% /*@@
%   @file      documentation.tex
%   @date      20 May 2002
%   @author    Gabrielle Allen
%   @desc 
%              IDConstraintViolate
%   @enddesc 
%   @version $Header$
% @@*/

\documentclass{article}

\usepackage{../../../../doc/latex/cactus}

\begin{document}
\title{Creating Constraint Violating Initial Data}
\author{Gabrielle Allen}
\date{$Date$}

\maketitle

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\begin{abstract}
The \texttt{IDConstraintViolate} thorn creates initial data
which purposefully violates the constraint equations for testing purposes.
\end{abstract}


\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}.

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\end{document}