[cig-commits] r15334 - short/3D/PyLith/trunk/doc/userguide/materials

[willic3 at geodynamics.org]

Author: willic3
Date: 2009-06-18 14:29:10 -0700 (Thu, 18 Jun 2009)
New Revision: 15334

Modified:
   short/3D/PyLith/trunk/doc/userguide/materials/materials.lyx
Log:
Fixed a few equations.



Modified: short/3D/PyLith/trunk/doc/userguide/materials/materials.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/materials/materials.lyx	2009-06-18 20:54:31 UTC (rev 15333)
+++ short/3D/PyLith/trunk/doc/userguide/materials/materials.lyx	2009-06-18 21:29:10 UTC (rev 15334)
@@ -1,4 +1,4 @@
-#LyX 1.6.2 created this file. For more info see http://www.lyx.org/
+#LyX 1.6.0 created this file. For more info see http://www.lyx.org/
 \lyxformat 345
 \begin_document
 \begin_header
@@ -2777,13 +2777,13 @@
 
 Then using the quotient rule for derivatives,
 \begin_inset Formula \begin{gather}
-\frac{\partial\sqrt{^{\tau}J_{2}^{\prime}}}{\partial{}^{t+\Delta t}e_{k}^{\prime\prime}}=\frac{\delta_{ik}\left[\frac{^{t+\Delta t}e_{i}^{\prime\prime}}{2}+a_{E}S_{i}^{I}-\Delta t\left(1-\alpha\right)^{t}S_{i}\,^{\tau}\gamma\right]}{\frac{2aK_{2}}{\alpha^{2}}\left(\alpha\Delta tK_{1}K_{2}+a\right)+K_{1}\left(c-2d^{2}\,^{\tau}\gamma\right)}\,.\label{eq:77}\end{gather}
+\frac{\partial\sqrt{^{\tau}J_{2}^{\prime}}}{\partial{}^{t+\Delta t}e_{k}^{\prime\prime}}=\frac{\left[\frac{^{t+\Delta t}e_{k}^{\prime\prime}}{2}+a_{E}S_{k}^{I}-\Delta t\left(1-\alpha\right)^{t}S_{k}\,^{\tau}\gamma\right]}{\frac{2aK_{2}}{\alpha^{2}}\left(\alpha\Delta tK_{1}K_{2}+a\right)+K_{1}\left(c-2d^{2}\,^{\tau}\gamma\right)}\,.\label{eq:77}\end{gather}
 
 \end_inset
 
 This yields
 \begin_inset Formula \begin{gather}
-\frac{\partial\sqrt{^{\tau}J_{2}^{\prime}}}{\partial{}^{t+\Delta t}e_{j}^{\prime\prime}}=\frac{\delta_{ik}K_{1}\left[\frac{^{t+\Delta t}e_{i}^{\prime\prime}}{2}+a_{E}S_{i}^{I}-\Delta t\left(1-\alpha\right)^{t}S_{i}\,^{\tau}\gamma\right]}{\frac{2aK_{2}}{\alpha^{2}}\left(\alpha\Delta tK_{1}K_{2}+a\right)+K_{1}\left(c-2d^{2}\,^{\tau}\gamma\right)}\,.\label{eq:78}\end{gather}
+\frac{\partial\sqrt{^{\tau}J_{2}^{\prime}}}{\partial{}^{t+\Delta t}e_{k}^{\prime\prime}}=\frac{K_{1}\left[\frac{^{t+\Delta t}e_{k}^{\prime\prime}}{2}+a_{E}S_{k}^{I}-\Delta t\left(1-\alpha\right)^{t}S_{k}\,^{\tau}\gamma\right]}{\frac{2aK_{2}}{\alpha^{2}}\left(\alpha\Delta tK_{1}K_{2}+a\right)+K_{1}\left(c-2d^{2}\,^{\tau}\gamma\right)}\,.\label{eq:78}\end{gather}
 
 \end_inset