Seminars and Colloquia by Series

Monday, November 8, 2010 - 13:00 , Location: Skiles 002 , Ernie Esser , University of California, Irvine , Organizer: Sung Ha Kang
In this talk, based on joint work with Xiaoqun Zhang and Tony Chan, we showhow to generalize the primal dual hybrid gradient (PDHG) algorithm proposedby Zhu and Chan to a broader class of convex optimization problems. A mainfocus will also be to survey several closely related methods and explain theconnections to PDHG. We point out convergence results for some modifiedversions of PDHG that have similarly good empirical convergence rates fortotal variation (TV) minimization problems. We also show how to interpretPDHG applied to TV denoising as a projected averaged gradient method appliedto the dual functional. We present some numerical comparisons of thesealgorithms applied to TV denoising and discuss some novel applications suchas convexified multiphase segmentation.
Monday, October 25, 2010 - 13:00 , Location: Skiles 002 (Ground floor, entrance from Skiles courtyard) , Christopher Larsen , WPI , Organizer:
I will describe a sequence of models for predicting crack paths in brittlematerials, with each model based on some type of variational principleconcerning the energy. These models will cover the natural range ofstatics, quasi-statics, and dynamics. Some existence results will bedescribed, but the emphasis will be on deficiencies of the models and openquestions.
Monday, October 11, 2010 - 13:00 , Location: Skiles 002 , Thorsten Stoesser , Georgia Tech Civil Engineering , Organizer:
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.
Monday, October 4, 2010 - 13:00 , Location: Skiles 002 , Michael Burkhart , Gatech, Math , Organizer: Luca Dieci
The over-abundance of remotely sensed data has resulted inthe realization that we do not have nor could ever acquire asufficient number of highly trained image analysts to parse theavailable data.  Automated techniques are needed to perform low levelfunctions, identifying scenarios of importance from the availabledata, so that analysts may be reserved for higher level interpretativeroles. Data fusion has been an important topic in intelligence sincethe mid-1980s and continues to be a necessary concept in thedevelopment of these automated low-level functions. We propose anapproach to multimodal data fusion to combine images of varyingspatial and spectral resolutions with digital elevation models.Furthermore, our objective is to perform this fusion at the imagefeature level, specifically utilizing Gabor filters because of theirresemblance to the human visual system.
Monday, September 20, 2010 - 13:00 , Location: Skiles 002 , Christopher Rorden , Center for Advanced Brain Imaging (Gatech/GSU) , Organizer: Sung Ha Kang
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.
Monday, August 23, 2010 - 13:00 , Location: Skiles 002 , Maria Cameron , U Maryland , Organizer:

I will propose two numerical approaches for minimizing the MFF. Approach
I is good for high-dimensional systems and fixed endpoints. It is
based on temperature relaxation strategy and Broyden's method. Approach
II is good for low-dimensional systems and only one fixed endpoint. It
is based on Sethian's Fast Marching Method.I will show the
application of Approaches I and II to the problems of rearrangement of
Lennard-Jones cluster of 38 atoms and of CO escape from the Myoglobin protein
respectively.

At low temperatures, a system evolving according to the overdamped Langevin equation spends most of the time near the potential minima and performs rare transitions between them. A number of methods have been developed to study the most likely transition paths. I will focus on one of them: the MaxFlux Functional (MFF), introduced by Berkowitz in 1983.I will reintepret the MFF from the point of view of the Transition Path Theory (W. E & E. V.-E.) and show that the MaxFlux approximation is equivalent to the Eikonal Approximation of the Backward Kolmogorov Equation for the committor function.
Friday, August 20, 2010 - 13:00 , Location: Skiles 154 , Xiao-Ping Wang , Hong Kong University of Science and Technology , Organizer: Haomin Zhou
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.
Monday, April 26, 2010 - 13:00 , Location: Skiles 255 , Elena Kartaschova , Johannes Kepler University , Organizer:
Nonlinear Resonance Analysis (NRA) is a natural next step after Fourieranalysis developed for linear PDEs. The main subject of NRA isevolutionary nonlinear PDEs, possessing resonant solutions. Importance ofNRA is due to its wide application area -- from climatepredictability to cancer diagnostic to breaking of the wing of an aircraft.In my talk I plan to give a brief overview of the methods and resultsavailable in NRA, and illustrate it with some examples from fluid mechanics.In particular, it will be shown how1) to use a general method of q-class decomposition for computing resonantmodes for a variety of physically relevant dispersion functions;2) to construct NR-reduced models for numerical simulations basing on theresonance clustering; theoretical comparision with Galerkin-like models willbe made and illustrated by the results of some numerical simulations withnonlinear PDE.3) to employ NR-reduced models for interpreting of real-life phenomena (inthe Earth`s atmosphere) and results of laboratory experiments with watertanks.A short presentation of the software available in this area will be given.
Monday, April 26, 2010 - 13:00 , Location: Skiles 255 , Luca Dieci , School of Mathematics, Georgia Tech , Organizer:
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]

Monday, April 19, 2010 - 13:00 , Location: Skiles 255 , Jae-Hun Jung , Mathematics, SUNY Buffalo , Organizer: Sung Ha Kang
Solutions of differential equations with singular source terms easily becomenon-smooth or even discontinuous. High order approximations of suchsolutions yield the Gibbs phenomenon. This results in the deterioration ofhigh order accuracy. If the problem is nonlinear and time-dependent it mayalso destroy the stability. In this presentation, we focus on thedevelopment of high order methods to obtain high order accuracy rather thanregularization methods. Regularization yields a good stability condition,but may lose the desired accuracy. We explain how high order collocationmethods can be used to enhance accuracy, for which we will adopt severalmethods including the Green’s function approach and the polynomial chaosmethod. We also present numerical issues associated with the collocationmethods. Numerical results will be presented for some differential equationsincluding the nonlinear sine-Gordon equation and the Zerilli equation.

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