Efficient calculation of gluon amplitudes with n legs and an implementation of parton showers using the dipole formalism

The conventional way to calculate hard scattering processes in perturbation theory using Feynman diagrams is not efficient enough to calculate all necessary processes - for example for the Large Hadron Collider - to a sufficient precision. Two alternatives to order-by-order calculations are studied in this thesis.rnrnIn the first part we compare the numerical implementations of four different recursive methods for the efficient computation of Born gluon amplitudes: Berends-Giele recurrence relations and recursive calculations with scalar diagrams, with maximal helicity violating vertices and with shifted momenta. From the four methods considered, the Berends-Giele method performs best, if the number of external partons is eight or bigger. However, for less than eight external partons, the recursion relation with shifted momenta offers the best performance. When investigating the numerical stability and accuracy, we found that all methods give satisfactory results.rnrnIn the second part of this thesis we present an implementation of a parton shower algorithm based on the dipole formalism. The formalism treats initial- and final-state partons on the same footing. The shower algorithm can be used for hadron colliders and electron-positron colliders. Also massive partons in the final state were included in the shower algorithm. Finally, we studied numerical results for an electron-positron collider, the Tevatron and the Large Hadron Collider.

Numerical study of homogeneous and heterogeneous crystal nucleation in colloidal systems

Im Rahmen dieser Arbeit wurden Computersimulationen von Keimbildungs- und Kris\-tallisationsprozessen in rnkolloidalen Systemen durchgef\"uhrt. rnEine Kombination von Monte-Carlo-Simulationsmethoden und der Forward-Flux-Sampling-Technik wurde rnimplementiert, um die homogene und heterogene Nukleation von Kristallen monodisperser Hart\-kugeln zu untersuchen. rnIm m\"a\ss{ig} unterk\"uhlten Bulk-Hartkugelsystem sagen wir die homogenen Nukleationsraten voraus und rnvergleichen die Resultate mit anderen theoretischen Ergebnissen und experimentellen Daten. rnWeiterhin analysieren wir die kristallinen Cluster in den Keimbildungs- und Wachstumszonen, rnwobei sich herausstellt, dass kristalline Cluster sich in unterschiedlichen Formen im System bilden. rnKleine Cluster sind eher l\"anglich in eine beliebige Richtung ausgedehnt, w\"ahrend gr\"o\ss{ere} rnCluster kompakter und von ellipsoidaler Gestalt sind. rn rnIm n\"achsten Teil untersuchen wir die heterogene Keimbildung an strukturierten bcc (100)-W\"anden. rnDie 2d-Analyse der kristallinen Schichten an der Wand zeigt, dass die Struktur der rnWand eine entscheidende Rolle in der Kristallisation von Hartkugelkolloiden spielt. rnWir sagen zudem die heterogenen Kristallbildungsraten bei verschiedenen \"Ubers\"attigungsgraden voraus. rnDurch Analyse der gr\"o\ss{ten} Cluster an der Wand sch\"atzen wir zus\"atzlich den Kontaktwinkel rnzwischen Kristallcluster und Wand ab. rnEs stellt sich heraus, dass wir in solchen Systemen weit von der Benetzungsregion rnentfernt sind und der Kristallisationsprozess durch heterogene Nukleation stattfindet. rn rnIm letzten Teil der Arbeit betrachten wir die Kristallisation von Lennard-Jones-Kolloidsystemen rnzwischen zwei ebenen W\"anden. rnUm die Erstarrungsprozesse f\"ur ein solches System zu untersuchen, haben wir eine Analyse des rnOrdnungsparameters f\"ur die Bindung-Ausrichtung in den Schichten durchgef\"urt. rnDie Ergebnisse zeigen, dass innerhalb einer Schicht keine hexatische Ordnung besteht, rnwelche auf einen Kosterlitz-Thouless-Schmelzvorgang hinweisen w\"urde. rnDie Hysterese in den Erhitzungs-Gefrier\-kurven zeigt dar\"uber hinaus, dass der Kristallisationsprozess rneinen aktivierten Prozess darstellt.

Symplectic Lagrangian fibrations

In this work we investigate the deformation theory of pairs of an irreducible symplectic manifold X together with a Lagrangian subvariety Y in X, where the focus is on singular Lagrangian subvarieties. Among other things, Voisin's results [Voi92] are generalized to the case of simple normal crossing subvarieties; partial results are also obtained for more complicated singularities.rnAs done in Voisin's article, we link the codimension of the subspace of the universal deformation space of X parametrizing those deformations where Y persists, to the rank of a certain map in cohomology. This enables us in some concrete cases to actually calculate or at least estimate the codimension of this particular subspace. In these cases the Lagrangian subvarieties in question occur as fibers or fiber components of a given Lagrangian fibration f : X --> B. We discuss examples and the question of how our results might help to understand some aspects of Lagrangian fibrations.

Untersuchung der Kernstruktur von 3 He mittels Polarisationsobservablen

Durch die Möglichkeit, gleichzeitig mehrere Polarisationsfreiheitsgradernin der quasi-elastischen Elektronstreuung an $^3mathrm{He}$ zurnmessen, bietet sich ein neuer experimenteller Zugang zu kleinen, aber rnwichtigen Partialwellenbeiträgen ($S'$, $D$-Welle) desrn$^3mathrm{He}$-Grundzustands. Dies ermöglicht nicht nur ein tieferesrnVerständnis des Drei-Körper-Systems, sondern bietet auch diernMöglichkeit, Erkenntnisse über die $^3mathrm{He}$-Struktur undrnDynamik zu erlangen. Mit Hilfe dieser Informationen lassen sich abrninitio Rechnungen testen, sowie Korrekturen berechnen, die für anderernExperimente (z.B. Messung von $G_{en}$) benötigt werden. rnrnModerne Faddeev-Rechnungen liefern nicht nur eine quantitativernBeschreibung des $^3mathrm{He}$-Grundzustands, sondern geben auchrneinen Einblick in die sogenannten spinabhängigenrnImpulsverteilungen. Eine gründliche experimentelle Untersuchung ist in rndiesem Zusammenhang nötig, um eine solide Basis für die Üperprüfungrnder theoretische Modelle zu liefern. EinrnDreifach-Polarisationsexperiment liefert hier zum einen wichtigernDaten, zum anderen kann damit untersucht werden, ob mit der Methoderndes glqq Deuteron-Tagginggrqq polarisiertes $^3mathrm{He}$ alsrneffektives polarisiertes Protonentarget verwendet werden kann. rnrnDas hier vorgestellte Experiment kombiniert erstmals Strahl- undrnTargetpolarisation sowie die Messung der Polarisation des auslaufendenrnProtons. Das Experiment wurde im Sommer 2007 an derrnDrei-Spektrometer-Anlage der A1-Kollaboration an MAMI rndurchgeführt. Dabei wurde mit einer Strahlenergie vonrn$E=855,mathrm{MeV}$ bei $q^2=-0,14,(mathrm{GeV/c})^2$rn$(omega=0,13,mathrm{GeV}$, $q=0,4,mathrm{GeV/c})$ gemessen.rnrnDie bestimmten Wirkungsquerschnitte, sowie die Strahl-Target- und diernDreifach-Asymmetrie werden mit theoretischen Modellrechnungen vonrnJ. Golak (Plane Wave Impuls Approximation PWIA, sowie ein Modell mitrnEndzustandswechselwirkung) verglichen. Zudem wurde das Modell von dernForest verwendet, welches den Wirkungsquerschnitt über eine gemessenernSpektralfunktion berechnet. Der Vergleich mit den Modellrechnungenrnzeigt, dass sowohl der Wirkungsquerschnitt, als auch die Doppel- undrnDreifach-Asymmetrie gut mit den theoretischen Rechnungenrnübereinstimmen. rnrnDie Ergebnisse dieser Arbeit bestätigen, dass polarisiertesrn$^3mathrm{He}$ nicht nur als polarisiertes Neutronentarget, sondernrndurch Nachweis des Deuterons ebenfalls als polarisiertesrnProtonentarget verwendet werden kann.

Femtosecond laser-based investigations of magnetic circular dichroism in near-threshold photoemission

During the last decades magnetic circular dichroism (MCD) has attracted much interest and evolved into various experimental methods for the investigation of magnetic thin films. For example, synchrotron-based X-ray magnetic circular dichroism (XMCD) displays the absolute values of spin and orbital magnetic moments. It thereby benefits from large asymmetry values of more than 30% due to the excitation of atomic core-levels. Similarly large values are also expected for threshold photoemission magnetic circular dichroism (TPMCD). Using lasers with photon energies in the range of the sample work function this method gives access to the occupied electronic structure close to the Fermi level. However, except for the case of Ni(001) there exist only few studies on TPMCD moreover revealing much smaller asymmetries than XMCD-measurements. Also the basic physical mechanisms of TPMCD are not satisfactorily understood. In this work we therefore investigate TPMCD in one- and two-photon photoemission (1PPE and 2PPE) for ferromagnetic Heusler alloys and ultrathin Co films using ultrashort pulsed laser light. The observed dichroism is explained by a non-conventional photoemission model using spin-resolved band-structure calculations and linear response theory. For the two Heusler alloys Ni2MnGa and Co2FeSi we give first evidence of TPMCD in the regime of two-photon photoemission. Systematic investigations concerning general properties of TPMCD in 1PPE and 2PPE are carried out at ultrathin Co films grown on Pt(111). Here, photon-energy dependent measurements reveal asymmetries of 1.9% in 1PPE and 11.7% in 2PPE. TPMCD measurements at decreased work function even yield larger asymmetries of 6.2% (1PPE) and 17% (2PPE), respectively. This demonstrates that enlarged asymmetries are also attainable for the TPMCD effect on Co(111). Furthermore, we find that the TPMCD asymmetry is bulk-sensitive for 1PPE and 2PPE. This means that the basic mechanism leading to the observed dichroism must be connected to Co bulk properties; surface effects do not play a crucial role. Finally, the enhanced TPMCD asymmetries in 2PPE compared to the 1PPE case are traced back to the dominant influence of the first excitation step and the existence of a real intermediate state. The observed TPMCD asymmetries cannot be interpreted by conventional photoemission theory which only considers direct interband transitions in the direction of observation (Γ-L). For Co(111), these transitions lead to evanescent final states. The excitation to such states, however, is incompatible with the measured bulk-sensitivity of the asymmetry. Therefore, we generalize this model by proposing the TPMCD signal to arise mostly from direct interband transitions in crystallographic directions other than (Γ-L). The necessary additional momentum transfer to the excited electrons is most probably provided by electron-phonon or -magnon scattering processes. Corresponding calculations on the basis of this model are in reasonable agreement with the experimental results so that this approach represents a promising tool for a quantitative description of the TPMCD effect. The present findings encourage an implementation of our experimental technique to time- and spatially-resolved photoemission electron microscopy, thereby enabling a real time imaging of magnetization dynamics of single excited states in a ferromagnetic material on a femtosecond timescale.

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.

Röntgenabsorptionsspektroskopie und magnetischer Röntgenzirkulardichroismus an dünnen Heusler-Filmen

Verbindungen aus nicht ferromagnetischen Bestandteilen, die ferromagnetische Eigenschaf-ten zeigen, sind seit Anfang des 20. Jahrhunderts bekannt und werden nach ihrem Entdecker als Heusler-Verbindungen bezeichnet. Seitdem haben sie nichts von ihrer Faszination eingebüßt, besitzen sie doch eine Fülle besonderer Eigenschaften mit Anwendungen z.B. in der Spintronik.rnAuf der Suche nach geeigneten Legierungen ist es wünschenswert, zunächst grundlegende Eigenschaften wie das magnetische Moment elementspezifisch bestimmen zu können. Hierfür sind Methoden wie Röntgenabsorptionsspektroskopie und magnetischer Röntgenzirkulardichroismus (XAS/XMCD) prädestiniert.rnIm Rahmen dieser Arbeit wurde eine Apparatur entwickelt, mit deren Hilfe XAS- und XMCD-Messungen an dünnen Heusler-Filmen durchgeführt werden können. Da Grenzflächeneigenschaften von besonderem Interesse sind, wurde der experimentelle Aufbau so gewählt, dass gleichzeitig Volumen und Oberflächeneigenschaften untersucht werden können. Durch Vergleich dieser Messdaten erhält man Zugang zu den Grenzflächeneigenschaften.rnSo konnte mit XAS-Messungen nachgewiesen werden, dass sich die chemischen Eigenschaften an der Grenzfläche mancher Filme von denen im Volumen des Films unterscheiden (Oxidation bzw. Interdiffusion der Abdeckschicht). Auch stöchiometrische Unterschiede zwischen Oberfläche und Volumen konnten so identifiziert werden.rnMit Hilfe von XMCD-Messungen wurden elementspezifische magnetische Momente bestimmt und mit theoretischen Vorhersagen verglichen. Auch hierbei konnten Oberflächen- und Volumenmomente miteinander verglichen werden. So wurde z.B. unter Verwendung einer Schichtserie die Anzahl magnetischer Totlagen an beiden Grenzflächen bestimmt. Diese Informationen sind wichtig, um die Qualität dünner Filme steigern zu können.rnDes Weiteren war es auch möglich, temperaturabhängige Änderungen in der Ni2MnGa Zustandsdichte, die von der Theorie vorhergesagt wurden, in den XAS-Spektren nachzuweisen. Schließlich wurde noch eine Methode entwickelt, die es erlaubt, unter bestimmten Voraussetzungen auf die partielle unbesetzte Zustandsdichte (PDOS) zu schließen. Dies liefert wichtige Hinweise auf Lage und Breite der bisher nur theoretisch vorhergesagten Bandlücke. Es ist mit der hier vorgestellten Methode nicht möglich, die gesamte PDOS für alle Elemente zu vermessen, doch können so relativ leicht vielversprechende Kandidaten für weitere Untersuchungen gefunden werden.rn

Chemical composition measurements of cloud condensation nuclei and ice nuclei by aerosol mass spectrometry

In this study the Aerodyne Aerosol Mass Spectrometer (AMS) was used during three laboratory measurement campaigns, FROST1, FROST2 and ACI-03. The FROST campaigns took place at the Leipzig Aerosol Cloud Interaction Simulator (LACIS) at the IfT in Leipzig and the ACI-03 campaign was conducted at the AIDA facility at the Karlsruhe Institute of Technology (KIT). In all three campaigns, the effect of coatings on mineral dust ice nuclei (IN) was investigated. During the FROST campaigns, Arizona Test Dust (ATD) particles of 200, 300 and 400 nm diameter were coated with thin coatings (< 7 nm) of sulphuric acid. At these very thin coatings, the AMS was operated close to its detection limits. Up to now it was not possible to accurately determine AMS detection limits during regular measurements. Therefore, the mathematical tools to analyse the detection limits of the AMS have been improved in this work. It is now possible to calculate detection limits of the AMS under operating conditions, without losing precious time by sampling through a particle filter. The instrument was characterised in more detail to enable correct quantification of the sulphate loadings on the ATD particle surfaces. Correction factors for the instrument inlet transmission, the collection efficiency, and the relative ionisation efficiency have been determined. With these corrections it was possible to quantify the sulphate mass per particle on the ATD after the condensation of sulphuric acid on its surface. The AMS results have been combined with the ice nucleus counter results. This revealed that the IN-efficiency of ATD is reduced when it is coated with sulphuric acid. The reason for this reduction is a chemical reaction of sulphuric acid with the particle's surface. These reactions are increasingly taking place when the aerosol is humidified or heated after the coating with sulphuric acid. A detailed analysis of the solubility and the evaporation temperature of the surface reaction products revealed that most likely aluminium sulphate is produced in these reactions.

Coarse-grained peptide models: conformational sampling, peptide association and dynamical properties for peptides

In dieser Arbeit wird ein vergröbertes (engl. coarse-grained, CG) Simulationsmodell für Peptide in wässriger Lösung entwickelt. In einem CG Verfahren reduziert man die Anzahl der Freiheitsgrade des Systems, so dass manrngrössere Systeme auf längeren Zeitskalen untersuchen kann. Die Wechselwirkungspotentiale des CG Modells sind so aufgebaut, dass die Peptid Konformationen eines höher aufgelösten (atomistischen) Modells reproduziert werden.rnIn dieser Arbeit wird der Einfluss unterschiedlicher bindender Wechsel-rnwirkungspotentiale in der CG Simulation untersucht, insbesondere daraufhin,rnin wie weit das Konformationsgleichgewicht der atomistischen Simulation reproduziert werden kann. Im CG Verfahren verliert man per Konstruktionrnmikroskopische strukturelle Details des Peptids, zum Beispiel, Korrelationen zwischen Freiheitsgraden entlang der Peptidkette. In der Dissertationrnwird gezeigt, dass diese “verlorenen” Eigenschaften in einem Rückabbildungsverfahren wiederhergestellt werden können, in dem die atomistischen Freiheitsgrade wieder in die CG-Strukturen eingefügt werden. Dies gelingt, solange die Konformationen des CG Modells grundsätzlich gut mit der atomistischen Ebene übereinstimmen. Die erwähnten Korrelationen spielen einerngrosse Rolle bei der Bildung von Sekundärstrukturen und sind somit vonrnentscheidender Bedeutung für ein realistisches Ensemble von Peptidkonformationen. Es wird gezeigt, dass für eine gute Übereinstimmung zwischen CG und atomistischen Kettenkonformationen spezielle bindende Wechselwirkungen wie zum Beispiel 1-5 Bindungs- und 1,3,5-Winkelpotentiale erforderlich sind. Die intramolekularen Parameter (d.h. Bindungen, Winkel, Torsionen), die für kurze Oligopeptide parametrisiert wurden, sind übertragbarrnauf längere Peptidsequenzen. Allerdings können diese gebundenen Wechselwirkungen nur in Kombination mit solchen nichtbindenden Wechselwirkungspotentialen kombiniert werden, die bei der Parametrisierung verwendet werden, sind also zum Beispiel nicht ohne weiteres mit einem andere Wasser-Modell kombinierbar. Da die Energielandschaft in CG-Simulationen glatter ist als im atomistischen Modell, gibt es eine Beschleunigung in der Dynamik. Diese Beschleunigung ist unterschiedlich für verschiedene dynamische Prozesse, zum Beispiel für verschiedene Arten von Bewegungen (Rotation und Translation). Dies ist ein wichtiger Aspekt bei der Untersuchung der Kinetik von Strukturbildungsprozessen, zum Beispiel Peptid Aggregation.rn

First measurements of the aSPECT spectrometer

The aSPECT spectrometer has been constructed to measure, with high precision, the integral proton spectrum of the free neutron decay. From this spectrum the neutrino electron angular correlation coefficient a can be inferred. The coefficient a is involved in several Standard Model tests, like the unitarity test of the Cabibbo-Kobayashi-Maskawa quark mixing matrix. aSPECT has been designed to determine the coefficient a with an accuracy better than 3×10−4, that is, one order of magnitude better than the best current accuracy. First measurements with neutron beam with the aSPECT spectrometer were performed in the Forschungsneutronenquelle Heinz Maier-Leibnitz, in Munich. A study of the data taken in this period is presented in this thesis, demonstrating the proof of principle of the spectrometer. However, the observation of situation and time-dependent background instabilities impedes the report of a new value of the coefficient a. A thorough data analysis is carried out to identify sources of these background instabilities in order to improve the aSPECT experiment for future beam times. The investigation indicates that trapped particles are most likely the reason for the background problems. Furthermore, it has been observed that measurements containing less trapped particles provide a-values closer to the currently Particle Data Group value. Based on this findings, different measures are proposed to eliminate potential traps in the spectrometer. Indeed, with the proposed modifications realized for the following beam-times, the observed background instabilities were greatly reduced.

Mode-coupling theory: generalizations, high dimensions and microscopic dynamics

This work contains several applications of the mode-coupling theory (MCT) and is separated into three parts. In the first part we investigate the liquid-glass transition of hard spheres for dimensions d→∞ analytically and numerically up to d=800 in the framework of MCT. We find that the critical packing fraction ϕc(d) scales as d²2^(-d), which is larger than the Kauzmann packing fraction ϕK(d) found by a small-cage expansion by Parisi and Zamponi [J. Stat. Mech.: Theory Exp. 2006, P03017 (2006)]. The scaling of the critical packing fraction is different from the relation ϕc(d)∼d2^(-d) found earlier by Kirkpatrick and Wolynes [Phys. Rev. A 35, 3072 (1987)]. This is due to the fact that the k dependence of the critical collective and self nonergodicity parameters fc(k;d) and fcs(k;d) was assumed to be Gaussian in the previous theories. We show that in MCT this is not the case. Instead fc(k;d) and fcs(k;d), which become identical in the limit d→∞, converge to a non-Gaussian master function on the scale k∼d^(3/2). We find that the numerically determined value for the exponent parameter λ and therefore also the critical exponents a and b depend on the dimension d, even at the largest evaluated dimension d=800. In the second part we compare the results of a molecular-dynamics simulation of liquid Lennard-Jones argon far away from the glass transition [D. Levesque, L. Verlet, and J. Kurkijärvi, Phys. Rev. A 7, 1690 (1973)] with MCT. We show that the agreement between theory and computer simulation can be improved by taking binary collisions into account [L. Sjögren, Phys. Rev. A 22, 2866 (1980)]. We find that an empiric prefactor of the memory function of the original MCT equations leads to similar results. In the third part we derive the equations for a mode-coupling theory for the spherical components of the stress tensor. Unfortunately it turns out that they are too complex to be solved numerically.

Electroweak precision observables and effective four-fermion interactions in warped extra dimensions

In this thesis, we study the phenomenology of selected observables in the context of the Randall-Sundrum scenario of a compactified warpedrnextra dimension. Gauge and matter fields are assumed to live in the whole five-dimensional space-time, while the Higgs sector is rnlocalized on the infrared boundary. An effective four-dimensional description is obtained via Kaluza-Klein decomposition of the five dimensionalrnquantum fields. The symmetry breaking effects due to the Higgs sector are treated exactly, and the decomposition of the theory is performedrnin a covariant way. We develop a formalism, which allows for a straight-forward generalization to scenarios with an extended gauge group comparedrnto the Standard Model of elementary particle physics. As an application, we study the so-called custodial Randall-Sundrum model and compare the resultsrnto that of the original formulation. rnWe present predictions for electroweak precision observables, the Higgs production cross section at the LHC, the forward-backward asymmetryrnin top-antitop production at the Tevatron, as well as the width difference, the CP-violating phase, and the semileptonic CP asymmetry in B_s decays.

Deriving Deligne-Mumford stacks with perfect obstruction theories

Intersection theory on moduli spaces has lead to immense progress in certain areas of enumerative geometry. For some important areas, most notably counting stable maps and counting stable sheaves, it is important to work with a virtual fundamental class instead of the usual fundamental class of the moduli space. The crucial prerequisite for the existence of such a class is a two-term complex controlling deformations of the moduli space. Kontsevich conjectured in 1994 that there should exist derived version of spaces with this specific property. Another hint at the existence of these spaces comes from derived algebraic geometry. It is expected that for every pair of a space and a complex controlling deformations of the space their exists, under some additional hypothesis, a derived version of the space having the chosen complex as cotangent complex. In this thesis one version of these additional hypothesis is identified. We then show that every space admitting a two-term complex controlling deformations satisfies these hypothesis, and we finally construct the derived spaces.

Numerical studies of colloidal systems

The interplay of hydrodynamic and electrostatic forces is of great importance for the understanding of colloidal dispersions. Theoretical descriptions are often based on the so called standard electrokinetic model. This Mean Field approach combines the Stokes equation for the hydrodynamic flow field, the Poisson equation for electrostatics and a continuity equation describing the evolution of the ion concentration fields. In the first part of this thesis a new lattice method is presented in order to efficiently solve the set of non-linear equations for a charge-stabilized colloidal dispersion in the presence of an external electric field. Within this framework, the research is mainly focused on the calculation of the electrophoretic mobility. Since this transport coefficient is independent of the electric field only for small driving, the algorithm is based upon a linearization of the governing equations. The zeroth order is the well known Poisson-Boltzmann theory and the first order is a coupled set of linear equations. Furthermore, this set of equations is divided into several subproblems. A specialized solver for each subproblem is developed, and various tests and applications are discussed for every particular method. Finally, all solvers are combined in an iterative procedure and applied to several interesting questions, for example, the effect of the screening mechanism on the electrophoretic mobility or the charge dependence of the field-induced dipole moment and ion clouds surrounding a weakly charged sphere. In the second part a quantitative data analysis method is developed for a new experimental approach, known as "Total Internal Reflection Fluorescence Cross-Correlation Spectroscopy" (TIR-FCCS). The TIR-FCCS setup is an optical method using fluorescent colloidal particles to analyze the flow field close to a solid-fluid interface. The interpretation of the experimental results requires a theoretical model, which is usually the solution of a convection-diffusion equation. Since an analytic solution is not available due to the form of the flow field and the boundary conditions, an alternative numerical approach is presented. It is based on stochastic methods, i. e. a combination of a Brownian Dynamics algorithm and Monte Carlo techniques. Finally, experimental measurements for a hydrophilic surface are analyzed using this new numerical approach.

Tracking, b-tagging and measurement of the b-jet production cross section with the ATLAS detector

The Standard Model of elementary particle physics was developed to describe the fundamental particles which constitute matter and the interactions between them. The Large Hadron Collider (LHC) at CERN in Geneva was built to solve some of the remaining open questions in the Standard Model and to explore physics beyond it, by colliding two proton beams at world-record centre-of-mass energies. The ATLAS experiment is designed to reconstruct particles and their decay products originating from these collisions. The precise reconstruction of particle trajectories plays an important role in the identification of particle jets which originate from bottom quarks (b-tagging). This thesis describes the step-wise commissioning of the ATLAS track reconstruction and b-tagging software and one of the first measurements of the b-jet production cross section in pp collisions at sqrt(s)=7 TeV with the ATLAS detector. The performance of the track reconstruction software was studied in great detail, first using data from cosmic ray showers and then collisions at sqrt(s)=900 GeV and 7 TeV. The good understanding of the track reconstruction software allowed a very early deployment of the b-tagging algorithms. First studies of these algorithms and the measurement of the b-tagging efficiency in the data are presented. They agree well with predictions from Monte Carlo simulations. The b-jet production cross section was measured with the 2010 dataset recorded by the ATLAS detector, employing muons in jets to estimate the fraction of b-jets. The measurement is in good agreement with the Standard Model predictions.