REU 2015: DIFFERENTIAL EQUATIONS AND APPLICATIONSThis summer the Department of Mathematics will again run a Research Experience for Undergraduates (REU) program. It will be organized by Profs. Craciun, Spagnolie, Thiffeault, and Zlatoš, with the help of several junior members of the department. The areas of research will include ordinary as well as partial differential equations, and their applications in the modeling of natural phenomena.
Spagnolie: Random growth in random media
Inspired by the shapes and growth of leaves, we will investigate numerically the behavior of thin elastic shells that stretch, buckle, and fold as they grow. We may also pursue analytical solutions using a partial differential equation that describes the dynamics.
Craciun: Mathematical models of biological interaction networks
We will study nonlinear dynamical systems that represent mathematical models of biological interaction networks. Our understanding of the dynamical systems of interest will be based on both theoretical analysis and numerical simulations.
Thiffeault: Mixing and the Cahn-Hilliard equation
The Cahn-Hilliard equation is a simple model of a two-phase flow, such as of oil mixed with water. The two components may naturally separate - a phenomenon known as coarsening - but do also mix when they are stirred. We will study theoretically and numerically how these two phenomena interact and achieve a balance.
Zlatoš: Reaction-diffusion equations
Reaction-diffusion equations are mathematical models of natural phenomena such as combustion, chemical reactions, and population dynamics. We will undertake a theoretical study of some of their special solutions which model spreading of reaction/population through a reactive medium/environment.
The REU will run from May 18, 2015 (Monday after finals week) to June 26, 2015 (Friday one week before July 4). Participants must be present in Madison during this period and be devoted to the REU full time (i.e., not holding part-time jobs or taking summer classes). Students should be flexible with their plans between June 26 and Independence Day, in case a few extra days are required to finish the work. In addition, participants may be asked to acquire knowledge of background material prior to the start of the REU, in which case either introductory lectures will be offered late in the spring semester or relevant texts will be provided by the research mentors.
Any UW-Madison undergraduate student who will not graduate prior to July 2015 is eligible to apply. Applicants are expected to have taken at least Math 521 and a course in ordinary differential equations by the start of the REU. An exception to the former requirement may be made in the case of a very strong student from Math 375/376.
A stipend of $4000 will be offered to those participants who are US citizens or permanent residents, and likely a similar level of funding will be available to a limited number of students who are not US residents. Participants will be expected to make their own housing and meals arrangements.
How to apply
Please fill out this application form by Monday, February 23, 2015. We expect to admit up to 12 students and you will be notified about the decision on your application by mid March. If you have other questions, please contact one of the organizers (their email addresses are listed on their web-pages).