[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 63)

[roland.haas at physics.gatech.edu]

User: rhaas
Date: 2011/04/18 08:43 AM

Modified:
 /
  ET.tex

Log:
 improve readability in Coordinates and Symmetries section
 
 only minor changes. Give Steve White as author of SymBase image (according to
 the svn log).

File Changes:

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

File [modified]: ET.tex
Delta lines: +22 -23
===================================================================
--- ET.tex	2011-04-18 06:20:06 UTC (rev 62)
+++ ET.tex	2011-04-18 13:43:30 UTC (rev 63)
@@ -1584,10 +1584,8 @@
 domain, i.e.\ that the discrete domains converge to the physical
 domain in the limint of infinite resolution.
 \codename{CoordBase} exposes a public interface that allows other
-modules to query the domain and description in a uniform way. This
-information is used e.g.\ by modules computing the total barionic mass of
-the system to determine the region over which to intergrate the mass
-density. \codename{Carpet} queries \codename{CoordBase} for the discrete
+modules to query the domain and description in a uniform way. 
+\codename{Carpet} queries \codename{CoordBase} for the discrete
 grid when creating the hierarchy of grids. Evolution modules use this
 information to decide which points are evolved and therefore require the
 evaluation of the righ-hand-side expression and which ones are set via
@@ -1597,7 +1595,9 @@
 The Einstein Toolkit includes a set of modules, \codename{Boundary}
 and \codename{SymBase}, to provide a generic interface to boundary and
 symmetry conditions.
-The Einstein Toolkit offers a set of reflecting or rotating symmetry
+
+The toolkit includes built-in suppport for a set of reflecting or 
+rotating symmetry
 conditions that can be used to reduce the size of the simulation
 domain. These symmetries include periodicity in any of the coordinate
 directions
@@ -1607,7 +1607,7 @@
 (via the \codename{RotatingSymmetry90} and
 \codename{RotatingSymmetry180} modules respectively)
 symmetries about the $z$ axis. 
-\codename{Cartoon2D} is a special case since it provides continuous
+\codename{Cartoon2D} provides a continuous
 rotational symmetry rather than a discrete
 symmetry~\cite{Alcubierre1999ab}. \codename{Cartoon2D} allows fully
 three dimensional codes to be used in axissymmtric problems by evolving
@@ -1622,14 +1622,16 @@
     Denis Pollney.\todo{RH: ask Denis if we can use his figure}}
     \label{fig:cartoon-plane}
 \end{figure}
-In applying these symmetries, the
+
+In applying symmetries, the
 transformation behaviour of tensorial quantities (including tensor
 densities and non-tensors such as Christoffel symbols) is correctly
 taken into account.
+
 The interpolation routines present in \codename{Cactus} automatically
 take the existing symmetries into account, transparently mapping points
 to the numerical domain and respecting the transformation behaviour of
-tensorial quantities. Symmetries therefore are handled transparently
+tensorial quantities. Symmetries are handled transparently
 from the point of view of user modules (see Figure~\ref{fig:faces} for an
 illustration).
 \begin{figure}[htbp]
@@ -1641,13 +1643,10 @@
     point $x''$ for which there is actual data stored. In this
     example, two reflection symmetries along the horizontal and vertical axis
     are present. notice how the vector components change in
-    transformations $A$ and $B$. Image courtesy of Erik Schnetter\todo{RH:
-    Erik, are you ok with this paper re-using your image from
-    SymBase?}\todo{ES: Yes, I think using figures from the Cactus
-      users' guide is fine. However, this particular image is not from
-      me.}}
+    transformations $A$ and $B$. Image courtesy of Steve White.}
     \label{fig:faces}
 \end{figure}
+
 Thorn \codename{Boundary} provides basic boundary conditions. A boundary
 condition suitable for matter fields which approach a constant
 (atmosphere) value is provided via either the ``flat'' or ``scalar''
@@ -1664,7 +1663,7 @@
     \label{eqn:robin-falloff}
 \end{equation}
 for a given decay rate $n$, value at infinity $f_0$ and scaling constant
-$k$. $r$ is taken to be the coordinate direction perpendicular to the
+$k$. $r$ is taken to be the coordinate distance perpendicular to the
 domain boundary under consideration when the boundary condition is
 applied. 
 Radiative (Sommerfeld) and extrapolation
@@ -1708,18 +1707,18 @@
     \codename{RotatingSymmetry180} to reduce the computational domain.}
     \label{fig:bbh-boxes}
 \end{figure}
-\codename{CarpetRegrid} provides a number of different way to specify
+\codename{CarpetRegrid} provides a number of different ways to specify
 the refined regions, either as a set of boxes centered around the origin
 or as an explicit list of boxes that make up the grid hierarchy.
 Traditionally groups using \codename{CarpetRegrid} have employed
 auxiliary thorns, that are not part of the Einstein Toolkit, to create
-the list of boxes based on information obtained eg. from apparent
+the list of boxes based on information obtained e.g. from apparent
 horizon tracking. \codename{CarpetRegrid2} provides a user friendly
 interface to define sets of nested boxes that follow black holes or
 other tracked objects. \codename{CarpetRegrid2} supports up to 10 sets
 of nested regions which can be either moving or stationary. The number
 of refinement levels in each region as well as the radii of each nested
-box are allowed to change during runtime, making it possible to eg.
+box are allowed to change during runtime, making it possible to e.g.
 adapt the shape of the refined region to the surface of a star.
 \codename{CarpetRegrid2} contains code to handle the $\pi$-symmetry
 provided by \codename{RotatingSymmetry180}, enforcing the symmetry on
@@ -1729,7 +1728,8 @@
         \includegraphics[width=0.3\textwidth]{rot180-grid}
     \end{center}
     \caption{Grid layout created by \codename{CarpetRegrid2}. In this
-    example we use one ghost point, one boundary, and two buffer points
+    example we use one ghost point, one boundary point, and two buffer 
+    points
     as well as \codename{RotatingSymmetry180}. There are two refinement
     levels present, a coarse one represented by big red circles and a
     fine one represented by small black circles. The
@@ -1738,18 +1738,17 @@
     points, indicated by the cyan filled circles. The open circles are
     ghost and boundary points which are maintained by \codename{Carpet}.
     The presence of the $\pi$-symmetry forces \codename{CarpetRegrid2}
-    to create the tiny region to the bottom left of the grid. They serve
-    only as source points for the boundary condition.}
+    to create the tiny region to the bottom left of the grid. It serves
+    only as a source for the boundary condition.}
     \label{fig:rot180-grid}
 \end{figure}
 \codename{CarpetTracker} provides a simple interface to slave
 \codename{CarpetRegrid2}'s regions to the object trackers
 \codename{PunctureTracker} and \codename{NSTracker} (see
-section~\ref{sec:object-tracking}) by copying their
+section~\ref{sec:object-tracking}) by copying the position of tracker 
+objects
 positions out of a \codename{SphericalSurface} into
 \codename{CarpetRegrid2}. 
-%Figure~\ref{fig:bbh-boxes} shows a typical
-%grid layout during the inspiral phase of a binary black hole simulation.