[cig-commits] r14697 - doc/snac

[echoi at geodynamics.org]

Author: echoi
Date: 2009-04-14 12:39:56 -0700 (Tue, 14 Apr 2009)
New Revision: 14697

Modified:
   doc/snac/snac.lyx
Log:
fixed a few typos.



Modified: doc/snac/snac.lyx
===================================================================
--- doc/snac/snac.lyx	2009-04-14 19:33:50 UTC (rev 14696)
+++ doc/snac/snac.lyx	2009-04-14 19:39:56 UTC (rev 14697)
@@ -2029,7 +2029,7 @@
 
 :
 \begin_inset Formula \begin{align*}
-\sigma_{n+1}^{(k)} & =\mathbf{a}\cdot(\epsilon_{n+1}-\epsilon_{n+1}^{p(k)})\\
+\sigma_{n+1}^{(k)} & =\mathbf{a}^{e}\cdot(\epsilon_{n+1}-\epsilon_{n+1}^{p(k)})\\
 F_{n+1}^{(k)} & =F(\sigma_{n+1}^{(k)},\epsilon_{n+1}^{p*(k)})\end{align*}
 
 \end_inset
@@ -2044,7 +2044,7 @@
 \begin_layout Enumerate
 Incremental upate:
 \begin_inset Formula \begin{align*}
-\Delta^{2}\beta & =\frac{F_{n+1}^{(k)}}{-\frac{\partial F}{\partial\Delta\beta}}=\frac{F_{n+1}^{(k)}}{\frac{\partial F}{\partial\sigma}\cdot\mathbf{a}\cdot\frac{\partial G}{\partial\sigma}+\frac{\partial F}{\partial\epsilon^{p*}}r}\\
+\Delta^{2}\beta & =\frac{F_{n+1}^{(k)}}{-\frac{\partial F}{\partial\Delta\beta}}=\frac{F_{n+1}^{(k)}}{\frac{\partial F}{\partial\sigma}\cdot\mathbf{a}^{e}\cdot\frac{\partial G}{\partial\sigma}+\frac{\partial F}{\partial\epsilon^{p*}}r}\\
 \epsilon_{n+1}^{p(k+1)} & =\epsilon_{n+1}^{p(k)}+\Delta^{2}\beta\frac{\partial G}{\partial\sigma}(\sigma_{n+1}^{(k)},\epsilon_{n+1}^{p*(k)})\\
 \epsilon_{n+1}^{p*(k+1)} & =\epsilon_{n+1}^{p*(k)}-\Delta^{2}\beta r(\sigma_{n+1}^{(k)},\epsilon_{n+1}^{p*(k)})\\
  & =\epsilon_{n+1}^{p*(k)}+\Delta^{2}\beta\left[\left(\frac{\partial\epsilon^{p*}}{\partial\epsilon^{p}}\right)_{n+1}^{(k)}\cdot\frac{\partial G}{\partial\sigma}(\sigma_{n+1}^{(k)},\epsilon_{n+1}^{p*(k)})\right]\\
@@ -2151,10 +2151,10 @@
 \end_inset
 
  becomes 
-\begin_inset Formula $\sim$
+\begin_inset Formula $\sim-1$
 \end_inset
 
-1.
+.
  Since the dilation angle is often set to be zero or a small value, and
  the cohesion is always defined as a piecewise linear function, 
 \begin_inset Formula $F$