Alien Registration- Beggs, Elizabeth S. (Brunswick, Cumberland County)

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Almost commutative Riemannian geometry: wave operators

Associated to any (pseudo)-Riemannian manifold $M$ of dimension $n$ is an $n+1$-dimensional noncommutative differential structure (\Omega^1,\extd) on the manifold, with the extra dimension encoding the classical Laplacian as a noncommutative `vector field'. We use the classical connection, Ricci tensor and Hodge Laplacian to construct (\Omega^2,\extd) and a natural noncommutative torsion free connection $(\nabla,\sigma)$ on $\Omega^1$. We show that its generalised braiding \sigma:\Omega^1\tens\Omega^1\to \Omega^1\tens\Omega^1 obeys the quantum Yang-Baxter or braid relations only when the original $M$ is flat, i.e their failure is governed by the Riemann curvature, and that \sigma^2=\id only when $M$ is Einstein. We show that if $M$ has a conformal Killing vector field $\tau$ then the cross product algebra $C(M)\rtimes_\tau\R$ viewed as a noncommutative analogue of $M\times\R$ has a natural $n+2$-dimensional calculus extending $\Omega^1$ and a natural spacetime Laplacian now directly defined by the extra dimension. The case $M=\R^3$ recovers the Majid-Ruegg bicrossproduct flat spacetime model and the wave-operator used in its variable speed of light preduction, but now as an example of a general construction. As an application we construct the wave operator on a noncommutative Schwarzschild black hole and take a first look at its features. It appears that the infinite classical redshift/time dilation factor at the event horizon is made finite.Comment: 39 pages, 4 pdf images. Removed previous Sections 5.1-5.2 to a separate paper (now ArXived) to meet referee length requirements. Corresponding slight restructure but no change to remaining conten

User's manual for three dimensional FDTD version B code for scattering from frequency-dependent dielectric materials

The Penn State Finite Difference Time Domain Electromagnetic Code Version B is a three dimensional numerical electromagnetic scattering code based upon the Finite Difference Time Domain Technique (FDTD). The supplied version of the code is one version of our current three dimensional FDTD code set. This manual provides a description of the code and corresponding results for several scattering problems. The manual is organized into 14 sections: introduction, description of the FDTD method, operation, resource requirements, Version B code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file, a discussion of radar cross section computations, a discussion of some scattering results, a sample problem setup section, a new problem checklist, references and figure titles

User's manual for three dimensional FDTD version C code for scattering from frequency-independent dielectric and magnetic materials

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code Version C is a three dimensional numerical electromagnetic scattering code based upon the Finite Difference Time Domain Technique (FDTD). The supplied version of the code is one version of our current three dimensional FDTD code set. This manual provides a description of the code and corresponding results for several scattering problems. The manual is organized into fourteen sections: introduction, description of the FDTD method, operation, resource requirements, Version C code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file (COMMONC.FOR), a section briefly discussing Radar Cross Section (RCS) computations, a section discussing some scattering results, a sample problem setup section, a new problem checklist, references and figure titles