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% If you are using CVS use this line to give version information
% $Header$
\documentclass{article}
% Use the Cactus ThornGuide style file
% (Automatically used from Cactus distribution, if you have a
% thorn without the Cactus Flesh download this from the Cactus
% homepage at www.cactuscode.org)
\usepackage{../../../../doc/latex/cactus}
\begin{document}
% The author of the documentation
\author{Gabrielle Allen}
% The title of the document (not necessarily the name of the Thorn)
\title{Orbiting Scalar Charges}
% the date your document was last changed, if your document is in CVS,
% please us:
\date{$ $Date$ $}
\maketitle
% Do not delete next line
% START CACTUS THORNGUIDE
% Add all definitions used in this documentation here
% \def\mydef etc
% Add an abstract for this thorn's documentation
\begin{abstract}
\end{abstract}
% The following sections are suggestive only.
% Remove them or add your own.
\section{Introduction}
This thorn provides a source term to the scalar field evolution
for two rotating binary charges.
\section{Physical System}
The 3D scalar wave equation with a source term $\rho(t,x,y,z)$ is written
$$
\nabla \phi = 4 \pi \rho
$$
Each scalar source with charge $Q$ and radius $R$ contributes
$$
\rho = \frac{3Q}{4\pi R^3}
$$
\section{Numerical Implementation}
The only involved part of this thorn arise in working out where the
sources are located (if at all) on each local grid for a multiprocessor
run. The source terms are not numerically evolved, but are calculated
exactly, based on the physical time and their orbital velocity.
A routine is scheduled to run {\it after} the homogeneous equation
for the scalar field has been evolved, and simply updates the value
of the scalar field by adding on the source contribution.
% Do not delete next line
% END CACTUS THORNGUIDE
\end{document}
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