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-0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\xi^0 & = & \frac{\xi_O}{m} = \frac{\xi_C}{n} \\ +\frac{\beta_O}{\sqrt{m}} & = & \frac{\beta_C}{\sqrt{n}} = \xi^0 \frac{\sqrt{m}+\sqrt{n}}{2}\\ +\end{eqnarray*} + +\end{document} \ No newline at end of file diff --git a/doc/doc2/Eqs/pair_vashishta.jpg b/doc/doc2/Eqs/pair_vashishta.jpg new file mode 100644 index 0000000000000000000000000000000000000000..ca5f118a874cb28836144855edb1b60662528726 GIT binary patch literal 73306 zcmc$_2Ut^2*Do4+6Ok?;q7>;MN>MQ1StuMv_L`$ffR0h-|u|ibMATWbM8I&p63qP?6qglo;_=3)?TxIYt8Y@@e<(F zEfaGS0231vAeZq6IL0wwH#al{-LbVcF~4ohxB&n#U%X*-)0p`b0N@`G9B6BL^PHoT z^Er+m08Ri8KoD>lpy%!p^!Ub|JGTLh6aWeE{CocI6KM*-s0jcVSN&Vpe}C_Pdd2PW zI53z|ipn@HJ@gFn005XSGH7sE@MA_k(;EgY^Z@)X`r}_Z@Sd$9BfpP9pY;AWJ@J=* z@NfFpUpkP%1f$H}-}2u7qM14W(hvSkpZQA%dxrmgFTfD;I3m#3+b8(krHdCYp1bi7 z^1$=l-H4!IPye8E<^dj%z{ik4_h8S5jI#f3-`}SI{QoZax5pGTu3o*O_^;gm5C8og 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z8xP?I%%RK6PD9edGrhT+6{+>uaK$M%=MjOy#jg-ntlzItU9aDHpGvU_{{F#Usdr)w zajLVbpuf>o!kl9^;M4hn^5%?{*EgRg{kkUka~tDKcEs)2Y;5KUutZ}t)!`+*L*UUPkv+onP4gbdYBf1Xw!gjZ%!~Qi`9&MVT zu?F4HlLIv&Y>?}O`>1L65_uE{pOI!g6>nt31BH)+kvx|K^rPLMJlQ+LreDIy%D`8! zfbV>TK`68vHR%k0DSi{bKIXe#!%k;K|3)pqT=$vj>~vsnKz4w^=eCFe@Q%vfWOT_| zkWY6HY|j=0Ab9sQf->4Dl~k-6bkU&Lo8~=ez$Wal6=~O{38HAH0b=mrBRV-0{pjIJ z1atAKxT=ukflO8uLNGHC1@#fL$2bxGwI_7U^^0;v@(RQf8SJT?@Lsm@)*mu180FPF z$;bm(BhzIAj<>2?2i`uDpF@&QRorAQhNO`}flD^C;2=PC9 zc8R>!JC6KWKzE=0XTW%FVKL?q!Y_Rk{W0tVAy1gVFxUv&D!)`5WF`NB@Eo8U6537ek`4kcPT>eHY)p~9Urf4D^1bKQe9f@#(ZufE|r(! z82U~So9^~3<;pYWO i}^N U_{ij}^{(2)} (r_{ij}) + + \sum_i^N \sum_{j \neq i}^N \sum_{k > j, k \neq i}^N + U_{ijk}^{(3)} (r_{ij}, r_{ik}, \theta_{ijk}) + \\ + U_{ij}^{(2)} (r) & = & \frac{H_{ij}}{r^{\eta_{ij}}} + + \frac{Z_i Z_j}{r}\exp(-r/\lambda_{1,ij}) + - \frac{D_{ij}}{r^4}\exp(-r/\lambda_{4,ij}) + - \frac{W_{ij}}{r^6}, r < r_{c,{ij}} + \\ + U_{ijk}^{(3)}(r_{ij},r_{ik},\theta_{ijk}) & = & B_{ijk} + \frac{\left[ \cos \theta_{ijk} - \cos \theta_{0ijk} \right]^2} + {1+C_{ijk}\left[ \cos \theta_{ijk} - \cos \theta_{0ijk} \right]^2} \times \\ +& & \exp \left( \frac{\gamma_{ij}}{r_{ij} - r_{0,ij}} \right) + \exp \left( \frac{\gamma_{ik}}{r_{ik} - r_{0,ik}} \right), r_{ij} < r_{0,ij}, r_{ik} < r_{0,ik} +\end{eqnarray*} + +\end{document} diff --git a/doc/doc2/Eqs/polymorphic1.tex b/doc/doc2/Eqs/polymorphic1.tex new file mode 100644 index 0000000000..b4b925ccf8 --- /dev/null +++ b/doc/doc2/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/doc2/Eqs/polymorphic2.tex b/doc/doc2/Eqs/polymorphic2.tex new file mode 100644 index 0000000000..80b1c93821 --- /dev/null +++ b/doc/doc2/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/doc2/Eqs/polymorphic3.tex b/doc/doc2/Eqs/polymorphic3.tex new file mode 100644 index 0000000000..71db8d81b0 --- /dev/null +++ b/doc/doc2/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/doc2/Eqs/polymorphic4.tex b/doc/doc2/Eqs/polymorphic4.tex new file mode 100644 index 0000000000..b792df82a0 --- /dev/null +++ b/doc/doc2/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/doc2/Eqs/polymorphic5.tex b/doc/doc2/Eqs/polymorphic5.tex new file mode 100644 index 0000000000..a5451b98d6 --- /dev/null +++ b/doc/doc2/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/doc2/Eqs/polymorphic6.tex b/doc/doc2/Eqs/polymorphic6.tex new file mode 100644 index 0000000000..c8f9f2f25b --- /dev/null +++ b/doc/doc2/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}