QQˉQ\bar Q potential from AdS-CFT relation at T≥0T\geq 0: Dependence on orientation in internal space and higher curvature corrections

Within the classical approximation we calculate the static $Q\bar Q$ potential via the AdS/CFT relation for nonzero temperature and arbitrary internal orientation of the quarks. We use a higher order curvature corrected target space background. For timelike Wilson loops there arises a critical line in the orientation-distance plane which is shifted to larger distances relative to the calculation with uncorrected background. Beyond that line there is no $Q\bar Q$-force. The overall vanishing of the force for antipodal orientation known from zero tempera ture remains valid. The spacelike Wilson loops yield a string tension for a (2+1)-dimensional gauge theory, independent of the relative internal orientation, but sensitive to the background correction.Comment: Used background has been adapted to hep-th/9808126 and revised version of hep-th/9805156, slightly changed comment on 1/L ter

Two and three-point functions in Liouville theory

Based on our generalization of the Goulian-Li continuation in the power of the 2D cosmological term we construct the two and three-point correlation functions for Liouville exponentials with generic real coefficients. As a strong argument in favour of the procedure we prove the Liouville equation of motion on the level of three-point functions. The analytical structure of the correlation functions as well as some of its consequences for string theory are discussed. This includes a conjecture on the mass shell condition for excitations of noncritical strings. We also make a comment concerning the correlation functions of the Liouville field itself.Comment: 15 pages, Latex, Revised version: A sign error in formula (50) is correcte

Bayesian analysis of interiors of HD 219134b, Kepler-10b, Kepler-93b, CoRoT-7b, 55 Cnc e, and HD 97658b using stellar abundance proxies

Using a generalized Bayesian inference method, we aim to explore the possible interior structures of six selected exoplanets for which planetary mass and radius measurements are available in addition to stellar host abundances: HD~219134b, Kepler-10b, Kepler-93b, CoRoT-7b, 55~Cnc~e, and HD~97658b. We aim to investigate the importance of stellar abundance proxies for the planetary bulk composition (namely Fe/Si and Mg/Si) on prediction of planetary interiors. We performed a full probabilistic Bayesian inference analysis to formally account for observational and model uncertainties while obtaining confidence regions of structural and compositional parameters of core, mantle, ice layer, ocean, and atmosphere. We determined how sensitive our parameter predictions depend on (1) different estimates of bulk abundance constraints and (2) different correlations of bulk abundances between planet and host star. [...] Although the possible ranges of interior structures are large, structural parameters and their correlations are constrained by the sparse data. The probability for the tested exoplanets to be Earth-like is generally very low. Furthermore, we conclude that different estimates of planet bulk abundance constraints mainly affect mantle composition and core size.Comment: Astronomy & Astrophysics, 597, A38 (15 pages, 9 figures

Application of discontinuity layout optimization to plane plasticity problems

A new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described. The procedure is used here to determine the critical layout of discontinuities and associated upper-bound limit load for plane plasticity problems. Potential discontinuities, which interlink nodes laid out over the body under consideration, are permitted to crossover one another giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient linear programming solvers can be employed when certain popular failure criteria are specified (e. g. Tresca or Mohr Coulomb in plane strain). Stress/velocity singularities are automatically identified and visual interpretation of the output is straightforward. The procedure, coined 'discontinuity layout optimization' (DLO), is related to that used to identify the optimum layout of bars in trusses, with discontinuities (e. g. slip-lines) in a translational failure mechanism corresponding to bars in an optimum truss. Hence, a recently developed adaptive nodal connection strategy developed for truss layout optimization problems can advantageously be applied here. The procedure is used to identify critical translational failure mechanisms for selected metal forming and soil mechanics problems. Close agreement with the exact analytical solutions is obtained

Biomimetic bilayer membranes made from polymers and lipids

Amphiphile Blockcopolymere sind in der Lage in Wasser Morphologien auszubilden, die analog sind zur hydrophil-hydrophob-hydrophil-Struktur von natürlichen Lipiddoppelschichten. In dieser Arbeit wird zum ersten Mal die Präparation und Charakterisierung von oberflächengestützten Polymerdoppelschichten aus Polybutadien-b-Polyethylenoxid (PB-PEO) beschrieben. Für die Herstellung dieser Strukturen wurden zwei unterschiedliche Präparationsstrategien verfolgt. Der erste Weg besteht aus einer zweistufigen Methode, bei der im ersten Schritt organisierte Monoschichten mittels Langmuir-Blodgett-Transfer auf Gold übertragen und kovalent angebunden werden. Im zweiten Schritt werden hydrophobe Wechselwirkungen ausgenutzt, um über Langmuir-Schaefer-Transfer eine weitere Schicht aufzubringen. Somit wurden homogene Architekturen erzeugt, die oberflächengestützten Lipiddoppelschichten gleichen. Als alternativer, einstufiger Ansatz zur Herstellung von Polymerdoppelschichten wurde das Spreiten von Polymervesikeln auf Gold verfolgt. Auch hierdurch ließen sich Doppelschichtstrukturen mit einer vollständigen Oberflächenbedeckung erzeugen. Die hergestellten Polymerdoppelschichten besitzen eine Dicke von 11-14 nm, die von der Präparationsmethode abhängt. Die Polymerstrukturen weisen bei Trocknung für 1.5 h eine Stabilität gegenüber Luft auf. Bei längeren Trocknungszeiten von ca. 12 h kommt es zu einer Reorganisation der Oberfläche. Dies deutet darauf hin, dass Wasser dazu notwendig ist die Strukturen auf lange Sicht zu stabilisieren. Um die Biokompatibilität der Polymerschichten nachzuweisen, wurden die Wechselwirkungen mit dem membranaktiven Peptid Polymyxin B und dem Transmembranprotein α-Haemolysin gezeigt. Mobilität ist ein wichtiger Faktor für die korrekte Funktion vieler Transmembranproteine. Um die laterale Diffusionsdynamik innerhalb der künstlichen Strukturen zu untersuchen, wurde die Mobilität eines integralen Modellpeptids und von fluoreszierenden Membransonden gemessen. Es konnte mit einzelmolekülempfindlichen Techniken gezeigt werden, dass das α-helikale Peptid und die kleinen Fluoreszenzfarbstoffe frei im hydrophoben Kern der Polymerdoppelschicht diffundieren können. Die Diffusion von beiden Spezies scheint stark von der Fluidität der Polymermatrix beeinflusst zu sein. Ein weiterer Teil dieser Arbeit widmet sich der Entwicklung eines angemessenen, lipidbasierten Referenzsystems für zukünftige Proteinuntersuchungen. Hierzu wurde eine neue Methode zu Herstellung von peptidgestützten Lipiddoppelschichtmembranen entwickelt. Dies wurde durch kovalente Befestigung eines Thiopeptids an einen Goldfilm und darauffolgende Anbindung eines Lipids erreicht. Zur Ausbildung der Lipiddoppelschicht auf dem Lipopeptidunterbau wurder der Rapid Solvent Exchange verwendet. Die Ausbildung der Lipiddoppelschicht wurde sowohl auf microskopischer als auch auf makroskopischer Ebene nachgewiesen. Im letzten Schritt wurde die Anwendbarkeit des Modelsystems für elektrochemische Messungen durch den funktionalen Einbau des Ionentransporters Valinomycin unter Beweis gestellt.Amphiphilic block copolymers form morphologies in water which are similar to the hydrophilic-hydrophobic-hydrophilic structure of natural lipid bilayers. In this thesis the preparation of solid supported polymer bilayers from poly (butadiene)-b-poly(ethylene oxide) (PB-PEO) and their physicochemical characterization is presented. Two different strategies for the preparation of polymeric bilayers were developed. The first route is a two step process utilizing an organized monolayer which was covalently attached to ultrasmooth gold upon Langmuir-Blodgett transfer. Hydrophobic interactions, on the other hand, were exploited to attach the second monolayer via Langmuir-Schaefer transfer. As a result, a homogeneous structure, similar to supported lipid bilayers was obtained. Alternatively vesicle spreading on gold is presented as an easy one step route to supported polymer bilayers. Again this produces bilayer coated surfaces with a high coverage. The prepared polymer bilayers possess a thickness of 11-14 nm depending on the preparation technique. The polymer structures resist drying for about 1.5 hours but disassemble after longer drying periods of 12 hours. This means that water is still necessary to stabilize these morphologies in the long term. To prove the biocompatibility it was shown that the membrane active peptide polymyxin B and the transmembrane protein α-haemolysin interact with the artificial membrane structure. rnMobility is an important factor for the correct function of many transmembrane proteins. To evaluate the lateral mobility of an integral model peptide and fluorescent membrane probes within the polymer bilayer plane 2D-diffusion was studied. It was proven by single molecule sensitive techniques that an α-helical peptide as well as small fluorescent probes can diffuse freely along the bilayer. The diffusion of either species seems to be strongly coupled to the fluidity of the membrane constituting matrix.rnA separate part of this thesis was dedicated to the search for an appropriate lipid based reference system for future protein studies. Therefore a new preparation route towards a peptide tethered lipid bilayer membrane was developed. This was achieved by covalent binding of a thiopeptide to a gold support and subsequent coupling of a lipid to that layer. The bilayer built-up on top of the produced lipopeptide support is completed through rapid solvent exchange. The lipid bilayer formation was proven microscopically as well as macroscopically. Finally the applicability of the model system for electrochemical measurements of transmembrane proteins was demonstrated with the functional incorporation of the ion carrier valinomycin.r