[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 22)

[tanja.bode at physics.gatech.edu]

User: tbode
Date: 2011/01/30 04:54 PM

Modified:
 /
  ET.tex

Log:
 Analysis section draft.

File Changes:

Directory: /
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--- ET.tex	2011-01-24 19:24:58 UTC (rev 21)
+++ ET.tex	2011-01-30 22:54:11 UTC (rev 22)
@@ -508,14 +508,42 @@
 
 
 \subsection{Analysis}
-\todo{1/2 page Tanja}
+%\todo{1/2 page Tanja}
 
-\paragraph{Masses}
+Any simulated system may have many applicable quantities for analysis which 
+are most efficiently calculated during evolution.  The Einstein Toolkit 
+currently includes modules to facilitate the calculation of the most common
+analysis quantities: masses, horizons, and gravitational waves.  In addition
+to these, detailed below, the \codename{ADMConstraints} module calculates the 
+constraints required, but not imposed by, the formulation for assessing the
+simulation's accuracy and stability.  Finally, \codename{ADMAnalysis} calculates
+several quantities often needed in analyzing the spacetime evolution: the trace 
+of the extrinsic curvature $K$, the determinant of the 3-metric, the spatial
+metric and extrinsic curvature in spherical coordinates, and the spatial Ricci 
+tensor and trace.
 
-\paragraph{Event and Apparent Horizons}
+\subsubsection*{Horizons} For spacetimes which contain a \bh{,} the Toolkit 
+contains modules to find both the event and apparent horizons and their 
+properties. The \codename{EHFinder} module traces null surfaces backwards in 
+time through a pre-evolved spacetime.  The Toolkit also includes two separate
+apparent horizon finders: Thornburg's \codename{AHFinderDirect} and 
+\codename{AHFinder}.
 
-\paragraph{Gravitational Waves}
+\subsubsection*{Masses} In analyzing spacetimes, it is important to calculate 
+the masses and momenta of the system. Several Toolkit modules include the 
+capability of calculating several types of masses.  The apparent horizon modules 
+include in their output the areal masses of the found horizons.  The 
+\codename{Extract} module calculates ADM mass and momenta when extracting 
+gravitational waves.  Additionally, \codename{HydroAnalysis} calculates finds 
+the center of mass and the point of maximum matter density of a hydronamic 
+field.
 
+\subsubsection*{Gravitational Waves} Within the Toolkit are modules for extracting 
+gravitational waves using two formulations: the Moncrief formalism assuming
+the spacetime approximates spherical symmetry \codename{Extract}) and the Weyl 
+scalar $\Psi_4$ constructed on a fiducial tetrad (\codename{WeylScal4}).  The 
+Weyl scalars, as well as any other quantity, can be projected onto a basis 
+of spin-weighted spherical harmonics using the \codename{Multipole} module.
 
 \subsection{Relativity Tools}
 \todo{1/2 page Peter}