My interest lies in fluid dynamics, specifically in the singularity formation in flows with free surface. Dynamics of the ocean surface in the high steepness regime often demonstrates breaking waves, and whitecapping at the crests of the steep waves. These spectacular events are associated with singularity formation, and its evolution in the Euler (or Navier-Stokes) equations with the free boundary. In small steepness regime the envelope of a train of periodic travelling waves on the ocean surface is described by the nonlinear Schroedinger equation (NLSE), which is a spectacularly rich and interesting equation. The NLSE and other integrable systems are in the list of my most favoured models to work with. My toolbox consists of computational mathematics and methods of applied mathematics. I enjoy coding in C, Python, Matlab and Julia.
- Ph.D. Applied Mathematics, University of New Mexico, August 2014