Simulations of physics and chemistry of polar stratospheric clouds with a general circulation model

A polar stratospheric cloud submodel has been developed and incorporated in a general circulation model including atmospheric chemistry (ECHAM5/MESSy). The formation and sedimentation of polar stratospheric cloud (PSC) particles can thus be simulated as well as heterogeneous chemical reactions that take place on the PSC particles. For solid PSC particle sedimentation, the need for a tailor-made algorithm has been elucidated. A sedimentation scheme based on first order approximations of vertical mixing ratio profiles has been developed. It produces relatively little numerical diffusion and can deal well with divergent or convergent sedimentation velocity fields. For the determination of solid PSC particle sizes, an efficient algorithm has been adapted. It assumes a monodisperse radii distribution and thermodynamic equilibrium between the gas phase and the solid particle phase. This scheme, though relatively simple, is shown to produce particle number densities and radii within the observed range. The combined effects of the representations of sedimentation and solid PSC particles on vertical H2O and HNO3 redistribution are investigated in a series of tests. The formation of solid PSC particles, especially of those consisting of nitric acid trihydrate, has been discussed extensively in recent years. Three particle formation schemes in accordance with the most widely used approaches have been identified and implemented. For the evaluation of PSC occurrence a new data set with unprecedented spatial and temporal coverage was available. A quantitative method for the comparison of simulation results and observations is developed and applied. It reveals that the relative PSC sighting frequency can be reproduced well with the PSC submodel whereas the detailed modelling of PSC events is beyond the scope of coarse global scale models. In addition to the development and evaluation of new PSC submodel components, parts of existing simulation programs have been improved, e.g. a method for the assimilation of meteorological analysis data in the general circulation model, the liquid PSC particle composition scheme, and the calculation of heterogeneous reaction rate coefficients. The interplay of these model components is demonstrated in a simulation of stratospheric chemistry with the coupled general circulation model. Tests against recent satellite data show that the model successfully reproduces the Antarctic ozone hole.

Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.

A planar Penning trap

In this thesis I present theoretical and experimental results concern- ing the operation and properties of a new kind of Penning trap, the planar trap. It consists of circular electrodes printed on an isolating surface, with an homogeneous magnetic field pointing perpendicular to that surface. The motivation of such geometry is to be found in the construction of an array of planar traps for quantum informa- tional purposes. The open access to radiation of this geometry, and the long coherence times expected for Penning traps, make the planar trap a good candidate for quantum computation. Several proposals for quantum 2-qubit interactions are studied and estimates for their rates are given. An expression for the electrostatic potential is presented, and its fea- tures exposed. A detailed study of the anharmonicity of the potential is given theoretically and is later demonstrated by experiment and numerical simulations, showing good agreement. Size scalability of this trap has been studied by replacing the original planar trap by a trap twice smaller in the experimental setup. This substitution shows no scale effect apart from those expected for the scaling of the parameters of the trap. A smaller lifetime for trapped electrons is seen for this smaller trap, but is clearly matched to a bigger misalignment of the trap’s surface and the magnetic field, due to its more difficult hand manipulation. I also give a hint that this trap may be of help in studying non-linear dynamics for a sextupolarly perturbed Penning trap.

Inverse problems in classical and quantum physics

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A promising result is that one can qualitatively reconstruct the conductivity inside the cross-section of a human chest. Even though the human volunteer is neither two-dimensional nor circular, such reconstructions can be useful in medical applications: monitoring for lung problems such as accumulating fluid or a collapsed lung and noninvasive monitoring of heart function and blood flow.

Realisierung der IceCube MonteCarlo-Produktion im WLCG und Untersuchung von Auswirkungen meteorologischer Parameter auf die Erzeugung atmosphärischer Myonen

Das am Südpol gelegene Neutrinoteleskop IceCube detektiert hochenergetische Neutrinos über die schwache Wechselwirkung geladener und neutraler Ströme. Die Analyse basiert auf einem Vergleich mit Monte-Carlo-Simulationen, deren Produktion global koordiniert wird. In Mainz ist es erstmalig gelungen, Simulationen innerhalb der Architektur des Worldwide LHC Computing Grid (WLCG) zu realisieren, was die Möglichkeit eröffnet, Monte-Carlo-Berechnungen auch auf andere deutsche Rechnerfarmen (CEs) mit IceCube-Berechtigung zu verteilen. Atmosphärische Myonen werden mit einer Rate von über 1000 Ereignissen pro Sekunde aufgezeichnet. Eine korrekte Interpretation dieses dominanten Signals, welches um einen Faktor von 10^6 reduziert werden muss um das eigentliche Neutrinosignal zu extrahieren, ist deswegen von großer Bedeutung. Eigene Simulationen mit der Software-Umgebung CORSIKA wurden durchgeführt um die von Energie und Einfallswinkel abhängige Entstehungshöhe atmosphärischer Myonen zu bestimmen. IceCube Myonraten wurden mit Wetterdaten des European Centre for Medium-Range Weather Forcasts (ECMWF) verglichen und Korrelationen zwischen jahreszeitlichen sowie kurzzeitigen Schwankungen der Atmosphärentemperatur und Myonraten konnten nachgewiesen werden. Zudem wurde eine Suche nach periodischen Effekten in der Atmosphäre, verursacht durch z.B. meteorologische Schwerewellen, mit Hilfe einer Fourieranalyse anhand der IceCube-Daten durchgeführt. Bislang konnte kein signifikanter Nachweis zur Existenz von Schwerewellen am Südpol erbracht werden.

Quantifying and modeling financial market fluctuations

Die Entstehung eines Marktpreises für einen Vermögenswert kann als Superposition der einzelnen Aktionen der Marktteilnehmer aufgefasst werden, die damit kumulativ Angebot und Nachfrage erzeugen. Dies ist in der statistischen Physik mit der Entstehung makroskopischer Eigenschaften vergleichbar, die von mikroskopischen Wechselwirkungen zwischen den beteiligten Systemkomponenten hervorgerufen werden. Die Verteilung der Preisänderungen an Finanzmärkten unterscheidet sich deutlich von einer Gaußverteilung. Dies führt zu empirischen Besonderheiten des Preisprozesses, zu denen neben dem Skalierungsverhalten nicht-triviale Korrelationsfunktionen und zeitlich gehäufte Volatilität zählen. In der vorliegenden Arbeit liegt der Fokus auf der Analyse von Finanzmarktzeitreihen und den darin enthaltenen Korrelationen. Es wird ein neues Verfahren zur Quantifizierung von Muster-basierten komplexen Korrelationen einer Zeitreihe entwickelt. Mit dieser Methodik werden signifikante Anzeichen dafür gefunden, dass sich typische Verhaltensmuster von Finanzmarktteilnehmern auf kurzen Zeitskalen manifestieren, dass also die Reaktion auf einen gegebenen Preisverlauf nicht rein zufällig ist, sondern vielmehr ähnliche Preisverläufe auch ähnliche Reaktionen hervorrufen. Ausgehend von der Untersuchung der komplexen Korrelationen in Finanzmarktzeitreihen wird die Frage behandelt, welche Eigenschaften sich beim Wechsel von einem positiven Trend zu einem negativen Trend verändern. Eine empirische Quantifizierung mittels Reskalierung liefert das Resultat, dass unabhängig von der betrachteten Zeitskala neue Preisextrema mit einem Anstieg des Transaktionsvolumens und einer Reduktion der Zeitintervalle zwischen Transaktionen einhergehen. Diese Abhängigkeiten weisen Charakteristika auf, die man auch in anderen komplexen Systemen in der Natur und speziell in physikalischen Systemen vorfindet. Über 9 Größenordnungen in der Zeit sind diese Eigenschaften auch unabhängig vom analysierten Markt - Trends, die nur für Sekunden bestehen, zeigen die gleiche Charakteristik wie Trends auf Zeitskalen von Monaten. Dies eröffnet die Möglichkeit, mehr über Finanzmarktblasen und deren Zusammenbrüche zu lernen, da Trends auf kleinen Zeitskalen viel häufiger auftreten. Zusätzlich wird eine Monte Carlo-basierte Simulation des Finanzmarktes analysiert und erweitert, um die empirischen Eigenschaften zu reproduzieren und Einblicke in deren Ursachen zu erhalten, die zum einen in der Finanzmarktmikrostruktur und andererseits in der Risikoaversion der Handelsteilnehmer zu suchen sind. Für die rechenzeitintensiven Verfahren kann mittels Parallelisierung auf einer Graphikkartenarchitektur eine deutliche Rechenzeitreduktion erreicht werden. Um das weite Spektrum an Einsatzbereichen von Graphikkarten zu aufzuzeigen, wird auch ein Standardmodell der statistischen Physik - das Ising-Modell - auf die Graphikkarte mit signifikanten Laufzeitvorteilen portiert. Teilresultate der Arbeit sind publiziert in [PGPS07, PPS08, Pre11, PVPS09b, PVPS09a, PS09, PS10a, SBF+10, BVP10, Pre10, PS10b, PSS10, SBF+11, PB10].

Der Renormierungsgruppen-Fluß der konform-reduzierten Quantengravitation

Wir analysieren die Rolle von "Hintergrundunabhängigkeit" im Zugang der effektiven Mittelwertwirkung zur Quantengravitation. Wenn der nicht-störungstheoretische Renormierungsgruppen-(RG)-Fluß "hintergrundunabhängig" ist, muß die Vergröberung durch eine nicht spezifizierte, variable Metrik definiert werden. Die Forderung nach "Hintergrundunabhängigkeit" in der Quantengravitation führt dazu, daß die funktionale RG-Gleichung von zusätzlichen Feldern abhängt; dadurch unterscheidet sich der RG-Fluß in der Quantengravitation deutlich von dem RG-Fluß einer gewöhnlichen Quantentheorie, deren Moden-Cutoff von einer starren Metrik abhängt. Beispielsweise kann in der "hintergrundunabhängigen" Theorie ein Nicht-Gauß'scher Fixpunkt existieren, obwohl die entsprechende gewöhnliche Quantentheorie keinen solchen entwickelt. Wir untersuchen die Bedeutung dieses universellen, rein kinematischen Effektes, indem wir den RG-Fluß der Quanten-Einstein-Gravitation (QEG) in einem "konform-reduzierten" Zusammenhang untersuchen, in dem wir nur den konformen Faktor der Metrik quantisieren. Alle anderen Freiheitsgrade der Metrik werden vernachlässigt. Die konforme Reduktion der Einstein-Hilbert-Trunkierung zeigt exakt dieselben qualitativen Eigenschaften wie in der vollen Einstein-Hilbert-Trunkierung. Insbesondere besitzt sie einen Nicht-Gauß'schen Fixpunkt, der notwendig ist, damit die Gravitation asymptotisch sicher ist. Ohne diese zusätzlichen Feldabhängigkeiten ist der RG-Fluß dieser Trunkierung der einer gewöhnlichen $phi^4$-Theorie. Die lokale Potentialnäherung für den konformen Faktor verallgemeinert den RG-Fluß in der Quantengravitation auf einen unendlich-dimensionalen Theorienraum. Auch hier finden wir sowohl einen Gauß'schen als auch einen Nicht-Gauß'schen Fixpunkt, was weitere Hinweise dafür liefert, daß die Quantengravitation asymptotisch sicher ist. Das Analogon der Metrik-Invarianten, die proportional zur dritten Potenz der Krümmung ist und die die störungstheoretische Renormierbarkeit zerstört, ist unproblematisch für die asymptotische Sicherheit der konform-reduzierten Theorie. Wir berechnen die Skalenfelder und -imensionen der beiden Fixpunkte explizit und diskutieren mögliche Einflüsse auf die Vorhersagekraft der Theorie. Da der RG-Fluß von der Topologie der zugrundeliegenden Raumzeit abhängt, diskutieren wir sowohl den flachen Raum als auch die Sphäre. Wir lösen die Flußgleichung für das Potential numerisch und erhalten Beispiele für RG-Trajektorien, die innerhalb der Ultraviolett-kritischen Mannigfaltigkeit des Nicht-Gauß'schen Fixpunktes liegen. Die Quantentheorien, die durch einige solcher Trajektorien definiert sind, zeigen einen Phasenübergang von der bekannten (Niederenergie-) Phase der Gravitation mit spontan gebrochener Diffeomorphismus-Invarianz zu einer neuen Phase von ungebrochener Diffeomorphismus-Invarianz. Diese Hochenergie-Phase ist durch einen verschwindenden Metrik-Erwartungswert charakterisiert.

Interacting fermionic atoms in optical lattices - A quantum simulator for condensed matter physics

This thesis reports on the creation and analysis of many-body states of interacting fermionic atoms in optical lattices. The realized system can be described by the Fermi-Hubbard hamiltonian, which is an important model for correlated electrons in modern condensed matter physics. In this way, ultra-cold atoms can be utilized as a quantum simulator to study solid state phenomena. The use of a Feshbach resonance in combination with a blue-detuned optical lattice and a red-detuned dipole trap enables an independent control over all relevant parameters in the many-body hamiltonian. By measuring the in-situ density distribution and doublon fraction it has been possible to identify both metallic and insulating phases in the repulsive Hubbard model, including the experimental observation of the fermionic Mott insulator. In the attractive case, the appearance of strong correlations has been detected via an anomalous expansion of the cloud that is caused by the formation of non-condensed pairs. By monitoring the in-situ density distribution of initially localized atoms during the free expansion in a homogeneous optical lattice, a strong influence of interactions on the out-of-equilibrium dynamics within the Hubbard model has been found. The reported experiments pave the way for future studies on magnetic order and fermionic superfluidity in a clean and well-controlled experimental system.

Total internal reflection fluorescence cross-correlation spectroscopy: theory and application for studying boundary slip phenomenon

I present a new experimental method called Total Internal Reflection Fluorescence Cross-Correlation Spectroscopy (TIR-FCCS). It is a method that can probe hydrodynamic flows near solid surfaces, on length scales of tens of nanometres. Fluorescent tracers flowing with the liquid are excited by evanescent light, produced by epi-illumination through the periphery of a high NA oil-immersion objective. Due to the fast decay of the evanescent wave, fluorescence only occurs for tracers in the ~100 nm proximity of the surface, thus resulting in very high normal resolution. The time-resolved fluorescence intensity signals from two laterally shifted (in flow direction) observation volumes, created by two confocal pinholes are independently measured and recorded. The cross-correlation of these signals provides important information for the tracers’ motion and thus their flow velocity. Due to the high sensitivity of the method, fluorescent species with different size, down to single dye molecules can be used as tracers. The aim of my work was to build an experimental setup for TIR-FCCS and use it to experimentally measure the shear rate and slip length of water flowing on hydrophilic and hydrophobic surfaces. However, in order to extract these parameters from the measured correlation curves a quantitative data analysis is needed. This is not straightforward task due to the complexity of the problem, which makes the derivation of analytical expressions for the correlation functions needed to fit the experimental data, impossible. Therefore in order to process and interpret the experimental results I also describe a new numerical method of data analysis of the acquired auto- and cross-correlation curves – Brownian Dynamics techniques are used to produce simulated auto- and cross-correlation functions and to fit the corresponding experimental data. I show how to combine detailed and fairly realistic theoretical modelling of the phenomena with accurate measurements of the correlation functions, in order to establish a fully quantitative method to retrieve the flow properties from the experiments. An importance-sampling Monte Carlo procedure is employed in order to fit the experiments. This provides the optimum parameter values together with their statistical error bars. The approach is well suited for both modern desktop PC machines and massively parallel computers. The latter allows making the data analysis within short computing times. I applied this method to study flow of aqueous electrolyte solution near smooth hydrophilic and hydrophobic surfaces. Generally on hydrophilic surface slip is not expected, while on hydrophobic surface some slippage may exists. Our results show that on both hydrophilic and moderately hydrophobic (contact angle ~85°) surfaces the slip length is ~10-15nm or lower, and within the limitations of the experiments and the model, indistinguishable from zero.

Warped extra dimensions: flavor, precision tests and Higgs physics

In this thesis, the phenomenology of the Randall-Sundrum setup is investigated. In this context models with and without an enlarged SU(2)_L x SU(2)_R x U(1)_X x P_{LR} gauge symmetry, which removes corrections to the T parameter and to the Z b_L \bar b_L coupling, are compared with each other. The Kaluza-Klein decomposition is formulated within the mass basis, which allows for a clear understanding of various model-specific features. A complete discussion of tree-level flavor-changing effects is presented. Exact expressions for five dimensional propagators are derived, including Yukawa interactions that mediate flavor-off-diagonal transitions. The symmetry that reduces the corrections to the left-handed Z b \bar b coupling is analyzed in detail. In the literature, Randall-Sundrum models have been used to address the measured anomaly in the t \bar t forward-backward asymmetry. However, it will be shown that this is not possible within a natural approach to flavor. The rare decays t \to cZ and t \to ch are investigated, where in particular the latter could be observed at the LHC. A calculation of \Gamma_{12}^{B_s} in the presence of new physics is presented. It is shown that the Randall-Sundrum setup allows for an improved agreement with measurements of A_{SL}^s, S_{\psi\phi}, and \Delta\Gamma_s. For the first time, a complete one-loop calculation of all relevant Higgs-boson production and decay channels in the custodial Randall-Sundrum setup is performed, revealing a sensitivity to large new-physics scales at the LHC.

Atomic-scale characterization of diamond surfaces and fullerene self-assembly

In this thesis, elemental research towards the implantation of a diamond-based molecular quantum computer is presented. The approach followed requires linear alignment of endohedral fullerenes on the diamond C(100) surface in the vicinity of subsurface NV-centers. From this, four fundamental experimental challenges arise: 1) The well-controlled deposition of endohedral fullerenes on a diamond surface. 2) The creation of NV-centers in diamond close to the surface. 3) Preparation and characterization of atomically-flat diamondsurfaces. 4) Assembly of linear chains of endohedral fullerenes. First steps to overcome all these challenges were taken in the framework of this thesis. Therefore, a so-called “pulse injection” technique was implemented and tested in a UHV chamber that was custom-designed for this and further tasks. Pulse injection in principle allows for the deposition of molecules from solution onto a substrate and can therefore be used to deposit molecular species that are not stable to sublimation under UHV conditions, such as the endohedral fullerenes needed for a quantum register. Regarding the targeted creation of NV-centers, FIB experiments were carried out in cooperation with the group of Prof. Schmidt-Kaler (AG Quantum, Physics Department, Johannes Gutenberg-Universität Mainz). As an entry into this challenging task, argon cations were implanted into (111) surface-oriented CaF2 crystals. The resulting implantation spots on the surface were imaged and characterized using AFM. In this context, general relations between the impact of the ions on the surface and their valency or kinetic energy, respectively, could be established. The main part of this thesis, however, is constituted by NCAFM studies on both, bare and hydrogen-terminated diamond C(100) surfaces. In cooperation with the group of Prof. Dujardin (Molecular Nanoscience Group, ISMO, Université de Paris XI), clean and atomically-flat diamond surfaces were prepared by exposure of the substrate to a microwave hydrogen plasma. Subsequently, both surface modifications were imaged in high resolution with NC-AFM. In the process, both hydrogen atoms in the unit cell of the hydrogenated surface were resolved individually, which was not achieved in previous STM studies of this surface. The NC-AFM images also reveal, for the first time, atomic-resolution contrast on the clean, insulating diamond surface and provide real-space experimental evidence for a (2×1) surface reconstruction. With regard to the quantum computing concept, high-resolution NC-AFM imaging was also used to study the adsorption and self-assembly potential of two different kinds of fullerenes (C60 and C60F48) on aforementioned diamond surfaces. In case of the hydrogenated surface, particular attention was paid to the influence of charge transfer doping on the fullerene-substrate interaction and the morphology emerging from self-assembly. Finally, self-assembled C60 islands on the hydrogen-terminated diamond surface were subject to active manipulation by an NC-AFM tip. Two different kinds of tip-induced island growth modes have been induced and were presented. In conclusion, the results obtained provide fundamental informations mandatory for the realization of a molecular quantum computer. In the process it was shown that NC-AFM is, under proper circumstances, a very capable tool for imaging diamond surfaces with highest resolution, surpassing even what has been achieved with STM up to now. Particular attention was paid to the influence of transfer doping on the morphology of fullerenes on the hydrogenated diamond surface, revealing new possibilities for tailoring the self-assembly of molecules that have a high electron affinity.

Numerical precision calculations for LHC physics

In dieser Arbeit stelle ich Aspekte zu QCD Berechnungen vor, welche eng verknüpft sind mit der numerischen Auswertung von NLO QCD Amplituden, speziell der entsprechenden Einschleifenbeiträge, und der effizienten Berechnung von damit verbundenen Beschleunigerobservablen. Zwei Themen haben sich in der vorliegenden Arbeit dabei herauskristallisiert, welche den Hauptteil der Arbeit konstituieren. Ein großer Teil konzentriert sich dabei auf das gruppentheoretische Verhalten von Einschleifenamplituden in QCD, um einen Weg zu finden die assoziierten Farbfreiheitsgrade korrekt und effizient zu behandeln. Zu diesem Zweck wird eine neue Herangehensweise eingeführt welche benutzt werden kann, um farbgeordnete Einschleifenpartialamplituden mit mehreren Quark-Antiquark Paaren durch Shufflesummation über zyklisch geordnete primitive Einschleifenamplituden auszudrücken. Ein zweiter großer Teil konzentriert sich auf die lokale Subtraktion von zu Divergenzen führenden Poltermen in primitiven Einschleifenamplituden. Hierbei wurde im Speziellen eine Methode entwickelt, um die primitiven Einchleifenamplituden lokal zu renormieren, welche lokale UV Counterterme und effiziente rekursive Routinen benutzt. Zusammen mit geeigneten lokalen soften und kollinearen Subtraktionstermen wird die Subtraktionsmethode dadurch auf den virtuellen Teil in der Berechnung von NLO Observablen erweitert, was die voll numerische Auswertung der Einschleifenintegrale in den virtuellen Beiträgen der NLO Observablen ermöglicht. Die Methode wurde schließlich erfolgreich auf die Berechnung von NLO Jetraten in Elektron-Positron Annihilation im farbführenden Limes angewandt.