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Mathematical models are important tools for addressing problems that exceed experimental capabilities. In this work, I present ordinary and partial differential equation (ODE, PDE) models for two problems: Vicodin abuse and impact cratering.

The prescription opioid Vicodin is the nation's most widely prescribed pain reliever. The majority of Vicodin abusers

Mathematical models are important tools for addressing problems that exceed experimental capabilities. In this work, I present ordinary and partial differential equation (ODE, PDE) models for two problems: Vicodin abuse and impact cratering.

The prescription opioid Vicodin is the nation's most widely prescribed pain reliever. The majority of Vicodin abusers are first introduced via prescription, distinguishing it from other drugs in which the most common path to abuse begins with experimentation. I develop and analyze two mathematical models of Vicodin use and abuse, considering only those patients with an initial Vicodin prescription. Through adjoint sensitivity analysis, I show that focusing efforts on prevention rather than treatment has greater success at reducing the total population of abusers. I prove that solutions to each model exist, are unique, and are non-negative. I also derive conditions for which these solutions are asymptotically stable.

Verification and Validation (V&V) are necessary processes to ensure accuracy of computational methods. Simulations are essential for addressing impact cratering problems, because these problems often exceed experimental capabilities. I show that the Free Lagrange (FLAG) hydrocode, developed and maintained by Los Alamos National Laboratory, can be used for impact cratering simulations by verifying FLAG against two analytical models of aluminum-on-aluminum impacts at different impact velocities and validating FLAG against a glass-into-water laboratory impact experiment. My verification results show good agreement with the theoretical maximum pressures, and my mesh resolution study shows that FLAG converges at resolutions low enough to reduce the required computation time from about 28 hours to about 25 minutes.

Asteroid 16 Psyche is the largest M-type (metallic) asteroid in the Main Asteroid Belt. Radar albedo data indicate Psyche's surface is rich in metallic content, but estimates for Psyche's composition vary widely. Psyche has two large impact structures in its Southern hemisphere, with estimated diameters from 50 km to 70 km and estimated depths up to 6.4 km. I use the FLAG hydrocode to model the formation of the largest of these impact structures. My results indicate an oblique angle of impact rather than a vertical impact. These results also support previous claims that Psyche is metallic and porous.
ContributorsCaldwell, Wendy K (Author) / Wirkus, Stephen (Thesis advisor) / Asphaug, Erik (Committee member) / Camacho, Erika T (Committee member) / Crook, Sharon (Committee member) / Plesko, Catherine S (Committee member) / Smith, Hal (Committee member) / Arizona State University (Publisher)
Created2019
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Description
Affect is a domain of psychology that includes attitudes, emotions, interests, and values. My own affect influenced the choice of topics for my dissertation. After examining asteroid interiors and the Moon’s thermal evolution, I discuss the role of affect in online science education. I begin with asteroids, which are collections

Affect is a domain of psychology that includes attitudes, emotions, interests, and values. My own affect influenced the choice of topics for my dissertation. After examining asteroid interiors and the Moon’s thermal evolution, I discuss the role of affect in online science education. I begin with asteroids, which are collections of smaller objects held together by gravity and possibly cohesion. These “rubble-pile” objects may experience the Brazil Nut Effect (BNE). When a collection of particles of similar densities, but of different sizes, is shaken, smaller particles will move parallel to the local gravity vector while larger objects will do the opposite. Thus, when asteroids are shaken by impacts, they may experience the BNE as possibly evidenced by large boulders seen on their surfaces. I found while the BNE is plausible on asteroids, it is confined to only the outer layers. The Moon, which formed with a Lunar Magma Ocean (LMO), is the next topic of this work. The LMO is due to the Moon forming rapidly after a giant impact between the proto-Earth and another planetary body. The first 80% of the LMO solidified rapidly at which point a floatation crust formed and slowed solidification of the remaining LMO. Impact bombardment during this cooling process, while an important component, has not been studied in detail. Impacts considered here are from debris generated during the formation of the Moon. I developed a thermal model that incorporates impacts and find that impacts may have either expedited or delayed LMO solidification. Finally, I return to affect to consider the differences in attitudes towards science between students enrolled in fully-online degree programs and those enrolled in traditional, in-person degree programs. I analyzed pre- and post-course survey data from the online astrobiology course Habitable Worlds. Unlike their traditional program counterparts, students enrolled in online programs started the course with better attitudes towards science and also further changed towards more positive attitudes during the course. Along with important conclusions in three research fields, this work aims to demonstrate the importance of affect in both scientific research and science education.
ContributorsDingatantrige Perera, Jude Viranga (Author) / Asphaug, Erik (Thesis advisor) / Semken, Steven (Thesis advisor) / Anbar, Ariel (Committee member) / Elkins-Tanton, Linda T. (Committee member) / Robinson, Mark (Committee member) / Arizona State University (Publisher)
Created2017