The existence of generalized symmetries of Maxwell's equations in Gödel's Universe is investigated. It is shown that their existence is in turn tied to the existence of certain spinorial objects called Killing spinors.
The conformal algebra, corresponding to valence (1; 1) Killing spinors, for Gödel's Universe is discussed in detail....
A numerical method based on the the method of characteristics for hyperbolic systems
of partial differential equations in four independent variables is developed and used
for solving time domain Maxwell's equations. The method uses the characteristic
hypersurfaces and the characteristic conditions to derive a set of independent equations
relating the...
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...
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...