diff --git a/doc/Eqs/polymorphic1.jpg b/doc/Eqs/polymorphic1.jpg index dd609ea6b0..4757cb7ad8 100644 Binary files a/doc/Eqs/polymorphic1.jpg and b/doc/Eqs/polymorphic1.jpg differ diff --git a/doc/Eqs/polymorphic1.tex b/doc/Eqs/polymorphic1.tex new file mode 100644 index 0000000000..b4b925ccf8 --- /dev/null +++ b/doc/Eqs/polymorphic1.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +E=\frac{1}{2}\sum_{i=1}^{i=N}\sum_{j=1}^{j=N}\left[\left(1-\delta_{ij}\right)\cdot U_{IJ}\left(r_{ij}\right)-\left(1-\eta_{ij}\right)\cdot F_{IJ}\left(r_{ij}\right)\cdot V_{IJ}\left(r_{ij}\right)\right] +$$ + +\end{document} diff --git a/doc/Eqs/polymorphic2.jpg b/doc/Eqs/polymorphic2.jpg index 95ff19514f..05133f4849 100644 Binary files a/doc/Eqs/polymorphic2.jpg and b/doc/Eqs/polymorphic2.jpg differ diff --git a/doc/Eqs/polymorphic2.tex b/doc/Eqs/polymorphic2.tex new file mode 100644 index 0000000000..80b1c93821 --- /dev/null +++ b/doc/Eqs/polymorphic2.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +X_{ij}=\sum_{k=i_1,k\neq i,j}^{i_N}W_{IK}\left(r_{ik}\right)\cdot G_{JIK}\left(\theta_{jik}\right)\cdot P_{IK}\left(\Delta r_{jik}\right) +\label{X_eq2} +$$ + +\end{document} diff --git a/doc/Eqs/polymorphic3.jpg b/doc/Eqs/polymorphic3.jpg index d39f0c27fc..c8eb8df895 100644 Binary files a/doc/Eqs/polymorphic3.jpg and b/doc/Eqs/polymorphic3.jpg differ diff --git a/doc/Eqs/polymorphic3.tex b/doc/Eqs/polymorphic3.tex new file mode 100644 index 0000000000..71db8d81b0 --- /dev/null +++ b/doc/Eqs/polymorphic3.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +\Delta r_{jik}=r_{ij}-\xi_{IJ}\cdot r_{ik} +\label{Dr_eq3} +$$ + +\end{document} diff --git a/doc/Eqs/polymorphic4.jpg b/doc/Eqs/polymorphic4.jpg index c8805b7114..7a094d6a21 100644 Binary files a/doc/Eqs/polymorphic4.jpg and b/doc/Eqs/polymorphic4.jpg differ diff --git a/doc/Eqs/polymorphic4.tex b/doc/Eqs/polymorphic4.tex new file mode 100644 index 0000000000..b792df82a0 --- /dev/null +++ b/doc/Eqs/polymorphic4.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\left\{\begin{array}{l} +\eta_{ij}=\delta_{ij},\xi_{IJ}=0 \\ +U_{IJ}\left(r\right)=A_{IJ}\cdot\epsilon_{IJ}\cdot \left(\frac{\sigma_{IJ}}{r}\right)^q\cdot \left[B_{IJ}\cdot \left(\frac{\sigma_{IJ}}{r}\right)^{p-q}-1\right]\cdot exp\left(\frac{\sigma_{IJ}}{r-a_{IJ}\cdot \sigma_{IJ}}\right) \\ +V_{IJ}\left(r\right)=\sqrt{\lambda_{IJ}\cdot \epsilon_{IJ}}\cdot exp\left(\frac{\gamma_{IJ}\cdot \sigma_{IJ}}{r-a_{IJ}\cdot \sigma_{IJ}}\right) \\ +F_{IJ}\left(X\right)=-X \\ +P_{IJ}\left(\Delta r\right)=1 \\ +W_{IJ}\left(r\right)=\sqrt{\lambda_{IJ}\cdot \epsilon_{IJ}}\cdot exp\left(\frac{\gamma_{IJ}\cdot \sigma_{IJ}}{r-a_{IJ}\cdot \sigma_{IJ}}\right) \\ +G_{JIK}\left(\theta\right)=\left(cos\theta+\frac{1}{3}\right)^2 +\end{array}\right. +\end{eqnarray*} + +\end{document} diff --git a/doc/Eqs/polymorphic5.jpg b/doc/Eqs/polymorphic5.jpg index 0f86a79e61..500238b2a9 100644 Binary files a/doc/Eqs/polymorphic5.jpg and b/doc/Eqs/polymorphic5.jpg differ diff --git a/doc/Eqs/polymorphic5.tex b/doc/Eqs/polymorphic5.tex new file mode 100644 index 0000000000..a5451b98d6 --- /dev/null +++ b/doc/Eqs/polymorphic5.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\left\{\begin{array}{l} +\eta_{ij}=\delta_{ij},\xi_{IJ}=1 \\ +U_{IJ}\left(r\right)=\frac{D_{e,IJ}}{S_{IJ}-1}\cdot exp\left[-\beta_{IJ}\sqrt{2S_{IJ}\left(r-r_{e,IJ}\right)}\right]\cdot f_{c,IJ}\left(r\right) \\ +V_{IJ}\left(r\right)=\frac{S_{IJ}\cdot D_{e,IJ}}{S_{IJ}-1}\cdot exp\left[-\beta_{IJ}\sqrt{\frac{2}{S_{IJ}}\left(r-r_{e,IJ}\right)}\right]\cdot f_{c,IJ}\left(r\right) \\ +F_{IJ}\left(X\right)=\left(1+X\right)^{-\frac{1}{2}} \\ +P_{IJ}\left(\Delta r\right)=exp\left(2\mu_{IK}\cdot \Delta r\right) \\ +W_{IJ}\left(r\right)=f_{c,IK}\left(r\right) \\ +G_{JIK}\left(\theta\right)=\gamma_{IK}\left[1+\frac{c_{IK}^2}{d_{IK}^2}-\frac{c_{IK}^2}{d_{IK}^2+\left(h_{IK}+cos\theta\right)^2}\right] +\end{array}\right. +\end{eqnarray*} + +\end{document} diff --git a/doc/Eqs/polymorphic6.jpg b/doc/Eqs/polymorphic6.jpg index b94e3514f8..65ea78bf21 100644 Binary files a/doc/Eqs/polymorphic6.jpg and b/doc/Eqs/polymorphic6.jpg differ diff --git a/doc/Eqs/polymorphic6.tex b/doc/Eqs/polymorphic6.tex new file mode 100644 index 0000000000..c8f9f2f25b --- /dev/null +++ b/doc/Eqs/polymorphic6.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +f_{c,IJ}=\left\{\begin{array}{lr} +1, & r\leq r_{s,IJ} \\ +\frac{1}{2}+\frac{1}{2} cos \left[\frac{\pi \left(r-r_{s,IJ}\right)}{r_{c,IJ}-r_{s,IJ}}\right], & r_{s,IJ}