published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

In this work there are analized the realization of the most important numerical methods in computer algebra systems. There are analyzed and comparised the opportiunities of three CAS – Maple, Matlab and Mathcad – for the reason how to solve the mathematical tasks by using the numerical methods. Therefore are given the discription of the methods for solving systems of linear equations, function interpolation, numerical integration and for solving the first order differential equations. There is analyzed how those methods are realized in the CAS. In the last unit the numerical methods of those systems are compared by their complication, convinience for the user and the variety of functions of the numerical methods. After the description of every method there are proposed the examples of the task solutions by using CAS.

The widespread recognition of (ultra)high-pressure ((U)HP) metamorphic rocks in orogens worldwide suggests that subduction and exhumation of crustal rocks from mantle depths are normal processes at convergent plate margins. However, the dynamics of these processes, in particular the comparative roles of erosion and crustal extension, and the driving forces of extension during (U)HP rock exhumation, remain controversial. This thesis presents numerical modeling and field/analytical studies that address the geodynamics of crustal subduction and exhumation in two intensely studied orogens, the Alps and the Caledonides. The 2D numerical models show how different scales and durations of orogeny and plate motions can lead to marked contrasts in the style of orogenic growth, crustal subduction, and (U)HP exhumation. In the Western Alps, rapid exhumation (1-3 cm/a) can be explained by local, syn-orogenic extension driven by the buoyant ascent of deforming (U)HP crust from the subduction channel. Later trans-crustal exhumation probably resulted from the combined effects of syn-convergent thrusting, local extension, and erosion. The low temperatures (500-700°C) of Alpine (U)HP metamorphism are attributable to the small size of the orogen and short duration of subduction/exhumation. Contrary to recent suggestions, neither erosion nor absolute extension is required to explain (U)HP exhumation in the Alps. The Western Gneiss Region (WGR) (Norwegian Caledonides), in contrast, can be explained by subduction to (U)HP conditions followed by plate divergence. Gravitational spreading of a thick, hot orogenic wedge leads to a short period of coeval thrusting and extension. Exhumation of (U)HP crust from the subduction channel is achieved by normal-sense shearing along the top of the (U)HP terrane, with minor associated shortening. Trans-crustal exhumation by vertical thinning of the orogenic wedge results from continued absolute extension and erosion. The comparatively high temperatures (700-800°C) achieved by Caledonian (U)HP rocks reflect the orogen's greater size, slower exhumation rates, and possible stalling of the (U)HP terrane at depth. These contrasting models underscore the variety of possible mechanisms responsible for (U)HP exhumation, and represent new benchmarks in the understanding of Alpine and Caledonian tectonics and (U)HP rock exhumation in general.

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An understanding of the shape and nature of galaxy density profiles remains a major challenge to galaxy structure studies. The physical mechanisms thought to control these profiles include star formation rates and dynamical interactions, but we focus in this thesis on the contribution of dynamical parameters associated with the dark and baryonic matter. We follow the evolution of mass density profiles, and investigate the development of a truncation radius. Using GADGET-2, an N-body/SPH code with a prescription for star formation and feedback, and the SHARCNET computational facilities, we have generated over 200 galaxy models covering a full range of structural parameters. The galaxy models have a minimum of 1.4 million particles and most are evolved over a period of 10 Gyr. We find that the evolution of the galaxy mass density profile is controlled by the ratio of the disk mass fraction, $m_{d}$, to the halo spin parameter, $\lambda$. The strength of the two-component structure in disk profiles and speed at which this structure develops, is directly proportional to $m_{d}/\lambda$. While the development of a two-component profile is coupled to bar formation, not all barred galaxies develop a two-component profile. We also show that the slope of the outer profile is in close agreement with that of the initial profile and remains stable over time, whereas the inner profile slope evolves considerably. This result will greatly improve comparisons of observed with predicted measures of galaxy density profiles. Our galaxy database is the largest of its kind and a valuable resource for many potential galaxy structural studies. We conclude with a list of future investigations based on our study and new database. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2007-07-30 14:46:24.568

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