[cig-commits] r15833 - doc/geodynamics.org/benchmarks/trunk/long

[luis at geodynamics.org]

Author: luis
Date: 2009-10-18 00:19:07 -0700 (Sun, 18 Oct 2009)
New Revision: 15833

Modified:
   doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html
   doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst
Log:
Updated long/drucker-prager.rst

Modified: doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html	2009-10-18 07:18:59 UTC (rev 15832)
+++ doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html	2009-10-18 07:19:07 UTC (rev 15833)
@@ -24,10 +24,14 @@
 into principal stresses [;\sigma_{I};], [;\sigma_{II};], and [;\sigma_{III};]
 gives</p>
 <blockquote>
-[;\sin(2\Theta)(\sigma_{I}-\sigma_{III})/2=\tan\varphi\left((\sigma_{I}+\sigma_{III})/2+\cos(2\Theta)(\sigma_{I}-\sigma_{III})/2\right)+C,;]</blockquote>
+[;\sin(2\Theta)(\sigma_{I}-\sigma_{III})/2
+=\tan\varphi
+\left((\sigma_{I}+\sigma_{III})/2
++\cos(2\Theta)(\sigma_{I}-\sigma_{III})/2
+\right) + C,;]</blockquote>
 <p>where [;\Theta;] is the angle that the fault makes relative to the
 maximum shear stress. Assuming that the fault forms where the
-shear stress [;\sigma_{I}-\sigma_{III};] is a minimum,
+shear stress [;(\sigma_{I}-\sigma_{III});] is a minimum,
 a little algebra gives us</p>
 <blockquote>
 [;\Theta=\pm\left(\frac{\pi}{4} + \frac{\varphi}{2}\right).;]</blockquote>
@@ -53,7 +57,7 @@
 <h1>Numerical Results</h1>
 <p><a class="reference internal" href="#figure-2">Figure 2</a> shows the results for three different resolutions
 for [;\varphi=45^{\circ};]. There is not much difference between
-the medium ([;256 \times 256;]) and high ([;512 \times 512;])
+the medium (256 × 256) and high (512 × 512)
 results, suggesting that we have sufficient resolution.
 <a class="reference internal" href="#figure-3">Figure 3</a> shows a plot of the numerical vs. analytic
 results for several different angles for medium resolution.
@@ -65,7 +69,7 @@
 <p class="caption"><span class="target" id="figure-2">Figure 2</span>:
 Strain rate invariant for the shortening experiment where
 [;\varphi=45^{\circ};] with three different resolutions:
-[;128 \times 128;], [;256 \times 256;], [;512 \times 512;].
+128 × 128, 256 × 256, 512 × 512.
 Any differences between the medium and high resolution runs
 are swamped by uncertainties in determining the overall
 angle of faulting.</p>

Modified: doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst	2009-10-18 07:18:59 UTC (rev 15832)
+++ doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst	2009-10-18 07:19:07 UTC (rev 15833)
@@ -16,11 +16,15 @@
 into principal stresses [;\\sigma_{I};], [;\\sigma_{II};], and [;\\sigma_{III};]
 gives
 
-    [;\\sin(2\\Theta)(\\sigma_{I}-\\sigma_{III})/2=\\tan\\varphi\\left((\\sigma_{I}+\\sigma_{III})/2+\\cos(2\\Theta)(\\sigma_{I}-\\sigma_{III})/2\\right)+C,;]
+    [;\\sin(2\\Theta)(\\sigma_{I}-\\sigma_{III})/2
+    =\\tan\\varphi
+    \\left((\\sigma_{I}+\\sigma_{III})/2
+    +\\cos(2\\Theta)(\\sigma_{I}-\\sigma_{III})/2
+    \\right) + C,;]
 
 where [;\\Theta;] is the angle that the fault makes relative to the
 maximum shear stress. Assuming that the fault forms where the
-shear stress [;\\sigma_{I}-\\sigma_{III};] is a minimum,
+shear stress [;(\\sigma_{I}-\\sigma_{III});] is a minimum,
 a little algebra gives us
 
     [;\\Theta=\\pm\\left(\\frac{\\pi}{4} + \\frac{\\varphi}{2}\\right).;]
@@ -53,7 +57,7 @@
 
 `Figure 2`_ shows the results for three different resolutions
 for [;\\varphi=45^{\\circ};]. There is not much difference between
-the medium ([;256 \\times 256;]) and high ([;512 \\times 512;])
+the medium (256 |times| 256) and high (512 |times| 512)
 results, suggesting that we have sufficient resolution.
 `Figure 3`_ shows a plot of the numerical vs. analytic
 results for several different angles for medium resolution.
@@ -69,7 +73,7 @@
    _`Figure 2`:
    Strain rate invariant for the shortening experiment where
    [;\\varphi=45^{\\circ};] with three different resolutions:
-   [;128 \\times 128;], [;256 \\times 256;], [;512 \\times 512;].
+   128 |times| 128, 256 |times| 256, 512 |times| 512.
    Any differences between the medium and high resolution runs
    are swamped by uncertainties in determining the overall
    angle of faulting.
@@ -83,3 +87,4 @@
    Numerical vs. analytic results for fault angles as a function of
    internal angle of friction.
 
+.. |times| unicode:: U+00D7