[cig-commits] r15776 - doc/geodynamics.org/benchmarks/trunk/long

[luis at geodynamics.org]

Author: luis
Date: 2009-10-05 15:49:54 -0700 (Mon, 05 Oct 2009)
New Revision: 15776

Modified:
   doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.html
   doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.rst
Log:
Fixes to long/relaxation-topography.rst

Modified: doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.html	2009-10-05 22:49:46 UTC (rev 15775)
+++ doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.html	2009-10-05 22:49:54 UTC (rev 15776)
@@ -13,22 +13,28 @@
 
 <p>Given an infinitely deep purely viscous medium with an infinitesimal
 sinusoidal height profile, the topography will decay exponentially
-with the timescale [Folds] $$t_r = frac{4pieta}{gL},$$ where
-$eta$ is the viscosity, $g$ is the gravitational constant, and $L$ is
-the wavelength of the initial sinusoid.</p>
+with the timescale [Folds]</p>
+<blockquote>
+[;t_r = \frac{4\pi\eta}{gL},;]</blockquote>
+<p>where [;eta;] is the viscosity, [;g;] is the gravitational constant,
+and [;L;] is the wavelength of the initial sinusoid.</p>
 <p>In our case, we simulate a medium with finite depth and finite height.
 The internal fields decay exponentially with depth with a length scale of
-$L/{2pi}$. The error in the solution due to a finite height is of order
-$(2pi{A}/L)^2$, where $A$ is the amplitude of the sinusoid. We use $L=1$
-and $A=0.01$, giving errors of order $0.02%$ and $0.4%$.</p>
-<p>The file <cite>input/benchmarks/sinusoid/README</cite> explains how to run this
+[;L/{2\pi};]. The error in the solution due to a finite height is of
+order [;(2pi{A}/L)^2;], where [;A;] is the amplitude of the sinusoid.
+We use [;L=1;] and [;A=0.01;], giving errors of order 0.02% and 0.4%.</p>
+<p>The file <tt class="docutils literal"><span class="pre">input/benchmarks/sinusoid/README</span></tt> explains how to run this
 benchmark. Figure [fig:Strain-topo] shows the results of a low-resolution
-run. Even this run is not particularly small ($128 times 256$), because
-we need fairly high resolution to be able to accurately resolve the small
-($1%$) height difference. Also note that we use symmetry to only
+run. Even this run is not particularly small ([;128 \times 256;]),
+because we need fairly high resolution to be able to accurately resolve
+the small (1%) height difference. Also note that we use symmetry to only
 simulate half of the wavelength.</p>
 <div class="figure">
-<img alt="images/Paraview_topography.pngFigure[Strain-topo]Strainrateandvelocitiesforasinusoidaltopographyrelaxingundergravity." src="images/Paraview_topography.pngFigure[Strain-topo]Strainrateandvelocitiesforasinusoidaltopographyrelaxingundergravity." />
+<img alt="images/Paraview_topography.png" src="images/Paraview_topography.png" />
+<p class="caption">Figure [Strain-topo]</p>
+<div class="legend">
+Strain rate and velocities for a sinusoidal topography relaxing
+under gravity.</div>
 </div>
 <p>Running the code with multiple resolutions and measuring the error in the
 height in the trough gives Figure [fig:topo-error]. Scaling the error
@@ -36,10 +42,18 @@
 linearly with increasing resolution, giving us confidence in our ability
 to accurately track topography.</p>
 <div class="figure">
-<img alt="images/topo_error.epsFigure[fig:topo-error]Errorintheheightatthetrough" src="images/topo_error.epsFigure[fig:topo-error]Errorintheheightatthetrough" />
+<img alt="images/topo_error.png" src="images/topo_error.png" />
+<p class="caption">Figure [fig:topo-error]</p>
+<div class="legend">
+Error in the height at the trough</div>
 </div>
 <div class="figure">
-<img alt="images/topo_scaled_error.epsFigure[fig:scaled-topo-error]AsinFigure[fig:topo-error],butwiththeerrorscaledwith$h$.Sothemedium-resolutionerrorismultipliedby2andthehigh-resolutionerrorismultipliedby4." src="images/topo_scaled_error.epsFigure[fig:scaled-topo-error]AsinFigure[fig:topo-error],butwiththeerrorscaledwith$h$.Sothemedium-resolutionerrorismultipliedby2andthehigh-resolutionerrorismultipliedby4." />
+<img alt="images/topo_scaled_error.png" src="images/topo_scaled_error.png" />
+<p class="caption">Figure [fig:scaled-topo-error]</p>
+<div class="legend">
+As in Figure [fig:topo-error], but with the error scaled with [;h;].
+So the medium-resolution error is multiplied by 2 and the
+high-resolution error is multiplied by 4.</div>
 </div>
 </div>
 </body>

Modified: doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.rst	2009-10-05 22:49:46 UTC (rev 15775)
+++ doc/geodynamics.org/benchmarks/trunk/long/relaxation-topography.rst	2009-10-05 22:49:54 UTC (rev 15776)
@@ -4,41 +4,50 @@
 
 Given an infinitely deep purely viscous medium with an infinitesimal
 sinusoidal height profile, the topography will decay exponentially
-with the timescale [Folds] $$t_r = \frac{4\pi\eta}{gL},$$ where
-$\eta$ is the viscosity, $g$ is the gravitational constant, and $L$ is
-the wavelength of the initial sinusoid.
+with the timescale [Folds]
 
+    [;t_r = \\frac{4\\pi\\eta}{gL},;]
+
+where [;\eta;] is the viscosity, [;g;] is the gravitational constant,
+and [;L;] is the wavelength of the initial sinusoid.
+
 In our case, we simulate a medium with finite depth and finite height.
 The internal fields decay exponentially with depth with a length scale of
-$L/{2\pi}$. The error in the solution due to a finite height is of order
-$(2\pi{A}/L)^2$, where $A$ is the amplitude of the sinusoid. We use $L=1$
-and $A=0.01$, giving errors of order $0.02\%$ and $0.4\%$.
+[;L/{2\\pi};]. The error in the solution due to a finite height is of
+order [;(2\pi{A}/L)^2;], where [;A;] is the amplitude of the sinusoid.
+We use [;L=1;] and [;A=0.01;], giving errors of order 0.02% and 0.4%.
 
-The file `input/benchmarks/sinusoid/README` explains how to run this
+The file ``input/benchmarks/sinusoid/README`` explains how to run this
 benchmark. Figure [fig:Strain-topo] shows the results of a low-resolution
-run. Even this run is not particularly small ($128 \times 256$), because
-we need fairly high resolution to be able to accurately resolve the small
-($1\%$) height difference. Also note that we use symmetry to only
+run. Even this run is not particularly small ([;128 \\times 256;]),
+because we need fairly high resolution to be able to accurately resolve
+the small (1%) height difference. Also note that we use symmetry to only
 simulate half of the wavelength.
 
 .. figure:: images/Paraview_topography.png
+
    Figure [Strain-topo]
-   Strain rate and velocities for a sinusoidal topography relaxing under
-   gravity.
 
+   Strain rate and velocities for a sinusoidal topography relaxing
+   under gravity.
+
 Running the code with multiple resolutions and measuring the error in the
 height in the trough gives Figure [fig:topo-error]. Scaling the error
 with resolution gives Figure [fig:scaled-topo-error]. The error decreases
 linearly with increasing resolution, giving us confidence in our ability
 to accurately track topography.
 
-.. figure:: images/topo_error.eps
+.. figure:: images/topo_error.png
+
    Figure [fig:topo-error]
+
    Error in the height at the trough
 
-.. figure:: images/topo_scaled_error.eps
+.. figure:: images/topo_scaled_error.png
+
    Figure [fig:scaled-topo-error]
-   As in Figure [fig:topo-error], but with the error scaled with $h$.
+
+   As in Figure [fig:topo-error], but with the error scaled with [;h;].
    So the medium-resolution error is multiplied by 2 and the
    high-resolution error is multiplied by 4.