Research Interests

Interfacial Fluid Mechanics

Many natural and technological processes involve interfacial phenomena occuring within the regions of intersection of several fluid and/or solid phases. Applications range from coating processes (the deposition of a liquid film on a solid substrate), to foams. In addition to capillary and gravitational effects, interfacial phenomena typically involve the interplay of complex processes such as wetting/dewetting, surface active materials, adhesion, temperature and/or compositional gradients, evaporation, etc. The goal of our research group is to improve our understanding of the fundamentals of interfacial phenomena by using a combination of mathematical modeling and advanced computational techniques.

Nonlinear Dynamics

Many dynamical systems are modeled by nonlinear equations which correctly predict many complex responses, such as subharmonic resonances, jump phenomenon, and chaos. In addition, the presence of noisy perturbations may drastically alter the long-term behavior of nonlinear systems and can lead to new phenomena. We study the complex interplay between nonlinearity, noise, and periodic forcing in dynamical systems. For instance we study the noise-induced transitions from one attractor to another, and predict the probability of these transitions. In a more general context, we examine first-passage problems in randomly perturbed dynamical systems. We also study the effect of noise on systems near bifurcation. This work is relevant to both physical and engineering systems.