Monte-Carlo-Simulationen zum Phasen- und Keimbildungsverhalten von Polymerlösungen

Das Phasenverhalten und die Grenzflächeneigenschaften vonPolymeren in superkritischer Lösung werden anhand einesvergröberten Kugel-Feder-Modells für das ReferenzsystemHexadekan-CO2 untersucht. Zur Bestimmung der Parameter imPotential setzt man die kritischen Punkte von Simulation undExperiment gleich. Wechselwirkungen zwischen beidenKomponenten werden durch eine modifizierteLorentz-Berthelot-Regel modelliert. Die Übereinstimmung mitden Experimenten ist sehr gut - insbesondere kann dasPhasendiagramm des Mischsystems inklusive kritischer Linienreproduziert werden. Ein Vergleich mit numerischenStörungsrechnungen (TPT1) liefert eine qualitativeÜbereinstimmung und Hinweise zur Verbesserung derverwendeten Zustandsgleichung. Aufbauend auf diesen Betrachtungen werden die Frühstadiender Keimbildung untersucht. Für das Lennard-Jones-Systemwird zum ersten Mal der Übergang vom homogenen Gas zu einemeinzelnen Tropfen im endlichen Volumen direkt nachgewiesenund quantifiziert. Die freie Energie von kleinen Clusternwird mit einem einfachen, klassischen Nukleationsmodellbestimmt und nach oben abgeschätzt. Die vorgestellten Untersuchungen wurden durch eineWeiterentwicklung des Umbrella-Sampling-Algorithmusermöglicht. Hierbei wird die Simulation in mehrereSimulationsfenster unterteilt, die nacheinander abgearbeitetwerden. Die Methode erlaubt eine Bestimmung derFreien-Energie-Landschaft an einer beliebigen Stelle desPhasendiagramms. Der Fehler ist kontrollierbar undunabhängig von der Art der Unterteilung.

Geochronology, geochemistry and isotopic compositions of the volcanic rocks from oceanic (Hawaii) and continental (Eifel) intra-plate environments

The Eifel volcanism is part of the Central European Volcanic Province (CEVP) and is located in the Rhenish Massif, close to the Rhine and Leine Grabens. The Quaternary Eifel volcanism appears to be related to a mantle plume activity. However, the causes of the Tertiary Hocheifel volcanism remain debated. We present geochronological, geochemical and isotope data to assess the geotectonic settings of the Tertiary Eifel volcanism. Based on 40Ar/39Ar dating, we were able to identify two periods in the Hocheifel activity: from 43.6 to 39.0 Ma and from 37.5 to 35.0 Ma. We also show that the pre-rifting volcanism in the northernmost Upper Rhine Graben (59 to 47 Ma) closely precede the Hocheifel volcanic activity. In addition, the volcanism propagates from south to north within the older phase of the Hocheifel activity. At the time of Hocheifel volcanism, the tectonic activity in the Hocheifel was controlled by stress field conditions identical to those of the Upper Rhine Graben. Therefore, magma generation in the Hocheifel appears to be caused by decompression due to Middle to Late Eocene extension. Our geochemical data indicate that the Hocheifel magmas were produced by partial melting of a garnet peridotite at 75-90 km depth. We also show that crustal contamination is minor although the magmas erupted through a relatively thick continental lithosphere. Sr, Nd and Pb isotopic compositions suggest that the source of the Hocheifel magmas is a mixing between depleted FOZO or HIMU-like material and enriched EM2-like material. The Tertiary Hocheifel and the Quaternary Eifel lavas appear to have a common enriched end-member. However, the other sources are likely to be distinct. In addition, the Hocheifel lavas share a depleted component with the other Tertiary CEVP lavas. Although the Tertiary Hocheifel and the Quaternary Eifel lavas appear to originate from different sources, the potential involvement of a FOZO-like component would indicate the contribution of deep mantle material. Thus, on the basis of the geochemical and isotope data, we cannot rule out the involvement of plume-type material in the Hocheifel magmas. The Ko’olau Scientific Drilling Project (KSDP) has been initiated in order to evaluate the long-term evolution of Ko’olau volcano and obtain information about the Hawaiian mantle plume. High precision Pb triple spike data, as well as Sr and Nd isotope data on KSDP lavas and Honolulu Volcanics (HVS) reveal compositional source variations during Ko’olau growth. Pb isotopic compositions indicate that, at least, three Pb end-members are present in Ko’olau lavas. Changes in the contributions of each component are recorded in the Pb, Sr and Nd isotopes stratigraphy. The radiogenic component is present, at variable proportion, in all three stages of Ko’olau growth. It shows affinities with the least radiogenic “Kea-lo8” lavas present in Mauna Kea. The first unradiogenic component was present in the main-shield stage of Ko’olau growth but its contribution decreased with time. It has EM1 type characteristics and corresponds to the “Ko’olau” component of Hawaiian mantle plume. The second unradiogenic end-member, so far only sampled by Honololu lavas, has isotopic characteristics similar to those of a depleted mantle. However, they are different from those of the recent Pacific lithosphere (EPR MORB) indicating that the HVS are not derived from MORB-related source. We suggest, instead, that the HVS result from melting of a plume material. Thus the evolution of a single Hawaiian volcano records the geochemical and isotopic changes within the Hawaiian plume.

Renormalization of fermion mixing

Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by hermiticity. After analysing the complete renormalized Lagrangian in a general theory including vector and scalar bosons with arbitrary renormalizable interactions, we consider two specific models: quark mixing in the electroweak Standard Model and mixing of Majorana neutrinos in the seesaw mechanism. A counter term for fermion mixing matrices can not be fixed by only taking into account self-energy corrections or fermion field renormalization constants. The presence of unstable particles in the theory can lead to a non-unitary renormalized mixing matrix or to a gauge parameter dependence in its counter term. Therefore, we propose to determine the mixing matrix counter term by fixing the complete correction terms for a physical process to experimental measurements. As an example, we calculate the decay rate of a top quark and of a heavy neutrino. We provide in each of the chosen models sample calculations that can be easily extended to other theories.

Effect of mixing, particle interaction, and spatial dimension on the glass transition

In this thesis, the influence of composition changes on the glass transition behavior of binary liquids in two and three spatial dimensions (2D/3D) is studied in the framework of mode-coupling theory (MCT).The well-established MCT equations are generalized to isotropic and homogeneous multicomponent liquids in arbitrary spatial dimensions. Furthermore, a new method is introduced which allows a fast and precise determination of special properties of glass transition lines. The new equations are then applied to the following model systems: binary mixtures of hard disks/spheres in 2D/3D, binary mixtures of dipolar point particles in 2D, and binary mixtures of dipolar hard disks in 2D. Some general features of the glass transition lines are also discussed. The direct comparison of the binary hard disk/sphere models in 2D/3D shows similar qualitative behavior. Particularly, for binary mixtures of hard disks in 2D the same four so-called mixing effects are identified as have been found before by Götze and Voigtmann for binary hard spheres in 3D [Phys. Rev. E 67, 021502 (2003)]. For instance, depending on the size disparity, adding a second component to a one-component liquid may lead to a stabilization of either the liquid or the glassy state. The MCT results for the 2D system are on a qualitative level in agreement with available computer simulation data. Furthermore, the glass transition diagram found for binary hard disks in 2D strongly resembles the corresponding random close packing diagram. Concerning dipolar systems, it is demonstrated that the experimental system of König et al. [Eur. Phys. J. E 18, 287 (2005)] is well described by binary point dipoles in 2D through a comparison between the experimental partial structure factors and those from computer simulations. For such mixtures of point particles it is demonstrated that MCT predicts always a plasticization effect, i.e. a stabilization of the liquid state due to mixing, in contrast to binary hard disks in 2D or binary hard spheres in 3D. It is demonstrated that the predicted plasticization effect is in qualitative agreement with experimental results. Finally, a glass transition diagram for binary mixtures of dipolar hard disks in 2D is calculated. These results demonstrate that at higher packing fractions there is a competition between the mixing effects occurring for binary hard disks in 2D and those for binary point dipoles in 2D.