Experimental Performance Study of a Lab-Scale Hydrokite System

Hydropower plants are the main source of renewable energy from moving water. However, traditional dam systems are somewhat controversial since they are large and often require population relocation, disrupt fish migration, and change the natural flow of the river. Hydrokinetic systems are currently being developed which can harness energy from flowing water with less ecological impact. One hydrokinetic system that may be promising, a hydrokite system, consists of an oscillating arm, boom, and a translating hydrofoil. Due to the hydrodynamic forces caused by the water\u27s velocity, the hydrokite moves back and forth extracting energy from the flow. Previous simulations have shown that power production for this system depends on at least ten different parameters. Little experimental work has been done on hydrokite systems to validate the results of these simulations. This work focused on the experimental testing of a lab-scale hydrokite system. Tests were run to determine the system power trends with respect to hydrofoil angles, boom flip angles, pivot-point location on hydrofoil, tow speed, and hydrofoil submerged depth. Single dimension parameter tests were done to determine the changes in average cycle power for the system as a function of a given parameter. Power production was highly sensitive to changes in hydrofoil angles (for hydrofoils pivoting at both the quarter and half-chord point). The optimal hydrofoil angle for the tests that were run was approximately β = 60° - 80°. As predicted, the power production increases with increased tow speed and submerged depth, neglecting energy used to flip the hydrofoil. Changes in boom flip angle did not significantly affect power production for the quarter-chord tests, but appeared to be significant in the half-chord tests. Although the largest power produced in all of this testing was approximately 0.14 Watts, this initial testing of the lab-scale system has given us some insight into the important design decisions that will need to be made in order to scale-up the system

Generalized period-index problem with an application to quadratic forms

Let $F$ be the function field of a curve over a complete discretely valued field. Let $\ell$ be a prime not equal to the characteristic of the residue field. Given a finite subgroup $B$ in the $\ell$ torsion part of the Brauer group ${}_{\ell}Br(F)$, we define the index of $B$ as the minimum of the degrees of field extensions which split all elements in $B$. In this manuscript, we give an upper bound for the index of any finite subgroup $B$ in terms of arithmetic invariants of $F$. As a simple application of our result, given a quadratic form $q/F$, where $F$ is the function field of a curve over an $n$-local field, we provide an upper bound to the minimum of degrees of field extensions $L/F$ so that the Witt index of $q\otimes L$ becomes the largest possible.Comment: 18 page

Analyzing Responses from Likert Surveys and Risk-Adjusted Ranking: A Data Analytics Perspective

We broadly consider the topic of ranking entities from surveys/opinions. Often, numerous ranks from different respondents are available for the same entity, e.g., a candidate from a pool, and yet an averaging of those ranks may not serve the purpose of identifying a consensus candidate. We first consider a risk-adjusted paradigm for ranking, where the rank is defined as the average (mean) rank plus a scalar times the risk in the rank; we use standard deviation as a risk metric. In case of a candidate being ranked either on the basis of opinions of a selection committee\u27s members or on social interactions in a social network such as Facebook, risk-adjusted ranking can result in selecting a consensus candidate who/which does not secure the best average rank, but is acceptable to a large number of the opinion providers. Second, we present an approach to develop the margin of error in Likert surveys, which are increasingly being used in data analytics, where the responses are on a five-point scale, but one is interested in a binary response, e.g., yes-no, agree-disagree. Computing the margin of error in Likert surveys is an open problem

Salary Cap Efficiency: A Study of the Relationship between a NFL Quarterback’s Salary and their Team’s Performance

For years, sports economists have attempted to understand the impact of salary caps in sports leagues, as they can have an impact on a team’s favored personnel approach. In the National Football League (NFL), one of the more important positions is the team’s quarterback, who has the ability to command large contracts. This paper examines the work of past researchers, and attempts to add to the literature by analyzing data from the past ten NFL seasons. I find inconclusive results relating to the relationship between a NFL team’s winning percentage and the amount of salary cap space allocated for their starting quarterback

On Step Sizes, Stochastic Shortest Paths, and Survival Probabilities in Reinforcement Learning

Reinforcement learning (RL) is a simulation-based technique useful in solving Markov decision processes if their transition probabilities are not easily obtainable or if the problems have a very large number of states. We present an empirical study of (i) the effect of step-sizes (learning rules) in the convergence of RL algorithms, (ii) stochastic shortest paths in solving average reward problems via RL, and (iii) the notion of survival probabilities (downside risk) in RL. We also study the impact of step sizes when function approximation is combined with RL. Our experiments yield some interesting insights that will be useful in practice when RL algorithms are implemented within simulators

Magneto Acoustic Spin Hall Oscillators

This paper introduces a novel oscillator that combines the tunability of spin Hall-driven nano oscillators with the high quality factor (Q) of high overtone bulk acoustic wave resonators (HBAR), integrating both reference and tunable oscillators on the same chip with CMOS. In such magneto acoustic spin Hall (MASH) oscillators, voltage oscillations across the magnetic tunnel junction (MTJ) that arise from a spin-orbit torque (SOT) are shaped by the transmission response of the HBAR that acts as a multiple peak-bandpass filter and a delay element due to its large time constant, providing delayed feedback. The filtered voltage oscillations can be fed back to the MTJ via a) strain, b) current, or c) magnetic field. We develop a SPICE-based circuit model by combining experimentally benchmarked models including the stochastic Landau-Lifshitz-Gilbert (sLLG) equation for magnetization dynamics and the Butterworth Van Dyke (BVD) circuit for the HBAR. Using the self-consistent model, we project up to $\sim$ 50X enhancement in the oscillator linewidth with Q reaching up to 52825 at 3 GHz, while preserving the tunability by locking the STNO to the nearest high Q peak of the HBAR. We expect that our results will inspire MEMS-based solutions to spintronic devices by combining attractive features of both fields for a variety of applications