Georgia Institute of Technology College of Sciences

Expander graphs are known to facilitate effective routing and most real-world networks have expansion properties. At the other extreme, it has been shown that in some special graphs, removing certain edges can lead to more efficient routing. This phenomenon is known as Braess¹s paradox and is usually regarded as a rare event. In contrast to what one might expect, we show that Braess¹s paradox is ubiquitous in expander graphs. Specifically, we prove that Braess¹s paradox occurs in a large class of expander graphs with continuous convex latency functions. Our results extend previous work which held only when the graph was both denser and random and for random linear latency functions. We identify deterministic sufficient conditions for a graph with as few as a linear number of edges, such that Braess¹s Paradox almost always occurs, with respect to a general family of random latency functions. Joint work with Fan Chung and Wenbo Zhao. (* Note that this is an ARC/Theory Seminar and is in Klaus 1116W *)

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.

Further discussion of co-transcriptional RNA folding, and the potential for trap models to capture these dynamics.

We will discuss how best to model and predict the co-transcriptional effects of RNA folding. That is, using the fact that the RNA molecule begins folding as the sequence is still being transcribed, can we find better predictions for the secondary structure? And what is a good mathematical model for the process?