Nathan Louis Gibson

Works (4)

Updated: July 5th, 2023 15:57

2006 journal article

Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters

QUARTERLY OF APPLIED MATHEMATICS, 64(4), 749–795.

By: H. Banks n & N. Gibson n

author keywords: electromagnetic interrogation; pulsed antenna source microwaves; inverse problems; complex dielectric materials; distributions of relaxation parameters and mechanisms
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Added: August 6, 2018

2006 journal article

Homogenization of periodically varying coefficients in electromagnetic materials

JOURNAL OF SCIENTIFIC COMPUTING, 28(2-3), 191–221.

By: H. Banks n, V. Bokil n, D. Cioranescu*, N. Gibson n, G. Griso * & B. Miara*

author keywords: Homogenization; Maxwell's equations; debye dielectric materials; pulsed antenna source microwaves
TL;DR: The periodic unfolding method for simulating the electromagnetic field in a composite material exhibiting heterogeneous microstructures which are described by spatially periodic parameters is employed. (via Semantic Scholar)
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2006 journal article

Void detection in foam with knit lines using THz pulse interrogation

MATHEMATICAL AND COMPUTER MODELLING, 44(9-10), 807–815.

By: H. Banks n & N. Gibson n

author keywords: terahertz electromagnetic waves; heterogeneous materials; numerical simulations
TL;DR: This work describes its 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. (via Semantic Scholar)
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2005 journal article

Well-posedness in Maxwell systems with distributions of polarization relaxation parameters

APPLIED MATHEMATICS LETTERS, 18(4), 423–430.

By: H. Banks n & N. Gibson n

author keywords: well-posedness; Maxwell's equations with polarization; relaxation parameters
TL;DR: This work presents existence, uniqueness and continuous dependence (with respect to probability distributions on polarization parameters) of solutions in Maxwell systems and provides a theoretical and computational foundation for associated inverse problems. (via Semantic Scholar)
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