O (alpha 4 s) loop-by-loop contributions to heavy quark pair production in hadronic collisions

The present state of the theoretical predictions for the hadronic heavy hadron production is not quite satisfactory. The full next-to-leading order (NLO) ${cal O} (alpha_s^3)$ corrections to the hadroproduction of heavy quarks have raised the leading order (LO) ${cal O} (alpha_s^2)$ estimates but the NLO predictions are still slightly below the experimental numbers. Moreover, the theoretical NLO predictions suffer from the usual large uncertainty resulting from the freedom in the choice of renormalization and factorization scales of perturbative QCD.In this light there are hopes that a next-to-next-to-leading order (NNLO) ${cal O} (alpha_s^4)$ calculation will bring theoretical predictions even closer to the experimental data. Also, the dependence on the factorization and renormalization scales of the physical process is expected to be greatly reduced at NNLO. This would reduce the theoretical uncertainty and therefore make the comparison between theory and experiment much more significant. In this thesis I have concentrated on that part of NNLO corrections for hadronic heavy quark production where one-loop integrals contribute in the form of a loop-by-loop product. In the first part of the thesis I use dimensional regularization to calculate the ${cal O}(ep^2)$ expansion of scalar one-loop one-, two-, three- and four-point integrals. The Laurent series of the scalar integrals is needed as an input for the calculation of the one-loop matrix elements for the loop-by-loop contributions. Since each factor of the loop-by-loop product has negative powers of the dimensional regularization parameter $ep$ up to ${cal O}(ep^{-2})$, the Laurent series of the scalar integrals has to be calculated up to ${cal O}(ep^2)$. The negative powers of $ep$ are a consequence of ultraviolet and infrared/collinear (or mass ) divergences. Among the scalar integrals the four-point integrals are the most complicated. The ${cal O}(ep^2)$ expansion of the three- and four-point integrals contains in general classical polylogarithms up to ${rm Li}_4$ and $L$-functions related to multiple polylogarithms of maximal weight and depth four. All results for the scalar integrals are also available in electronic form. In the second part of the thesis I discuss the properties of the classical polylogarithms. I present the algorithms which allow one to reduce the number of the polylogarithms in an expression. I derive identities for the $L$-functions which have been intensively used in order to reduce the length of the final results for the scalar integrals. I also discuss the properties of multiple polylogarithms. I derive identities to express the $L$-functions in terms of multiple polylogarithms. In the third part I investigate the numerical efficiency of the results for the scalar integrals. The dependence of the evaluation time on the relative error is discussed. In the forth part of the thesis I present the larger part of the ${cal O}(ep^2)$ results on one-loop matrix elements in heavy flavor hadroproduction containing the full spin information. The ${cal O}(ep^2)$ terms arise as a combination of the ${cal O}(ep^2)$ results for the scalar integrals, the spin algebra and the Passarino-Veltman decomposition. The one-loop matrix elements will be needed as input in the determination of the loop-by-loop part of NNLO for the hadronic heavy flavor production.

Atomistic simulations of cosolvent/water mixtures

In this thesis, atomistic simulations are performed to investigate hydrophobic solvation and hydrophobic interactions in cosolvent/water binary mixtures. Many cosolvent/water binary mixtures exhibit non-ideal behavior caused by aggregation at the molecular scale level although they are stable and homogenous at the macroscopic scale. Force-field based atomistic simulations provide routes to relate atomistic-scale structure and interactions to thermodynamic solution properties. The predicted solution properties are however sensitive to the parameters used to describe the molecular interactions. In this thesis, a force field for tertiary butanol (TBA) and water mixtures is parameterized by making use of the Kirkwood-Buff theory of solution. The new force field is capable of describing the alcohol-alcohol, water-water and alcohol-water clustering in the solution as well as the solution components’ chemical potential derivatives in agreement with experimental data. With the new force field, the preferential solvation and the solvation thermodynamics of a hydrophobic solute in TBA/water mixtures have been studied. First, methane solvation at various TBA/water concentrations is discussed in terms of solvation free energy-, enthalpy- and entropy- changes, which have been compared to experimental data. We observed that the methane solvation free energy varies smoothly with the alcohol/water composition while the solvation enthalpies and entropies vary nonmonotonically. The latter occurs due to structural solvent reorganization contributions which are not present in the free energy change due to exact enthalpy-entropy compensation. It is therefore concluded that the enthalpy and entropy of solvation provide more detailed information on the reorganization of solvent molecules around the inserted solute. Hydrophobic interactions in binary urea/water mixtures are next discussed. This system is particularly relevant in biology (protein folding/unfolding), however, changes in the hydrophobic interaction induced by urea molecules are not well understood. In this thesis, this interaction has been studied by calculating the free energy (potential of mean force), enthalpy and entropy changes as a function of the solute-solute distance in water and in aqueous urea (6.9 M) solution. In chapter 5, the potential of mean force in both solution systems is analyzed in terms of its enthalpic and entropic contributions. In particular, contributions of solvent reorganization in the enthalpy and entropy changes are studied separately to better understand what are the changes in interactions in the system that contribute to the free energy of association of the nonpolar solutes. We observe that in aqueous urea the association between nonpolar solutes remains thermodynamically favorable (i.e., as it is the case in pure water). This observation contrasts a long-standing belief that clusters of nonpolar molecules dissolve completely in the presence of urea molecules. The consequences of our observations for the stability of proteins in concentrated urea solutions are discussed in the chapter 6 of the thesis.

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.

Radiolabeling of defined polymer architectures with fluorine-18 and iodine-131 for ex vivo and in vivo evaluation : visualization of structure-property relationships

Nuclear medicine imaging techniques such as PET are of increasing relevance in pharmaceutical research being valuable (pre)clinical tools to non-invasively assess drug performance in vivo. Therapeutic drugs, e.g. chemotherapeutics, often suffer from a poor balance between their efficacy and toxicity. Here, polymer based drug delivery systems can modulate the pharmacokinetics of low Mw therapeutics (prolonging blood circulation time, reducing toxic side effects, increasing target site accumulation) and therefore leading to a more efficient therapy. In this regard, poly-N-(2-hydroxypropyl)-methacrylamide (HPMA) constitutes a promising biocompatible polymer. Towards the further development of these structures, non-invasive PET imaging allows insight into structure-property relationships in vivo. This performant tool can guide design optimization towards more effective drug delivery. Hence, versatile radiolabeling strategies need to be developed and establishing 18F- as well as 131I-labeling of diverse HPMA architectures forms the basis for short- as well as long-term in vivo evaluations. By means of the prosthetic group [18F]FETos, 18F-labeling of distinct HPMA polymer architectures (homopolymers, amphiphilic copolymers as well as block copolymers) was successfully accomplished enabling their systematic evaluation in tumor bearing rats. These investigations revealed pronounced differences depending on individual polymer characteristics (molecular weight, amphiphilicity due to incorporated hydrophobic laurylmethacrylate (LMA) segments, architecture) as well as on the studied tumor model. Polymers showed higher uptake for up to 4 h p.i. into Walker 256 tumors vs. AT1 tumors (correlating to a higher cellular uptake in vitro). Highest tumor concentrations were found for amphiphilic HPMA-ran-LMA copolymers in comparison to homopolymers and block copolymers. Notably, the random LMA copolymer P4* (Mw=55 kDa, 25% LMA) exhibited most promising in vivo behavior such as highest blood retention as well as tumor uptake. Further studies concentrated on the influence of PEGylation (‘stealth effect’) in terms of improving drug delivery properties of defined polymeric micelles. Here, [18F]fluoroethylation of distinct PEGylated block copolymers (0%, 1%, 5%, 7%, 11% of incorporated PEG2kDa) enabled to systematically study the impact of PEG incorporation ratio and respective architecture on the in vivo performance. Most strikingly, higher PEG content caused prolonged blood circulation as well as a linear increase in tumor uptake (Walker 256 carcinoma). Due to the structural diversity of potential polymeric carrier systems, further versatile 18F-labeling strategies are needed. Therefore, a prosthetic 18F-labeling approach based on the Cu(I)-catalyzed click reaction was established for HPMA-based polymers, providing incorporation of fluorine-18 under mild conditions and in high yields. On this basis, a preliminary µPET study of a HPMA-based polymer – radiolabeled via the prosthetic group [18F]F-PEG3-N3 – was successfully accomplished. By revealing early pharmacokinetics, 18F-labeling enables to time-efficiently assess the potential of HPMA polymers for efficient drug delivery. Yet, investigating the long-term fate is essential, especially regarding prolonged circulation properties and passive tumor accumulation (EPR effect). Therefore, radiolabeling of diverse HPMA copolymers with the longer-lived isotope iodine-131 was accomplished enabling in vivo evaluation of copolymer P4* over several days. In this study, tumor retention of 131I-P4* could be demonstrated at least over 48h with concurrent blood clearance thereby confirming promising tumor targeting properties of amphiphilic HPMA copolymer systems based on the EPR effect.

Strukturen des menschlichen Miteinander - auf dem Weg zum Anderen : dialogische Ansätze vor dem Hintergrund von Robert Musils Roman ´Der Mann ohne Eigenschaften´

Diese Ausarbeitung zeigt Strukturen des menschlichen Miteinander im Rahmen einer systematisch-komparatistischen Annäherung ´auf dem Weg zum Anderen´ vor dem Hintergrund von Musils Roman ´Der Mann ohne Eigenschaften´ auf; sie verweist auf die Gefahren des zunehmend selbstzentrierten Identitätsdenkens, indem sie mit Blick auf den Anfang des 20. Jahrhunderts eine Auswahl philosophischer Denker aus dieser Zeit auf Grundlage einer poetischen Orientierung in ein Gespräch geführt, das damals in Wirklichkeit leider nicht stattgefunden hat: Ulrich, der Protagonist des Romans, übernimmt in dieser Ausarbeitung neben der poetisch-orientierenden Funktion die Rolle des Begleiters; er leitet den Leser durch die Arbeit und verbindet ´auf dem Weg zum Anderen´ philosophische Richtungen mit Musils Roman. Mit der Metapher vom ´Konflikt der beiden Bäume´, den Ulrich in sich bemerkt, beginnt der ´Weg zum Anderen´: Unter beiden Bäumen wird menschlichem Miteinander nachgespürt,indem phänomenologische Ansätze dargestellt, analysiert und komparatistisch betrachtet werden. Der ´Baum des harten Gewirrs´ steht für distanziertes Erkennen; Husserls Intentionalität und Intersubjektivität führen in ein ´Konzert einsamer Monaden´. Der ´Baum der Schatten und Träume´ - repräsentiert durch Klages - steht für verschmelzend mystisch-pathisches Erleben, das Menschen ebenfalls isoliert. Eine Verbindung der beiden Bäume erfolgt in der ´Begegnung zwischen den Bäumen´ im menschlichen Miteinander von Ulrich und seiner Schwester Agathe; hier gedeiht – um im Bild zu bleiben – der ´Baum des Lebens´ auf dem Boden der ´Notwendigkeit des Du für das Ich´. Dieser Baum wird vorgestellt hinsichtlich seiner Verwurzelung: Ansätze Feuerbachs, Diltheys und Plessners verweisen auf Gemeinschaftlichkeit, Geschichtlichkeit und Exzentrizität des Menschen. Daran schließt sich die Analyse der Struktur des Baumes an: Hier verweist Löwiths Ansatz auf die im Menschen angelegte ontologisch-konstitutionelle Zweideutigkeit. In der Krone des ´Lebensbaumes´ suchen die Dialogiker Buber, Rosenzweig und Rosenstock-Huessy nach Gleichursprünglichkeit in der ´Sphäre des Zwischen´ und beschreiten den Weg von der Menschwerdung in der ´Sphäre des Zwischen´ zu einer gelebten voraussetzungsvollen Mitmenschlichkeit im Horizont gesprochener Sprache. Komparatistische Betrachtungen offenbaren divergierende Tendenzen, die im Resümee verdichtet aufgezeigt werden: Unter philosophisch-inhaltlichem Aspekt wird dargestellt, warum Menschen ´unter beiden Bäumen´ in einsamer Beschränktheit und Endlichkeit verharren, während sie in ´Begegnung zwischen den Bäumen´ - im menschlichen Miteinander - Freiheit und Unendlichkeit erlangen: ´Haltung versus Eingebundenheit´ entscheidet über isoliertes oder gelingendes Leben. Unter philosophisch-kulturwissenschaftlichem Aspekt werden Spuren in Musils Roman ´Der Mann ohne Eigenschaften´ aufgedeckt, die vermuten lassen, Musil habe über seinen Roman Dialogisches Denken ´inkognito´ vermitteln wollen; die darin erweckte Sehnsucht nach menschlichem Miteinander gilt es, im Leben zu verantworten – zwischen Menschen, konkret und immer wieder...