Presentation Title

Approximating Dispersive Materials with Parameter Distributions in the Lorentz Model

Faculty Mentor

Nathan L. Gibson

Start Date

18-11-2017 9:15 AM

End Date

18-11-2017 9:30 AM

Location

9-239

Session

Physical Sciences 4

Type of Presentation

Oral Talk

Subject Area

physical_mathematical_sciences

Abstract

Electromagnetic wave propagation in complex dispersive media is governed by the time dependent Maxwell’s equations coupled to auxiliary differential equations that describe the evolution of the induced macroscopic polarization. We consider “polydispersive” materials represented by distributions of dielectric parameters in a polarization model. The work focuses on a computational framework for such problems involving Polynomial Chaos Expansions as a method to improve the modeling accuracy of the Lorentz model and allow for easy simulation using the Finite Difference Time Domain (FDTD) method. Using a least squares cost formulation and chi-square significance test, we explore the inverse problem in the frequency domain for saltwater data.

Summary of research results to be presented

Our results showed that applying a distribution to the square of the natural resonant frequency can produce significantly better fits than the deterministic Lorentz model. We used Polynomial Chaos and finite differences with the first order Yee Scheme to discretize our system in the time domain. Through simulations it was shown that the Polynomial Chaos method converged quickly in the number of polynomials used in the expansion. For the inverse problem, we compared a single frequency interrogating signal with a ultra-wideband (UWB) pulse. The distributed model only fit better than the deterministic model over a range of frequencies as implied by the complex permittivity plots in the frequency domain. In the frequency domain, the results after our hypothesis testing allow us to conclude that a distributed model provides a statistically significantly better fit than a deterministic model.

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Nov 18th, 9:15 AM Nov 18th, 9:30 AM

Approximating Dispersive Materials with Parameter Distributions in the Lorentz Model

9-239

Electromagnetic wave propagation in complex dispersive media is governed by the time dependent Maxwell’s equations coupled to auxiliary differential equations that describe the evolution of the induced macroscopic polarization. We consider “polydispersive” materials represented by distributions of dielectric parameters in a polarization model. The work focuses on a computational framework for such problems involving Polynomial Chaos Expansions as a method to improve the modeling accuracy of the Lorentz model and allow for easy simulation using the Finite Difference Time Domain (FDTD) method. Using a least squares cost formulation and chi-square significance test, we explore the inverse problem in the frequency domain for saltwater data.