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A Molecular Dynamics simulation of 16 particles in a box. The particles interact via the Lennard Jones potential and thus the force:\n", "$$\n", "\\mathbf{f} (r) = \\frac{48}{r^2}\n", "\\left[\\left( \\frac{1}{r}\\right)^{12} - \\frac{1}{2}\n", "\\left(\\frac{1}{r} \\right)^6 \\right] \\mathbf{r}.\n", "$$\n", "The positions and velocities of the particles obey the Verlet-velocity algorithm:\n", "\\begin{eqnarray}\n", "\\mathbf{r}_i(t+h) & \\simeq & \\mathbf{r}_i(t) + h \\mathbf{v}_i(t) + \\frac{h^2}\n", "{2} \\mathbf{F}_i(t) + \\mbox{O}(h^3), \\label{VV1}\\\\[6pt]\n", "\\mathbf{v}_i(t+h) & \\simeq & \\mathbf{v}_i(t) + h \\,\n", "\\overline{\\mathbf{a}(t)}+ \\mbox{O}(h^2) \\\\[6pt]\n", "& \\simeq &\\mathbf{v}_i(t) + h \\left[ \\frac{\\mathbf{F}_i(t+h)+\\mathbf{F}_i(t)}{2}\n", "\\right] + \\mbox{O}(h^2). \\label{VV2}\n", " \\end{eqnarray}\n", " The specific capacity at constant volume is:\n", "$$\n", "C_V= \\frac{\\partial E}{\\partial T}\\Bigr )_V\n", "$$\n", "The program computes the energy versus temperature and $C_V$.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "
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