[Commits] [svn:einsteintoolkit] AHFinderDirect/trunk/doc/ (Rev. 1544)
hinder at einsteintoolkit.org
hinder at einsteintoolkit.org
Sat May 22 08:24:43 CDT 2010
User: hinder
Date: 2010/05/22 08:24 AM
Modified:
/trunk/doc/
documentation.tex
Log:
Replace \text{...} with {\text{...}} in documentation to work with htlatex.
Patch by Barry Wardell.
File Changes:
Directory: /trunk/doc/
======================
File [modified]: documentation.tex
Delta lines: +18 -18
===================================================================
--- trunk/doc/documentation.tex 2010-04-28 19:46:23 UTC (rev 1543)
+++ trunk/doc/documentation.tex 2010-05-22 13:24:42 UTC (rev 1544)
@@ -910,7 +910,7 @@
The 3~regions are defined as follows: For a grid point a distance $r[i]$
from horizon~$i$'s local coordinate origin, with horizon~$i$'s radius
in this same direction (again, measured from its local coordinate origin)
-being $r_\text{horizon}[i]$,%%%
+being $r_{\text horizon}[i]$,%%%
\footnote{%%%
Note that these are flat-space distances
$[(x-x_0)^2 + (y - y_0)^2 + (z-z_0)^2]^{1/2}$
@@ -920,15 +920,15 @@
\begin{equation}
\renewcommand{\arraystretch}{1.333}
\begin{tabular}{l@{~}lll@{~}lll}
-$r[i] \le r_\text{inner}[i]$ & \text{for some $i$}
+$r[i] \le r{ ext{r}}[i]$ & \text{for some $i$}
&
& &
& $\Rightarrow$ & \text{inner} \\
-$r[i] > r_\text{inner}[i]$ & \text{for all $i$}
+$r[i] > r_{\text{r}}[i]$ & \text{for all $i$}
& \text{and} &
- $r[i] \le r_\text{outer}[i]$ & \text{for some $i$}
+ $r[i] \le r_{\text{r}}[i]$ & \text{for some $i$}
& $\Rightarrow$ & \text{buffer} \\
-$r[i] > r_\text{outer}[i]$ & \text{for all $i$}
+$r[i] > r_{\text{r}}[i]$ & \text{for all $i$}
&
& &
& $\Rightarrow$ & \text{outer} %%%\\
@@ -938,20 +938,20 @@
\begin{equation}
\renewcommand{\arraystretch}{1.333}
\begin{array}{lcl}
-r_\text{inner}
- & = & \verb|mask_radius_multiplier| \times r_\text{horizon}
+r_{\text{r}}
+ & = & \verb|mask_radius_multiplier| \times r_{\text{n}}
\,\,+\,\,
- \verb|mask_radius_offset| \times {\Delta x}_\text{base}
+ \verb|mask_radius_offset| \times {\Delta x}_{\text{e}}
\\
-r_\text{outer}
- & = & r_\text{inner}
+r_{\text{r}}
+ & = & r_{\text{r}}
\,\,+\,\,
- \verb|mask_buffer_thickness| \times {\Delta x}_\text{base}
+ \verb|mask_buffer_thickness| \times {\Delta x}_{\text{e}}
%%%\\
\end{array}
\label{AHFinderDirect/eqn-r-inside-outside}
\end{equation}
-and where ${\Delta x}_\text{base}$ is the base-grid Cactus grid spacing
+and where ${\Delta x}_{\text{e}}$ is the base-grid Cactus grid spacing
(more precisely, the geometric mean of the base grid's $x$, $y$,
and $z$ Cactus grid spacings)%%%
\footnote{%%%
@@ -971,8 +971,8 @@
\end{tabular}
]
\mbox{}\\
- These parameters are used to define the radia $r_\text{inner}$
- and $r_\text{outer}$ in
+ These parameters are used to define the radia $r_{\text{r}}$
+ and $r_{\text{r}}$ in
equation~\eqref{AHFinderDirect/eqn-r-inside-outside} above.
Note that the sign convention here is that
@@ -1051,7 +1051,7 @@
* {\Delta x}_{\text{current},\max}
\end{equation}
where $r_{\text{inner},\min}$ is the minimum over all angles
- of $r_\text{inner}$ as defined by
+ of $r_{\text{r}}$ as defined by
equation~\eqref{AHFinderDirect/eqn-r-inside-outside},
and ${\Delta x}_{\text{current},\max}$ is the maximum of the
Cactus $x$, $y$, and~$z$ grid spacings on the current Cactus
@@ -1060,7 +1060,7 @@
Note that this is the {\bf current\/} Cactus
grid spacing, not the {\bf base\/} Cactus grid
spacing that's used when calculating
- $r_\text{outer}$ and $r_\text{inner}$ by
+ $r_{\text{r}}$ and $r_{\text{r}}$ by
equation~\eqref{AHFinderDirect/eqn-r-inside-outside}.
}%%%
{} If this condition isn't satisfied, then \thorn{AHFinderDirect}
@@ -1582,11 +1582,11 @@
black hole diagnostics file(s), are typically computed to accuracies
on the order of a part per million or so.
-Note, however, that the irreducible mass $m_\text{irreducible}$
+Note, however, that the irreducible mass $m_{\text{e}}$
may differ considerably from the black hole's local mass or its
contribution to the slice's ADM mass. For example, for Kerr spacetime
in Kerr-Schild coordinates,
-$m_\text{irreducible}/m_\text{ADM} = 0.949$, $0.894$, and $0.723$
+$m_{\text{e}}/m_{\text{M}} = 0.949$, $0.894$, and $0.723$
for spin parameters $a \equiv J/m^2 = 0.6$, $0.8$, and $0.999$, respectively.
It would be better to (also) use the ``isolated horizons'' formalism of
\cite{AHFinderDirect/Dreyer-etal-2002-isolated-horizons};
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