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
our understanding of the
fundamentals of interfacial phenomena by using a combination of mathematical modeling
and advanced computational techniques.
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.