Georgia Institute of Technology College of Sciences

Nanoengineered surfaces offer new possibilities to manipulate fluidic and thermal transport processes for a variety of applications including lab-on-a-chip, thermal management, and energy conversion systems. In particular, nanostructures on these surfaces can be harnessed to achieve superhydrophilicity and superhydrophobicity, as well as to control liquid spreading, droplet wetting, and bubble dynamics. In this talk, I will discuss fundamental studies of droplet and bubble behavior on nanoengineered surfaces, and the effect of such fluid-structure interactions on boiling and condensation heat transfer. Micro, nano, and hierarchical structured arrays were fabricated using various techniques to create superhydrophilic and superhydrophobic surfaces with unique transport properties. In pool boiling, a critical heat flux >200W/cm2 was achieved with a surface roughness of ~6. We developed a model that explains the role of surface roughness on critical heat flux enhancement, which shows good agreement with experiments. In dropwise condensation, we elucidated the importance of structure length scale and droplet nucleation density on achieving the desired droplet morphology for heat transfer enhancement. Accordingly, with functionalized copper oxide nanostructures, we demonstrated a 20% higher heat transfer coefficient compared to that of state-of-the-art dropwise condensing copper surfaces. These studies provide insights into the complex physical processes underlying fluid-nanostructure interactions. Furthermore, this work shows significant potential for the development and integration of nanoengineered surfaces to advance next generation thermal and energy systems.

A basic strategy for linear optimization over a complicated convex set is to try to express the set as the projection of a simpler convex set that admits efficient algorithms. This philosophy underlies all "lift-and-project" methods in optimization which attempt to find polyhedral or spectrahedral lifts of complicated sets. In this talk I will explain how the existence of a lift is equivalent to the ability to factorize a certain operator associated to the convex set through a cone. This theorem extends a result of Yannakakis who showed that polyhedral lifts of polytopes are controlled by the nonnegative factorizations of the slack matrix of the polytope. The connection between cone lifts and cone factorizations of convex sets yields a uniform framework within which to view all lift-and-project methods, as well as offers new tools for understanding convex sets. I will survey this evolving area and the main results that have emerged thus far.

Consider electrostatic plasmas described by Vlasov-Poisson with a fixed ion background. In 1946, Landau discovered the linear decay of electric field near a stable homogeneous state. This phenomena has been puzzling since the Vlasov-Poisson system is time reversible and non-dissipative. The nonlinear Landau damping was proved for analytic perturbations by Mouhot and Villani in 2009, but for general perturbations it is still largely open. I will discuss some recent results with C. Zeng on the failure of nonlinear daming in low regularity neighborhoods and a regularity threshold for the existence of nontrivial invariant structures near homogeneous states. A related problem to be discussed is nonlinear inviscid damping of Couette flow, for which the linear decay was first observed by Orr in 1907.

In this talk we will give a very elementary explanation of issues associated with the unique global solvability of three dimensional Navier-Stokes equation and then discuss various modifications of the classical system for which the unique solvability is resolved. We then discuss some of the fascinating issues associated with the stochastic Navier-Stokes equations such as Gaussian & Levy Noise, large deviations and invariant measures.