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2003 Spring Visit of CRSC to University of Paris VI

Once again a group of graduate students and post-docs from the CRSC traveled to Paris for a research and cultural exchange. In April, 2003, Dr. H. T. Banks and five of his advisees visited Universite de Paris VI. The group was warmly welcomed by Alain Damlamian, Doina Cioranescu, and many other faculty and students at Paris VI.

In addition to the traditional sight-seeing, taste-testing, and relaxing outside of sidewalk cafes, the students participated in several intellectual discussions with their Parisian counterparts. The conversations were mostly research-oriented and scientific in nature, but occassionally drifted toward politics (considering the strained relations between the respective governments at the time). In exchange for a detailed and exhaustive summary of current student research at Paris VI, the CRSC representatives offered the following presentations (click to see the abstracts):

Brian Adams -- Population Dynamics Models in Plant-Insect Herbivore-Pesticide Interactions


Ecologists studying insect pest control are interested in the potentially combined effects of pesticide application and environmental factors including the presence of surrounding vegetation and natural predators. We consider several population dynamics models in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare ground or weedy) and three levels of insecticide spray (no, light, or heavy spray). We carry out parameter estimation computations along with statistical analysis to compare autonomous versus nonautonomous model dynamics. We offer a positive example of how one might combine a priori biological hypothesis and intuition with rather sophisticated (from a field biology viewpoint) mathematical methodologies to investigate pesticide-environment synergisms. This work involves collaborations with field zoologists J.E.Banks(University of Washington -- Tacoma) and J. D. Stark (Washington State University).

Brandy Benedict -- Inverse Problems in Electromagnetic Interrogation


Electromagnetic interrogation is a technique in which reflected electromagnetic waves incident upon a dielectric medium are observed and evaluated to determine material properties of the dielectric. We describe the general inverse problem and briefly present previous theoretical results. Various input waves (i.e., truncated sine, truncated square waves) are compared in one-dimensional forward computational simulations. An apparatus for experimental testing and verification of the previously developed theory is discussed in detail.

Nathan L. Gibson -- Crack Detection using Electromagnetic Interrogation


We consider the problem of detecting a crack inside of a dielectric material using electromagnetic interrogation. The technique is to measure the reflected and/or transmitted signals, and solve a parameter identification problem to determine the dimensions of any gaps. Details of the problem formulation, discussion of numerical methods, and computational results will be presented.

Johnathan M. Bardsley -- The Scattering of Electromagnetic Radiation by Dispersive Dielectrics: The FDTD Method


Our goal is the solution of certain inverse scattering problems for dispersive dielectrics in the time domain and in two spatial dimensions. Achieving this goal requires the ability to obtain fast and accurate solutions of Maxwell's equations. To this end, the finite-difference time-domain (FDTD) method is used. As opposed to other approaches, the solution of a linear system is not required at each time step. A dramatic increase in speed for a forward calculation is therefore obtained. In addition, implementation of the Perfectly Matched Layer (PML) absorbing boundary condition is straightforward, and is highly effective in reducing reflections off of the computationally induced boundaries. We will discuss some important implementation details of this approach. Our goal of solving certain inverse scattering problems for dispersive dielectrics motivates us to seek solutions of Maxwell's equations that are not only accurate, but are fast.

Nicholas Luke -- Active Sound Field Attenuation via Acoustic Arrays


We formulate a model for suppression of a diffusive random acoustic field using arrays of micro-acoustic actuators as an active control surface. Boundary dissipation is effected by a proportional feedback gain described by a distributed shape function. A computational method based on Fourier transforms is developed and analyzed as to its effectiveness in providing decay rates for various gains. Several geometries are discussed.




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