Global ETD Search

11	Invariante Deformationsquantisierung und Quantenimpulsabbildungen Müller-Bahns, Michael. January 2003 (has links) Mannheim, Univ., Diss., 2004.
12	Lagrangian invariant subspaces of Hamiltonian matrices Mehrmann, Volker, Xu, Hongguo 14 September 2005 (has links) (PDF) 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. Hamiltonian matrix Lagrangian invariant subspace ddc:510 Algebraische Riccati-Gleichung Eigenwertproblem Symplektische Matrix
13	Lagrangian invariant subspaces of Hamiltonian matrices Mehrmann, Volker, Xu, Hongguo 14 September 2005 (has links) 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. info:eu-repo/classification/ddc/510 ddc:510
14	Towards Discretization by Piecewise Pseudoholomorphic Curves / Zur Diskretisierung durch stückweise pseudoholomorphe Kurven Bauer, David 27 January 2014 (has links) (PDF) This thesis comprises the study of two moduli spaces of piecewise J-holomorphic curves. The main scheme is to consider a subdivision of the 2-sphere into a collection of small domains and to study collections of J-holomorphic maps into a symplectic manifold. These maps are coupled by Lagrangian boundary conditions. The work can be seen as finding a 2-dimensional analogue of the finite-dimensional path space approximation by piecewise geodesics on a Riemannian manifold (Q,g). For a nice class of target manifolds we consider tangent bundles of Riemannian manifolds and symplectizations of unit tangent bundles. Via polarization they provide a rich set of Lagrangians which can be used to define appropriate boundary value problems for the J-holomorphic pieces. The work focuses on existence theory as a pre-stage to global questions such as combinatorial refinement and the quality of the approximation. The first moduli space of lifted type is defined on a triangulation of the 2-sphere and consists of disks in the tangent bundle whose boundary projects onto geodesic triangles. The second moduli space of punctured type is defined on a circle packing domain and consists of boundary punctured disks in the symplectization of the unit tangent bundle. Their boundary components map into single fibers and at punctures the disks converge to geodesics. The coupling boundary conditions are chosen such that the piecewise problem always is Fredholm of index zero and both moduli spaces only depend on discrete data. For both spaces existence results are established for the J-holomorphic pieces which hold true on a small scale. Each proof employs a version of the implicit function theorem in a different setting. Here the argument for the moduli space of punctured type is more subtle. It rests on a connection to tropical geometry discovered by T. Ekholm for 1-jet spaces. The boundary punctured disks are constructed in the vicinity of explicit Morse flow trees which correspond to the limiting objects under degeneration of the boundary condition. Pseudoholomorphe Kurven Symplektische Geometrie Tangentialbündel Endlich-dimensionale Approximation Diskretisierung Pseudoholomorphic Curves Symplectic Geometry Tangent Bundle Finite-dimensional approximation Discretization ddc:515 ddc:516
15	Rabinowitz-Floer homology on Brieskorn manifolds Fauck, Alexander 19 May 2016 (has links) In dieser Dissertation werden Kontaktstrukturen auf beliebigen differenzierbaren Mannigfaltigkeiten ungerader Dimension untersucht. Dies geschiet vermöge der Rabinowitz-Floer-Homologie (RFH), welche 2009 von Cieliebak und Frauenfelder eingeführt wurde. Ein großer Teil der Arbeit widmet sich den technischen Problemen bei der Definition von RFH. Insbesondere wird die Transversalität für die benötigten Modulräume gezeigt. In einem weiteren Abschnitt wird bewiesen, dass RFH im wesentlichen invariant unter subkrittischer Henkelanklebung ist. Schließlich enthält die Arbeit die Berechnung von RFH für einige Brieskorn-Mannigfaltigkeiten. Die dabei gewonnenen Resultate werden dazu verwendet zu zeigen, dass es auf jeder Mannigfaltigkeit, welche füllbare Kontaktstukturen zulässt, entweder unendlich viele verschiedene füllbare Kontaktstrukturen gibt, oder eine Kontaktstruktur mit unendlich vielen verschiedenen Füllungen oder das für alle füllbaren Kontaktstrukturen die RFH von unendlicher Dimension ist für alle Grade. / This thesis considers fillable contact structures on odd-dimensional manifolds. For that purpose, Rabinowitz-Floer homology (RFH) is used which was introduced by Cieliebak and Frauenfelder in 2009. A major part of the thesis is devoted to technical problems in the definition of RFH. In particular, it is shown that the moduli spaces involved are cut out transversally. Moreover, it is proved that RFH is essentially invariant under subcritical handle attachment. Finally, RFH is calculated for some Brieskorn manifolds. The obtained results are then used to show for every manifold, which supports fillable contact structures, that there exist either infinitely many different fillable contact structures, or one contact structure with infinitely many different fillings or for every fillable contact structure holds that RFH is infinite dimensional in every degree. dynamische Systeme Kontaktgeometrie symplektische Geometrie Floer Homologie dynamical systems contact geometry symplectic geometry Floer homology 510 Mathematik 27 Mathematik SK 370 ddc:510
16	Towards Discretization by Piecewise Pseudoholomorphic Curves Bauer, David 04 December 2013 (has links) This thesis comprises the study of two moduli spaces of piecewise J-holomorphic curves. The main scheme is to consider a subdivision of the 2-sphere into a collection of small domains and to study collections of J-holomorphic maps into a symplectic manifold. These maps are coupled by Lagrangian boundary conditions. The work can be seen as finding a 2-dimensional analogue of the finite-dimensional path space approximation by piecewise geodesics on a Riemannian manifold (Q,g). For a nice class of target manifolds we consider tangent bundles of Riemannian manifolds and symplectizations of unit tangent bundles. Via polarization they provide a rich set of Lagrangians which can be used to define appropriate boundary value problems for the J-holomorphic pieces. The work focuses on existence theory as a pre-stage to global questions such as combinatorial refinement and the quality of the approximation. The first moduli space of lifted type is defined on a triangulation of the 2-sphere and consists of disks in the tangent bundle whose boundary projects onto geodesic triangles. The second moduli space of punctured type is defined on a circle packing domain and consists of boundary punctured disks in the symplectization of the unit tangent bundle. Their boundary components map into single fibers and at punctures the disks converge to geodesics. The coupling boundary conditions are chosen such that the piecewise problem always is Fredholm of index zero and both moduli spaces only depend on discrete data. For both spaces existence results are established for the J-holomorphic pieces which hold true on a small scale. Each proof employs a version of the implicit function theorem in a different setting. Here the argument for the moduli space of punctured type is more subtle. It rests on a connection to tropical geometry discovered by T. Ekholm for 1-jet spaces. The boundary punctured disks are constructed in the vicinity of explicit Morse flow trees which correspond to the limiting objects under degeneration of the boundary condition. info:eu-repo/classification/ddc/515 ddc:515 info:eu-repo/classification/ddc/516 ddc:516
17	Space Charge Modeling at the Integer Resonance for the CERN PS and SPS Titze, Malte 11 June 2020 (has links) Die elektromagnetische Wechselwirkung der Teilchen untereinander, wie sie typischerweise in einem Strahl hoher Intensität in den CERN Beschleunigern auftritt, kann in Langzeitsimulationen nicht vernachlässigt werden. Simulationen sind insbesondere notwendig, um diese Beschleuniger zu optimieren und die zugrundeliegende kohärente und inkohärente Dynamik besser zu verstehen. Die Auswirkungen der unumgänglichen Vereinfachungen in der Modellierung der komplizierten Dynamik müssen deshalb untersucht werden. Wir gehen diese Aufgabe an, indem wir sechs verschiedene Strahlführungsmodelle am CERN Proton Synchrotron (PS) und am Super Proton Synchrotron (SPS) untersuchen, die wir dynamisch in der Nähe von horizontalen Integer-Resonanzen operieren. Die sechs Modelle, welche insgesamt in den beiden bewährten Programmpaketen MAD-X und PyOrbit implementiert sind, werden mit den jeweiligen Messungen an beiden Maschinen verglichen, wobei der Schwerpunkt hier auf dem PS liegt. / In long-term tracking simulations of high-intensity beams which are typical in the CERN accelerators, the electromagnetic interaction between the individual particles can not be neglected. Simulations are required to optimize the performance of the accelerators, and to better understand the involved coherent and incoherent dynamics. The impact due to the unavoidable simplifications when modeling the complex dynamics must therefore be studied. We approach this task by examining six different tracking models, applied to the CERN Proton Synchrotron (PS) and the Super Proton Synchrotron (SPS), both of which were dynamically operated near horizontal integer resonances. The six models, which are overall implemented in the well-known program packages MAD-X and PyOrbit, are compared to beam-based measurements on both machines, with the PS as the main emphasis. Teilchenbeschleuniger Raumladung Resonanz PyOrbit MAD-X Symplektische Abbildung Proton Synchrotron Super Proton Synchrotron CERN Speicherring Kombinierte-Funktionen Magnet Teilchendynamik particle accelerator space charge resonance PyOrbit MAD-X symplectic map Proton Synchrotron CERN storage ring Super Proton Synchrotron Combined function magnet particle dynamics 530 Physik UN 6100 ddc:530

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