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New Horizons VMI Journal of Undergraduate Research Volume 3 Issue 1 April 2009 TABLE OF CONTENTS 1 From the Executive Editor Sciences 5 Mathematical Model of Rabbit Haemorrhagic Disease Cadet Marshall H. Jarrett (Civil Engineering, ’11) Faculty Mentor: Dr. Lea R. Lanz, Assistant Professor of Mathematics and Computer Science 15 Adaptive Numerical Analysis of Laser Pulses Cadet Thomas M. Shaffner (Physics, ’08) Faculty Mentors: Dr. John R. Thompson, Professor and Head, Department of Physics and Astronomy and Dr. Troy J. Siemers, Associate Professor of Mathematics and Computer Science 31 A Kinematic Model for Hand Movements Cadet Christopher M.P. Leach (Mechanical Engineering, ’10) Faculty Mentor: Dr. Vonda K. Walsh, Professor of Mathematics and Computer Science Engineering 41 Two-Dimensional Transient Heat Transfer Experiment Cadet Hsin-sheng, Lee (Mechanical Engineering, ’09) Faculty Mentor: Dr. Robert L. McMasters, Professor of Mechanical Engineering 49 Thermal Distortion of a Subscale Membrane Mirror Cadet Scott T. MacDonald (Mechanical Engineering, ’10) Faculty Mentor: Dr. Joseph R. Blandino, Professor of Mechanical Engineering Interdisciplinary 59 The Rhetoric of Science: A Case Study of Susumu Tonegawa’s Landmark Discovery Cadet Joshua C. Kenny (Biology, ’09) Faculty Mentor: Dr. Christina R. McDonald, Institute Writing Director Humanities 67 Learning to See: The Black Mountain College Experiment Cadet Even T. Rogers (English and Fine Arts, ’10) Faculty Mentor: Dr. Robert L. McDonald, Professor of English 83 Kitchener to the Somme: British Strategy on the Western Front during the Great War Cadet Gregory E. Lippiatt (History and English, ’09) Faculty Mentor: Dr. Charles F. Brower IV, Acting Director, VMI Center for Leadership and Ethics 93 Marshall and the Politics of Command: 1906-June 6, 1944 Cadet John M. Curtis (History, ’10) Faculty Mentor: Dr. Malcolm Muir, Henry King Burgwyn, Jr. Boy Colonel of the Confederacy Chair in Military History 111 About the Contributing Editors 115 Undergraduate Research at VMI 117 In Memoriam New Horizons r Volume 3 r Number 1 r 2009 From the Executive Editor No hay lı´mites salvo el cielo. [The sky’s the limit.] Miguel de Cervantes hree years have passed since New through any concerted effort by the editorial T Horizons editorial board first presented board, however, but rather by the level of its vision for the new journal to the VMI academic excellence established by the cadet faculty and Corps of Cadets. With only a authors themselves in volumes 1 (2007) and blueprint in our collective conscience, we had 2 (2008) of New Horizons. little to show our first audience except a Like their predecessors, the nine cadets conceptual diagram and a bulleted list of goals whose research appears in this year’s print and aspirations. We had set demanding edition—as well as the three cadets whose standards, too demanding many commented, work will appear in the electronic version of when they learned of the multi-layered process New Horizons, volume 3—have successfully we had set forth for prospective authors. met the demands of an eight-month review/ “Daunting,” said some, “too ambitious,” revise process, including recommendation for retorted others, while still others just shook publication by an anonymous third-party their heads with gentle kindness and reader. More likely than not, the reviewer’s sympathetically expounded on the futility of response is the first ungraded qualitative tilting at windmills. evaluation of their work these cadets have Undoubtedly, we have learned many lessons ever received, and at first glance they may about publishing a journal of undergraduate have found the comments overly critical or research since 2006 and even tilted at the even dispiriting. Academic review, after all, occasional windmill. But we have never had does not tend towards gentle kindness, but to compromise the standards we put forth at rather constructive criticism, which can the inception of the journal. To the contrary, sometimes overwhelm even the most the bar for publication has been raised, not seasoned writer. 1 2 New Horizons / April 2009 The cadet authors and cover designer science, and philosophy in representation of whose work comprise this third volume of six different institutions. The New Horizons New Horizons—along with their faculty Editorial Board and the Institute are indebted mentors—represent eight departments across to them for the generosity of their time and VMI’s three academic divisions. And while expertise on behalf of our cadets. interdisciplinarity is not a new feature in our We are equally grateful to all our colleagues journal, the extent and breadth of the at the Institute who were no less generous with collaborative efforts across the curriculum and their time and intellect in their service to cadet throughout the inquiry/writing/review development by serving as research mentors process in this year’s issue merit special and contributing editors for this third volume mention. Chapeau bas as well to the VMI of New Horizons. The unconditional support Department of Physics and Astronomy, who and enthusiasm we receive from faculty make their drum-roll debut in New Horizons colleagues, the dean’s office, our “Friends of with nothing less than one article, a New Horizons” and especially Dr. Jim contributing editorship, the cover design, and Turner, Director of the VMI Undergraduate the newest member of the New Horizons Research Initiative, continue to inspire us, as Editorial Board, Dr. George M. Brooke, IV, cadets set and re-set the standard of Assistant Professor of Physics. undergraduate research at the Institute In addition to the cross-disciplinary evermore skyward. investigative endeavors that define the 2009 Finally, my heartfelt thanks to my fellow edition of our journal, the editorial board editors Alexis Hart, Bob McMasters, and takes exceptional pride in the number of Merce Brooke, without whom this intellectual colleagues who graciously served as quest would be only an endless row of extramural reviewers. This year’s directory windmills on the horizon. of contributing editors includes non-VMI teacher/scholars from the fields of rhetoric, Mary Ann Dellinger engineering, American literature, political Executive Editor, New Horizons New Horizons is published annually through the VMI Undergraduate Research Initiative. For information, contact: [email protected] or Ms. Leslie Joyce, Undergraduate Research, 309 Science Building, VMI, Lexington, VA 24450. SCIENCES New Horizons r Volume 3 r Number 1 r 2009 Mathematical Model of Rabbit Haemorrhagic Disease Cadet Marshall H. Jarrett Faculty Mentor: Dr. Lea R. Lanz, Assistant Professor of Mathematics ABSTRACT Scientists and mathematicians have developed mathematical models to describe the spread of diseases in populations. An epidemic recently modeled is Rabbit Haemorrhagic Disease (RHD), a disease that first surface in China in the early 1980’s. There are many different mathematical models employed to describe epidemics, and specifically RHD. One type of classical epidemic model, the MSEIR, divides an infected population into different subclasses and uses differential equations to represent population changes in each subclass. From history of the disease, disease characteristics, and mathematical analysis of the model, variations of the MSEIR model, the SIR and SIRS models, are considered as appropriate models for RHD. However, because a replenishment of the susceptible class is not a characteristic of RHD, the SIRS model is more applicable to RHD. INTRODUCTION numbers of domestic rabbits on farms (Cooke 2002). The loss of millions of In 1984, an epidemic severely attacked consumer rabbits could have crippled millions of Angora rabbits in the People’s businesses relying on the rabbits for meat Republic of China. Spreading rapidly, the and fur (Cooke 2002). However, the disease killed millions of wild rabbits (Cooke uncontrolled spread of the disease led to 2002; Mitro & Krauss 1993). During the research geared toward using the disease to next twelve years, reports of the disease control inflated rabbit populations causing killing thousands of both wild and domestic harm to an area’s natural ecosystem. During rabbits traveled from Asia to Europe, Africa, the mid 1990’s, a research center was and Central America (Cooke 2002). Caused established on Wardang Island in Australia by a calicivirus, the now classified Rabbit to see how the climate could affect the Haemorrhagic Disease (RHD) has become spread of the disease. Before research could endemic among domestic and wild rabbit be completed, the virus escaped to mainland populations. Because of its worldwide Australia and began to spread through wild prominence, research continues to uncover rabbit populations all over the country. At new information about how fast the disease the time of the unwanted release, the spreads and what factors contribute to its epidemic raised concern for Australia’s wild proliferation. rabbit population, but actually turned out to Initially, researchers studied RHD to find be a successful means of biologically ways to prevent the virus from killing large controlling the millions of rabbits that 5 6 New Horizons / April 2009 Australian farmers and naturalists considered populations, B.D. Cooke outlines the as pests (Cooke 2002). The introduction of importance of understanding death rates of the disease dramatically decreased the infected rabbits to better “assist the number of rabbits to a more desirable level. management of wild rabbit populations