REU Opportunities Summer 2009
Dynamics, Patterns, and Waves
Arnd Scheel
I plan to offer two REU stipends in the summer of 2009.
The REU will take place at the University of Minnesota, Minneapolis. Topics will be in the area of dynamical systems, pattern formation, and nonlinear waves.
The participants are expected to spend 8 weeks in residence
sometime between May 11, 2009 and July 15, 2009. Support will be approximately $4000.
Students will need to be US
citizens or permanent residents (green card holder) to participate in this program, and
to have not yet completed their undergraduate degree by summer 2009.
Prerequisites.
Coursework in either Dynamical Systems and Ordinary Differential Equations, or in Partial Differential Equations. Some computational background can be helpful.
Potential topics.
- Modeling of Liesegang patterns.
Liesegang patterns form as a result of a simple chemical reaction, typically in gels, when the reaction product precipitates in a recurrent fashion. We will look at simple models for this phenomenon and try to understand the formation of regular and irregular patterns. For information see the introduction of Robustness of Liesegang patterns, the review article Recent Theoretical Developments on the Formation of Liesegang Patterns , or the slides from a recent presentation Slides.
- Defects in Turing patterns.
Turing patterns are self-organized patterns, driven by chemical reaction and diffusion. They emerge spontaneously in both chemical experiments and numerical simulations. While theory predicts periodic patterns for a whole band of wavenumbers, real patterns often show a dominant wavenumber. The project will investigate wavelength selection mechanisms both theoretically and experimentally.
For more information see for instance chapter 4 in Patterns and Interfaces in Dissipative Dynamics, or Chapter V in the review article Pattern formation outside of equilibrium.
How to apply.
Please send, or have sent, the following material to me, via email, scheel@math.umn.edu, or by surface mail.
- A list of upper level math courses you have completed or
are taking, along with your grades in these courses
- Two letters of recommendation
- A statement of your interest in the program.
Deadline for your application: February 19, 2009