Amgen Scholars: Announcements of Opportunity
Below are Announcements of Opportunity posted by Caltech faculty for the Amgen Scholars program.
Announcements of Opportunity are posted as they are received. Please check back regularly for new AO submissions! Remember: This is just one way that you can go about identifying a suitable project and/or mentor. For additional tips on identifying a mentor click here.
Please remember:
- Students pursuing Amgen must be U.S. citizens, U.S. permanent residents, or students with DACA status.
- Students pursuing Amgen must complete the 10-week program from June 21 - August 25, 2023. Students must commit to these dates. No exceptions will be made.
- Accepted students must live in provided Caltech housing.
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| Project: | Stability of Periodic Traveling Waves | ||||||||
| Disciplines: | Mathematics, Computational and Mathematical Sciences | ||||||||
| Mentor: |
Jared Bronski,
Professor of Mathematics, (PMA),
bronski@illinois.edu, |
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| Background: |
NOTE: This project is being offered by a Caltech alum and is open only to Caltech students. The project will be conducted at University of Illinois, Urbana-Champaign located in Urbana, Illinois. Many nonlinear dispersive partial differential equations support coherent structures such as traveling waves. One very physically important question is that of stability: whether nearby initial conditions remain close to the traveling wave or diverge from it. We are particularly interested in studying this question for partial differential equations with Hamiltonian structure, such as the Korteweg-DeVries and nonlinear Schrödinger equations. |
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| Description: | We have a couple of potential projects, mostly focusing on the stability of periodic wavetrains (as opposed to localized solutions such as solitary waves). Depending on the interests and skill set of the student the project could range from primarily numerical to primarily analytical. | ||||||||
| References: |
The book “Spectral and Dynamical Stability of Nonlinear waves” by Kapitula and Promislow covers a lot of the basic ideas https://link.springer.com/book/10.1007/978-1-4614-6995-7 Margaret Beck’s lecture notes are a nice introduction, though they are primarily focused on dissipative equations, not Hamiltonian equations. http://math.bu.edu/people/mabeck/bremen-lecture-notes.pdf |
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| Student Requirements: | none listed | ||||||||
| Programs: |
This AO can be done under the following programs:
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