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2001 Spring Visit of CRSC to University of Paris VI

(from left to right) Alain Damlamian (U. Paris XII), Ricardo De Arcangelis (U. Napoli "Federico II"), Laura Potter (NCSU), Greg Hicks (NCSU), Diana Baltean (U. Paris VI), Nadia Ansini (U. Napoli), Doina Cioranescu (U. Paris VI), Michele Joyner (NCSU), H.T. Banks (NCSU), Patrizia Donato (U. Paris VI), Sara Monsurro (U. Napoli), David Bortz (NCSU), Julie Raye (NCSU).

During April, 2001, a group of 5 graduate students (L. Potter, M. Joyner, J. Raye, D. Bortz, and G. Hicks) and 1 faculty (H. T. Banks) from the CRSC visited Universite de Paris VI for a research exchange and collaborations with faculty, postdocs and graduate students from U. Paris VI and Universita di Napoli "Federico II". In addition to a number of scientific discussions during this visit, the following lectures were given by CRSC graduate students:

A Physiologically-based Model for the Systemic Transport of Trichloroethylene

Laura K. Potter
Center for Research in Scientific Computation
North Carolina State University
Raleigh, NC

A physiologically based pharmacokinetic (PBPK) model for the systemic transport of the environmental toxin trichloroethylene (TCE) will be discussed. Of particular interest is the distribution of TCE in the adipose (fat) tissue, where TCE is known to accumulate. Adipose tissue exhibits wide variations in fat cell size, blood flow properties and lipid distribution, suggesting a spatially-varying distribution of TCE inside the tissue.

To account for these heterogeneities, our PBPK model includes a PDE-based axial dispersion model for the adipose tissue compartment, with ODE-based compartments for the remaining tissues and organs. Theoretical and computational results relating to this model will be presented.

Modeling of HIV Infection Dynamics using Delay Equations

D. M. Bortz
Center for Research in Scientific Computation
North Carolina State University
Raleigh, NC

We investigate the viral dynamics of different strains of the Human Immunodeficiency Virus (HIV), motivated by the observation of different strains of the lentivirus in vivo and in vitro. Simulations of competition models are of particular interest to clinicians studying this phenomena. The corresponding systems consist of nonlinear distributed delay equations, to which we apply spline approximations. Analysis of different models as well as numerical results are presented during this talk.

Development and Testing of a Reduced Order Methodology for Eddy Current Based Nondestructive Evaluation Techniques

Michele L. Joyner
Center for Research in Scientific Computation
North Carolina State University
Raleigh, NC

In the field of nondestructive evaluation, new and improved techniques are constantly being sought to facilitate the detection of hidden corrosion and flaws in structures such as air foils and pipelines. We use eddy current based nondestructive evaluation techniques and reduced order modeling to explore the feasibility of detecting such subsurface damages. To explicitly identify the geometry of a damage, an optimization algorithm is employed which requires solving the forward problem numerous times. To implement these methods in a practical setting, the forward algorithm must be solved with extremely fast and accurate solution methods. Therefore, our computational methods are based on reduced order Proper Orthogonal Decomposition (POD) techniques. For proof-of-concept, we implement the methodology first on a 2-D simulated problem and then on an experimental test problem using a giant magnetoresistive (GMR) sensor and in both instances find the methods to be efficient and robust. Furthermore, the methods were fast; our findings suggest a significant reduction in computational time.

A Pressure-Dependent Model for Electromagnetic Interrogation

Julie K. Raye
Center for Research in Scientific Computation
North Carolina State University
Raleigh, NC

We consider an electromagnetic interrogation technique in which a travelling acoustic wave acts as a virtual interface for an oncoming electromagnetic wave. We propose that the coefficients in the polarization model are pressure-dependent and use this as a mechanism to describe the interaction between the waves. We present both computational and theoretical results.

Smart Endoscopes for Non-Destructive Evaluation

Gregory P.Hicks
Center for Research in Scientific Computation
North Carolina State University
Raleigh, NC

A topic of recent interest in the fields of robotics and control is snake- like mechanical devices to be used in NDE interrogation. Of the three primary types of snake motion observed, lateral undulation is the most difficult to explain. Successful attempts at explaining the mechanisms that allow for such motion have been formulated in the language of mechanical engineering. We are pursuing a mathematical model of the requirements for motion to be used in developing mathematical control laws for snake like devices. This talk will summarize our progress to date.




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