<P> In this thesis, we mainly study geodesics on various two dimensional surfaces. All the background material needed throughout the thesis is provided, including an explanation of the theory of geodesics. We will calculate geodesics using two numerical methods: Euler's method and Runge-Kutta method of fourth order. Using Maple, we will test the accuracy of the numerical methods on a test case surface, the Poincare half plane. Later, we proceed to investigate several interesting surfaces by numerically calculating geodesics. From the investigated surfaces, we will draw similarities between the human cerebral cortex and certain surfaces. The human cerebral cortex is the most intensely studied part of the brain and it is believe that their exists a relation between the function and structure of the cortex. Geodesic analysis can possibly be an essential tool in better understanding the cortical surface as it is in many disciplines of science to understand the nature of physical based problems. </P> / Thesis / Master of Science (MSc)

The aim of this study is to seek to determine the philosophic grounds which prompt this painter in particular to incorporate both two- and three-dimensional space within each painting.

In treating the motion of a fluid mathematically, it is convenient to make some simplifying assumptions. The assumptions which are made will be justifiable if they save long and laborious computations in practical problems, and if the predicted results agree closely enough with experimental results for practical use. In dealing with the flow of air about an airfoil, at subsonic speeds, the fluid will be considered as a homogeneous, incompressible, inviscid fluid.

Modern semiconductor fabrication techniques allow for the fabrication of semiconductor heterostructures which host electron transport with a minimum of scattering sites. In such devices, electrons populate a two-dimensional electron gas (2DEG) in which electrons propagate in exactly two dimensions, and may be further confined by potential barriers to form electron billiards. At sub-Kelvin temperatures, electron trajectories are determined largely by reflections from the billiard walls, while net conduction through the device depends on quantum mechanical wave interference. Measurements of magnetoconductance fluctuations (MCF) serve as a probe of dynamics within the electron billiard. Many prior studies have utilized heterostructures employing the modulation doping architecture, in which the 2DEG is spatially removed from the donor atoms to minimize electron scattering. Theoretical studies have claimed that MCF will be fractal when the confinement potential defining the billiard is soft-walled, regardless of the presence of smooth potentials within the billiard such as those introduced by remote ionized donors. The small-angle scattering sites resulting from these potentials are often disregarded as negligible; we use MCF measurements to investigate such claims. To probe the effect of remote ionized donor scattering on the phase space in electron billiards, we compare MCF measured on billiards in a modulation-doped heterostructure to those measured on billiards in an undoped heterostructure, in which this potential landscape is believed to be absent. Fractal studies are performed on these MCF traces, and we find that MCF measured on the undoped billiards do not exhibit measurably different fractal characteristics than those measured on the modulation-doped billiards. Having confirmed that the potential landscapes in modulation-doped heterostructures do not affect the electron phase space, we then investigate the effect of these impurities on the distribution of electron trajectories through the billiards. By employing thermal cycling experiments, we demonstrate that this distribution is highly sensitive to the precise potential landscape within the billiard, suggesting that modulation-doped heterostructures do not support fully ballistic electron transport. We compare our MCF correlation data with the dynamics of charge transfer within heterostructure systems to make qualitative conclusions regarding these dynamics.

Development of sustainable and environmentally friendly chemical processes is of vital importance nowadays. Although there is a palette of different synthetic methods for the formation of epoxides, sulphoxides and sulphones, from both economic and environmental points of view, a direct oxidation with a simple oxidant is highly appreciated. The main goals of the thesis were design and synthesis of novel titanium containing zeolitic materials with the ability to catalyse selective oxidation of sterically demanding organic compounds, particularly epoxidation of cyclic olefins and terpenes and oxidation of bulky thioethers to corresponding sulphoxides and sulphones with hydrogen peroxide as the oxidant. Two novel extra-large pore titanosilicates were prepared by means of hydrothermal synthesis (Ti-CFI, Ti-UTL), three large-pore titanosilicates (Ti-CON, Ti-AFI, Ti-IFR) were prepared using two step deboronation - liquid phase titanium impregnation procedure and two groups of lamellar materials were prepared. One group was based on modified nanosheet TS-1; the other was prepared from Ti-IPC- 1P lamellar precursor, which was prepared by means of top-down transformation of Ti-UTL. Last but not least, the Ti-UTL was transformed into new titanosilicates Ti-IPC-2 (OKO structure) and Ti-IPC-4 (PCR structure) by...

The subject of this thesis is the asymptotic behaviour of generating functions of different combinatorial models of two-dimensional lattice walks and polygons, enumerated with respect to different parameters, such as perimeter, number of steps and area. These models occur in various applications in physics, computer science and biology. In particular, they can be seen as simple models of biological vesicles or polymers. Of particular interest is the singular behaviour of the generating functions around special, so-called multicritical points in their parameter space, which correspond physically to phase transitions. The singular behaviour around the multicritical point is described by a scaling function, alongside a small set of critical exponents. Apart from some non-rigorous heuristics, our asymptotic analysis mainly consists in applying the method of steepest descents to a suitable integral expression for the exact solution for the generating function of a given model. The similar mathematical structure of the exact solutions of the different models allows for a unified treatment. In the saddle point analysis, the multicritical points correspond to points in the parameter space at which several saddle points of the integral kernels coalesce. Generically, two saddle points coalesce, in which case the scaling function is expressible in terms of the Airy function. As we will see, this is the case for Dyck and Schröder paths, directed column-convex polygons and partially directed self-avoiding walks. The result for Dyck paths also allows for the scaling analysis of Bernoulli meanders (also known as ballot paths). We then construct the model of deformed Dyck paths, where three saddle points coalesce in the corresponding integral kernel, thereby leading to an asymptotic expression in terms of a bivariate, generalised Airy integral.

In this thesis, we investigate how the optical and electronic properties of graphene may be modified in proximity to various other materials. We present several examples of how modification in this way can help make graphene better suited for specific device applications. We develop a method of up-scaling the fabrication of FeCl3-intercalated few-layer graphene from micron-sized flakes to macroscopic films so that it may be used as a transparent electrode in flexible light-emitting devices. We also find that photo-responsive junctions can be arbitrarily written into FeCl3-intercalated few-layer graphene by means of optical lithography. These junctions produce photocurrent signals that are directly proportional to incident optical power over an extended range compared to other graphene photodetectors. Through theoretical analysis of these junctions, we conclude that the enhanced cooling of hot carriers with lattice phonons is responsible for this behaviour. Finally, we trial rubrene single crystals as the light-absorbing layer in a graphene phototransistor. We find that rubrene single crystal-graphene interfaces exhibit enhanced charge transfer efficiencies under illumination with extremely weak light signals. Through a comparative study with similar devices, we conclude that the wide variation in sensitivity amongst graphene phototransistors is largely due to extraneous factors relating to device geometry and measurement conditions.

The topics of Grounding and Metaphysical Explanation have been at the forefront of research and debate within metaphysics for the last decade. Grounding is commonly taken to be a relation of non-causal dependence. In this thesis I address the pertinent question as to what sorts of entities are related in instances of grounding. There has so far been little enquiry into this issue, and it therefore requires urgent attention. I argue here that the entities involved in grounding are facts, where facts are true Fregean propositions. True Fregean propositions are abstract entities composed of senses, and are individuated according the senses which they involve. I proceed by setting out some desiderata which the entities involved in grounding will fulfil. Firstly, they will be individuated sufficiently finely as to provide instances of grounding to back all putative cases of non-causal explanation. Secondly, they will ensure that there is unity between instances of grounding and instances of causation. Finally, they will be mind- independent. I survey different types of entity and show that true Fregean propositions are best-equipped to fulfil these desiderata. We therefore have reason to believe that grounding relates facts, so understood. The conclusion of this thesis therefore makes it incumbent upon us to extend our ontology to include true Fregean propositions.

Two-dimensional (2D) transition metal dichalcogenides (TMDs) with intrinsic band gaps are considered to be prospective alternatives for graphene in the applications of emerging nano-semiconductor devices. As a significant member of the TMDs family, WSe₂ with superior optical properties attracts increasing attention, especially in the optoelectronics. In this thesis, the electronic and mechanical properties of 2D WSe₂ have been studied experimentally and theoretically. Firstly, the fabrication of substrate-supported and suspended pre-patterned WSe₂ FETs with the low-cost optical lithography and vapour HF etching technology have been realised. The subsequent electrical measurement of the fabricated WSe₂ FETs indicates that the WSe₂/dielectric interface can affect the electrical performance of 2D WSe₂ negatively. To gain more insights on the impact of field-effect on 2D WSe₂, first-principle calculations have been conducted in this research to study the evolutions of the crystal structure, electronic band structure, conductive channel size, and electrical transport property of WSe2 under various levels of field-effect. Furthermore, a layer thinning and chemical doping method of 2D WSe₂ by vapour XeF₂ exposure featured with good air-stability, scalability, and controllability has been developed to enable the layer engineering of 2D WSe₂ and integration of 2D WSe₂ to logic circuits, solar cells, and light-emitting diodes (LED). The thinning and doping mechanism has been investigated with a combination of Raman spectroscopy, photoluminescence (PL) spectroscopy, and Xray photoelectron spectroscopy (XPS) characterization techniques. Afterwards, the inplane elastic properties (including the Young's modulus, breaking strain, and etc.) of 2D WSe₂ have been measured with nanoindentation experiments implemented by atomic force microscopy (AFM). The results prove the suitability of 2D WSe₂ in the applications of flexible devices and nanoelectromechanical systems (NEMS) operating in the audio resonance frequency, such as acoustic sensors and loudspeakers. To provide a comprehensive understanding of the strain engineering of 2D WSe₂, the strain induced variations of the crystal structure, electronic band structure, and electrical transport property of 2D WSe₂ have been further studied with first-principle calculations, which paves the way for the performance tuning of 2D WSe₂ devices via strain and applications of 2D WSe₂ in strain sensors.

Numerical modeling of extreme flooding in an urban area in eastern Iowa is presented. Modeling is performed using SRH-2D, an unstructured grid, finite volume model that solves the depth-averaged shallow-water equations. Data from a photogrammetric stereo compilation, contour maps, a hydrographic survey and building records were used to create a digital elevation model depicting the river channel and floodplain. A spatially distributed Manning coefficient based on land cover classification, derived from aerial photography is also used. The model is calibrated with high-resolution inundation depth data derived from a 1 m light detection and ranging survey, collected during the falling limb of the flood hydrograph, and discrete global positioning system measurements of water surface elevation at a bankfull condition. The model is validated with discrete high water marks collected immediately after the flood event. Results show the model adequately represents the water surface elevation in the main channel and floodplain and that exclusion of the discharges from minor creeks did not affect simulation accuracy. Reach scale results are not affected by the presence of buildings, but local inconsistencies occur in shallow water if buildings are not removed from the mesh. An unsteady hydrograph approximates flood hydrodynamics better than a steady-state simulation, but extreme computation time is not feasible for most investigations. The two-dimensional model was also compared to a comparable one-dimensional model of the study reach. The 1D model suffered from an inability to accurately predict inundation depth throughout the entire study area.