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.

Nanoscopic studies of conjugated polymer blends by (electric) scanning probe microscopy

Conjugated polymers and conjugated polymer blends have attracted great interest due to their potential applications in biosensors and organic electronics. The sub-100 nm morphology of these materials is known to heavily influence their electromechanical properties and the performance of devices they are part of. Electromechanical properties include charge injection, transport, recombination, and trapping, the phase behavior and the mechanical robustness of polymers and blends. Electrical scanning probe microscopy techniques are ideal tools to measure simultaneously electric (conductivity and surface potential) and dielectric (dielectric constant) properties, surface morphology, and mechanical properties of thin films of conjugated polymers and their blends.rnIn this thesis, I first present a combined topography, Kelvin probe force microscopy (KPFM), and scanning conductive torsion mode microscopy (SCTMM) study on a gold/polystyrene model system. This system is a mimic for conjugated polymer blends where conductive domains (gold nanoparticles) are embedded in a non-conductive matrix (polystyrene film), like for polypyrrole:polystyrene sulfonate (PPy:PSS), and poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS). I controlled the nanoscale morphology of the model by varying the distribution of gold nanoparticles in the polystyrene films. I studied the influence of different morphologies on the surface potential measured by KPFM and on the conductivity measured by SCTMM. By the knowledge I gained from analyzing the data of the model system I was able to predict the nanostructure of a homemade PPy:PSS blend.rnThe morphologic, electric, and dielectric properties of water based conjugated polymer blends, e.g. PPy:PSS or PEDOT:PSS, are known to be influenced by their water content. These properties also influence the macroscopic performance when the polymer blends are employed in a device. In the second part I therefore present an in situ humidity-dependence study on PPy:PSS films spin-coated and drop-coated on hydrophobic highly ordered pyrolytic graphite substrates by KPFM. I additionally used a particular KPFM mode that detects the second harmonic electrostatic force. With this, I obtained images of dielectric constants of samples. Upon increasing relative humidity, the surface morphology and composition of the films changed. I also observed that relative humidity affected thermally unannealed and annealed PPy:PSS films differently. rnThe conductivity of a conjugated polymer may change once it is embedded in a non-conductive matrix, like for PPy embedded in PSS. To measure the conductivity of single conjugated polymer particles, in the third part, I present a direct method based on microscopic four-point probes. I started with metal core-shell and metal bulk particles as models, and measured their conductivities. The study could be extended to measure conductivity of single PPy particles (core-shell and bulk) with a diameter of a few micrometers.

Production of antihydrogen via double charge exchange

Spectroscopy of the 1S-2S transition of antihydrogen confined in a neutral atom trap and comparison with the equivalent spectral line in hydrogen will provide an accurate test of CPT symmetry and the first one in a mixed baryon-lepton system. Also, with neutral antihydrogen atoms, the gravitational interaction between matter and antimatter can be tested unperturbed by the much stronger Coulomb forces.rnAntihydrogen is regularly produced at CERN's Antiproton Decelerator by three-body-recombination (TBR) of one antiproton and two positrons. The method requires injecting antiprotons into a cloud of positrons, which raises the average temperature of the antihydrogen atoms produced way above the typical 0.5 K trap depths of neutral atom traps. Therefore only very few antihydrogen atoms can be confined at a time. Precision measurements, like laser spectroscopy, will greatly benefit from larger numbers of simultaneously trapped antihydrogen atoms.rnTherefore, the ATRAP collaboration developed a different production method that has the potential to create much larger numbers of cold, trappable antihydrogen atoms. Positrons and antiprotons are stored and cooled in a Penning trap in close proximity. Laser excited cesium atoms collide with the positrons, forming Rydberg positronium, a bound state of an electron and a positron. The positronium atoms are no longer confined by the electric potentials of the Penning trap and some drift into the neighboring cloud of antiprotons where, in a second charge exchange collision, they form antihydrogen. The antiprotons remain at rest during the entire process, so much larger numbers of trappable antihydrogen atoms can be produced. Laser excitation is necessary to increase the efficiency of the process since the cross sections for charge-exchange collisions scale with the fourth power of the principal quantum number n.rnThis method, named double charge-exchange, was demonstrated by ATRAP in 2004. Since then, ATRAP constructed a new combined Penning Ioffe trap and a new laser system. The goal of this thesis was to implement the double charge-exchange method in this new apparatus and increase the number of antihydrogen atoms produced.rnCompared to our previous experiment, we could raise the numbers of positronium and antihydrogen atoms produced by two orders of magnitude. Most of this gain is due to the larger positron and antiproton plasmas available by now, but we could also achieve significant improvements in the efficiencies of the individual steps. We therefore showed that the double charge-exchange can produce comparable numbers of antihydrogen as the TBR method, but the fraction of cold, trappable atoms is expected to be much higher. Therefore this work is an important step towards precision measurements with trapped antihydrogen atoms.

Enteric coated mucoadhesive micropellets in rotary agglomeration process for wet spheronization

In this work a generally applicable method for the preparation of mucoadhesive micropellets of 250 to 600µm diameter is presented using rotor processing without the use of electrolytes. The mucoadhesive micropellets were developed to combine the advantages of mucoadhesion and microparticles. It was possible to produce mucoadhesive micropellets based on different mucoadhesive polymers Na-CMC, Na-alginate and chitosan. These micropellets are characterized by a lower friability (6 to 17%) when compared to industrial produced cellulose pellets (Cellets®) (41.5%). They show great tapped density and can be manufactured at high yields. The most influencing variables of the process are the water content at the of the end spraying period, determined by the liquid binder amount, the spraying rate, the inlet air temperature, the airflow and the humidity of the inlet air and the addition of the liquid binder, determined by the spraying rate, the rotor speed and the type of rotor disc. In a subsequent step a fluidized bed coating process was developed. It was possible to manifest a stable process in the Hüttlin Mycrolab® in contrast to the Mini-Glatt® apparatus. To reach enteric resistance, a 70% coating for Na-CMC micropellets, an 85% for chitosan micropellets and a 140% for Na-alginate micropellets, based on the amount of the starting micropellets, was necessary. Comparative dissolution experiments of the mucoadhesive micropellets were performed using the paddle apparatus with and without a sieve inlay, the basket apparatus, the reciprocating cylinder and flow-through cell. The paddle apparatus and the modified flow-through cell method turned out to be successful methods for the dissolution of mucoadhesive micropellets. All dissolution profiles showed an initial burst release followed by a slow release due to diffusion control. Depending on the method, the dissolution profiles changed from immediate release to slow release. The dissolution rate in the paddle apparatus was mainly influenced by the agitation rate whereas the flow-through cell pattern was mainly influenced by the particle size. Also, the logP and the HLB values of different emulsifiers were correlated to transfer HLB values of excipients into logP values and logP values of API´s into HLB values. These experiments did not show promising results. Finally, it was shown that manufacture of mucoadhesive micropellets is successful resulting in product being characterized by enteric resistency combined with high yields and convincing morphology.

Vancomycin-resistente Enterokokken (VRE) bei Patienten und in der aquatischen Umwelt

Vancomycin-resistente Enterokokken (VRE) treten als Erreger von nosokomialen Infektionen immer häufiger auf und schränken die Therapiemöglichkeiten deutlich ein. In den eigenen Untersuchungen wurde das Vorkommen von Vancomycin-resistenten Enterococcus faecium (VREf) bei Patienten und in der aquatischen Umwelt (Abwasser und Oberflächenwasser) über einen Zeitraum von sechs Jahren (2004 bis 2009) untersucht. Eine Genotypisierung mittels Pulsfeld-Gelelektrophorese (PFGE) von 294 VREf sollte Aufschluss über genetische Verwandtschaften geben. rnEs konnte gezeigt werden, dass VREf in der aquatischen Umwelt weit verbreitet sind. In Bezug auf ihre genetische Diversität zeigten sie ein breites Spektrum an Variabilität. Ebenso konnte im zeitlichen Auftreten von VREf-Typen eine Dynamik beobachtet werden, wodurch sich Veränderungen der Population mit zeitlichem Wechsel ergaben. Enge Verwandtschaften zwischen VREf von Patienten und VREf aus der aquatischen Umwelt konnten nachgewiesen werden. Für zwei VREf gelang der Nachweis des Eintrags in die aquatische Umwelt, von Patienten aus dem Krankenhaus als Eintragsquelle ausgehend, während Zeiten eines Ausbruchs mit nosokomialen Erregern auf den Stationen. rnZusätzlich zur VREf-Population wurden außerdem die Wirkungsweise und Effizienz einer Elektroimpulsanlage untersucht, um ein zukunftsorientiertes Verfahren zur Desinfektion von bakteriell belasteten Abwässern zu entwickeln. Weiterführend wurde getestet, inwiefern sich verschiedene klinisch relevante VREf durch ein gepulstes elektrisches Feld abtöten lassen. rnEs konnte gezeigt werden, dass das synergistische Zusammenwirken des elektrischen Feldes und der Prozesstemperatur die Höhe der Keimzahlreduktion der Enterokokken beeinflussen. Dabei wurde eine isolatabhängige Elektroresistenz der VREf gegenüber gepulsten elektrischen Feldern bewiesen. Die untersuchten VREf ließen sich, im Gegensatz zu einem Vancomycin-sensiblen Stamm, nicht effizient durch die Elektroimpulsanlage abtöten, was den praktischen Einsatz einer solchen Elektroimpulsanlage als wirkungsvolles Desinfektionsverfahren in Frage stellte.

Feasibility studies of the pp pi 0 e + e - electromagnetic channel at PANDA

Among all possible realizations of quark and antiquark assembly, the nucleon (the proton and the neutron) is the most stable of all hadrons and consequently has been the subject of intensive studies. Mass, shape, radius and more complex representations of its internal structure are measured since several decades using different probes. The proton (spin 1/2) is described by the electric GE and magnetic GM form factors which characterise its internal structure. The simplest way to measure the proton form factors consists in measuring the angular distribution of the electron-proton elastic scattering accessing the so-called Space-Like region where q2 < 0. Using the crossed channel antiproton proton <--> e+e-, one accesses another kinematical region, the so-called Time-Like region where q2 > 0. However, due to the antiproton proton <--> e+e- threshold q2th, only the kinematical domain q2 > q2th > 0 is available. To access the unphysical region, one may use the antiproton proton --> pi0 e+ e- reaction where the pi0 takes away a part of the system energy allowing q2 to be varied between q2th and almost 0. This thesis aims to show the feasibility of such measurements with the PANDA detector which will be installed on the new high intensity antiproton ring at the FAIR facility at Darmstadt. To describe the antiproton proton --> pi0 e+ e- reaction, a Lagrangian based approach is developed. The 5-fold differential cross section is determined and related to linear combinations of hadronic tensors. Under the assumption of one nucleon exchange, the hadronic tensors are expressed in terms of the 2 complex proton electromagnetic form factors. An extraction method which provides an access to the proton electromagnetic form factor ratio R = |GE|/|GM| and for the first time in an unpolarized experiment to the cosine of the phase difference is developed. Such measurements have never been performed in the unphysical region up to now. Extended simulations were performed to show how the ratio R and the cosine can be extracted from the positron angular distribution. Furthermore, a model is developed for the antiproton proton --> pi0 pi+ pi- background reaction considered as the most dangerous one. The background to signal cross section ratio was estimated under different cut combinations of the particle identification information from the different detectors and of the kinematic fits. The background contribution can be reduced to the percent level or even less. The corresponding signal efficiency ranges from a few % to 30%. The precision on the determination of the ratio R and of the cosine is determined using the expected counting rates via Monte Carlo method. A part of this thesis is also dedicated to more technical work with the study of the prototype of the electromagnetic calorimeter and the determination of its resolution.