REU 2017
Subject of Study
Tsunami waves are a mesmerizing yet destructive natural phenomenon, and their study is important for establishing effective policy to accommodate the damages they may cause. These destructive events are typically generated by either the motion of tectonic plates or landslides. Tectonic tsunamis are the most common and can cause devastating destruction. (e.g., the 2011 Japan and 2004 Sumatra events). Landslides can also generate noticeable tsunamis such as the one in Lituya Bay, Alaska in 1958 that produced a wave that surged 1,700 feet up a hillside. In many physical situations, such as the aforementioned landslides and near shore earthquakes, waves originate near the shore directly on the sloping bay. The resultant waves can be modeled by nonlinear partial differential equations, and the most important issues are their formation, propagation, and the flooding that they cause. From the mathematical point of view, these equations are very challenging to deal with, and to analyze them, a large bulk of diverse mathematics should be employed. The initial value problem that arises is typically solved by the means of the generalized Carrier-Greenspan transformation, a type of hodograph transformation that reduces our equations, the cross-sectionally averaged shallow-water wave equations, to a linear system. Moreover, because the initial conditions are given on a curve, rather than on a line, this problem cannot be solved by standard analytical or numerical methods. This leads to a non-trivial problem in mathematical physics which we tackle here.
Students
Amir
Amir Raz has been in the REU program for the past two years, has recently graduated with a B.S. in physics from UAF in Spring 2017, and will be pursuing a Masters at the Weizmann Institute of Science. Apart from research, he enjoys hiking, climbing, birdwatching and drinking good beer.
Jody
Jody Gaines is currently a Graduate student in the Mathematics Program. He has a Bachelors in Mathematics and a minor in Music Performance. This is his second time in the REU program, with his first time being in Summer 2015. Jody hopes to earn his Master’s degree by Spring 2018.
Julia
Julia Olson is currently an undergraduate student in both the Mathematics and Psychology programs at UAF. This is her first time participating in research, and she is fascinated by everything she is learning through the program. After hopefully earning her Bachelor’s degree in Fall 2017, Julia intends to spend time traveling abroad.
Faculty
Rybkin, Alexei
Professor of Mathematics, UAF Department of Mathematics and Statistics
CHAP 304B 474-6002
Nicolsky, Dmitry
Research Assistant Professor, UAF Geophysical Institute
474-7397