nematic-order.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "4d38e2c3-1a4d-485a-9a71-98e531329f00",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20, 20, 20)\n",
      "Time: 0.0031387805938720703 s for 40 molecules with 20 atoms\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nematic order parameter: 0.9998966455459595\n"
     ]
    }
   ],
   "source": [
    "import freud\n",
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "import csv\n",
    "\n",
    "\n",
    "start_time = time.time()  # Starting a timer\n",
    "nematic = freud.order.Nematic() # Required for NOP\n",
    "\n",
    "class System:  # The array within which the molecules will sit\n",
    "    def __init__(self, mol_len, num_mols, atom_sequence=0, density=1):  # Default density is 1 gram per cm^3\n",
    "        self.mol_len = mol_len\n",
    "        self.num_mols = num_mols\n",
    "        self.atom_sequence = atom_sequence\n",
    "        self.density = density\n",
    "        self.all_paths = []\n",
    "        self.sys_state = np.array([])\n",
    "        self.sys_hist = []\n",
    "        self.array = np.array([0])\n",
    "        self.box_length = 0\n",
    "        self.rollback = 5 + int(np.ceil(self.mol_len / 1000))\n",
    "        self.rollback_count = 0\n",
    "        self.mega_undo_count = 0\n",
    "        self.pos = np.array([])\n",
    "        self.pos_hist = []\n",
    "        self.finished_mols = np.array([])\n",
    "        self.mol_pos = []\n",
    "        self.bonds = []\n",
    "        self.bondshistory = []\n",
    "\n",
    "    def save(self, position):\n",
    "        \"\"\"Saves the system such that it can be rolled back.\"\"\"\n",
    "        self.sys_state = np.copy(self.array)\n",
    "        self.pos = position.copy()\n",
    "        self.sys_hist.append(np.copy(self.sys_state))\n",
    "        self.pos_hist.append(self.pos.copy())\n",
    "\n",
    "    def undo(self):\n",
    "        \"\"\"Returns system state back to before the random moves were made.\"\"\"\n",
    "        self.array = np.copy(self.sys_state)\n",
    "        position = self.pos.copy()\n",
    "        self.rollback_count += 1\n",
    "        return position\n",
    "\n",
    "    def mega_undo(self):\n",
    "        \"\"\"Reverts system state back to a previous version.\"\"\"\n",
    "        if len(self.sys_hist) > 0:\n",
    "            self.sys_state = self.sys_hist.pop()\n",
    "            self.array = self.sys_state\n",
    "            self.pos = self.pos_hist.pop()\n",
    "            self.mega_undo_count += 1\n",
    "            self.rollback_count = 0\n",
    "        return self.pos\n",
    "\n",
    "    def save_mol(self, position):\n",
    "        \"\"\"Saves a system state where a molecule was successfully created.\"\"\"\n",
    "        self.finished_mols = np.copy(self.array)\n",
    "        self.mol_pos = position.copy()\n",
    "\n",
    "    def undo_mol(self):\n",
    "        \"\"\"Reverts system and position to where a molecule was last successfully created.\"\"\"\n",
    "        if len(self.finished_mols) > 0:\n",
    "            self.array = np.copy(self.finished_mols)\n",
    "            position = self.mol_pos.copy()\n",
    "            self.rollback_count = 0  # Reset counters after undo_mol\n",
    "            self.mega_undo_count = 0\n",
    "        else:\n",
    "            self.reset()\n",
    "            position = self.start_pos()\n",
    "        return position\n",
    "\n",
    "    def start_pos(self):\n",
    "        \"\"\"Checks to see if a random starting position is occupied.\"\"\"\n",
    "        while True:\n",
    "            temp = np.array([random.randint(0, self.box_length - 1), random.randint(0, self.box_length - 1), random.randint(0, self.box_length - 1)])\n",
    "            if self.array[temp[0], temp[1], temp[2]] != 1:\n",
    "                break\n",
    "        return temp\n",
    "\n",
    "    def reset(self):\n",
    "        \"\"\"Removes all placed atoms.\"\"\"\n",
    "        self.array.fill(0)\n",
    "        self.sys_hist = []\n",
    "        self.pos_hist = []\n",
    "        self.rollback_count = 0\n",
    "        self.mega_undo_count = 0\n",
    "\n",
    "    def plot(self):\n",
    "        \"\"\"Graphs the paths of the creation of the molecules.\"\"\"\n",
    "        print(\"Time:\", time.time() - start_time, \"s for\", len(self.all_paths), \"molecules with\", self.mol_len, \"atoms\")\n",
    "        fig = plt.figure()\n",
    "        ax = fig.add_subplot(111, projection='3d')\n",
    "        for path in self.all_paths:\n",
    "            path = np.array(path)\n",
    "            ax.plot(path[:, 0], path[:, 1], path[:, 2], marker='o')\n",
    "        ax.set_xlim([-1, self.box_length])\n",
    "        ax.set_ylim([-1, self.box_length])\n",
    "        ax.set_zlim([-1, self.box_length])\n",
    "        plt.show()\n",
    "\n",
    "\n",
    "    def arrayarize(self):\n",
    "        \"\"\"Converts all paths into an array and computes the nematic order parameter.\"\"\"\n",
    "        distances = []\n",
    "        for path in self.all_paths:\n",
    "            orientations = np.array(path[1:]) - np.array(path[:-1])\n",
    "            np.append(distances, orientations)\n",
    "        orientations = np.array(orientations)\n",
    "        nematic.compute(orientations)\n",
    "        print(\"Nematic order parameter:\", nematic.order)\n",
    "\n",
    "        \n",
    "    def check(self, move, position):\n",
    "        \"\"\"Checks to see if a move is possible.\"\"\"\n",
    "        temp = position + move\n",
    "        temp_tuple = tuple(temp)  # Allowing comparison to array position\n",
    "        if (temp[0] >= self.box_length or temp[1] >= self.box_length or temp[2] >= self.box_length or\n",
    "                temp[0] < 0 or temp[1] < 0 or temp[2] < 0 or\n",
    "                temp_tuple in {tuple(pos) for path in self.all_paths for pos in path}):  # Check if move is occupied by previous molecule\n",
    "            return False, position\n",
    "        elif self.array[temp[0], temp[1], temp[2]] == 0:  # Check if move is possible\n",
    "            position = temp\n",
    "            self.array[position[0], position[1], position[2]] = 1\n",
    "            return True, position\n",
    "        else:\n",
    "            return False, position\n",
    "\n",
    "    def output(self):\n",
    "        \"\"\"Writes path to a csv file\"\"\"\n",
    "        with open('positions.csv', 'w', newline='') as file:\n",
    "            writer = csv.writer(file)            \n",
    "            for path in self.all_paths:\n",
    "                writer.writerow(path)        \n",
    "\n",
    "    def add_straight(self):\n",
    "        self.box_length = (self.mol_len)\n",
    "        x = 0\n",
    "        y = 0\n",
    "        z = 0\n",
    "        self.position = [x, y, z]\n",
    "        self.array = np.zeros((self.box_length, self.box_length, self.num_mols))\n",
    "        print(self.array.shape)\n",
    "        for mols in range(self.num_mols):\n",
    "            path = []\n",
    "            if x <= (self.box_length - 1):\n",
    "                for atom in range(self.mol_len):\n",
    "                    self.array[x, y, z] = 1\n",
    "                    y += 1\n",
    "                    self.position = [x, y, z]\n",
    "                    path.append(np.copy(self.position))\n",
    "                self.all_paths.append(path)\n",
    "                x += 1\n",
    "                y = 0\n",
    "                position = np.copy(self.position)\n",
    "                self.save_mol(position)\n",
    "            # if z <= (self.box_length - 1):\n",
    "            #     for atom in range(self.mol_len):\n",
    "            #         self.array[x, y, z] = 1\n",
    "            #         y += 1\n",
    "            #         self.position = [x, y, z]\n",
    "            #         path.append(np.copy(self.position))\n",
    "            #     self.all_paths.append(path)\n",
    "            #     z += 1\n",
    "            #     x = 0\n",
    "            #     y = 0\n",
    "            #     position = np.copy(self.position)\n",
    "            #     self.save_mol(position)\n",
    "\n",
    "    \n",
    "    def walk(self):\n",
    "        \"\"\"Creates a path taken by a Monte-Carlo simulation to make a chain of atoms.\"\"\"\n",
    "        self.box_length = 1 + int(np.ceil(2 * np.cbrt(self.num_mols))) * int(np.ceil(np.cbrt(self.mol_len / self.density)))  # Calculates requisite box size\n",
    "        self.array = np.zeros((self.box_length, self.box_length, self.box_length))  # The 'box'\n",
    "        moves = np.array([[1, 0, 0], [-1, 0, 0], [0, 1, 0], [0, -1, 0], [0, 0, 1], [0, 0, -1],\n",
    "                          [1, 1, 0], [1, -1, 0], [-1, 1, 0], [-1, -1, 0],\n",
    "                          [1, 0, 1], [1, 0, -1], [-1, 0, 1], [-1, 0, -1],\n",
    "                          [0, 1, 1], [0, 1, -1], [0, -1, 1], [0, -1, -1],\n",
    "                          [1, 1, 1], [1, 1, -1], [1, -1, 1], [1, -1, -1],\n",
    "                          [-1, 1, 1], [-1, 1, -1], [-1, -1, 1], [-1, -1, -1]])  # Possible moves for the random walk\n",
    "        for path_num in range(self.num_mols):\n",
    "            path = []\n",
    "            position = self.start_pos() # Check for open space to instantiate a molecule\n",
    "            self.array[position[0], position[1], position[2]] = 1 # Set the initial position to be occupied\n",
    "            path.append(position.tolist())\n",
    "            self.save(position)  # Save initial position\n",
    "\n",
    "            i = 1  # Count of atoms placed\n",
    "            j = 0  # Count of rejected moves\n",
    "\n",
    "            while i < self.mol_len:\n",
    "                move = moves[random.randint(0, 25)]\n",
    "                success, position = self.check(move, position)\n",
    "                if not success:\n",
    "                    j += 1\n",
    "                    if j >= self.rollback * 5:  # Check if too many erroneous moves have been made\n",
    "                        position = self.undo()\n",
    "                        j = 0\n",
    "                        if self.rollback_count >= 5:\n",
    "                            position = self.mega_undo()\n",
    "                            if self.mega_undo_count >= 5:\n",
    "                                position = self.undo_mol()\n",
    "                                self.array[position[0], position[1], position[2]] = 1\n",
    "                                path = [position.tolist()]  # Reset path\n",
    "                                i = 1\n",
    "                    continue\n",
    "                self.save(position)\n",
    "                path.append(position.tolist())\n",
    "                i += 1\n",
    "                j = 0\n",
    "            self.save_mol(position)\n",
    "            self.all_paths.append(path)\n",
    "            print(f\"Molecule {path_num + 1}: Length {len(path)}\")\n",
    "\n",
    "PPS = System(10, 10)\n",
    "# PPS.walk()\n",
    "PPS.add_straight()\n",
    "PPS.plot()\n",
    "PPS.arrayarize()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9da5372e-defa-4c99-9373-41b99632a402",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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