Upcoming REU Summer 2020
Patterns and PDEs (2020)
We are organizing a summer REU program, to be held at the Mathematical Institute at Leiden University in The Netherlands. We are seeking motivated undergraduate students to spend 6 weeks between June 15, 2020 and July 24, 2020 in Leiden, to work on research related to nonlinear waves and pattern formation, using the theory of dynamical systems and partial differential equations. Applications include vegetation pattern formation and other topics in mathematical biology and ecology.
See the program flyer for additional information.
Faculty mentors: Paul Carter (University of Minnesota), Arjen Doelman (Leiden University)
Application deadline: February 14, 2020
Apply at: MathPrograms.org
Past REU Projects
Stellar winds (2019)
In the setting of viscous stationary spherically symmetric equations of gas dynamics, we are interested in the existence of subtosupersonic transitions which describe the phenomena of stellar wind and stellar accretion. These transitions arise as canard solutions in an appropriate fastslow framework and can be constructed using geometric singular perturbation theory. In this project, we analyzed the effects of viscosity and heat conduction on the structure of stellar winds.
REU Students: Adam Bauer
Publications:

A Bauer and P Carter.
Existence of transonic solutions in the stellar wind problem with viscosity and heat conduction. (Submitted for publication)
Existence of transonic solutions in the stellar wind problem with viscosity and heat conduction. (Submitted for publication)
Localized roll patterns (2016)
In a project hosted by the Summer@ICERM program in 2016, groups of undergraduate students studied snaking localized roll patterns in the SwiftHohenberg equation. They analyzed the effect of the underlying geometry/topology of the equation on the structure of the associated snaking curves, as well as implications for higher dimensional patterns.
Collaborators: T. Aougab, M. Beck, J. Bramburger, B. Sandstede
REU Students: Dylan Altschuler, Chloe Avery, Surabhi Desai, Tharathep Sangsawang, Melissa Stadt, Aric Wheeler
Publications:

T Aougab, M Beck, P Carter, S Desai, B Sandstede, M Stadt, and A Wheeler.
Isolas versus snaking of localized rolls.
Journal of Dynamics and Differential Equations 31(3) (2019), pp. 11991222. (preprint)

J Bramburger, D Altschuler, C Avery, T Sangsawang, M Beck, P Carter, and B Sandstede.
Localized radial roll patterns in higher space dimensions.
SIAM Journal on Applied Dynamical Systems 18(3) (2019), pp. 14201453. (preprint)
Isolas versus snaking of localized rolls.
Journal of Dynamics and Differential Equations 31(3) (2019), pp. 11991222. (preprint)
Localized radial roll patterns in higher space dimensions.
SIAM Journal on Applied Dynamical Systems 18(3) (2019), pp. 14201453. (preprint)
Traffic flow (2014)
In this REU project, undergraduate students studied the application of data assimilation to models of traffic flow. In particular, a framework was developed to assimilate both Eulerian (fixed sensor) and Lagrangian (GPS) observations in order to predict traffic states and estimate model parameters.
Collaborators: B. Sandstede, L. Slivinski, C. Xia
REU Students: Courtney Cochrane, Joseph DeGuire, Bridget Fan, Emma Holmes, Melissa McGuirl, Patrick Murphy, Jenna Palmer
Publications:

C Xia, C Cochrane, J DeGuire, G Fan, E Holmes, M McGuirl, P Murphy, J Palmer, P Carter, L Slivinski, and B Sandstede.
Assimilating Eulerian and Lagrangian data in trafficflow models.
Physica D 346 (2017), pp. 5972. (preprint)
Assimilating Eulerian and Lagrangian data in trafficflow models.
Physica D 346 (2017), pp. 5972. (preprint)