Seminars and Colloquia by Series

High Resolution Numerical Simulations of Complex Hydraulic Engineering Flows

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 11, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 002
Speaker
Thorsten StoesserGeorgia Tech Civil Engineering
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.

Feature Based Fusion of Multimodal Data for Object Classification

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 4, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 002
Speaker
Michael BurkhartGatech, Math
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.

The left frontal lobe´s role in language

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 20, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 002
Speaker
Christopher Rorden Center for Advanced Brain Imaging (Gatech/GSU)
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.

Computing transition paths for rare events

Series
Applied and Computational Mathematics Seminar
Time
Monday, August 23, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 002
Speaker
Maria CameronU Maryland

Please Note: 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.

Modeling and simulation of two phase flow on rough surface

Series
Applied and Computational Mathematics Seminar
Time
Friday, August 20, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 154
Speaker
Xiao-Ping Wang Hong Kong University of Science and Technology
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.

CANCELLED - Nonlinear resonance analysis as a base for novel numerical models

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 26, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Elena KartaschovaJohannes Kepler University
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.

Sliding Modes and Fundamental Matrix Solutions of Piecewise Smooth Differential Systems

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 26, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Luca DieciSchool of Mathematics, Georgia Tech
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]

High order numerical methods for differential equations with singular sources

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 19, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Jae-Hun JungMathematics, SUNY Buffalo
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.

Influence of Cellular Substructure on Gene Expression and Regulation

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 12, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Samuel IsaacsonBoston University Mathematics Dept.
We will give an overview of our recent work investigating the influence of incorporating cellular substructure into stochastic reaction-diffusion models of gene regulation and expression. Extensions to the reaction-diffusion master equation that incorporate effects due to the chromatin fiber matrix are introduced. These new mathematical models are then used to study the role of nuclear substructure on the motion of individual proteins and mRNAs within nuclei. We show for certain distributions of binding sites that volume exclusion due to chromatin may reduce the time needed for a regulatory protein to locate a binding site.

Tight frame, Sparsity and Bregman algorithms

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 5, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Jianfeng CaiDep. of Math. UCLA
 Tight frame is a generalization of orthonormal basis. It  inherits most good properties of orthonormal basis but gains more  robustness to represent signals of intrests due to the redundancy. One can  construct tight frame systems under which signals of interests have sparse  representations. Such tight frames include translation invariant wavelet,  framelet, curvelet, and etc. The sparsity of a signal under tight frame systems has three different formulations, namely, the analysis-based sparsity, the synthesis-based one, and the balanced one between them. In this talk, we discuss Bregman algorithms for finding signals that are sparse under tight frame systems with the above three different formulations. Applications of our algorithms include image inpainting, deblurring, blind deconvolution, and cartoon-texture decomposition. Finally, we apply the linearized Bregman, one of the Bregman algorithms, to solve the problem of matrix completion, where we want to find a low-rank matrix from its incomplete entries. We view the low-rank matrix as a sparse vector under an adaptive linear transformation which depends on its singular vectors. It leads to a singular value thresholding (SVT) algorithm.

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