The first people to thank are the ones whose support has been longest-standing. These are my mother (thanks, Ma'), my brother (thanks, Karl), and Professor Sherman D. Brown of MatSE at UIUC, who has been extremely supportive, even after I finished my B.S. and M.S. in Ceramic Engineering. My transition to physics and applied mathematics (inspired by my stay at the Technical University of Munich) has been a very rewarding process. I am very happy to have made the acquaintance of my advisor in applied mathematics, Michael Tabor. We share many common research interests, and he has afforded the essentials of freedom, funding, and facilities, allowing my work and education to truly flourish. Additionally, as a classroom instructor, he has the ability to succinctly present the essence of very complicated methods with great clarity. The rest of my committee is in physics, and has been as supportive of my work as a committee can be. In particular, working in Don Huffman's lab has served to encourage my natural tendency to do ``seat-of-the-pants'' research. On the theoretical side, the envigorating interaction with Dave Levermore has resonated with my affinity for rigor...``if the math and physics don't agree, find out why!''. For all of the helpful ``mathematical'' discussion and interaction, I am grateful to Moysey Brio, Jack Xin, Mac Hyman, and Jim Cushing. On the side of Materials Science, I must thank David Poirier, not only for our discussions, but also for helping facilitate enlightening interactions with Ken Jackson, Bill Boettinger, Michel Rappaz, and Rohit Trivedi. In addition to this, I can not begin to list all of the supportive friends at LANL and ANL. The experimental work would not have taken place without the expertise of Glen Galloway and Dave Burnett, and many of the very interesting phenomena would have gone completely unobserved, had it not been for the curiosity and meticulous work of Heather Seifert. I must also thank Scott Fernandez for any velocity measurements in this work. For their never-ending supply of insight and help with the silicon beasts, I am to no end endebted to Bob Condon, Mark Hays, and J.J. Chae. If I've learned nothing else during my time here, it is to coexist with the crazy new tools available to us! In addition to the actual tickings of the beasts, I was helped through the graphics jungle by Dave Scruton, Marvin Landes, and Donna Kent. In addition, Mark Jackson and Ken Avery must also be thanked for their careful proofreading. On a final note comes the yang and ying of beaurocracy. An ultimate thank you goes to the NSF and DOE for funding my years here, while a much more personal gratitude goes to Iris Wright (...and Mike Shupe...yeah...he's ying), Eva Ramirez, Lois Gorski, and Kathleen Leick. Without them, life'd be more difficult for everyone. In my final semester, I've also had the opportunity to teach with Bill Bickel, for whose teaching abilities I've developed a great respect. He does more for education, than anyone I've ever met.