272 lines
115 KiB
Plaintext
272 lines
115 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Cartesian mesh\n",
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"\n",
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"For this assignment, you are required to generate a Cartesian mesh and map particle positions onto the grid using two techniques: Nearest-Neighbour (NN) and Cloud-in-Cell (CIC). Then reconstruct the density field for both methods and compare the resulting densities between NN and CIC. Finally, compute the radial density profile directly from the particle positions and compare it with the densities obtained from both methods, discussing any observed differences.\n",
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"\n",
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"The columns are x, y, z.\n",
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"\n",
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"cloud_full.ascii is the same but also contains the density (for them to check) and an internal energy (x, y, z, rho, u).\n",
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"\n",
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"The mass of the particles should be chosen such that the full system amounts to M = 1."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"load_stars (generic function with 1 method)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"function load_stars() :: Array{Float64}\n",
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" stars = Array{Float64,2}\n",
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" display(stars)\n",
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" open(\"cloud_positions.ascii\") do file\n",
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" nstars = countlines(file)\n",
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" stars = zeros(nstars, 3)\n",
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" for (index, line) in enumerate(eachline(file))\n",
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" single = [parse(Float64, i) for i in split(line, \" \")]\n",
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" println(single)\n",
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" stars[index, :] = single\n",
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" end\n",
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" end\n",
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" return stars\n",
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"plot_cloud (generic function with 1 method)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"using Plots\n",
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"function plot_cloud(stars::Array{Float64,2})\n",
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" plot(\n",
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" stars[1, :, :],\n",
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" stars[2, :, :],\n",
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" stars[3, :, :],\n",
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" seriestype = :scatter,\n",
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" markersize = 1,\n",
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" legend = false,\n",
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" xlabel = \"x\",\n",
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" ylabel = \"y\",\n",
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" zlabel = \"z\",\n",
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" )\n",
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"Matrix{Float64}\u001b[90m (alias for \u001b[39m\u001b[90mArray{Float64, 2}\u001b[39m\u001b[90m)\u001b[39m"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/plain": [
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"65494×3 Matrix{Float64}:\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" ⋮ \n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0\n",
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" 0.0 0.0 0.0"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": 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}
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],
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"source": [
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"stars = load_stars()\n",
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