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.
Adderall remains to be one of the most commonly abused drug among college campuses. Although it is a prescription drug that is primarily used to treat attention deficit hyperactivity disorder (ADHD), it has become one of the many "study drugs" due to its usage among college students during stressful school times, such as exams, where increased concentration and energy levels are thought to improve work efficiency. However, Adderall is notable for having a high potential for abuse and a risk of psychological and physical side effects. In this paper, we conducted a mathematical analysis on an existing epidemiological model of Adderall abuse. We started by verifying the positivity of solutions using techniques from dynamical systems because this is a population model dealing with people. Then, we found and investigated different equilibrium solutions to analyze their stability using both analytical and graphical approaches. Finally, the results were tied back into the Adderall model and conclusions were drawn.
The objective of this work is to perform LCAs three wastewater treatement alternatives at battalion-sized (500 soldier) FOBs. Three systems will be explored: traditional wastewater treatment of combined blackwater and graywater streams using activated sludge and anaerobic digestion (the status quo); MXC treatment of blackwater to produce H2O2 for disinfection of blackwater and graywater; a hybrid system of blackwater treatments with MXCs to produce electricity with graywater disinfection using H2O2 produced offsite. Environmental impacts are assessed using Impact 2002+ midpoint and endpoint categories, primarily reported for human health and environmental impacts. Uncertainity analysis is performed using two techniques. First, a pedigree matrix is developed to identify the highest areas of uncertainties in data. Second, a sensitivity analysis is used to explore the effects on endpoint categories from varying transportation distance, the percentage of wastewater that is reused as nonpotable water, and coagulant doses.
Microbial peroxide producing cells (MPPCs) are a type of microbial electrochemical cells that are used to produce hydrogen peroxide (H2O2). Different catholytes were evaluated in biotic and abiotic reactors to determine their impacts on reactor performance. The abiotic reactor produced cathode efficiencies of less than 1%, leading us to investigate the potential causes of the low efficiency. An acid wash of the reactor parts was observed to significantly decrease the degradation rate of peroxide in the reactor, indicating that metal impurities in the catholyte solution was the driving cause of the low peroxide yields in the reactor. Diffusion testing confirmed that peroxide diffused across the anion exchange membrane (AEM) at a rate of 13.3 mg/L/hr, but had no significant impact on the overall peroxide produced in the reactor. We also confirmed that auto-decay of H2O2 was not responsible for the low observed yields.
This outlines a mathematical model created in MATLAB for the purposes of predicting nitrous oxide emissions from wastewater treatment plants with updated an updated understanding of AOB metabolic pathway.