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\documentclass{article}
\parskip = 2 pt
\oddsidemargin = 0 cm
\textwidth = 16 cm
\topmargin = -1 cm
\textheight = 24 cm
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MANPAGE like description setting for options, use as
% \begin{Lentry} \item[text] text \end{Lentry}
\usepackage{ifthen,calc}
\newcommand{\entrylabel}[1]{\mbox{\textsf{#1}}\hfil}
\newenvironment{entry}
{\begin{list}{}
{\renewcommand{\makelabel}{\entrylabel}
\setlength{\labelwidth}{90pt}
\setlength{\leftmargin}{\labelwidth+\labelsep}
}
}
{\end{list}}
\newlength{\Mylen}
\newcommand{\Lentrylabel}[1]{%
\settowidth{\Mylen}{\textsf{#1}}%
\ifthenelse{\lengthtest{\Mylen > \labelwidth}}%
{\parbox[b]{\labelwidth} % term > labelwidth
{\makebox[0pt][l]{\textsf{#1}}\\}} %
{\textsf{#1}} %
\hfil\relax}
\newenvironment{Lentry}
{\renewcommand{\entrylabel}{\Lentrylabel}
\begin{entry}}
{\end{entry}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\title{IDScalarWave}
\author{Gabrielle Allen, Horst Beyer}
\date{2001}
\maketitle
\abstract{Initial Data for the 3D Scalar Wave Equation}
\section{Purpose}
This thorn provides different initial data for the 3D scalar wave
equation.
\section{Spherically Symmetric Solutions}
The general spherically symmetric solution can be written
\begin{equation}
\Psi(r,t) = \frac{1}{r}\left(f(r+t)+g(r-t)\right)
\end{equation}
where the functions $f$ and $g$ can be freely chosen.
Making the additional requirement of time symmetry at $t=0$, forces
\begin{equation}
f(r)=g(r)
\end{equation}
Thus if the solution at t=0 is given by $\phi(r)$, the general solution
will be
\begin{equation}
\Psi(r,t) = \frac{1}{2r}\left( (r+t)\phi(r+t)+(r-t)\phi(r-t) \right)
\end{equation}
\section{Gaussian}
The gaussian solution is {\it spherically symmetric} about the
origin of the Cartesian coordinate system, and is {\it time symmetric}.
The initial profile is
\begin{equation}
\phi(r) = A \exp (- (r-r_0)^2/\sigma)
\end{equation}
and is set with the parameters
\begin{itemize}
\item {\tt amplitude} = $A$
\item {\tt radius} = $r_0$
\item {\tt sigma} = $\sigma$
\end{itemize}
% Automatically created from the ccl files by using gmake thorndoc
\include{interface}
\include{param}
\include{schedule}
\end{document}
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