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};