During the summer of 1999, nine undergraduates from across the United States met on the Iowa State University campus for the NSF sponsored REU program on Scientific Computing. The participants were:
There were three ISU mathematics faculty mentors for the program:
In addition, three ISU mathematics graduate students worked with the participants in the program:The students spent their first week in Ames getting acquainted with each other, their surroundings, and the goals of the program. The group projects were introduced and the participants worked on some "mini-projects" to get them familiar with the available computing facilities, and a programming language such as FORTAN, C, or C++. Mathematical software such as Mathematica and Matlab was introduced.
The students broke up into project groups and worked with their mentor on their main project for the rest of the summer. Each group wrote a paper describing their project and results, and presented their results at a final session. The papers were written in LATEX (something else the participants had to learn!). During the summer, the students visited the "cave" at the Virtual Reality Applications Center and the Pioneer Seed Company, where biotechnological research is done. They also had weekly informal get-togethers with the ISU faculty and graduate students, where they got a chance to talk about their research interests, graduate school, and just to relax.
Michael Brauwerman, Chris Farmer, and Sara Zoll worked with Professor Gunzburger on a project involving computational geometry. The specific topic was centroidal Voronoi tesselations. They studied some known results concerning the mathematical theory of centroidal Voronoi tesselations, applications to problems, and methods for calculating such regions. They wrote code in C++ to implement both the K-means and Lloyd methods, and then compared the efficiency of these methods. They then studied the more complicated problems that arise when the generating points come from a nonuniform probability density function. The students discovered a tool on the Internet that would allow them to display pictures of the tesselations they were computing. You can read their summary report, entitled Centroidal Voronoi Tesselations Are Not Good Jigsaw Puzzles or copy some of their C++ codes.
Kelly McNamara and Scott Simon investigated the numerical simulation of superconductivity. The students started with an existing computer program written in FORTRAN, which could compute the behavior of a superconducting material. The program used a finite element discretization of the nonlinear partial differential Ginzburg-Landau equations. Once they got comfortable with the theory behind the code, and the way it was used, they were able to modify it to investigate some new questions, include a normal inclusion model. They used this new program to simulate junctions between superconducting and normal materials, and to model Josephson junctions. They also looked at flux pinning with various physical materials. They made a movie of some of their simulations using Macromind Director. You can read their summary report, entitled Type II Superconductivity: Normal Inclusion Models.
Jessie Campbell and Mitul Vora worked on a project in control theory. They were given a computer program that used finite element methods to simulate and solve a control problem. They then learned about the concept of control, and its use in industrial processes, aircraft design and other problems. With their mentor, they developed a control problem that studied an exterior adobe wall. The temperature of the outside of the adobe wall was subjected to the usual daily fluctuations. Depending on the thickness and material properties of the adobe, this temperature variation was transmitted, over time, to the interior of the structure. The desire was to determine whether it was possible to find a shape for the wall that would result in the interior wall being warm at night and cool in the day. The students experimented with a variety of materials and thicknesses, and compared their results to typical construction methods used in actual adobe buildings. Their paper, entitled "Adobe Wall Design", is available as
Josh Kortbein and Katherine Rasing worked on a project in artificial intelligence with Professor Ashlock. These students were both ISU undergraduates, and had taken several mathematical biology courses already. Their project was to use evolved structures to enhance virtual robotics. They developed computer codes to perform robotic simulations.
Last Updated: 27 August 2001