HardDisks(quadtree).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Phase transition in a hard-disk fluid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "include(\"gnuplot.jl\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The box\n",
    "\n",
    "A box is created with random points. This points will become the centers of particles of a given radius. Notice that the distance from point to point (or center to center) restricts the possible radii that the particles can take without overlapping. To get any desired radius is just a matter of rescaling the system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "ename": "ErrorException",
     "evalue": "invalid redefinition of constant QuadTree",
     "output_type": "error",
     "traceback": [
      "invalid redefinition of constant QuadTree",
      "",
      "Stacktrace:",
      " [1] top-level scope at none:0"
     ]
    }
   ],
   "source": [
    "mutable struct Particle\n",
    "    x::Float64\n",
    "    y::Float64\n",
    "    radius::Float64\n",
    "end\n",
    "\n",
    "struct Rectangle\n",
    "    w::Float64\n",
    "    h::Float64\n",
    "    x::Float64\n",
    "    y::Float64\n",
    "end\n",
    "\n",
    "mutable struct QuadTree\n",
    "    boundary::Rectangle\n",
    "    capacity::Int\n",
    "    particles::Vector{Particle}\n",
    "    divided::Bool\n",
    "    tr::QuadTree\n",
    "    tl::QuadTree\n",
    "    br::QuadTree\n",
    "    bl::QuadTree\n",
    "    QuadTree(boundary, capacity) = new(boundary, capacity,\n",
    "        [], false)\n",
    "end\n",
    "\n",
    "mutable struct Box\n",
    "    width::Float64\n",
    "    height::Float64\n",
    "    \n",
    "    particles::Vector{Particle}\n",
    "    \n",
    "    quadtree::QuadTree\n",
    "    \n",
    "    function Box(n::Int, radii::Vector{Float64})\n",
    "        # Random particles inside a unit box.\n",
    "        particles = [Particle(rand(),rand(),rand(radii)) for i in 1:n]\n",
    "        \n",
    "        # Get minimum separation distance between all\n",
    "        # pairs of points.\n",
    "        ii::Int = 1\n",
    "        jj::Int = 1\n",
    "        d2::Float64 = Inf\n",
    "        for i in 1:n-1\n",
    "            p::Particle = particles[i]\n",
    "            for j in i+1:n\n",
    "                q::Particle = particles[j]\n",
    "                rx::Float64 = p.x - q.x\n",
    "                ry::Float64 = p.y - q.y\n",
    "                r2::Float64 = rx*rx + ry*ry\n",
    "                if r2 < d2\n",
    "                    ii = i\n",
    "                    jj = j\n",
    "                    d2 = r2\n",
    "                end\n",
    "            end\n",
    "        end\n",
    "        d::Float64 = sqrt(d2)/2.0 - 1e-10\n",
    "\n",
    "        # Scale the system to get d to have two times\n",
    "        # the size of the maximum possible radius.\n",
    "        maxRadius = maximum(radii)\n",
    "        particles[ii].radius = maxRadius\n",
    "        particles[jj].radius = maxRadius\n",
    "        f::Float64 = 2*maxRadius/d # scaling factor\n",
    "        for p in particles\n",
    "            p.x = f * p.x + maxRadius\n",
    "            p.y = f * p.y + maxRadius\n",
    "        end\n",
    "        width = f + 2*maxRadius\n",
    "        height = width    \n",
    "        \n",
    "        # Define space partitioning structure\n",
    "        qt = QuadTree(Rectangle(width, height, 0, 0), 4)\n",
    "        for p in particles; insert!(qt, p); end\n",
    "        \n",
    "        return new(width, height, particles, qt)\n",
    "    end\n",
    "end\n",
    "\n",
    "function getDensity(box::Box)\n",
    "    area::Float64 = 0\n",
    "    for p in box.particles\n",
    "        r::Float64 = p.radius\n",
    "        area += π*r*r\n",
    "    end\n",
    "    return area / (box.width * box.height)\n",
    "end\n",
    "\n",
    "function contains(r::Rectangle, p::Particle)\n",
    "    return r.x < p.x < r.x + r.w && r.y < p.y < r.y + r.h\n",
    "end\n",
    "\n",
    "function intersects(r::Rectangle, p::Particle)\n",
    "    halfwidth::Float64 = r.w/2\n",
    "    halfheight::Float64 = r.h/2\n",
    "    x::Float64 = r.x\n",
    "    y::Float64 = r.y\n",
    "    radius::Float64 = p.radius\n",
    "\n",
    "    # Get distance from circle's center to box's center\n",
    "    dx_circle2center::Float64 = abs(p.x - (x + halfwidth))\n",
    "    dy_circle2center::Float64 = abs(p.y - (y + halfheight))\n",
    "\n",
    "    if (dx_circle2center > halfwidth + radius); return false; end\n",
    "    if (dy_circle2center > halfheight + radius); return false; end\n",
    "\n",
    "    # Get distance from circle's center to box's corner\n",
    "    dx_circle2edge::Float64 = dx_circle2center - halfwidth\n",
    "    dy_circle2edge::Float64 = dy_circle2center - halfheight\n",
    "    drdr_circle2corner::Float64 = dx_circle2edge * dx_circle2edge + \n",
    "                                  dy_circle2edge * dy_circle2edge\n",
    "\n",
    "    if (dx_circle2center < halfwidth); return true; end\n",
    "    if (dy_circle2center < halfheight); return true; end\n",
    "    return drdr_circle2corner < radius*radius\n",
    "end\n",
    "\n",
    "function subdivide!(qt::QuadTree)\n",
    "    w::Float64 = qt.boundary.w/2.0\n",
    "    h::Float64 = qt.boundary.h/2.0\n",
    "    x::Float64 = qt.boundary.x\n",
    "    y::Float64 = qt.boundary.y\n",
    "    \n",
    "    trb = Rectangle(w, h, x+w, y+h)\n",
    "    tlb = Rectangle(w, h, x,   y+h)\n",
    "    brb = Rectangle(w, h, x+w, y)\n",
    "    blb = Rectangle(w, h, x,   y)\n",
    "    \n",
    "    n::Int = qt.capacity\n",
    "    qt.tr = QuadTree(trb, n)\n",
    "    qt.tl = QuadTree(tlb, n)\n",
    "    qt.br = QuadTree(brb, n)\n",
    "    qt.bl = QuadTree(blb, n)\n",
    "    qt.divided = true\n",
    "end\n",
    "\n",
    "function search(qt::QuadTree, p::Particle)\n",
    "    if     contains(qt.tr.boundary, p); return qt.tr\n",
    "    elseif contains(qt.tl.boundary, p); return qt.tl\n",
    "    elseif contains(qt.br.boundary, p); return qt.br\n",
    "    else   contains(qt.bl.boundary, p); return qt.bl\n",
    "    end\n",
    "end\n",
    "\n",
    "isAtCapacity(qt::QuadTree) = length(qt.particles) == qt.capacity\n",
    "\n",
    "function insert!(qt::QuadTree, p::Particle)\n",
    "    current::QuadTree = qt\n",
    "    while current.divided\n",
    "        current = search(current, p)\n",
    "    end\n",
    "    if isAtCapacity(current)\n",
    "        subdivide!(current)\n",
    "        current = search(current, p)\n",
    "    end\n",
    "    push!(current.particles, p)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hard-disks collisions, a montecarlo process\n",
    "\n",
    "Instead of physically colliding disks inside the box, we are simulating their dynamics with a montecarlo process:\n",
    "\n",
    "- Randomly pick a disk inside the box and move it in a random direction with magnitude between 0 and 1. \n",
    "- If the particle overlaps with another one or if it leaves the box, then return particle to original position.\n",
    "\n",
    "We can also reduce the volume of the box cuasi-statically to reach an optimal packing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "incrementVolume! (generic function with 1 method)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function overlaps(p::Particle, qt::QuadTree)\n",
    "    quadtrees::Vector{QuadTree} = [qt]\n",
    "    while length(quadtrees) > 0\n",
    "        current::QuadTree = pop!(quadtrees)\n",
    "        if current.divided\n",
    "            if intersects(current.tr.boundary, p)\n",
    "                push!(quadtrees, current.tr)\n",
    "            end\n",
    "            if intersects(current.tl.boundary, p)\n",
    "                push!(quadtrees, current.tl)\n",
    "            end\n",
    "            if intersects(current.br.boundary, p)\n",
    "                push!(quadtrees, current.br)\n",
    "            end\n",
    "            if intersects(current.bl.boundary, p)\n",
    "                push!(quadtrees, current.bl)\n",
    "            end\n",
    "        end\n",
    "\n",
    "        # If there's at least one overlap then\n",
    "        # just return true.\n",
    "        for q in current.particles\n",
    "            if p === q; continue; end\n",
    "            d::Float64 = p.radius + q.radius\n",
    "            rx::Float64 = p.x - q.x\n",
    "            ry::Float64 = p.y - q.y\n",
    "            if rx*rx + ry*ry < d*d\n",
    "                return true\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    return false\n",
    "end\n",
    "\n",
    "function getFirstNonEmptyNonDivided(qt::QuadTree)\n",
    "    quadtrees::Vector{QuadTree} = [qt]\n",
    "    while length(quadtrees) > 0\n",
    "        current::QuadTree = pop!(quadtrees)\n",
    "        if current.divided\n",
    "            push!(quadtrees, current.tr,\n",
    "                current.tl, current.br, current.bl)\n",
    "        elseif length(current.particles) > 0\n",
    "            return current\n",
    "        end\n",
    "    end\n",
    "    return qt\n",
    "end\n",
    "\n",
    "function findLocation(p::Particle, qt::QuadTree)\n",
    "    current::QuadTree = qt\n",
    "    while current.divided\n",
    "        for q in current.particles\n",
    "            if p === q; return current; end\n",
    "        end\n",
    "        current = search(current, p)\n",
    "    end\n",
    "    return current\n",
    "end\n",
    "\n",
    "function montecarlo!(box::Box)\n",
    "    # Random disk\n",
    "    p::Particle = rand(box.particles)\n",
    "    radius::Float64 = p.radius\n",
    "    # Find p's location before moving it.\n",
    "    location::QuadTree = findLocation(p, box.quadtree)\n",
    "    \n",
    "    # Random movement of magnitude ∈ (0,radius).\n",
    "    x::Float64 = -1 + 2*rand()\n",
    "    y::Float64 = -1 + 2*rand()\n",
    "    n::Float64 = sqrt(x*x + y*y) # Norm\n",
    "    A::Float64 = rand() * radius # Random amplitude\n",
    "    x = p.x + A*x/n\n",
    "    y = p.y + A*y/n\n",
    "    \n",
    "    # Update particle position but save its previous\n",
    "    # just in case there's an overlap.\n",
    "    xp::Float64 = p.x\n",
    "    yp::Float64 = p.y\n",
    "    p.x = x\n",
    "    p.y = y\n",
    "    \n",
    "    # Are there any overlaps inside the box?\n",
    "    w::Float64 = box.width\n",
    "    h::Float64 = box.height\n",
    "    if (radius < x < w - radius) && (radius < y < h - radius)\n",
    "        if overlaps(p, box.quadtree)\n",
    "            p.x = xp\n",
    "            p.y = yp\n",
    "            return\n",
    "        end\n",
    "        for q in box.particles\n",
    "            if p === q; continue; end\n",
    "            if overlaps(q, box.quadtree)\n",
    "                p.x = xp\n",
    "                p.y = yp\n",
    "                return\n",
    "            end\n",
    "        end\n",
    "        # At this point we know there are no overlaps.\n",
    "        # If p's container is not divided just re-insert p.\n",
    "        # else find a non-empty, non-divided container and\n",
    "        # replace p for a particle in that container, then\n",
    "        # re-insert p.\n",
    "        k::Int = findfirst(x -> x === p, location.particles)\n",
    "        deleteat!(location.particles, k)\n",
    "        insert!(box.quadtree, p)\n",
    "        if location.divided\n",
    "            subqt::QuadTree = getFirstNonEmptyNonDivided(location)\n",
    "            if subqt !== location\n",
    "                replacement::Particle = pop!(subqt.particles)\n",
    "                push!(location.particles, replacement)\n",
    "            end\n",
    "        end\n",
    "    else\n",
    "        p.x = xp\n",
    "        p.y = yp\n",
    "    end\n",
    "end\n",
    "\n",
    "function reduceVolume!(box::Box)\n",
    "    w::Float64 = box.width\n",
    "    \n",
    "    rx2wall::Float64 = Inf\n",
    "    ry2wall::Float64 = Inf\n",
    "    for p in box.particles\n",
    "        x::Float64 = w - p.x - p.radius\n",
    "        y::Float64 = w - p.y - p.radius\n",
    "        if x < rx2wall; rx2wall = x; end\n",
    "        if y < ry2wall; ry2wall = y; end\n",
    "    end\n",
    "    box.width = w - min(rx2wall, ry2wall)/2.0\n",
    "    box.height = box.width\n",
    "    boundary::Rectangle = Rectangle(box.width, box.height, 0, 0)\n",
    "    qt::QuadTree = QuadTree(boundary, box.quadtree.capacity)\n",
    "    for p in box.particles; insert!(qt, p); end\n",
    "    box.quadtree = qt\n",
    "end\n",
    "\n",
    "function incrementVolume!(box::Box)\n",
    "    box.width *= 1.001 # 0.1% increment\n",
    "    updateGrid!(box)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A fresh new box\n",
    "\n",
    "Let's start a new box with $n$ disks of radius $r$ and measure its packing fraction $\\phi$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.000033 seconds (111 allocations: 7.266 KiB)\n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "function test()\n",
    "    n::Int = 30\n",
    "    radii::Vector{Float64} = [0.5]\n",
    "    @time box::Box = Box(n,radii)\n",
    "    w::Float64 = box.width\n",
    "    h::Float64 = box.height\n",
    "    phi::Float64 = getDensity(box)\n",
    "\n",
    "    gp = gnuplot(20, 20)\n",
    "    println(gp,\n",
    "        \"set size ratio -1;\",\n",
    "        \"set tics out nomirror;\",\n",
    "        \"set style fill solid 0.5 border 1;\",\n",
    "        \"set xrange [0:$w];\",\n",
    "        \"set yrange [0:$h];\",\n",
    "        \"set title '\\$\\\\phi = $phi\\$';\",\n",
    "        \"plot '-' with circles lc 2 notitle;\")\n",
    "    for p in box.particles\n",
    "        println(gp, p.x, \" \", p.y, \" \", p.radius)\n",
    "    end\n",
    "    plot(gp)\n",
    "    return box\n",
    "end\n",
    "box = test();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An old box\n",
    "\n",
    "Take the previous box and let the montecarlo process simulate its dynamics. After a given number of montecarlo steps try reducing the system's volume. This way, with each volume reducing step, the packing fraction will increase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  2.061992 seconds (8.97 M allocations: 726.646 MiB, 4.50% gc time)\n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "function simulation(box::Box, n::Int)\n",
    "    steps::Int = length(box.particles)\n",
    "    @time for i in 1:n\n",
    "        for k in 1:steps; montecarlo!(box); end\n",
    "        reduceVolume!(box)\n",
    "    end\n",
    "\n",
    "    w::Float64 = box.width\n",
    "    h::Float64 = box.height\n",
    "    phi::Float64 = getDensity(box)\n",
    "\n",
    "    gp = gnuplot(20, 20)\n",
    "    println(gp,\n",
    "        \"set size ratio -1;\",\n",
    "        \"set tics out nomirror;\",\n",
    "        \"set style fill solid 0.5 border 1;\",\n",
    "        \"set xrange [0:$w];\",\n",
    "        \"set yrange [0:$w];\",\n",
    "        \"set title '\\$\\\\phi = $phi\\$';\",\n",
    "        \"plot '-' with circles lc 2 notitle;\")\n",
    "    for p in box.particles\n",
    "        println(gp, p.x, \" \", p.y, \" \", p.radius)\n",
    "    end\n",
    "    plot(gp)\n",
    "end\n",
    "simulation(box, 10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Orientational order parameter\n",
    "\n",
    "$$ \\psi_6(R) = \\frac{1}{N}\\sum_{j=1}^N \\bigg| \\frac{1}{n} \\sum_{k=1}^n \\exp(i 6 \\theta_{jk})\\bigg| $$\n",
    "\n",
    "where $R$ is a radius defining a circle concentric with particle $p_j$ and enclosing all particles $p_k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "function psi6(pts::Vector{Vector{Float64}}, r::Float64)\n",
    "    RePsi = 0\n",
    "    ImPsi = 0\n",
    "    psi6 = 0\n",
    "    N = length(pts)\n",
    "    for p in pts\n",
    "        n = 0 # count p-neighbours\n",
    "        for q in pts\n",
    "            if p === q; continue; end\n",
    "            rx = q[1] - p[1]\n",
    "            ry = q[2] - p[2]\n",
    "            d = rx*rx + ry*ry\n",
    "            th = atan(ry,rx)\n",
    "            if d < r\n",
    "                RePsi += cos(6*th)\n",
    "                ImPsi += sin(6*th)\n",
    "                n += 1\n",
    "            end\n",
    "        end\n",
    "        if n > 0\n",
    "            psi6 += sqrt(RePsi*RePsi + ImPsi*ImPsi)/n\n",
    "        end\n",
    "    end\n",
    "    return psi6/N\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting $\\psi_6(R)$ for different densities $\\phi$.\n",
    "\n",
    "Plotted in units of the particles' diameter, $d$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 100; r = 0.5\n",
    "box = Box(n,r)\n",
    "\n",
    "gp = gnuplot(32,14)\n",
    "println(gp, \"set cblabel '\\$\\\\phi\\$'; set palette negative;\n",
    "    set format x '\\$%1.0f d\\$'; set ylabel '\\$\\\\psi_6\\$';\n",
    "    set xrange [2*$r:128*$r];\n",
    "    plot '-' w l lc palette notitle;\")\n",
    "for i in 1:4\n",
    "    # Change box's density\n",
    "    for j in 1:20000\n",
    "        for k in 1:length(box.pts)\n",
    "            montecarlo!(box)\n",
    "        end\n",
    "        reduceVolume!(box)\n",
    "    end\n",
    "\n",
    "    # Plot psi6(R) for fixed density\n",
    "    phi = getDensity(box)\n",
    "    for R in 2*r:1e-1:128*r\n",
    "        p = psi6(box.pts, R)\n",
    "        println(gp, \"$R $p $phi\")\n",
    "    end\n",
    "    println(gp)\n",
    "end\n",
    "plot(gp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fixing $R$ and measuring $\\psi_6^{(R)}(\\phi)$\n",
    "\n",
    "We observed in the previous result the values of $R$ that make the order parameter a measurable quantity. Taking one of this values we can then slowly change the box's density and measure $\\psi_6$ to see where the phase transition takes place."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 100; r = 0.5; R = 10*r;\n",
    "box = Box(n,r)\n",
    "\n",
    "gp = gnuplot(32,14)\n",
    "println(gp, \"set xlabel '\\$\\\\phi\\$'; set ylabel '\\$\\\\psi_6^{(R)}\\$';\n",
    "    plot '-' w l notitle;\")\n",
    "for i = 1:1000\n",
    "    phi = getDensity(box)\n",
    "    psi = psi6(box.pts, R)\n",
    "    println(gp, \"$phi $psi\")\n",
    "    for j in 1:100\n",
    "        for k in 1:length(box.pts)*2\n",
    "            montecarlo!(box)\n",
    "        end\n",
    "        reduceVolume!(box)\n",
    "    end\n",
    "end\n",
    "plot(gp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[10] Repite el ejercicio 9, esta vez comenzando con un sistema muy denso y ordenado para después bajar la densidad. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[11] Prueba diferentes velocidades con las que incrementes o disminuyas la densidad cerca del punto crítico. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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