{ "cells": [ { "cell_type": "markdown", "id": "39798053e938702d", "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "source": [ "# My first simulation\n", "\n", "As introduction to the `gamdpy` package let us setting up a simulation\n", "of a Lennard-Jones FCC crystal in the constant $NVT$ ensemble.\n", "For a short summary, see the [minimal.py](../examples/minimal.py) example script. Also, the line `sim = gp.get_default_simulation()` will create a simulation object similar to the below.\n", "\n", "If `gamdpy` is installed correctly, the following package should be imported without any errors. It is recommended to import the package as `gp`." ] }, { "cell_type": "code", "execution_count": 1, "id": "fdbe2ed79de5260f", "metadata": { "ExecuteTime": { "end_time": "2025-06-03T08:52:24.934435Z", "start_time": "2025-06-03T08:52:24.477189Z" } }, "outputs": [], "source": [ "import gamdpy as gp" ] }, { "cell_type": "markdown", "id": "272994b9cf64bd48", "metadata": {}, "source": [ "*We will also import NumPy for numerical calculations and Matplotlib for plotting." ] }, { "cell_type": "code", "execution_count": 2, "id": "4847c36563bf71ed", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:56.684867Z", "start_time": "2025-05-26T18:49:56.683163Z" } }, "outputs": [], "source": [ "import numpy as np # For numerical operations\n", "import matplotlib.pyplot as plt # For plotting" ] }, { "cell_type": "markdown", "id": "8a72b43d82522780", "metadata": {}, "source": [ "## Initial particle positions\n", "\n", "We wish to set up a configuration of a FCC lattice with $8 \\times 8 \\times 8$ unit cells, with a density of $\\rho = 0.973$. First we create an empty configuration object." ] }, { "cell_type": "code", "execution_count": 3, "id": "eca912f8cf53045", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:56.733571Z", "start_time": "2025-05-26T18:49:56.731629Z" } }, "outputs": [], "source": [ "configuration = gp.Configuration(D=3)" ] }, { "cell_type": "markdown", "id": "d5d79c20db8a9b9e", "metadata": {}, "source": [ "Information for a few crystal unit cells are avalible with the `gamdpy` package. For example, the FCC unit cell is stored as `rp.unit_cells.FCC`." ] }, { "cell_type": "code", "execution_count": 4, "id": "b39d89cc213277c8", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:56.784510Z", "start_time": "2025-05-26T18:49:56.780245Z" } }, "outputs": [ { "data": { "text/plain": [ "{'fractional_coordinates': [[0.0, 0.0, 0.0],\n", " [0.5, 0.5, 0.0],\n", " [0.5, 0.0, 0.5],\n", " [0.0, 0.5, 0.5]],\n", " 'lattice_constants': [1.0, 1.0, 1.0]}" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gp.unit_cells.FCC" ] }, { "cell_type": "markdown", "id": "12ee7e31dbba7918", "metadata": {}, "source": [ "We use the `make_lattice` method to assign positions and a simulation box to the configuration object." ] }, { "cell_type": "code", "execution_count": 5, "id": "f2bc351e-3578-4f51-b786-71e845bd07d4", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:56.877342Z", "start_time": "2025-05-26T18:49:56.871792Z" } }, "outputs": [], "source": [ "# Setup configuration: FCC Lattice\n", "configuration.make_lattice(\n", " unit_cell=gp.unit_cells.FCC,\n", " cells=[8, 8, 8],\n", " rho=0.973\n", ")" ] }, { "cell_type": "markdown", "id": "8bfbc6d96f2080d4", "metadata": {}, "source": [ "The positions can be accessed with `['r']`. All vector properties, like the positions, are NumPy arrays." ] }, { "cell_type": "code", "execution_count": 6, "id": "c48e7dffc54f7b62", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:56.942633Z", "start_time": "2025-05-26T18:49:56.940020Z" } }, "outputs": [ { "data": { "text/plain": [ "numpy.ndarray" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "positions = configuration['r']\n", "type(positions)" ] }, { "cell_type": "markdown", "id": "8fa2ef37792d3364", "metadata": {}, "source": [ "To confirm that the positions are as expected, we can visualize the configuration using Matplotlib. " ] }, { "cell_type": "code", "execution_count": 7, "id": "3c1f34c579af36ab", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.133255Z", "start_time": "2025-05-26T18:49:57.012795Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make 3D plot using matplotlib\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.set_title('Initial configuration')\n", "ax.scatter(positions[:,0], positions[:,1], positions[:,2])\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')\n", "ax.set_zlabel('z')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "686d719eba828b28", "metadata": {}, "source": [ "The configuration object also contains a simulation box. Here we use an orthorhombic box. The box lengths can be accessed as seen below." ] }, { "cell_type": "code", "execution_count": 8, "id": "16d0f453d82aaa29", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:52:49.817035Z", "start_time": "2025-05-26T18:52:49.814132Z" } }, "outputs": [ { "data": { "text/plain": [ "array([12.815602, 12.815602, 12.815602], dtype=float32)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "configuration.simbox.get_lengths() # Box lengths" ] }, { "cell_type": "markdown", "id": "f283a4b3544c0a76", "metadata": {}, "source": [ "## Masses and initial velocities\n", "\n", "We set all particle masses to one (the value is broadcast to all particles)." ] }, { "cell_type": "code", "execution_count": 9, "id": "813a39221147cfa2", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.283191591Z", "start_time": "2025-05-14T09:11:22.943393Z" } }, "outputs": [], "source": [ "configuration['m'] = 1.0 # Set all masses to 1.0" ] }, { "cell_type": "markdown", "id": "fab961ce1c4b4678", "metadata": {}, "source": [ "Note that `configuration['m']` refer to an NumPy array. For convenience, we above used a `float` to set all masses to the same value. This value will automatically be broadcast to all particles." ] }, { "cell_type": "code", "execution_count": 10, "id": "b1b6ea40a14a352a", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.297887189Z", "start_time": "2025-05-14T09:11:22.993299Z" } }, "outputs": [ { "data": { "text/plain": [ "numpy.ndarray" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(configuration['m']) # configuration['m'] is a NumPy array" ] }, { "cell_type": "markdown", "id": "cb081d5657bbecc6", "metadata": {}, "source": [ "After masses are set, we can assign random velocities corresponding to an initial kinetic temperature $T = 0.7$." ] }, { "cell_type": "code", "execution_count": 11, "id": "cba45546423ba6f6", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.300665786Z", "start_time": "2025-05-14T09:11:23.047241Z" } }, "outputs": [], "source": [ "temperature = 0.7\n", "configuration.randomize_velocities(temperature=temperature)" ] }, { "cell_type": "markdown", "id": "cbb4cc11d857168d", "metadata": {}, "source": [ "To confirm that the initial velocity distribution is as expected, we can compare it the the theoretical Maxwell-Boltzmann distribution." ] }, { "cell_type": "code", "execution_count": 12, "id": "91f8fbcd8b81050b", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.310908859Z", "start_time": "2025-05-14T09:11:23.105070Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "# Histogram of particle speeds\n", "vel = configuration['v']\n", "speeds = np.linalg.norm(vel, axis=1)\n", "bins = np.linspace(0, 5, 25)\n", "plt.hist(speeds, bins=bins, density=True, label='Simulation')\n", "# Theoretical Maxwell-Boltzmann distribution\n", "v = np.linspace(0, 5, 100)\n", "maxwell_boltzmann = (2*np.pi*temperature)**(-3/2)*4*np.pi*v**2*np.exp(-v**2/(2*temperature))\n", "plt.plot(v, maxwell_boltzmann, label='Maxwell-Boltzmann', color='r')\n", "# Plot settings\n", "plt.xlabel(r'Particle speeds, $|v|$')\n", "plt.ylabel(r'Probability density, $P(|v|)$')\n", "plt.xlim(0, None)\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "14e8e0d8fd2046c2", "metadata": {}, "source": [ "## Pair potential\n", "Next, we set up the Lennard-Jones pair potential. We use the 12-6 Lennard-Jones potential\n", "\n", "$$\n", " v_\\infty(r) = 4\\varepsilon \\left[\\left(\\frac{\\sigma}{r}\\right)^{12} - \\left(\\frac{\\sigma}{r}\\right)^{6}\\right]\n", "$$\n", "\n", "(the substript refer to a \"truncation\" at $\\infty$). Here $\\sigma$ (`sigma`) is length, and $\\varepsilon$ (`epsilon`) is an energy. We will use Lennard-Jones units, where $\\sigma = 1$ and $\\varepsilon = 1$.\n", "\n", "Several pair potentials functions are implemented in `gamdpy`, and the above 12-6 Lennard-Jones potential is implemented as `gp.LJ_12_6_sigma_epsilon`. This is a Python function that takes distances, parameters as input and returns the potential energy, the force and the second derivative of the potential energy.\n", "\n", "Let us confirm values are as expected in the minimum of the potential:\n", "\n", "\\begin{align}\n", " r_{min} &= 2^{1/6} \\\\\n", " v(r_{min}) &= -\\varepsilon \\\\\n", " f(r_{min}) &= 0 \\\\\n", " \\left.\\frac{d^2v}{dr^2}\\right|_{r_{min}} &= (624\\cdot2^{-7/3}-168\\cdot2^{-4/3})\\frac{\\varepsilon}{\\sigma^2} \\simeq 57.146\\frac{\\varepsilon}{\\sigma^2}\n", "\\end{align}\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "fe824ac1e21e981", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.311905134Z", "start_time": "2025-05-14T09:11:23.439889Z" } }, "outputs": [ { "data": { "text/plain": [ "(np.float32(-0.99999994), np.float32(-5.6769886e-07), np.float32(57.146423))" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pair_func = gp.LJ_12_6_sigma_epsilon # Pair potential function\n", "r_min = 2**(1/6)\n", "u_min, f_min, curvature_min = pair_func(r_min, (1.0, 1.0, np.inf))\n", "u_min, f_min, curvature_min" ] }, { "cell_type": "markdown", "id": "48ed360ea8a7b0c2", "metadata": {}, "source": [ "\n", "To allow for a $O(N)$ algorithm for force calculations, we truncate the pair potential at radius of $r_c = 2.5\\sigma$ (`cutoff`). The potential is shifted to zero at the cutoff radius, so the actual potential is\n", "\n", "$$\n", " v(r) = v_\\infty(r) - v_\\infty(r_c)\n", "$$\n", "\n", "For this, we can use `gp.apply_shifted_potential_cutoff` to modify the pair potential." ] }, { "cell_type": "code", "execution_count": 14, "id": "a01cea8854dcfd66", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.312271888Z", "start_time": "2025-05-14T09:11:23.495448Z" } }, "outputs": [], "source": [ "pair_func = gp.apply_shifted_potential_cutoff(gp.LJ_12_6_sigma_epsilon)" ] }, { "cell_type": "markdown", "id": "e09505ebb8d74724", "metadata": {}, "source": [ "Let us plot the pair potential, so confirm that it looks as we expect." ] }, { "cell_type": "code", "execution_count": 15, "id": "ecd5a40e2dab39f7", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.312533212Z", "start_time": "2025-05-14T09:11:23.548911Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sigma, epsilon, cutoff = 1.0, 1.0, 2.5\n", "pair_distances = np.linspace(0.95, 3.0, 128)\n", "pair_energies = [pair_func(dist, [sigma, epsilon, cutoff])[0] for dist in pair_distances]\n", "\n", "plt.figure()\n", "plt.plot(pair_distances, pair_energies)\n", "plt.xlabel(r'Pair distance, r')\n", "plt.ylabel(r'Pair energy, $v(r)$')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "e997fab41eea0a32", "metadata": {}, "source": [ "We can now create an interaction objects using this pair potential function we made." ] }, { "cell_type": "code", "execution_count": 16, "id": "7bf0bd18026a4321", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.312908382Z", "start_time": "2025-05-14T09:11:24.116557Z" } }, "outputs": [], "source": [ "pair_pot = gp.PairPotential(pair_func, params=[sigma, epsilon, cutoff], max_num_nbs=1000)" ] }, { "cell_type": "markdown", "id": "f441989eba2b5afc", "metadata": {}, "source": [ "Finally, we create a list will all the interactions in our simulations. In this simulation, we only have one, but later we may want to include more like bonds, walls, or gravity." ] }, { "cell_type": "code", "execution_count": 17, "id": "eb9766512348e5ff", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.313388230Z", "start_time": "2025-05-14T09:11:24.166222Z" } }, "outputs": [], "source": [ "interactions = [pair_pot, ]" ] }, { "cell_type": "markdown", "id": "4fb178da11418e73", "metadata": {}, "source": [ "## Integrator\n", "\n", "Next, create an integrator object. These are available in the submodule `gamdpy.integrators`.\n", "Here, we chose to use and implementation of the Nosé-Hoover thermostat discretion using the Leap-Frog scheme (others are available).\n", "We set a time-step of $dt=0.005$ and a thermostat relaxation time to $\\tau = 0.2$ (both in Lennard-Jones units)." ] }, { "cell_type": "code", "execution_count": 18, "id": "416ac50cfb432a21", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.313682547Z", "start_time": "2025-05-14T09:11:24.229156Z" } }, "outputs": [], "source": [ "# Setup integrator: Nosé-Hoover NVT, Leap-frog algorithm\n", "integrator = gp.integrators.NVT(temperature=temperature, tau=0.2, dt=0.005)" ] }, { "cell_type": "markdown", "id": "d756518abb2b8422", "metadata": {}, "source": [ "## Runtime actions\n", "We typically wants to do some actions during the simulations. Below we specify that we want to store configurations (particle positions, velocities, ...).\n", "\n", "* The `gp.TrajectorySaver` does this using a logarithmic timescale in each timeblock.\n", "* The `gp.ScalarSaver` save scalar properties like energy every `steps_between_output=16` timestep.\n", "* During long-time simulations, there might be a drift of the total momentum due to floating point rounding erros. Thus, the `gp.MomentumReset` reset the total momentum every `steps_between_reset=100` timestep. All the runtime actions are collected in a list." ] }, { "cell_type": "code", "execution_count": 19, "id": "8b77075a994d96f5", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.313935907Z", "start_time": "2025-05-14T09:11:24.467147Z" } }, "outputs": [], "source": [ "steps_between_output = 16\n", "runtime_actions = [\n", " gp.TrajectorySaver(),\n", " gp.ScalarSaver(steps_between_output=steps_between_output),\n", " gp.MomentumReset(steps_between_reset=100),\n", "]" ] }, { "cell_type": "markdown", "id": "6f7755310cb229a6", "metadata": {}, "source": [ "\n", "## The Simulation object\n", "\n", "We now have all the components to set up a simulation object.\n", "\n", "* An configuration object (particle positions, velocities, masses, ...).\n", "* A list of interactions (here the Lennard-Jones potential).\n", "* An integrator object (here the Nosé-Hoover thermostat).\n", "* A list of runtime actions\n", "\n", "For the simulation object we also specify that we want `num_timeblocks=32` time blocks of `steps_per_timeblock=1024` steps. We also specify that we want to store the simulation data in a file with `storage='LJ_T0.70.h5'`. Change to `storage='memory'` if you do not want to save a file to the disk." ] }, { "cell_type": "code", "execution_count": 20, "id": "b32d06aec385921a", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.314153518Z", "start_time": "2025-05-14T09:11:24.529827Z" } }, "outputs": [], "source": [ "# Setup Simulation\n", "sim = gp.Simulation(configuration, interactions, integrator, runtime_actions,\n", " num_timeblocks=32,\n", " steps_per_timeblock=1024,\n", " storage='LJ_T0.70.h5')" ] }, { "cell_type": "markdown", "id": "825e5830d1317551", "metadata": {}, "source": [ "## Running the simulation\n", "\n", "Finally, we run the simulation using the `sim.run_timeblocs` iterator that will loop over all the timeblocs.\n", "Below we print the status of the simulation after each timeblock." ] }, { "cell_type": "code", "execution_count": 21, "id": "7c705329b8979a50", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.314384355Z", "start_time": "2025-05-09T08:29:34.262359Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "timeblock= 0 time= 5.120 U= -6.256 W= 0.885 K= 1.053 \n", "timeblock= 1 time= 10.240 U= -6.310 W= 0.590 K= 1.058 \n", "timeblock= 2 time= 15.360 U= -6.294 W= 0.669 K= 1.045 \n", "timeblock= 3 time= 20.480 U= -6.314 W= 0.563 K= 1.032 \n", "timeblock= 4 time= 25.600 U= -6.292 W= 0.685 K= 1.073 \n", "timeblock= 5 time= 30.720 U= -6.262 W= 0.847 K= 1.007 \n", "timeblock= 6 time= 35.840 U= -6.329 W= 0.480 K= 1.033 \n", "timeblock= 7 time= 40.960 U= -6.309 W= 0.586 K= 1.030 \n", "timeblock= 8 time= 46.080 U= -6.273 W= 0.789 K= 1.033 \n", "timeblock= 9 time= 51.200 U= -6.279 W= 0.749 K= 1.048 \n", "timeblock= 10 time= 56.320 U= -6.295 W= 0.663 K= 1.029 \n", "timeblock= 11 time= 61.440 U= -6.278 W= 0.763 K= 1.060 \n", "timeblock= 12 time= 66.560 U= -6.265 W= 0.830 K= 1.015 \n", "timeblock= 13 time= 71.680 U= -6.267 W= 0.835 K= 1.043 \n", "timeblock= 14 time= 76.800 U= -6.276 W= 0.760 K= 1.039 \n", "timeblock= 15 time= 81.920 U= -6.303 W= 0.610 K= 1.034 \n", "timeblock= 16 time= 87.040 U= -6.307 W= 0.585 K= 1.053 \n", "timeblock= 17 time= 92.160 U= -6.271 W= 0.811 K= 1.057 \n", "timeblock= 18 time= 97.280 U= -6.308 W= 0.580 K= 1.040 \n", "timeblock= 19 time= 102.400 U= -6.275 W= 0.776 K= 1.058 \n", "timeblock= 20 time= 107.520 U= -6.303 W= 0.639 K= 1.048 \n", "timeblock= 21 time= 112.640 U= -6.274 W= 0.794 K= 1.054 \n", "timeblock= 22 time= 117.760 U= -6.274 W= 0.798 K= 1.075 \n", "timeblock= 23 time= 122.880 U= -6.306 W= 0.583 K= 1.049 \n", "timeblock= 24 time= 128.000 U= -6.300 W= 0.637 K= 1.048 \n", "timeblock= 25 time= 133.120 U= -6.271 W= 0.783 K= 1.058 \n", "timeblock= 26 time= 138.240 U= -6.313 W= 0.571 K= 1.053 \n", "timeblock= 27 time= 143.360 U= -6.293 W= 0.665 K= 1.029 \n", "timeblock= 28 time= 148.480 U= -6.270 W= 0.799 K= 1.041 \n", "timeblock= 29 time= 153.600 U= -6.292 W= 0.685 K= 1.042 \n", "timeblock= 30 time= 158.720 U= -6.279 W= 0.743 K= 1.028 \n", "timeblock= 31 time= 163.840 U= -6.264 W= 0.846 K= 1.046 \n", "Particles : 2048 \n", "Steps : 32 * 1024 = 32_768 \n", "Total run time (incl. time spent between timeblocks): 1.37 s ( TPS: 2.39e+04 )\n", "Simulation time (excl. time spent between timeblocks): 1.17 s ( TPS: 2.80e+04 )\n", "\n" ] } ], "source": [ "for timeblock in sim.run_timeblocks():\n", " print(sim.status(per_particle=True))\n", "print(sim.summary())" ] }, { "cell_type": "markdown", "id": "ae8b2b40-9d6b-48c0-8927-449b5da8d7a0", "metadata": {}, "source": [ "The `sim.status()` and `sim.summary()` methods prints some basic information.\n", "\n", "## Analysis of data in memory\n", "\n", "Simulation data, also written to the `*.h5` file, is stored in memory and is accecible in `sim.output`:" ] }, { "cell_type": "code", "execution_count": 22, "id": "cf44a691-05a4-4691-93cc-15d74162bfe1", "metadata": {}, "outputs": [], "source": [ "output = sim.output # Data stored in memory" ] }, { "cell_type": "markdown", "id": "306f7174-469a-4b6a-91af-0cad0e6c207f", "metadata": {}, "source": [ "Below, we extract some thermodynamic quantities stored in the simulation object." ] }, { "cell_type": "code", "execution_count": 23, "id": "3db65137c4f731de", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.314623718Z", "start_time": "2025-05-09T08:29:35.770216Z" } }, "outputs": [ { "data": { "text/plain": [ "numpy.ndarray" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Extract potential energy, virial and kinetic energy\n", "U, W, K = gp.extract_scalars(output, ['U', 'W', 'K'])\n", "type(U)" ] }, { "cell_type": "markdown", "id": "3141dcd71b41bfcb", "metadata": {}, "source": [ "The variables `U`, `W` and `K` are NumPy arrays with the potential energy, virial and kinetic energy, respectively, for selected timesteps. The number of stored timestep can be found with `len(U)`." ] }, { "cell_type": "code", "execution_count": 24, "id": "f7c1efeb15c7234f", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.314877959Z", "start_time": "2025-05-09T08:29:35.951375Z" } }, "outputs": [ { "data": { "text/plain": [ "2048" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(U)" ] }, { "cell_type": "markdown", "id": "b2b9bbc3769cf520", "metadata": {}, "source": [ "Below we compute the times related to when the scalar quantities were stored (in Lennard-Jones units)." ] }, { "cell_type": "code", "execution_count": 25, "id": "2fa6ea65ca92f5f0", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.315118264Z", "start_time": "2025-05-09T08:29:36.055800Z" } }, "outputs": [], "source": [ "dt = output.attrs['dt'] # Time-step for integrator\n", "time = np.arange(len(U)) * dt * output['scalar_saver'].attrs['steps_between_output']" ] }, { "cell_type": "markdown", "id": "c1564e3c98f831d7", "metadata": {}, "source": [ "We can use Matplotlib to plot the potential energy per particle as a function of time. We use `sim.configuration.N` to get the number of particles." ] }, { "cell_type": "code", "execution_count": 26, "id": "899e99f81dcb7751", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.315370712Z", "start_time": "2025-05-09T08:29:36.114957Z" } }, "outputs": [ { "data": { "image/png": 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HuXPnsG/fPuzatQtHjhzBxIkTtYpRwQHGiYiIDI+gpVWrVgm+vr7CyZMnBRsbG+Ho0aPC999/L7i4uAgff/yxtrutFrlcLjRq1Ej46quvqr2NQqEQ3NzchLVr14rLcnJyBKlUKvz444+CIAjC+fPnBQDC6dOnxTJ79uwRJBKJkJ6eXu3Pys3NFQAIL32wr9rbEBERUd0qO3/n5uZWWk7rlqf58+dj2LBhCAkJQV5eHoKDgzF+/Hi8/vrrmDZtms6Su/LExsYiPT0dRkZG6NChA9zd3dG3b18kJiZWuM3Vq1eRlZWFXr16icvs7OwQEBCAqKgoAEBUVBTs7e3h7+8vlunVqxeMjIwQHR1d4b4LCwshk8lUXgCnZyEiIjJEWidPEokECxcuxN27d5GYmIiTJ0/i1q1bWLFihS7jK9eVK1cAlA7CuWjRIuzatQsODg7o3r077t69W+42WVlZAABXV1eV5a6uruK6rKwsNGjQQGW9iYkJHB0dxTLlCQ8Ph52dnfjy8PAAwKEKiIiIDJFGI4zPmjWr2mXXrVuncTDz58/HmjVrKi2TlJQExcPORAsXLsSgQYMAABEREWjcuDG2bduG119/XePProkFCxao/G5kMhk8PDxQwuSJiIjI4GiUPMXFxVWrnEQi0SqY2bNni1O7VMTb2xuZmZkAAF9fX3G5VCqFt7c30tLSyt3Ozc0NAHDz5k24u7uLy2/evIn27duLZbKzs1W2Ky4uxt27d8XtyyOVSiGVStWWc6gCIiIiw6NR8nTw4MHaigMA4OLiAhcXlyrL+fn5QSqVIjk5Gd26dQMAyOVypKamokmTJuVu4+XlBTc3N0RGRorJkkwmQ3R0NCZPngwACAwMRE5ODmJiYuDn5wcAOHDgABQKBQICAjSuj8CWJyIiIoOjl3Pb2draYtKkSVi6dCn27t2L5ORkMQEaPHiwWM7Hxwc7duwAUNoaNnPmTKxcuRI7d+7E2bNnMWrUKDRs2FAcH6pVq1bo06cPJkyYgFOnTuH48eOYOnUqhgwZgoYNG2ocJ2/bERERGR6NWp6UhYeHw9XVFa+99prK8s2bN+PWrVuYN29ejYOrzNq1a2FiYoKRI0fiwYMHCAgIwIEDB+Dg4CCWSU5ORm5urvj+zTffxP379zFx4kTk5OSgW7du+Ouvv2Bubi6W2bJlC6ZOnYqQkBAYGRlh0KBB+Pjjj7WKkbkTERGR4ZEIWt5batq0KX744QcEBQWpLI+OjsaQIUNw9epVnQSoj2QyGezs7BAS/if2z+9b1+EQERFRNZSdv3Nzc2Fra1thOa1v22VlZal0vC7j4uIiduh+0pWwxzgREZHB0Tp58vDwwPHjx9WWHz9+XKv+QYaI4zwREREZHq37PE2YMAEzZ86EXC5Hz549AQCRkZF48803MXv2bJ0FqM+YOxERERkerZOnuXPn4s6dO3jjjTdQVFQEADA3N8e8efOwYMECnQWoz9jyREREZHi0Tp4kEgnWrFmDxYsXIykpCRYWFmjRokW5g0U+qdjliYiIyPBonTyVsba2RqdOnXQRi8Fhh3EiIiLDo/HcditWrICVlVWV89xpM7edoeEI40RERIZH47nt5HK5+HNFtJ3bztCwzxMREZHh0Xpuu2+++QaNGzeGkZHqaAeCIOD69eu6iU7P8a4dERGR4dF6nCcvLy/cvn1bbfndu3fh5eVVo6AMhYLZExERkcHROnmqqD9PXl6eylxxTzLetiMiIjI8Gj9tV9ZRXCKRYMmSJbC0tBTXlZSUIDo6Gu3bt9dZgPqshMkTERGRwdE4eSrrKC4IAs6ePQszMzNxnZmZGdq1a4c5c+boLkI9xrt2REREhkfj5Kms0/jYsWPx8ccfw8bGRudBGQretiMiIjI8WvV5ksvlSEtLQ1ZWlq7jMSglirqOgIiIiHRNq+TJ1NQUZ86c0XUsBocNT0RERIZH66ftRowYgU2bNukyFoPD23ZERESGR+u57YqLi7F582bs378ffn5+sLKyUlnP6Vk4tx0REZEh0jp5SkxMRMeOHQEAFy9eVFnH6VkeEQSBvw8iIiIDonXypDxVC1WsRCHAxJjJExERkaHQus8TVQ/v3BERERkWrVueypw/fx5paWkoKipSWd6/f/+a7togsNM4ERGRYdE6ebpy5QpeeuklnD17FhKJRJzrrqx/T0lJiW4i1HPsNE5ERGRYtL5tN2PGDHh5eSE7OxuWlpY4d+4cjhw5An9/fxw6dEiHIeo3tjwREREZFq1bnqKionDgwAE4OzvDyMgIRkZG6NatG8LDwzF9+nRxDrwnnYKjjBMRERkUrVueSkpKxHntnJ2dkZGRAQBo0qQJkpOTdROdAShhyxMREZFB0brlqXXr1khISICXlxcCAgLw7rvvwszMDBs3boS3t7cuY9Rrck5wR0REZFC0Tp4WLVqE+/fvAwDefvtt/O9//8MzzzwDJycn/PTTTzoLUN8Vypk8ERERGRKtk6fQ0FDx5+bNmyMpKQn//vsvHBwcOKK2kiI+dUhERGRQajRI5qZNm9C6dWuYm5vD3NwcwcHBnCz4MQVseSIiIjIoWrc8LVmyBOvWrcO0adMQGBgIoPQJvLCwMKSlpWH58uU6C1KfFbHPExERkUHROnlav349vvzySwwdOlRc1r9/f7Rt2xbTpk1j8vQQ+zwREREZFq1v28nlcvj7+6st9/PzQ3FxcY2CMiSFxezzRGQolv9xHnO3JYgzKhDRk0nr5GnkyJFYv3692vKNGzdi+PDhNQrKkBQVs+WJyBAUlyiw+fhVbIu5gWt38us6HCKqQzWaGHjTpk3Yu3cvunTpAgCIjo5GWloaRo0ahVmzZonl1q1bV7Mo9Vghkycig1CsNE8l/66JnmxaJ0+JiYno2LEjAODy5csASkcad3Z2RmJioljuSR+2gAdZIsOgPE9lcT2bdyk27V84W0nh6WRZ16EQPRG0Tp4OHjyoyzgMVnVv2+1MyMCDomK82smzliOi+kwQhCf+gqO+Um55KlHUnz5PV2/fx8DPTwAAUlf3q+No6En3V2ImWrjaoJmLtc72WVhcAjNjo3p1bKzROE9UtRv/Vt03QqEQMP3HOMzbfhbZsgKNP6O4RIGvj1/FhSyZNiFSJfIKizH9xzjsPZdV65/12tenMXhDFBRanJgL5CVYues8oi7fqYXICABKSspPnq7fzcf3J6/p5OEQbfpIJqbn1vhzdUlWIK/rEHSODwhUz+GLtzDp+1iEvH9YXHbs0m0M3nACKdn3tNpn9r0CtH97H2ZsjddRlLqh18nT7t27ERAQAAsLCzg4OODFF1+ssKxcLse8efPQpk0bWFlZoWHDhhg1apQ4oXGZpk2bQiKRqLxWr16tdYyfH7qMyKSbKH443tPtvEJ8cfgy7uQVimWUx4KSFZQ+qXghS4b8ouo9tfjjqTQs++M8+nx4FEDpgX38N/9g3b6LWsddEUEQcDr1Lv69X6SyfNeZDPz8z3XczivEX4mZYn313ecHU7AzIQMTv4up1c8pLlHgwIVs/HPtX1y5fV/j7Tcdu4qvjl3F0C9PYvCGE3xQQQsF8sqTH+WWJ+WfB3x2HIt+S8RnB1LEZXmFxUit4P8xW1aApb8n4tJN1ZPJx5GX4LvkL5y5kaNR3Nq0gh1MzkZS5qOLrY8jLyH8zySN9wOUtnwlZ5XW5buT19B22V7siLuh1b7qo6+OXkH75ftq/eK0RCFg6g+x+OxgStWFtXAhS4adCRlVF6yB6CvqF28jNkXjdOq/mLIlTuP9/R6fjs7vROKBvKTWY9eU3iZP27dvx8iRIzF27FgkJCTg+PHjGDZsWIXl8/PzERsbi8WLFyM2Nha//vorkpOT0b9/f7Wyy5cvR2ZmpviaNm1ajWId980/aL5wDy7evIdlO88hfM8FjIk4La5XPhBLJMDRS7fQ58OjeHl9VLX2n3BD9crzeMpt7E+6iY8jL6mVvXwrD7eVEreqpOc8QO6DR1eS+87fxOANUej70VFxWekffRze/OUMAsMjMen7WHx9IrXan1GZAnkJvjt5DdfvPmrB+/d+Eb6LSkVOflElW6rXo7qtMiUKAReyZFAoBGTkPNA4Zm0ofwcEQYAgCHhn93l8Us7/obICeQkEQVD5/ZxO/RfX7jw6cf97vwi/x6eLycHlW3nYeOQybsoKVK6oc/KL8HHkJZV91Xcx11Trqq339ybDZ/FfiEv7V2X5R/sv4Y0tMVAoBJUkRTk5vfvwQmLv+ZvispD3D6H7e4fEpELZ7G0J+CbqGgZ8dlyllXHdvosoVghYseu82jbZ9wpw9NItlf+vvMJifHfyGrKUWqsFofQ7+/Pp6xUm0Jdu3sPYiNPi33BxiQLr9l3EF0euqPzfF8hLkJtfcSvSv/eLkPtAjh7vHULoh0dwr0COxb+V9ncN+ymhwu30zcrdSch98Khu5SkuUWDVn0nY9/A7cDuvsNILGIVCwKcHLuHE5dv48VQaeq07jG+jUrHrTCbW/p0s7uPKrTyd1aPPh0cx/cc4HL10q9rbCIIgHv/P3MjByl3nK21ZrGxGjex7BQ/LlOD3+PRqHb/rW2uTsho9bVdXiouLMWPGDKxduxbjxo0Tl/v6+la4jZ2dHfbt26ey7NNPP0Xnzp2RlpYGT89HfY1sbGzg5uZW7XgKCwtRWPgoIZHJyr9CGf5VNOQPW2TOpufi6+NXkVdYjBFdmohl3tmdhAMXsgEA5zOrd6Vj/Nh9YOU/2m9OpGJ4gCdMjI2QnvNAbE6tqm/ExZv3sHDHWZxO/RemxhJceud5AMBfD29fZckKcCg5G3+fu4k3Q1uK28kf3trYe/4mxj/jXa34K/Nx5CV8fugyHCxNEbekNx4UlSD43YO4V1iMv8/dxGvdmqJTU0fYmJtWup9e7x/GA3kJvh7bCQpBQFAzZ5ibGgMA4tL+xY64dMzu3RJ2FqZ4b28y1h+6jNnPPYWKrumTs+7ho8iLmNnrKTzlalPh5wqCgLV/J6N5A2sM7NgYWbkFyHlQBB83W5VycqWWOgHApew8fHn0KgBgSo/mMDJSv9efkn0PoR8excguTWBqrHodNOWHWFy8mYchnTyQmJGLxHQZJjzjhYX9fPH+3mT8eTYLq/68ABMjCVq62WD9cD98FHkJ22Nv4Nuoa/hnUa9Kf59l7hcWY9FviejXxh29fF0rLCcvUSAuLQenU+9ibNemsDQr/9Bzv7AYOxMy0KuVK1xspJV+dthP8dgRlw6gen19rt/NR06+HCev3EHUlTtY+WJrNLS3AAB88rDVaNWfSdg2KQgnUm5j4W+JuPqw9ehkwB2VFuKU7Dx0be6ssv8rt+8jJTsPzVyscFNWejyIvHATLd1Uvx+x10oTtPyiErR7ey+6tXDGh0Paq5SRlyhU/k+fW3cEuQ/kiBjbCT1aNhBj/SE67bHtBLz42XFk3ytElqwAU3s0R1GJQvyul8VZJubaXfi624nv8woftXb3//QYLt7MQ8yiXnCyVv2/yC8qRocVqsfTO3mPTob2lhX/PX5/8hp+ibmBzWM6wdHKrMJyQGnLw9Xb9zEjpIVKf5eK+gYWFpdg//lsmJkYwc7CFLN+jse8Pj74X7uGamVX7DqPg8nZ+Pa1zli28zwGtG9YbrkyRSUVt/B9fSIVG49cwcYjV3BoTnd0f+8QfN1t8eeMZ8otv+tsJt7bq3pn4MP9qhdKg9afwLU7+Tg0pzuaOltV+NmPEwQBnx+6DFdbc4Q+7ap2bEzKlOGZFi4AgMzcB3j1i5MY2tkTk7s3U9vX23+cx9cnUrF1YhcM2XgSQOl3c+KzzfDe38kY180LrRuVfn/uFxbjgVLr7c+nr6NbC2e1fa76MwnfRl1DR097/PpGV/wScwO/x6fj02EdYWdR+XG8PtEqeZLL5ejTpw82bNiAFi1a6DqmKsXGxiI9PR1GRkbo0KEDsrKy0L59e6xduxatW7eu9n5yc3MhkUhgb2+vsnz16tVYsWIFPD09MWzYMISFhcHEpOJfVXh4ON5+++0qP+/WvUI0srdAzsOruWV/lF5hBj/lIpYpS5zKFMhL8PYf5xH6tCu6PzxoAsCDohKUCAKspSYqJ9YzN3Jw+OKjK4ulO8/B1NgIwwI8xYN2mRv/5uPopdsY2LERpCbGKute/SIK/z6MU6580FD6saz1zMJUdVsAMDGS4IfoNPyTehdrXm6rdnKvym9x6WhobyFezZfFMibiFO49PMAfS7mNYym30a25M74fHwAAOHsjF0mZMrzSyQNA6e9pT2Km+EddFvPAjo2w7pX2AICXHna23XUmE2tfbov1h0qfHn1/38UKD6ZjIk4hM7cAf57NwuYx/sjMLUC7xvbigaRM9NW7+Pzh/gZ2bIwu4ZGlsc/rgcikbHg6WqKHTwMUK/2O3/7jHMZ3e5R4FhYr8Ft8Ojp7OcLDwRIx1/6FXxMHfBSZghKFgK9PpOK1rl4qn3vxZukV69bT18Vlf57NwsJ+vvjz7KP+W8UKAecyZAhe++gBkNt5hfjpdBpe8feosoPm54dSsCMuHTvi0vHRkPYY0L5RueUGrT+BMw9bSO8VFGN+X59yy73zMCH41v0a9lRw4gGA1Nv3xcSpPN9FpeKTAykYHdQUO+LSMTqoqVrLwbztZ/DduAC1bSOOX8Xbf6i2/iRl3VNpEVq68xyKihVo3uBRp9iiYgV6rTussl1JOSdc5SX3CouxJzELxj8/aqk5nfovWi/9G5vHdBITtLKr/5OX7yDAyxFLfz+HbTHqt8bOpucg+15p4vZXYhaOp9xG/PUcDPJrjAHtGiLA20nlYmvQ+ij0a+suvp/yQyyu3LqPlS+2Fr9DRy7dgoeDJX6NS8eboS2R+0Au/o0oM1Y6DpkYGeHIxVtY8OtZrBnUVuUkuujh/8PHkZewrP/TEAQBd+8XqSVowKOWB3c7c5ibGqN/u4b4PjoNa/+6gK9Gd0JHT3v0/vAIrty6j58mdkHkhWxsPHJFZR/TfowT/45LFAIOX8xGu8b22HSs9OJkwKfHced+EfYn3YRCELAzPgOzej+FTw+k4PVnHyUUlfVFPHX1rvhzWYue8sVvaUtyElq4WuPVTp64nK3eoqT8NKcgCOJYYn8kZGBaiOp59l6BHPuTbsLYyAj/3i/C6KCm4rq952+KrVdztgEXVvRRSZ5X/XkBfk0c4WZnjuB3D6JEIWDNXxfKTZ7K7iC893B/QOmx5Y0tsUi4noM/z2bi3NuheH/fRbXvxJvbz8DW/NF58998Oc7eyMWvsaV/t7FpOZiyJRa7z2YCKD2WLOjbCkXFCuQ+kJd78XTs0m3cK5CjdSM7NLS3UPnO/de0Sp5MTU1x5swZXcdSbVeulP5xLFu2DOvWrUPTpk3x/vvvo3v37rh48SIcHR2r3EdBQQHmzZuHoUOHwtb2USvA9OnT0bFjRzg6OuLEiRNYsGABMjMzKx2rasGCBSrjWslkMnh4eJRbtrxz0eANFd+e23f+Jn48lYYfT6Xh0jt9kXA9B20b2yN47UH8e78IiW+HqvQ/6v/pcbV9vLXjLC5l30MbpRN7iUJAz/cPo6hYgRKFgBFdmuD7k9fwoKgEAzo0FJOVMsUlCmw6dhW/lnPCKu9e9InLd3Di4W2yX+PSkbq6HwRBQGGxAqM2nULyzXv4bUpXeJVzRZWYnouZP8Wr7zPlNqKVDlJljqXchiAIeCAvwf8+PQYAmPfrGXw2rCO+P3lNjEPZr7HpYvJU5u79Ioz75h/xvYWpscoBDQA2HrmMwxdvITP30a2S175+tM1LHRrhg1cf7ffWvfJvkW6JThMPNqmr+0Gu9Oj78ZQ7Ksns1ydSseav0laiIZ098P3JNAwP8MQFpYPz5uNXy/0cZek5DzDiq+gqywHAvO1n0cDGHE7WZog4noq5oS3FVhplh5IfJeoztsajo6cDrt6+j7aN7TB9azw8HCwwMdhbTJwAqPTpUSgEzN6WgFbuNpgY3Ax/JZYmdkmPtbrO3ZaA85kybJ8cBHNTY9x67NazIAi4c78Izg9PwIt/PwcA4kmkvFsuRy/dxpCNUWr/R48nTgDKvZX2TjX6CO0+m4kXOzTC8ZTbSMqU4bVuXiiv7/GuM5kq7wuLFXjzlzM4Pr+nSkvyF0eu4IvHkgNlg5Ru9RcUl+D81dLf4w/RafghOg2pq/vB2Fj1ILRb6bOv3CptlVqk9PtKu/NAvA1nZ2FabuIEAM+8q5qAj9p8CkBpn5eUd/rifKYMexIfJe6yhwnh+3sv4tODKWLyffBCNqKv3sXwgEd3A+ZtPwsAiLp8R7wgeOWLKKwf3lGM+dWHLSMVuZAlw4Rv/8H1u6q34u8oHT/LkrXIhxexyvGW3bY9eeUO5CUKNHG0wp37hejg6aBynHhQTt+54yl38NXDZO3VTp5qxxUAKll1WYIBAJ8dSsG0kBbIlhVg+FfRGNLZE6eu3sHf5x7dJu7a3Akejpa4evs+4tJyVHZ7+VYetv2jmmgPWn8C1lITlVvRBfISMclKzrqn8pDMP0oX3hIJkHC99DMKixVY/Hsifjz16CJNWVkf3jJlx+cyZYkTAHxx+Arm9/FB/0+P4ULWPfRq1QCPG7Hp0fHr9MJeVbZO1yatb9uNGDECmzZtqlFn6sfNnz8fa9asqbRMUlISFA9PNAsXLsSgQYMAABEREWjcuDG2bduG119/vdJ9yOVyvPLKKxAEQW2UdOUkqG3btjAzM8Prr7+O8PBwSKXl/0dJpdIK1z3uxr/qfWgqGwtK+b7wil3n8W3UNZX17/6VLN5Kq0zE8VSsGdRGfP9AXiIelBf9loh2je3FA+aqPeonhftFJQjfc6HcfVenD1X89Ry8+JlqYtfjvUPl3m6pqG/SsEpO/B/su4iPlTrsCgLwxpbYKuOa90vFFwEP5CUqJ5aRm6Jx9NLtSve3Iy5dTJ5u/JuPy0p9FpRvzSl3Ju7z4RF8NVp1qiPl9T+eKr01U6wQ8P3J0p+3PHa7prqOpVQev7Kz6bniQwc74tLx8dAO6K/UEnfx5j2cy1BNcpRPoGUej9XMxAh7z2UhJ1+Ot3acRbFCwI44YFw3b7H/EAA0nb8bAPD58I5iK8uJy7exKyFTpZ8PUJokfX7oMoZ29tCoA/XJK+rJuC5dyLqn8jv5PjoNJtW8WjYzKW2t/emf8k9MVSlLKh6n6bX6B/sf3V66XcHFQFWaL9yjtqzkYQLx6cMO0jO2xmPNngvIeHhh8nu8+oWacksqAEyuxt84UHpB9sInx6ouWInzmTLculco3r4qs3/WsxV+5+4VyGFjbqr2fS2vvPKS2dsetUQWyBVY8nsiTl65g0vZeeUm8nmFJZiyJQ77k26ioZ25yrrPD11WOY492kY1sXn3r2S80M4dGw5dRuSF7Arr9PjFaEWJkzb+SszChYf9BPcnZVda1ty0brtsSwQtn8GcNm0avv32W7Ro0QJ+fn6wslJtQdBmVPFbt27hzp3KO/V6e3vj+PHj6NmzJ44ePYpu3bqJ6wICAtCrVy+88847FW5fljhduXIFBw4cgJOTU6Wfd+7cObRu3RoXLlxAy5YtKy1bRiaTwc7ODh4zf4aRtP4MWregr4+YAJ16KwSdV0VWe1szYyOVPh+6si8sGJuPX8WuM5n4apQ/Uu/cF68ya9v0kBbldqrXhdef9cYXh1VbCAb7NS73VgsA9G3tpnKVWx84WJqqtUDumtYNrRvZQRAENHvrT+hyuKN2je3UHn543MRgb7XbMobs6Js9yk1ItZW6uh/2nsvS+unRIZ081BIYqpy7nTmeb+Mu3iasiKmxRLWLhI54OloirZoPgTR2sCj3Av+/8rJfY/xSwTHycRdX9hUvMHSp7Pydm5urclfqcToZYfziRdWOb9oOZOXi4gIXF5cqy/n5+UEqlSI5OVlMnuRyOVJTU9GkSZMKtytLnC5duoSDBw9WmTgBQHx8PIyMjNCggXoTor5JVZqPKyC8+okTgFpJnADguQ+OiD9X1eyua7WVOAFQS5wAVJg4Aah3iRMAtcQJAF5/eNJNr4WnEKtKnIDSK/knyeO3L2uqrDVPW0ycNJeZW1Bl4gSgVhInANVOnIDy74z8l6qbOAGlyWZd0ssRxm1tbTFp0iQsXboUHh4eaNKkCdauXQsAGDx4sFjOx8cH4eHheOmllyCXy/Hyyy8jNjYWu3btQklJCbKySk9Yjo6OMDMzQ1RUFKKjo9GjRw/Y2NggKioKYWFhGDFiBBwcHOqkrrpUdvsHQLn9LoiqUhtJkyZ0eYtAH3xVjZMu0ZOorkcb18uhCgBg7dq1MDExwciRI/HgwQMEBATgwIEDKklOcnIycnNLr2bT09Oxc+dOAED79u1V9nXw4EF0794dUqkUW7duxbJly1BYWAgvLy+EhYWp9IPSRNfmToi6XrcnGyLSX6fKeUCCiOqe1n2eAODo0aP44osvcPnyZfzyyy9o1KgRvvvuO3h5ean0RXrSlN0zXb79NDaduln1BkRERFRttTWPY3X7PGnd22r79u0IDQ2FhYUF4uLixEEic3NzsWrVKm13a1DMjNXHPyKqiqdj/XnIwJC92ad6D4AQET1O6+Rp5cqV2LBhA7788kuYmj4aFbRr166Ija3e46OGrpJxNWtk+YCn0buS0Zz7PK06OvrGkX44vzy0wvI+bhWPkE2lnnLVzQzhB+d0x4n5PSst8/uUruLPa19uq5PP1da4bl5qy1YPbIM3yhlQTxsOlYxEXRNOVmbYFxaMF9tXPGJ0iE/Ff0P1ia25Cf6cXvGAobpmLdXb3hw1Fvp07X0nnm9T/VkrKjM39L9L+ssbh49KaZ08JScnIzg4WG25nZ0dcnJyahKTwTDTcFTt6ujX1h2jAptiZGD5TxXODW2JDSP9xPd2Fqbo/bQbLM1MMOu5p8rd5s/pz2Ben/JHfAZKH7X1drGq8qRfmRYNrOHjZoNPh3XADxMC8OmwDmplqpqqoTJ9W6semPq1ca9Ws24r90fNsjbmJmhZwVQrj4+Q/nhfxbaN7fBSB/XRtV/q0Ah7ZjwDe0tTvOzXGF7OVuUONqnMwuxRi+XjI5b/1xa/4Itf3wgS30/t0RxDOnvizT4+KkleGb8mDhol449PU/P4Z3f2qnrA2zJOSt+fbi2c0cLVBq928qywvJW0blqG+7VxL3d5Rd+9Hyd2QVPn/641cofS/3eZqlrpPhnaodwLDEcrMzS0M0dTJ0usePHR7A++7hX/v9em8d28Kny83cbcBBtG+JW7riLVHbNr02h/fD7cDwM7lj8CvyY8/sOW6QOzn8WKAU9XWa6ic8vjPhvWsaYh1Rtan93d3NyQkqI++/OxY8fg7V3zOc0MQXl/pK3cbdHF2xELn2+l0b56tXLFhRV98OnQ0qTjmRYu2DPjGWx6bHBFo8fO6spvp4e0wN8z1RNeIyMJJndvhgsr+mD2c0/h9yldsex/j+YJPDC7O/bODIa70uBr5SUKEWM7iT/P7+sDvyaPOu+3bmSHv2YG44W2DRHUzBkvtH3UIuBsbYYfxgfg75nBGN/NCzZSE/w9MxhXVj2PpOV9xHKfDeuIda+0E99feqev+PNg/8biz91buuCjh3OFfftaZ7z1vA+efcoFi/o9+p1vmxSIc2+HYkqPRy0oZ5b2xl8zn8GGER0RMaaTyh+68tQRh+d2xx9TH/Xpe29wO/wyKQhrBrXFM0rTUByb1wMfvNoerdxtcXphL7w3+FHsZUKfdsWoxxJhqYkRXGykMDM2qvDK7xX/xrAyM4a3i/r6ykbdHaM0jUN5lFstO3raP/zXAamr++HKqucxR+mqt52HPWY8Nm2EIAjYONK/3Cv4oGbqQ4MIEPBaVy9IJFBLqJ99yhkrX1Sfbql/u4Y4PLe7yrKWrjY4rpTcl01BUtnjzFITY0xXir+i342urr6XvOAL/yYOmNqzubhsaOdHyZ1UadC/rRO7iD+bmxrD0swEH7yq/v0pXa96nPlQaYT7MjGLeuH7cqaiKY+3i7Va0tq/XUO87NcYM0JaoJG9BZo3sMauad3wQlt3/DA+AP9r1xBbxnfBs8pTTc1+Fkff7IHDb/bAobk9MFJpDs91r7ardgvKuG5emBjsjfHdvPDTxC74fPijv0vlpK6pk6X43V/10qMBgSPGdMLRN3vgavjzWPSCL1xt1f8+nKzMsDcsGBKJBKsHtlFbD5R/O11qYoSjb/bAd+M6lzt7RJmOnqXHwrLfj4WpcZXzuL3W1Qupq/th/6xgNFK64Grd8FHi+YrScQ9QPSZWRPl3A5SOnVYRiUSCkYFNq9znpGebYW9YsNrf0MLnW4nHYqD0eFc2Hdn0kBawNFO/gHl3UGlr++MXxMqUv2d1Rev22QkTJmDGjBnYvHkzJBIJMjIyEBUVhTlz5mDx4sW6jFFvmRqpJ09fjvJDY4fSP0JPJ0u8+csZDGjfEN9GXYN/EwcMaN9QnFoCKD353/j3Afq1cVeZnwgoTcRaudvii5F+eP27GFiYGuPVTqrTwpg/Nmfd419W5RO3uamxOIdSm0Z2OHzxFuwtzVRaQvaFBeN4ym2MCmyKBjZScaqIslae0wt7wVpqAgszY0x6tpk4rkx5BxZrqQnyCovR0dMBQQ/n8Fr0gi/m9fURW3oszIzxsl9jnM+QoZdvA5gYGeFchgwBXo4wNTbC9slBOJeRi2dauGD/rGBEX72LIZ08xTmPgp9yQfBTLpgY3AyZuQ+wcneS+NlWUhOVFqWyR1/7tC5tGRAEAQv6+iD1Tj7m9H4Kk7fEoqdPAzRxskK20ojB7nbmYqL8wavt8drXpzHYr7H4/wyot1x9N64zPjuYgrmhPmjewLr0xLS1dBJTiUSCo2/2QIlCUPs/LzO/byuseqkNjI0k+PpEKjYduyqO0fL4MyAnF4Rg2z/X4eVihX5t3PFCW3e8/HBKIOWBU4HSW8I37xXAy9kKyweoJi7lTU4c9txTaOlmI47m3tDeAp5OlvhipD+av/Unih+OovlG92ZwspaqjU6sEEoT7de6NUVjB0tM/SFOaa0ELtaPWpN6+7piUvdm4olIeUC/LRMCVH5XZf+XJkq/913TuuHwxVvilC2WZsaY9dxT6NrMCccv38G4bl7iXF5lbM1NsH5ER/T58Kha3Us/p3TYD1NjCeb3bYUAL0dsPn4Vr3X1wr7zN/GR0lhiY7s2xWvdvFRG5G/i9Og7YqM0D1gzl0etOGUt2Mon71butuIYUJvHdMKwLx+Nvl+gND2IjdQEM3q1gJO1FN1aSBH9VggCKhgcd8OIjrAwM4GxkURldGlLM2M4WUnF5D9MqZXhU6ULDBcbKTaP6YT+nx6DvaUpvF3UW6J2vBGEm7IC+LjZwsRIIv5fhD7tiik9muPMjVzk5BeJk+aGD2yDlzo0Uvm/PZj8aOTpsUFe6OjpgJ//uY5F/XxhY26ComIFrKQm6OLtiLv3i+DfVDUR/HyYnzhNSGcvR/wwPkDlezKksyde8fdA7oPSSaTLRjEv73bm8C5N4OFoCQ9HS/w4oQt+j08Xh9Po4u2Iz4Z1hJFEAoeHraL92zWElZkJWjeyg5EEeG9vMn7+p/yxjUIeTk/SvEHphcGNf/MhLxFUEqnZvVvixQ6NkJx1D87WUrXjTIhPA3wx0g/v/JmEiOOpAIBhAZ64KSsQv5vVeeI/YmwnfLjvospYbJGzn8W8X87AwcoMZiZGeMrVBsv6P63yN/Rat9K/gzImxkb4ekwnSCSlf6PbY24gv+jRE+ntPOzxSicP9PBpAGdrM1y7k4/u7x0CUHoxt/R/T+Pu/SJ00qBFurZonTzNnz8fCoUCISEhyM/PR3BwMKRSKebMmYNp06bpMka9Vd5kuMqtUaFPu6G3ryskEgneer4VzE2NcURpUt/Ph3dUmTS4IqFPuyF1dT+UKAS1iRIfT5aslA4AnwztUGF2b2QkQcTYzmrLW7jaoMXD2wsTg71xKvUuXvZ7dPVTUavH4y1iALBzalf89M91THxG9crn8d/b4y02i1941Crm18RBbOFq3sAGzRtUfMtIeb64ss/o3tIFrRvZok0je7XyEolEZWLQn18PFH+2U+qro3wydLaWYufUqp80faaFizizOQC0bWyPg3O6i++VTxavdfXC5uNXMTzAE88+5QJjI4nKLc6xXb0wtquXmKhaS01w++EM9+525nCzM1eZWFS5JaWVuy2aOlki9U4+No32RwNbc+x4Q/12XGWeb+OOb1/rjC3R17D0f4+a+KMWhODopVu4KSvEmKCm+CYqVX1jofRvoizR/Oa1zhi9+RRszE3g6WgJMxOjh/PZGeHphqq3MH9+PRC7z2Ti1c4esH04c7yHowWu332AF9qVJsDKLU9mJkYqiWXZ30aAtxMCvEtbxYZ29sBfiVniAKEH53RXm7A2rNdT+GD/RXTwtMfPrwfiz7OZCPR2QgPb0pbZsjkTWzeywxs9muHKrfuQmhiJCZ3yRZXypNoWpo/+Nm0tHv1c9jfd0dMBU3s0R/MG1ujl64rWS/9W2c8DeQk6ezmqJE/xS3urHBNcbVWn7gBKWwRbN7ITLxoA1elDfpkUpHIBVRljIwl2Tav4+9/B81FrdPMGNjgxvyccrczE73vbxvYAgBfaNkRRiQJPlXMrU640nZW5qRG6eDuhi/ejVs2yv21vF2t4l3P4bNPYDjGLemFHXDoGdmyskjiVMTIqTXiUf3fKP2+bFIg7eUXo4fPoA8rieNnPAzvibmBubx+V4wRQekzppdRf9d2X22FhP1+89NlxOFqZwd7SDDN7tYBCEFTmIgWgcjH20ZD2eFBUAldbc7jamiOombPKurI5+ub39YGJsRFmPfcUsu8V4n8PW/yVf6/PPuWCLw5fQVAzJ7zzUhvsSsjA+/tUB77u0bIBerRsIB5jhnb2QDMXa/wyWf0Wb5mhnUsvYh+/5lK+CNswwg8zf4rDm318YG9hiqcf1rnsPNLU2QotXW2QfPMeBnZsjHYe9hV+3n9N6+RJIpFg4cKFmDt3LlJSUpCXlwdfX19YW+umY60hMC3ntp30sSfwyg6oZQcP5UlAlQ8I1VHeDNOPt1wo9/No08iu3ANHdTlZS6s80QY1c8KJy3cwLEC974m3izUW9NXs9mVNSE2UW5nKlhlj1zTNO+NKTYzRrrEdEjNkCPDS7P9JU0v+54sFz/uUm4wr+3x4R6zecwEfDemAAQ/nESwuZ/4U5QTeSmqMv8OCIQjq3xVNlLXwKXOxkWJgx0eJdYhPA6zecwGN7C3EwTYf73f07FMuuPROX5QoBDFO5du/yhraW2DCY7ccdk9/Bqm374snHuV+h6625iqDw5Y3yF74wLZY+WIbHLl0Cw+KStQSJ/8mDpjWszmCmjuhlbstTI2NMKB9xf1YpCbGKv3qAMBEKaFT/k662UlVtpvT+yncKywW+8hJJBLxtqlC6f+1uETAzqldsXrPBbzRoxn+SX00iWt5xwRvFytx3ru5oS0xpUdztTIv+zVG/PUctG1sB9+GmvVP0mTwwor6/zWt5Fap8gWatgMlOllLMf6Zim9XlVH+8/F0tMTZ9NKWl05NK275UL6gqw47C1McULpwqo7KvnMD2jdSW29jbqrSDeE5X1d09nJE64Z2CGrmjJMLQuBkbQZTYyNM7t4Md+4XlXv+ebF9Q/wWn4HXuqo/SFJm0rPN8OOpNPGhkmdbusDX3RbtPNT7b7ZpbIfI2d0rrevPkwJx9kZuubf961KNH6swMzNDq1alJ8C6HvGzvmlZTsdZU5PKf0duSv2KavIkUllrQv/HnjaSmhjjhbbuyH0gV7llUFu+fa0z7t4vEq/K65Lyiaq6HT0r88vkINwrKK5RR/fqqipxAkpbgJ5/rDOyoorkycLURKVFrja1cLXB0Td7wMnaDHvOZmHjkStY1l+9M6qpsRG0zeNszU3F1gsAaN7AGtN6NoenoyXsLEzxUsdGeH/fRZW+aY8zNpKgR0vV6Zh2vBGEr45exfy+PjAyklR68qyKcvLkqvT3Pvu5lsjJlyP4YYvk1J4t1LYto3z1LqD0d7tpTGmfQxdrc4TvuYC2jct/2GDrhC7Yl3QTL7ZvpNISrWxYZ080b2CNpzVMnP4LHTwd8NbzPvByrv0LdeUWt7LvankXgvrGzMRIpSVd+bxjYmxU7t8lUNot4Z2X2lT4vQFKW7vmhrYUE3epiTH+nKH906J2FqboVsnfa12p0SCZmzZtwgcffIBLl0rvnbZo0QIzZ87E+PHjdRagPlIeZCsxuwg5D+Rin5CUd/pW2tojCAIik7LRrIF1jTqq3rpXiNOpd9Hb17VGrUuGZunviZAVFGPdK+0MOtl/+49ziDieirUvt8Vgf9V+cIIgIGBVJHLy5TizrHeNWpz0UW6+HNbmJuW2yvwXFAoB3m/9CQD4Z1EvKBQC5ArVvizVsfT3RJzLkOHHiV3Ukut/7xfBxtyEf/s1VKIQMH1rHHzdbcttoSPDU91BMrVOnpYsWYJ169Zh2rRpCAwszWCjoqLw6aefIiwsDMuXL9cucgPw+C+/sLgEbZbtha25Kf5Z1Kuuw6MngCAIyJIVwN2u/BNygbwECkGApdmTO6ZPXbqQJYO8WECbClqHiKhu1Hry5OLigo8//hhDhw5VWf7jjz9i2rRpuH37tja7NQjl/fIL5CUwkkgqHGOEiIiI6lZ1kyetLzvlcjn8/f3Vlvv5+aG4uFjb3RqsJ+3WCBERkaHSuhlk5MiRWL9+vdryjRs3Yvjw4TUKioiIiKi+qlGHh02bNmHv3r3o0qV0NNzo6GikpaVh1KhRmDVrllhu3bp1NYuSiIiIqJ7QOnlKTExEx46l40ZcvnwZAODs7AxnZ2ckJiaK5Qz5iSYiIiJ68midPB08eFCXcRARERHpBT76RURERKQBJk9EREREGmDyRERERKQBJk9EREREGtA6eRo9ejSOHDmiy1iIiIiI6j2tk6fc3Fz06tULLVq0wKpVq5Cenq7LuIiIiIjqJa2Tp99++w3p6emYPHkyfvrpJzRt2hR9+/bFL7/8ArlcrssYiYiIiOqNGvV5cnFxwaxZs5CQkIDo6Gg0b94cI0eORMOGDREWFoZLly7pKk4iIiKiekEnHcYzMzOxb98+7Nu3D8bGxnj++edx9uxZ+Pr64oMPPtDFRxARERHVC1onT3K5HNu3b8cLL7yAJk2aYNu2bZg5cyYyMjLwzTffYP/+/fj555+xfPlyXcZLREREVKe0np7F3d0dCoUCQ4cOxalTp9C+fXu1Mj169IC9vX0NwiMiIiKqX7ROnj744AMMHjwY5ubmFZaxt7fH1atXtf0IIiIionpH6+Rp5MiRuoyDiIiISC9onTzNmjWr3OUSiQTm5uZo3rw5BgwYAEdHR62DIyIiIqpvJIIgCNps2KNHD8TGxqKkpAQtW7YEAFy8eBHGxsbw8fFBcnIyJBIJjh07Bl9fX50GXd/JZDLY2dkhNzcXtra2dR0OERERVUN1z99aP203YMAA9OrVCxkZGYiJiUFMTAxu3LiB5557DkOHDkV6ejqCg4MRFham7UcQERER1Ttatzw1atQI+/btU2tVOnfuHHr37o309HTExsaid+/euH37tk6C1RdseSIiItI/td7ylJubi+zsbLXlt27dgkwmA1D6tF1RUZG2H0FERERU79Tott1rr72GHTt24MaNG7hx4wZ27NiBcePG4cUXXwQAnDp1Ck899ZSuYiUiIiKqc1rftsvLy0NYWBi+/fZbFBcXAwBMTEwwevRofPDBB7CyskJ8fDwAlDuApiHjbTsiIiL9U93zt9bJU5m8vDxcuXIFAODt7Q1ra+ua7M4gMHkiIiLSP7Xa50kulyMkJASXLl2CtbU12rZti7Zt2zJxIiIiIoOnVfJkamqKM2fO6DoWje3evRsBAQGwsLCAg4OD2NeqImPGjIFEIlF59enTR6XM3bt3MXz4cNja2sLe3h7jxo1DXl5eLdaCiIiI9InWHcZHjBiBTZs26TIWjWzfvh0jR47E2LFjkZCQgOPHj2PYsGFVbtenTx9kZmaKrx9//FFl/fDhw3Hu3Dns27cPu3btwpEjRzBx4sTaqgYRERHpGa2nZykuLsbmzZuxf/9++Pn5wcrKSmX9unXrahxcZZ89Y8YMrF27FuPGjROXV2ckc6lUCjc3t3LXJSUl4a+//sLp06fh7+8PAPjkk0/w/PPP47333kPDhg3L3a6wsBCFhYXi+7KhGoiIiMjwaN3ylJiYiI4dO8LGxgYXL15EXFyc+Cp7yq62xMbGIj09HUZGRujQoQPc3d3Rt29fJCYmVrntoUOH0KBBA7Rs2RKTJ0/GnTt3xHVRUVGwt7cXEycA6NWrF4yMjBAdHV3hPsPDw2FnZye+PDw8alZBIiIiqre0bnk6ePCgLuPQSNnTfcuWLcO6devQtGlTvP/+++jevTsuXrxY4WTEffr0wcCBA+Hl5YXLly/jrbfeQt++fREVFQVjY2NkZWWhQYMGKtuYmJjA0dERWVlZFcazYMEClYmSZTIZEygiIiIDpXXLEwAcPXoUI0aMQFBQENLT0wEA3333HY4dO6bV/ubPn6/Wofvx14ULF6BQKAAACxcuxKBBg+Dn54eIiAhIJBJs27atwv0PGTIE/fv3R5s2bfDiiy9i165dOH36NA4dOqRVvGWkUilsbW1VXkRERGSYtE6etm/fjtDQUFhYWCA2Nlbs85Obm4tVq1Zptc/Zs2cjKSmp0pe3tzfc3d0BqPZxkkql8Pb2RlpaWrU/z9vbG87OzkhJSQEAuLm5qU05U1xcjLt371bYT4qIiIieLFrftlu5ciU2bNiAUaNGYevWreLyrl27YuXKlVrt08XFBS4uLlWW8/Pzg1QqRXJyMrp16wagdOyp1NRUNGnSpNqfd+PGDdy5c0dMxgIDA5GTk4OYmBj4+fkBAA4cOACFQoGAgAAtakRERESGRuuWp+TkZAQHB6stt7OzQ05OTk1iqpKtrS0mTZqEpUuXYu/evUhOTsbkyZMBAIMHDxbL+fj4YMeOHQBKR0KfO3cuTp48idTUVERGRmLAgAFo3rw5QkNDAQCtWrVCnz59MGHCBJw6dQrHjx/H1KlTMWTIkAqftCMiIqIni9YtT25ubkhJSUHTpk1Vlh87dgze3t41jatKa9euhYmJCUaOHIkHDx4gICAABw4cgIODg1gmOTkZubm5AABjY2OcOXMG33zzDXJyctCwYUP07t0bK1asgFQqFbfZsmULpk6dipCQEBgZGWHQoEH4+OOPa70+REREpB+0ntsuPDwc33//PTZv3oznnnsOf/75J65du4awsDAsXrwY06ZN03WseoNz2xEREemf6p6/tW55mj9/PhQKBUJCQpCfn4/g4GBIpVLMmTPniU6ciIiIyLBp3fJUpqioCCkpKcjLy4Ovry8nBwZbnoiIiPRRrbc8lTEzM6vWtChEREREhqBGyVNkZCQiIyORnZ0tDlxZZvPmzTUKjIiIiKg+0jp5evvtt7F8+XL4+/vD3d0dEolEl3ERERER1UtaJ08bNmzA119/jZEjR+oyHiIiIqJ6TetBMouKihAUFKTLWIiIiIjqPa2Tp/Hjx+OHH37QZSxERERE9Z7Wt+0KCgqwceNG7N+/H23btoWpqanK+nXr1tU4OCIiIqL6Ruvk6cyZM2jfvj0AIDExUWUdO48TERGRodI6eTp48KAu4yAiIiLSC1r3eSIiIiJ6EtUoeTp69ChGjBiBwMBApKenAwC+++47HDt2TCfBEREREdU3WidP27dvR2hoKCwsLBAXF4fCwkIAQG5uLlatWqWzAImIiIjqE62Tp5UrV2LDhg348ssvVZ6069q1K2JjY3USHBEREVF9o3XylJycjODgYLXldnZ2yMnJqUlMRERERPWW1smTm5sbUlJS1JYfO3YM3t7eNQqKiIiIqL7SOnmaMGECZsyYgejoaEgkEmRkZGDLli2YM2cOJk+erMsYiYiIiOoNrcd5mj9/PhQKBUJCQpCfn4/g4GBIpVLMmTMH06ZN02WMRERERPWGRBAEoSY7KCoqQkpKCvLy8uDr6wtra2tdxaa3ZDIZ7OzskJubC1tb27oOh4iIiKqhuudvrVueypiZmcHX17emuyEiIiLSCxxhnIiIiEgDTJ6IiIiINMDkiYiIiEgDTJ6IiIiINKBRh/FZs2ZVu+y6des0DoaIiIiovtMoeYqLi6tWOYlEolUwRERERPWdRsnTwYMHaysOIiIiIr3APk9EREREGqjxIJnnz59HWloaioqKVJb379+/prsmIiIiqne0Tp6uXLmCl156CWfPnoVEIkHZLC9l/Z1KSkp0EyERERFRPaL1bbsZM2bAy8sL2dnZsLS0xLlz53DkyBH4+/vj0KFDOgyRiIiIqP7QuuUpKioKBw4cgLOzM4yMjGBkZIRu3bohPDwc06dPr/aTeURERET6ROuWp5KSEtjY2AAAnJ2dkZGRAQBo0qQJkpOTdRMdERERUT2jdctT69atkZCQAC8vLwQEBODdd9+FmZkZNm7cCG9vb13GSERERFRvaJ08LVq0CPfv3wcALF++HC+88AKeeeYZODk5YevWrToLkIiIiKg+kQhlj8npwN27d+Hg4PDEjzAuk8lgZ2eH3Nxc2Nra1nU4REREVA3VPX9rPLfdihUrYGVlVeU8d5zbjoiIiAyRRh3G4+LiIJfLxZ8resXHx9dGrGp2796NgIAAWFhYwMHBAS+++GKl5SUSSbmvtWvXimWaNm2qtn716tW1XBMiIiLSF1rPbVfX89xt374dEyZMwKpVq9CzZ08UFxcjMTGx0m0yMzNV3u/Zswfjxo3DoEGDVJYvX74cEyZMEN+XPVVIREREpHWH8bS0NHh4eJTbvyktLQ2enp41CqwyxcXFmDFjBtauXYtx48aJy319fSvdzs3NTeX977//jh49eqg9HWhjY6NWtjKFhYUoLCwU38tksmpvS0RERPpF63GevLy8cOvWLbXld+7cgZeXV42CqkpsbCzS09NhZGSEDh06wN3dHX379q2y5UnZzZs3sXv3bpXkq8zq1avh5OSEDh06YO3atSguLq50X+Hh4bCzsxNfHh4eGteJiIiI9IPWyZMgCOW2OuXl5cHc3LxGQVXlypUrAIBly5Zh0aJF2LVrFxwcHNC9e3fcvXu3Wvv45ptvYGNjg4EDB6osnz59OrZu3YqDBw/i9ddfx6pVq/Dmm29Wuq8FCxYgNzdXfF2/fl27ihEREVG9p/Ftu7Kn7CQSCRYvXgxLS0txXUlJCaKjo9G+fXutgpk/fz7WrFlTaZmkpCQoFAoAwMKFC8X+ShEREWjcuDG2bduG119/vcrP2rx5M4YPH66W6Ck/Rdi2bVuYmZnh9ddfR3h4OKRSabn7kkqlFa4jIiIiw6Jx8lQ2Z50gCDh79izMzMzEdWZmZmjXrh3mzJmjVTCzZ8/GmDFjKi3j7e0tdvxW7uMklUrh7e2NtLS0Kj/n6NGjSE5Oxk8//VRl2YCAABQXFyM1NRUtW7assjwREREZNo2Tp7Kn7MaOHYuPPvpIp4NAuri4wMXFpcpyfn5+kEqlSE5ORrdu3QAAcrkcqampaNKkSZXbb9q0CX5+fmjXrl2VZePj42FkZIQGDRpUXQEiIiIyeFo/bRcREaHLODRia2uLSZMmYenSpfDw8ECTJk3EsZoGDx4slvPx8UF4eDheeuklcZlMJsO2bdvw/vvvq+03KioK0dHR6NGjB2xsbBAVFYWwsDCMGDECDg4OtV8xIiIiqve0Tp4AIDIyEpGRkcjOzhb7IZXZvHlzjQKrytq1a2FiYoKRI0fiwYMHCAgIwIEDB1SSnOTkZOTm5qpst3XrVgiCgKFDh6rtUyqVYuvWrVi2bBkKCwvh5eWFsLCwKkdTJyIioieH1nPbvf3221i+fDn8/f3h7u6u9uTdjh07dBKgPuLcdkRERPqnVua2U7ZhwwZ8/fXXGDlypLa7ICIiItI7Wo/zVFRUhKCgIF3GQkRERFTvaZ08jR8/Hj/88IMuYyEiIiKq97S+bVdQUICNGzdi//79aNu2LUxNTVXWr1u3rsbBEREREdU3WidPZ86cEUcSf3xOufKmbSEiIiIyBFonT2WDZRIRERE9SbTu8wSUTnMyYsQIBAUFIT09HQDw3Xff4dixYzoJjoiIiKi+0Tp52r59O0JDQ2FhYYHY2FgUFhYCAHJzc7Fq1SqdBUhERERUn2idPK1cuRIbNmzAl19+qdJZvGvXroiNjdVJcERERET1jdbJU3JyMoKDg9WW29nZIScnpyYxEREREdVbWidPbm5uSElJUVt+7NgxeHt71ygoIiIiovpK6+RpwoQJmDFjBqKjoyGRSJCRkYEtW7Zgzpw5mDx5si5jJCIiIqo3tB6qYP78+VAoFAgJCUF+fj6Cg4MhlUoxZ84cTJs2TZcxEhEREdUbEkEQhJrsoKioCCkpKcjLy4Ovry+sra11FZvequ6szERERFR/VPf8rXXLU1paGjw8PGBmZgZfX1+1dZ6entrumoiIiKje0rrPk5eXF27duqW2/M6dO/Dy8qpRUERERET1ldbJkyAI5c5hl5eXB3Nz8xoFRURERFRfaXzbbtasWQBKJ/9dvHgxLC0txXUlJSWIjo4WJwwmIiIiMjQaJ09xcXEASluezp49CzMzM3GdmZkZ2rVrhzlz5uguQiIiIqJ6ROPk6eDBgwCAsWPH4qOPPuLTZERERPRE0fppu4iICOTk5OD9999HUlISAODpp5/Ga6+9Bjs7O50FSERERFSfaN1h/J9//kGzZs3wwQcf4O7du7h79y7WrVuHZs2acWJgIiIiMlhaD5L5zDPPoHnz5vjyyy9hYlLagFVcXIzx48fjypUrOHLkiE4D1SccJJOIiEj/VPf8rXXyZGFhgbi4OPj4+KgsP3/+PPz9/ZGfn6/Nbg0CkyciIiL9U93zt9a37WxtbZGWlqa2/Pr167CxsdF2t0RERET1mtbJ06uvvopx48bhp59+wvXr13H9+nVs3boV48ePx9ChQ3UZIxEREVG9ofXTdu+99x4kEglGjRqF4uJiAICpqSkmT56M1atX6yxAIiIiovpE6z5PZfLz83H58mUAQLNmzVRGHH9Ssc8TERGR/qnu+VvjlieFQoG1a9di586dKCoqQkhICJYuXQoLC4saBUxERESkDzTu8/TOO+/grbfegrW1NRo1aoSPPvoIU6ZMqY3YiIiIiOodjZOnb7/9Fp9//jn+/vtv/Pbbb/jjjz+wZcsWKBSK2oiPiIiIqF7ROHlKS0vD888/L77v1asXJBIJMjIydBoYERERUX2kcfJUXFwMc3NzlWWmpqaQy+U6C4qIiIiovtK4w7ggCBgzZgykUqm4rKCgAJMmTYKVlZW47Ndff9VNhERERET1iMbJ0+jRo9WWjRgxQifBEBEREdV3GidPERERtREHERERkV7QenoWIiIioicRkyciIiIiDehl8nTo0CFIJJJyX6dPn65wu4KCAkyZMgVOTk6wtrbGoEGDcPPmTZUyaWlp6NevHywtLdGgQQPMnTtXnLuPiIiISC+Tp6CgIGRmZqq8xo8fDy8vL/j7+1e4XVhYGP744w9s27YNhw8fRkZGBgYOHCiuLykpQb9+/VBUVIQTJ07gm2++wddff40lS5b8F9UiIiIiPVDjiYHrA7lcjkaNGmHatGlYvHhxuWVyc3Ph4uKCH374AS+//DIA4MKFC2jVqhWioqLQpUsX7NmzBy+88AIyMjLg6uoKANiwYQPmzZuHW7duwczMrNx9FxYWorCwUHwvk8ng4eHBiYGJiIj0SHUnBtbLlqfH7dy5E3fu3MHYsWMrLBMTEwO5XI5evXqJy3x8fODp6YmoqCgAQFRUFNq0aSMmTgAQGhoKmUyGc+fOVbjv8PBw2NnZiS8PDw8d1IqIiIjqI4NInjZt2oTQ0FA0bty4wjJZWVkwMzODvb29ynJXV1dkZWWJZZQTp7L1ZesqsmDBAuTm5oqv69eva1kTIiIiqu/qVfI0f/78CjuCl70uXLigss2NGzfw999/Y9y4cXUUNSCVSmFra6vyIiIiIsOk8SCZtWn27NkYM2ZMpWW8vb1V3kdERMDJyQn9+/evdDs3NzcUFRUhJydHpfXp5s2bcHNzE8ucOnVKZbuyp/HKyhAREdGTrV4lTy4uLnBxcal2eUEQEBERgVGjRsHU1LTSsn5+fjA1NUVkZCQGDRoEAEhOTkZaWhoCAwMBAIGBgXjnnXeQnZ2NBg0aAAD27dsHW1tb+Pr6alkrIiIiMiT16radpg4cOICrV69i/PjxauvS09Ph4+MjtiTZ2dlh3LhxmDVrFg4ePIiYmBiMHTsWgYGB6NKlCwCgd+/e8PX1xciRI5GQkIC///4bixYtwpQpU1QmQiYiIqInV71qedLUpk2bEBQUBB8fH7V1crkcycnJyM/PF5d98MEHMDIywqBBg1BYWIjQ0FB8/vnn4npjY2Ps2rULkydPRmBgIKysrDB69GgsX778P6kPERER1X8GMc5TfVPdcSKIiIio/niixnkiIiIi+q8weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg0weSIiIiLSAJMnIiIiIg3oZfJ06NAhSCSScl+nT58ud5u7d+9i2rRpaNmyJSwsLODp6Ynp06cjNzdXpVx5+9y6det/US0iIiLSAyZ1HYA2goKCkJmZqbJs8eLFiIyMhL+/f7nbZGRkICMjA++99x58fX1x7do1TJo0CRkZGfjll19UykZERKBPnz7ie3t7e53XgYiIiPSTXiZPZmZmcHNzE9/L5XL8/vvvmDZtGiQSSbnbtG7dGtu3bxffN2vWDO+88w5GjBiB4uJimJg8+lXY29ur7J+IiIiojF7etnvczp07cefOHYwdO1aj7XJzc2Fra6uSOAHAlClT4OzsjM6dO2Pz5s0QBKHS/RQWFkImk6m8iIiIyDDpZcvT4zZt2oTQ0FA0bty42tvcvn0bK1aswMSJE1WWL1++HD179oSlpSX27t2LN954A3l5eZg+fXqF+woPD8fbb7+tdfxERESkPyRCVc0q/6H58+djzZo1lZZJSkqCj4+P+P7GjRto0qQJfv75ZwwaNKhanyOTyfDcc8/B0dERO3fuhKmpaYVllyxZgoiICFy/fr3CMoWFhSgsLFTZv4eHh9iyRURERPWfTCaDnZ1dlefvepU83bp1C3fu3Km0jLe3N8zMzMT3K1aswCeffIL09PRKk6Ay9+7dQ2hoKCwtLbFr1y6Ym5tXWn737t144YUXUFBQAKlUWq16VPeXT0RERPVHdc/f9eq2nYuLC1xcXKpdXhAEREREYNSoUdVKnGQyGUJDQyGVSrFz584qEycAiI+Ph4ODQ7UTJyIiIjJs9Sp50tSBAwdw9epVjB8/Xm1deno6QkJC8O2336Jz586QyWTo3bs38vPz8f3336t07HZxcYGxsTH++OMP3Lx5E126dIG5uTn27duHVatWYc6cOf911YiIiKie0uvkadOmTQgKClLpA1VGLpcjOTkZ+fn5AIDY2FhER0cDAJo3b65S9urVq2jatClMTU3x2WefISwsDIIgoHnz5li3bh0mTJhQ+5UhIiIivVCv+jwZCvZ5IiIi0j/VPX8bxDhPRERERP8VJk9EREREGtDrPk/1VdmdUI40TkREpD/KzttV9Whi8lQLysaq8vDwqONIiIiISFP37t2DnZ1dheuZPNUCR0dHAEBaWlqlv3x9VjaK+vXr1w26UzzraTiehDoCrKcheRLqCNSvegqCgHv37qFhw4aVlmPyVAuMjEq7ktnZ2dX5F6G22draGnwdAdbTkDwJdQRYT0PyJNQRqD/1rE6jBzuMExEREWmAyRMRERGRBpg81QKpVIqlS5ca9Hx4T0IdAdbTkDwJdQRYT0PyJNQR0M96coRxIiIiIg2w5YmIiIhIA0yeiIiIiDTA5ImIiIhIA0yeiIiIiDTA5EnHPvvsMzRt2hTm5uYICAjAqVOn6jqkGgkPD0enTp1gY2ODBg0a4MUXX0RycrJKmYKCAkyZMgVOTk6wtrbGoEGDcPPmzTqKuOZWr14NiUSCmTNnissMpY7p6ekYMWIEnJycYGFhgTZt2uCff/4R1wuCgCVLlsDd3R0WFhbo1asXLl26VIcRa66kpASLFy+Gl5cXLCws0KxZM6xYsUJlrip9q+eRI0fwv//9Dw0bNoREIsFvv/2msr469bl79y6GDx8OW1tb2NvbY9y4ccjLy/sPa1G1yuopl8sxb948tGnTBlZWVmjYsCFGjRqFjIwMlX3oez0fN2nSJEgkEnz44Ycqyw2lnklJSejfvz/s7OxgZWWFTp06IS0tTVxfX4+9TJ506KeffsKsWbOwdOlSxMbGol27dggNDUV2dnZdh6a1w4cPY8qUKTh58iT27dsHuVyO3r174/79+2KZsLAw/PHHH9i2bRsOHz6MjIwMDBw4sA6j1t7p06fxxRdfoG3btirLDaGO//77L7p27QpTU1Ps2bMH58+fx/vvvw8HBwexzLvvvouPP/4YGzZsQHR0NKysrBAaGoqCgoI6jFwza9aswfr16/Hpp58iKSkJa9aswbvvvotPPvlELKNv9bx//z7atWuHzz77rNz11anP8OHDce7cOezbtw+7du3CkSNHMHHixP+qCtVSWT3z8/MRGxuLxYsXIzY2Fr/++iuSk5PRv39/lXL6Xk9lO3bswMmTJ8udKsQQ6nn58mV069YNPj4+OHToEM6cOYPFixfD3NxcLFNvj70C6Uznzp2FKVOmiO9LSkqEhg0bCuHh4XUYlW5lZ2cLAITDhw8LgiAIOTk5gqmpqbBt2zaxTFJSkgBAiIqKqqswtXLv3j2hRYsWwr59+4Rnn31WmDFjhiAIhlPHefPmCd26datwvUKhENzc3IS1a9eKy3JycgSpVCr8+OOP/0WIOtGvXz/htddeU1k2cOBAYfjw4YIg6H89AQg7duwQ31enPufPnxcACKdPnxbL7NmzR5BIJEJ6evp/FrsmHq9neU6dOiUAEK5duyYIgmHV88aNG0KjRo2ExMREoUmTJsIHH3wgrjOUer766qvCiBEjKtymPh972fKkI0VFRYiJiUGvXr3EZUZGRujVqxeioqLqMDLdys3NBfBo8uOYmBjI5XKVevv4+MDT01Pv6j1lyhT069dPpS6A4dRx586d8Pf3x+DBg9GgQQN06NABX375pbj+6tWryMrKUqmnnZ0dAgIC9KqeQUFBiIyMxMWLFwEACQkJOHbsGPr27QvAcOpZpjr1iYqKgr29Pfz9/cUyvXr1gpGREaKjo//zmHUlNzcXEokE9vb2AAynngqFAiNHjsTcuXPx9NNPq603hHoqFArs3r0bTz31FEJDQ9GgQQMEBASo3Nqrz8deJk86cvv2bZSUlMDV1VVluaurK7KysuooKt1SKBSYOXMmunbtitatWwMAsrKyYGZmJh68yuhbvbdu3YrY2FiEh4errTOUOl65cgXr169HixYt8Pfff2Py5MmYPn06vvnmGwAQ66Lv3+H58+djyJAh8PHxgampKTp06ICZM2di+PDhAAynnmWqU5+srCw0aNBAZb2JiQkcHR31ss5AaV+YefPmYejQoeJksoZSzzVr1sDExATTp08vd70h1DM7Oxt5eXlYvXo1+vTpg7179+Kll17CwIEDcfjwYQD1+9hrUqefTnplypQpSExMxLFjx+o6FJ26fv06ZsyYgX379qncazc0CoUC/v7+WLVqFQCgQ4cOSExMxIYNGzB69Og6jk53fv75Z2zZsgU//PADnn76acTHx2PmzJlo2LChQdXzSSaXy/HKK69AEASsX7++rsPRqZiYGHz00UeIjY2FRCKp63BqjUKhAAAMGDAAYWFhAID27dvjxIkT2LBhA5599tm6DK9KbHnSEWdnZxgbG6s9BXDz5k24ubnVUVS6M3XqVOzatQsHDx5E48aNxeVubm4oKipCTk6OSnl9qndMTAyys7PRsWNHmJiYwMTEBIcPH8bHH38MExMTuLq66n0dAcDd3R2+vr4qy1q1aiU+2VJWF33/Ds+dO1dsfWrTpg1GjhyJsLAwsVXRUOpZpjr1cXNzU3twpbi4GHfv3tW7OpclTteuXcO+ffvEVifAMOp59OhRZGdnw9PTUzweXbt2DbNnz0bTpk0BGEY9nZ2dYWJiUuUxqb4ee5k86YiZmRn8/PwQGRkpLlMoFIiMjERgYGAdRlYzgiBg6tSp2LFjBw4cOAAvLy+V9X5+fjA1NVWpd3JyMtLS0vSm3iEhITh79izi4+PFl7+/P4YPHy7+rO91BICuXbuqDTNx8eJFNGnSBADg5eUFNzc3lXrKZDJER0frVT3z8/NhZKR6aDM2NhavdA2lnmWqU5/AwEDk5OQgJiZGLHPgwAEoFAoEBAT85zFrqyxxunTpEvbv3w8nJyeV9YZQz5EjR+LMmTMqx6OGDRti7ty5+PvvvwEYRj3NzMzQqVOnSo9J9fr8Uqfd1Q3M1q1bBalUKnz99dfC+fPnhYkTJwr29vZCVlZWXYemtcmTJwt2dnbCoUOHhMzMTPGVn58vlpk0aZLg6ekpHDhwQPjnn3+EwMBAITAwsA6jrjnlp+0EwTDqeOrUKcHExER45513hEuXLglbtmwRLC0the+//14ss3r1asHe3l74/fffhTNnzggDBgwQvLy8hAcPHtRh5JoZPXq00KhRI2HXrl3C1atXhV9//VVwdnYW3nzzTbGMvtXz3r17QlxcnBAXFycAENatWyfExcWJT5lVpz59+vQROnToIERHRwvHjh0TWrRoIQwdOrSuqlSuyupZVFQk9O/fX2jcuLEQHx+vcjwqLCwU96Hv9SzP40/bCYJh1PPXX38VTE1NhY0bNwqXLl0SPvnkE8HY2Fg4evSouI/6euxl8qRjn3zyieDp6SmYmZkJnTt3Fk6ePFnXIdUIgHJfERERYpkHDx4Ib7zxhuDg4CBYWloKL730kpCZmVl3QevA48mTodTxjz/+EFq3bi1IpVLBx8dH2Lhxo8p6hUIhLF68WHB1dRWkUqkQEhIiJCcn11G02pHJZMKMGTMET09PwdzcXPD29hYWLlyocoLVt3oePHiw3L/D0aNHC4JQvfrcuXNHGDp0qGBtbS3Y2toKY8eOFe7du1cHtalYZfW8evVqhcejgwcPivvQ93qWp7zkyVDquWnTJqF58+aCubm50K5dO+G3335T2Ud9PfZKBEFp2F0iIiIiqhT7PBERERFpgMkTERERkQaYPBERERFpgMkTERERkQaYPBERERFpgMkTERERkQaYPBERERFpgMkTERERkQaYPBERERFpgMkTEVEdO3PmDCQSSZ29iEgzJnUdABHRk27nzp3gTFlE+oMtT0REdaiwsBDm5uZ1HQYRaYDJExHVme7du2PmzJl1HYZGunfvLt7uio+Pr/H+IiMjERISUvPAtDRmzBixPr/99ludxUGkT5g8EVGtqKqfzbJly/Drr79ixYoVdR2qKCwsDAMHDqyy3IQJE5CZmYnWrVvX+DPj4uLQoUOHGu+nzNixY7Fo0aJql//oo4+QmZmps88nehKwzxMR1QrlE/JPP/2EJUuWIDk5WVxmbW0Na2vrugitQqdOnUK/fv2qLGdpaQk3N7caf55CoYCxsXGN91OmpKQEu3btwu7du6u9jZ2dHezs7HQWA9GTgC1PRFQr3NzcxJednR0kEonKMmtra7Xbdt27d8e0adMwc+ZMODg4wNXVFV9++SXu37+PsWPHwsbGBs2bN8eePXvEbRQKBcLDw+Hl5QULCwu0a9cOv/zyi0axFhUVwdTUFCdOnMDChQshkUjQpUsXjfZx8uRJhISEwMnJSa2VTSaTlbvNsWPH0LVrV5VlqampkEgk2L59O4KDg2FhYYFOnTohLS0NR48eRZcuXWBpaYmQkBDk5OSobHvixAmYmpqiU6dO4rKvvvoKbdu2hYWFBezs7NCzZ0+N6kVE6pg8EVG98s0338DZ2RmnTp3CtGnTMHnyZAwePBhBQUGIjY1F7969MXLkSOTn5wMAwsPD8e2332LDhg04d+4cwsLCMGLECBw+fLjan2liYoLjx48DAOLj45GZmYm//vqr2tsnJCSge/fu6NChA44ePYq//voLjo6OCAkJwU8//QRbW1sAwP3791W2O378uFrylJCQAABYv349Vq1ahRMnTuDmzZsYMWIEVq9ejU8//RQHDx5EQkICIiIiVLbduXMn/ve//4nDD/z666948803sXjxYiQnJ+PEiROYPXt2tetFROXjbTsiqlfatWsn9tlZsGABVq9eDWdnZ0yYMAEAsGTJEqxfvx5nzpxBhw4dsGrVKuzfvx+BgYEAAG9vbxw7dgxffPEFnn322Wp9ppGRETIyMuDk5IR27dppHPP06dMxcOBAvPfeewAAX19fDB06FDExMXjllVcgCALef/99REZGqrWaGRmpXsPGx8fD0dERP/30E5ycnAAAzz77LI4dO4Zz587B0tISANCpUydkZWWpbPv777/jgw8+EN8nJyejSZMmeO6552Bvbw8AePrppzWuHxGpYssTEdUrbdu2FX82NjaGk5MT2rRpIy5zdXUFAGRnZyMlJQX5+fl47rnnxD5U1tbW+Pbbb3H58mWNPjcuLk6rxOnmzZs4duwY3njjDZXlVlZWYguQRCLB7NmzkZGRId5qi42NRceOHdX2l5CQgJdeeklMnAAgLS0Nr776qpg4lS3z8vIS3yclJSEjI0Plyb0JEyZAEAQ4OjrC2toaV69e1bh+RKSOyRMR1SumpqYq7yUSicqysoREoVAgLy8PALB7927Ex8eLr/Pnz2vc7yk+Pl6r5CkmJgYKhUJt25iYGPj7+6vEPWDAAOzcuRNAxUMUxMfHIyAgQGVZQkKCSh+sgoICJCcnq3zmzp078dxzz4ljRsnlcgwZMgRBQUE4ffo04uPj0bRpU43rR0TqmDwRkd7y9fWFVCpFWloamjdvrvLy8PDQaF9nz55F+/btNY5BoVAAUO3PdObMGRw5cgTDhg1TKTto0CBs374dQGkndTMzM5X1MpkMqampKkMXXL16Fbm5uSrLzp49C0EQVFrkfv/9dwwYMEB8v2PHDqSkpODzzz+Hn58fmjdvzqlYiHSEfZ6ISG/Z2Nhgzpw5CAsLg0KhQLdu3ZCbm4vjx4/D1tYWo0ePrva+FAoFkpOTkZGRASsrq2o/vh8QEAALCwvMnTsXCxcuxOXLlzFlyhRMmTJF7Ym9du3a4fLly4iNjUXLli3V9pWQkABjY2OV8aPK+kA1adJEZVmzZs3EoR6ys7Pxzz//iK1aQGlylpmZie+++w7PPPMM8vLycPz4cYwbNw4mJjz0E9UEW56ISK+tWLECixcvRnh4OFq1aoU+ffpg9+7dKv2Bvv766ypbXVauXImvv/4ajRo1wsqVK6v9+S4uLvj5559x6tQptG3bFjNmzMDUqVPx/vvvl1v++eefx8yZM9G3b1+1dQkJCWjZsqXKdC0JCQlqg2gmJCSo3LL7448/0LlzZzg7O4vLhgwZgqlTp+Ktt97CU089hV69euHIkSNMnIh0QCJwNkoiMnBLly7F4cOHcejQoRrvq3v37mjfvj0+/PBDrbaPjo7GqlWr8Pvvv9c4ljL9+/dHt27d8Oabb2q9D4lEgh07duDFF1/UWVxEhootT0Rk8Pbs2YN3331XZ/v7/PPPYW1tjbNnz2q8befOnREeHq6zWACgW7duGDp0qFbbTpo0qd6N9E5U37HliYhIA+np6Xjw4AEAwNPTU63Tt77Jzs4WR0B3d3eHlZVVHUdEVP8xeSIiIiLSAG/bEREREWmAyRMRERGRBpg8EREREWmAyRMRERGRBpg8EREREWmAyRMRERGRBpg8EREREWmAyRMRERGRBpg8EREREWmAyRMRERGRBv4P8OOJjqiJMKwAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = sim.configuration.N # Number of particles\n", "\n", "plt.figure()\n", "plt.plot(time, U/N)\n", "plt.xlabel(r'Time, $t$ [$\\sigma\\sqrt{m/\\varepsilon}$]') # Time in LJ units\n", "plt.ylabel(r'Potential energy per particle, $U$ [$\\varepsilon$]') # Energy in LJ units\n", "plt.xlim(0, None)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "32c872d6a4d0e40d", "metadata": {}, "source": [ "The first part of the simulation show large fluctuations in the potential energy since the system is not yet equilibrated (it was setup in a perfect crystal). Since we are not interested in the equilibration phase, we can discard the fir st timeblock by using the `first_block=1` argument in the `extract_scalars` function. We then need to recalculate the time array." ] }, { "cell_type": "code", "execution_count": 27, "id": "8fc00eb8a9982271", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.315603783Z", "start_time": "2025-05-09T08:29:36.202148Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U, W, K = gp.extract_scalars(sim.output, ['U', 'W', 'K'], first_block=1)\n", "time = np.arange(len(U)) * dt * steps_between_output\n", "\n", "plt.figure()\n", "plt.plot(time, U/N, label='Potential energy per particle')\n", "plt.xlabel(r'Time, $t$ [$\\sigma\\sqrt{m/\\varepsilon}$]') # Time in LJ units\n", "plt.ylabel(r'Energy [$\\varepsilon$]') # Energy in LJ units\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "3100c824223f3433", "metadata": {}, "source": [ "After we have ensured that we have an equilibrium simulation, the expectation value of the potential energy per particle can be found with the `np.mean` NumPy function." ] }, { "cell_type": "code", "execution_count": 28, "id": "84cdd1e4317e81ca", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.315861630Z", "start_time": "2025-05-09T08:29:36.303617Z" } }, "outputs": [ { "data": { "text/plain": [ "np.float32(-6.281101)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(U/N)" ] }, { "cell_type": "markdown", "id": "b67418bdee40433a", "metadata": {}, "source": [ "In an $NVT$ simulation the pressure is often an important quantity, but is not stored in the simulation data directly. The pressure can be calculated from the virial, $W$. Recall,\n", "\n", "$$\n", " pV = Nk_BT + W\n", "$$\n", "\n", "where $p$ is the pressure, $V$ is the volume, $N$ is the number of particles, $k$ is the Boltzmann constant and $T$ is the temperature. The volume can be calculated from the box lengths. In Lennard-Jones units boltzmann constant is $k_B = 1$. Below we use this to calculate the pressure." ] }, { "cell_type": "code", "execution_count": 29, "id": "efefc91dd982ae25", "metadata": { "ExecuteTime": { "end_time": "2025-05-26T18:49:57.316088991Z", "start_time": "2025-05-09T08:29:36.361215Z" } }, "outputs": [ { "data": { "text/plain": [ "np.float32(1.4027747)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "V = sim.configuration.get_volume() # Volume\n", "dof = 3*N - 3 # Degrees of freedom\n", "T_kin = 2*K/dof # Kinetic temperature\n", "p = (N*T_kin + W)/V # Pressure\n", "np.mean(p) # Mean pressure" ] }, { "cell_type": "markdown", "id": "27ad045fdfbc27e3", "metadata": {}, "source": [ "## Concluding remarks\n", "Congratulations! You have now set up and executed your first simulation with `gamdpy`.\n", "Simulation data have been stored to the disk for later analysis." ] } ], "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": "3.11.2" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 5 }