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Monday, December 6, 2010 - 13:00 ,
Location: Skiles 255 ,
Shawn Walker ,
LSU Mathematics Dept. ,
Organizer:

Locomotion at the micro-scale is important in biology and in industrialapplications such as targeted drug delivery and micro-fluidics. Wepresent results on the optimal shape of a rigid body locomoting in 3-DStokes flow. The actuation consists of applying a fixed moment andconstraining the body to only move along the moment axis; this models theeffect of an external magnetic torque on an object made of magneticallysusceptible material. The shape of the object is parametrized by a 3-Dcenterline with a given cross-sectional shape. No a priori assumption ismade on the centerline. We show there exists a minimizer to the infinitedimensional optimization problem in a suitable infinite class ofadmissible shapes. We develop a variational (constrained) descent methodwhich is well-posed for the continuous and discrete versions of theproblem. Sensitivities of the cost and constraints are computedvariationally via shape differential calculus. Computations areaccomplished by a boundary integral method to solve the Stokes equations,and a finite element method to obtain descent directions for theoptimization algorithm. We show examples of locomotor shapes with andwithout different fixed payload/cargo shapes.

Monday, November 29, 2010 - 13:00 ,
Location: Skiles 255 ,
Yunho Kim ,
University of California, Irvine ,
Organizer: Sung Ha Kang

It has been suggested by Y. Meyer and numerically confirmed by many othersthat dual spaces are good for texture recovery. Among the dual spaces, ourwork focuses on Sobolev spaces of negative differentiability to recovertexture from noisy blurred images. Such Sobolev spaces are good to modeloscillatory component, on the other hand, the spaces themselves hardlydistinguishes texture component from noise component because noise is alsoconsidered to be a highly oscillatory component. In this talk, in additionto oscillatory component recovery, we will further investigate aone-parameter family of Sobolev norms to achieve such a separation task.

Monday, November 22, 2010 - 13:00 ,
Location: Skiles 255 ,
Antonio Capella-Kort ,
Universidad Nacional Autónoma de México (UNAM) ,
Organizer:

We are interested in the cubic to tetragonal phase transition in a shape memory alloy. We consider geometrically linear elasticity. In this framework, Dolzmann and Mueller have shown the following rigidity result:The only stress-free configurations are (locally) twins (i.e. laminates of just two of the three Martensitic variants).However, configurations with arbitrarily small elastic energy are not necessarily close to these twins: The formation of microstructure allows to mix all three Martensitic variants at arbitrary volume fractions. We take an interfacial energy into account and establish a (local) lower bound on elastic + interfacial energy in terms of the Martensitic volume fractions. The model depends on a non-dimensional parameter that measures the strength of the interfacial energy. Our lower, ansatz-free bound has optimal scaling in this parameter. It is the scaling predicted by a reduced model introduced and analyzed by Kohn and Mueller with the purpose to describe the microstructure near an interface between Austenite and twinned Martensite. The optimal construction features branching of the Martensitic twins when approaching this interface.

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.