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% /*@@
% @file documentation.tex
% @date 20 May 2002
% @author Gabrielle Allen
% @desc
% IDConstraintViolate
% @enddesc
% @version $Header$
% @@*/
\documentclass{article}
\newif\ifpdf
\ifx\pdfoutput\undefined
\pdffalse % we are not running PDFLaTeX
\else
\pdfoutput=1 % we are running PDFLaTeX
\pdftrue
\fi
\ifpdf
\usepackage[pdftex]{graphicx}
\else
\usepackage{graphicx}
\fi
\parskip = 0 pt
\parindent = 0pt
\oddsidemargin = 0 cm
\textwidth = 16 cm
\topmargin = -1 cm
\textheight = 24 cm
\begin{document}
\title{Creating Constraint Violating Initial Data}
\author{Gabrielle Allen}
\date{$Date$}
\maketitle
\abstract{The \texttt{IDConstraintViolate} thorn creates initial data
which purposefully violates the constraint equations for testing purposes.
}
\section{Gaussian}
Choosing the {\tt ADMBase} parameter {\tt initial\_data} to have the
value {\tt Constraint violating gaussian} creates initial data with the
form
\begin{eqnarray*}
g_{xx} = g_{yy} = g_{zz} &=& 1 + A \exp \left(\frac{-(r-r_0)^2}{\sigma^2}\right)
\\
g_{xy} = g_{xz} = g_{yz} &=& 0
\\
K_{ij} &=& 0
\end{eqnarray*}
where the size and shape of the Gaussian is specified by parameters, $A$={\tt amplitude}, $r_0$={\tt radius} and $\sigma$={\tt sigma}.
\end{document}
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