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Episode 001 of the Tennessee Tech Athletics weekly podcast. Duration 21 minutes, 40 seconds. Originally published at https://www.youtube.com/watch?v=zSfy3MGV27s

This thesis investigates orthogonality in normed linear spaces. Several potential definitions for orthogonality in a normed space are given, while special attention is given to Birkhoff orthogonality and isosceles orthogonality. These definitions of orthogonality in normed spaces will be shown to be basic generalizations of orthogonality in inner product spaces. Basic properties of orthogonality in inner product spaces are gathered together and used to explore properties of Birkhoff and isosceles orthogonality. After this analysis, Birkhoff orthogonality of the trigonemetric system {1,sin(nx),cos(nx)}∞ n=1 in Lp[0,2π],p ≥ 1 is studied. It is shown that the trigonometric system is not Birkhoff orthogonal for p 6= 2, while sin(nx) and cos(mx) are Birkhoff orthogonal in L1[0,2π] for all natural numbers m and n. The last major topic covered deals with the best approximation of elements of a normed space by elements of a closed convex subset. In Banach spaces that are uniformly convex and in Banach spaces that are reflexive and strictly convex, it is shown that the best approximation exists and is unique. We conclude our discussion of best approximations by demonstrating a simple connection between them and Birkhoff orthogonality.

Structural health monitoring (SHM) is a relatively new multidisciplinary field with applications in many mechanical, civil, and aerospace structural systems. The goal of SHM is to evaluate a structure for changes in comparison to a previous measurement (a baseline). The content of this thesis focuses on the electromechanical impedance (EMI) method of SHM which uses a piezoelectric transducer for monitoring the mechanical impedance of a structure. Traditionally, SHM has been used for static structures undergoing slow changes over time. However, many structures operate in dynamic environments where damage and failure may occur quickly and rapid evaluation in the microsecond to millisecond timescale would be beneficial for structural integrity and safety of the operator. Advances in data acquisition and processing techniques have opened the possibility for acquiring and analyzing data using the EMI method at speeds necessary to monitor dynamic structures. To fully realize the capabilities of the state of the art, the EMI method and algorithmic process must be highly efficient. Reducing the time to evaluate the structure is perhaps the most important source of improvement yet to be achieved. In this work, high frequency excitation signals are suggested as a means to decrease the measurement time. An experimental study has shown that high frequencies up to 1.88 MHz are damage sensitive, and the resonance peaks of the piezoelectric transducer may be used to further increase the measuring range. Further, a novel multi-narrowband excitation signal has been implemented to target only damage sensitive frequencies. By reducing the frequency content excited and post-processed, these signals have shown decreases in the time of structural evaluation by over 77%, and reduction in signal energy by over 93%, which may be useful for low-power embedded sensors. In addition, the algorithmic process of continuously monitoring a structure has yet to be fully developed for the EMI method with real-time data. This work has taken a comprehensive survey at the requirements of a fully functional detection program. A program developed as a proof of concept successfully completed the algorithmic process from raw data at an average of 20.47 ms on an Intel® Core™ i7-4470 processor on a 64-bit Windows 10 OS with 8.00 GB of random-access memory (RAM) with a LabVIEW 2018 SP1 64-bit program, yielding tremendous promise and a foundation for more efficient future programs.

The development of low-cost raw materials and process for achieving high-quality cathode-side interconnect coating and contact layer is critical to the commercial deployment of solid oxide fuel cell. The transitional metal-containing spinels are widely used as coating materials for protecting ferritic stainless steel interconnects. This study focuses on developing a cost-effective approach to achieve high-performance interconnect coatings and investigating spinel-based materials to replace conventional perovskite contact at the cathode-interconnect interface. A mixture of Fe+CoO or Co+Mn3O4 is applied on the interconnect via screen printing and then thermally converted into a dense and adherent spinel layer in air at the elevated temperature. The synthesized layers inhibit the Cr2O3 scale growth on the stainless steel and reduce the scale ASR. When commercial reactive element-free alloys are used as the interconnect materials, Ce element can be readily added into the spinel, further improving the behavior of the interconnect/coating system. A variety of spinel-based contact layers are synthesized with different precursors and evaluated with regard to the electrical performance and microstructural evolution. The metal-containing precursor layers are fully converted after thermal exposure to 900℃ x 2 h in air due to the enhanced sinterability. It is observed that the contact layer derived from the alloy precursor is more uniform in microstructure and composition due to the shorter diffusion distance. Also, with the use of two optimal spinel-forming precursors, a dual-layer structure with a dense protective coating layer and a porous contact layer can be formed simultaneously at the stack firing temperature without the need of any reduction treatment, further simplifying the cell assembling process and thus reducing the overall fabrication cost.

Identifying the optimal geometry that would lead to maximized aerodynamic performance is an essential part of engineering design. There are well established commercial software packages that are widely used for engineering design and analysis, such as ANSYS and SolidWorks; however, there is no smart platform that can take advantage of these highly verified/validated packages for optimization purposes. Optimization via computational fluid dynamics (CFD) is an expensive process. Hence, developing an optimization platform that employs highly efficient commercial codes such as ANSYS-Fluent is of essence. This research was focused on developing such platform based on the genetic algorithm (GA) logic, where an in-house developed python script communicates with SolidWorks and ANSYS through a fully automated process until the optimal geometry is identified. Development of a bladeless wind turbine was considered to test functionality and performance of this optimization platform. This case was selected due to the complex geometry that will ensure a robust optimization platform. Additionally, developing an efficient bladeless turbine can address many of the challenges that wind power industry faces. Contemporary wind turbine systems rely on blades which operate on the principle of the airfoil. Designing such bladed turbines to operate in low wind speed environments is a major challenge as low wind speeds produce a lift on the blades which is insufficient to run the rotor. This means those designs suffer from high "cut-in wind speeds". A bladeless wind turbine is presented which converts low speed wind energy into a high velocity, rotational jet output through convergent nozzles. Wind energy is extracted by directing a portion of the stream through the proposed structure. Initially, a prototype was 3D printed and tested and it was found that most of the air was diverting around the object instead of passing through the funnel. In order to find a more effective geometry for the funnel without the time and cost of 3D printing many additional designs, the above-described optimization platform was applied to the geometry of this bladeless wind turbine.

In this thesis, we will explore approximating convolution integrals for Laplace and exponential Fourier transformations. For Laplace transforms, we will use the composite Simpson's Rule to make approximations firstly for convolutions with known results to compare and provide validity and then again for some without known results. For the exponential Fourier type, we first use the composite Simpson's Rule on a known result using different methods (two changes of variable and truncation) and compare to the known results to validate using the methods for convolution integrals without known results. Then, we will compare all methods per integral together.

The snapping shrimp genera Alpheus and Synalpheus, are two of the most well described and speciose genera of marine crustaceans and they offer unique opportunities to investigate the origins of biodiversity in the sea. Here we investigate how genome size, geography, and ecology contribute to species diversification within snapping shrimp. We examined five well resolved clades within the two genera (A. armatus, A. armillatus, A. bouvieri, A. floridanus, and S. gambarelloides). We find that genome size ranges approximately four-fold across the species examined within Alpheus. We reconstructed the ancestral state of genome size and found that, of the clades examined, genome size estimates were similar across ancestral nodes but exhibited high variance across contemporary species. Age-range correlation (ARC) analyses were used to quantify pre-dominant geographic mode of speciation of free-living and symbiotic clades. Free-living clades all were consistent with an allopatric mode of speciation while ARC results from symbiotic clades suggested multiple instances of speciation in sympatry. Linear regressions from ARC analyses between free-living and symbiotic snapping shrimp clades were significantly different (P = 0.02) which suggests that ecology (specifically symbiotic interactions) may facilitate reproductive isolation despite geographic overlap. Results from this study contribute to our understanding of the geographic mode and underlying mechanisms of diversification in snapping shrimp and may serve as a model for investigating the evolutionary origins of biodiversity in other marine invertebrates.

The process of improving one’s retention of information through retrieval practice known as the testing effect has been well documented, as has a similar effect referred to as hypermnesia. These concepts have been implemented in various ways over the years, and with varying forms of study material, response format, and time delay. However, these concepts have not yet been addressed in combination with virtual reality as a means of presenting the to-be-learned material. This study sought to be the first to incorporate these cognitive psychology principles into the virtual reality literature as a means of helping to address the overall lack of empirical research utilizing virtual reality in assessing learning outcomes. The present study utilized the Mann-Whitney U test for two independent samples to evaluate the impact of medium of study (i.e., VR-restudy v. VR-retrieval practice) on retention measured as performance on an anatomy test after a two-week delay. The experiment consisted of two conditions in which participants studied heart anatomy content presented in VR using either the restudy or the retrieval practice studying strategy. There were two primary goals in the present study to utilize the testing effect and hypermnesia to assess the effectiveness of VR as an educational tool and to determine how these constructs can be effective in other educational settings. The Mann-Whitney U test revealed a nonsignificant difference between conditions which demonstrates a failure to replicate the findings of the testing effect literature. Possible explanations and rationale for these null findings are discussed.