diff --git a/templates/writing-tools/equations.tex b/templates/writing-tools/equations.tex new file mode 100644 index 0000000..9d6f939 --- /dev/null +++ b/templates/writing-tools/equations.tex @@ -0,0 +1,46 @@ +%% General Equations +%Newtonian F=ma +\newcommand{\fma}{ +\begin{equation}\label{eq:fma} + F = ma +\end{equation} +} + +%Force derived from energy +\newcommand{\forceenergy}{ +\begin{equation}\label{eq:force-energy} + F = \dfrac{-dV}{dx} +\end{equation} +} + +%% MD Functional Forces +% Lennard Jones 12-6 +\newcommand{\pairljeq}{ +\begin{equation}\label{eq:pairlj} + V_{LJ}(r) = 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right] +\end{equation} +} +% Harmonic bond stretching +\newcommand{\bondharmoniceq}{ +\begin{equation}\label{eq:bond-harmonic} + V_{bond}(l) = \frac{1}{2}k\left(l-l_0\right)^2 +\end{equation} +} +% Harmonic bond bending +\newcommand{\angleharmoniceq}{ +\begin{equation}\label{eq:angle-harmonic} + V_{angle}(\theta) = \frac{1}{2}k\left(\theta-\theta_0\right)^2 +\end{equation} +} +% Dihedrals (Periodic) +\newcommand{\dihedralperiodiceq}{ +\begin{equation}\label{eq:dihedral-periodic} + V_{torsion}(\phi) = \frac{1}{2}k(1+d\cos{(n\phi - \phi_0)}) +\end{equation} +} +% Dihedrals (OPLS) +\newcommand{\dihedraloplseq}{ +\begin{equation}\label{eq:dihedral-opls} + V_{torsion}(\phi) = \frac{1}{2}\left[k_1\left(1+\cos{\phi})+k_2(1-\cos{2\phi})+k_3(1+\cos{3\phi})+k_4(1-\cos{4\phi})\right)\right] +\end{equation} +} \ No newline at end of file diff --git a/templates/writing-tools/figures/lj-potential-no-title.png b/templates/writing-tools/figures/lj-potential-no-title.png new file mode 100644 index 0000000..9d52365 Binary files /dev/null and b/templates/writing-tools/figures/lj-potential-no-title.png differ diff --git a/templates/writing-tools/figures/lj-potential.png b/templates/writing-tools/figures/lj-potential.png new file mode 100644 index 0000000..95c1300 Binary files /dev/null and b/templates/writing-tools/figures/lj-potential.png differ diff --git a/templates/writing-tools/figures/make-figs.ipynb b/templates/writing-tools/figures/make-figs.ipynb new file mode 100644 index 0000000..cc075cc --- /dev/null +++ b/templates/writing-tools/figures/make-figs.ipynb @@ -0,0 +1,142 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "0d862a35-cda7-406d-8246-c5aa2f225cf0", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import scienceplots\n", + "\n", + "plt.style.use('science')" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "358cbaf7-0b70-41e3-9a93-1224ba098db7", + "metadata": {}, + "outputs": [], + "source": [ + "plt.rcParams[\"figure.figsize\"] = (4, 4)\n", + "plt.rcParams[\"axes.labelsize\"] = 12\n", + "plt.rcParams[\"legend.fontsize\"] = 7\n", + "plt.rcParams['lines.markersize'] = 1\n", + "plt.rcParams[\"lines.linestyle\"] = \"-\"\n", + "plt.rcParams[\"lines.linewidth\"] = 1\n", + "plt.rcParams[\"figure.dpi\"] = 1200\n", + "plt.rcParams[\"legend.markerscale\"] = 3" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "76e33287-5bba-419a-ad74-c4d6364a0ca1", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "fd3ebd12-7c89-4e0b-8a2a-c48181f5d3e6", + "metadata": {}, + "source": [ + "# Plot of the LJ 12-6 potential function:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "07787cc2-fc0e-49eb-8cc1-bab635e1040a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def lj_potential(r, sigma=1, epsilon=1, m=12, n=6):\n", + " v = 4*epsilon*((sigma/r)**m-(sigma/r)**n)\n", + " return v\n", + "\n", + "x = np.arange(0.01, 10, 0.01)\n", + "\n", + "fig = plt.figure()\n", + "\n", + "ymax = 3\n", + "ymin = -1.5\n", + "xmax = 4.0\n", + "\n", + "# Plot the potential\n", + "plt.plot(\n", + " x,\n", + " lj_potential(x),\n", + " #label=\"V(r)\"\n", + ")\n", + "\n", + "# Plot the force\n", + "#plt.plot(x, -np.gradient(lj_potential(x), 0.01), color=\"maroon\", label=\"F(r)\")\n", + "\n", + "# Plot dashed lines showing where V = 0 (r=sigma)\n", + "#plt.hlines(y=0, xmin=0, xmax=1, linestyles=\"--\", colors=\"k\")\n", + "#plt.vlines(x=1, ymin=ymin, ymax=0, linestyles=\"--\", colors=\"k\")\n", + "#plt.plot(1, 0, marker=\"o\", c=\"k\", markersize=3, label=\"$r = 1\\sigma$\", linewidth=0)\n", + "\n", + "# Plot dashed lines showing where V = min (r=1.12sigma)\n", + "plt.hlines(y=-1, xmin=0, xmax=2**(1/6), linestyles=\"--\", colors=\"g\")\n", + "plt.vlines(x=2**(1/6), ymin=ymin, ymax=-1, linestyles=\"--\", colors=\"g\")\n", + "plt.plot(1.12, -1, marker=\"o\", c=\"g\", markersize=3, label=\"$r_{min} (r = 2^{1/6}\\sigma)$\", linewidth=0)\n", + "plt.text(1.16, -1.15, \"$r_{min}$\")\n", + "\n", + "#plt.title(\"12-6 Lennard Jones Potential\")\n", + "plt.xlabel(\"$r\\,(\\sigma)$\")\n", + "plt.ylabel(\"$V(r)\\,(\\epsilon)$\")\n", + "plt.ylim(ymin, ymax)\n", + "plt.xlim(0, xmax)\n", + "#plt.legend()\n", + "\n", + "# Save the fig\n", + "plt.savefig(\"lj-potential-no-title.png\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2d45084a-d7b2-44c3-8566-904a8bb0fce3", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}