From: hackbard Date: Wed, 13 Jun 2007 19:46:07 +0000 (+0000) Subject: potentials, and thermo obs not yet finished X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=74bdf88a71df101efc703ee94986c45418f56ad7;p=lectures%2Flatex.git potentials, and thermo obs not yet finished --- diff --git a/posic/talks/md_simulation_von_silizium.tex b/posic/talks/md_simulation_von_silizium.tex index 5c8db3b..47e144a 100644 --- a/posic/talks/md_simulation_von_silizium.tex +++ b/posic/talks/md_simulation_von_silizium.tex @@ -39,6 +39,9 @@ \def\slideleftmargin{5.1cm} \def\slidetopmargin{-0.6cm} +\newcommand{\ham}{\mathcal{H}} +\newcommand{\pot}{\mathcal{V}} + % topic \begin{slide} @@ -515,14 +518,27 @@ Problemstellung: Finden der Nachbarn f"ur Wechselwirkung \begin{itemize} \item Innere Energie: \[ - E = + = < \sum_i \frac{|{\bf p}_i|^2}{2m_i} > + + E = + = < \sum_i \frac{{\bf p}_i^2}{2m_i} > + + \] + \item Temperatur/Druck + \begin{eqnarray} + &=& k_BT \nonumber \\ + &=& k_BT \nonumber + \end{eqnarray} + \begin{center} + "Aquipartitionstheorem + \end{center} + Temperatur: + \[ + \sum_i {\bf p}_i \frac{{\bf p}_i}{m_i} = 3Nk_BT \quad + \Rightarrow \quad T=\frac{1}{3Nk_B} \sum_i \frac{{\bf p}_i^2}{m_i} \] - \item Temperatur: + Druck: \[ - E_{kin}==\frac{3}{2}Nk_BT - \Rightarrow T=\frac{1}{3Nk_B} \sum_i \frac{|{\bf p}_i|^2}{m_i} + \sum_i {\bf q}_i \nabla_{{\bf q}_i} \pot = 3Nk_BT \quad + \stackrel{\textrm{kart. Koord.}}{\Rightarrow} \quad + - \sum_i {\bf r}_i \nabla_{{\bf r}_i} \pot = -3Nk_BT \quad \] - \item Druck \item W"armekapazit"at \item Struktur Werte \item Diffusion @@ -539,6 +555,7 @@ Problemstellung: Finden der Nachbarn f"ur Wechselwirkung {\large\bf EAM } + \end{slide} \begin{slide}