[cig-commits] r11473 - long/3D/Gale/trunk/documentation

[sue at geodynamics.org]

Author: sue
Date: 2008-03-19 11:14:58 -0700 (Wed, 19 Mar 2008)
New Revision: 11473

Modified:
   long/3D/Gale/trunk/documentation/gale.lyx
Log:
fixed a few typos and improved equations

Modified: long/3D/Gale/trunk/documentation/gale.lyx
===================================================================
--- long/3D/Gale/trunk/documentation/gale.lyx	2008-03-19 08:06:11 UTC (rev 11472)
+++ long/3D/Gale/trunk/documentation/gale.lyx	2008-03-19 18:14:58 UTC (rev 11473)
@@ -1,4 +1,4 @@
-#LyX 1.5.3 created this file. For more info see http://www.lyx.org/
+#LyX 1.5.1 created this file. For more info see http://www.lyx.org/
 \lyxformat 276
 \begin_document
 \begin_header
@@ -562,8 +562,7 @@
 \end_inset
 
  do not include the effect of gravity.
- Gravity is accounted for by adding a body force term to eq.
- 
+ Gravity is accounted for by adding a body force term to Equation 
 \begin_inset LatexCommand ref
 reference "eq:simple momentum conservation"
 
@@ -590,8 +589,7 @@
 
 \end_inset
 
- This modifies eq.
- 
+ This modifies Equation 
 \begin_inset LatexCommand ref
 reference "eq:matrix form"
 
@@ -658,8 +656,7 @@
 \end_inset
 
  is the rate of energy production (e.g., from radiogenic sources).
- Note that eq.
- 
+ Note that Equation 
 \begin_inset LatexCommand ref
 reference "eq:energy"
 
@@ -6008,7 +6005,7 @@
 
 \begin_layout Standard
 The thickness of the mantle in the center is set to isostatically compensate
- the thicker crust.
+ for the thicker crust.
  There is also a nonlinear temperature gradient, going from 273 K at the
  surface to 1333 K at the bottom.
 \end_layout
@@ -6062,7 +6059,7 @@
 \begin_inset Formula $10^{20}kg\, m^{-1}s^{-1}$
 \end_inset
 
-at the bottom.
+ at the bottom.
  The crust's yielding behavior is modeled with a Mohr-Coulomb rheology,
  with a cohesion of 
 \begin_inset Formula $4.4\cdot10^{6}kg\, m^{-1}s^{-2}$
@@ -6121,7 +6118,11 @@
 \begin_layout Standard
 The top cover image shows the strain rate invariant after the model has
  extended 30 km.
- The resolution is 2048x512, and we used a direct solver (Mumps).
+ The resolution is 2048 
+\begin_inset Formula $\times$
+\end_inset
+
+ 512, and we used a direct solver (Mumps).
  The most prominent faults occur near where the crust thickens, although
  smaller faults occur throughout the crust.
  The depth of the faults is limited by the relatively low viscosity deeper
@@ -6130,7 +6131,11 @@
 \end_layout
 
 \begin_layout Standard
-The 3D input file models a region 1000km x 1000km.
+The 3D input file models a region 1000km 
+\begin_inset Formula $\times$
+\end_inset
+
+ 1000km.
  Topography is imported from a data file.
  Underneath, the crust extends further down 32 km, and the mantle is 68
  km thick beyond that.
@@ -6178,7 +6183,15 @@
 \begin_layout Standard
 The bottom cover image shows the strain rate invariant after the model has
  extended 24 km.
- The resolution is 128x128x16, and we used an iterative solver (GMRES).
+ The resolution is 128 
+\begin_inset Formula $\times$
+\end_inset
+
+ 128 
+\begin_inset Formula $\times$
+\end_inset
+
+ 16, and we used an iterative solver (GMRES).
  The fault locations are determined by the variations in topography.
 \end_layout
 
@@ -14879,6 +14892,8 @@
 \end_layout
 
 \begin_layout Standard
+\noindent
+\align center
 \begin_inset Float figure
 wide false
 sideways false
@@ -15052,7 +15067,7 @@
 \begin_layout Standard
 In our case, we simulate a rigid sphere with a high viscosity sphere.
  This allows some internal circulation within the sphere, and so the expression
- for the velocity becomes TODO: what? 
+ for the velocity becomes 
 \begin_inset LatexCommand cite
 key "Intro to Fluid Dynamics"
 
@@ -15078,8 +15093,8 @@
 \end_layout
 
 \begin_layout Standard
-The analytic solution also assumes infinitely small Reynolds number.
- Expanding the drag in terms of the Reynolds number gives TODO: what? 
+The analytic solution also assumes an infinitely small Reynolds number.
+ Expanding the drag in terms of the Reynolds number gives 
 \begin_inset LatexCommand cite
 key "Landau & Lifschitz"
 
@@ -15094,7 +15109,7 @@
 
 \end_inset
 
- which gives a correction of order 0.1%.
+ which gives a correction on the order of 0.1%.
  If we had made 
 \begin_inset Formula $\delta\rho$
 \end_inset
@@ -15107,7 +15122,7 @@
 \end_layout
 
 \begin_layout Standard
-Finally, the solution assumes that the boundaries are inifinitely far away.
+Finally, the solution assumes that the boundaries are infinitely far away.
  So we vary the distance to the boundary to gauge exactly how much the boundarie
 s affect the solution.
 \end_layout
@@ -15190,9 +15205,12 @@
 \end_inset
 
  shows the results of a low resolution run.
- Even this run is not particularly small (128x256), because we need fairly
- high resolution to be able to accurately resolve the small (1%) height
- difference.
+ Even this run is not particularly small (128 
+\begin_inset Formula $\times$
+\end_inset
+
+ 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.
  
 \end_layout