REU Supplement
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National Science Foundation |
Overview
Traveling waves are ubiquitous in nature, occurring everywhere from population dynamics in ecology to the propagation of tsunamis in the oceanic sciences, or from the formation of shock waves from a supersonic jet to the flickering pulses of light in a fiber optic cable. In this program, we present students with research opportunities to do research in nonlinear partial differential equations (PDE), with a particular emphasis in traveling waves.
Program Areas
- Stability: The stability properties of evolutionary systems describe the degree to which they can propagate and persist in the presence of disturbances. This work focuses on the mathematics of traveling waves and develops computational methods for exploring their stability in a myriad of areas in the pure and applied sciences.
- Dynamics of Traveling Waves: This project focuses on front propagation arising in the continuum and kinetic theories of compressible flow. This class of problems models key real-world phenomena such as shock waves in a viscous gas or plasma, detonations in a reactive gas, and the propagation of phase boundaries in a viscous fluid.
- Applications of Nonlinear Waves: Projects include shock wave methods in image analysis, reaction-diffusion equations, and modeling in finance.
REU Students
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