Reservoir simulation models are becoming increasingly sophisticated in tandem with the rapid development of geological modeling methods. Widely used commercial simulators usually model flow through heavily faulted and structurally complex geometries with the flexibility provided by corner-point geometry. However, the nonorthogonality component present within these frameworks may compromise the solution accuracy of the model and the subsequent operational decisions involved. We propose a systematic methodology to evaluate the impact of complex gridding introducing a new streamline formulation for corner-point geometry. Based on a new time-like variable, the new formulation provides a significantly simpler and more robust development to handle the complexity in structurally demanding and faulted systems. It retains the simplicity and speed of streamline-based flow models and provides an efficient way to visualize nonorthogonal effects. Applied to various geometries showing challenging features of geology and flow, the displacement fronts obtained from streamline-derived analytic calculation identified the discrepancies characteristic between known solutions and results from two widely used commercial simulators.

We propose the study of robustness measures for signal detection in non-stationary noise using differential geometric tools in conjunction with empirical distribution analysis. Our approach shows that the gradient can be viewed as a random variable and therefore used to generate sample densities allowing one to draw conclusions regarding the robustness. As an example, one can apply the geometric methodology to the detection of time varying deterministic signals in imperfectly known dependent nonstationary Gaussian noise. We also compare stationary to non-stationary noise and prove that robustness is barely reduced by admitting non-stationarity. In addition, we show that robustness decreases with larger sample sizes, but there is a convergence in this decrease for sample sizes greater than 14. We then move on to compare the effect on robustness for signal detection between non-Gaussian tail effects and residual dependency. The work focuses on robustness as applied to tail effects for the noise distribution, affecting discrete-time detection of signals in independent non-stationary noise. This approach makes use of the extension to the generalized Gaussian case allowing the comparison in robustness between the Gaussian and Laplacian PDF. The obtained results are contrasted with the influence of dependency on robustness for a fixed tail category and draws consequences on residual dependency versus tail uncertainty.

Thesis (doctoral)--Universität Bern, 1911. / Cover title.

Thesis (doctoral)--Königl. Sächs. Technischen Hochschule zu Dresden, 1914. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, 1933. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois."

Inaug.-Diss.-Bonn.

Thesis (M.S. Science in Education)--Shenandoah University, 2003. / Includes bibliographical references.

Thesis--University of Alberta. / Title from screen (viewed Mar. 26, 2003). Includes bibliographical references.

Thesis--Ph. D., University of Hong Kong.

This report explores several geometric representations of quadratic equations and their solutions. Topics discussed include applications of geometry relating to solving quadratic equations using graphs and constructions as well as deriving compatible pairs of equations from Pythagorean triples. A brief discussion on the inclusion of advanced graphing methods and constructions into a secondary mathematics class is also included. / text