Physical Sciences and Mathematics Commons^™

Model Reduction For Simulation, Optimization And Control, Oleg Edward Roderick

Dissertations and Theses

Many tasks of simulation, optimization and control can be performed more efficiently if the intermediate complexity of the numerical model is reduced. In our work, we investigate model reduction, as applied to reaction-transport systems of atmospheric chemistry. We use a Proper Orthogonal Decomposition-based approach to extract information from a set of model observations, and to project the model equations onto a reduced order space chosen in such a way that the essential model behavior is preserved in the solution of the reduced version. We examine and improve many features of the method. In particular, we show how to measure sensitivities …

Quantum Multiplexers, Parrondo Games, And Proper Quantization, Faisal Shah Khan

Dissertations and Theses

A quantum logic gate of particular interest to both electrical engineers and game theorists is the quantum multiplexer. This shared interest is due to the facts that an arbitrary quantum logic gate may be expressed, up to arbitrary accuracy, via a circuit consisting entirely of variations of the quantum multiplexer, and that certain one player games, the history dependent Parrondo games, can be quantized as games via a particular variation of the quantum multiplexer. However, to date all such quantizations have lacked a certain fundamental game theoretic property.

The main result in this dissertation is the development of quantizations of …

Quaternions, Octonions, And The Quantization Of Games, Aden Omar Ahmed

Dissertations and Theses

We present an effect on classical games that is obtained by replacing the notion of probability distribution with the notions of quantum superposition and measurement. Our particular focus will be on two and three player games where each player has precisely two pure strategic choices. Games in normal form are represented as "payoff" functions.

Game quantization requires the extension of these functions to much larger domains. The main result of this work is the co-ordinatization of these extended functions by either the quaternions or octonions in order to obtain computationally friendly versions of these functions. This computational capability is then …

Data Assimilation, Adaptive Observations And Applications, Humberto Carlos Godinez Vasquez

Dissertations and Theses

Sensitivity analysis, data assimilation and targeting observation strategies are methods that are applied to various complex mathematical models of fluid dynamics. In this research we investigate new directions to improve on the current strategies used to deploy additional observational resources (targeting strategies) for data assimilation in dynamical systems of fluid mechanics.

Targeting strategies aim to determine optimal locations where additional observations will improve the solution of the data assimilation process by identifying regions where state errors in the model have a high potential to grow.

Properly accounting for nonlinear error growth is an unresolved issue in targeted observations for numerical …