Department of Mathematical Sciences
REU: Research experience for undergraduates

Multidisciplinary REU Program in Computational Mathematics and Nonlinear Dynamics of Biological, Bio-inspired and Engineering Systems

The Department of Mathematical Sciences at GMU will host a multidisciplinary undergraduate research program in computational mathematics and nonlinear dynamics of biological, bio-inspired and engineering systems, from May 31 to July 30, 2010. The overall goal of this program is to encourage students and teachers to learn by discovery and enhance their understanding of the multidisciplinary role of mathematics in engineering, science and medicine.

Objective

The primary goal of the REU program is to expose eight qualified mathematics undergraduate students and a K-12 teacher each year, to advanced topics in mathematics, problem-solving techniques and applications to biological, bio-inspired and engineering systems. Participants will have an opportunity to interact with renowned faculty members from a variety of areas that includes mathematics, computational science and engineering. Through this program, we will not only provide the participants with a real-world experience of how mathematics can be applied to qualitatively and quantitatively study biological and engineering systems, but will also make it our priority to encourage women and under-represented minorities to pursue multidisciplinary careers that bridge the biological, mathematical, and computational sciences. This program will also help to train two K-12 teachers over the two years who will be able to use their problem-solving skills and research experience from the program to do open-ended exploration and develop related lesson studies in their high-school mathematics classrooms. In addition, three graduate students will be involved in this program as graduate mentors for the participants. The program will help nurture the intellectual growth and development of graduate students and also provide them with a valuable experience of mentoring.

Focus Areas

The three subprograms under the broad theme of computational mathematics and nonlinear dynamics that will help understand the quantitative behavior of biological, bio-inspired and engineering systems include:

• Modeling using Deterministic and Stochastic Differential Equations
  
  The students in this subprogram will be mentored to develop a thorough understanding of modeling, analysis and simulation of the problem within the context of the originating scientific discipline. They will be encouraged to suggest and explore possible modifications and then be shown how to systematically investigate the resulting processes. They will either write their own computational routines or be given access to more sophisticated numerical tools, as appropriate. Proposed research projects include:
  
  1. Computational modeling of Micro-Air Vehicles.
  2. Mathematical modeling and simulation of coupled processes.
  3. Agent-based Modeling of Financial Markets.
  
  
• Computational Biology and Neuroscience
  
  The students in this subprogram will learn about existing computational biology models, perform basic theoretical analysis and numerical simulation of the solutions. The students will employ and build on the models that the faculty mentors in the subprogram have successfully developed in collaboration with undergraduate and graduate students. Proposed projects include:
  
  1. Data Assimilation in Nonlinear Systems.
  2. Reconstruction of Protein Networks from Small, Noisy Data Sets.
  3. Numerical continuation of solutions in a neuronal field model.
  
  
• Mathematics of Materials
  
  In this REU subprogram, we will focus on reviewing existing mathematical optimization and modeling techniques that have helped materials scientists and engineers in obtaining more accurate results while utilizing efficient analytical and computational techniques. The students will be exposed to real world problems arising in interdisciplinary collaborations and will be trained in assessing complex problems and utilizing mathematical skills to build new and improve upon existing solutions - skills that are in great demand on both academic and industrial job market today. Possible projects include:
  
  1. Comparison study of materials microstructure models.
  2. Free-boundary Problems in Fluid Mechanics: Liquid Droplets on Surfaces.
  3. Phase diagram calculation.
  
  

Participant Support and Available Resources

All students will be selected on a competitive basis to participate in the program. Each selected student will receive a stipend of $3,375 and up to $550 travel allowance in addition to free housing and dining in the University residence hall for the duration of the program.

The Department of Mathematical Sciences will provide lab and office space. Participants will additionally be provided with unlimited access to campus computing, library, and recreational facilities and reduced admission fees to many campus events. Computational resources on campus include a large Beowulf-class parallel computing cluster with 134 CPUs (67 dual-processor Pentium III 600 Mhz nodes) running the Linux operating system. Each node is a Dell Precision410 Workstation with 512MB of RAM and 13GB of disk storage. Students will have access to several other Linux computer labs on campus 24 hours a day to support their research.

Application process

To apply, please submit the following materials by April 2, 2010:

1. Application form
2. Statement of purpose
3. Reference Form
   (Two to three reference letters must be received)
4. An official college transcript as of Spring 2010

You can submit these materials via email to reu AT math.gmu.edu, via fax to (703) 993-1491 or hard copies via regular mail to:

ATTN: REU Program Coordinators
Department of Mathematical Sciences
MS 3F2
George Mason University
4400 University Dr, Fairfax VA 22030.

Participating faculty

Dr. Padmanabhan Seshayier (PI)
Dr. Padmanabhan Seshaiyer is specially trained in numerical analysis, finite element methods, computational mechanics and scientific computing. Over the last few years, he has done extensive work on the theoretical and computational aspects of non-conforming hp finite element methods which will be used extensively for the computational modeling aspects of this research program. Dr. Seshaiyer's research in computational mathematics is highly multidisciplinary and has been funded by the NSF, the Whitaker foundation and the Texas ARP.

Dr. Maria Emelianenko (co-PI)
Dr. Maria Emelianenko's research is in the area of applied mathematics with main focus on the analysis and development of efficient numerical algorithms. Her research interests include working on problems arising on the interface between mathematical and physical sciences/engineering. Dr. Emelianenko has experience supervising undergraduate research and has been playing an active role in various Women in Science and Engineering organizations.

Dr. Daniel Anderson
Dr. Daniel Anderson's research interests involve mathematical modeling and computational techniques applied to problems arising in fluid mechanics and materials science. He has been advising undergraduate research projects for the past several years and is one of the co-PIs on the NSF-sponsored CSUMS program in the Mathematical Sciences at GMU.

Dr. Harbir Lamba
Dr. Harbir Lamba's research areas include dynamical systems, numerical analysis and stochastic differential equations. Practical application areas of his research have included electrical engineering, mechanical engineering, and the modeling of financial markets. He has advised one recent PhD thesis in Computational Sciences.

Dr. Domenico Napoletani
Dr. Domenico Napoletani's research interest is in the development of signal processing, data analysis and network reconstruction algorithms for highly structured, large data sets. He is currently an assistant professor in the department of Mathematical Sciences at GMU where he is working on problems of classification and model inference of protein networks from sparse microarray data.

Dr. Evelyn Sander
Dr. Evelyn Sander's research is in the area of dynamical systems, as applied to both materials science and computational neuroscience problems. She has advised two undergraduate senior theses, a masters thesis, and is currently advising two undergraduates in the CSUMS program as a Co-PI and two Ph.D. students.

Dr. Thomas Wanner
Dr. Thomas Wanner's current research focuses on the dynamics of stochastic evolution equations with an emphasis on materials science applications, as well as on pattern analysis via topological and stochastic methods. He advised several undergraduate research projects in the past, and is currently advising two undergraduate research projects, as well as three PhD students. He is one of the co-PIs on the NSF-sponsored CSUMS program at GMU.