Summer 2013 Undergrad Research Program
This summer the topic of interest is the tsunami run-up problem in sloping bays of finite length with constant cross-sections. The run-up of long waves can be modeled by the 2D nonlinear shallow water wave equations. In sloping bays of constant cross-sections the Carrier-Greenspan (CG) transformation can simplify shallow water wave equations into a linear system with coulomb potential. The main feature of the new system is that the shoreline becomes a fixed point.
Using the CG transformation, an analytic solution can be found for tsunami run-up in bays of parabolic cross-section. An example of such a bay is:
Our program focused on using the CG transform to model run-up parabolic shaped bays via a spectral method. For the boundary conditions we assume that at the moving shoreline the wave velocity is bounded and for the offshore boundary the wave velocity is 0. The second boundary condition can , among other things, represent a vertical "wall". See here for more information.
Mentors and Students
Prof. Alexei Rybkin is the main coordinator of the REU program. He has a PhD in mathematics from Leningrad University (1985). Dr. Rybkin's area of research includes operator theory, complex analysis and mathematical physics.
Prof. Efim Pelinovsky (left) has contributed greatly to the world in terms of Tsunami modelling. He obtained his PhD in Physics and Mathematics from Gorky State University, Russia. His research interests are nonlinear waves, the ocean, and natural hazards.
Dmitry Nicolsky (left) is a tsunami numerical modeler at the UAF Geophysical Institute. His research is focused on the development and implementation of various geophysical models.
Matthew Harris has just recieved his undergraduate degree in mathematics. He worked on the REU last year and now he is leading the project for the rest of us undergraduates. Matthew is enrolled in the Masters of Mathematics program at UAF in the upcoming Fall semester.
John Pender (left) is studying undergraduate computer science at UAF.
Dr. Daniel Balkanov (right) is studying undergraduate computer engineering at UAF.
Christian Burns Shafer (left) is an undergraduate mathematics major. He enjoys web design, graphic design, most forms of art, and of course, mathematics. He studies mathematics for the purpose of improving his reasoning abilities. Once he obtains his bachelors degree, he intends to continue his education in mathematics and business administration.