Current Research
Arrhythimic Dynamics of Cardiac Tissue
Our research uses the tools and techniques of dynamical systems to study cardiac arrhythmias ranging from mild tachycardia to lethal fibrillation, with the ultimate goal of developing effective and reliable defibrillation methods. Numerical simulations and experimental studies have identified fibrillation with the breakup of spiral waves of excitation in the heart tissue. However, neither approach has produced a clear picture of what the mechanism responsible for initiating and sustaining fibrillation is. Furthermore, it is well known that both the normal beating and fibrillation are natural behaviors even in healthy hearts. Fibrillation can be provoked and stopped by an external perturbation. However the threshold for fibrillatory dynamics is much lower in disease-ridden hearts. The transition mechanism therefore is not related to the classical supercritical instabilities typical of pattern-forming systems but rather involves a subcritical instability akin to the transition to turbulence in fluid flows.
Transition to Turbulence in Fluid Flows
Fluids tend to undergo a transition from laminar to turbulent flow as the rate of shear increases. Although both transition mechanisms and the statistics of turbulent motion can differ widely, turbulent flows in any geometry some key common features. While the flow is generally very complicated and seemingly disorganized, it occasionally organizes itself to resemble, for a short time, one or another recurrent structure. These structures have been identified as exact regular (steady, time-periodic, and so on) solutions of the Navier-Stokes equation. Our research is focused on testing the hypothesis that these unstable regular solutions can be used to construct a reduced-order model of weakly turbulent flows. Once constructed, this low-dimensional description will be used to develop a nonlinear flow control algorithms capable of relaminarizing fully developed turbulence. This problem is currently being explored in the context of several canonical geometries: 2D Kolmogorov flow, Taylor-Couette flow, and 2D/3D channel flow.
Free Surface Flows with Phase Change
Rayleigh-Benard and Marangoni convection in a layer of a homogeneous fluid with a free surface in the absence of phase change is a classic (and extensively studied) problem of fluid mechanics. In particular, for binary fluids, the thermocapillary stresses at the free surface can be augmented (or, more commonly, opposed) by solutocapillary stresses which arise due to the Soret effect (the concentration flux caused by an imposed temperature gradient), resulting in considerably richer dynamics. Phase change has a major effect on the convection problem. Most notably, significant latent heat generated at the free surface as a result of phase change can dramatically alter the interfacial temperature, and hence, the thermocapillary stresses. Furthermore, differential evaporation in binary fluids provides a substantially more efficient mechanism, compared with the Soret effect, for enhancing the variation in the concentration field, and can generate significant solutocapillary stresses. Our research focuses on constructing a comprehensive quantitative description of mass and heat flux in this nonequilibrium system.
Movies of unsteady convection in a layer of silicone oil can be downloaded here.
Financial support provided by
- National Science Foundation
- Army Research Office
- Office of Naval Research
- National Aeronautics and Space Administration
- Petroleum Research Fund