Next, we perform a boundary layer analysis on the nondimensionalized equation, identifying the different asymptotic models according to the most interesting regimes. We study the well- or ill-posedness of each model, either in a linearised case or either in a completely non-linear case. In particular, we show the stabilizing effect provided by a magnetic field tangent to the wall. Finally, we illustrate with numerical simulations the comparison between stability and instability for some of those models
30
Coghi, Michele. "Mean field limit for interacting particles and filaments." Doctoral thesis, Scuola Normale Superiore, 2016. http://hdl.handle.net/11384/85731.
Full textAbstract:
In this thesis several systems of interacting particles are considered. The manuscript is divided in three parts. The first two parts are dedicated to the study of stochastic point particles, in the last part a system of interacting filaments is considered.
As opposed to the usual model, where the noise perturbations acting on different particles are independent, the particles studied in the first part are subject to the same space-dependent noise. A result of propagation of chaos is proved and it is shown that the limit PDE is stochastic and of inviscid type, as opposed to the case when independent noises drive the different particles.
In the second part a system similar as before is considered. Here the limit equation is not regular anymore but it is the stochastic Euler equation for the vorticity of a fluid with multiplicative noise. A mean field approximation of these equation is proved, where the particles are subject to a regularized interaction.
In the last part, families of interacting curves are considered, with long range, mean field type interaction. A family of curves defines a 1-current analog to the empirical measure of interacting point particles. This current is proved to converge to a mean field current, solution of a nonlinear, vector valued, partial differential equation. This set-up is inspired from vortex filaments in turbulent fluids, but here a smooth interaction is considered, instead of the singular Biot-Savart kernel.
31
Joachimbauer, Florian. "Concise Modeling of Humanoid Dynamics." Thesis, Högskolan i Halmstad, Akademin för informationsteknologi, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-35094.
Full textAbstract:
Simulation of mechanical systems like walking robots, is an essential part in developingnew and more applicable solutions in robotics. The increasing complexity of methodsand technologies is a key challenge for common languages. That problem creates a needfor flexible and scalable languages. The thesis concludes that an equation-based toolusing the Euler-Lagrange can simplify the process cycle of modeling and simulation. Itcan minimize the development effort, if the tool supports derivatives. Regretfully, it isnot common to use equation-based tools with this ability for simulation of humanoidrobots.The research in this thesis illustrates the comparison of equation-based tools to commonused tools. The implementation uses the Euler-Lagrange method to model andsimulate nonlinear mechanical systems. The focus of this work is the comparison ofdifferent tools, respectively the development of a humanoid robot in a stepwise mannerbased on the principle of passive walking. Additionally, each developed model has givenan informal argument to its stability. To prove the correctness of the thesis statementthe equation-based tool called Acumen is evaluated in contrast to a common used tool,MATLAB.Based on the achieved results, it can be concluded that the use of equation-based toolsusing Euler-Lagrange formalism is convenient and scalable for humanoid robots. Additionally,the development process is significantly simplified by the advantages of suchtools. Due to the experimental nature of Acumen further research could investigatethe possibilities for different mechanical systems as well as other techniques.
32
Flores, Ana Paula Ximenes [UNESP]. "Cálculo variacional: aspectos teóricos e aplicações." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/94375.
Full textAbstract:
Made available in DSpace on 2014-06-11T19:27:10Z (GMT). No. of bitstreams: 0
Previous issue date: 2011-02-03Bitstream added on 2014-06-13T18:07:05Z : No. of bitstreams: 1
flores_apx_me_rcla.pdf: 626396 bytes, checksum: bbb4081c4e9cec255b879824f0d39683 (MD5)O principal objetivo deste trabalho é o estudo da teoria do Cálculo de Variações com ênfase na Equação de Euler, que trata de uma condição necessária para uma função ser extremo de um funcional. Existe uma grande variedade de problemas, mas neste trabalho trataremos de problemas com fronteiras fixas, tempo final livre, estado final livre, funcional dependente de mais de uma função e problemas com alguns tipos de restrições. Dois problemas do Cálculo de uma variável e um exemplo de controle ótimo são estudados para ilustrar a aplicabilidade do Cálculo Variacional
The main purpose of this work is the study of the theory of the Calculus of Variations, with emphasis on the Euler equation, that is a necessary condition for a function to be an extreme of a functional. There are a large variety of problems but we will consider the problem of xed boundary, free nal time, free nal state, functionals that contain several independent functions and problems with some constraints. Two problems of the Calculus of one variable and an example of optimal control problem are studied to illustrate the applicability of Variational Calculus
33
Báča, Petr. "RBC model - aplikace na ČR." Master's thesis, Vysoká škola ekonomická v Praze, 2009. http://www.nusl.cz/ntk/nusl-76667.
Full textAbstract:
The diploma thesis deals with the basic Real Business Cycle (RBC) model. RBC theory provides pure supply-side explanation of economic fluctuations. Generaly acknowledged contribution of RBC theory is the fact that the model is developed strictly on microeconomic basis. The thesis consists of two basic parts, theoretical and practical. First, historical background of RBC theory is mentioned. Then the basic RBC model is step-by-step derived and all equations are provided with explanations. In the last theoretical part section RBC theory critisism is discussed. In the practical part the derived basic model is applied to the Czech economy. First certain properties of the Czech business cycles are examined. Then, the basic model is calibrated, simulated and the results are commented.
34
Sengul, Sevgi. "Discrete Fractional Calculus and Its Applications to Tumor Growth." TopSCHOLAR®, 2010. http://digitalcommons.wku.edu/theses/161.
Full textAbstract:
Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus while developing the simplest discrete fractional variational theory. Some applications of the theory to tumor growth are also studied. The first chapter is a brief introduction to discrete fractional calculus that presents some important mathematical functions widely used in the theory. The second chapter shows the main fractional difference and sum operators as well as their important properties. In the third chapter, a new proof for Leibniz formula is given and summation by parts for discrete fractional calculus is stated and proved. The simplest variational problem in discrete calculus and the related Euler-Lagrange equation are developed in the fourth chapter. In the fifth chapter, the fractional Gompertz difference equation is introduced. First, the existence and uniqueness of the solution is shown and then the equation is solved by the method of successive approximation. Finally, applications of the theory to tumor and bacterial growth are presented.
35
Ndiaye, Moctar. "Stabilisation et simulation de modèles d'interaction fluide-structure." Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30323/document.
Full textAbstract:
L'objet de cette thèse est l'étude de la stabilisation de modèles d'interaction fluide-structure par des contrôles de dimension finie agissant sur la frontière du domaine fluide. L'écoulement du fluide est décrit par les équations de Navier-Stokes incompressibles tandis que l'évolution de la structure, située à la frontière du domaine fluide, satisfait une équation d'Euler-Bernoulli avec amortissement. Dans le chapitre 1, nous étudions le cas où le contrôle est une condition aux limites de Dirichlet sur les équations du fluide (contrôle par soufflage/aspiration). Nous obtenons des résultats de stabilisation locale du système non-linéaire autour d'une solution stationnaire instable de ce système. Dans les chapitres 2 et 3, nous nous intéressons au cas où le contrôle est une force appliquée sur la structure (contrôle par déformation de paroi). Dans le chapitre 2, nous considérons un modèle simplifié, où l'équation d'Euler-Bernoulli pour la structure est remplacée par un système de dimension finie. Nous construisons des lois de contrôle pour les systèmes de dimension infinie, ou pour leurs approximations semi-discrètes, capables de stabiliser les systèmes linéarisés avec un taux de décroissance exponentielle prescrit, et localement les systèmes non-linéaires. Nous présenterons des résultats numériques permettant de vérifier l'efficacité de ces lois de contrôlesThe aim of this thesis is to study the stabilization of fluid-structure interaction models by finite dimensional controls acting at the boundary of the fluid domain. The fluid flow is described by the incompressible Navier-Stokes equations while the displacement of the structure, localized at the boundary of the fluid domain, satisfies a damped Euler-Bernoulli beam equation. First, we study the case where the control is a Dirichlet boundary condition in the fluid equations (control by suction/blowing). We obtain local feedback stabilization results around an unstable stationary solution of this system. Chapters 2 and 3 are devoted to the case where control is a force applied to the structure (control by boundary deformation). We consider, in chapter 2, a simplified model where the Euler-Bernoulli equation for the structure is replaced by a system of finite dimension. We construct feedback control laws for the infinite dimensional systems, or for their semi-discrete approximations, able to stabilize the linearized systems with a prescribed exponential decay rate, and locally the nonlinear systems. We present some numerical results showing the efficiency of the feedback laws
36
Hanss, Grégoire. "Schémas numériques compacts basés sur le résidu en maillage irrégulier pour les équations de Navier-Stokes en compressible." Paris, ENSAM, 2002. http://www.theses.fr/2002ENAM0013.
Full textAbstract:
Nous nous intéressons dans ce mémoire à une approche qui exploite l'annulation du résidu à l'état stationnaire pour construire des schémas de résolution des équations d'Euler et Navier-Stokes, d'ordre 2 ou 3 en espace, qui soient à la fois simples, compacts, robustes et efficaces. Dans la première partie de ce mémoire, nous rappelons les principes de cette approche en formulation différences finies, puis nous montrons sur un ensemble de problèmes modèles que le schéma d'ordre 3 basé sur le résidu se compare très favorablement à une approche d'ordre 3 classique. Nous étendons ensuite de façon rigoureuse ce schéma dans des maillages cartésiens quelconques en préservant sa précision d'ordre 3. Dans la deuxième partie de cette étude, nous proposons une extension volumes finis du schéma basé sur le résidu qui garantit, de façon simple, la précision d'ordre 2 du schéma dans des maillages curvilignes très irréguliers. Cette extension rigoureuse est rendue possible par le caractère compact de la dissipation basée sur le résidu. La très bonne précision de cette version VF du schéma basé sur le résidu est démontrée pour des calculs d'écoulements de fluide parfait et visqueux sur des profils et sur une aile. Dans la dernière partie de ce travail, nous développons un schéma basé sur le résidu pour la simulation d'écoulements instationnaires. Nous nous plaçons pour ce faire dans un cadre pas de temps dual et nous travaillons alors avec un résidu qui contient la dérivée en temps physique et s'annule à l'état stationnaire en temps fictif. Nous construisons ainsi un schéma précis à l'ordre 2 en temps et 3 en espace dont les propriétés de précision s'avèrent supérieures à celles d'une approche directionnelle classique pour un problème modèle d'advection et un écoulement visqueux instationnaire complexeThis work is devoted to an approach which makes use of the residual vanishing at steady-state tobuild 2,d or 3d_order space-accurate numerical schemes for the Euler and Navier-Stokes équations, which aresùnple, compact, robust and efficient. In the first part of this memoir, the design principles of this approach are recalled in a fuiite-differenceframework and the 3d order residual-based scheme is proved to compare very favourably with a conventional 3dorder approach on a set of model problems. Next, the residual-based scheme is extended in a rigorous way onirregular Cartesian grids so as to preserve its accuracy order. In the second part of this study, we propose a fmite-volume extension of the residual-based scheme thatguarantees, in a simple way, 2 ,d order accuracy on highly irregular grids. This accuracy-preserving extension ismade possible thanks to the compactness of the residual-based dissipation. The very good accuracy of this FVversion is demonstrated for inviscid and viscous flows over airfoils and a wing. In the last part of this work, a residual-based scheme is developed for unsteady flow problems within a dual-time framework. In this case, the residual used to build the scheme contains the derivative with respect to the physicaltime and vanishes at steady-state on a fictitious time. A 2d order time-accurate and 3d order space-accurate residual-based scheme is then devised, which yields better solution than a conventional directional scheme both for a model advection problem and a complex unsteady viscous flow. The implementation of a new organisation is a way to answer the pressure that an external environment firm may experience. We decide to manage this work as a project. The mainpoint of this project will be a new organisation design and implementation. We link design phase with an anticipated risk project management approach. In order to change we decide to propose an original approach which is an alternation between breaking change and continuous improvement change. We also identify the need for helping change adaptation people. All of our proposals are born of a work in a pharmaceutical firm. This research leads to the creation of a model based on three processes: project management, strategic management and people management. In order to answer the need for controlling theses processes, we propose a control method. This method is composed by five phases created from our model and by eight principles coming from our fieldwork
37
Rydström, Sara. "Regularization of Parameter Problems for Dynamic Beam Models." Licentiate thesis, Växjö University, School of Mathematics and Systems Engineering, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-7367.
Full textAbstract:
The field of inverse problems is an area in applied mathematics that is of great importance in several scientific and industrial applications. Since an inverse problem is typically founded on non-linear and ill-posed models it is a very difficult problem to solve. To find a regularized solution it is crucial to have a priori information about the solution. Therefore, general theories are not sufficient considering new applications.
In this thesis we consider the inverse problem to determine the beam bending stiffness from measurements of the transverse dynamic displacement. Of special interest is to localize parts with reduced bending stiffness. Driven by requirements in the wood-industry it is not enough considering time-efficient algorithms, the models must also be adapted to manage extremely short calculation times.
For the developing of efficient methods inverse problems based on the fourth order Euler-Bernoulli beam equation and the second order string equation are studied. Important results are the transformation of a nonlinear regularization problem to a linear one and a convex procedure for finding parts with reduced bending stiffness.
38
Evans, Katie Allison. "Reduced Order Controllers for Distributed Parameter Systems." Diss., Virginia Tech, 2003. http://hdl.handle.net/10919/11063.
Full textAbstract:
Distributed parameter systems (DPS) are systems defined on infinite dimensional spaces. This includes problems governed by partial differential equations (PDEs) and delay differential equations. In order to numerically implement a controller for a physical system we often first approximate the PDE and the PDE controller using some finite dimensional scheme. However, control design at this level will typically give rise to controllers that are inherently large-scale. This presents a challenge since we are interested in the design of robust, real-time controllers for physical systems. Therefore, a reduction in the size of the model and/or controller must take place at some point. Traditional methods to obtain lower order controllers involve reducing the model from that for the PDE, and then applying a standard control design technique. One such model reduction technique is balanced truncation. However, it has been argued that this type of method may have an inherent weakness since there is a loss of physical information from the high order, PDE approximating model prior to control design. In an attempt to capture characteristics of the PDE controller before the reduction step, alternative techniques have been introduced that can be thought of as controller reduction methods as opposed to model reduction methods. One such technique is LQG balanced truncation. Only recently has theory for LQG balanced truncation been developed in the infinite dimensional setting. In this work, we numerically investigate the viability of LQG balanced truncation as a suitable means for designing low order, robust controllers for distributed parameter systems. We accomplish this by applying both balanced reduction techniques, coupled with LQG, MinMax and central control designs for the low order controllers, to the cable mass, Klein-Gordon, and Euler-Bernoulli beam PDE systems. All numerical results include a comparison of controller performance and robustness properties of the closed loop systems.Ph. D.
39
Molitor, Mathieu. "Grassmanniennes non-linéaires, groupes de difféomorphismes unimodulaires et quelques équations hamiltoniennes en dimension infinie." Metz, 2007. http://www.theses.fr/2007METZ015S.
Full textAbstract:
L'objet de cette thèse est l'étude de l'équation d'un filament de vorticité dans ses diverses formes, l'équation d'Euler d'un fluide parfait incompressible G-invariant pour l'action d'un groupe de Lie ainsi que l'étude de la grassmannienne non-linéaire. Le corps de la thèse se découpe en trois chapitres : dans le premier chapitre, nous donnons la forme locale de l'équation d'un filament de vorticité et montrons que l'astuce d'Hasimoto s'étend aux cas des filaments plongés dans une variété riemannienne tridimensionnelle quelconque. Dans le deuxièeme chapitre, nous étudions le groupe des automorphismes unimodulaires de l'espace total d'un fibré principal. Nous déterminons les équations d'Euler associées et exhibons certaines suites exactes de groupes de Lie fréchétiques. Le troisièeme chapitre étudie en détail la grassmannienne non-linéaire, les diverses structures que l'on peut lui adjoindre et quelques équations hamiltoniennes associées. Un premier appendice traite de la notion de calcul différentiel sur un espace fréchétique et un deuxième appendice montre qu'il existe une structure de groupe de Lie sur le groupe des difféomorphismes unimodulaires d'une variété compacteIn this thesis, we study the vortex filament equation, the Euler equation of an incompressible fluid which is G-invariant with respect to a Lie group action and we also study the non-linear grassmanniann. Our study is organized in three chapter and two appendices : in the first chapter, we study the local form of the vortex filament equation and we show that Hasimoto's trisk extends to the the case of a filament embedded in a general three-dimensional riemannian manifold. In the second chapter, we study the group of unimodular automorphisms of the total space of a principal bundle. We compute the Euler equations associated to this group and derive some short exact sequences. In the third chapter, we study the non-linear grassmannian, some geometrical structures on it and we consider also some hamiltonian equations associated. The first appendix treats the notion of differentiable calculus on a frechet space and the second is devoted to the group of unimodular diffeomorphisms of a compact manifold
40
Sousa, Júnior José Ribamar Alves de [UNESP]. "O cálculo variacional e o problema da braquistócrona." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/94359.
Full textAbstract:
Made available in DSpace on 2014-06-11T19:27:10Z (GMT). No. of bitstreams: 0
Previous issue date: 2010-12-16Bitstream added on 2014-06-13T19:26:07Z : No. of bitstreams: 1
sousajunior_jra_me_rcla.pdf: 1174734 bytes, checksum: cbdf2669884098c54b72817cfc625edd (MD5)Neste trabalho estudamos o problema da Braquistócrona de duas formas distintas: através da teoria do Cálculo Variacional para problemas com fronteiras xas e também através das considerações feitas por Johann Bernoulli, utilizando conceitos de Óptica e Geometria. Apresentamos também uma simulação computacional dos resultados obtidos
In this work we study the Brachistochrone Problem of two di erent ways; by theory of Variational Calculus for problems with xed boundary and by considerations of Johann Bernoulli, with concepts of Optics and Geometry. A computational simulation of the obtained results, is presented too
41
Paião, Ana Pedro Lemos. "Introduction to optimal control theory and its application to diabetes." Master's thesis, Universidade de Aveiro, 2015. http://hdl.handle.net/10773/16806.
Full textAbstract:
Mestrado em Matemática e AplicaçõesO Cálculo das Variações e o Controlo Ótimo são dois ramos da Matemática que estão muito interligados entre si e também com outras áreas. Como exemplo, podemos citar a Geometria, a Física, a Mecânica, a Economia, a Biologia, bem como a Medicina. Nesta tese estudamos vários tipos de problemas variacionais e de Controlo Ótimo, estabelecendo a ligação entre alguns destes. Fazemos uma breve introdução sobre a Diabetes Mellitus, uma vez que estudamos um modelo matemático que traduz a interação entre a glicose e a insulina no sangue por forma a otimizar o estado de uma pessoa com diabetes tipo 1.
The Calculus of Variations and the Optimal Control are two branches of Mathematics that are very interconnected with each other and with other areas. As example, we can mention Geometry, Physics, Mechanics, Economics, Biology and Medicine. In this thesis we study various types of variational problems and of Optimal Control, establishing the connection between some of these. We make a brief introduction to the Diabetes Mellitus, because we study a mathematical model that reflects the interaction between glucose and insulin in the blood in order to optimize the state of a person with diabetes type 1.
42
Sow, Cheickh Tidiane. "Utilisation du calcul formel dans la mécanique de Hamilton : modélisation et applications." Paris 9, 1987. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1987PA090011.
Full textAbstract:
Macsyma est utilisé pour la construction d'un macro langage: language. Ce fichier génère automatiquement du code fortran à partir de programmes écrits dans une syntaxe proche de celle du lispo et du prolog. Un système expert est construit dans l'environnement macsyma pour la modélisation des systèmes mécaniques non bouclés. Le lien entre le calcul formel et le calcul numérique est montré. L'obtention des équations de mouvement des systèmes mécaniques se fait par la formulation lagrangienne dans macsyma et leur intégration numérique par la méthode de Gear à pas variable dans les fichiers fortran générés.
43
Schulze, Bert-Wolfgang, and Nikolai N. Tarkhanov. "Euler solutions of pseudodifferential equations." Universität Potsdam, 1998. http://opus.kobv.de/ubp/volltexte/2008/2521/.
Full textAbstract:
We consider a homogeneous pseudodifferential equation on a cylinder C = IR x X over a smooth compact closed manifold X whose symbol extends to a meromorphic function on the complex plane with values in the algebra of pseudodifferential operators over X. When assuming the symbol to be independent on the variable t element IR, we show an explicit formula for solutions of the equation. Namely, to each non-bijectivity point of the symbol in the complex plane there corresponds a finite-dimensional space of solutions, every solution being the residue of a meromorphic form manufactured from the inverse symbol. In particular, for differential equations we recover Euler's theorem on the exponential solutions. Our setting is model for the analysis on manifolds with conical points since C can be thought of as a 'stretched' manifold with conical points at t = -infinite and t = infinite.
44
Chterental, Igor. "Two-dimensional Euler equations solver." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0018/MQ45872.pdf.
Full text
45
Fanelli, Francesco. "Mathematical analysis of models of non-homogeneous fluids and of hyperbolic equations with low regularity coefficients." Phd thesis, Université Paris-Est, 2012. http://tel.archives-ouvertes.fr/tel-00794508.
Full textAbstract:
The present thesis is devoted both to the study of strictly hyperbolic operators with low regularity coefficients and of the density-dependent incompressible Euler system. On the one hand, we show a priori estimates for a second order strictly hyperbolic operator whose highest order coefficients satisfy a log-Zygmund continuity condition in time and a log-Lipschitz continuity condition with respect to space. Such an estimate involves a time increasing loss of derivatives. Nevertheless, this is enough to recover well-posedness for the associated Cauchy problem in the space $H^infty$ (for suitably smooth second order coefficients).In a first time, we consider acomplete operator in space dimension $1$, whose first order coefficients were assumed Hölder continuous and that of order $0$only bounded. Then, we deal with the general case of any space dimension, focusing on a homogeneous second order operator: the step to higher dimension requires a really different approach. On the other hand, we consider the density-dependent incompressible Euler system. We show its well-posedness in endpoint Besov spaces embedded in the class of globally Lipschitz functions, producing also lower bounds for the lifespan of the solution in terms of initial data only. This having been done, we prove persistence of geometric structures, such as striated and conormal regularity, for solutions to this system. In contrast with the classical case of constant density, even in dimension $2$ the vorticity is not transported by the velocity field. Hence, a priori one can expect to get only local in time results. For the same reason, we also have to dismiss the vortex patch structure. Littlewood-Paley theory and paradifferential calculus allow us to handle these two different problems .A new version of paradifferential calculus, depending on a parameter $ggeq1$, is also needed in dealing with hyperbolic operators with nonregular coefficients. The general framework is that of Besov spaces, which includes in particular Sobolev and Hölder sets. Intermediate classes of functions, of logaritmic type, come into play as well
46
Fogelklou, Oswald. "Computer-Assisted Proofs and Other Methods for Problems Regarding Nonlinear Differential Equations." Doctoral thesis, Uppsala universitet, Analys och tillämpad matematik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-161314.
Full textAbstract:
This PhD thesis treats some problems concerning nonlinear differential equations. In the first two papers computer-assisted proofs are used. The differential equations there are rewritten as fixed point problems, and the existence of solutions are proved. The problem in the first paper is one-dimensional; with one boundary condition given by an integral. The problem in the second paper is three-dimensional, and Dirichlet boundary conditions are used. Both problems have their origins in fluid dynamics. Paper III describes an inverse problem for the heat equation. Given the solution, a solution dependent diffusion coefficient is estimated by intervals at a finite set of points. The method includes the construction of set-valued level curves and two-dimensional splines. In paper IV we prove that there exists a unique, globally attracting fixed point for a differential equation system. The differential equation system arises as the number of peers in a peer-to-peer network, which is described by a suitably scaled Markov chain, goes to infinity. In the proof linearization and Dulac's criterion are used.
47
Pit, Fabienne. "Modélisation du mélange pour la simulation d'écoulements réactifs turbulents : essais de modèles eulériens lagrangiens." Rouen, 1993. http://www.theses.fr/1993ROUE5020.
Full textAbstract:
Ce travail porte sur la modélisation et la simulation d'écoulements réactifs turbulents à chimie non infiniment rapide par une fonction densité de probabilité conjointe. La résolution de l'équation d'évolution temporelle de la PDF conjointe analytiquement ou numériquement est très complexe. En fait, le problème est simplifié en intégrant cette équation dans l'espace des vitesses. On obtient ainsi une approche hybride probabiliste eulérienne lagrangienne. Une méthode de Monte-Carlo est utilisée ensuite, pour simuler cette équation. Dans cette équation, le phénomène de mélange a petite échelle doit être représenté par un modèle. La comparaison d'un nouveau modèle de mélange avec des modèles classiques d'échange avec la moyenne a été faite dans le cas d'une couche de mélange thermique et dans le cas d'une couche de mélange réactive. Les résultats des calculs sont encourageants. La possibilité de l'appliquer à des configurations industrielles complexes 2D axisymétrique (le bluff-body) et 3D (chambre de combustion dextre) est démontrée
48
Caillau, Philippe. "Modélisation et simulation de la combustion turbulente par une approche probabiliste eulérienne lagrangienne." Rouen, 1994. http://www.theses.fr/1994ROUES080.
Full textAbstract:
L'objet de cette thèse concerne la modélisation des écoulements réactifs turbulents. L'objectif visé consiste à développer un modèle susceptible de prédire la formation des polluants comme le monoxyde d'azote NO ou le monoxyde de carbone CO dans des foyers tridimensionnels complexes. Pour y parvenir, on fait appel à une approche probabiliste eulérienne lagrangienne (PEUL) où le champ de vitesse est calculé à l'aide des équations eulériennes de bilan moyennées et le champ de composition et de température par une méthode dite à transport de PDF (probability density function) lagrangienne. La modélisation des termes inconnus de dispersion turbulente et de mélange aux petites échelles est détaillée. Des mécanismes réduits et un mécanisme détaillé d'oxydation du combustible (qui est ici le méthane, CH4) ainsi que le mécanisme de formation du NO thermique sont introduits et testés. On présente les résultats obtenus avec le modèle PEUL dans trois configurations expérimentales. Les comparaisons calcul-expérience démontrent la capacité du modèle à prédire la formation du NO thermique et (partiellement) du prompt NO, du CO dans des configurations bi- et tridimensionnelles ainsi qu'à représenter correctement un régime d'extinction locale de la flamme.
49
Lundvall, Johan. "Data Assimilation in Fluid Dynamics using Adjoint Optimization." Doctoral thesis, Linköping : Matematiska institutionen, Linköpings universitet, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-9684.
Full text
50
Dakin, Gautier. "Couplage fluide-structure d'ordre (très) élevé pour des schémas volumes finis 2D Lagrange-projection." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066404/document.
Full textAbstract:
Ce travail est consacré à l’étude numérique de l’interaction entre un fluide compressible et une structure indéformable, en adaptant une famille récente de schémas d’ordre très élevé à la prise en compte de conditions aux bords particulières entre le fluide et la structure. Plus précisément,on évalue l’apport de schémas d’ordre strictement supérieur à 3 par rapport à des stratégies plus classiques dans la littérature restreintes aux ordres 1 et 2. Un résultat important est qu’il est possible de réaliser le couplage à tout ordre et qu’il existe des configurations pour lesquelles on observe un gain important pour les ordres élevés. Une revue bibliographique est faite rappelant les résultats théoriques concernant les systèmes hyperboliques et décrivant les méthodes utilisées dans la littérature pour la simulation de la dynamique des gaz et la prise en compte des conditions aux bords. Un schéma sur grilles cartésiennes décalées et d’ordre très élevé est proposé pour la résolution des équations d’Euler en 1D/2D. Ce schéma est basé sur le formalisme Lagrange-projection et bien que formulé en énergie interne assure conservation et consistance faible grâce à un correctif en énergie interne. Parallèlement, l’étude pour les systèmes hyperboliques linéaires de discrétisation à l’ordre très élevé des conditions aux bords est faite. Elle met en évidence la nécessité pour l’ordre élevé de s’intéresser à la stabilité des schémas ainsi obtenus. À partir de ces travaux, la prise en compte de conditions aux bords en vitesse normale imposée est réalisée pour les équations d’Euler en 1D et 2D. Enfin, une procédure de couplage entre fluide compressible et structure indéformable est proposéeThis work is devoted to the construction of stable and high-order numerical methods in order to simulate fluid - rigid body interactions. In this manuscript, a bibliographic overview is done, which highlights theoretical results about hyperbolic system of conservation laws, as well as the methods available in the literature for the hydrodynamics simulation and the numericalboundary treatment. A high-order accurate scheme is proposed on staggered Cartesian grids to approximate the solution of Euler equations in 1D and 2D. The scheme relies on Lagrange-remap formalism, and although formulated in internal energy, ensures both conservation and weak consistency thanks to an internal energy corrector. In the same time, the study of high-order numerical boundary treatment for linear hyperbolic system is done. It highlights the necessity to focus especially on the linear stability of the effective scheme. Starting from the linear results, the numerical boundary treatment with imposed normal velocity is done for Euler equations in 1D and 2D. Last, the coupling between a compressible fluid and a rigid body is realized, using the designed procedure for numerical boudary treatment