From: hackbard Date: Fri, 4 Nov 2011 13:21:18 +0000 (+0100) Subject: added simulation methods X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=246b317e6fcfc986641a3c20cf8722f40ae131ac;p=lectures%2Flatex.git added simulation methods --- diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex index 6564df2..f588e1d 100644 --- a/posic/talks/mpi_app.tex +++ b/posic/talks/mpi_app.tex @@ -1001,23 +1001,34 @@ r = \unit[2--4]{nm} Utilized computational methods } - \vspace{0.1cm} +\vspace{0.2cm} - \small +\small -{\bf Molecular dynamics (MD):}\\ +{\bf Molecular dynamics (MD)}\\ \scriptsize -\begin{tabular}{p{5cm}|p{7cm}} -\hline +\begin{tabular}{p{4.5cm} p{7.5cm}} +%\hline Basics & Details\\ \hline -Microscopic description of N particle system & \\ -\multicolumn{2}{c}{}\\ -Numerical integration using Newtons equation of motion as a propagation rule in 6N-dimensional phase space & Velocity Verlet | timestep: \unit[1]{fs} \\ -\multicolumn{2}{c}{}\\ -Analytical interaction potential & Tersoff-like bond order potential (Erhart/Albe) \\ -\multicolumn{2}{c}{}\\ -Observables obtained by time and/or ensemble averages & NpT (isothermal-isobaric)\\ +System of $N$ particles & +$N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\ +\hline +Phase space propagation & +Velocity Verlet | timestep: \unit[1]{fs} \\ +\hline +Analytical interaction potential & +Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential +(Erhart/Albe) +$\displaystyle +E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad + \pot_{ij} = {\color{red}f_C(r_{ij})} + \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right] +$\\ +\hline +%\multicolumn{2}{c}{}\\ +Observables: time/ensemble averages & +NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\ %\begin{itemize} %\item Berendsen thermostat: % $\tau_{\text{T}}=100\text{ fs}$ @@ -1028,37 +1039,40 @@ Observables obtained by time and/or ensemble averages & NpT (isothermal-isobaric \hline \end{tabular} - \begin{itemize} - \item Microscopic description of N particle system - \item Analytical interaction potential - \item Numerical integration using Newtons equation of motion\\ - as a propagation rule in 6N-dimensional phase space - \item Observables obtained by time and/or ensemble averages - \end{itemize} - {\bf Details of the simulation:} - \begin{itemize} - \item Integration: Velocity Verlet, timestep: $1\text{ fs}$ - \item Ensemble: NpT (isothermal-isobaric) - \begin{itemize} - \item Berendsen thermostat: - $\tau_{\text{T}}=100\text{ fs}$ - \item Berendsen barostat:\\ - $\tau_{\text{P}}=100\text{ fs}$, - $\beta^{-1}=100\text{ GPa}$ - \end{itemize} - \item Erhart/Albe potential: Tersoff-like bond order potential - \vspace*{12pt} - \[ - E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad - \pot_{ij} = {\color{red}f_C(r_{ij})} - \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right] - \] - \end{itemize} +\small + +\vspace{0.1cm} + +{\bf Density functional theory (DFT)} + +\scriptsize + +\begin{minipage}[t]{6cm} +\underline{Basics} +\begin{itemize} + \item Born-Oppenheimer approximation:\\ + Decouple electronic \& ionic motion + \item Hohenberg-Kohn theorem:\\ + $n_0(r) \stackrel{\text{uniquely}}{\rightarrow}$ + $V_0$ / $H$ / $\Phi_i$ / \underline{$E_0$} +\end{itemize} +\underline{Details} +\begin{itemize} +\item Code: \textsc{vasp} +\item Plane wave basis set $\{\phi_j\}$\\[0.1cm] +$\displaystyle +\Phi_i=\sum_{|G+k|