[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 295)

Mon Mar 12 21:32:05 CDT 2012

User: jfaber
Date: 2012/03/12 09:32 PM

Modified:
 /
  ET.tex

Log:
 Minor stylistic changes to examples.
 MAde sure to thank the refs.

File Changes:

Directory: /
============

File [modified]: ET.tex
Delta lines: +23 -22
===================================================================

--- ET.tex	2012-03-12 20:37:30 UTC (rev 294)
+++ ET.tex	2012-03-13 02:32:05 UTC (rev 295)
@@ -2469,14 +2469,14 @@
 evolution of the black hole is not influenced by the imperfect boundary
 condition.
 We performed runs at 3 different
-resolutions: the low resolution was $0.024\mathrm{M} (3.072\mathrm{M})$, medium was 
-$0.016\mathrm{M} (2.048\mathrm{M})$ and high was $0.012\mathrm{M} (1.536\mathrm{M})$, where the numbers refer to the 
-resolution on the finest (coarsest) grid. Each refined grid had twice the
+resolutions: the low resolution grid spacings were $0.024\mathrm{M}/3.072\mathrm{M}$, medium were 
+$0.016\mathrm{M}/2.048\mathrm{M}$ and high were $0.012\mathrm{M}/1.536\mathrm{M}$, where the numbers refer to the 
+resolution on the finest/coarsest grid. Each refined grid had twice the
 resolution and half the side length of the containing grid.
 The runs were performed using the tapering
 evolution scheme in \codename{Carpet} to avoid interpolation in
 time during prolongation. The initial data correspond to a rotating, stationary Kerr BH
-perturbed by a Brill wave\cite{Brandt:1996si} and, as such, has a non-zero
+perturbed by a Brill wave\cite{Brandt:1996si} and, as such, have a non-zero
 gravitational wave content. We evolved the BH using 4th-order finite differencing from
 $T=0\mathrm{M}$ until it had settled down to a stationary state at $T=120\mathrm{M}$.
 
@@ -2513,7 +2513,7 @@
 waveforms while the blue (dashed) curve shows the absolute value of the 
 difference between the high and medium resolution waveforms in a log-plot.
 The red (dotted) curve is the same as the blue (dashed) curve, except it is
-scaled for 4th order convergence, demonstrating fourth-order convergence.
+scaled for 4th order convergence, demonstrating we indeed achieve this.
 With the resolutions used here this factor is
 $\left (0.016^4-0.024^4\right )/\left ( 0.012^4-0.016^4\right) \approx 5.94$.
 
@@ -2663,15 +2663,15 @@
 \codename{ReflectionSymmetry} and \codename{RotatingSymmetry180}). The outer
 radius is located at $R = 120\mathrm{M}$, where $\mathrm{M}$ is the initial
 ADM mass of the binary system. We performed runs at 5 different resolutions:
-$3.125\mathrm{M}\times10^{-2} (2.0\mathrm{M})$, 
-$2.344\mathrm{M}\times10^{-2} (1.5\mathrm{M})$, 
-$1.953\mathrm{M}\times10^{-2} (1.25\mathrm{M})$, 
-$1.563\mathrm{M}\times10^{-2} (1.0\mathrm{M})$ and 
-$1.172\mathrm{M}\times10^{-2} (0.75\mathrm{M})$, where the numbers refer to
-the resolution on the finest (coarsest) grid. Two set of moving boxes, each
-centered on one of the black holes, are used, with the finest grid having side
+$0.03125\mathrm{M}/2.0\mathrm{M}$, 
+$0.02344\mathrm{M}/1.5\mathrm{M}$, 
+$0.01953\mathrm{M}/1.25\mathrm{M}$, 
+$0.01563\mathrm{M}/1.0\mathrm{M}$ and 
+$0.01172\mathrm{M}/0.75\mathrm{M}$, where the numbers refer to
+the resolution on the finest/coarsest grid. Two sets of moving boxes, each
+centered on one of the black holes, are used, with the finest grid having a side
 length of $2\mathrm{M}$ and each coarser grid having twice the size and half
-the resolution of the contained finer grid.
+the resolution of the grid it contained.
 
 Figure~\ref{fig:tracks_waveform} shows the two puncture tracks 
 throughout all phases of the binary evolution, 
@@ -2683,7 +2683,7 @@
 horizons were found by the \codename{AHFinderDirect} module and their
 radius and location information stored as a $2$-surface with
 spherical topology by the \codename{SphericalSurface} module.
-The irreducible mass and angular momentum (spin) of the merged BH were 
+The irreducible mass and spin angular momentum of the merged BH were 
 calculated by the \codename{QuasiLocalMeasures} module, 
 and were found to be $0.884 \mathrm{M}$ and $0.625 \mathrm{M}^{2}$, respectively.
 
@@ -2838,9 +2838,9 @@
 centered around the star at the origin, each doubling the resolution, with sizes
 of $240\mathrm{M}$, $120\mathrm{M}$, $60\mathrm{M}$ and $30\mathrm{M}$.
 We perform runs at 3 different
-resolutions: the low resolution is $0.500\mathrm{M} (8.0\mathrm{M})$, medium was 
-$0.250\mathrm{M} (4.0\mathrm{M})$ and high was $0.125\mathrm{M} (2.0\mathrm{M})$,
-where the numbers refer to the resolution on the finest (coarsest) grid. 
+resolutions: the low resolution is $0.500\mathrm{M}/8.0\mathrm{M}$, medium was 
+$0.250\mathrm{M}/4.0\mathrm{M}$ and high was $0.125\mathrm{M}/2.0\mathrm{M}$,
+where the numbers refer to the resolution on the finest/coarsest grid. 
 Each refined grid had twice the resolution and half the side length of the
 containing grid, with the finest grid completely covering the star.
 
@@ -2961,11 +2961,11 @@
 region during collapse.
 The outer boundaries were placed at $R=204.8\mathrm{M}$.  We perform runs at 4
 different resolutions: from lowest to highest the resolution are 
-$0.025\mathrm{M} (3.2\mathrm{M})$,  
-$0.0188\mathrm{M} (2.4\mathrm{M})$,  
-$0.0125\mathrm{M} (1.6\mathrm{M})$ and
-$4.67\times10^{-3}\mathrm{M} (0.6\mathrm{M})$, 
-where the numbers refer to the resolution on the finest (coarsest) grid.
+$0.025\mathrm{M}/3.2\mathrm{M}$,  
+$0.0188\mathrm{M}/2.4\mathrm{M}$,  
+$0.0125\mathrm{M}/1.6\mathrm{M}$ and
+$4.67\times10^{-3}\mathrm{M}/0.6\mathrm{M}$, 
+where the numbers refer to the resolution on the finest/coarsest grid.
 
 We use the PPM
 reconstruction method and the HLLE Riemann solver (see
@@ -3203,6 +3203,7 @@
 We are also grateful to the large number of people who contributed to
 the Einstein Toolkit via ideas, code, documentation, and testing;
 without these contributions, this toolkit would not exist today.
+We thank our referees for their diligence and their many helpful suggestions.
 
 The Einstein Toolkit is directly supported by
 the National Science Foundation in the USA under the grant numbers

