Merge remote-tracking branch 'origin/master' into development

applications/nucleationModel/tex_files/KKS_nucleation.tex

@@ -220,7 +220,7 @@ \subsection{Variational formulation}
 
 The concentration in each phase is determined by the following system of equations:
 \begin{gather}
-c =  c_{\alpha} \left( 1- H(\eta)\right) + c_{\beta} H(\eta \\
+c =  c_{\alpha} \left( 1- H(\eta)\right) + c_{\beta} H(\eta) \\
 \frac{\partial f_{\alpha}(c_{\alpha})}{\partial c_{\alpha}} = \frac{\partial f_{\beta}(c_{\beta})}{\partial c_{\beta}}
 \end{gather}
 
@@ -253,7 +253,7 @@ \subsection{Variational treatment}
 We obtain chemical potentials for the concentration and the structural order parameter by taking variational derivatives of $\Pi$:
 \begin{align}
   \mu_{c}  &= f_{\alpha,c} \left( 1- H(\eta)\right) +f_{\beta,c} H(\eta) \\
-  \mu_{\eta}  &= \left[ f_{\beta}-f_{\alpha} -(c_{\beta}-c_{\alpha}) f_{\beta,c_{\beta}} \right] H(\eta)_{,\eta} + W f_{Landau,\eta}- \kappa\eta
+  \mu_{\eta}  &= \left[ f_{\beta}-f_{\alpha} -(c_{\beta}-c_{\alpha}) f_{\beta,c_{\beta}} \right] H(\eta)_{,\eta} + W f_{Landau,\eta}- \kappa\nabla^2\eta
 \end{align}
 
 \subsection{Kinetics}
@@ -297,7 +297,7 @@ \subsection{Weak formulation}
 \begin{equation}
 \begin{split}
 \int_\Omega w \eta^{n+1} dV = &\int_\Omega w \Bigg\{\underbrace{\eta^{n}-\Delta t L \bigg[(f_{\beta}-f_{\alpha})H(\eta^n)_{,\eta} -(c_{\beta}-c_{\alpha}) f_{\beta,c_{\beta}}H(\eta^n)_{,\eta} + W f_{Landau,\eta}}_{r_{\eta}}\\ 
-&+ \nabla w \cdot (\underbrace{-\Delta t  L \kappa \eta^n}_{r_{\eta x}} ) dV 
+&+ \nabla w \cdot (\underbrace{-\Delta t  L \kappa \nabla \eta^n}_{r_{\eta x}} ) dV 
 \end{split}
 \end{equation}
 

applications/nucleationModel_preferential/tex_files/KKS_nucleation.tex

@@ -220,7 +220,7 @@ \subsection{Variational formulation}
 
 The concentration in each phase is determined by the following system of equations:
 \begin{gather}
-c =  c_{\alpha} \left( 1- H(\eta)\right) + c_{\beta} H(\eta \\
+c =  c_{\alpha} \left( 1- H(\eta)\right) + c_{\beta} H(\eta) \\
 \frac{\partial f_{\alpha}(c_{\alpha})}{\partial c_{\alpha}} = \frac{\partial f_{\beta}(c_{\beta})}{\partial c_{\beta}}
 \end{gather}
 
@@ -253,7 +253,7 @@ \subsection{Variational treatment}
 We obtain chemical potentials for the concentration and the structural order parameter by taking variational derivatives of $\Pi$:
 \begin{align}
   \mu_{c}  &= f_{\alpha,c} \left( 1- H(\eta)\right) +f_{\beta,c} H(\eta) \\
-  \mu_{\eta}  &= \left[ f_{\beta}-f_{\alpha} -(c_{\beta}-c_{\alpha}) f_{\beta,c_{\beta}} \right] H(\eta)_{,\eta} + W f_{Landau,\eta}- \kappa\eta
+  \mu_{\eta}  &= \left[ f_{\beta}-f_{\alpha} -(c_{\beta}-c_{\alpha}) f_{\beta,c_{\beta}} \right] H(\eta)_{,\eta} + W f_{Landau,\eta}- \kappa\nabla^2\eta
 \end{align}
 
 \subsection{Kinetics}
@@ -297,7 +297,7 @@ \subsection{Weak formulation}
 \begin{equation}
 \begin{split}
 \int_\Omega w \eta^{n+1} dV = &\int_\Omega w \Bigg\{\underbrace{\eta^{n}-\Delta t L \bigg[(f_{\beta}-f_{\alpha})H(\eta^n)_{,\eta} -(c_{\beta}-c_{\alpha}) f_{\beta,c_{\beta}}H(\eta^n)_{,\eta} + W f_{Landau,\eta}}_{r_{\eta}}\\ 
-&+ \nabla w \cdot (\underbrace{-\Delta t  L \kappa \eta^n}_{r_{\eta x}} ) dV 
+&+ \nabla w \cdot (\underbrace{-\Delta t  L \kappa \nabla \eta^n}_{r_{\eta x}} ) dV 
 \end{split}
 \end{equation}
 
@@ -333,7 +333,7 @@ \subsection{Nucleation probability}
 \end{equation}
 \subsection{Hold time}
 
-After each nuclei is added there is a `hold' time, $\Delta t_h$ interval during which the order parameter value is fixed within a window that encompasses the new nucleus. The purpose of this hold time is to provide the concentration is allowed to evolve within the nucleus to a value close to the coexistance composition for $\beta$ phase and to create small a solute depleted zone around the nucleus. After the hold time, the nucleus is about to evolve into a precipitate.
+After each nucleus is added, there is a `hold' time interval, $\Delta t_h$, during which the order parameter value is fixed within a small window that encompasses the new nucleus. The purpose of this hold time is to allow the concentration to evolve within the nucleus to a value close to the coexistance composition for $\beta$ phase, and therefore, to create small a solute depleted zone around the nucleus. After the hold time, the nucleus is allowed to evolve into a precipitate.
 
 \subsection{Required nucleation inputs}
 \begin{itemize}

src/matrixfree/computeLHS.cc

@@ -41,7 +41,7 @@ MatrixFreePDE<dim, degree>::vmult(vectorType &dst, const vectorType &src) const
     {
       if (dst.in_local_range(it.first))
         {
-          dst(it.first) = src(it.first);
+          dst(it.first) = src(it.first); //*jacobianDiagonal(it->first);
         }
     }