The concept of distribution is one of the core ideas of probability theory and inferential statistics, if not the core idea. Many introductory statistics textbooks pay lip service to stochastic/random processes but how do students think about these processes? This study sought to explore what understandings of stochastic process students develop as they work through materials intended to support them in constructing the long-run behavior meaning for distribution.

I collected data in three phases. First, I conducted a set of task-based clinical interviews that allowed me to build initial models for the students’ meanings for randomness and probability. Second, I worked with Bonnie in an exploratory teaching setting through three sets of activities to see what meanings she would develop for randomness and stochastic process. The final phase consisted of me working with Danielle as she worked through the same activities as Bonnie but this time in teaching experiment setting where I used a series of interventions to test out how Danielle was thinking about stochastic processes.

My analysis shows that students can be aware that the word “random” lives in two worlds, thereby having conflicting meanings. Bonnie’s meaning for randomness evolved over the course of the study from an unproductive meaning centered on the emotions of the characters in the context to a meaning that randomness is the lack of a pattern. Bonnie’s lack of pattern meaning for randomness subsequently underpinned her image of stochastic/processes, leading her to engage in pattern-hunting behavior every time she needed to classify a process as stochastic or not. Danielle’s image of a stochastic process was grounded in whether she saw the repetition as being reproducible (process can be repeated, and outcomes are identical to prior time through the process) or replicable (process can be repeated but the outcomes aren’t in the same order as before). Danielle employed a strategy of carrying out several trials of the process, resetting the applet, and then carrying out the process again, making replicability central to her thinking.

Researchers have described two fundamental conceptualizations for division, known as partitive and quotitive division. Partitive division is the conceptualization of a÷b as the amount of something per copy such that b copies of this amount yield the amount a. Quotitive division is the conceptualization of a÷b as the number of copies of the amount b that yield the amount a. Researchers have identified many cognitive obstacles that have inhibited the development of robust meanings for division involving non-whole values, while other researchers have commented on the challenges related to such development. Regarding division with fractions, much research has been devoted to quotitive conceptualizations of division, or on symbolic manipulation of variables. Research and curricular activities have largely avoided the study and development of partitive conceptualizations involving fractions, as well as their connection to the invert-and-multiply algorithm. In this dissertation study, I investigated six middle school mathematics teachers’ meanings related to partitive conceptualizations of division over the positive rational numbers. I also investigated the impact of an intervention that I designed with the intent of advancing one of these teachers’ meanings. My findings suggested that the primary cognitive obstacles were difficulties with maintaining multiple levels of units, weak quantitative meanings for fractional multipliers, and an unawareness of (and confusion due to) the two quantitative conceptualizations of division. As a product of this study, I developed a framework for characterizing robust meanings for division, indicated directions for future research, and shared implications for curriculum and instruction.

In recent years, a new type of ionic salt based solid propellant, considered inert until the application of an electric current induces an electro-chemical reaction, has been under investigation due to its broad range of possible uses. However, while many electric propellant formulations and applications have been explored over the years, a fundamental understanding of the operational mechanisms of this propellant is necessary in order to move forward with development and implementation of this technology. It has been suggested that the metallic additive included in the formulation studied during this investigation may be playing an additional, currently unknown role in the operation and performance of the propellant. This study was designed to examine variations of an electric propellant formulation with the purpose of investigating propellant bulk volume electrical resistivity in order to attempt to determine information regarding the fundamental science behind the operation of this material. Within a set of fractional factorial experiments, variations of the propellant material made with tungsten, copper, carbon black, and no additive were manufactured using three different particle size ranges and three different volume percentage particle loadings. Each of these formulations (a total of 21 samples and 189 specimens) were tested for quantitative electrical resistivity values at three different pulse generator input voltage values. The data gathered from these experiments suggests that this electric propellant formulation’s resistivity value does change based upon the included additive. The resulting data has also revealed a parabolic response behavior noticeable in the 2D and 3D additive loading percentage versus additive particle size visualizations, the lowest point of which, occurring at an approximately 2.3% additive loading percentage value, could be indicative of the effects of the percolation phenomena on this material. Finally, the investigation results have been loosely correlated to power consumption testing results from previous work that may indicate that it is possible to relate propellant electrical resistivity and operating requirements. Throughout this study, however, it is obvious based on the data gathered that more information is required to be certain of these conclusions and in order to fully understand how this technology can be controlled for future use.

Advances in computational processing have made big data analysis in fields like music information retrieval (MIR) possible. Through MIR techniques researchers have been able to study information on a song, its musical parameters, the metadata generated by the song's listeners, and contextual data regarding the artists and listeners (Schedl, 2014). MIR research techniques have been applied within the field of music and emotions research to help analyze the correlative properties between the music information and the emotional output. By pairing methods within music and emotions research with the analysis of the musical features extracted through MIR, researchers have developed predictive models for emotions within a musical piece. This research has increased our understanding of the correlative properties of certain musical features like pitch, timbre, rhythm, dynamics, mel frequency cepstral coefficients (MFCC's), and others, to the emotions evoked by music (Lartillot 2008; Schedl 2014) This understanding of the correlative properties has enabled researchers to generate predictive models of emotion within music based on listeners' emotional response to it. However, robust models that account for a user's individualized emotional experience and the semantic nuances of emotional categorization have eluded the research community (London, 2001). To address these two main issues, more advanced analytical methods have been employed. In this article we will look at two of these more advanced analytical methods, machine learning algorithms and deep learning techniques, and discuss the effect that they have had on music and emotions research (Murthy, 2018). Current trends within MIR research, the application of support vector machines and neural networks, will also be assessed to explain how these methods help to address the two main issues within music and emotion research. Finally, future research within the field of machine and deep learning will be postulated to show how individuate models may be developed from a user or a pool of user's listening libraries. Also how developments of semi-supervised classification models that assess categorization by cluster instead of by nominal data, may be helpful in addressing the nuances of emotional categorization.

Energy production is driven by economic needs, which sometimes results in the environment and wildlife being an afterthought. Unfortunately, many animals are killed as a result of flying too close to wind turbines, and the addition of animal deterrent devices are a promising alternative. This thesis seeks to provide a solution as a part of post- construction considerations regarding wildlife and wind turbine interactions through the introduction of a blade mounted ecological device. After testing the hypothesis, the data revealed the device is effective for increasing power output when placed at the root, middle, and tip of the blade. The middle position yielded the lowest increase at all speeds tested. The device was designed and attached to blades along the estimated line of separation. The blades were then mounted on a tower and tested with wind speed as an input and power as an output. The data was analyzed by fixing speed as a parameter and then looking at the distribution of the power output data. A comparison of blades with and without the device demonstrates a potential for increasing power output by 144% when the device is attached at the blade’s root, 7.5% in the middle, and 21% near the tip. The analysis for this study was descoped due to the constraints of the system to be scaled up. As such, this analysis will hold for turbines with a blade length of no more than approximately eight feet. Blades of this type would be used in single building energy grid supplement turbines or turbines in areas with power requirements of equal or less than 1kW per turbine installed. Single building energy grid supplement turbines are most often mounted to the tops of buildings and take advantage of higher speeds of wind at those heights. As the ecological devices are designed to be similar to vortex generators, which have been tested on large blades, their addition to large blades could prove to have a similar effect.

Keywords: Wind turbine ecosystem, post-construction turbine considerations, wildlife deterrents

The project consists of steps that a Formula SAE team could take into developing their first carbon fiber monocoque chassis. The project is based on an interview with a successful team that has build carbon monocoques for the last several years. The project covers the steps into designing a carbon monocoque, including aspects that need to be highlighted in the design process as well as an outline of the overall rules and regulations regarding carbon fiber monocoques. The project also encompasses simple finite element analysis procedure that would introduce teams into carbon fiber composite sandwich analysis and its applications in racecar monocoques. The project also includes steps in manufacturing a carbon fiber monocoque beginning from methods to acquire necessary materials to the final process of de-molding the monocoque. The method has been used before from several FSAE teams, proving its viability. The goal is that through this report, teams could have an idea of where to start in developing their carbon monocoques and have a clear path to take on going from initial designs up until a final finished product.

This paper outlines the development of a script which utilizes a series of user-defined input parameters to construct base-level CAD models of aircraft landing gear. With an increased focus on computation development of aircraft models to allow for a rapidprototyping design process, this program seeks to allow designers to check for the validity of design integration before moving forward on systems testing. With this script, users are able to visually analyze the landing gear configurations on an aircraft in both the gear up and gear down configuration. The primary purpose this serves is to determine the validity of the gear's potential to fit within the limited real estate on an aircraft body. This, theoretically, can save time by weeding out infeasible designs before moving forward with subsystem performance testing. The script, developed in Python, constructs CAD models of dual and dual-tandem main landing gear configurations in the CAD program Rhino5. With an included design template consisting of 33 parameters, the script allows for a reasonable trade off between conciseness and flexibility of design.

The Doghouse Plot visually represents an aircraft’s performance during combined turn-climb maneuvers. The Doghouse Plot completely describes the turn-climb capability of an aircraft; a single plot demonstrates the relationship between climb performance, turn rate, turn radius, stall margin, and bank angle. Using NASA legacy codes, Empirical Drag Estimation Technique (EDET) and Numerical Propulsion System Simulation (NPSS), it is possible to reverse engineer sufficient basis data for commercial and military aircraft to construct Doghouse Plots. Engineers and operators can then use these to assess their aircraft’s full performance envelope. The insight gained from these plots can broaden the understanding of an aircraft’s performance and, in turn, broaden the operational scope of some aircraft that would otherwise be limited by the simplifications found in their Airplane Flight Manuals (AFM). More importantly, these plots can build on the current standards of obstacle avoidance and expose risks in operation.

This paper describes the research done to attempt to scale up thrusts produced by ionic wind thrusters, or "lifters" to magnitudes needed to power a 2 kg hobbyist remote-control airplane. It includes background information on the Biefeld-Brown effect and the thrust it produces, an experiment that attempted to prove that thrust can be scaled up from smaller ionic wind thrusters to larger scales, and two models predicting thruster geometries and power sources needed to reach these thrusts. An ionic wind thruster could not be created that would power the hobbyist remote as a high-voltage power source with voltage and power high enough could not be obtained. Thrusters were created for the experiment using balsa wood, aluminum foil, and thin copper wire, and were powered using a 30 kV transformer. The thrusters attempted to test for correlations between thrust, electrode length, and current; electric field strength, and thrust; and thrust optimization through opening up air flow through the collector electrode. The experiment was inconclusive as all the thrusters failed to produce measurable thrust. Further experimentation suggests the chief failure mode is likely conduction from the collector electrode to the nearby large conductive surface of the scale.

This research was intended to investigate the effects of various motivational variables on high school students' declaration of a STEM major in college, focusing on PSEM majors. It made use of data from the High School Longitudinal Study of 2009, including the first and second follow-up years (2011 and 2013). The advantage of this study over others is due to this data set, which was designed to be a representative sample of the national population of US high school students. Effects of motivational factors were considered in the context of demographic groups, with the analysis conducted on PSEM declaration illuminating a problem in the discrepancy between male and female high school students. In general, however, PSEM retention from intention to declaration is abysmal, with only 35% of those students who intended towards PSEM actually enrolling.