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Creator:: McGregor, D. A.
Abstract:: In this thesis we construct compatible discretizations of Maxwell's equations. We use the term compatible to describe numerical methods for Maxwell's equations which obey many properties of vector Calculus in a discrete setting. Compatible discretizations preserve the exterior Calculus ensuring that the divergence of the curl and the curl of...
Resource Type:: Dissertation
Full Text:: Nathan L. Gibson In this thesis we construct compatible discretizations of Maxwell’s equations. We use

Creator:: Stallcup, Isaac A.
Abstract:: In this thesis, we consider Maxwell's Equations and their numerical discretization using finite difference and finite element methods. We first describe Maxwell's equations in linear dielectrics and then present finite difference and finite element methods for this case. We then describe Maxwell's equations in linear metamaterials using the Lorentz and...
Resource Type:: Honors College Thesis
Full Text:: APPROVED: Vrushali Bokil, Mentor, representing Mathematics Nathan Gibson, Committee Member, representing

Creator:: Tro, Sara K.
Abstract:: In this thesis we analyze a model for Kerr optical materials consisting of Maxwell's equations along with the dispersive Duffing model. We consider Duffing models with cubic and quintic polynomial nonlinearities. We assume a traveling wave solution to this nonlinear electromagnetic system and analyze it using the theory of dynamical...
Resource Type:: Honors College Thesis
Full Text:: Nathan L. Gibson, Committee Member, representing Department of Mathematics Toni Doolen, Dean, Oregon

Creator:: Kirk, Anna Rae
Abstract:: We construct an implicit derivative matching (IDM) technique for restoring the accuracy of the Yee scheme for Maxwell's equations in dispersive media with material interfaces in one dimension. We consider media exhibiting orientational polarization, which are represented using a Debye dispersive model, examples of which are water and living tissue....
Resource Type:: Masters Thesis
Full Text:: Dr. Nathan Gibson, Dr. Malgorzata Peszynska, and Dr. Molly Shor for serving on my committee

Creator:: Henderson, Scott Edward
Abstract:: In this thesis, we investigate the problem of simulating Maxwell's equations in dispersive dielectric media. We begin by explaining the relevance of Maxwell's equations to 21st century problems. We also discuss the previous work on the numerical simulations of Maxwell's equations. Introductions to Maxwell's equations and the Yee finite difference...
Resource Type:: Masters Thesis
Full Text:: her guidance, this thesis would not be possible. I would also like to thank Dr. Nathan Gibson for his

Creator:: Sakkaplangkul, Puttha
Abstract:: In this dissertation, we introduce a family of fully discrete finite difference time-domain (FDTD) methods for Maxwell’s equations in linear and nonlinear materials. Onecategory of methods is constructed using multiscale techniques involving operator splittings. We present the sequential splitting scheme, the Strang Marchuk splitting scheme,the weighted sequential splitting scheme including...
Resource Type:: Dissertation
Full Text:: , none of this would be possible. Many thanks to my committee members: to Dr. Nathan L. Gibson for

Creator:: Keefer, Olivia A.
Abstract:: Accurate modeling and simulation of wave propagation in dispersive dielectrics such as water, human tissue and sand, among others, has a variety of applications. For example in medical imaging, electromagnetic waves are used to interrogate human tissue in a non-invasive manner to detect anomalies that could be cancerous. In non-destructive...
Resource Type:: Masters Thesis
Full Text:: like to thank Dr. Ted Brekken, Dr. Nathan Gibson, and Dr. Robert Higdon for dedicating their time to

Creator:: Manore, Carrie Anna
Abstract:: Modeling and analyzing the combined effects of disease and population dynamics is important in understanding the effects of mechanisms such as pathogen transmission and direct competition between host species on the distribution and abundance of different species in an ecological community. Mathematical analysis of such models in a spatially explicit...
Resource Type:: Dissertation
Full Text:: Differential Equations and Dynamical Systems Let x′ = f(x) be a system of autonomous ordinary differential

ScholarsArchive@OSU