Ensemble_LangevinDynamics2D.ipynb

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    "## Ensemble Langevin dynamics in two dimensions"
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   "source": [
    "# Import useful packages\n",
    "import numpy as np\n",
    "import time\n",
    "from collections import deque\n",
    "import ipywidgets as widgets\n",
    "from IPython.display import display\n",
    "from bokeh.io import show, output_notebook, push_notebook\n",
    "from bokeh.plotting import figure \n",
    "output_notebook()"
   ]
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    "# Defines a class for the Langevin simulation\n",
    "class Langevin2D:\n",
    "    \n",
    "    # Initializing variables\n",
    "    def __init__(self, mass_density_of_particle, \n",
    "                 fluid_viscosity, temperature):\n",
    "        self.partrad = 10e-6\n",
    "        self.dt = 0.5e-3\n",
    "        self.boxsize = 60e-6\n",
    "        self.center = self.boxsize / 2\n",
    "        self.partden = mass_density_of_particle\n",
    "        self.flvisc = fluid_viscosity\n",
    "        self.temp = temperature\n",
    "        self.reset()\n",
    "        self.calc_params()\n",
    "        \n",
    "    # Reseting positions and velocities to zero\n",
    "    def reset(self):\n",
    "        self.x = np.zeros(2)\n",
    "        self.p = np.zeros(2)\n",
    "        self.pmid = np.zeros(2)\n",
    "        \n",
    "    # Calculating useful parameters used in solving the Langevin equation\n",
    "    def calc_params(self):\n",
    "        self.partmass = self.partden * 1.333 * np.pi * self.partrad**3\n",
    "        self.stokes = 6.0 * np.pi * self.flvisc * self.partrad\n",
    "        self.gamma = self.stokes / self.partmass\n",
    "        self.gravity = self.partmass * 9.81\n",
    "        self.c1 = np.exp(-self.gamma * self.dt)\n",
    "        self.c2 = np.sqrt(kb * self.temp * (1 - self.c1**2))\n",
    "        \n",
    "    # Run the Langevin update\n",
    "    def run(self):\n",
    "        global pos_x, pos_y\n",
    "        self.pmid = self.p + [0, -self.dt * self.gravity * 0.5]\n",
    "        self.x = self.x + self.dt * self.pmid / 2 / self.partmass\n",
    "        self.pmid = self.c1 * self.pmid + self.c2 * np.random.randn(2) * np.sqrt(self.partmass)\n",
    "        self.x = self.x + self.dt * self.pmid / 2 / self.partmass\n",
    "        self.p = self.pmid + [0, -self.dt * self.gravity * 0.5]\n",
    "        self.check_boundary()\n",
    "    \n",
    "    # Apply periodic boundary conditions \n",
    "    def check_boundary(self):\n",
    "        # Applying periodic boundaries\n",
    "        for i in range(2):\n",
    "            if self.x[i] <  -self.boxsize * 0.5: \n",
    "                self.x[i] = self.x[i] + self.boxsize\n",
    "            if self.x[i] >=  self.boxsize * 0.5:\n",
    "                self.x[i] = self.x[i] - self.boxsize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "kb = 1.380e-23  # Boltzmann constant\n",
    "\n",
    "# Start the Langevin simulation\n",
    "def start_Langevin_sim(number_of_particles=10, mass_density_of_particle=1000.0, \n",
    "                       fluid_viscosity=9e-4, temperature=300,\n",
    "                       simulation_duration=0.5):\n",
    "    pos = np.zeros([number_of_particles, 2])\n",
    "    mom = np.zeros([number_of_particles, 2])\n",
    "    \n",
    "    # Update arrays for plotting\n",
    "    def plot_trajectories():\n",
    "        r1.data_source.data['x'] = pos[:, 0]\n",
    "        r1.data_source.data['y'] = pos[:, 1]\n",
    "        push_notebook(handle=target)\n",
    "    \n",
    "    # Create langevin class object\n",
    "    l2d = Langevin2D(mass_density_of_particle, fluid_viscosity, temperature)\n",
    "    # Initialize figure for plotting trajectories\n",
    "    p1 = figure(plot_width=500, plot_height=400, tools='',\n",
    "                x_range=(-l2d.boxsize*1e6/2, l2d.boxsize*1e6/2), \n",
    "                y_range=(-l2d.boxsize*1e6/2, l2d.boxsize*1e6/2))\n",
    "    p1.xaxis.axis_label = 'x (um)'\n",
    "    p1.yaxis.axis_label = 'y (um)'\n",
    "    p1.toolbar.logo = None\n",
    "    runtime = simulation_duration * 0.1 \n",
    "    r1 = p1.circle(pos[:, 0], pos[:, 1], size=5, color='chocolate', alpha=0.6)\n",
    "    target = show(p1, notebook_handle=True)\n",
    "    print('Diffusion Coefficient (um^2/s) = ', 1e12 * kb*l2d.temp / (l2d.stokes))\n",
    "    print('Total simulation duration (s) = ', runtime)\n",
    "    # Langevin time-steping loop\n",
    "    for t in range(int(runtime/l2d.dt)):\n",
    "        time.sleep(0.2)\n",
    "        for n in range(number_of_particles):\n",
    "            l2d.x = pos[n, :] * 1e-6\n",
    "            l2d.p = mom[n, :]\n",
    "            l2d.run()\n",
    "            pos[n, :] = l2d.x * 1e6\n",
    "            mom[n, :] = l2d.p\n",
    "            plot_trajectories()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"0ef7e4bf-dbde-49db-9927-9726d1e6b51c\" data-root-id=\"1002\"></div>\n"
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     },
     "metadata": {},
     "output_type": "display_data"
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     "data": {
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       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = {\"f5480b65-61c1-4d86-8f7d-f898c65d0c55\":{\"roots\":{\"references\":[{\"attributes\":{\"below\":[{\"id\":\"1011\"}],\"center\":[{\"id\":\"1014\"},{\"id\":\"1018\"}],\"left\":[{\"id\":\"1015\"}],\"plot_height\":400,\"plot_width\":500,\"renderers\":[{\"id\":\"1024\"}],\"title\":{\"id\":\"1027\"},\"toolbar\":{\"id\":\"1019\"},\"x_range\":{\"id\":\"1003\"},\"x_scale\":{\"id\":\"1007\"},\"y_range\":{\"id\":\"1005\"},\"y_scale\":{\"id\":\"1009\"}},\"id\":\"1002\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{},\"id\":\"1016\",\"type\":\"BasicTicker\"},{\"attributes\":{},\"id\":\"1032\",\"type\":\"Selection\"},{\"attributes\":{},\"id\":\"1031\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"axis_label\":\"y (um)\",\"formatter\":{\"id\":\"1031\"},\"ticker\":{\"id\":\"1016\"}},\"id\":\"1015\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1029\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"axis\":{\"id\":\"1011\"},\"ticker\":null},\"id\":\"1014\",\"type\":\"Grid\"},{\"attributes\":{\"text\":\"\"},\"id\":\"1027\",\"type\":\"Title\"},{\"attributes\":{},\"id\":\"1012\",\"type\":\"BasicTicker\"},{\"attributes\":{\"axis_label\":\"x (um)\",\"formatter\":{\"id\":\"1029\"},\"ticker\":{\"id\":\"1012\"}},\"id\":\"1011\",\"type\":\"LinearAxis\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.6},\"fill_color\":{\"value\":\"chocolate\"},\"line_alpha\":{\"value\":0.6},\"line_color\":{\"value\":\"chocolate\"},\"size\":{\"units\":\"screen\",\"value\":5},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1022\",\"type\":\"Circle\"},{\"attributes\":{},\"id\":\"1009\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1007\",\"type\":\"LinearScale\"},{\"attributes\":{\"source\":{\"id\":\"1021\"}},\"id\":\"1025\",\"type\":\"CDSView\"},{\"attributes\":{\"fill_alpha\":{\"value\":0.1},\"fill_color\":{\"value\":\"chocolate\"},\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"chocolate\"},\"size\":{\"units\":\"screen\",\"value\":5},\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1023\",\"type\":\"Circle\"},{\"attributes\":{\"data_source\":{\"id\":\"1021\"},\"glyph\":{\"id\":\"1022\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"1023\"},\"selection_glyph\":null,\"view\":{\"id\":\"1025\"}},\"id\":\"1024\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"end\":30.0,\"start\":-30.0},\"id\":\"1005\",\"type\":\"Range1d\"},{\"attributes\":{\"data\":{\"x\":{\"__ndarray__\":\"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA==\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[5]},\"y\":{\"__ndarray__\":\"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA==\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[5]}},\"selected\":{\"id\":\"1032\"},\"selection_policy\":{\"id\":\"1033\"}},\"id\":\"1021\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"end\":30.0,\"start\":-30.0},\"id\":\"1003\",\"type\":\"Range1d\"},{\"attributes\":{},\"id\":\"1033\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"active_drag\":\"auto\",\"active_inspect\":\"auto\",\"active_multi\":null,\"active_scroll\":\"auto\",\"active_tap\":\"auto\",\"logo\":null},\"id\":\"1019\",\"type\":\"Toolbar\"},{\"attributes\":{\"axis\":{\"id\":\"1015\"},\"dimension\":1,\"ticker\":null},\"id\":\"1018\",\"type\":\"Grid\"}],\"root_ids\":[\"1002\"]},\"title\":\"Bokeh Application\",\"version\":\"2.1.1\"}};\n",
       "  var render_items = [{\"docid\":\"f5480b65-61c1-4d86-8f7d-f898c65d0c55\",\"notebook_comms_target\":\"1034\",\"root_ids\":[\"1002\"],\"roots\":{\"1002\":\"0ef7e4bf-dbde-49db-9927-9726d1e6b51c\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1002"
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Diffusion Coefficient (um^2/s) =  0.024403757940757283\n",
      "Total simulation duration (s) =  0.05\n"
     ]
    }
   ],
   "source": [
    "# Interactive controls\n",
    "style = {'description_width': 'initial'}    \n",
    "number_of_particles = widgets.IntSlider(description='Number of particles', \n",
    "                                              style=style, min=5, max=100, \n",
    "                                              step=5, value=5, continuous_update=False)\n",
    "mass_density_of_particle = widgets.IntSlider(description='Particle mass density', \n",
    "                                              style=style, min=500, max=5000, \n",
    "                                              step=100, value=1000, continuous_update=False)\n",
    "fluid_viscosity = widgets.FloatLogSlider(description='Dynamic viscosity', \n",
    "                                         style=style, base=10, min=-6, max=-1, \n",
    "                                         step=-4, value=9e-4, continuous_update=False)\n",
    "temperature = widgets.IntSlider(description='Temperature (K)', \n",
    "                                style=style, min=50, max=600, \n",
    "                                step=50, value=300, continuous_update=False)\n",
    "simulation_duration = widgets.ToggleButtons(options=[('Short', 0.5), ('Regular', 2), ('Long', 5)],\n",
    "                                            description='Simulation duration', disabled=False, style=style)\n",
    "\n",
    "# Creating the interactive controls ui\n",
    "widget_ui = widgets.VBox([widgets.HBox([number_of_particles, mass_density_of_particle]), \n",
    "                         widgets.HBox([fluid_viscosity, temperature]), simulation_duration])\n",
    "widget_out = widgets.interactive_output(start_Langevin_sim, \n",
    "                                        {'number_of_particles': number_of_particles,\n",
    "                                         'mass_density_of_particle': mass_density_of_particle,\n",
    "                                         'fluid_viscosity': fluid_viscosity,\n",
    "                                         'temperature': temperature,\n",
    "                                         'simulation_duration': simulation_duration})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0d55300c5bd8469a80177297592e26e3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(HBox(children=(IntSlider(value=5, continuous_update=False, description='Number of particles', m…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0a8a4fa663ac484f848900a179f688b8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the controls and output\n",
    "display(widget_ui, widget_out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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