Spring 2003 GSS Schedule

Organizer: Art Gorka

Date Speaker Topic Abstract
January 20 MLK Holiday
January 27 Art Gorka Statistical properties of the Random Method of Feasible Directions In this talk we will be looking at the working of the Random Method of Feasible Directions. The algorithm is considered to be a mapping transforming uniform distributions to some other type (skewd normal, dychotomic, increasing or decreasing etc) distributions. We atempt to describe these distributions and use the findings to improve the performance of the algorithm.
February 3 Jira Limbupasiriporn Permutation Decoding Permutation decoding is a technique for decoding linear codes, which was developed in 1964 by F.J. McWilliams. The decoding can be used when a code has a large group of automorphisms to ensure the existence of a set S of automorphisms that satisfies certain conditions. Thus a PD-set S for a code C is a set of automorphisms of C such that if C can correct t errors, then the non-zero entries in every possible error vector of weight <= t can be moved by some member of S out of the information positions. The set S will then be used to assist in decoding a received vector.

In this talk, we will introduce some basic concepts on coding theory that are necessary for our purpose and then discuss the algorithm for permutation decoding. We will also give some simple examples to explain the decoding.
February 10 Jeff Farr Interpolating Points in Higher Dimensions The well-known problem of polynomial interpolation involves finding a suitable (usually small) polynomial f such that f(Pj)=0 for a collection of points P1,..., Pn. There are many ways to find an interpolating polynomial in the two-dimensional case, i.e., when Pj=(aj,bj). Standard algorithms include Lagrange interpolation and Newton interpolation. However, interpolating points in higher dimensions presents more of a challenge. We discuss solutions to this problem, including a new generalization of Newton interpolation. We also apply this algorithm to a decoding problem for algebraic geometry codes.
February 17 David Szurley Optimal Control For Polymer Process Modelling The fibers and films industry provides a wealth of mathematical modeling opportunities. For example, the processes by which the polymeric fibers and films are manufactured can be formulated as a system of nonlinear partial differential equations. Accurate simulation can significantly reduce trial-and-error experiments needed to determine optimal operating conditions for the process lines. The introduction of optimization techniques moves the simulation effort from prediction to design, automating the search for optimal process conditions. In this talk, optimization-based simulation is presented for fiber melt spinning and film casting. A system of ordinary differential equations governs the one-dimensional approximation under the assumption of steady-state behavior. Both simple and advanced optimization strategies are demonstrated. Here's an example where the fibers are used.
February 24 Kelly Waters Implementation and Numerical Results for a massively parallel generalized Stokes solver The generalized Stokes problem often arises as an iterated subproblem in solving time dependent flow problems. Glowinski & Pironneau developed a means of decomposing the velocity and pressure variables for this problem. In the FEM setting, the divergence-free condition is enforced by the computation of an appropriate value for the pressure along the boundary of the domain of the flow governing PDE. Phase one includes building two large linear operators, U & P, and a relatively small but costly linear operator, B, to calculate the boundary pressure directly. Once phase one is accomplished, it need not be repeated. Phase two makes use of U, P, and B, and produces solutions for successive input values - that is, phase two is the iterated subproblem in the time dependent flow problem.

In this talk we briefly present the method of Glowinski and Pironneau, along with a discussion of our parallel implementation using a Peaceman Rachford linear solver that decomposes the U & P operators into two permuted block diagonal symmetric positive definite systems. We also present numerical results including FEM error estimates, a parameter study, and timing results from solving a few example problems on up to 32 nodes on a Beowulf Cluster.

Ya'll come - it'll be fun:)
March 3 John Paul Roop Investigating fractional order diffusive processes: Analysis and numerics In this talk, we will discuss the physical implications of modeling diffusive processes using fractional dimensional operators. We will discuss analytic results which show the mapping properties of these operators in a Hilbert space setting. We introduce a least-squares finite element variational method which is used to solve the steady-state and transient problems. Numerical results are included which show error convergence as well as the differences between different sets of modeling equations. Here there are a few profiles for the same problem.
March 10 Robert Beeler Mental Illness and the Mathematician It is said that there is a thin line between genius and insanity. In this talk, we will take a brief look at mathematicians who stepped over this line and were plagued by schizophrenia, paranoia, and emotional imbalance. Tragically , the lives and careers of several great mathematicians were diminished due to their struggle with menal illness. Mathematicians to be included are Blaise Pascal, Isaac Newton, Georg Cantor, Kurt Godel, John Nash, and the infamous Unabomber, Theodore Kaczynski. Other mathemaicians may be discussed if time permits.
March 17 Spring Break
March 24 Thomas McCoy An Introduction to Multivariate Statistical Quality Control In this talk we will be discussing the advantages of introducing multivariate techniques to traditional quality control tools, specifically, control charts for process average and dispersion. When looking at process characteristics simultaneously, the region of control is elliptical due to the correlation structure of the monitoring characteristics. A discussion of univariate control charts will be provided, with their important connection with Process Capability, and examples given. The motivation for the extension to the multivariate case will be also given, noting the important considerations of controlling the accumulation of Type I errors in monitoring many processes individually.

Multivariate control charts will be introduced by looking primarily at Hotelling's T2 charts for process averages and dispersion. Connections with Mahalanobis distance and the incorporation of correlation among process monitoring characteristics will be examined.
March 31 Darek Wlodarczyk Dynamic Multi-Body Contact Problems with Friction Dynamic multi-body contact problems arise in several research areas. Modeling the dynamic behaviour of rigid bodies in contact is difficult, especially when friction is present and the number of contacts is large.

In this talk we will formulate the problem as a linear complementarity problem (LCP). We will introduce LCPs and discuss a few algorithms that solve LCPs. Simple 2-D simulations will be presented.
April 7 Mark Liu What's Fair? Fairness has always been a topic of interest to mankind. (This applies to other animals as well but we spare them of that spotlight at the moment.) If Jack and Jill came up with $5 each and bought a $10 cake, what should be the fair way of dividing the cake? If a bank rupts, what is a fair way to divide the available money to its account holders? Or more applicably, if you and your buddy decide to share an apartment here at the Clemson Metropolitan, how much of the rent should each person pay? How about divorces? How about dividing estate?

This talk will be somewhere at the intersection of simple Equity Theory, Social Choice Theory, and Mechanism Design. The content should be accessible enough for new undergrads. We will also talk about the Talmud (a subset of the Jewish civil and canonical laws) and one of its many wonders as well.
April 14 Rachel Keller What do you get when you cross a Swiss psychologist with 2 Dutch educators? Are your students not understanding the material you present? Do you think that your students are understanding you, but you find they disappoint you come test day? Ever wonder who is to blame for this? Although many of us blame our students, some of the experts would disagree. Piaget claims that the students are not to blame for this problem because many of them have not yet acquired crucial cognitive skills necessary for this level of math. The van Hieles claim that the students are not to blame because with the proper instruction, any student can achieve success at any level of mathematics.

Throughout this talk, we will examine Piaget's model of cognitive development, as well as the van Hiele model of the development of geometric thought. We will compare and contrast these two models, and also look at suggestions for implementation in the classroom.
April 21 Kevin Hutson My Experiences with the Academic Job Search Looking for a job in academics? The process of finding a (first academic) job can be overwhelming and exhausting. In this talk, I describe my recent experiences while on the job market. The topics I will discuss are: how to prepare early, the interview process, juggling offers, and frequently asked questions.