My main research interest lies in theoretical understanding of the emergence of nonequilibrium patterns in nonlinear systems with applications to diverse problems in materials science and biology that are both of fundamental and practical relevance. This research makes extensive uses of mathematical models and computational approaches rooted in nonequilibrium statistical physics and nonlinear dynamics. In the materials arena, a main focus in my group has been the application of the phase-field method to microstructural pattern formation in alloys. A more recent focus is the extension of this method to stress driven processes leading to materials failure such as crack propagation and crystal decohesion. In the biological arena, our efforts have focused on understanding basic mechanisms of "cardiac arrhythmias", a term commonly used to describe irregular heart rhythms. Of particular interest is ventricular fibrillation, a turbulent rhythm that stops the heart from pumping and is the leading cause of sudden death among industrialized nations. Our recent studies have focused on elucidating the origin of spatiotemporal patterns of period doubling oscillations of calcium and voltage signals in cardiac cells and tissue (networks of cardiac cells) that make the heart susceptible to the onset of life-threatening arrhythmias and fibrillation. This research has the potential to improve current means to identify high risk patients and to prevent cardiac fibrillation beyond the limitations of current therapies, either pharmacologically, or using low amplitude electrical stimuli as an alternative to a massive defibrillatory shock.
Articles
Unidirectional pinning and hysteresis of spatially discordant alternans in cardiac tissue (with Per S. Skardal and Juan G. Restrepo), Physics Faculty Publications (2012)
Spatially discordant alternans is a widely observed pattern of voltage and calcium signals in cardiac...
Amplitude equations for polycrystalline materials with interaction between composition and stress, Physics Faculty Publications (2010)
We investigate the ability of frame-invariant amplitude equations [G. H. Gunaratne, Q. Ouyang, and H....
Coupled dynamics of voltage and calcium in paced cardiac cells (with Yohannes Shiferaw and Daisuke Sato), Physics Faculty Publications (2005)
We investigate numerically and analytically the coupled dynamics of transmembrane voltage and intracellular calcium cycling...