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2004 Spring Semester Visit of CRSC to University of Paris VI


Saying good-bye after dinner.


In March, 2004, during NCSU's spring break, Dr. H. T. Banks and eight of his graduate student advisees visited the Laboratoire J.-L. Lions at Universite de Paris VI for a formal exchange of presentations on current research, aptly named "Journees Jeunes" or "Days of the Youth". The conference was organized by Doina Cioranescu and divided into two days of alternating presentations from French and American students and post-docs. The first day was devoted to numerical methods and modeling related to various physical science applications including acoustics, electromagnetics and hysteresis. The second day featured research in biological sciences such as population dynamics, HIV infection dynamics, and modeling of human organs. More details on the CRSC contributed talks can be found below.

After two days and nearly 20 presentations full of research and computational results, the group was happy to enjoy a festive dinner at a local restaurant with their Parisian hosts. Other recreational activities included sight-seeing, wine and cheese tasting, and numerous museums.

Click the title to skip to the abstract:

Nicholas Luke -- Noise Reduction in a Cylindrical Duct


In this lecture, we will investigate a method for noise reduction in a cylindrical geometry (such as a duct). We propose that the addition of waveguides having particular fundamental frequencies should create destructive interference in the geometry, thus causing a reduction in the sound emitted from the duct. The proposed method will be outlined, preliminary experimental results are presented, and future proposals and concerns shall be addressed.

Brandy Benedict -- Computational Eddy Current-Based Methods in Nondestructive Damage Detection


Nondestructive evaluation of material integrity in a practical setting requires real-time implementation of computational methods which are both fast and highly accurate. A summary of research efforts in this field to date will be presented, including a 2D model of eddy-current behavior in conductive materials, a comparison between simulated solutions and experimental data, and the reduced-order numerical methods used to solve the inverse problem of characterizing the damage given the measured data. Our results suggest that a Proper Orthogonal Decomposition (POD) method can be a very effective tool in nondestructive evaluation, especially when one is treating full 3D systems. Proposed new efforts required will be discussed. This work is in collaboration with W. Winfree and B. Wincheski at NASA Langley Research Center.

Nathan L. Gibson -- Gap Detection with Electromagnetic Terahertz Pulses


We apply an inverse problem formulation to determine characteristics of a defect from a perturbed electromagnetic interrogating signal. A defect (gap) inside of a dielectric material causes a disruption, via reflections and refractions at the material interfaces, in the windowed interrogating signal. We model the electromagnetic waves inside the material with Maxwell's equations. Using simulations as forward solves, our Newton-based, iterative optimization scheme resolves the dimensions and location of the defect. Numerical results, including standard errors, will be presented, and computational issues will be addressed. Our research (in collaboration with W. Winfree) is supported by NASA with the ultimate goal of designing devices for damage detection for use in applications such as preventing separation of foam from the space shuttle fuel tanks.

Jeffrey Braidon Hood -- Molecular-Based Models for Hysteresis


Several papers have been written which deal with hysteresis of polymers on a larger, macro-molecular scale. We present an alternative approach to understanding this hysteresis, on a molecular level. We will discuss the materials we work with, and what is meant by hysteresis of these materials. We present a model for the motion of a polymer in a melt (a viscous fluid, such as agar-agar) along with simulation results, as well as a means of detecting such polymers using wave scattering. This research is done, in collaboration with Dr. H.T. Banks and Dr. N.G. Medhin, through the CRSC at NCSU, and is supported by a U.S. Air Force grant with future goals of designing molecular scaled machines.

Jimena Davis and Sarah Grove -- Distributions of Growth Rates in Size-Structured Mosquitofish Population Models


Mosquitofish are used in place of chemicals to control mosquito populations in rice fields. While biologists have used mosquitofish in the place of chemicals for some time, they have not fully understood the mechanisms behind the growth of the mosquitofish populations. With more knowledge of mosquitofish populations dynamics, biologists would be able to better control the mosquito populations in rice fields. Thus, a mathematical model that accurately describes the growth and decline in the mosquitofish population would be beneficial in this application as well as in other research areas involving population dynamics and aggregate data. We will be presenting the Sinko-Streifer population model as well as the Growth Rate Distribution model of Banks-Botsford-Kappel-Wang. Included are our results for the initial condition driven solution to the models. This work is supported through fellowships from the Statistical and Applied Mathematical Sciences Institute (SAMSI).

Lara K. Dick -- Prediction of Life History Traits in Invertebrate Species Exposed to Pesticides


Due to environmental concerns, newer pesticides are becoming less lethal than older pesticides, thus leaving more survivors behind. The main concern has shifted from LC_50 (concentration that kills 50% of a population) to survival and recovery delays, therefore evaluating efficacy of the pesticides requires more than just counting dead species. A deterministic age structured matrix model that incorporates a species' life history traits (such as birth rate, death rate and fecundity) has been developed by Wennergren and Stark. This model will be presented along with a proposed continuous age structured population model that would permit more detailed investigations of sublethal changes in population traits. This research is in collaboration with J. E. Banks (University of Washington) and J. D. Stark (Washington State University).

Brian Adams -- Modeling and Parameter Estimation in HIV Infection Dynamics


Structured Treatment Interruptions (STIs) of HIV drug therapy have recently excited researches interested in reducing side effects of drugs and stimulating or self-vaccinating the immune system. We summarize features necessary for nonlinear differential equation models of in-host HIV dynamics to predict possible STI outcomes. We report on an inverse problem methodology (including sensitivity analysis and generalized least squares) using simulated data, based on experience with actual patient data, and discuss implications of available data on estimating particular model parameters. Work presented in this talk is part of a larger initiative based at NCSU, including statistics, modeling, and control theory, and is in collaboration with Marie Davidian, Hien Tran, Hee-Dae Kwon, Shannon Wynne, and Yanyuan Ma.




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