@article{banks_gibson_2006, title={Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters}, volume={64}, ISSN={["1552-4485"]}, DOI={10.1090/S0033-569X-06-01036-X}, abstractNote={We consider electromagnetic interrogation problems for complex materials involving distributions of polarization mechanisms and also distributions for the parameters in these mechanisms. A theoretical and computational framework for such problems is given. Computational results for specific problems with multiple Debye mechanisms are given in the case of discrete, uniform, log-normal, and log-bi-Gaussian distributions.}, number={4}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, H. T. and Gibson, N. L.}, year={2006}, month={Dec}, pages={749–795} }
@article{banks_bokil_cioranescu_gibson_griso_miara_2006, title={Homogenization of periodically varying coefficients in electromagnetic materials}, volume={28}, ISSN={["1573-7691"]}, DOI={10.1007/s10915-006-9091-y}, abstractNote={In this paper, we employ the periodic unfolding method for simulating the electromagnetic field in a composite material exhibiting heterogeneous microstructures which are described by spatially periodic parameters. We consider cell problems to calculate the effective parameters for a Debye dielectric medium in the case of a circular microstructure in two dimensions. We assume that the composite materials are quasi-static in nature, i.e., the wavelength of the electromagnetic field is much larger than the relevant dimensions of the microstructure.}, number={2-3}, journal={JOURNAL OF SCIENTIFIC COMPUTING}, author={Banks, H. T. and Bokil, V. A. and Cioranescu, D. and Gibson, N. L. and Griso, G. and Miara, B.}, year={2006}, month={Sep}, pages={191–221} }
@article{banks_gibson_2006, title={Void detection in foam with knit lines using THz pulse interrogation}, volume={44}, ISSN={["0895-7177"]}, DOI={10.1016/j.mcm.2006.02.014}, abstractNote={We model the electromagnetic interrogation of a polyurethane foam using the transverse electric (TE) mode of the two-dimensional (2D) Maxwell’s equations reduced to the wave equation for a fixed frequency in the terahertz (THz) regime. The foam block target contains knit lines which are modeled by modifying the speed of propagation, i.e., by altering the index of refraction. We describe our efforts to estimate the dielectric constant in the knit lines, as well as in the surrounding foam, by use of the classical Clausius–Mossotti equation, assuming only a change in density. We compare the numerical simulations accounting for knit lines to those in which knit lines are neglected, each in the context of modeling reflections of plane waves in foam with voids.}, number={9-10}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, H. T. and Gibson, N. L.}, year={2006}, month={Nov}, pages={807–815} }
@article{banks_gibson_2005, title={Well-posedness in Maxwell systems with distributions of polarization relaxation parameters}, volume={18}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2004.02.008}, abstractNote={We present existence, uniqueness and continuous dependence (with respect to probability distributions on polarization parameters) of solutions in Maxwell systems. This provides a theoretical and computational foundation for associated inverse problems.}, number={4}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, HT and Gibson, NL}, year={2005}, month={Apr}, pages={423–430} }