08 Fakultät Mathematik und Physik

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9

Browse

Now showing 1 - 20 of 1230

Open Access
12C(alpha,gamma)16O - die Schlüsselreaktion im Heliumbrennen der Sterne
(2002) Kunz, Ralf; Kneissl, Ulrich (Prof. Dr. rer. nat.)
Die Reaktion 12C(alpha,gamma)16O nimmt eine Schlüsselstellung für die Nukleosynthese und bei der Durchführung von Sternmodellrechnungen ein. Von Astrophysikern, die solche Rechnungen durchführen, wurde wiederholt eine genauere experimentelle Bestimmung der Reaktionsrate angefordert, denn ihre Unsicherheiten wirken sich auf die gesamten Nukleosyntheserechnungen aus. Man sieht in der Reaktion 12C(alpha,gamma)16O die wichtigste zu bestimmende Reaktion der nuklearen Astrophysik neben Ne22(alpha,n)Mg25. Deshalb wurde diese Reaktion im Energiebereich Ecm = 0.95 MeV - 2.79 MeV mit weit empfindlicheren Detektoren als bei vorherigen Experimenten neu untersucht. Um eine für die Extrapolation in den astrophysikalisch relevanten Energiebereich um Ecm = 0.3 MeV notwendige Trennung von E1- und E2-Anteil des Wirkungsquerschnittes zu erreichen, wurden im gesamten Energiebereich Winkelverteilungen gemessen. Dies wurde ermöglicht, indem eine dichtgepackte Anordnung aus 3-4 großen Reinstgermaniumdetektoren mit aktiver Abschirmung aus BGO auf einem Drehtisch um das Target aufgestellt wurde. Hierdurch konnten Winkelverteilungen mit 8 bzw. 9 Datenpunkten aufgenommen werden, was genügend Information für eine zuverlässige Bestimmung des E1- und E2-Anteils beim alpha-Einfang liefert. Die Extrapolation in den astrophysikalischen Energiebereich wurde mit der R-Matrix-Methode für E1- und E2-Anteil getrennt durchgeführt. Für den E1-Anteil wurde ein 3-Level-R-Matrix-Fit an die Daten aus dieser Arbeit, an Daten aus Experimenten zur elastischen Streuung und dem beta-verzögerten \alpha-Zerfall von 16N durchgeführt. Dabei wurden alle möglichen Kombinationen für die Interferenzen der Zustände im (alpha,gamma)-Kanal separat behandelt und für den Extrapolationswert der beste Fit ausgewählt. Der E2-Anteil wurde erstmalig durch einen 5-Level-R-Matrix-Fit an die Daten aus dieser Arbeit und an Daten aus Experimenten zur elastischen Streuung beschrieben. Auch hier wurden die Interferenzen getrennt behandelt und der Extrapolationswert aus dem besten Fit extrahiert. Für die S-Faktoren ergeben sich die Werte SE1(0.3 MeV) = 76 +- 20 keV b und SE2(0.3 MeV) = 85 +- 30 keV b. Für die Kaskadenübergänge, also den gamma-Einfang in angeregte Zustände des 16O-Kerns, konnten die Anregungskurven nur aus den zugehörigen Folgeübergängen bestimmt werden. Als Extrapolationswert für den astrophysikalisch relevanten Energiebereich ergibt sich Scasc(0.3 MeV) < 8 keV b als Grenzwert. Aus den R-Matrix-Fits wurde durch numerische Integration die astrophysikalische Reaktionsrate im Temperaturbereich 0.001 <= T9 <= 10 gewonnen. Zusätzlich zu den R-Matrix-Fits für den E1- und E2-Anteil wurden sämtliche bekannten gamma-Übergänge durch Breit-Wigner-Kurven mit energieabhängigen Breiten berücksichtigt. Auch diese Kurven wurden numerisch integriert. Die astrophysikalische Reaktionsrate von 12C(alpha,gamma)16O wird tabellarisch und außerdem mit zwei unterschiedlichen analytischen Formeln wiedergegeben, wie sie heutzutage in den theoretischen Modellen gebräuchlich sind. Sie gelten im Temperaturbereich 0.001 <= T9 <= 10 bzw. 0.02 <= T9 <= 10 und haben eine Genauigkeit von 8% bzw. 12%.
Open Access
2-Teilchen Systeme in der Relativistischen Schrödingertheorie
(2001) Rupp, Stefan; Weidlich, Wolfgang (Prof. Dr. Dr. h.c.)
In der vorliegenden Arbeit geht es um die Relativistische Schrödingertheorie (RST), welche eine neue Methode zur Behandlung relativistischer Mehrteilchensysteme darstellt. Die RST und die ihr zugrunde liegenden Konzepte, d.h. Eichtheorien und Faserbündel, werden kurz vorgestellt sowie der RST-Formalismus auf den 2-Teilchen Fall mit elektromagnetischer Wechselwirkung spezialisiert. Es wird bewiesen, daß die in der RST auftretenden Mischungs- und Austauscheffekte, welche die zwei Teilchen zusätzlich zur Eichwechselwirkung aneinander koppeln, keine physikalischen Auswirkungen haben, sofern sie nicht gemeinsam auftreten. Der Mischungseffekt läßt sich auf eine Gruppenstruktur, die sogenannte Mischungsgruppe, zurückführen. Zur Behandlung des Austauscheffektes werden neue Feldgrößen eingeführt, welche die RST-Dynamik stark vereinfachen und die Konstruktion einer Lagrange-Dichte für das 2-Teilchen-RST-Feldgleichungssystem ermöglichen. Die physikalischen Auswirkungen des gemeinsamen Auftretens von Mischungs- und Austauscheffekten werden durch die Berechnung der Bindungszustände des He-Atoms in erster Ordnung Störungstheorie und den Vergleich sowohl mit den experimentellen Werten als auch mit den Resultaten der konventionellen Quantentheorie verdeutlicht.
Open Access
2D calculations for atoms and ions in strong magnetic fields of white dwarfs and neutron stars
(2014) Schimeczek, Christoph; Wunner, Günter (Prof. Dr.)
The following work is devoted to the description of atoms and ions in strong magnetic fields as they can occur in the vicinity of magnetic white dwarfs and neutron stars. The ultimate goal of this work is the contribution to an understanding of unique absorption features detected in the spectra of such stars. One natural explanation for these features are atomic absorptions in the stars' strongly magnetized atmospheres. Models for the atmospheres of magnetic white dwarfs and corresponding spectra have already been applied with great success to observed data, and absorption features of the light elements hydrogen and helium were identified. A comparable success in the modeling of neutron star atmospheres has still to be accomplished. This is related to the extreme conditions in neutron star atmospheres, namely very high temperatures, magnetic fields, and particle densities. Also, the progenitors of neutron stars produce heavy elements up to iron, which are likely to contribute to the composition of the neutron star atmosphere. The poor knowledge of atomic data of heavier elements in strong magnetic fields hampers the further understanding of neutron star emission spectra. In this work we present reliable and fast programs that are capable of creating a large database for atomic states and transitions in a wide range of the magnetic field strength. Based upon previous work we implemented a two-dimensional Hartree-Fock-Roothaan method that overcomes former restrictions, namely the adiabatic approximation and the Landau orbital product ansatz. This software suite allows for a precise description of atomic wave functions and energy values in an extended range of magnetic field strengths. Additionally, the programs are capable of calculating atomic transition energies and strengths. During the development of these programs we focused on automated data production and processing, and payed special attention to program reliability and execution speed. The results for the hydrogen atom presented in this work have already proven useful in the context of an astrophysical application, and improve current atmosphere model calculations of magnetic white dwarfs. Further, our results enhance the understanding of atomic energy spectra at neutron star magnetic fields. The wave functions and energy values calculated in this thesis serve as a starting point for other methods, e.g. the fixed-phase diffusion quantum Monte Carlo method, as well as for photoionization calculations of atoms in strong magnetic fields.
Open Access
3D direct laser writing of highly absorptive photoresist for miniature optical apertures
(2022) Schmid, Michael D.; Toulouse, Andrea; Thiele, Simon; Mangold, Simon; Herkommer, Alois; Giessen, Harald
The importance of 3D direct laser writing as an enabling technology increased rapidly in recent years. Complex micro-optics and optical devices with various functionalities are now feasible. Different possibilities to increase the optical performance are demonstrated, for example, multi-lens objectives, a combination of different photoresists, or diffractive optical elements. It is still challenging to create fitting apertures for these micro optics. In this work, a novel and simple way to create 3D-printed opaque structures with a highly absorptive photoresist is introduced, which can be used to fabricate microscopic apertures increasing the contrast of 3D-printed micro optics and enabling new optical designs. Both hybrid printing by combining clear and opaque resists, as well as printing transparent optical elements and their surrounding opaque apertures solely from a single black resist by using different printing thicknesses are demonstrated.
Open Access
3D printed micro-optics for quantum technology: Optimised coupling of single quantum dot emission into a single-mode fibre
(2021) Sartison, Marc; Weber, Ksenia; Thiele, Simon; Bremer, Lucas; Fischbach, Sarah; Herzog, Thomas; Kolatschek, Sascha; Jetter, Michael; Reitzenstein, Stephan; Herkommer, Alois; Michler, Peter; Portalupi, Simone Luca; Giessen, Harald
Open Access
3D printed micro-optics: materials, methods and applications
(2022) Weber, Ksenia; Giessen, Harald (Prof. Dr.)
Open Access
3D printed stacked diffractive microlenses
(2019) Thiele, Simon; Pruss, Christof; Herkommer, Alois; Giessen, Harald
Open Access
3D printing of sub-micrometer accurate ultra-compact free-form optics
(2016) Gissibl, Timo; Giessen, Harald (Prof. Dr.)
Additive manufacturing enables novel and unprecedented engineering and production possibilities, which are predicted to have an enormous impact in the 21st century. The technology allows for the straightforward three-dimensional printing of volumetric objects as designed. In this thesis, we present a novel concept in optics, which overcomes many difficulties in the fabrication of micro-optics and opens the new field of 3D printed micro- and nano-optics with complex lens designs. Our work is just at the interface between micro- and nano-optics and represents a paradigm shift for micro-optics. It takes only a few hours from lens design, to production, testing, and the final working optical device. Using dip-in femtosecond two-photon direct laser writing, our method goes far beyond state-of-the art attempts to manufacture simple micro-lenses by lithography. We prove the versatility of this method by writing different optics. Collimation optics, toric lenses, free-form surfaces with polynomials of up to 10th order for intensity beam shaping, as well as chiral photonic crystals for circular polarization filtering, all aligned onto the core of single mode fibers are shown. In addition, we show that three-dimensional direct laser writing is a suitable tool for the fabrication of complex multi-lens optical systems that show high quality optical imaging, beam shaping performance, and tremendous compactness with sizes below 300 µm. We determine the accuracy of our optics by analyzing the imaging and beam shaping quality as well as characterizing the surfaces by atomic force microscope measurements and interferometric measurements. The method yields high fabrication accuracy and allows to manufacture of lenses with a rms (root mean square) surface roughness of less than 15 nm. The surfaces deviate from their designs by less than ±1 µm. Our 3D printed compound lenses feature resolving powers of up to 500 line pairs per millimeter. Our printed micro-optical elements can thus achieve sufficient performance in order to enable compound lenses for high quality imaging. In addition, we show the performance of diffractive optical elements with diameters of just 4.4 µm, which enable beam shaping at the end facet of an optical fiber. The intensity is shaped into a uniform or into a donut-shaped intensity distribution. For this purpose, the diffractive optics are directly fabricated onto the end facet of the optical fiber and show unprecedented performance for optical beam shaping. Our method allows for a plethora of novel applications with tremendous impact on optical trapping of atoms and in-vivo imaging in the human body. In addition, applications for imaging and illumination in endoscopy, multiple sensors, and eyes for micro-robots can be realized.
Open Access
3D stimulated Raman spectral imaging of water dynamics associated with pectin-glycocalyceal entanglement
(2023) Floess, Moritz; Steinle, Tobias; Werner, Florian; Wang, Yunshan; Wagner, Willi Linus; Steinle, Verena; Liu, Betty; Zheng, Yifan; Chen, Zi; Ackermann, Maximilian; Mentzer, Steven J.; Giessen, Harald
Open Access
3D-printed miniature spectrometer for the visible range with a 100 × 100 μm2 footprint
(2021) Toulouse, Andrea; Drozella, Johannes; Thiele, Simon; Giessen, Harald; Herkommer, Alois
Open Access
A sieve formula for chains of p-subgroups : extending Wielandt’s proof of Sylow-Frobenius to a congruence modulo p^(ℓ+1)
(2024) Schwesig, Elias
Given a finite group G and a prime p, we establish the sieve formula, which is a congruence containing as summands numbers of chains of p-subgroups of G of certain orders. This generalises the Theorem of Sylow-Frobenius. Its name stems from the sieve formula from set theory because of formal similarities.
Open Access
Absence of the Efimov effect in dimensions one and two
(2021) Barth, Simon; Weidl, Timo (Prof. TeknD)
Open Access
Absorbing state phase transition with Clifford circuits
(2024) Makki, Nastasia; Lang, Nicolai; Büchler, Hans Peter
Open Access
Actions of compact groups on spheres and on generalized quadrangles
(1999) Biller, Harald; Stroppel, Markus (PD Dr.)
Alle Wirkungen kompakter zusammenhängender Gruppen von genügend großer Dimension auf Sphären und auf zwei Arten von verallgemeinerten Vierecken werden im einzelnen beschrieben. Für Sphären läßt sich das Ergebnis wie folgt zusammenfassen: Jede treue stetige Wirkung einer kompakten zusammenhängenden Gruppe, deren Dimension 1 + dim SO(n-2) übersteigt, auf einer n-Sphäre ist linear, also äquivalent zur natürlichen Wirkung einer Untergruppe von SO(n+1). Unter ähnlichen Voraussetzungen untersuchen wir Wirkungen auf endlichdimensionalen kompakten verallgemeinerten Vierecken, deren Punktreihen Dimension 1 oder 4 haben. Hier zeigen wir, daß jede treue Wirkung einer kompakten Gruppe von genügend großer Dimension äquivalent ist zu einer Wirkung auf einem Moufang-Viereck, also auf einer Nebenklassengeometrie einer einfachen Lie-Gruppe, die durch ein BN-Paar beschrieben wird. Die vorliegende Arbeit steht in der Tradition der Untersuchung kompakter projektiver Ebenen und neuerdings anderer kompakter verallgemeinerter Polygone durch Salzmann und seine Schule. Der dabei entstandene Leitgedanke, nur die Wirkung einer Gruppe von genügend großer Dimension vorauszusetzen, wird in dieser Arbeit erstmals für verallgemeinerte Vierecke durchgeführt. Wir setzen zusätzlich voraus, daß die Gruppe kompakt ist, um die hochentwickelte Theorie der Wirkungen kompakter Gruppen auf (Kohomologie-) Mannigfaltigkeiten für die topologische Inzidenzgeometrie weiter zu erschließen. Umgekehrt ermöglicht erst die spezifische Salzmannsche Fragestellung die Ergebnisse über Sphären, die ja dem Bereich der klassischen Theorie angehören. Indem die Klassifikation der kompakten Lie-Gruppen konsequent ausgenutzt wird, läßt sich das Problem auf die Behandlung weniger Serien von Gruppen zurückführen. Bei verallgemeinerten Vierecken zeigt man dagegen zuerst die Transitivität der Wirkung und benutzt dann die bestehende (teilweise hier neu bewiesene) Klassifikation.
Open Access
Active, phoretic motion
(2012) Sabaß, Benedikt C.; Seifert, Udo (Prof. Dr.)
This work is dedicated to different aspects of the motion of micro- and nanoparticles that are driven by interaction with a concentration gradient. The swimming of particles in a solution is called diffusiophoresis if it results from the interaction with nonionic solvent gradients. Motion driven by ionic concentration gradients is called electrophoresis or chemiphoresis, depending on whether or not an electric field moves the particle. Recently, the concept of active phoresis has emerged. The new idea is here that the swimming particle produces the concentration gradient by itself. In corresponding experiments the particle mostly catalyzes a chemical reaction in an asymmetric way on its surface. Various realizations of such systems have been explored experimentally during the last years. These swimmers are a unique model system for the investigation of microscale non-equilibrium phenomena. The aim of the thesis is to contribute to an improved understanding of active, phoretic motion. In particular energetic aspects of this type of swimming are investigated for the first time.
Open Access
An adaptive finite element method for control-constrained optimal control problems
(2012) Kohls, Kristina; Siebert, Kunibert G. (Prof. Dr.)
Many problems from physics like heat conduction and energy conservation lead to partial differential equations (PDEs). Only some of them can be solved directly; in general one has to rely on approximation techniques like the Finite Element Method (FEM). Adaptive Finite Elements intend to only increase accuracy in those parts of the domain where the error is large relative to the rest of the domain. The gain in accuracy that can be achieved by this, in comparison to the classical FEM, depends on the exact solution itself. In this thesis the weak formulation of a PDE constitutes the side-constraint of an optimizing problem. Usually this consists of a convex functional that is minimized with respect to two variables - control and state - which are connected via the side-constraint. Additionally the control has to satisfy further constraints. To be able to apply Adaptive Finite Elements one needs to construct error- estimators that satisfy certain properties. In contrast to previous results in this field, this thesis uses a general approach to find error-estimators. This approach includes distributed and boundary-control as well as the cases of discretized and non-discretized control. The particularities of the involved PDE are only of interest when choosing the appropriate estimators for the linear subproblems from the toolbox. The other main contribution of this thesis consists of three convergence results. One for non-discretized control, one for discontinuous and one for continuous control-discretizations. We not only prove the convergence of the solution but also of the estimator which implies that the algorithm terminates for any given tolerance TOL > 0. Finally, a few numerical examples with boundary-control are investigated for varying marking strategies and estimators.
Open Access
Adaptive finite elements for state-constrained optimal control problems - convergence analysis and a posteriori error estimation
(2014) Steinig, Simeon; Siebert, Kunibert G. (Prof. Dr.)
Optimal control problems and in particular state-constrained optimal control problems fre- quently occur in all sorts of fields of science, from aerospace engineering to robotics, from process engineering to vehicle simulations. Against this backdrop, it is of interest to solve these kinds of problems in an efficient manner. Optimal control problems are characterised by the existence of a control u acting on a state y which is governed by a (ordinary/partial/stochastic) differential equation. In this PhD thesis, we considered linear, stationary partial differential equations (PDE); in particular, the state y is a linear function of the control u, y = Su. Now, solving such optimal control problems numerically involves solving two linear PDEs in each iterate of an optimisation algorithm. Over the last decades much research has been undertaken to numerically solve such linear PDEs efficiently, especially discretisations with adaptive finite elements have been proven to be highly useful for such a task. Thus, trying to apply these adaptive finite element methods to the specific setting of state-constrained optimal control problems suggested itself as an appropriate approach: The aim of this thesis was twofold: 1. The first goal was to prove a basic convergence result, i.e.: the sequence of discrete solutions obtained by discretising the optimal control problem with finite elements, U_k, converges to the true solution of the undiscretised problem u. 2. The second goal was to derive a reliable a posteriori error estimator, i.e., here an upper bound up to constants depending solely on data containing only known discrete or continuous functions and linear errors. 1st aim: We succeeded in characterising convergence U_k to u exactly, Theorem 3.3.8 and Theorem 3.3.10, i.e. we derived a necessary and sufficient condition for convergence U_k to u in terms of a discrete quantity which can potentially be used to steer a numerical algorithm, as we did in Section 6.3. We could not find an example, where this condition is fulfilled; nevertheless, because this result was achieved without assuming any additional regularity for the sequence of triangulations or the problem itself, it constitutes a major contribution to the convergence analysis for adaptive finite element methods for state-constrained optimal control problems. 2nd aim: The second goal, the a posteriori error estimator, was achieved in Theorem 4.2.12 and Theorem 4.2.13. Remarkably, the derived a posteriori estimator was proved to converge under relatively mild assumptions, Theorem 4.3.14. In the concluding chapters of this thesis, we constructed an adaptive algorithm on the basis of our a posteriori error estimator, Chapter 5, before successfully testing it for two problems, Chapter 6.
Open Access
Adaptive higher order discontinuous Galerkin methods for porous-media multi-phase flow with strong heterogeneities
(2018) Kane, Birane; Siebert, Kunibert (Prof. Dr.)
In this thesis, we develop, analyze, and implement adaptive discontinuous Galerkin (DG) finite element solvers for the efficient simulation of porous-media flow problems. We consider 2d and 3d incompressible, immiscible, two-phase flow in a possibly strongly heterogeneous and anisotropic porous medium. Discontinuous capillarypressure functions and gravity effects are taken into account. The system is written in terms of a phase-pressure/phase-saturation formulation. First and second order Adams-Moulton time discretization methods are combined with various interior penalty DG discretizations in space, such as the symmetric interior penalty Galerkin (SIPG), the nonsymmetric interior penalty Galerkin (NIPG) and the incomplete interior penalty Galerkin (IIPG). These fully implicit space time discretizations lead to fully coupled nonlinear systems requiring to build a Jacobian matrix at each time step and in each iteration of a Newton-Raphson method. We provide a stability estimate of the saturation and the pressure with respect to initial and boundary data. We also derive a-priori error estimates with respect to the L2(H1) norm for the pressure and the L∞(L2)∩L2(H1) norm for the saturation. Moving on to adaptivity, we implement different strategies allowing for a simultaneous variation of the element sizes, the local polynomial degrees and the time step size. These approaches allow to increase the local polynomial degree when the solution is estimated to be smooth and refine locally the mesh otherwise. They also grant more flexibility with respect to the time step size without impeding the convergence of the method. The aforementioned adaptive algorithms are applied in series of homogeneous, heterogeneous and anisotropic test cases. To our knowledge, this is the first time the concept of local hp-adaptivity is incorporated in the study of 2d and 3d incompressible, immiscible, two-phase flow problems. Delving into the issue of efficient linear solvers for the fully-coupled fully-implicit formulations, we implement a constrained pressure residual (CPR) two-stage preconditioner that exploits the algebraic properties of the Jacobian matrices of the systems. Furthermore, we provide an open-source DG two-phase flow simulator, based on the software framework DUNE, accompanied by a set of programs including instructions on how to compile and run them.
Open Access
Adaptive piecewise Poly-Sinc methods for ordinary differential equations
(2022) Khalil, Omar; El-Sharkawy, Hany; Youssef, Maha; Baumann, Gerd
We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for the approximation. Our work extends the adaptive piecewise Poly-Sinc method to function approximation, for which we derived an a priori error estimate for our adaptive method and showed its exponential convergence in the number of iterations. In this work, we show the exponential convergence in the number of iterations of the a priori error estimate obtained from the piecewise collocation method, provided that a good estimate of the exact solution of the ordinary differential equation at the Sinc points exists. We use a statistical approach for partition refinement. The adaptive greedy piecewise Poly-Sinc algorithm is validated on regular and stiff ordinary differential equations.
Open Access
Adaptive two-scale models for processes with evolution of microstructures
(2014) Redeker, Magnus; Rohde, Christian (Prof. Dr.)
In this dissertation two combinable numerical solution schemes are developed that - either in combination or on their own - allow for an efficient numerical solution of two-scale models that describe physical processes with changing microstructures via the combination of partial differential equations on a macro- and a microscopic length-scale. Furthermore, a two-scale phase-field model is established, that describes in a porous medium a pore-scale precipitation and a Darcy-scale diffusion process of in a fluid dissolved particles. One of the developed solution schemes is used in order to solve this model efficiently in a large time-space-cylinder. Numerical results show the interdependence of the pore-scale precipitation and the Darcy-scale diffusion process.