{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Walkthrough" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The magcolloids module provides the class `sim`, which contains the simulation parameters.\n", "After a `sim` object is created, it can be used to generate a lammps input script, run it and read it's results. \n", "\n", "The basic usage of the module consists of defining a `sim` object." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import sys\n", "import os\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "\n", "sys.path.insert(0, '../../')\n", "\n", "import magcolloids as mgc\n", "\n", "%reload_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### To run simulations from any directory\n", "In the imports above, the command `sys.path.insert(0, '../../')` adds a folder to the current kernel's path. This is useful if you want to use the program without placing the folder in the system path. The kernel's path is reset to default when the kernel is restarted. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Units\n", "\n", "The package defines a set of units using [`pint`](https://pint.readthedocs.io/en/latest/). This helps keep consistent units across the program, and allows the user to introduce the parameter in different units. \n", "\n", "`pint` works by defining a unit registry. The unit registry used within the package is accessed by:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "ureg = mgc.ureg" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To assign a unit to a quantity its as simple as multiplying. For example:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3 micrometer\n" ] } ], "source": [ "d = 3*ureg.um\n", "print(d)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Afterwards, we can convert this to other units, as in:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "3×10-6 meter" ], "text/latex": [ "$3\\times 10^{-6}\\ \\mathrm{meter}$" ], "text/plain": [ "3e-06 " ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d.to(ureg.m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Parameter objects" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are three objects that need to be defined before a simulation can be performed:\n", "* `particles`\n", "* `field`\n", "* `world`\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Details of the definition can be found in the API.\n", "\n", "### `particles` Object\n", "A `particles` object defines the properties of a set of particles. For a simulation, several `particles` objects can be used (future), to have polydisperse mixture of particles. The object also includes an array of initial conditions. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "region, initial_conditions = mgc.initial_setup(150, packing = 0.3, height = 4, radius = 1.4)\n", "\n", "particles = mgc.particles(\n", " initial_conditions*ureg.um,\n", " radius = 1.4*ureg.um,\n", " susceptibility = 0.4,\n", " diffusion=0.07*ureg.um**2/ureg.s,\n", " density = 1000*ureg.kg/ureg.m**3,\n", " temperature=300*ureg.K)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the cell above, we use the function `initial_setup` that creates a region of a certain size, and a set of particles. This function is useful for setting the initial conditions of a system with a predetermined packing fraction. The resulting array can be directly input to the `copy` method to create many particles. \n", "\n", "Notice how most of the parameters have units. The susceptibility is an exception, because it is an adimentional unit. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Temperature of the `particles` object" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the `temperature` defined above is only a way to convert the diffusion coefficient to a drag coefficient. The actual temperature of the system is defined below in the `world` parameters. Another alternative is to define the `drag` coefficient, and then the `temperature` parameter is not necessary here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `field` Object" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `field` object defines exclusively the magnetic field. The easiest option is to use the definition below, where the parameters of `magnitude`, `frequency` and `angle` are used to calculate a rotating field with a $\\hat{z}$ component. There are three more arguments, `fieldx`, `fieldy`, `fieldz`, which can accept strings to be evaluated as lammps variables (see below). The field magnitude can be given in any units, but should be the magnetic flux density $\\bf{B}$, as opposed to the magnetic field intensity $\\bf{H}$\n", "\n", "As an alternative, these values can also be passed as lammps parseable strings (see details of how to define functions in lammps in the [lammps docs](http://lammps.sandia.gov/doc/variable.html)). The biggest disadvantage of this approach, is that the units can't be checked for consistency, and they have to be given in $\\textrm{pg}, $\\mu{}\\textrm{m}$, and $\\mu\\textrm{s}$. The angle must be in radians\n", "\n", "Furthermore, the magnitude of the field has strange units in lammps (due to their deffinition of the dipole-dipole interaction), and must be therefore given by:\n", "\n", "$$\\bf{H}_{lammps} = \\frac{\\bf{B}_{m\\mathrm{T}}}{\\mu_0}\\times10/2.99$$.\n", "\n", "All this should be clarified in the future. For the moment, a simple rotating field can be defined by:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "field = mgc.field(magnitude = 5*ureg.mT, frequency = 10*ureg.Hz, angle = 15*ureg.degrees)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### world Object\n", "\n", "The `world` object defines characteristics of the world like the temperature, the region, and the interaction parameters. In the example below we use the `region` array defined before by the `initial_conditions` command. \n", "\n", "It's important to mention that the seed is defined when a world is defined, so that if the world is reused, the seed remains the same. However, the `world` object has a `reset_seed` method that can be used to set a new seed. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "world = mgc.world(particles, temperature = 300*ureg.K,\n", " region=region*ureg.um, boundaries = ['p','p','f'], walls = [False,False,True],\n", " dipole_cutoff = 20*ureg.um)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finaly all the three objects, `particle_array`, `field`, and `world` can be used to create a simulation object. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## `simulation` Object\n", "\n", "The simulation object accepts the final set of parameters, such as the total time, the simulation type, the number of parallel cores, or the place where the simulation has to be saved. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "sim = mgc.sim(dir_name = \"/Users/aortiza/Desktop/\",\n", " timestep = 1e-4*ureg.s, framerate = 30*ureg.Hz, total_time = 60*ureg.s,\n", " particles = particles, world = world, field = field)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before running the simulation, the simulation object needs to create the scripts. This method creates a lammps input script." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "sim.generate_scripts()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `run()` method uses the operating system interface to run the script generated in the command line. It saves the output in the same directory, in a `.lammpstrj` file." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "sim.run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## `simulation` load\n", "\n", "To load the simulation, the easiest and more efficient option is to use the `load` method" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "sim.load()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `load` method creates a subobject `lazy_read`, that stores the position in the `.lammpstrj` file of every timestep. This allows us to selectively load certain frames faster, which is very useful for large files." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "trj = sim.lazy_read[::10]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Displaying results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are several ways to display results in the support functions. However, the most common one is as an animation. For this, we can use the `display_animation_direct()` function:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import HTML\n", "\n", "HTML(mgc.display_animation_direct(sim,trj,speedup=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Be careful. This function returns a HTML5 video object. If the `HTML` function is not used, jupyter will try to display as a string the contents of the HTML5, wich will likely result in a hung system. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Checking that simulation has correct parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bellow we do some tests to the simulation framework to ensure that things are working" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Freely diffusing particle" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We simulate a freely diffusing particle in three dimensions, and we compare the resulting MSD to the diffusion coefficient that we give as input. This tells us that the damping coefficient is being set properly. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "region, initial_conditions = mgc.initial_setup(9, packing = 0.3, height = 4, radius = 1.4)\n", "\n", "initial_conditions = [[0,0,0]]\n", "particles = mgc.particles(\n", " initial_conditions*ureg.um,\n", " radius = 1.4*ureg.um,\n", " diffusion=0.07*ureg.um**2/ureg.s,\n", " density = 0*ureg.kg/ureg.m**3,\n", " temperature=300*ureg.K)\n", "\n", "field = mgc.field(magnitude = 0*ureg.mT, frequency = 10*ureg.Hz, angle = 15*ureg.degrees)\n", "world = mgc.world(particles, temperature = 300*ureg.K,\n", " region=region*ureg.um, boundaries = ['s','s','s'], walls = [False,False,False],\n", " dipole_cutoff = 20*ureg.um)\n", "\n", "sim = mgc.sim(dir_name = \"/Users/aortiza/Desktop/\",\n", " timestep = 1e-3*ureg.s, framerate = 30*ureg.Hz, total_time = 60*ureg.s,\n", " particles = particles, world = world, field = field)\n", "\n", "sim.generate_scripts()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "sim.run()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "sim.load()\n", "trj = sim.lazy_read[::]" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'z $\\\\mu{}m$')" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, (ax1,ax2) = plt.subplots(1,2,figsize=(10,5))\n", "\n", "ax1.plot(trj.x,trj.y)\n", "ax1.set_xlabel(r\"x $\\mu{}m$\")\n", "ax1.set_ylabel(r\"y $\\mu{}m$\")\n", "\n", "ax2.plot(trj.x,trj.z)\n", "ax2.set_xlabel(r\"x $\\mu{}m$\")\n", "ax2.set_ylabel(r\"z $\\mu{}m$\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### MSD and Diffusion Coefficient" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "import trackpy as tp" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "idx = pd.IndexSlice\n", "trj_msd = trj.loc[idx[:,1],:].filter([\"x\",\"y\"])\n", "trj_msd = trj_msd.reset_index(level=[1])\n", "trj_msd['frame'] = range(len(trj_msd.index))\n", "\n", "run_step = int(np.round(sim.total_time.to(ureg.s)/sim.timestep.to(ureg.s)))\n", "fps = sim.framerate.to(ureg.Hz).magnitude\n", "\n", "msd = tp.msd(trj_msd,1,fps,max_lagtime=int(run_step))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\aortiza\\Anaconda3\\lib\\site-packages\\pint\\quantity.py:1377: UnitStrippedWarning: The unit of the quantity is stripped.\n", " warnings.warn(\"The unit of the quantity is stripped.\", UnitStrippedWarning)\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, 'MSD\\xa0[$\\\\mu{}m^2$]')" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "D = (4*(ureg.pN*ureg.nm)/sim.particles.drag).to(ureg.um**2/ureg.s)\n", "\n", "plt.loglog(msd.lagt,msd.msd)\n", "plt.loglog([1/fps,10],4*D*np.array([1/fps,10]));\n", "plt.xlabel(\"\\Delta t [s]\")\n", "plt.ylabel(\"MSD [$\\mu{}m^2$]\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice here that the diffusion is being calculated as $MSD = 4Dt$. This is because the MSD calculated by the [`trackpy`](https://soft-matter.github.io/trackpy/v0.3.2/tutorial/walkthrough.html) package is in 2D. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two magnetic particles" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now test that the dipole moment is correct by placing two particles close to each other and observing the distance between then. We do this at very low temperature ($1K$) to obtain almost deterministic curves. We define two confining walls to prevent the particles from towering." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "region, initial_conditions =mgc.initial_setup(9, packing = 0.3, height = 3, radius = 1.4)\n", "\n", "initial_conditions = [[-1.4,0,0],[1.4,0,0]]\n", "particles = mgc.particles(\n", " initial_conditions*ureg.um,\n", " radius = 1.4*ureg.um,\n", " diffusion=0.07*ureg.um**2/ureg.s,\n", " density = 0*ureg.kg/ureg.m**3,\n", " temperature=300*ureg.K)\n", "\n", "field = mgc.field(magnitude = 3*ureg.mT, frequency = 0*ureg.Hz, angle = 0*ureg.degrees)\n", "world = mgc.world(particles, temperature = 1*ureg.K,\n", " region=region*ureg.um, boundaries = ['s','s','f'], walls = [False,False,True],\n", " dipole_cutoff = 20*ureg.um)\n", "\n", "sim = mgc.sim(dir_name = \"/Users/aortiza/Desktop/\",\n", " timestep = 1e-3*ureg.s, framerate = 30*ureg.Hz, total_time = 60*ureg.s,\n", " particles = particles, world = world, field = field)\n", "\n", "sim.generate_scripts()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "sim.run()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "sim.load()\n", "trj = sim.lazy_read[::]" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "distance = (\n", " trj.loc[idx[:,1],:].reset_index(level=[1]) - \\\n", " trj.loc[idx[:,2],:].reset_index(level=[1]) ).filter([\"x\",\"y\",\"z\"])\n", "distance = np.sqrt(distance.x**2+distance.y**2+distance.z**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model for the distance between the dipoles, as a function of time, is well known and often used for susceptibility calibration in experiments. The distance is given by:\n", "\n", "$$d = \\sqrt[5]{5At+(2\\sigma)^5}$$\n", "\n", "where $\\sigma$ is the particle radius, $A$ is:\n", "\n", "$$A \\equiv \\frac{8\\pi}{3\\mu_0\\gamma}\\left(\\sigma^3\\chi\\bf{B}\\right)^2$$\n", "\n", "and $\\gamma = \\frac{k_bT}{D}$ is the drag coefficient." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'distance [$\\\\mu{m}$]')" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sgm = sim.particles.radius\n", "B = sim.field.magnitude\n", "drag = sim.particles.drag\n", "mu0 = (4e5*np.pi)*ureg.pN/ureg.A**2\n", "xi = sim.particles.susceptibility\n", "\n", "A = (8*np.pi/(3*mu0*drag)*(sgm**3*xi*B)**2).to(ureg.um**5/ureg.s)\n", "\n", "t = np.linspace(0,60,1000)*ureg.s\n", "plt.plot(t,(5*A*t+(2*sgm)**5)**(1/5))\n", "plt.plot(distance.index.values*sim.timestep,distance.values)\n", "\n", "plt.legend(['d_{ij}','$\\sqrt[5]{5At+2\\sigma^5}$'])\n", "plt.xlabel(\"time [s]\")\n", "plt.ylabel(\"distance [$\\mu{m}$]\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The agreement between the two curves tells us that the dipolar interaction is being calculated correctly." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gravity" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The prescence of gravity in the simulations is the recent addition. The gravitational force is calculated from the density parameter, which in reality corresponds to the excess density ($\\rho_{ex} \\equiv \\rho_{colloid}-\\rho_{medium}$)\n", "To see if it is working correctly, we run a simulation of many particles in a losely packed system. " ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "region, initial_conditions = mgc.initial_setup(150, packing = 0.1, height = 4, radius = 1.4)\n", "\n", "particles = mgc.particles(\n", " initial_conditions*ureg.um,\n", " radius = 1.4*ureg.um,\n", " diffusion=0.07*ureg.um**2/ureg.s,\n", " density = 1e3*ureg.kg/ureg.m**3,\n", " temperature=300*ureg.K)\n", "\n", "field = mgc.field(magnitude = 5*ureg.mT, frequency = 10*ureg.Hz, angle = 15*ureg.degrees)\n", "world = mgc.world(particles, temperature = 300*ureg.K,\n", " region=region*ureg.um, boundaries = ['p','p','f'], walls = [False,False,True],\n", " dipole_cutoff = 20*ureg.um)\n", "\n", "\n", "sim = mgc.sim(dir_name = \"/Users/aortiza/Desktop/\",\n", " timestep = 1e-3*ureg.s, framerate = 30*ureg.Hz, total_time = 60*ureg.s,\n", " particles = particles, world = world, field = field)\n", "\n", "sim.generate_scripts()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "sim.run()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "sim.load()\n", "trj = sim.lazy_read[::10]" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HTML(mgc.display_animation_direct(sim,trj,speedup=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see how many particles are now in the lower configuration. It will be interesting to observe the structure formed by the particles that are in the top. " ] } ], "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": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }