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, the main thrust of my group’s research has been the development and the application of phase-field methods to a wide range of interface dynamical problems with ongoing projects spanning microstructural pattern formation in alloy solidification, stress-driven grain boundary motion and polycrystalline pattern evolution, semiconductor nanowire growth, as well as fracture phenomena and crack propagation in brittle materials. Phase field models typically employ a single or multiple order parameters to avoid explicit interface tracking and incorporate multiple physical phenomena (such as capillarity, interface kinetics, atomic diffusion, stress, etc) into a self-consistent set of nonlinear partial different equations that can be analyzed in certain limits and simulated on massively parallel computer architectures. Much of the excitement in this line of research has been generated by recent successes to combine atomistic and phase-field methods to make materials specific predictions on experimentally relevant length and time scales, which is becoming increasingly feasible due to the rapid advances in computer power. The phase-field crystal method that resolves the crystal density field has also emerged as an exciting new avenue for extending atomistic simulations to diffusive time scales. Our ongoing research tackles some important challenges involved in making this approach quantitative for crystalline solids. An ultimate practical goal of this research is to use computer simulations to guide the design and optimize the properties of a wide range of advanced technological materials.
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. Ventricular fibrillation claims about 300,000 lives per year in the US. While high risk patients can carry implantable defibrillators, reducing mortality in the wider population of patients who die suddenly and unpredictably from ventricular fibrillation has remained a major challenge. 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.