In dieser Dissertation wird erstmalig ein theoretisches Fundament zur Beschneiung virtueller Szenen entwickelt. Das theoretische Fundament wird als analytisches Modell in Form einer Diffusionsgleichung formuliert. Aus dem analytischen Modell lässt sich eine Gruppe von Algorithmen zur Beschneiung virtueller Szenen ableiten. Eingehende Voruntersuchungen zur allgemeinen Modellierung natürlicher Phänomene in der Computergraphik sowie eine Klassifikation der bestehenden Literatur über mathematische Schneemodellierung bilden den Anfang der Arbeit. Aus der umfassenden Darstellung der Eigenschaften von Schnee, wie er in der Natur vorkommt, ergeben sich die Grundlagen für die Modellbildung. Die Modellbildung fußt auf den grundlegenden Ansätzen der klassischen Mechanik und der statistischen Physik. Für die Beschneiung auf visueller Skala erweist sich der Diffusionsprozess als geeignete Beschreibung. Mit der Beschreibung lassen sich diffusiv Schneeoberflächen erzeugen. Der konkrete computergraphische Wert des theoretischen Fundaments wird anhand zweier Implementierungen exemplarisch dargestellt, und zwar in der Distanzfeldmethode und der Diffusionskernmethode. Die Ergebnisse werden mithilfe dreidimensionaler Rauschtexturen und Alpha-Masken an den Rändern fotorealistisch visualisiert. / In this dissertation for the first time a theoretical foundation is developed for snow accumulation in virtual scenes. The theoretical foundation is formulated in an analytical model as diffusion equation. The analytical model leads to a group of algorithms for virtual snow accumulation. Comprehensive investigations for the modelling of natural phenomena in computer graphics in general are used to develop a method classification scheme. Another classification is given for an overview over the aspects of snow in the real world. This allows an efficient presentation of related literature on snow modelling. A new approach of snow modelling is then drawn from first principles of classical mechanics and statistical physics. Diffusion processes provide an efficient theoretical framework for snow accumulation. The mathematical structure of diffusion equations is discussed and demonstrated to be adequate to snow modelling in visual scales. The value of the theoretical foundation for computer graphics is demonstrated with two exemplary implementations, a distance field method and the diffusion kernel method. Results are visualized with 3D noise textures and alpha masks near borders delivering photorealistic snow pictures.

No description available.

No description available.

No description available.

No description available.

No description available.

Topological states of matter are a novel family of phases that elude the conventional Landau paradigm of phase transitions. Topological phases are characterized by global topological invariants which are typically reflected in the quantization of physical observables. Moreover, their characteristic bulk-boundary correspondence often gives rise to robust surface modes with exceptional features, such as dissipationless charge transport or non-Abelian statistics. In this way, the study of topological states of matter not only broadens our knowledge of matter but could potentially lead to a whole new range of technologies and applications. In this light, it is of great interest to find novel topological phases and to study their unique properties. In this work, novel manifestations of topological states of matter are studied as they arise when materials are subject to additional symmetries. It is demonstrated how symmetries can profoundly enrich the topology of a system. More specifically, it is shown how symmetries lead to additional nontrivial states in systems which are already topological, drive trivial systems into a topological phase, lead to the quantization of formerly non-quantized observables, and give rise to novel manifestations of topological surface states. In doing so, this work concentrates on weakly interacting systems that can theoretically be described in a single-particle picture. In particular, insulating and semi-metallic topological phases in one, two, and three dimensions are investigated theoretically using single-particle techniques.

The thesis is devoted to some aspects of the solid-state electronic transport in the so-called viscous or hydrodynamic regime. Hydrodynamic regime in this context means that due to the large carrier density and non-negligible carrier-carrier interactions, the transport properties follow from collective, rather than single-particle phenomena. To capture the dynamics of such a system one may use description based on the conserved quantities, i.e. momentum, energy or charge. If the interactions between the constituents of the system are strong enough, such a description is provided by the hydrodynamic equations which for conserved momentum and energy are the Navier-Stokes equations or their relativistic counterparts. This thesis focuses on such a situation: when the equations governing transport properties follow from conservation of the momentum or, at most, can be treated as a modification of such equations due to weak momentum relaxation. Presented here are two lines of investigation. The first one focuses on the mesoscopic effects, i.e. on the dependence of the outcome of the transport measurements on the physical parameters of the sample such as size and shape. Here also the effects of the weak momentum relaxation are studied. In the second one, the issue of parity and time reversal symmetry breaking, occurring in a 2 dimensional system due to the presence of an external magnetic field, is investigated. An effective model of a strongly coupled quantum system is introduced and used to compute the odd (Hall) viscosity -- a transport coefficient allowed once the discrete symmetries are broken -- as a function of magnetic field, temperature and chemical potential. The first part of results concerns the behaviour of the electronic fluid in a typical AC measurement -- modeled by an elongated channel in which the fluid is subject to a periodically time dependent electric potential. Assuming standard, no-slip boundary conditions, the spatial distribution of the current density is found to be much different to the one known for Ohmic conduction. For small frequency the current distribution has a parabolic profile across the channel, while for high frequency the current in the bulk of the channel becomes flat (position-independent), while two maxima terminating a so-called boundary layer develop. In these boundary layers large gradients of current can be found, contributing to high local entropy production due to the viscous force. Despite this differences in the local current density profile, when the global conductance is measured as a function of the frequency, the result much resembles the well known Drude curve, with a distinct maximum visible in the imaginary part of the AC conductance. There is, however, a global signature of the boundary layer formation -- the scaling of the conductance with the channel width, that changes from quadratic (for parabolic flow) to asymptotically constant (for a flow with boundary layers). Moreover, in the hydrodynamic regime, the position of the Drude peak is not only determined by microscopic parameter but again by a combination of microscopic (viscosity) and mesoscopic (width) parameters. Since the Drude peak occurs for experimentally feasible values of parameters, the mentioned mesoscopic dependence may be used to measure the value of viscosity coefficient. The results discussed above are obtained assuming, as is traditional for hydrodynamics on everyday length-scales, a no-slip boundary condition which forces the fluid to be immobile at the boundary. This boundary condition was also assumed in most of the previous works on the electronic hydrodynamics. However, this is not the only possibility. There exists a one-parameter family of consistent boundary conditions involving velocity and its derivative on the boundary, parametrized by a coefficient called the slip length. Recent theoretical and experimental publications suggest that it may be dependent on the state parameters of the system (i.e temperature, chemical potential) and its value may be relatively large for some experimental situations. One of the consequences of the slip length being large is that hydrodynamic effects are obscured in the simple AC set-up discussed before. In this work it is shown that by an appropriate micro-structuring of the boundary, the effects of slip can be suppressed. Once the array of defects is introduced on the edges of the sample, the no-slip behavior is restored for all the values of the microscopic slip length. Furthermore, the interplay between the microscopic slip length and the sample geometry is investigated and used to propose a simple device for measuring the dependence of the microscopic slip length on the state parameters such as the temperature or the chemical potential. The final part of this thesis is devoted to a different aspect of the hydrodynamic transport -- a computation of the value of hydrodynamic transport coefficients using a microscopic theory. The physical situation of interest is one in which time reversal and parity invariance of a 2-dimensional system are broken, due to the presence of an external magnetic field. In such a situation an unusual class of transport coefficients is allowed in the hydrodynamic description, so-called odd coefficients. The term comes from the fact that they encode response that is transverse to the applied perturbation. These odd coefficients for 2 dimensions were previously studied mostly at weak coupling, i.e. using descriptions based on quasi-particles. This work, however, presents the way of calculating them for strongly coupled model system. To achieve this a high-energy-physics-inspired framework of holographic duality (AdS/CFT) is used. In that approach, an effective model involving magnetically-sourced parity-breaking interactions is constructed for the system at finite temperature and chemical potential. Performing a linear response analysis around the thermal states in that model allows one to read off the transport coefficients, especially the odd (Hall) viscosity coefficient that is of central interest in this study. The mentioned Hall viscosity is found to be non-zero whenever the magnetic field is present, even for zero chemical potential. This is unusual, as odd viscosity is expected to only be non-zero for non-zero charge density states. The mechanism responsible for the presence of Hall viscosity in the discussed case turns out to be the following: charge density in the model is induced by either the chemical potential or the magnetic field, i.e. for non-zero magnetic field even at zero chemical potential some density of charge is present. This charge contributes to the Hall viscosity in the usual way. The odd viscosity coefficient is found to have different scaling behaviors for weak and strong magnetic field. Interestingly, it turns out that the computations of the Hall (and shear) viscosities are relatively straightforward and analytically tractable in the proposed model. This means that the results could be generalized to the zero-temperature case, which however is yet to be done. It also suggests that the model may capture some universal mechanisms of generating the odd viscosity due to the presence of the magnetic field. That intuition is backed by the fact that some of the effective models of quantum Hall states also predict similar mechanism in which charge density is induced by the presence of the magnetic field. Despite these similarities, further studies are needed to establish a solid connection between these systems. In particular, in the model under consideration no mechanism of quantization of the Hall viscosity is found, while the mentioned models of quantum Hall states predict quantization of that transport coefficient.

This work is about the reaction around both isomeres of formylcations, formylcation (HCO+) and isoformylcation (HOC+). In interstellar chemistry these isomeres are of significant importance: radio astronomic measurements have detected the metastabil isomere HOC+ in present of the stabil isomere HCO+ in many objects. The HOC+ was found in photon dominated regions like (SgrB2, NGC 7538 und NGC 2024) as well as in dense clouds like DR21 (OH), W51M, W3 (OH), Orion (3N, 1E)). The ratecoefficiants for reactions forming both isomeres have been measured. Further more the ratecoefficiant for the isomerisation of isoformyl (HOC+) with molecular hydrogen has been measured at 25 K. / In der vorliegenden Arbeit werden Untersuchungen zu dem Ionensystem Formylkationen (HCO+) / Isoformylkationen (HOC+) vorgestellt. In der interstellaren Chemie kommt diesen Isomeren eine hohe Bedeutung zu: neuere radioastronomische Beobachtungen haben das metastabile Ion HOC+ in Anwesenheit des stabilen Isomers HCO+ in einer Vielzahl von interstellaren Umgebungen nachgewiesen. Das HOC+ - Isomer ist in signifikanter Dichte sowohl in Photon - dominierten Gebieten (wie z.B. SgrB2, NGC 7538 und NGC 2024) als auch in Dichten Molekularen Wolken (wie z.B. DR21 (OH), W51M, W3 (OH), Orion (3N, 1E), Orion KL, und G34.3) festgestellt worden. Es konnten die Ratenkoeffizienten für die Bildungsreaktionen beider Isomere bestimmt werden. Des weiteren konnte die Isomerisierung von Isoformylkationen (HOC+) mit Wasserstoff (H2) bei 25 K estimmt werden.

Gegenstand dieser Arbeit ist die Herstellung und Charakterisierung von metall-organisch deponierten (MOD) Pufferschichten für den Hochtemperatursupraleiter YBa2Cu3O7 . Dazu wurde die Texturbildung in CeO2, Gd-dotiertem CeO2 (CGO) und Yttrium-stabilisiertem Zirkondioxid (YSZ) durch epitaktisches Wachstum auf YSZ-Substraten verschiedener Rauhigkeit und Textur untersucht. Nach Deposition der Precursorlösung (Ce-Acetylacetonat in einem Essigsäure/iso-Propanolgemisch) mittels Spin-coating wurden die Proben in einer Ar/H2-Athmosphäre bzw. an Luft bei 700-1300°C ausgelagert, wobei zunächst ein nanokristallines Gefüge entsteht.Nach Bildung einer epitaktischen Keimschicht an der Substratoberfläche konkurrieren während des weiteren Wachstums Kornvergröberung in der polykristallinen Deckschicht und epitaktisches Schichtwachstum miteinander. Die treibende Kraft für beide Prozesse resultiert dabei aus der hohen Korngrenzenergiedichte des nanokristallinen Precursorgefüges. Das Schichtwachstum wurde u.a. mit Röntgenverfahren und RHEED (Reflection High Energy Electron Diffraction) verfolgt. Eine biaxiale Textur wurde mit Röntgenverfahren im Falle des CGO auf YSZ-(001)-Einkristallen schon bei Auslagerungstemperaturen von ca. 790°C beobachtet, während eine epitaxiefähige Oberfläche erst bei Temperaturen von 1200-1300°C auftrat. Bei Auslagerungstemperaturen von 790°C verhindert eine untexturierte Deckschicht in der MOD-Schicht ein epitaktisches Anwachsen des YBa2Cu3O7.Die Untersuchung des Wachstumsverhaltens auf technischen IBAD(Ion-Beam-Assisted-Deposition)-YSZ Substraten ergab, daß die Oberflächenrauhigkeit die maßgebliche Einflussgröße ist, die die Erhöhung der mit Röntgenmethoden gemessenen optimalen Auslagerungsbedingungen bestimmt.Die Eignung der mit MOD hergestellten Pufferschichten als Substrat für ein biaxiales Aufwachsen der supraleitenden Schicht wurde durch die hohen Stromtragfähigkeiten nachgewiesen, die in den supraleitenden Filmen erreicht wurden.