Georgia Institute of Technology College of Sciences

In this talk, results of high-resolution numerical simulations of some complex flows that are occurring in the area of hydraulic engineering will be presented. The method of large-eddy simulation is employed to study details of the flow over rough and porous channel beds, flow in an ozone contactor and the flow through idealized emergent vegetation. The main objective of the simulations is to gain insight into physical mechanisms at play. In particular, flow unsteadiness and coherent turbulence structures are important contributors to mass and momentum transfer in open channels. The performed large-eddy simulations allow revealing and quantifying these coherent structures.

This talk showcases how we can use emerging methods to understand brainfunction. Many of the techniques described could be optimized usingtechniques being developed by researchers in the GT Mathematicsdepartment. A primary tenet of neuroscience is that the left frontal lobeis crucial for speech production and the posterior regions of the lefthemisphere play a critical role in language comprehension and wordretrieval. However, recent work shows suggests the left frontal lobe mayalso aid in tasks classically associated with posterior regions, such asvisual speech perception. We provide new evidence for this notion based onthe use brain imaging (structural and functional MRI) and brainstimulation techniques (TMS and tDCS) in both healthy individuals andpeople with chronic stroke. Our work takes these theoretical findings andtests them in a clinical setting. Specifically, our recent work suggeststhat stimulation of the frontal cortex may complement speech therapy inchronic stroke. Our recent brain stimulation work using transcranialdirect current stimulation supports this hypothesis, illustrating smallbut statistically significant benefits in anomia following brainstimulation.

In this talk, I will  describe a newly developed phase field model for two phase fluid flow based on Cahn Hilliard  Navier Stokes equation with generalized Navier boundary condition.  Homogenization method is used to derive  the Wenzel's and Cassie's equations for two phase flow on rough surfaces. Efficient numerical method for the model will also be discussed. We then present some numerical results on two phase flow on rough and patterned surfaces.

In this seminar we consider piecewise smooth differential systems of Filippov type, in which the vector field varies discontinuously as solution trajectories reach one or more surfaces. Emphasis is on the fundamental matrix solution associated to these systems. We consider the cases of transversal intersection and of sliding motion on a co-dimension one surface and when sliding motion takes place on a co-dimension two surface (the intersection of two co-dimension one surfaces). [Joint work with L.Lopez, Univ. of Bari]