Computer simulation studies of vector spin glasses

Die vorliegende Doktorarbeit befasst sich mit klassischen Vektor-Spingläsern eine Art von ungeordneten Magneten - auf verschiedenen Gittertypen. Da siernbedeutsam für eine experimentelle Realisierung sind, ist ein theoretisches Verständnis von Spinglas-Modellen mit wenigen Spinkomponenten und niedriger Gitterdimension von großer Bedeutung. Da sich dies jedoch als sehr schwierigrnerweist, sind neue, aussichtsreiche Ansätze nötig. Diese Arbeit betrachtet daher den Limesrnunendlich vieler Spindimensionen. Darin entstehen mehrere Vereinfachungen im Vergleichrnzu Modellen niedriger Spindimension, so dass für dieses bedeutsame Problem Eigenschaften sowohl bei Temperatur Null als auch bei endlichen Temperaturenrnüberwiegend mit numerischen Methoden ermittelt werden. Sowohl hyperkubische Gitter als auch ein vielseitiges 1d-Modell werden betrachtet. Letzteres erlaubt es, unterschiedliche Universalitätsklassen durch bloßes Abstimmen eines einzigen Parameters zu untersuchen. "Finite-size scaling''-Formen, kritische Exponenten, Quotienten kritischer Exponenten und andere kritische Größen werden nahegelegt und mit numerischen Ergebnissen verglichen. Eine detaillierte Beschreibung der Herleitungen aller numerisch ausgewerteter Gleichungen wird ebenso angegeben. Bei Temperatur Null wird eine gründliche Untersuchung der Grundzustände und Defektenergien gemacht. Eine Reihe interessanter Größen wird analysiert und insbesondere die untere kritische Dimension bestimmt. Bei endlicher Temperatur sind der Ordnungsparameter und die Spinglas-Suszeptibilität über die numerisch berechnete Korrelationsmatrix zugänglich. Das Spinglas-Modell im Limes unendlich vieler Spinkomponenten kann man als Ausgangspunkt zur Untersuchung der natürlicheren Modelle mit niedriger Spindimension betrachten. Wünschenswert wäre natürlich ein Modell, das die Vorteile des ersten mit den Eigenschaften des zweiten verbände. Daher wird in Modell mit Anisotropie vorgeschlagen und getestet, mit welchem versucht wird, dieses Ziel zu erreichen. Es wird auf reizvolle Wege hingewiesen, das Modell zu nutzen und eine tiefergehende Beschäftigung anzuregen. Zuletzt werden sogenannte "real-space" Renormierungsgruppenrechnungen sowohl analytisch als auch numerisch für endlich-dimensionale Vektor-Spingläser mit endlicher Anzahl von Spinkomponenten durchgeführt. Dies wird mit einer zuvor bestimmten neuen Migdal-Kadanoff Rekursionsrelation geschehen. Neben anderen Größen wird die untere kritische Dimension bestimmt.

Analysis of nonlinear diffusion equations of second and fourth order

Wegen der fortschreitenden Miniaturisierung von Halbleiterbauteilen spielen Quanteneffekte eine immer wichtigere Rolle. Quantenphänomene werden gewöhnlich durch kinetische Gleichungen beschrieben, aber manchmal hat eine fluid-dynamische Beschreibung Vorteile: die bessere Nutzbarkeit für numerische Simulationen und die einfachere Vorgabe von Randbedingungen. In dieser Arbeit werden drei Diffusionsgleichungen zweiter und vierter Ordnung untersucht. Der erste Teil behandelt die implizite Zeitdiskretisierung und das Langzeitverhalten einer degenerierten Fokker-Planck-Gleichung. Der zweite Teil der Arbeit besteht aus der Untersuchung des viskosen Quantenhydrodynamischen Modells in einer Raumdimension und dessen Langzeitverhaltens. Im letzten Teil wird die Existenz von Lösungen einer parabolischen Gleichung vierter Ordnung in einer Raumdimension bewiesen, und deren Langzeitverhalten studiert.

Gene therapy for a novel mouse model of Canavan disease

Canavan disease (CD) is a rare leukodystrophy caused by loss-of-function mutations in the gene encoding aspartoacylase (ASPA), an oligodendrocyte-enriched enzyme. It is characterised by the accumulation of the ASPA substrate N-acetylaspartate (NAA) in brain, blood and urine, leading to a spongiform vacuolisation of the brain, severe motoric and cognitive impairments and premature death. To date, no therapy is available due to the lack of a gene-transfer system allowing transgene expression in oligodendrocytes (OLs) and the restoration of the missing enzyme. Hence, the aim of this study was to establish a novel gene-transfer system and its preclinical evaluation in a CD animal model.rnIn the first part of this thesis, a novel ASPA mouse mutant was generated. A βgeo cassette (including the genes encoding β-galactosidase and neomycin) flanked by frt sites was inserted into intron 1 of the intact aspa gene. Additionally, exon 2 was flanked by loxP sites for optional conditional deletion of the targeted locus. The resulting ASPA-deficient aspalacZ/lacZ-mouse was found to be an accurate model of CD and an important tool to identify novel aspects of its complex pathology. Homozygous mutants showed a CD-like histopathology, neurological impairment, behavioural deficits as well as a reduced body weight. Additionally, MRI data revealed changes in brain metabolite composition. rnRecombinant adeno-associated viral (rAAV) vectors have become a versatile tool for gene transfer to the central nervous system because they are efficient, non-toxic and replication-deficient. Based on the natural neurotropism of AAV vectors, AAV-based gene delivery has entered the clinics for the treatment of neurodegenerative diseases. However, the lack of AAV vectors with oligodendroglial tropism has precluded gene therapy for leukodystrophies. In the second part of this work, it was shown that the transduction profile of established AAV serotypes can be targeted towards OLs in a transcriptional approach, using the oligodendrocyte-specific myelin basic protein (MBP) promoter to drive transgene expression in OLs.rnIn the last part of this work, the therapeutic efficacy of AAV-mediated aspa gene transfer to OLs of juvenile aspalacZ/lacZ mice was evaluated. AAV-aspa injections into multiple sites of the brain parenchyma resulted in transduction of OLs in the grey and white matter throughout the brain. Histological abnormalities in the brain of ASPA-deficient mice were ameliorated and accompanied by a reduction of NAA levels. Furthermore, the treatment resulted in normalisation of body weight, motor function and nest-building behaviour. These data provide a proof-of-concept for a successful gene therapy of Canavan disease. This might pave the way towards translation into clinical application and serve as the basis for the genetic treatment of other leukodystrophies.

Multifunctional polyether architectures : versatile materials for surface attachment and functionalization

Chapter 1 of this thesis comprises a review of polyether polyamines, i.e., combinations of polyether scaffolds with polymers bearing multiple amino moieties. Focus is laid on controlled or living polymerization methods. Furthermore, fields in which the combination of cationic, complexing, and pH-sensitive properties of the polyamines and biocompatibility and water-solubility of polyethers promise enormous potential are presented. Applications include stimuli-responsive polymers with a lower critical solution temperature (LCST) and/or the ability to gel, preparation of shell cross-linked (SCL) micelles, gene transfection, and surface functionalization.rnIn Chapter 2, multiaminofunctional polyethers relying on the class of glycidyl amine comonomers for anionic ring-opening polymerization (AROP) are presented. In Chapter 2.1, N,N-diethyl glycidyl amine (DEGA) is introduced for copolymerization with ethylene oxide (EO). Copolymer microstructure is assessed using online 1H NMR kinetics, 13C NMR triad sequence analysis, and differential scanning calorimetry (DSC). The concurrent copolymerization of EO and DEGA is found to result in macromolecules with a gradient structure. The LCSTs of the resulting copolymers can be tailored by adjusting DEGA fraction or pH value of the environment. Quaternization of the amino moieties by methylation results in polyelectrolytes. Block copolymers are used for PEGylated gold nanoparticle formation. Chapter 2.2 deals with a glycidyl amine monomer with a removable protecting group at the amino moiety, for liberation of primary amines at the polyether backbone, which is N,N-diallyl glycidyl amine (DAGA). Its allyl groups are able to withstand the harsh basic conditions of AROP, but can be cleaved homogeneously after polymerization. Gradient as well as block copolymers poly(ethylene glycol)-PDAGA (PEG-PDAGA) are obtained. They are analyzed regarding their microstructure, LCST behavior, and cleavage of the protecting groups. rnChapter 3 describes applications of multi(amino)functional polyethers for functionalization of inorganic surfaces. In Chapter 3.1, they are combined with an acetal-protected catechol initiator, leading to well-defined PEG and heteromultifunctional PEG analogues. After deprotection, multifunctional PEG ligands capable of attaching to a variety of metal oxide surfaces are obtained. In a cooperative project with the Department of Inorganic and Analytical Chemistry, JGU Mainz, their potential is demonstrated on MnO nanoparticles, which are promising candidates as T1 contrast agents in magnetic resonance imaging. The MnO nanoparticles are solubilized in aqueous solution upon ligand exchange. In Chapter 3.2, a concept for passivation and functionalization of glass surfaces towards gold nanorods is developed. Quaternized mPEG-b-PqDEGA diblock copolymers are attached to negatively charged glass surfaces via the cationic PqDEGA blocks. The PEG blocks are able to suppress gold nanorod adsorption on the glass in the flow cell, analyzed by dark field microscopy.rnChapter 4 highlights a straightforward approach to poly(ethylene glycol) macrocycles. Starting from commercially available bishydroxy-PEG, cyclic polymers are available by perallylation and ring-closing metathesis in presence of Grubbs’ catalyst. Purification of cyclic PEG is carried out using α-cyclodextrin. This cyclic sugar derivative forms inclusion complexes with remaining unreacted linear PEG in aqueous solution. Simple filtration leads to pure macrocycles, as evidenced by SEC and MALDI-ToF mass spectrometry. Cyclic polymers from biocompatible precursors are interesting materials regarding their increased blood circulation time compared to their linear counterparts.rnIn the Appendix, A.1, a study of the temperature-dependent water-solubility of polyether copolymers is presented. Macroscopic cloud points, determined by turbidimetry, are compared with microscopic aggregation phenomena, monitored by continuous wave electron paramagnetic resonance (CW EPR) spectroscopy in presence of the amphiphilic spin probe and model drug (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO). These thermoresponsive polymers are promising candidates for molecular transport applications. The same techniques are applied in Chapter A.2 to explore the pH-dependence of the cloud points of PEG-PDEGA copolymers in further detail. It is shown that the introduction of amino moieties at the PEG backbone allows for precise manipulation of complex phase transition modes. In Chapter A.3, multi-hydroxyfunctional polysilanes are presented. They are obtained via copolymerization of the acetal-protected dichloro(isopropylidene glyceryl propyl ether)methylsilane monomer. The hydroxyl groups are liberated through acidic work-up, yielding versatile access to new multifunctional polysilanes.

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.