Skip to main content

Differential Equation Models for Understanding Phenomena beyond Experimental Capabilities


Abstract 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 treatme... (more)
Created Date 2019
Contributor Caldwell, Wendy K (Author) / Wirkus, Stephen (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)
Subject Applied mathematics / Applied physics / Asteroid 16 Psyche / hydrocode / ordinary differential equations / partial differential equaitons / verification and validation / Vicodin abuse
Type Doctoral Dissertation
Extent 174 pages
Language English
Copyright
Note Doctoral Dissertation Applied Mathematics 2019
Collaborating Institutions Graduate College / ASU Library
Additional Formats MODS / OAI Dublin Core / RIS


  Full Text
5.7 MB application/pdf
Download Count: 46

Description Dissertation/Thesis
  greyblack2.mp4
33.4 MB video/mp4
Download Count: 7

Description Psyche asteroid impact simulation initialization
  psycheimpact.mp4
6.3 MB video/mp4
Download Count: 8

Description Psyche asteroid impact simulation video