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Dissertations / Theses on the topic 'Hamiltonian and Lagrangian dynamics'
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Foxman, Jerome Adam. "The Maslov index in Hamiltonian dynamical systems." Thesis, University of Bristol, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.326680.
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Hosein, Falahaty. "Enhanced fully-Lagrangian particle methods for non-linear interaction between incompressible fluid and structure." Kyoto University, 2018. http://hdl.handle.net/2433/235070.
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Rypina, Irina I. "Lagrangian Coherent Structures and Transport in Two-Dimensional Incompressible Flows with Oceanographic and Atmospheric Applications." Scholarly Repository, 2007. http://scholarlyrepository.miami.edu/oa_dissertations/14.
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The Lagrangian dynamics of two-dimensional incompressible fluid flows is considered, with emphasis on transport processes in atmospheric and oceanic flows. The dynamical-systems-based approach is adopted; the Lagrangian motion in such systems is studied with the aid of Kolmogorov-Arnold-Moser (KAM) theory, and results relating to stable and unstable manifolds and lobe dynamics. Some nontrivial extensions of well-known results are discussed, and some extensions of the theory are developed. In problems for which the flow field consists of a steady background on which a time-dependent perturbation is superimposed, it is shown that transport barriers arise naturally and play a critical role in transport processes. Theoretical results are applied to the study of transport in measured and simulated oceanographic and atmospheric flows. Two particular problems are considered. First, we study the Lagrangian dynamics of the zonal jet at the perimeter of the Antarctic Stratospheric Polar Vortex during late winter/early spring within which lies the "ozone hole". In this system, a robust transport barrier is found near the core of a zonal jet under typical conditions, which is responsible for trapping of the ozone-depleted air within the ozone hole. The existence of such a barrier is predicted theoretically and tested numerically with use of a dynamically-motivated analytically-prescribed model. The second, oceanographic, application considered is the study of the surface transport in the Adriatic Sea. The surface flow in the Adriatic is characterized by a robust threegyre background circulation pattern. Motivated by this observation, the Lagrangian dynamics of a perturbed three-gyre system is studied, with emphasis on intergyre transport and the role of transport barriers. It is shown that a qualitative change in transport properties, accompanied by a qualitative change in the structure of stable and unstable manifolds occurs in the perturbed three-gyre system when the perturbation strength exceeds a certain threshold. This behavior is predicted theoretically, simulated numerically with use of an analytically prescribed model, and shown to be consistent with a fully observationally-based model.
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Mehrmann, Volker, and Hongguo Xu. "Lagrangian invariant subspaces of Hamiltonian matrices." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501133.
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The existence and uniqueness of Lagrangian invariant subspaces of Hamiltonian matrices is studied. Necessary and sufficient conditions are given in terms of the Jordan structure and certain sign characteristics that give uniqueness of these subspaces even in the presence of purely imaginary eigenvalues. These results are applied to obtain in special cases existence and uniqueness results for Hermitian solutions of continuous time algebraic Riccati equations.
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Schwingenheuer, Martin. "Hamiltonian unknottedness of certain monotone Lagrangian tori in S2xS2." Diss., lmu, 2010. http://nbn-resolving.de/urn:nbn:de:bvb:19-123969.
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Faber, Nicolas Boily Christian M. Portegies Zwart Simon. "Orbital complexity in Hamiltonian dynamics." Strasbourg : Université de Starsbourg, 2009. http://eprints-scd-ulp.u-strasbg.fr:8080/secure/00001111/01/FABER_Nicolas_2008-restrict.pdf.
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Thèse de doctorat : Astrophysique : Strasbourg 1 : 2008. Thèse de doctorat : Astrophysics : Universiteit van Amsterdam, Nederland : 2008.Thèse soutenue sur un ensemble de travaux. Thèse soutenue en co-tutelle. Titre provenant de l'écran-titre. Notes bibliogr.
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Faber, Nicolas. "Orbital complexity in Hamiltonian dynamics." Université Louis Pasteur (Strasbourg) (1971-2008), 2008. https://publication-theses.unistra.fr/restreint/theses_doctorat/2008/FABER_Nicolas_2008.pdf.
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L’observation d’un phénomène physique s’appuie en général sur l’évolution d’une observable en fonction du temps. Une telle série temporelle contient les informations de base sur l’état du système étudié. Dans cette thèse, nous exploitons ce concept afin d’explorer l’évolution dynamique complexe qui peut avoir lieu dans les systèmes autogravitants Hamiltoniens. Nous traitons les coordonnées dans l’espace des phases des corps célestes comme des signaux, que nous analysons par la suite en utilisant différentes méthodes de traitement du signal, plus particulièrement la fonction d’autocorrélation et la transformée d’ondelettes. Dans notre analyse nous considérons tour à tour la dynamique à grande échelle des galaxies et celle, interne, des amas stellaires densesThe monitoring of physical phenomena (often) rests on a mapping of an observable as a function of time. Such time series encode basic information about the state of the system under study. In this thesis, we build on this concept to explore the intricate evolution of gravitational Hamiltonian systems. We treat the phase-space coordinates of celestial bodies as signals which we then analyze using processing techniques, such as autocorrelation identification and wavelet transforms. We consider in turn the large-scale dynamics of galaxies, and the internal dynamics of dense stellar clusters. [. . . ]
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Schöberl, Markus. "Geometry and control of mechanical systems an Eulerian, Lagrangian and Hamiltonian approach." Aachen Shaker, 2007. http://d-nb.info/989019306/04.
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Salmon, Daniel. "Dynamics of Systems With Hamiltonian Monodromy." W&M ScholarWorks, 2018. https://scholarworks.wm.edu/etd/1550153890.
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A system is said to have monodromy if, when we carry the system around a closed circuit, it does not return to its initial state. The simplest example is the square-root function in the complex plane. A Hamiltonian system is said to have Hamiltonian monodromy if its fundamental action-angle loops do not return to their initial topological state at the end of a closed circuit. These changes in topology of angle loops carry through to other aspects of these systems, including the classical dynamics of families of trajectories, quantum spectra and even wavefunctions. This topological change in the evolution of a loop of classical trajectories has been observed experimentally for the rst time, using an apparatus consisting of a spherical pendulum subject to magnetic potentials and torques. Presented in this dissertation are the details of this experiment, as well as theoretical calculations on a novel system: a double welled Mexican-hat system with two monodromy points. This is part of a more general research program that is concerned with the Lagrangian torus bration of the phase spaces of integrable Hamiltonian systems. It is in this way the calculations on the double welled system are carried out. in this dissertation, static and dynamical manifestations of monodromy are shown to exist for this system. It has been shown previously that corresponding topological changes occur in wavefunctions of systems with monodromy. Here it is shown that results of quantum wavefunction monodomy carry over intuitively.
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Prieto, Martínez Pere Daniel. "Geometrical structures of higher-order dynamical systems and field theories." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/284215.
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Geometrical physics is a relatively young branch of applied mathematics that was initiated by the 60's and the 70's when A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, among many others, began to study various topics in physics using methods of differential geometry. This "geometrization" provides a way to analyze the features of the physical systems from a global viewpoint, thus obtaining qualitative properties that help us in the integration of the equations that describe them. Since then, there has been a strong development in the intrinsic treatment of a variety of topics in theoretical physics, applied mathematics and control theory using methods of differential geometry.
Most of the work done in geometrical physics since its first days has been devoted to study first-order theories, that is, those theories whose physical information depends on (at most) first-order derivatives of the generalized coordinates of position (velocities). However, there are theories in physics in which the physical information depends explicitly on accelerations or higher-order derivatives of the generalized coordinates of position, and thus more sophisticated geometrical tools are needed to model them acurately.
In this Ph.D. Thesis we pretend to give a geometrical description of some of these higher-order theories. In particular, we focus on dynamical systems and field theories whose dynamical information can be given in terms of a Lagrangian function, or a Hamiltonian that admits Lagrangian counterpart. More precisely, we will use the Lagrangian-Hamiltonian unified approach in order to develop a geometric framework for autonomous and non-autonomous higher-order dynamical system, and for second-order field theories. This geometric framework will be used to study several relevant physical examples and applications, such as the Hamilton-Jacobi theory for higher-order mechanical systems, relativistic spin particles and deformation problems in mechanics, and the Korteweg-de Vries equation and other systems in field theory.La física geomètrica és una branca relativament jove de la matemàtica aplicada que es va iniciar als anys 60 i 70 qua A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, entre molts altres, van començar a estudiar diversos problemes en física usant mètodes de geometria diferencial. Aquesta "geometrització" proporciona una manera d'analitzar les característiques dels sistemes físics des d'una perspectiva global, obtenint així propietats qualitatives que faciliten la integració de les equacions que els descriuen. D'ençà s'ha produït un fort desenvolupamewnt en el tractament intrínsic d'una gran varietat de problemes en física teòrica, matemàtica aplicada i teoria de control usant mètodes de geometria diferencial. Gran part del treball realitzat en la física geomètrica des dels seus primers dies s'ha dedicat a l'estudi de teories de primer ordre, és a dir, teories tals que la informació física depèn en, com a molt, derivades de primer ordre de les coordenades de posició generalitzades (velocitats). Tanmateix, hi ha teories en física en les que la informació física depèn de manera explícita en acceleracions o derivades d'ordre superior de les coordenades de posició generalitzades, requerint, per tant, d'eines geomètriques més sofisticades per a modelar-les de manera acurada. En aquesta Tesi Doctoral ens proposem donar una descripció geomètrica d'algunes d'aquestes teories. En particular, estudiarem sistemes dinàmics i teories de camps tals que la seva informació dinàmica ve donada en termes d'una funció lagrangiana, o d'un hamiltonià que prové d'un sitema lagrangià. Per a ser més precisos emprarem la formulació unificada Lagrangiana-Hamiltoniana per tal de desenvolupar marcs geomètrics per a sistemes dinàmics d'ordre superior autònoms i no autònoms, i per a teories de camps de segon ordre. Amb aquest marc geomètric estudiarem alguns exemples físics rellevants i algunes aplicacions, com la teoria de Hamilton-Jacobi per a sistemes mecànics d'ordre superior, partícules relativístiques amb spin i problemes de deformació en mecànica, i l'equació de Korteweg-de Vries i altres sistemes en teories de camps.
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Shchekinova, Elena Y. "Analysis of Multidimensional Phase Space Hamiltonian Dynamics: Methods and Applications." Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-03172006-083600/.
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Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2006.Mustafa Aral, Committee Member ; John Wood, Committee Member ; Kurt Wiesenfeld, Committee Member ; M. Raymond Flannery, Committee Member ; Turgay Uzer, Committee Chair.
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Reich, Sebastian. "Smoothed dynamics of highly oscillatory Hamiltonian systems." Universität Potsdam, 1995. http://opus.kobv.de/ubp/volltexte/2007/1563/.
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We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been successfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion of the smoothed dynamics of a highly oscillatory Hamiltonian system. Based on our analysis, we suggest a new constrained formulation that maintains the flexibility of the system while at the same time suppressing the high-frequency components in the solutions and thus allowing for larger time steps. The new constrained formulation is Hamiltonian and can be discretized by the well-known SHAKE method.
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Oms, Cédric. "Global Hamiltonian dynamics on singular symplectic manifolds." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669831.
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In this thesis, we study the Reeb and Hamiltonian dynamics on singular symplectic and contact manifolds. Those structures are motivated by singularities coming from classical mechanics and fluid dynamics.
We start by studying generalized contact structures where the non-integrability condition fails on a hypersurface, the critical hypersurface. Those structures, called $b$-contact structures, arise from hypersurfaces in $b$-symplectic manifolds that have been previously studied extensively in the past. Formerly, this odd-dimensional counterpart to $b$-symplectic geometry has been neglected in the existing vast literature. Examples are given and local normal forms are proved. The local geometry of those manifolds is examined using the language of Jacobi manifolds, which provides an adequate set-up and leads to understanding the geometric structure on the critical hypersurface. We further consider other types of singularities in contact geometry, as for instance higher order singularities, called $b^m$-contact forms, or singularities of folded type.
Obstructions to the existence of those structures are studied and the topology of $b^m$-contact manifolds is related to the existence of convex contact hypersurfaces and further relations to smooth contact structures are described using the desingularization technique.
We continue examining the dynamical properties of the Reeb vector field associated to a given $b^m$-contact form. The relation of those structures to celestial mechanics underlines the relevance for existence results of periodic orbits of the Hamiltonian vector field in the $b^m$-symplectic setting and Reeb vector fields for $b^m$-contact manifolds. In this light, we prove that in dimension $3$, there are always infinitely many periodic Reeb orbits on the critical surface, but describe examples without periodic orbits away from it in any dimension. We prove that there are traps for this vector field and discuss possible extensions to prove the existence of plugs. We will see that in the case of overtwisted disks away from the critical hypersurface and some additional conditions, Weinstein conjecture holds: more precisely there exists either a periodic Reeb orbit away from the critical hypersurface or a $1$-parametric family in the neighbourhood of it. The mentioned results shed new light towards a singular version for this conjecture.
The obtained results are applied to the particular case of the restricted planar circular three body problem, where we prove that after the McGehee change, there are infinitely many non-trivial periodic orbits at the manifold at infinity for positive energy values.En esta tesis, estudiamos la dinámica de Reeb y Hamiltoniana en variedades simplécticas y de contacto con singularidades. El estudio de estas variedades está motivado por singularidades que tienen su origen en la mecánica clásica y la dinámica de fluidos. Empezamos estudiando una generalización de las estructuras de contacto, en la cual la condición de no integrabilidad falla en una hipersuperficie, llamada la hipersuperficie crítica. Estas estructuras geométricas, llamadas estructuras de $b$-contacto, surgen de hipersuperficies en variedades $b$-simplécticas, estudiadas en el pasado. Hasta el momento, este equivalente de dimensión impar de la geometría $b$-simpléctica ha sido desatendido en la literatura existente. Después de los primeros ejemplos, probamos la existencia de formas locales. Estudiamos la geometría local de estas variedades usando el lenguaje de variedades de Jacobi, que resultan ser técnicas adecuadas para entender la estructura geométrica en la hipersuperficie crítica. Consideramos también singularidades de orden superior, formas de $b^m$-contacto, y singularidades de tipo folded. Continuamos con el estudio de las obstrucciones a la existencia de estas estructuras y relacionamos la topología de variedades de $b^m$-contacto con la existencia de hipersuperficies convexas. Describimos relaciones entre formas de $b^m$-contacto y formas de contacto diferenciables usando técnicas de desingularización. Examinamos las propiedades del campo de Reeb asociado a una forma de $b^m$-contacto dada. La relación de estas estructuras con la mecánica celeste pone en relieve la importancia del estudio de órbitas periódicas de este campo vectorial. Comprobamos que, en dimensión $3$, el campo de Reeb en la hipersuperficie crítica admite infinitas órbitas periódicas. Sin embargo, describimos ejemplos sin órbitas periódicas fuera de la hipersuperficie crítica en cualquier dimensión. Comprobamos la existencia de traps y discutimos la posible existencia de plugs. En el caso de un disco \emph{overtwisted} fuera de la hipersuperficie se satisface la conjetura de Weinstein: en concreto, o bien existe una órbita periódica de Reeb fuera de la hipersuperficie de contacto o bien existe una familia de órbitas periódicas en un entorno de la hipersuperficie. Estos resultados sugieren una versión singular de dicha conjetura. Aplicamos los resultados obtenidos al caso del problema de los tres cuerpos restringido circular: comprobamos que después del cambio de coordenadas de McGehee, existen infinitas órbitas periódicas en la variedad en el infinito para valores positivos de la energía.
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Koch, Christiane. "Quantum dissipative dynamics with a surrogate Hamiltonian." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2002. http://dx.doi.org/10.18452/14816.
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Diese Dissertation untersucht Quantensysteme in kondensierter Phase, welche mit ihrer Umgebung wechselwirken und durch ultrakurze Laserpulse angeregt werden. Die Zeitskalen der verschiedenen beteiligten Prozessen lassen sich bei solchen Problemen nicht separieren, weshalb die Standardmethoden zur Behandlung offener Quantensysteme nicht angewandt werden können. Die Methode des Surrogate Hamiltonian stellt ein Beispiel neuer Herangehensweisen an dissipative Quantendynamik dar. Die Weiterentwicklung der Methode und ihre Anwendung auf Phänomene, die zur Zeit experimentell untersucht werden, stehen im Mittelpunkt dieser Arbeit. Im ersten Teil der Arbeit werden die einzelnen dissipativen Prozesse klassifiziert und diskutiert. Insbesondere wird ein Modell der Dephasierung in die Methode des Surrogate Hamiltonian eingeführt. Dies ist wichtig für zukünftige Anwendungen der Methode, z.b. auf kohärente Kontrolle oder Quantencomputing. Diesbezüglich hat der Surrogate Hamiltonian einen großen Vorteil gegenüber anderen zur Verfügung stehenden Methoden dadurch, daß er auf dem Spin-Bad, d.h. auf einer vollständig quantenmechanischen Beschreibung der Umgebung, beruht. Im nächsten Schritt wird der Surrogate Hamiltonian auf ein Standardproblem für Ladungstransfer in kondensierter Phase angewandt, zwei nichtadiabatisch gekoppelte harmonische Oszillatoren, die in ein Bad eingebettet sind. Dieses Modell stellt eine große Vereinfachung von z.B. einem Molekül in Lösung dar, es dient hier jedoch als Testbeispiel für die theoretische Beschreibung eines prototypischen Ladungstransferereignisses. Alle qualitativen Merkmale eines solchen Experimentes können wiedergegeben und Defizite früherer Behandlungen identifiziert werden. Ultraschnelle Experimente beobachten Reaktionsdynamik auf der Zeitskala von Femtosekunden. Dies kann besonders gut durch den Surrogate Hamiltonian als einer Methode, die auf einer zeitabhängigen Beschreibung beruht, erfaßt werden. Die Kombination der numerischen Lösung der zeitabhängigen Schrödingergleichung mit der Wignerfunktion, die die Visualisierung eines Quantenzustands im Phasenraum ermöglicht, gestattet es, dem Ladungstransferzyklus intuitiv Schritt für Schritt zu folgen. Der Nutzen des Surrogate Hamiltonian wird weiterhin durch die Verbindung mit der Methode der Filterdiagonalisierung erhöht. Dies gestattet es, aus mit dem Surrogate Hamiltonian nur für relative kurze Zeite konvergierte Erwartungswerten Ergebnisse in der Frequenzdomäne zu erhalten. Der zweite Teil der Arbeit beschäftigt sich mit der theoretischen Beschreibung der laserinduzierten Desorption kleiner Moleküle von Metalloxidoberflächen. Dieses Problem stellt ein Beispiel dar, in dem alle Aspekte mit derselben methodischen Genauigkeit beschrieben werden, d.h. ab initio Potentialflächen werden mit einem mikroskopischen Modell für die Anregungs- und Relaxationsprozesse verbunden. Das Modell für die Wechselwirkung zwischen angeregtem Adsorbat-Substrat-System und Elektron-Loch-Paaren des Substrats beruht auf einer vereinfachten Darstellung der Elektron-Loch-Paare als ein Bad aus Dipolen und auf einer Dipol-Dipol-Wechselwirkung zwischen System und Bad. Alle Parameter können aus Rechnungen zur elektronischen Struktur abgeschätzt werden. Desorptionswahrscheinlichkeiten und Desorptionsgeschwindigkeiten werden unabhängig voneinander im experimentell gefundenen Bereich erhalten. Damit erlaubt der Surrogate Hamiltonian erstmalig eine vollständige Beschreibung der Photodesorptionsdynamik auf ab initio-Basis.This thesis investigates condensed phase quantum systems which interact with their environment and which are subject to ultrashort laser pulses. For such systems the timescales of the involved processes cannot be separated, and standard approaches to treat open quantum systems fail. The Surrogate Hamiltonian method represents one example of a number of new approaches to address quantum dissipative dynamics. Its further development and application to phenomena under current experimental investigation are presented. The single dissipative processes are classified and discussed in the first part of this thesis. In particular, a model of dephasing is introduced into the Surrogate Hamiltonian method. This is of importance for future work in fields such as coherent control and quantum computing. In regard to these subjects, it is a great advantage of the Surrogate Hamiltonian over other available methods that it relies on a spin, i.e. a fully quantum mechanical description of the bath. The Surrogate Hamiltonian method is applied to a standard model of charge transfer in condensed phase, two nonadiabatically coupled harmonic oscillators immersed in a bath. This model is still an oversimplification of, for example, a molecule in solution, but it serves as testing ground for the theoretical description of a prototypical ultrafast pump-probe experiment. All qualitative features of such an experiment are reproduced and shortcomings of previous treatments are identified. Ultrafast experiments attempt to monitor reaction dynamics on a femtosecond timescale. This can be captured particularly well by the Surrogate Hamiltonian as a method based on a time-dependent picture. The combination of the numerical solution of the time-dependent Schrödinger equation with the phase space visualization given by the Wigner function allows for a step by step following of the sequence of events in a charge transfer cycle in a very intuitive way. The utility of the Surrogate Hamiltonian is furthermore significantly enhanced by the incorporation of the Filter Diagonalization method. This allows to obtain frequency domain results from the dynamics which can be converged within the Surrogate Hamiltonian approach only for comparatively short times. The second part of this thesis is concerned with the theoretical treatment of laser induced desorption of small molecules from oxide surfaces. This is an example which allows for a description of all aspects of the problem with the same level of rigor, i.e. ab initio potential energy surfaces are combined with a microscopic model for the excitation and relaxation processes. This model of the interaction between the excited adsorbate-substrate complex and substrate electron-hole pairs relies on a simplified description of the electron-hole pairs as a bath of dipoles, and a dipole-dipole interaction between system and bath. All parameters are connected to results from electronic structure calculations. The obtained desorption probabilities and desorption velocities are simultaneously found to be in the right range as compared to the experimental results. The Surrogate Hamiltonian approach therefore allows for a complete description of the photodesorption dynamics on an ab initio basis for the first time.
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Sweet, Christopher Richard. "Hamiltonian thermostatting techniques for molecular dynamics simulation." Thesis, University of Leicester, 2004. http://hdl.handle.net/2381/30526.
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Molecular dynamics trajectories that sample from a Gibbs, or canonical, distribution can be generated by introducing a modified Hamiltonian with additional degrees of freedom as described by Nose [46]. Although this method has found widespread use in its time re-parameterized Nose-Hoover form, the lack of a Hamiltonian, and the need to 'tune' thermostatting parameters has limited, its use compared to stochastic methods. In addition, since the proof of the correct sampling is based on an ergodic assumption, thermostatting small of stiff systems often does not given the correct distributions unless the Nose-Hoover chains [43] method is used, which inherits the Nose-Hoover deficiencies noted above. More recently the introduction of the Hamiltonian Nose-Poincare method [11], where symplectic integrators can be used for improved long term stability, has renewed interest in the possibility of Hamiltonian methods which can improve dynamical sampling. This class of methods, although applicable to small systems, has applications in large scale systems with complex chemical structure, such as protein-bath and quantum-classical models.;For Nose dynamics, it is often stated that the system is driven to equilibrium through a resonant interaction between the self-oscillation frequency of the thermostat variable and a natural frequency of the underlying system. By the introduction of multiple thermostat Hamiltonian formulations, which are not restricted to chains, it has been possible to clarify this perspective, using harmonic models, and exhibit practical deficiencies of the standard Nose-chain approach. This has led to the introduction of two Hamiltonian schemes, the Nose-Poincare chains method and the Recursive Multiple Thermostat (RMT) method. The RMT method obtains canonical sampling without the stability problems encountered with chains with the advantage that the choice of Nose mass is independent of the underlying system.
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Demir, Ali Sait. "On The Algebraic Structure Of Relative Hamiltonian Diffeomorphism Group." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609301/index.pdf.
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Let M be smooth symplectic closed manifold and L a
closed Lagrangian submanifold of M. It was shown by Ozan that
Ham(M,L): the relative Hamiltonian diffeomorphisms on M fixing the
Lagrangian submanifold L setwise is a subgroup which is equal to
the kernel of the restriction of the flux homomorphism to the
universal cover of the identity component of the relative
symplectomorphisms.
In this thesis we show that Ham(M,L) is a non-simple perfect
group, by adopting a technique due to Thurston, Herman, and
Banyaga. This technique requires the diffeomorphism group be
transitive where this property fails to exist in our case.
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Fredriksson, Adam. "Visual Comparison of Lagrangian and Semi-Lagrangian fluid simulation." Thesis, Blekinge Tekniska Högskola, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-14838.
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Context. Fluid simulations are an important part for enhancing the visualization of games, movies and other graphical applications. Fluid simulations can be achieved in different type of context ranging between slow, high-quality simulations which is mainly used for movies, to fast lower-quality simulations which is primarily used for real-time applications such as games. Objectives. The goal was to compare the visual appearance of a Lagrangian method and a semiLagrangian method when it came to realistic appearance. Methods. Identical scenes of water being rendered are made for both the Lagrangian and the semiLagrangian algorithm. This is later measured by using a user study which will provide the result of which method that provides a more realistic appearance Results. The result of the tests showed that the visual realism between the semi-Lagrangian and Lagrangian were different depending on the scene environment. Conclusions. The conclusion of the data presented in the result yields that the Lagrangian and semiLagrangian looks very much alike and there is no real realistic difference between the methods, some scene yields a vast majority of votes in the favor of one method.
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Kompaneets, Roman. "Complex plasmas: Interaction potentials and non-Hamiltonian dynamics." Diss., lmu, 2007. http://nbn-resolving.de/urn:nbn:de:bvb:19-73804.
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Hecht, Michael. "Isomorphic chain complexes of Hamiltonian dynamics on tori." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-123279.
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In this thesis we construct for a given smooth, generic Hamiltonian
H on the 2n dimensional torus a chain-isomorphism between the Morse complex of the Hamiltonian action on the free loop space of the torus and the Floer-complex. Though both complexes are generated by the critical points of the Hamiltonian action, their boundary operators differ. Therefore the construction of the isomorphism is based on counting the moduli spaces of hybrid-type solutions which involves stating a new non-Lagrangian boundary value problem for Cauchy-Riemann type operators not yet studied in Floer theory.
It is crucial for the statement that the torus is compact, possesses trivial tangent bundle and an additive structure. We finally want to note that the problem is completely symmetric.
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Lambert, Paul. "Canonical analysis of double null relativistic Hamiltonian dynamics." Thesis, University of Southampton, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411862.
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Yudichak, Thomas William. "Hamiltonian methods in weakly nonlinear Vlasov-Poisson dynamics /." Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3008481.
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Mašek, Jan. "Modelování postkritických stavů štíhlých konstrukcí." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2016. http://www.nusl.cz/ntk/nusl-239983.
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The aim of the presented thesis is to create a compact publication which deals with properties, solution and examination of behavior of dynamical systems as models of mechanical structures. The opening portion of the theoretical part leads the reader through the subject of description of dynamical systems, offers solution methods and investigates solution stability. As the introduction proceeds, possible forms of structure loading, damping and response are presented. Following chapters discuss extensively the possible approaches to system behavior observation and identification of nonlinear and chaotic phenomena. The attention is also paid to displaying methods and color spaces as these are essential for the examination of complex and sensitive systems. The theoretical part of the thesis ends with an introduction to fractal geometry. As the theoretical background is laid down, the thesis proceeds with an application of the knowledge and shows the approach to numerical simulation and study of models of real structures. First, the reader is introduced to the single pendulum model, as the simplest model to exhibit chaotic behavior. The following double pendulum model shows the obstacles of observing systems with more state variables. The models of free rod and cantilever serve as examples of real structure models with many degrees of freedom. These models show even more that a definite or at least sufficiently relevant monitoring of behavior of such deterministic systems is a challenging task which requires sophisticated approach.
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Choo, Kiam. "Learning hyperparameters for neural network models using Hamiltonian dynamics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0008/MQ53385.pdf.
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Camarena, Julian Antolin Oks E. A. "Application of generalized Hamiltonian dynamics to modified Coulomb potential." Auburn, Ala, 2008. http://repo.lib.auburn.edu/EtdRoot/2008/FALL/Physics/Thesis/Camarena_Julian_6.pdf.
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Mangoubi, Oren (Oren Rami). "Integral geometry, Hamiltonian dynamics, and Markov Chain Monte Carlo." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104583.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 97-101).
This thesis presents applications of differential geometry and graph theory to the design and analysis of Markov chain Monte Carlo (MCMC) algorithms. MCMC algorithms are used to generate samples from an arbitrary probability density [pi] in computationally demanding situations, since their mixing times need not grow exponentially with the dimension of [pi]. However, if [pi] has many modes, MCMC algorithms may still have very long mixing times. It is therefore crucial to understand and reduce MCMC mixing times, and there is currently a need for global mixing time bounds as well as algorithms that mix quickly for multi-modal densities. In the Gibbs sampling MCMC algorithm, the variance in the size of modes intersected by the algorithm's search-subspaces can grow exponentially in the dimension, greatly increasing the mixing time. We use integral geometry, together with the Hessian of r and the Chern-Gauss-Bonnet theorem, to correct these distortions and avoid this exponential increase in the mixing time. Towards this end, we prove a generalization of the classical Crofton's formula in integral geometry that can allow one to greatly reduce the variance of Crofton's formula without introducing a bias. Hamiltonian Monte Carlo (HMC) algorithms are some the most widely-used MCMC algorithms. We use the symplectic properties of Hamiltonians to prove global Cheeger-type lower bounds for the mixing times of HMC algorithms, including Riemannian Manifold HMC as well as No-U-Turn HMC, the workhorse of the popular Bayesian software package Stan. One consequence of our work is the impossibility of energy-conserving Hamiltonian Markov chains to search for far-apart sub-Gaussian modes in polynomial time. We then prove another generalization of Crofton's formula that applies to Hamiltonian trajectories, and use our generalized Crofton formula to improve the convergence speed of HMC-based integration on manifolds. We also present a generalization of the Hopf fibration acting on arbitrary- ghost-valued random variables. For [beta] = 4, the geometry of the Hopf fibration is encoded by the quaternions; we investigate the extent to which the elegant properties of this encoding are preserved when one replaces quaternions with general [beta] > 0 ghosts.
by Oren Mangoubi.
Ph. D.
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Many, Manda Bertin. "Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems." Doctoral thesis, Faculty of Science, 2021. http://hdl.handle.net/11427/33780.
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In this thesis we study the chaotic behavior of multidimensional Hamiltonian systems in the presence of nonlinearity and disorder. It is known that any localized initial excitation in a large enough linear disordered system spreads for a finite amount of time and then halts forever. This phenomenon is called Anderson localization (AL). What happens to AL when nonlinearity is introduced is an interesting question which has been considered in several studies over the past decades. Recent works focussing on two widely–applicable systems, namely the disordered Klein-Gordon (DKG) lattice of anharmonic oscillators and the disordered discrete nonlinear Schr¨odinger (DDNLS) equation, mainly in one spatial dimension suggest that nonlinearity eventually destroys AL. This leads to an infinite diffusive spreading of initially localized wave packets whose extent (measured for instance through the wave packet's second moment m2) grows in time t as t αm with 0 < αm < 1. However, the characteristics and the asymptotic fate of such evolutions still remain an issue of intense debate due to their computational difficulty, especially in systems of more than one spatial dimension. Two different spreading regimes, the so-called weak and strong chaos regimes, have been theoretically predicted and numerically identified. As the spreading of initially localized wave packets is a non-equilibrium thermalization process related to the ergodic and chaotic properties of the system, in our work we investigate the properties of chaos studying the behavior of observables related to the system's tangent dynamics. In particular, we consider the DDNLS model of one (1D) and two (2D) spatial dimensions and develop robust, efficient and fast numerical integration schemes for the long-time evolution of the phase space and tangent dynamics of these systems. Implementing these integrators, we perform extensive numerical simulations for various sets of parameter values. We present, to the best of our knowledge for the first time, detailed computations of the time evolution of the system's maximum Lyapunov exponent (MLE–Λ) i.e. the most commonly used chaos indicator, and the related deviation vector distribution (DVD). We find that although the systems' MLE decreases in time following a power law t αΛ with αΛ < 0 for both the weak and strong chaos cases, no crossover to the behavior Λ ∝ t −1 (which is indicative of regular motion) is observed. By investigating a large number of weak and strong chaos cases, we determine the different αΛ values for the 1D and 2D systems. In addition, the analysis of the DVDs reveals the existence of random fluctuations of chaotic hotspots with increasing amplitudes inside the excited part of the wave packet, which assist in homogenizing chaos and contribute to the thermalization of more lattice sites. Furthermore, we show the existence of a dimension-free relation between the wave packet spreading and its degree of chaoticity between the 1D and 2D DDNLS systems. The generality of our findings is confirmed, as similar behaviors to the ones observed for the DDNLS systems are also present in the case of DKG models.
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Lamont, M. J. "Hamiltonian lattice gauge theory : A cluster expansion approach." Thesis, University of Liverpool, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382063.
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Lahiri, Sudeep Kumar. "Variationally consistent methods for Lagrangian dynamics in continuum mechanics." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/39597.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.Includes bibliographical references (p. 135-143).
Rapid dynamics are commonly encountered in industrial applications such as forging, crash tests and many others. These problems are typically non-linear due to large deformations and/or non-linear constitutive relations. Such problems are typically modelled from a Lagrangian viewpoint, where the mesh is attached to the body; hence, large deformations lead to large distortions in the mesh. Explicit numerical methods are considered to be efficient in these cases where large meshes and small time-steps are employed for spatial and temporal resolution. However, incompressible and nearly incompressible materials pose a problem as the timestep stability restriction in explicit methods becomes increasingly severe. Most of the numerical methods employed for such simulations, are developed from discretization of the equations of motion. Recently, Variational Integrators have been developed where the numerical time integration scheme is developed from a variational principle based on Hamilton's principle of stationary action. Such methods ensure conservation of linear and angular momentum, which lead to more physically consistent simulations.
(cont.) In this research, numerical methods addressing incompressibility and mesh distortions have been developed under a variational framework. A variational formulation for mesh adaptation procedures, involving local mesh changes for triangular meshes, is presented. Such procedures are very well suited for explicit methods, without significant expense. Conservation properties of such methods are proved and demonstrated. Further, a Fractional Time-Step method is developed, from a variational framework, for incompressible and nearly incompressible problems. Algorithmic details are presented, followed by examples demonstrating the performance of the method.
by Sudeep K. Lahiri.
Ph.D.
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Ellis, Truman Everett. "High Order Finite Elements for Lagrangian Computational Fluid Dynamics." DigitalCommons@CalPoly, 2010. https://digitalcommons.calpoly.edu/theses/282.
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A general finite element method is presented to solve the Euler equations in a Lagrangian reference frame. This FEM framework allows for separate arbitrarily high order representation of kinematic and thermodynamic variables. An accompanying hydrodynamics code written in Matlab is presented as a test-bed to experiment with various basis function choices. A wide range of basis function pairs are postulated and a few choices are developed further, including the bi-quadratic Q2-Q1d and Q2-Q2d elements. These are compared with a corresponding pair of low order bi-linear elements, traditional Q1-Q0 and sub-zonal pressure Q1-Q1d. Several test problems are considered including static convergence tests, the acoustic wave hourglass test, the Sod shocktube, the Noh implosion problem, the Saltzman piston, and the Sedov explosion problem. High order methods are found to offer faster convergence properties, the ability to represent curved zones, sharper shock capturing, and reduced shock-mesh interaction. They also allow for the straightforward calculation of thermodynamic gradients (for multi-physics calculations) and second derivatives of velocity (for monotonic slope limiters), and are more computationally efficient. The issue of shock ringing remains unresolved, but the method of hyperviscosity has been identified as a promising means of addressing this. Overall, the curvilinear finite elements presented in this thesis show promise for integration in a full hydrodynamics code and warrant further consideration.
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Piddington, Kyle C. "Eulerian on Lagrangian Cloth Simulation." DigitalCommons@CalPoly, 2017. https://digitalcommons.calpoly.edu/theses/1778.
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This thesis introduces a novel Eulerian-on-Lagrangian (EoL) approach for simulating cloth. This approach allows for the simulation of traditionally difficult cloth scenarios, such as draping and sliding cloth over sharp features like the edge of a table. A traditional Lagrangian approach models a cloth as a series of connected nodes. These nodes are free to move in 3d space, but have difficulty with sliding over hard edges. The cloth cannot always bend smoothly around these edges, as motion can only occur at existing nodes. An EoL approach adds additional flexibility to a Lagrangian approach by constructing special Eulerian on Lagrangian nodes (EoL Nodes), where cloth material can pass through a fixed point. On contact with the edge of a box, EoL nodes are introduced directly on the edge. These nodes allow the cloth to bend exactly at the edge, and pass smoothly over the area while sliding. Using this ‘Eulerian-on-Lagrangian’ discretization, a set of rules for introducing and constraining EoL Nodes, and an adaptive remesher, This simulator allows cloth to move in a sliding motion over sharp edges. The current implementation is limited to cloth collision with static boxes, but the method presented can be expanded to include contact with more complicated meshes and dynamic rigid bodies.
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Bremner, Michael J. "Characterizing entangling quantum dynamics /." [St. Lucia, Qld.], 2005. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe19023.pdf.
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Santos, Jaime Eduardo Moutinho. "Non-equilibrium dynamics of reaction-diffusion processes." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.361994.
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McCabe, Ryan Matthew. "Small-scale coastal dynamics and mixing from a Lagrangian perspective /." Thesis, Connect to this title online; UW restricted, 2008. http://hdl.handle.net/1773/10963.
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Lacey, Scott Michael. "Ray and wave dynamics in three dimensional asymmetric optical resonators /." view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3102173.
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Thesis (Ph. D.)--University of Oregon, 2003.Typescript. Includes vita and abstract. Includes bibliographical references (leaves 184-187). Also available for download via the World Wide Web; free to University of Oregon users.
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Fletcher, Steven James. "Higher order balance conditions using Hamiltonian dynamics for numerical weather prediction." Thesis, University of Reading, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.398406.
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Smale, Jonathan Ross. "Fitting and using model Hamiltonian in non-adiabatic molecular dynamics simulations." Thesis, University of Birmingham, 2012. http://etheses.bham.ac.uk//id/eprint/3764/.
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In order to study computationally increasingly complex systems using theoretical methods model Hamiltonians are required to accurately describe the potential energy surface they represent. Also ab-initio methods improve the calculation of the excited states of these complex systems becomes increasingly feasible. One such model Hamiltonian described herein, the Vibronic Coupling Hamiltonian, has previously shown its versitility and ability to describe a variety of non-adiabatic problems. This thesis describes a new method, a genetic algorithm, for the parameterisation of the Vibronic Coupling Hamiltonian to describe both previously calculated potential energy surfaces (allene and pentatetraene) and newly calculated (cyclo-butadiene and toluene) potential energy surfaces. In order to test this genetic algorithm quantum nuclear dynamics calculations were performed using the multi-configurational time dependent hartree method and the results compared to experiment.
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Leonard, Amaury. "Aspects of higher spin Hamiltonian dynamics: Conformal geometry, duality and charges." Doctoral thesis, Universite Libre de Bruxelles, 2017. https://dipot.ulb.ac.be/dspace/bitstream/2013/253872/4/main.pdf.
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Nous avons investigué les propriétés des champs de jauge de spin élevé libres à travers une étude de divers aspects de leur dynamique hamiltonienne. Pour des champs se propageant sur un espace-temps plat, les contraintes issues de l'analyse hamiltonienne de ces théories de jauge ont été identifiées et résolues par l'introduction de prépotentiels, dont l'invariance de jauge comprend, de façon intrigante, à la fois des difféomorphismes linéarisés généralisés et des transformations d'échelle de Weyl généralisées et linéarisées. Cela a motivé notre étude systématique des invariants conformes pour les spins élevés. Les invariants correspondants ont été construits à l'aide du tenseur de Cotton, dont nous avons établi les propriétés essentielles (symétrie, conservation, trace nulle; invariance, complétude). Avec ces outils géométriques, l'analyse hamiltonienne a pu être complétée et une action du premier ordre écrite en termes des prépotentiels. Nous avons constaté que cette action possédait une invariance manifeste par dualité électromagnétique; cette invariance, combinée à l'invariance de jauge des prépotentiels, fixe d'ailleurs uniquement l'action. En outre, de façon générale, cette action s'est révélée être exactement celle obtenue à travers une réécriture des équations du mouvement des spins élevés comme des conditions d'auto-dualité tordue (non manifestement covariantes).Avec un intérêt pour les extensions supersymétriques, nous avons amorcé la généralisation de cette étude aux champs fermioniques. Le champ de masse nulle libre de spin 5/2 a été soumis à la même analyse, et son prépotentiel s'est révélé partager l'invariance de jauge conforme déjà observée dans le cas bosonique général. Le supermultiplet incorporant les spins 2 et 5/2 a ensuite été considéré, et une symétrie rigide de son action, combinant une transformation de dualité électromagnétique du spin 2 avec une transformation de chiralité du spin 5/2 a été construite pour commuter avec la supersymétrie. Dans une autre direction, nous avons étudié les propriétés d'un champ tensoriel chiral de symétrie mixte dans un espace-temps plat à six dimensions: une (2,2)-forme. Son analyse hamiltonienne a été réalisée, des prépotentiels introduits et l'action de premier ordre obtenue s'est encore une fois révélée être la même que celle obtenue à travers une réécriture des équations du mouvement comme des conditions d'auto-chiralité (non manifestement covariante).Finalement, nous nous sommes penchés sur les charges de surface des champs fermioniques et bosoniques de spin élevé se propageant sur un espace-temps à courbure constante. Cela a été réalisé par une analyse hamiltonienne de ces systèmes, les contraintes étant identifiées aux générateurs des transformations de jauge. Injectant dans ces générateurs des valeurs des paramètres des transformations de jauge correspondant à des transformations impropres de jauge (imposant une réelle variation physique sur les champs) a ensuite permis d'évaluer la valeur de ces générateurs pour des champs résolvant les équations du mouvement: elle s'est bien révélée finie et non-nulle, constituant les charges de surface de ces théories.Doctorat en Sciences
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Leonard, Amaury. "Aspects of higher spin Hamiltonian dynamics: Conformal geometry, duality and charges." Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/253872.
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Nous avons investigué les propriétés des champs de jauge de spin élevé libres à travers une étude de divers aspects de leur dynamique hamiltonienne. Pour des champs se propageant sur un espace-temps plat, les contraintes issues de l'analyse hamiltonienne de ces théories de jauge ont été identifiées et résolues par l'introduction de prépotentiels, dont l'invariance de jauge comprend, de façon intrigante, à la fois des difféomorphismes linéarisés généralisés et des transformations d'échelle de Weyl généralisées et linéarisées. Cela a motivé notre étude systématique des invariants conformes pour les spins élevés. Les invariants correspondants ont été construits à l'aide du tenseur de Cotton, dont nous avons établi les propriétés essentielles (symétrie, conservation, trace nulle; invariance, complétude). Avec ces outils géométriques, l'analyse hamiltonienne a pu être complétée et une action du premier ordre écrite en termes des prépotentiels. Nous avons constaté que cette action possédait une invariance manifeste par dualité électromagnétique; cette invariance, combinée à l'invariance de jauge des prépotentiels, fixe d'ailleurs uniquement l'action. En outre, de façon générale, cette action s'est révélée être exactement celle obtenue à travers une réécriture des équations du mouvement des spins élevés comme des conditions d'auto-dualité tordue (non manifestement covariantes).Avec un intérêt pour les extensions supersymétriques, nous avons amorcé la généralisation de cette étude aux champs fermioniques. Le champ de masse nulle libre de spin 5/2 a été soumis à la même analyse, et son prépotentiel s'est révélé partager l'invariance de jauge conforme déjà observée dans le cas bosonique général. Le supermultiplet incorporant les spins 2 et 5/2 a ensuite été considéré, et une symétrie rigide de son action, combinant une transformation de dualité électromagnétique du spin 2 avec une transformation de chiralité du spin 5/2 a été construite pour commuter avec la supersymétrie. Dans une autre direction, nous avons étudié les propriétés d'un champ tensoriel chiral de symétrie mixte dans un espace-temps plat à six dimensions: une (2,2)-forme. Son analyse hamiltonienne a été réalisée, des prépotentiels introduits et l'action de premier ordre obtenue s'est encore une fois révélée être la même que celle obtenue à travers une réécriture des équations du mouvement comme des conditions d'auto-chiralité (non manifestement covariante).Finalement, nous nous sommes penchés sur les charges de surface des champs fermioniques et bosoniques de spin élevé se propageant sur un espace-temps à courbure constante. Cela a été réalisé par une analyse hamiltonienne de ces systèmes, les contraintes étant identifiées aux générateurs des transformations de jauge. Injectant dans ces générateurs des valeurs des paramètres des transformations de jauge correspondant à des transformations impropres de jauge (imposant une réelle variation physique sur les champs) a ensuite permis d'évaluer la valeur de ces générateurs pour des champs résolvant les équations du mouvement: elle s'est bien révélée finie et non-nulle, constituant les charges de surface de ces théories.Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Harter, Braxton Nicholas. "Lagrangian Coherent Structures in Vortex Ring Formation." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1565828293505214.
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Maksymczuk, J. "Nonlinear equilibration of fast dynamics." Thesis, University of Essex, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302631.
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Xu, Danya. "Lagrangian Study of Particle Transport Processes in the Coastal Gulf of Maine." Fogler Library, University of Maine, 2008. http://www.library.umaine.edu/theses/pdf/XuD2008.pdf.
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Gonzalez, David R. "Development of a Semi-Lagrangian Methodology for Jet Aeroacoustics Analysis." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1467201142.
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Martin, Stephan [Verfasser]. "Applied Kinetic PDEs: Collective behavior models and Hamiltonian energy dynamics / Stephan Martin." München : Verlag Dr. Hut, 2012. http://d-nb.info/1025821270/34.
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Capoani, Federico. "Adiabatic theory for slowly varying Hamiltonian systems with applications to beam dynamics." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16855/.
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In questo lavoro si presentano due modelli in cui la teoria dell'invarianza adiabatica può essere applicata per ottenere peculiari effetti nel campo della dinamica dei fasci, grazie all'attraversamento di separatrici nello spazio delle fasi causato dal passaggio attraverso determinate risonanze d'un sistema. In particolare, si esporrà un modello bidimensionale con cui è possibile trasferire emittanza tra due direzioni nel piano trasverso: si fornirà una spiegazione del meccanismo per cui tale fenomeno ha luogo e si mostrerà come prevedere i valori finali di emittanza che un sistema raggiunge in tale configurazione. Questi risultati sono confermati da simulazioni numeriche. Simulazioni numeriche e relativi studî parametrici sono anche i risultati che vengono presentati per un altro modello, stavolta unidimensionale: si mostrerà infatti come un eccitatore esterno oscillante dipolare la cui frequenza passi attraverso un multiplo del tune della macchina permetta di catturare le particelle d'un fascio in un certo numero d'isole stabili.
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Manos, Athanasios. "A study of hamiltonian dynamics with applications to models of barred galaxies." Aix-Marseille 1, 2008. http://www.theses.fr/2008AIX11080.
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Cette thèse aborde des questions et présente de résultats qui exigent la combinaison des deux disciplines: d’une part, nous souhaitons comprendre et développer des outils fondamentaux des systèmes hamiltoniens et d’autre part nous envisageons de les utiliser pour étudier la dynamique de certains modèles de galaxies barrées. Pour cette raison, nous allons commencer par étudier d’importants phénomènes dynamiques concernant la stabilité des oscillations périodiques dans les systèmes hamiltoniens à N degrés de liberté ainsi que les applications N–symplectiques couplées. Ensuite, nous allons étendre notre travail au voisinage de ces régions et analyser les orbites quasipériodiques pour trouver des conditions dans lesquelles ces phénomènes disparaissent et pour lesquelles le comportement devient chaotique. Ceci sera effectué, en calculant les indices de GALI le long de chaque orbite de référence. Si l’orbite est périodique stable, la méthode GALI peut être utilisée pour déterminer la dimensionnalité du tore autour de cette orbite dans l’espace des phases à 2N–dimensions. Cette méthode peut alors être appliqué pour détecter les régimes où ces tores n’existent plus et où la plupart des choix de conditions initiales conduisent à des orbites chaotiques. Nous étudierons donc un système de N– applications standard couplées et en cherchant des orbites périodiques stables limitées par le tore au–delà duquel le chaos apparait. Afin d’ atteindre cet objectif, nous choisissons deux types de conditions initiales : a) localisées dans l’ espace réel, en excitant un “petit” nombre de particules (appelé “breathers”) et en étudiant leur mouvement régulier ou chaotique et b) localisées dans l’espace de Fourier (appelé q–“breather”), en excitant maintenant un “petit” nombre de modes normaux et en étudiant les phénomènes récurrents. Nous passons ensuite au second thème principal de cette thèse en étudiant en détails un problème fondamental de dynamique astrophysique : les orbites d’étoiles dans le potentiel galactique. A partir de modèles qui décrivent des galaxies et leur mouvement d’étoiles, il est bien - connu que l’ analyse des orbites périodiques et leur stabilité, peut fournir des informations très utiles sur l’évolution des galaxies. Les orbites périodiques stable sont associées à un mouvement régulier, puisqu’ils sont entourés d’un tore quasi–périodique. Une question fondamentale qui se pose alors est l’étendue de ces régions de stabilité. Un autre résultat en dynamique galactique est la présence de plusieurs orbites chaotiques comportant des caractéristiques de galaxies, comme la rotation de barre. Le phénomène de “stickiness”(orbites “collantes”) est également très fréquent dans ce genre de systèmes Hamiltoniens, c’ est-à-dire que leurs orbites révèlent leur nature chaotiques lentement. Plusieurs nouvelles méthodes de détection du chaos ont été introduites et appliquées au cours des dernières années pour la détection de mouvement chaotique ou régulier dans des modèles de galaxies, soit en étudiant la comportement des vecteurs déviation ou par l’analyse de séries chronologiques construites par les coordonnées de chaque orbite. Dans cette thèse, nous nous consacrons au modèle de galaxies barrée de Ferrers et nous étudions non seulement la distinction entre les solutions régulières, “sticky” ou chaotiques, mais aussi l’ importance de ces conclusions sur un intervalle de temps ayant un sens physique, c’est-à-dire environ un temps de Hubble. Pour accomplir cela, nous utiliserons la méthode de “Generalized Alignment Indexes” (GALI) pour la distinction entre mouvement chaotique ou régulier ainsi que de nouvelles manières d’ interprétation des spectres de Fourier et de la distribution de vitesse ou de quantit´e de mouvement. La combinaison de tout cela nous permet d’atteindre deux objectifs : Tout d’abord, nous pouvons détecter rapidement et efficacement la véritable nature des orbites et d’autre part, nous pouvons distinguer entre orbites chaotiques de diffusion orbitale dans l’espace réel différente. Nous avons montré qu’ il existe des orbites chaotiques se comportant de manière “régulière” suffisamment longtemps pour que leur caractéristiques n’aient pas encore été révélées du point de vue observationnel. Nous donnons enfin quelques résultats sur des orbites régulières concernant leur complexité orbitale, en terme de dimension du toreThis thesis addresses questions and presents results that require the combination of two disciplines : on the one hand, we wish to develop and understand fundamental tools of Hamiltonian systems and, on the other hand, we plan to use them to study the dynamics of certain basic models of barred galaxies. For this reason we shall start by investigating some important dynamical phenomena concerning the stability of periodic oscillations in N degree of freedom Hamiltonian systems and N coupled symplectic maps. Furthermore, we will extend our study to the vicinity of such motions and analyze quasiperiodic orbits aiming to find conditions under which they break down and chaotic behavior settles in. This will be accomplished by computing the GALI indices along every reference orbit. If the central periodic orbit is stable, the GALI method can be used to determine the dimensionality of the tori surrounding this orbit in the 2N–dimensional phase space. Furthermore, it can be applied to detect regimes where such tori cease to exist and most choices of initial conditions lead to chaotic orbits. We shall do this by studying a system of N coupled standard maps, searching for stable periodic motion surrounded by of tori beyond which there is chaos. In order to achieve this goal, we choose two different types of initial conditions: a) localized in real space, exciting a “small” number of particles (called a breather) and studying their regular or chaotic motion and b) localized in Fourier space (called q–breather), exciting a “small” number of normal modes and studying recurrence phenomena. We then turn to the detailed study of orbital star motion in galactic potentials which constitutes a fundamental aspect of dynamical astronomy and is the second major theme of this thesis. Starting with models that describe galaxies and their star motion, it is well–known that the analysis of periodic orbits, and their stability, can provide very useful information about galaxy evolution. Stable periodic orbits are associated with regular motion, since they are surrounded by quasi– periodic tori. A fundamental question that arises therefore is what is the extent of these stability regions? Another recent result in galactic dynamics is that there are also several chaotic orbits that can support galaxy features, like rotating bars. The phenomenon of “stickiness” (“sticky” orbits) is also very common in this kind of Hamiltonian systems, i. E. Orbits that their chaotic nature takes a long time to be revealed. Several new chaos detection methods have been introduced and applied in the last years for the detection of chaotic and regular motion in galaxy models, either by studying the behavior of deviation vectors or by analyzing time series constructed by the coordinates of each orbit. In this thesis, we shall focus on a Ferrers’ barred galaxy model and study not only the distinction between regular, sticky and chaotic solutions but also the significance of these findings over time interval that have a physical meaning, i. E. Roughly a Hubble time. To accomplish this we will use the method Generalized Alignment Indexes (GALI) for the distinction between the chaotic and regular motion as well as new ways of interpreting Fourier spectra and momentum distribution. Combining all these we achieve two goals: First, we are able to detect fast and efficiently the true nature of the orbits and second, we can distinguish between chaotic orbits with different types of orbital diffusion in real space. We find that there are chaotic orbits that behave in a “regular–like” manner for long enough times that their characteristics are not yet revealed from an observational point of view. Finally, we present some results concerning several regular orbits with regard to their orbital complexity, in terms of torus dimensionality
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Wang, Yushi Politano Marcela Weber Larry Joseph. "A multidimensional Eulerian-Lagrangian model to predict organism distribution." [Iowa City, Iowa] : University of Iowa, 2009. http://ir.uiowa.edu/etd/447.
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Zschenderlein, Philipp [Verfasser], and A. H. [Akademischer Betreuer] Fink. "Lagrangian Dynamics of European heat waves / Philipp Zschenderlein ; Betreuer: A. H. Fink." Karlsruhe : KIT-Bibliothek, 2020. http://d-nb.info/1215190565/34.
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De, Sousa Dias Maria Esmeralda Rodrigues. "Local dynamics of symmetric Hamiltonian systems with application to the affine rigid body." Thesis, University of Warwick, 1995. http://wrap.warwick.ac.uk/107563/.
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This work is divided into two parts. The first one is directed towards the geometric theory of symmetric Hamiltonian systems and the second studies the so-called affine rigid body under the setting of the first part. The geometric theory of symmetric Hamiltonian systems is based on Poisson and symplectic geometries. The symmetry leads to the conservation of certain quantities and to the reduction of these systems. We take special attention to the reduction at singular points of the momentum map. We survey the singular reduction procedures and we give a method of reducing a symmetric Hamiltonian system in a neighbourhood of a group orbit which is valid even when the momentum map is singular. This reduction process, which we called slice reduction, enables us to partially reduce the (local) dynamics to the dynamics of a system defined on a symplectic manifold which is the product of a symplectic vector space (symplectic slice) with a coadjoint orbit for the original symmetry group. The reduction represents the local dynamics as a coupling between vibrational motion on the vector space and generalized rigid body dynamics on the coadjoint group orbits. Some applications of the slice reduction are described, namely the application to the bifurcation of relative equilibria. We lay the foundations for the study of the affine rigid body under geometric methods. The symmetries of this problem and their relationship with the physical quantities are studied. The symmetry for this problem is the semi-direct product of the cyclic group of order two Z2 by 50(3) x 50(3). A result of Dedekind on the existence of adjoint ellipsoids of a given ellipsoid of equilibrium follows as consequence of the Z2 symmetry. The momentum map for the Z2 x, (50(3) x 50(3)) action on the phase space corresponds to the conservation of the angular momentum and circulation. Using purely geometric arguments Riemann’s theorem on the admissible equilibria ellipsoids for the affine rigid body is established. The symmetries of different relative equilibria are found, based on the study of the lattice of isotropy subgroups of Z2 x, (50(3) x 50(3)) on the phase space. Slice reduction is applied in a neighbourhood of a spherical ellipsoid of equilibrium leading to different reduced dynamics. Based also on the slice reduction we establish the bifurcation of S-type ellipsoids from a nondegenerate ellipsoidal equilibrium.
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Silverberg, Jon P. "On Lagrangian meshless methods in free-surface flows." Thesis, (1.7 MB), 2005. http://edocs.nps.edu/AR/topic/theses/2005/Jan/05Jan_Silverberg.pdf.
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Thesis (Master of Engineering in Ocean Engineering)--University of California at Berkeley, 2004."January 2005." Description based on title screen as viewed on May 25, 2010. DTIC Descriptor(s): Fluid Dynamics, Lagrangian Functions, Equations Of Motion, Acceleration, Formulations, Grids, Continuum Mechanics, Gaussian Quadrature, Derivatives (Mathematics), Compact Disks, Boundary Value Problems, Polynomials, Interpolation, Pressure, Operators (Mathematics). DTIC Identifier(s): Multimedia (CD-Rom), Moving Grids, Meshless Discretization, Lifs (Lagrange Implicit Fraction Step), Lagrangian Dynamics, Meshless Operators, Mlip (Multidimensional Lagrange Interpolating Polynomials), Flux Boundary Conditions, Radial Basis Functions Includes bibliographical references (58-59).
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Wong, Brian 1978. "Dynamics of a multi-tethered satellite system near the sun-earth Lagrangian point." Thesis, McGill University, 2003. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=80151.
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This paper examines the dynamics of a tether connected multi-spacecraft system, arranged in a wheel-spoke configuration, in the vicinity of the L 2 Lagrangian point of the Sun-Earth system. First, the equations of motion of a N-body system are obtained and equilibrium configurations of the system are determined and small motions about one of these configurations are analyzed. Then, a numerical analysis of the free tether libration is carried out for a three-mass case when the system is near L2 and the parent mass is assumed to be in a halo orbit of different sizes. Finally, a set of control goals are defined and a time domain state feedback control system is integrated into the numerical model. The performance of the control system is tested under different conditions.