radial-distribution-function.ipynb

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    "# Radial Distribution Function (RDF)\n",
    "\n",
    "This notebook will demonstrate how to calculate the RDF of a gsd trajectory from a hoomd simulation, discuss how to interpret the RDF, and allow users to use the RDF to determine the phase transition temperature.\n",
    "\n",
    "Many images shown in this tutorial were found in the open textbook [Molecular Simulation](https://en.wikibooks.org/wiki/Molecular_Simulation), a useful introduction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import freud\n",
    "import gsd\n",
    "import hoomd\n",
    "import hoomd.md\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from utils.cg_utils import gsd_rdf\n",
    "from utils.draw_scene import snap_render, display_movie, from_gsd\n",
    "\n",
    "plt.rcParams['figure.figsize'] = 9.0, 6.0\n",
    "plt.rcParams['font.size'] = 18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rdf_from_gsd(gsd_file, r_max=None, r_min=0.1, nbins=50, start=0):\n",
    "    f = gsd.pygsd.GSDFile(open(gsd_file, \"rb\"))\n",
    "    trajectory = gsd.hoomd.HOOMDTrajectory(f)\n",
    "    \n",
    "    if r_max is None:\n",
    "        r_max = max(trajectory[0].configuration.box[:3]) * 0.45\n",
    "    freud_rdf = freud.density.RDF(bins=nbins, r_max=r_max, r_min=r_min)\n",
    "    for frame in trajectory[start:]:\n",
    "        freud_rdf.compute(system=frame, reset=False)\n",
    "    return freud_rdf"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our simulations use periodic boundary conditions, so we can simulate an \"infinite\" volume with a minimal amount of particles (think pac-man rules). We do this to minimize the effect of interfaces (e.g., surface of water) because they have different properties than the bulk. In a molecular dynamics simulation, each particle has a position and momentum. If we consider these for ALL particles in the system, that describes the microstate of the system. The RDF is calculated using just the positions of all particles.\n",
    "\n",
    "The RDF tells us the probability (normalized by the density of the system and volume of the shell swept out by that radius) of finding a particle at distance r from any other particle.\n",
    "\n",
    "The RDF algorithm goes like this:\n",
    "1. Get a histogram of distances between particles\n",
    "    1. Loop over all N particles\n",
    "    2. Calculate the distance between each particle and all its neighbors\n",
    "    3. Group the distances in \"bins\". (e.g., choose a step size, dr. If a distance is between $0 \\times dr$ and $1 \\times dr$, it goes in the first bin; a distance between $1 \\times dr$ and $2 \\times dr$ goes in the second bin, etc.)\n",
    "2. Normalize the histogram by dividing by the total number of pairs ($N\\times(N-1)$), the number density ($\\rho = \\frac{N}{V}$) and the volume of the spherical shell. This is important because it allows us to compare RDFs.\n",
    "\n",
    "The RDF plot will have the RDF (sometimes called $g(r)$ or $g_{2}(r)$ for \"pairwise correlation function\" [[1](#footnote1)]) on the y-axis and r (distance) on the x-axis. "
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"footnote1\"></a>\n",
    "\n",
    "[1] There are other correlation functions like $g_{3}$, $g_{4}$, that measure stuff like \"if you have two particles this distance apart, what's the likelihood of having a 3rd particle this far away from the first one\", etc, etc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initial structure and RDF\n",
    "\n",
    "In the cell below, we compare a perfect BCC crystal structure with its RDF. The function `from_gsd` loads a gsd file and creates an `mbuild.Compound` of a specified frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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0.0000    12.9000   -38.7000 C             1 RES     \\n     267 C            6.4500    19.3500   -19.3500 C             1 RES     \\n     268 C            0.0000    12.9000   -25.8000 C             1 RES     \\n     269 C            6.4500    19.3500    -6.4500 C             1 RES     \\n     270 C            0.0000    12.9000   -12.9000 C             1 RES     \\n     271 C            6.4500    19.3500     6.4500 C             1 RES     \\n     272 C            0.0000    12.9000     0.0000 C             1 RES     \\n     273 C            6.4500    19.3500    19.3500 C             1 RES     \\n     274 C            0.0000    12.9000    12.9000 C             1 RES     \\n     275 C            6.4500    19.3500    32.2500 C             1 RES     \\n     276 C            0.0000    12.9000    25.8000 C             1 RES     \\n     277 C            6.4500    32.2500   -32.2500 C             1 RES     \\n     278 C            0.0000    25.8000   -38.7000 C             1 RES     \\n     279 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-6.4500 C             1 RES     \\n     318 C           12.9000   -12.9000   -12.9000 C             1 RES     \\n     319 C           19.3500    -6.4500     6.4500 C             1 RES     \\n     320 C           12.9000   -12.9000     0.0000 C             1 RES     \\n     321 C           19.3500    -6.4500    19.3500 C             1 RES     \\n     322 C           12.9000   -12.9000    12.9000 C             1 RES     \\n     323 C           19.3500    -6.4500    32.2500 C             1 RES     \\n     324 C           12.9000   -12.9000    25.8000 C             1 RES     \\n     325 C           19.3500     6.4500   -32.2500 C             1 RES     \\n     326 C           12.9000     0.0000   -38.7000 C             1 RES     \\n     327 C           19.3500     6.4500   -19.3500 C             1 RES     \\n     328 C           12.9000     0.0000   -25.8000 C             1 RES     \\n     329 C           19.3500     6.4500    -6.4500 C             1 RES     \\n     330 C           12.9000  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           1 RES     \\n     382 C           25.8000   -25.8000    12.9000 C             1 RES     \\n     383 C           32.2500   -19.3500    32.2500 C             1 RES     \\n     384 C           25.8000   -25.8000    25.8000 C             1 RES     \\n     385 C           32.2500    -6.4500   -32.2500 C             1 RES     \\n     386 C           25.8000   -12.9000   -38.7000 C             1 RES     \\n     387 C           32.2500    -6.4500   -19.3500 C             1 RES     \\n     388 C           25.8000   -12.9000   -25.8000 C             1 RES     \\n     389 C           32.2500    -6.4500    -6.4500 C             1 RES     \\n     390 C           25.8000   -12.9000   -12.9000 C             1 RES     \\n     391 C           32.2500    -6.4500     6.4500 C             1 RES     \\n     392 C           25.8000   -12.9000     0.0000 C             1 RES     \\n     393 C           32.2500    -6.4500    19.3500 C             1 RES     \\n     394 C           25.8000   -12.9000  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420 C           25.8000    12.9000    25.8000 C             1 RES     \\n     421 C           32.2500    32.2500   -32.2500 C             1 RES     \\n     422 C           25.8000    25.8000   -38.7000 C             1 RES     \\n     423 C           32.2500    32.2500   -19.3500 C             1 RES     \\n     424 C           25.8000    25.8000   -25.8000 C             1 RES     \\n     425 C           32.2500    32.2500    -6.4500 C             1 RES     \\n     426 C           25.8000    25.8000   -12.9000 C             1 RES     \\n     427 C           32.2500    32.2500     6.4500 C             1 RES     \\n     428 C           25.8000    25.8000     0.0000 C             1 RES     \\n     429 C           32.2500    32.2500    19.3500 C             1 RES     \\n     430 C           25.8000    25.8000    12.9000 C             1 RES     \\n     431 C           32.2500    32.2500    32.2500 C             1 RES     \\n     432 C           25.8000    25.8000    25.8000 C             1 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       1 RES     \\n      37 C          -32.2500     6.4500   -32.2500 C             1 RES     \\n      38 C          -38.7000     0.0000   -38.7000 C             1 RES     \\n      39 C          -32.2500     6.4500   -19.3500 C             1 RES     \\n      40 C          -38.7000     0.0000   -25.8000 C             1 RES     \\n      41 C          -32.2500     6.4500    -6.4500 C             1 RES     \\n      42 C          -38.7000     0.0000   -12.9000 C             1 RES     \\n      43 C          -32.2500     6.4500     6.4500 C             1 RES     \\n      44 C          -38.7000     0.0000     0.0000 C             1 RES     \\n      45 C          -32.2500     6.4500    19.3500 C             1 RES     \\n      46 C          -38.7000     0.0000    12.9000 C             1 RES     \\n      47 C          -32.2500     6.4500    32.2500 C             1 RES     \\n      48 C          -38.7000     0.0000    25.8000 C             1 RES     \\n      49 C          -32.2500    19.3500   -32.2500 C             1 RES     \\n      50 C          -38.7000    12.9000   -38.7000 C             1 RES     \\n      51 C          -32.2500    19.3500   -19.3500 C             1 RES     \\n      52 C          -38.7000    12.9000   -25.8000 C             1 RES     \\n      53 C          -32.2500    19.3500    -6.4500 C             1 RES     \\n      54 C          -38.7000    12.9000   -12.9000 C             1 RES     \\n      55 C          -32.2500    19.3500     6.4500 C             1 RES     \\n      56 C          -38.7000    12.9000     0.0000 C             1 RES     \\n      57 C          -32.2500    19.3500    19.3500 C             1 RES     \\n      58 C          -38.7000    12.9000    12.9000 C             1 RES     \\n      59 C          -32.2500    19.3500    32.2500 C             1 RES     \\n      60 C          -38.7000    12.9000    25.8000 C             1 RES     \\n      61 C          -32.2500    32.2500   -32.2500 C             1 RES     \\n      62 C          -38.7000    25.8000   -38.7000 C             1 RES     \\n      63 C          -32.2500    32.2500   -19.3500 C             1 RES     \\n      64 C          -38.7000    25.8000   -25.8000 C             1 RES     \\n      65 C          -32.2500    32.2500    -6.4500 C             1 RES     \\n      66 C          -38.7000    25.8000   -12.9000 C             1 RES     \\n      67 C          -32.2500    32.2500     6.4500 C             1 RES     \\n      68 C          -38.7000    25.8000     0.0000 C             1 RES     \\n      69 C          -32.2500    32.2500    19.3500 C             1 RES     \\n      70 C          -38.7000    25.8000    12.9000 C             1 RES     \\n      71 C          -32.2500    32.2500    32.2500 C             1 RES     \\n      72 C          -38.7000    25.8000    25.8000 C             1 RES     \\n      73 C          -19.3500   -32.2500   -32.2500 C             1 RES     \\n      74 C          -25.8000   -38.7000   -38.7000 C             1 RES     \\n      75 C          -19.3500   -32.2500   -19.3500 C             1 RES     \\n      76 C          -25.8000   -38.7000   -25.8000 C             1 RES     \\n      77 C          -19.3500   -32.2500    -6.4500 C             1 RES     \\n      78 C          -25.8000   -38.7000   -12.9000 C             1 RES     \\n      79 C          -19.3500   -32.2500     6.4500 C             1 RES     \\n      80 C          -25.8000   -38.7000     0.0000 C             1 RES     \\n      81 C          -19.3500   -32.2500    19.3500 C             1 RES     \\n      82 C          -25.8000   -38.7000    12.9000 C             1 RES     \\n      83 C          -19.3500   -32.2500    32.2500 C             1 RES     \\n      84 C          -25.8000   -38.7000    25.8000 C             1 RES     \\n      85 C          -19.3500   -19.3500   -32.2500 C             1 RES     \\n      86 C          -25.8000   -25.8000   -38.7000 C             1 RES     \\n      87 C          -19.3500   -19.3500   -19.3500 C             1 RES     \\n      88 C          -25.8000   -25.8000   -25.8000 C             1 RES     \\n      89 C          -19.3500   -19.3500    -6.4500 C             1 RES     \\n      90 C          -25.8000   -25.8000   -12.9000 C             1 RES     \\n      91 C          -19.3500   -19.3500     6.4500 C             1 RES     \\n      92 C          -25.8000   -25.8000     0.0000 C             1 RES     \\n      93 C          -19.3500   -19.3500    19.3500 C             1 RES     \\n      94 C          -25.8000   -25.8000    12.9000 C             1 RES     \\n      95 C          -19.3500   -19.3500    32.2500 C             1 RES     \\n      96 C          -25.8000   -25.8000    25.8000 C             1 RES     \\n      97 C          -19.3500    -6.4500   -32.2500 C             1 RES     \\n      98 C          -25.8000   -12.9000   -38.7000 C             1 RES     \\n      99 C          -19.3500    -6.4500   -19.3500 C             1 RES     \\n     100 C          -25.8000   -12.9000   -25.8000 C             1 RES     \\n     101 C          -19.3500    -6.4500    -6.4500 C             1 RES     \\n     102 C          -25.8000   -12.9000   -12.9000 C             1 RES     \\n     103 C          -19.3500    -6.4500     6.4500 C             1 RES     \\n     104 C          -25.8000   -12.9000     0.0000 C             1 RES     \\n     105 C          -19.3500    -6.4500    19.3500 C             1 RES     \\n     106 C          -25.8000   -12.9000    12.9000 C             1 RES     \\n     107 C          -19.3500    -6.4500    32.2500 C             1 RES     \\n     108 C          -25.8000   -12.9000    25.8000 C             1 RES     \\n     109 C          -19.3500     6.4500   -32.2500 C             1 RES     \\n     110 C          -25.8000     0.0000   -38.7000 C             1 RES     \\n     111 C          -19.3500     6.4500   -19.3500 C             1 RES     \\n     112 C          -25.8000     0.0000   -25.8000 C             1 RES     \\n     113 C          -19.3500     6.4500    -6.4500 C             1 RES     \\n     114 C          -25.8000     0.0000   -12.9000 C             1 RES     \\n     115 C          -19.3500     6.4500     6.4500 C             1 RES     \\n     116 C          -25.8000     0.0000     0.0000 C             1 RES     \\n     117 C          -19.3500     6.4500    19.3500 C             1 RES     \\n     118 C          -25.8000     0.0000    12.9000 C             1 RES     \\n     119 C          -19.3500     6.4500    32.2500 C             1 RES     \\n     120 C          -25.8000     0.0000    25.8000 C             1 RES     \\n     121 C          -19.3500    19.3500   -32.2500 C             1 RES     \\n     122 C          -25.8000    12.9000   -38.7000 C             1 RES     \\n     123 C          -19.3500    19.3500   -19.3500 C             1 RES     \\n     124 C          -25.8000    12.9000   -25.8000 C             1 RES     \\n     125 C          -19.3500    19.3500    -6.4500 C             1 RES     \\n     126 C          -25.8000    12.9000   -12.9000 C             1 RES     \\n     127 C          -19.3500    19.3500     6.4500 C             1 RES     \\n     128 C          -25.8000    12.9000     0.0000 C             1 RES     \\n     129 C          -19.3500    19.3500    19.3500 C             1 RES     \\n     130 C          -25.8000    12.9000    12.9000 C             1 RES     \\n     131 C          -19.3500    19.3500    32.2500 C             1 RES     \\n     132 C          -25.8000    12.9000    25.8000 C             1 RES     \\n     133 C          -19.3500    32.2500   -32.2500 C             1 RES     \\n     134 C          -25.8000    25.8000   -38.7000 C             1 RES     \\n     135 C          -19.3500    32.2500   -19.3500 C             1 RES     \\n     136 C          -25.8000    25.8000   -25.8000 C             1 RES     \\n     137 C          -19.3500    32.2500    -6.4500 C             1 RES     \\n     138 C          -25.8000    25.8000   -12.9000 C             1 RES     \\n     139 C          -19.3500    32.2500     6.4500 C             1 RES     \\n     140 C          -25.8000    25.8000     0.0000 C             1 RES     \\n     141 C          -19.3500    32.2500    19.3500 C             1 RES     \\n     142 C          -25.8000    25.8000    12.9000 C             1 RES     \\n     143 C          -19.3500    32.2500    32.2500 C             1 RES     \\n     144 C          -25.8000    25.8000    25.8000 C             1 RES     \\n     145 C           -6.4500   -32.2500   -32.2500 C             1 RES     \\n     146 C          -12.9000   -38.7000   -38.7000 C             1 RES     \\n     147 C           -6.4500   -32.2500   -19.3500 C             1 RES     \\n     148 C          -12.9000   -38.7000   -25.8000 C             1 RES     \\n     149 C           -6.4500   -32.2500    -6.4500 C             1 RES     \\n     150 C          -12.9000   -38.7000   -12.9000 C             1 RES     \\n     151 C           -6.4500   -32.2500     6.4500 C             1 RES     \\n     152 C          -12.9000   -38.7000     0.0000 C             1 RES     \\n     153 C           -6.4500   -32.2500    19.3500 C             1 RES     \\n     154 C          -12.9000   -38.7000    12.9000 C             1 RES     \\n     155 C           -6.4500   -32.2500    32.2500 C             1 RES     \\n     156 C          -12.9000   -38.7000    25.8000 C             1 RES     \\n     157 C           -6.4500   -19.3500   -32.2500 C             1 RES     \\n     158 C          -12.9000   -25.8000   -38.7000 C             1 RES     \\n     159 C           -6.4500   -19.3500   -19.3500 C             1 RES     \\n     160 C          -12.9000   -25.8000   -25.8000 C             1 RES     \\n     161 C           -6.4500   -19.3500    -6.4500 C             1 RES     \\n     162 C          -12.9000   -25.8000   -12.9000 C             1 RES     \\n     163 C           -6.4500   -19.3500     6.4500 C             1 RES     \\n     164 C          -12.9000   -25.8000     0.0000 C             1 RES     \\n     165 C           -6.4500   -19.3500    19.3500 C             1 RES     \\n     166 C          -12.9000   -25.8000    12.9000 C             1 RES     \\n     167 C           -6.4500   -19.3500    32.2500 C             1 RES     \\n     168 C          -12.9000   -25.8000    25.8000 C             1 RES     \\n     169 C           -6.4500    -6.4500   -32.2500 C             1 RES     \\n     170 C          -12.9000   -12.9000   -38.7000 C             1 RES     \\n     171 C           -6.4500    -6.4500   -19.3500 C             1 RES     \\n     172 C          -12.9000   -12.9000   -25.8000 C             1 RES     \\n     173 C           -6.4500    -6.4500    -6.4500 C             1 RES     \\n     174 C          -12.9000   -12.9000   -12.9000 C             1 RES     \\n     175 C           -6.4500    -6.4500     6.4500 C             1 RES     \\n     176 C          -12.9000   -12.9000     0.0000 C             1 RES     \\n     177 C           -6.4500    -6.4500    19.3500 C             1 RES     \\n     178 C          -12.9000   -12.9000    12.9000 C             1 RES     \\n     179 C           -6.4500    -6.4500    32.2500 C             1 RES     \\n     180 C          -12.9000   -12.9000    25.8000 C             1 RES     \\n     181 C           -6.4500     6.4500   -32.2500 C             1 RES     \\n     182 C          -12.9000     0.0000   -38.7000 C             1 RES     \\n     183 C           -6.4500     6.4500   -19.3500 C             1 RES     \\n     184 C          -12.9000     0.0000   -25.8000 C             1 RES     \\n     185 C           -6.4500     6.4500    -6.4500 C             1 RES     \\n     186 C          -12.9000     0.0000   -12.9000 C             1 RES     \\n     187 C           -6.4500     6.4500     6.4500 C             1 RES     \\n     188 C          -12.9000     0.0000     0.0000 C             1 RES     \\n     189 C           -6.4500     6.4500    19.3500 C             1 RES     \\n     190 C          -12.9000     0.0000    12.9000 C             1 RES     \\n     191 C           -6.4500     6.4500    32.2500 C             1 RES     \\n     192 C          -12.9000     0.0000    25.8000 C             1 RES     \\n     193 C           -6.4500    19.3500   -32.2500 C             1 RES     \\n     194 C          -12.9000    12.9000   -38.7000 C             1 RES     \\n     195 C           -6.4500    19.3500   -19.3500 C             1 RES     \\n     196 C          -12.9000    12.9000   -25.8000 C             1 RES     \\n     197 C           -6.4500    19.3500    -6.4500 C             1 RES     \\n     198 C          -12.9000    12.9000   -12.9000 C             1 RES     \\n     199 C           -6.4500    19.3500     6.4500 C             1 RES     \\n     200 C          -12.9000    12.9000     0.0000 C             1 RES     \\n     201 C           -6.4500    19.3500    19.3500 C             1 RES     \\n     202 C          -12.9000    12.9000    12.9000 C             1 RES     \\n     203 C           -6.4500    19.3500    32.2500 C             1 RES     \\n     204 C          -12.9000    12.9000    25.8000 C             1 RES     \\n     205 C           -6.4500    32.2500   -32.2500 C             1 RES     \\n     206 C          -12.9000    25.8000   -38.7000 C             1 RES     \\n     207 C           -6.4500    32.2500   -19.3500 C             1 RES     \\n     208 C          -12.9000    25.8000   -25.8000 C             1 RES     \\n     209 C           -6.4500    32.2500    -6.4500 C             1 RES     \\n     210 C          -12.9000    25.8000   -12.9000 C             1 RES     \\n     211 C           -6.4500    32.2500     6.4500 C             1 RES     \\n     212 C          -12.9000    25.8000     0.0000 C             1 RES     \\n     213 C           -6.4500    32.2500    19.3500 C             1 RES     \\n     214 C          -12.9000    25.8000    12.9000 C             1 RES     \\n     215 C           -6.4500    32.2500    32.2500 C             1 RES     \\n     216 C          -12.9000    25.8000    25.8000 C             1 RES     \\n     217 C            6.4500   -32.2500   -32.2500 C             1 RES     \\n     218 C            0.0000   -38.7000   -38.7000 C             1 RES     \\n     219 C            6.4500   -32.2500   -19.3500 C             1 RES     \\n     220 C            0.0000   -38.7000   -25.8000 C             1 RES     \\n     221 C            6.4500   -32.2500    -6.4500 C             1 RES     \\n     222 C            0.0000   -38.7000   -12.9000 C             1 RES     \\n     223 C            6.4500   -32.2500     6.4500 C             1 RES     \\n     224 C            0.0000   -38.7000     0.0000 C             1 RES     \\n     225 C            6.4500   -32.2500    19.3500 C             1 RES     \\n     226 C            0.0000   -38.7000    12.9000 C             1 RES     \\n     227 C            6.4500   -32.2500    32.2500 C             1 RES     \\n     228 C            0.0000   -38.7000    25.8000 C             1 RES     \\n     229 C            6.4500   -19.3500   -32.2500 C             1 RES     \\n     230 C            0.0000   -25.8000   -38.7000 C             1 RES     \\n     231 C            6.4500   -19.3500   -19.3500 C             1 RES     \\n     232 C            0.0000   -25.8000   -25.8000 C             1 RES     \\n     233 C            6.4500   -19.3500    -6.4500 C             1 RES     \\n     234 C            0.0000   -25.8000   -12.9000 C             1 RES     \\n     235 C            6.4500   -19.3500     6.4500 C             1 RES     \\n     236 C            0.0000   -25.8000     0.0000 C             1 RES     \\n     237 C            6.4500   -19.3500    19.3500 C             1 RES     \\n     238 C            0.0000   -25.8000    12.9000 C             1 RES     \\n     239 C            6.4500   -19.3500    32.2500 C             1 RES     \\n     240 C            0.0000   -25.8000    25.8000 C             1 RES     \\n     241 C            6.4500    -6.4500   -32.2500 C             1 RES     \\n     242 C            0.0000   -12.9000   -38.7000 C             1 RES     \\n     243 C            6.4500    -6.4500   -19.3500 C             1 RES     \\n     244 C            0.0000   -12.9000   -25.8000 C             1 RES     \\n     245 C            6.4500    -6.4500    -6.4500 C             1 RES     \\n     246 C            0.0000   -12.9000   -12.9000 C             1 RES     \\n     247 C            6.4500    -6.4500     6.4500 C             1 RES     \\n     248 C            0.0000   -12.9000     0.0000 C             1 RES     \\n     249 C            6.4500    -6.4500    19.3500 C             1 RES     \\n     250 C            0.0000   -12.9000    12.9000 C             1 RES     \\n     251 C            6.4500    -6.4500    32.2500 C             1 RES     \\n     252 C            0.0000   -12.9000    25.8000 C             1 RES     \\n     253 C            6.4500     6.4500   -32.2500 C             1 RES     \\n     254 C            0.0000     0.0000   -38.7000 C             1 RES     \\n     255 C            6.4500     6.4500   -19.3500 C             1 RES     \\n     256 C            0.0000     0.0000   -25.8000 C             1 RES     \\n     257 C            6.4500     6.4500    -6.4500 C             1 RES     \\n     258 C            0.0000     0.0000   -12.9000 C             1 RES     \\n     259 C            6.4500     6.4500     6.4500 C             1 RES     \\n     260 C            0.0000     0.0000     0.0000 C             1 RES     \\n     261 C            6.4500     6.4500    19.3500 C             1 RES     \\n     262 C            0.0000     0.0000    12.9000 C             1 RES     \\n     263 C            6.4500     6.4500    32.2500 C             1 RES     \\n     264 C            0.0000     0.0000    25.8000 C             1 RES     \\n     265 C            6.4500    19.3500   -32.2500 C             1 RES     \\n     266 C            0.0000    12.9000   -38.7000 C             1 RES     \\n     267 C            6.4500    19.3500   -19.3500 C             1 RES     \\n     268 C            0.0000    12.9000   -25.8000 C             1 RES     \\n     269 C            6.4500    19.3500    -6.4500 C             1 RES     \\n     270 C            0.0000    12.9000   -12.9000 C             1 RES     \\n     271 C            6.4500    19.3500     6.4500 C             1 RES     \\n     272 C            0.0000    12.9000     0.0000 C             1 RES     \\n     273 C            6.4500    19.3500    19.3500 C             1 RES     \\n     274 C            0.0000    12.9000    12.9000 C             1 RES     \\n     275 C            6.4500    19.3500    32.2500 C             1 RES     \\n     276 C            0.0000    12.9000    25.8000 C             1 RES     \\n     277 C            6.4500    32.2500   -32.2500 C             1 RES     \\n     278 C            0.0000    25.8000   -38.7000 C             1 RES     \\n     279 C            6.4500    32.2500   -19.3500 C             1 RES     \\n     280 C            0.0000    25.8000   -25.8000 C             1 RES     \\n     281 C            6.4500    32.2500    -6.4500 C             1 RES     \\n     282 C            0.0000    25.8000   -12.9000 C             1 RES     \\n     283 C            6.4500    32.2500     6.4500 C             1 RES     \\n     284 C            0.0000    25.8000     0.0000 C             1 RES     \\n     285 C            6.4500    32.2500    19.3500 C             1 RES     \\n     286 C            0.0000    25.8000    12.9000 C             1 RES     \\n     287 C            6.4500    32.2500    32.2500 C             1 RES     \\n     288 C            0.0000    25.8000    25.8000 C             1 RES     \\n     289 C           19.3500   -32.2500   -32.2500 C             1 RES     \\n     290 C           12.9000   -38.7000   -38.7000 C             1 RES     \\n     291 C           19.3500   -32.2500   -19.3500 C             1 RES     \\n     292 C           12.9000   -38.7000   -25.8000 C             1 RES     \\n     293 C           19.3500   -32.2500    -6.4500 C             1 RES     \\n     294 C           12.9000   -38.7000   -12.9000 C             1 RES     \\n     295 C           19.3500   -32.2500     6.4500 C             1 RES     \\n     296 C           12.9000   -38.7000     0.0000 C             1 RES     \\n     297 C           19.3500   -32.2500    19.3500 C             1 RES     \\n     298 C           12.9000   -38.7000    12.9000 C             1 RES     \\n     299 C           19.3500   -32.2500    32.2500 C             1 RES     \\n     300 C           12.9000   -38.7000    25.8000 C             1 RES     \\n     301 C           19.3500   -19.3500   -32.2500 C             1 RES     \\n     302 C           12.9000   -25.8000   -38.7000 C             1 RES     \\n     303 C           19.3500   -19.3500   -19.3500 C             1 RES     \\n     304 C           12.9000   -25.8000   -25.8000 C             1 RES     \\n     305 C           19.3500   -19.3500    -6.4500 C             1 RES     \\n     306 C           12.9000   -25.8000   -12.9000 C             1 RES     \\n     307 C           19.3500   -19.3500     6.4500 C             1 RES     \\n     308 C           12.9000   -25.8000     0.0000 C             1 RES     \\n     309 C           19.3500   -19.3500    19.3500 C             1 RES     \\n     310 C           12.9000   -25.8000    12.9000 C             1 RES     \\n     311 C           19.3500   -19.3500    32.2500 C             1 RES     \\n     312 C           12.9000   -25.8000    25.8000 C             1 RES     \\n     313 C           19.3500    -6.4500   -32.2500 C             1 RES     \\n     314 C           12.9000   -12.9000   -38.7000 C             1 RES     \\n     315 C           19.3500    -6.4500   -19.3500 C             1 RES     \\n     316 C           12.9000   -12.9000   -25.8000 C             1 RES     \\n     317 C           19.3500    -6.4500    -6.4500 C             1 RES     \\n     318 C           12.9000   -12.9000   -12.9000 C             1 RES     \\n     319 C           19.3500    -6.4500     6.4500 C             1 RES     \\n     320 C           12.9000   -12.9000     0.0000 C             1 RES     \\n     321 C           19.3500    -6.4500    19.3500 C             1 RES     \\n     322 C           12.9000   -12.9000    12.9000 C             1 RES     \\n     323 C           19.3500    -6.4500    32.2500 C             1 RES     \\n     324 C           12.9000   -12.9000    25.8000 C             1 RES     \\n     325 C           19.3500     6.4500   -32.2500 C             1 RES     \\n     326 C           12.9000     0.0000   -38.7000 C             1 RES     \\n     327 C           19.3500     6.4500   -19.3500 C             1 RES     \\n     328 C           12.9000     0.0000   -25.8000 C             1 RES     \\n     329 C           19.3500     6.4500    -6.4500 C             1 RES     \\n     330 C           12.9000     0.0000   -12.9000 C             1 RES     \\n     331 C           19.3500     6.4500     6.4500 C             1 RES     \\n     332 C           12.9000     0.0000     0.0000 C             1 RES     \\n     333 C           19.3500     6.4500    19.3500 C             1 RES     \\n     334 C           12.9000     0.0000    12.9000 C             1 RES     \\n     335 C           19.3500     6.4500    32.2500 C             1 RES     \\n     336 C           12.9000     0.0000    25.8000 C             1 RES     \\n     337 C           19.3500    19.3500   -32.2500 C             1 RES     \\n     338 C           12.9000    12.9000   -38.7000 C             1 RES     \\n     339 C           19.3500    19.3500   -19.3500 C             1 RES     \\n     340 C           12.9000    12.9000   -25.8000 C             1 RES     \\n     341 C           19.3500    19.3500    -6.4500 C             1 RES     \\n     342 C           12.9000    12.9000   -12.9000 C             1 RES     \\n     343 C           19.3500    19.3500     6.4500 C             1 RES     \\n     344 C           12.9000    12.9000     0.0000 C             1 RES     \\n     345 C           19.3500    19.3500    19.3500 C             1 RES     \\n     346 C           12.9000    12.9000    12.9000 C             1 RES     \\n     347 C           19.3500    19.3500    32.2500 C             1 RES     \\n     348 C           12.9000    12.9000    25.8000 C             1 RES     \\n     349 C           19.3500    32.2500   -32.2500 C             1 RES     \\n     350 C           12.9000    25.8000   -38.7000 C             1 RES     \\n     351 C           19.3500    32.2500   -19.3500 C             1 RES     \\n     352 C           12.9000    25.8000   -25.8000 C             1 RES     \\n     353 C           19.3500    32.2500    -6.4500 C             1 RES     \\n     354 C           12.9000    25.8000   -12.9000 C             1 RES     \\n     355 C           19.3500    32.2500     6.4500 C             1 RES     \\n     356 C           12.9000    25.8000     0.0000 C             1 RES     \\n     357 C           19.3500    32.2500    19.3500 C             1 RES     \\n     358 C           12.9000    25.8000    12.9000 C             1 RES     \\n     359 C           19.3500    32.2500    32.2500 C             1 RES     \\n     360 C           12.9000    25.8000    25.8000 C             1 RES     \\n     361 C           32.2500   -32.2500   -32.2500 C             1 RES     \\n     362 C           25.8000   -38.7000   -38.7000 C             1 RES     \\n     363 C           32.2500   -32.2500   -19.3500 C             1 RES     \\n     364 C           25.8000   -38.7000   -25.8000 C             1 RES     \\n     365 C           32.2500   -32.2500    -6.4500 C             1 RES     \\n     366 C           25.8000   -38.7000   -12.9000 C             1 RES     \\n     367 C           32.2500   -32.2500     6.4500 C             1 RES     \\n     368 C           25.8000   -38.7000     0.0000 C             1 RES     \\n     369 C           32.2500   -32.2500    19.3500 C             1 RES     \\n     370 C           25.8000   -38.7000    12.9000 C             1 RES     \\n     371 C           32.2500   -32.2500    32.2500 C             1 RES     \\n     372 C           25.8000   -38.7000    25.8000 C             1 RES     \\n     373 C           32.2500   -19.3500   -32.2500 C             1 RES     \\n     374 C           25.8000   -25.8000   -38.7000 C             1 RES     \\n     375 C           32.2500   -19.3500   -19.3500 C             1 RES     \\n     376 C           25.8000   -25.8000   -25.8000 C             1 RES     \\n     377 C           32.2500   -19.3500    -6.4500 C             1 RES     \\n     378 C           25.8000   -25.8000   -12.9000 C             1 RES     \\n     379 C           32.2500   -19.3500     6.4500 C             1 RES     \\n     380 C           25.8000   -25.8000     0.0000 C             1 RES     \\n     381 C           32.2500   -19.3500    19.3500 C             1 RES     \\n     382 C           25.8000   -25.8000    12.9000 C             1 RES     \\n     383 C           32.2500   -19.3500    32.2500 C             1 RES     \\n     384 C           25.8000   -25.8000    25.8000 C             1 RES     \\n     385 C           32.2500    -6.4500   -32.2500 C             1 RES     \\n     386 C           25.8000   -12.9000   -38.7000 C             1 RES     \\n     387 C           32.2500    -6.4500   -19.3500 C             1 RES     \\n     388 C           25.8000   -12.9000   -25.8000 C             1 RES     \\n     389 C           32.2500    -6.4500    -6.4500 C             1 RES     \\n     390 C           25.8000   -12.9000   -12.9000 C             1 RES     \\n     391 C           32.2500    -6.4500     6.4500 C             1 RES     \\n     392 C           25.8000   -12.9000     0.0000 C             1 RES     \\n     393 C           32.2500    -6.4500    19.3500 C             1 RES     \\n     394 C           25.8000   -12.9000    12.9000 C             1 RES     \\n     395 C           32.2500    -6.4500    32.2500 C             1 RES     \\n     396 C           25.8000   -12.9000    25.8000 C             1 RES     \\n     397 C           32.2500     6.4500   -32.2500 C             1 RES     \\n     398 C           25.8000     0.0000   -38.7000 C             1 RES     \\n     399 C           32.2500     6.4500   -19.3500 C             1 RES     \\n     400 C           25.8000     0.0000   -25.8000 C             1 RES     \\n     401 C           32.2500     6.4500    -6.4500 C             1 RES     \\n     402 C           25.8000     0.0000   -12.9000 C             1 RES     \\n     403 C           32.2500     6.4500     6.4500 C             1 RES     \\n     404 C           25.8000     0.0000     0.0000 C             1 RES     \\n     405 C           32.2500     6.4500    19.3500 C             1 RES     \\n     406 C           25.8000     0.0000    12.9000 C             1 RES     \\n     407 C           32.2500     6.4500    32.2500 C             1 RES     \\n     408 C           25.8000     0.0000    25.8000 C             1 RES     \\n     409 C           32.2500    19.3500   -32.2500 C             1 RES     \\n     410 C           25.8000    12.9000   -38.7000 C             1 RES     \\n     411 C           32.2500    19.3500   -19.3500 C             1 RES     \\n     412 C           25.8000    12.9000   -25.8000 C             1 RES     \\n     413 C           32.2500    19.3500    -6.4500 C             1 RES     \\n     414 C           25.8000    12.9000   -12.9000 C             1 RES     \\n     415 C           32.2500    19.3500     6.4500 C             1 RES     \\n     416 C           25.8000    12.9000     0.0000 C             1 RES     \\n     417 C           32.2500    19.3500    19.3500 C             1 RES     \\n     418 C           25.8000    12.9000    12.9000 C             1 RES     \\n     419 C           32.2500    19.3500    32.2500 C             1 RES     \\n     420 C           25.8000    12.9000    25.8000 C             1 RES     \\n     421 C           32.2500    32.2500   -32.2500 C             1 RES     \\n     422 C           25.8000    25.8000   -38.7000 C             1 RES     \\n     423 C           32.2500    32.2500   -19.3500 C             1 RES     \\n     424 C           25.8000    25.8000   -25.8000 C             1 RES     \\n     425 C           32.2500    32.2500    -6.4500 C             1 RES     \\n     426 C           25.8000    25.8000   -12.9000 C             1 RES     \\n     427 C           32.2500    32.2500     6.4500 C             1 RES     \\n     428 C           25.8000    25.8000     0.0000 C             1 RES     \\n     429 C           32.2500    32.2500    19.3500 C             1 RES     \\n     430 C           25.8000    25.8000    12.9000 C             1 RES     \\n     431 C           32.2500    32.2500    32.2500 C             1 RES     \\n     432 C           25.8000    25.8000    25.8000 C             1 RES     \\n@<TRIPOS>BOND\\n@<TRIPOS>SUBSTRUCTURE\\n       1 RES             1 RESIDUE    0 **** ROOT      0\\n\",\"mol2\");\n",
       "\tviewer_1590794704966793.setStyle({\"stick\": {\"radius\": 0.2, \"color\": \"grey\"}, \"sphere\": {\"scale\": 0.3, \"colorscheme\": {}}});\n",
       "\tviewer_1590794704966793.zoomTo();\n",
       "viewer_1590794704966793.render();\n",
       "});\n",
       "</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gsdfile = 'trajectories/bcc_system.gsd'\n",
    "\n",
    "bcc_start = from_gsd(gsdfile, frame=0)\n",
    "\n",
    "bcc_start.visualize().show()\n",
    "    \n",
    "\n",
    "bcc_start_rdf = rdf_from_gsd(gsdfile)\n",
    "\n",
    "plt.plot(bcc_start_rdf.bin_centers, bcc_start_rdf.rdf)\n",
    "plt.title(\"RDF BCC crystal sructure\")\n",
    "plt.xlabel(\"r\")\n",
    "plt.ylabel(\"g(r)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above plot, r is the distance between particles and g(r) is the probability of finding a neighboring particle at that distance. Examining the RDF plot, we see sharp, distinct peaks; because the structure is crystalline, there are only a few nearest neighbor distances, as shown in the image below:\n",
    "\n",
    "![](https://www.princeton.edu/~maelabs/mae324/glos324/b109.gif)\n",
    "\n",
    "Image credit [Princeton University](https://www.princeton.edu/~maelabs/mae324/glos324/nearestneighbor.htm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we'll look at computing the accumulated RDF of a simulation trajectory. But before we do that, we need to know a little about these trajectories. The trajectories used in this tutorial were generated using the `build_system` and `hoomd_simulation` functions (shown below). These functions initialize a BCC or FCC system to run in the [NVT (Canonical) ensemble](https://en.wikibooks.org/wiki/Molecular_Simulation/Thermodynamic_ensembles) using the [Lennard-Jones potential](https://en.wikibooks.org/wiki/Molecular_Simulation/The_Lennard-Jones_Potential).\n",
    "\n",
    "Lennard-Jones is a pairwise potential which decribes the attractive or repulsive force between two particles. If the slope of the potential is positive, the particles be attracted; if it is negative, they will be repulsed.\n",
    "\n",
    "![](https://gifsdefisicacom.files.wordpress.com/2018/12/0184giphy.gif)\n",
    "\n",
    "Image credit [GIFs de Física](https://gifsdefisica.com/2018/12/18/potencial-de-lennard-jones/)\n",
    "\n",
    "This potential is controlled mainly by two parameters, epsilon and sigma:\n",
    "\n",
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Schematic_of_the_Lennard-Jones_6-12_Potential.png/1024px-Schematic_of_the_Lennard-Jones_6-12_Potential.png\" width=300 />\n",
    "\n",
    "Image credit [Christopher Rowley](https://commons.wikimedia.org/w/index.php?curid=44617468)\n",
    "\n",
    "Where epsilon, the depth of the potential well, controls the strength of attraction between two particles and sigma, the distance where the potential is zero, controls the effective particle size. Notice in the `hoomd_simulation` function the epsilon and sigma values in the [LJ force](https://hoomd-blue.readthedocs.io/en/stable/module-md-pair.html#hoomd.md.pair.lj) are set to 1:\n",
    "```\n",
    "lj.pair_coeff.set('C', 'C', epsilon=1.0, sigma=1.0)\n",
    "```\n",
    "The trajectories provided in this tutorial were run at kT = 0.25 (cold), 1.5 (mid), and 5 (hot). You might wonder how to determine whether a [unitless temperature](https://hoomd-blue.readthedocs.io/en/stable/units.html) is cold or hot, and in this case we can think of the temperature (the thermal kinetic energy) as relative to the potentials the particles experience. In this case a \"cold\" simulation (kT=0.25) does not have enough kinetic energy to escape the attractive potential of a neighboring particle (epsilon=1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_system(packing='bcc'):\n",
    "    '''\n",
    "    Generate a simple LJ particle system using hoomd's create_lattice function\n",
    "    packing \n",
    "    '''\n",
    "    if packing == 'fcc':\n",
    "        system = hoomd.init.create_lattice(unitcell=(hoomd.lattice.fcc(a=1.58)), n=6)\n",
    "    elif packing == 'bcc':\n",
    "        system = hoomd.init.create_lattice(unitcell=(hoomd.lattice.bcc(a=1.29)), n=6)\n",
    "    hoomd.dump.gsd('{}_system.gsd'.format(packing), group = hoomd.group.all(), period=None, overwrite=True)\n",
    "    return system\n",
    "\n",
    "\n",
    "def hoomd_simulation(packing, temp):  \n",
    "    hoomd.context.initialize(\"\")\n",
    "    system = build_system(packing)\n",
    "    nl = hoomd.md.nlist.cell()\n",
    "    lj = hoomd.md.pair.lj(r_cut=2.5, nlist=nl)\n",
    "    lj.pair_coeff.set('C', 'C', epsilon=1.0, sigma=1.0)\n",
    "    hoomd.md.integrate.mode_standard(dt=0.001)\n",
    "    _all = hoomd.group.all()\n",
    "    nvt = hoomd.md.integrate.nvt(group=_all, kT=temp, tau=1)\n",
    "    nvt.randomize_velocities(seed=23)\n",
    "    hoomd.analyze.log(filename='out.log',\n",
    "                      quantities=[\"time\", \"temperature\", \"potential_energy\"],\n",
    "                      period=100,\n",
    "                      overwrite=True\n",
    "                     )\n",
    "    hoomd.dump.gsd('{}-{}kT-trajectory.gsd'.format(packing, temp), period=5e3, group=_all, overwrite=True)\n",
    "    hoomd.run(3e5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With that understanding, let's look at the \"cold\" system. (We'll use the `start` argument to skip the first 10 frames of the trajectory--this will help show the influence of temperature by minimizing the influence of the initial configuration.)\n",
    "\n",
    "Cold system:\n",
    "\n",
    "![cold](images/cold.gif)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gsdfile = 'trajectories/bcc-cold.gsd'\n",
    "    \n",
    "bcc_cold_rdf = rdf_from_gsd(gsdfile, start=10)\n",
    "\n",
    "plt.plot(bcc_cold_rdf.bin_centers, bcc_cold_rdf.rdf)\n",
    "plt.title(\"RDF of cold system\")\n",
    "plt.xlabel(\"r\")\n",
    "plt.ylabel(\"g(r)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The RDF can tell us about the [phase](https://en.wikipedia.org/wiki/Phase_(matter)) of a system. A solid will have sharp, distinct peaks, a liquid will have smooth, continuous peaks, and a gas may only have one peak and most values of g(r) are close to 1.\n",
    "\n",
    "![](https://upload.wikimedia.org/wikipedia/commons/b/b8/Simulated_Radial_Distribution_Functions_for_Solid%2C_Liquid%2C_and_Gaseous_Argon.svg)\n",
    "\n",
    "Image credit [Christopher Rowley](https://commons.wikimedia.org/w/index.php?curid=44617468)\n",
    "\n",
    "Looking at the system and the RDF, we can see that the particles have not moved too much from their starting positions and the system is still semi-crystalline as determined by the distinct sharp peaks. But as the particles move around, those peaks begin to broaden.\n",
    "\n",
    "Let's look at the warmer trajectory (kT=1.5, epsilon=1).\n",
    "\n",
    "Mid system:\n",
    "\n",
    "![](images/mid.gif)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gsdfile = 'trajectories/bcc-mid.gsd'\n",
    "\n",
    "bcc_mid_rdf = rdf_from_gsd(gsdfile, start=10)\n",
    "plt.plot(bcc_mid_rdf.bin_centers, bcc_mid_rdf.rdf)\n",
    "plt.title(\"RDF of mid-temp system\")\n",
    "plt.xlabel(\"r\")\n",
    "plt.ylabel(\"g(r)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the temperature is increased, the peaks begin to smooth out and the system looks much more random. \n",
    "\n",
    "Finally, let's look at the \"hot\" (kT=5, epsilon=1) trajectory.\n",
    "\n",
    "Hot system:\n",
    "\n",
    "![](images/hot.gif)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gsdfile = 'trajectories/bcc-hot.gsd'\n",
    "\n",
    "bcc_hot_rdf = rdf_from_gsd(gsdfile, start=10)\n",
    "\n",
    "plt.plot(bcc_hot_rdf.bin_centers, bcc_hot_rdf.rdf)\n",
    "plt.title(\"RDF of hot system\")\n",
    "plt.xlabel(\"r\")\n",
    "plt.ylabel(\"g(r)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again the peaks are even smoother and the system configuration looks very random.\n",
    "\n",
    "Next, in the cells below, try running your own experiments using `hoomd_simulation`. (simulation time ~ 2min) Try to determine the phase transition temperature between solid (rdf with sharp peaks) and liquid (rdf with smooth continuous peaks). Or try changing the initial configuration to \"fcc\" to see how the rdf changes. \n",
    "\n",
    "(replace `INPUT_TEMP` and `INPUT_PACKING` with your own values.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# NBVAL_SKIP\n",
    "temp = INPUT_TEMP\n",
    "packing = INPUT_PACKING    # \"fcc\" or \"bcc\"\n",
    "\n",
    "hoomd_simulation(packing,temp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cell below will plot the RDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# NBVAL_SKIP\n",
    "gsdfile = f\"{packing}-{temp}kT-trajectory.gsd\"\n",
    "\n",
    "my_rdf = rdf_from_gsd(gsdfile, start=10)\n",
    "\n",
    "plt.plot(my_rdf.bin_centers, my_rdf.rdf)\n",
    "plt.title(f\"RDF of {packing} system kT={temp}\")\n",
    "plt.xlabel(\"r\")\n",
    "plt.ylabel(\"g(r)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cell below will visualize your system. (takes a minute)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# NBVAL_SKIP\n",
    "display_movie(snap_render, gsdfile)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}