Even simple observation of stock price graphs can reveal dominant patterns. In our work, we will refer to such re-occurring, dominant patterns as “coherent structures”, a term borrowed from the theory of turbulence in fluid dynamics. Stock price performance exhibits coherent structures, which by definition make it non-random, although a price-versus-time graph might seem totally chaotic to the naked eye. A novel low-order modeling technique for systems that are seemingly random has been developed. Though stock market data is used for the formulation and verification of the technique, its application in diverse fields is verified. The dissertation discusses some of the salient features of the novel technique along with a dynamic system analogy. The technique reduces many of the significant limitations associated with traditional methods like Fourier analysis and digital filters. Application of the technique to a nonlinear dynamical system and meteorological data are presented as well as the primary application on stock market securities.

Flow temperature sensing remains important for many hypersonic aerodynamics and propulsion applications. Flight test applications, in particular, demand robust and accurate sensing, making thermocouple sensors attractive. Even for these extremely well-developed sensors, the prediction of stresses (hoop, radial, and axial) within thermocouple sheaths for custom-configured probes remains a topic of great concern for ensuring adequate lifetime of sensors. In contemporary practice, high-fidelity simulations must be run to prove if a new design will work at all, albeit at significant time and expense. Given the time and money it takes to run high-fidelity simulations, rapid optimization of sensor configurations is often impossible, or at a minimum, impractical. The developments presented in this Thesis address the need for hypersonic flow temperature sensor structural predictions which are compatible with rapid design iteration. The derivation and implementation of a new analytical, low-order model to predict stresses (hoop, radial, and axial) within the sheath of a thermocouple are provided. The analytical model is compared to high-fidelity ANSYS mechanical simulations as well as simplified experimental data. The predictions using the newly developed structural low-order model are in excellent agreement with the numerically simulated results and experimental results with an absolute maximum percent error of approximately 4% and 9.5%, respectively, thus validating the model. A MATLAB GUI composed of the combination of a thermal low-order model outlined in additional references [1] through [6] and the new structural low-order model for thermocouples was developed. This code is capable of solving a highly generalized version of the 1-D pin fin equation, allowing for the solution of the temperature distribution in a sensor taking into account conduction, convection, and radiation heat transfer which is not possible with other existing analytical solutions. This temperature distribution is then used in the analytical structural low-order model. This combination allows for the thermal and structural performance of a thermocouple to be found analytically and compared quickly with other designs. / M.S. / Thermocouples are a device for measuring temperature, consisting of two wires of different metals connected at two different points. This configuration produces a temperature-dependent voltage as a result of the thermoelectric effect. Preexisting curves are used to relate the voltage to temperature. Thermocouples are extensively used in high-temperature high-stress environments such as in rockets, jet engines, or any high-corrosive environment. Accurately predicting the stresses within the sheath of a metal-clad thermocouple in extreme conditions is required for many research areas including hypersonic aerodynamics and various propulsion applications. Even for these extremely well-developed and widely used sensors, the accurate prediction of stresses within the metal sheath remains a topic of great concern for ensuring the sensor’s survivability in these extreme conditions. Current engineering practice is to use high-fidelity numerical simulations (Finite Element Analysis) to predict the stresses within the sheath. Perhaps the biggest drawback to this approach is the time it takes to model, mesh, and set-up these simulations. Comparative studies between different designs using numerical simulations are almost impossible due to the time requirement. This Thesis will present an analytically derived quasi-3D solution to find the stresses within the sheath. These equations were implemented into a low-order model that can handle varying temperature, geometry, and material inputs. This model was validated against both high-fidelity numerical simulations (ANSYS Mechanical) and a simplified experiment. The predictions using this newly developed structural low-order model are in excellent agreement with the numerically simulated results and experimental results.