My research belongs to applied nonlinear mathematics and physical applied mathematics, with focuses on the following three areas. A central theme is the study of nonlinear differential equations via analytical and numerical means.
Nonlinear waves; Metamaterials; Nonlinear optics: I am interested in nonlinear waves in optical and mechanical metamaterials. My prior work focused on nonlinear edge waves in optical and mechanical topological insulators. I have also worked on dispersive shock waves in the KP and 2D BO equations, and self-similar solutions to the 2D hyperbolic NLS equation.
Climate dynamics; Statistical physics; Fluid mechanics: I am interested in meltwater patterns under-represented in climate models. My prior work focused on using statistical physics to explain the geometric characteristics of Arctic melt ponds. I have also worked on some fluid problems including Rayleigh-Bénard convection and Homann stagnation-point flow.
Pattern formation; Dynamical systems: I am interested in spatially localized states in driven dissipative systems. These solutions are often found using dynamical systems methods. My prior work focused on 1D and 2D localized Turing patterns in forced oscillatory systems. I have also worked on Turing-Hopf localized states in the 1D Brusselator model.
PhD, Physics1 Dec 2011 - 31 Dec 2099