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- Creators: Department of Physics
Implicit in the design criteria of current ALT designs is the assumption that the form of the acceleration model is correct. This is unrealistic assumption in many real-world problems. Chapter 3 provides an approach for ALT optimum design for model discrimination. We utilize the Hellinger distance measure between predictive distributions. The optimal ALT plan at three stress levels was determined and its performance was compared to good compromise plan, best traditional plan and well-known 4:2:1 compromise test plans. In the case of linear versus quadratic ALT models, the proposed method increased the test plan's ability to distinguish among competing models and provided better guidance as to which model is appropriate for the experiment.
Chapter 4 extends the approach of Chapter 3 to ALT sequential model discrimination. An initial experiment is conducted to provide maximum possible information with respect to model discrimination. The follow-on experiment is planned by leveraging the most current information to allow for Bayesian model comparison through posterior model probability ratios. Results showed that performance of plan is adversely impacted by the amount of censoring in the data, in the case of linear vs. quadratic model form at three levels of constant stress, sequential testing can improve model recovery rate by approximately 8% when data is complete, but no apparent advantage in adopting sequential testing was found in the case of right-censored data when censoring is in excess of a certain amount.
To evaluate the performance of Dantzig selector, a simulation study was conducted and the results based on the percentage of type II errors are analyzed. Also, another alternative for 6 factor NC design, called the Alternate No-confounding design in six factors is introduced in this study. The performance of this Alternate NC design in 6 factors is then evaluated by using Dantzig selector as an analysis method. Lastly, a section is dedicated to comparing the performance of NC-6 and Alternate NC-6 designs.
Most asteroids originated in larger parent bodies that underwent accretion and heating during the first few million years of the solar system. We investigated the parent body of S-type asteroid 25143 Itokawa by developing a computational model which can approximate the thermal evolution of an early solar system body. We compared known constraints on Itokawa’s thermal history to simulations of its parent body and constrained its time of formation to between 1.6 and 2.5 million years after the beginning of the solar system, though certain details could allow for even earlier or later formation. These results stress the importance of precise data required of the material properties of asteroids and meteorites to place better constraints on the histories of their parent bodies. Additional mathematical and computational details are discussed, and the full code and data is made available online.
This creative project develops an environment in which three species inhabit a shared land and models the movement of the creatures to determine the survival rates over time in specific conditions. The three species modelled include a predator and a prey species with movement capabilities as well as a stagnant fruit species. There are a variety of configurable variables that can be used to modify and control the simulation to observe how the resulting population charts change. The big difference between this project and a normal approach to simulating a predation relationship is that actual creatures themselves are being created and their movement is simulated in this virtual environment which then leads to population counts, rather than integrating differential equations relating the population sizes of both species and purely tracking the populations but not the creatures themselves. Because of this difference, my simulation is not meant to handle all the complexities of life that come in the real-world but instead is intended as a simplified approach to simulating creatures' lives with the purpose of conveying the idea of a real predation relationship. Thus, the main objective of my simulation is to produce data representative of real-world predator-prey relationships, with the overall cyclical pattern that is observed in natural achieved through simulating creature movement and life itself rather than estimating population size change.
We implemented the well-known Ising model in one dimension as a computer program and simulated its behavior with four algorithms: (i) the seminal Metropolis algorithm; (ii) the microcanonical algorithm described by Creutz in 1983; (iii) a variation on Creutz’s time-reversible algorithm allowing for bonds between spins to change dynamically; and (iv) a combination of the latter two algorithms in a manner reflecting the different timescales on which these two processes occur (“freezing” the bonds in place for part of the simulation). All variations on Creutz’s algorithm were symmetrical in time, and thus reversible. The first three algorithms all favored low-energy states of the spin lattice and generated the Boltzmann energy distribution after reaching thermal equilibrium, as expected, while the last algorithm broke from the Boltzmann distribution while the bonds were “frozen.” The interpretation of this result as a net increase to the system’s total entropy is consistent with the second law of thermodynamics, which leads to the relationship between maximum entropy and the Boltzmann distribution.
The goal of this project was to develop a prototype for an educational tool that will help users understand how the voting system deployed by a government can affect the outcomes of elections. This tool was developed in Java SE, consisting of a model for the simulation of elections capable of supporting various voting systems, along with a variety of fairness measures, and educational and explanatory material. While a completed version of this tool would ideally be fully self-contained, easily accessible in-browser, and provide detailed visualizations of the simulated elections, the current prototype version consists of a GitHub repository containing the code, with the educational material and explanations contained within the thesis paper. Ultimately, the goal of this project was to be a stepping stone on the path to create a tool that will instill a measure of systemic skepticism in the user; to give them cause to question why our systems are built the way they are, and reasons to believe that they could be changed for the better. In undertaking this project, I hope to help in providing people with the political education needed to make informed decisions about how they want the government to function. The GitHub repository containing all the code can be found at, https://github.com/SpencerDiamond/Votes_that_Count