Seminars and Colloquia by Series

Exponential Time Differencing (ETD) Schemes for Nonlinear Reaction-Diffusion Systems

Series
Applied and Computational Mathematics Seminar
Time
Monday, August 27, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bruce A. WadeDepartment of Mathematical Sciences, University of Wisconsin-Milwaukee
We discuss various exponential time differencing (ETD) schemes designed to handle nonlinear parabolic systems. The ETD schemes use certain Pade approximations of the matrix exponential function. These ETD schemes have potential to be implemented in parallel and their performance is very robust with respect to the type of PDE. They are unconditionally stable and computationally very fast due to the technique of computing the nonlinear part explicitly. To handle the problem of irregular initial or boundary data an adaptive ETD scheme is utilized, which adds sufficient damping of spurious oscillations. We discuss algorithm development, theory and applications.

Slow feature analysis and decorrelation filtering for separating correlated images

Series
Applied and Computational Mathematics Seminar
Time
Wednesday, June 13, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Minh Ha-QuangItalian Institute of Technology
Slow Feature Analysis (SFA) is a method for extracting slowly varying features from input signals. In this talk, we generalize SFA to vector-valued functions of multivariables and apply it to the problem of blind source separation, in particular image separation. When the sources are correlated, we apply the following technique called decorrelation filtering: use a linear filter to decorrelate the sources and their derivatives, then apply the separating matrix obtained on the filtered sources to the original sources. We show that if the filtered sources are perfectly separated by this matrix, then so are the original sources.We show how to numerically obtain such a decorrelation filter by solving a nonlinear optimization problem. This technique can also be applied to other linear separation methods, whose output signals are uncorrelated, such as ICA.This is joint work with Laurenz Wiskott (Proceedings of the 13th IEEE International Conference in Computer Vision, ICCV 2011, Barcelona, Spain).

On Some Variational Models and Their Algorithms from Image Segmentation and Registration

Series
Applied and Computational Mathematics Seminar
Time
Friday, May 18, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
006 Skiles
Speaker
Ke ChenUniversity of Liverpool
Both segmentation and registration are important image processing tasks in a number of real life applications. While there exist powerful and effective models,many scientific challenges remain open. In this talk, I shall first present some image segmentation work of modelsand algorithms in two and three dimensions, followed by some recent works of selective segmentationThen I introduce some new work on multimodality image registration modelling.Numerical experiments will demonstrate the advantages of our new models and algorithms over existing results. Collaborators related to this work include Noor Badshah (Peshawar, Pakistan), Jian-ping Zhang and Bo Yu (Dalian, China),Lavdie Rada (Liverpool), C Brito (Mexico) and N Chumchob (Thailand).

Optimization of two-link and three-link snake-like locomotion

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 23, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Fangxu JingGT Math
We analyze two-link (or three-link) 2D snake like locomotions and discuss the optimization of the motion. The snake is modeled as two (or three) identical links connected via hinge joints and the relative angles between the links are prescribed as periodic actuation functions. An essential feature of the locomotion is the anisotropy of friction coefficients. The dynamics of the snake is analyzed numerically, as well as analytically for small amplitude actuations of the relative angles. Cost of locomotion is defined as the ratio between distance traveled by the snake and the energy expenditure within one period. Optimal conditions of the highest efficiency in terms of the friction coefficients and the actuations are discussed for the model.

Introduction to Synthetic-Aperture Radar Imaging

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 16, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Margaret CheneyRensselaer Polytechnic Institute
Radar imaging is a technology that has been developed, verysuccessfully, within the engineering community during the last 50years. Radar systems on satellites now make beautiful images ofregions of our earth and of other planets such as Venus. One of thekey components of this impressive technology is mathematics, and manyof the open problems are mathematical ones.This lecture will explain, from first principles, some of the basicsof radar and the mathematics involved in producing high-resolutionradar images.

A numerical study of vorticity enhanced heat transfer

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 9, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Xiaolin WangGT Math
The Glezer lab at Georgia Tech has found that vorticity can improve heat transfer efficiency in electronic hardware. Vortices are able to enhance the forced convection in the boundary layer and fully mix the heated fluid with cooler core flow. Some recent experiments showed the possibility of using a vibrated reed to produce vortices in heat sinks. In this work, we simulate both the fluid and the heat transfer process in a 3-dimensional plate fin heat sink. We propose a simplified model by considering flow and temperature in a 2-D channel, and extend the model to the third dimension using a 1-D heat fin model. We simulate periodically steady-state solutions. We show that the total heat flux transferred from the plate to the fluid can be improved with vortices given the same input power. A possible optimal solution for the largest heat transfer efficiency is proposed for the physical parameters of a real computer heat sink. We discuss the effect of the important parameters such as Reynolds number and thermal conductivities.

A Computational Approach to Understanding Cardiac Arrhythmias

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 2, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Elizabeth CherrySchool of Mathematical Sciences, Rochester Institute of Technology
The heart is an excitable system in which electrical waves normally propagate in a coordinated manner to produce an effective mechanical contraction. Rapid pacing can lead to the development of alternans, a period-doubling bifurcation in electrical response in which successive beats have long and short responses despite a constant pacing period. Alternans can develop into higher-order rhythms as well as spatiotemporally complex patterns that reflect large regions of dispersion in electrical response. These states disrupt synchrony and compromise the heart's mechanical function; indeed, alternans has been observed clinically as a precursor to dangerous arrhythmias, including ventricular fibrillation. In this talk, we will show experimental examples of alternans, describe how alternans develops using a mathematical and computational approach, and discuss the nonlinear dynamics of several possible mechanisms for alternans as well as the conditions under which they are likely to be important in initiating dangerous cardiac arrhythmias.

New Numerical Linear Algebra Techniques for Brownian Simulation of Macromolecules

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 26, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Edmond Chow School of Computational Science and Engineering, Georgia Institute of Technology
Brownian dynamics (BD) is a computational technique for simulating the motions of molecules interacting through hydrodynamic and non-hydrodynamic forces. BD simulations are the main tool used in computational biology for studying diffusion-controlled cellular processes. This talk presents several new numerical linear algebra techniques to accelerate large BD simulations, and related Stokesian dynamics (SD) simulations. These techniques include: 1) a preconditioned Lanczos process for computing Brownian vectors from a distribution with given covariance, 2) low-rank approximations to the hydrodynamic tensor suitable for large-scale problems, and 3) a reformulation of the computations to approximate solutions to multiple time steps simultaneously, allowing the efficient use of data parallel hardware on modern computer architectures.

Numerical methods for stochastic bio-chemical reacting networks with multiple time scales

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 5, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Di LiuDepatment of Mathematics, Michigan State Univeristy
Multiscale and stochastic approaches play a crucial role in faithfully capturing the dynamical features and making insightful predictions of cellular reacting systems involving gene expression. Despite theiraccuracy, the standard stochastic simulation algorithms are necessarily inefficient for most of the realistic problems with a multiscale nature characterized by multiple time scales induced by widely disparate reactions rates. In this talk, I will discuss some recent progress on using asymptotic techniques for probability theory to simplify the complex networks and help to design efficient numerical schemes.

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