658 lines
344 KiB
Plaintext
658 lines
344 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 92,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The autoreload extension is already loaded. To reload it, use:\n",
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" %reload_ext autoreload\n"
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]
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}
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],
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"source": [
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"# automatically reflect changes in imported modules\n",
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"%load_ext autoreload\n",
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"%autoreload 2\n",
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"\n",
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"from pathlib import Path\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"import astropy.units as u\n",
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"from astropy.visualization import quantity_support\n",
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"quantity_support()\n",
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"\n",
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"\n",
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"import utils\n",
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"import utils.logging_config\n",
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"utils.logging_config.set_log_level(\"info\")\n",
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"import logging\n",
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"logger = logging.getLogger(\"task1\")\n",
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"\n"
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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": 93,
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"metadata": {},
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"outputs": [],
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"source": [
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"DATA_ROOT = Path('data')\n",
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"DATA_NAME = 'data.txt'\n",
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"NBINS = 30\n",
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"CACHE_ROOT = Path('.cache')"
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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": 94,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"12:40:29 - utils.load - Loaded 50010 rows and 10 columns from data/data.txt\n"
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]
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}
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],
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"source": [
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"points, columns = utils.load_data(DATA_ROOT / DATA_NAME)\n",
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"logger.debug(f\"Fetched {points.shape[0]} points, columns: {columns}\")\n",
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"# reorder the columns to match the expected order (x, y, z, mass)\n",
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"particles = points[:, [2, 3, 4, 1]]\n",
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"\n",
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"# particles = particles[::10, ...]\n",
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"# particles = particles[:5000, ...]\n",
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"# particles = utils.remove_outliers(particles)\n",
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"# logger.warning(f\"Reduced selection to {particles.shape[0]} particles\")\n",
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"# TODO: make sure this is not executed in the final version"
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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": 95,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# plot the distribution of the particles\n",
|
|
"fig = plt.figure()\n",
|
|
"ax = fig.add_subplot(111, projection='3d')\n",
|
|
"ax.scatter(particles[:,0], particles[:,1], particles[:,2], cmap='viridis', c=particles[:,3])\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Choice of units\n",
|
|
"Recap of the particle properties:\n",
|
|
"- $\\sim 10^4$ particles\n",
|
|
"- spherical distribution\n",
|
|
"\n",
|
|
"$\\implies$ this seems to be a **globular cluster**"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 113,
|
|
"metadata": {
|
|
"tags": [
|
|
"plot_particle_distribution"
|
|
]
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stderr",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"18:12:23 - task1 - Considering a globular cluster - total mass of particles: 4622219.258999999, maximum radius of particles: 724.689657812915\n",
|
|
"18:12:23 - utils.units - Set scales: M_SCALE = 0.022 solMass, R_SCALE = 0.028 pc\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Set G = 1\n",
|
|
"G = 1\n",
|
|
"\n",
|
|
"\n",
|
|
"# Since we have a globular cluster, we can use typical values\n",
|
|
"M_TOT = 1e5 * u.M_sun\n",
|
|
"R_TOT = 20 * u.pc\n",
|
|
"\n",
|
|
"# Rescale the units of the particles\n",
|
|
"M_particles = particles[:,3].sum()\n",
|
|
"R_particles = np.max(np.linalg.norm(particles[:, :3], axis=1))\n",
|
|
"logger.info(f\"Considering a globular cluster - total mass of particles: {M_particles}, maximum radius of particles: {R_particles}\")\n",
|
|
"m_scale = M_TOT / M_particles\n",
|
|
"r_scale = R_TOT / R_particles\n",
|
|
"utils.seed_scales(r_scale, m_scale)\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"### Plot again with scales\n",
|
|
"reduced = utils.remove_outliers(particles.copy())\n",
|
|
"positions = utils.apply_units(reduced[:, :3], \"position\")\n",
|
|
"masses = utils.apply_units(reduced[:, 3], \"mass\")\n",
|
|
"utils.particles_plot_3d(positions, masses, title=\"Particle distribution\")\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 97,
|
|
"metadata": {
|
|
"tags": [
|
|
"plot_density_distribution"
|
|
]
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"all_r = utils.r_distribution(particles)\n",
|
|
"rbins = np.logspace(np.log10(np.min(all_r)), np.log10(np.max(all_r)), NBINS, endpoint=True)\n",
|
|
"\n",
|
|
"## Using the Hernquist model with parameters M and a\n",
|
|
"m = M_particles\n",
|
|
"a = utils.half_mass_radius(particles) / (1 + np.sqrt(2))\n",
|
|
"logger.debug(f\"Scale length: {a=:.2g}, total mass: {m=:.2g}\")\n",
|
|
"rho_t = utils.model_density_distribution(rbins, m, a)\n",
|
|
"\n",
|
|
"## Numerical density distribution\n",
|
|
"rho, err = utils.density_distribution(rbins, particles, ret_error=True)\n",
|
|
"\n",
|
|
"## Add the units\n",
|
|
"rho = utils.apply_units(rho, \"density\")\n",
|
|
"err = utils.apply_units(err, \"density\")\n",
|
|
"rho_t = utils.apply_units(rho_t, \"density\")\n",
|
|
"rbins = utils.apply_units(rbins, \"position\")\n",
|
|
"\n",
|
|
"\n",
|
|
"plt.figure()\n",
|
|
"plt.title('Density distribution')\n",
|
|
"plt.xscale('log')\n",
|
|
"plt.yscale('log')\n",
|
|
"plt.xlabel(\"R\")\n",
|
|
"plt.xlabel(f'r [{rbins.unit:latex}]')\n",
|
|
"plt.ylabel(f'$\\\\rho$ [{rho.unit:latex}]')\n",
|
|
"plt.errorbar(rbins, rho, yerr=err, fmt='o', label=\"Particle data\")\n",
|
|
"plt.plot(rbins, rho_t, 'o', label=\"Analytic model\")\n",
|
|
"plt.legend()\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"## Note that by construction, the first shell contains no particles\n",
|
|
"## => the numerical density is zero there\n",
|
|
"## Having more bins means to have shells that are nearly empty\n",
|
|
"## => the error is large, NBINS = 30 is a good compromise"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 98,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stderr",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"12:40:33 - utils.particles - Found mean interparticle distance: 0.010402746349924056\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"### Direct N body force computation and comparison with analytical model\n",
|
|
"epsilon = utils.mean_interparticle_distance(particles)\n",
|
|
"\n",
|
|
"\n",
|
|
"epsilon_range = np.logspace(-3, 3, 7)\n",
|
|
"n_squared_forces = []\n",
|
|
"for e in epsilon_range:\n",
|
|
" n_particles = particles.shape[0]\n",
|
|
" cache_file = CACHE_ROOT / f\"n_squared_forces__n_{n_particles}__softening_multiplier_{e:.0f}.npy\"\n",
|
|
" try:\n",
|
|
" f = np.load(cache_file)\n",
|
|
" except FileNotFoundError:\n",
|
|
" f = utils.n_body_forces(particles, G, e * epsilon)\n",
|
|
" np.save(cache_file, f)\n",
|
|
" logger.debug(f\"Saved forces to {cache_file}\")\n",
|
|
" n_squared_forces.append(f)\n",
|
|
"\n",
|
|
"analytical_force = utils.analytical_forces(particles)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 99,
|
|
"metadata": {
|
|
"tags": [
|
|
"plot_force_radial"
|
|
]
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"SKIP_N = 1\n",
|
|
"\n",
|
|
"## Plot the radial force behaviour\n",
|
|
"r = np.linalg.norm(particles[:,:3], axis=1)\n",
|
|
"r = utils.apply_units(r, \"position\")\n",
|
|
"\n",
|
|
"plt.figure()\n",
|
|
"f_analytical = np.linalg.norm(analytical_force, axis=1)\n",
|
|
"f_analytical = utils.apply_units(f_analytical, \"force\")\n",
|
|
"\n",
|
|
"plt.plot(r[::SKIP_N], f_analytical[::SKIP_N], '.', label=\"Analytical\", zorder=10, alpha=0.5, color='black')\n",
|
|
"\n",
|
|
"colors = plt.cm.Blues(np.linspace(0.3,1,len(epsilon_range)))\n",
|
|
"for e, f, c in zip(epsilon_range, n_squared_forces, colors):\n",
|
|
" # print((np.log(e)+10) * 10)\n",
|
|
" f_abs = np.linalg.norm(f, axis=1)\n",
|
|
" f_abs = utils.apply_units(f_abs, \"force\")\n",
|
|
" plt.plot(r[::SKIP_N], f_abs[::SKIP_N], '.', label=f\"$N^2$ - {e:.1g} * $\\\\epsilon$\", color=c)\n",
|
|
"\n",
|
|
"\n",
|
|
"plt.title('Radial force')\n",
|
|
"plt.xscale('log')\n",
|
|
"plt.yscale('log')\n",
|
|
"plt.xlabel(f'$r$ [{r.unit:latex}]')\n",
|
|
"plt.ylabel(f'$|F(r)|$ [{f_analytical.unit:latex}]')\n",
|
|
"plt.legend()\n",
|
|
"plt.show()\n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 100,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"'\\nparticles = utils.remove_outliers(particles)\\nr = np.linalg.norm(particles[:,:3], axis=1)\\nr = utils.apply_units(r, \"position\")\\n\\nplt.figure()\\nf_nsquare = utils.analytical_forces(particles)\\nf_abs = np.linalg.norm(f_nsquare, axis=1)\\nf_abs = utils.apply_units(f_abs, \"force\")\\nplt.plot(r.value[::SKIP_N], f_abs.value[::SKIP_N], \\'.\\', label=\"N^2\")\\n\\nf_mesh = utils.mesh_forces(particles, G, 405, utils.particle_to_cells_nn)\\nf_abs = np.linalg.norm(f_mesh, axis=1)\\nf_abs = utils.apply_units(f_abs, \"force\")\\nplt.plot(r.value[::SKIP_N], f_abs.value[::SKIP_N], \\'.\\', label=\"Mesh\")\\n\\nplt.title(\\'Radial force\\')\\nplt.xscale(\\'log\\')\\nplt.yscale(\\'log\\')\\nplt.xlabel(f\\'$r$ [{r.unit}]\\')\\nplt.ylabel(f\\'$F_r(r) [{f_analytical.unit}]$\\')\\nplt.legend()\\nplt.show()\\n'"
|
|
]
|
|
},
|
|
"execution_count": 100,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"## For fun, do this with the mesh solver as well:\n",
|
|
"\"\"\"\n",
|
|
"particles = utils.remove_outliers(particles)\n",
|
|
"r = np.linalg.norm(particles[:,:3], axis=1)\n",
|
|
"r = utils.apply_units(r, \"position\")\n",
|
|
"\n",
|
|
"plt.figure()\n",
|
|
"f_nsquare = utils.analytical_forces(particles)\n",
|
|
"f_abs = np.linalg.norm(f_nsquare, axis=1)\n",
|
|
"f_abs = utils.apply_units(f_abs, \"force\")\n",
|
|
"plt.plot(r.value[::SKIP_N], f_abs.value[::SKIP_N], '.', label=\"N^2\")\n",
|
|
"\n",
|
|
"f_mesh = utils.mesh_forces(particles, G, 405, utils.particle_to_cells_nn)\n",
|
|
"f_abs = np.linalg.norm(f_mesh, axis=1)\n",
|
|
"f_abs = utils.apply_units(f_abs, \"force\")\n",
|
|
"plt.plot(r.value[::SKIP_N], f_abs.value[::SKIP_N], '.', label=\"Mesh\")\n",
|
|
"\n",
|
|
"plt.title('Radial force')\n",
|
|
"plt.xscale('log')\n",
|
|
"plt.yscale('log')\n",
|
|
"plt.xlabel(f'$r$ [{r.unit}]')\n",
|
|
"plt.ylabel(f'$F_r(r) [{f_analytical.unit}]$')\n",
|
|
"plt.legend()\n",
|
|
"plt.show()\n",
|
|
"\"\"\""
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"#### Discussion\n",
|
|
"- basic $N^2$ matches analytical solution without dropoff. but: noisy data from \"bad\" samples\n",
|
|
"- $N^2$ with softening matches analytical solution but has a dropoff. No noisy data.\n",
|
|
" - softening $\\approx 1 \\varepsilon$ is a sweet spot since the dropoff is \"late\""
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Relaxation time\n",
|
|
"\n",
|
|
"For an estimate of the crossing time we use the half mass radius and the circular velocity at the half mass radius.\n",
|
|
"\n",
|
|
"$\\implies$ the crossing time is of order radius / velocity"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 101,
|
|
"metadata": {
|
|
"tags": [
|
|
"compute_relaxation_time"
|
|
]
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stderr",
|
|
"output_type": "stream",
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"text": [
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"12:40:50 - task1 - Central velocity @ HM 3098.502740746268 solMass(1/2) / pc(1/2)\n",
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"12:40:50 - task1 - Crossing time for half mass system: 1.7e-06 pc(3/2) / solMass(1/2)\n",
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"12:40:50 - task1 - Direct estimate of the relaxation timescale: 0.00078 pc(3/2) / solMass(1/2)\n"
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]
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}
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|
],
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"source": [
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"## Computes the relaxation timescale of a set of particles using the velocity at the half mass radius.\n",
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"\n",
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"# enclosed mass at half mass radius\n",
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"m_half = np.sum(particles[:, 3]) / 2\n",
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"r_half = utils.half_mass_radius(particles)\n",
|
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"# set the units\n",
|
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"m_half = utils.apply_units(m_half, \"mass\")\n",
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"r_half = utils.apply_units(r_half, \"position\")\n",
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"\n",
|
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"v_c = np.sqrt(G * m_half / r_half)\n",
|
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"logger.info(f\"Central velocity @ HM {v_c}\")\n",
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|
"\n",
|
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"t_c = r_half / v_c\n",
|
|
"logger.info(f\"Crossing time for half mass system: {t_c:.2g}\")\n",
|
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"# TODO: how to treat this unit?\n",
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"\n",
|
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"## Using the derived formula for the relaxation timescale\n",
|
|
"# Compute the relaxation timescale through the estimate\n",
|
|
"# t_relax = t_c *n_relax = t_c * N / (10 * log(N))\n",
|
|
"n = particles.shape[0]\n",
|
|
"n_relax = n / (10 * np.log(n))\n",
|
|
"t_rel = t_c * n_relax\n",
|
|
"logger.info(f\"Direct estimate of the relaxation timescale: {t_rel:.2g}\")\n"
|
|
]
|
|
},
|
|
{
|
|
"attachments": {
|
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"Pasted image 20250118155501.png": {
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"image/png": 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"
|
|
}
|
|
},
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"#### Discussion\n",
|
|
"\n",
|
|
"\n",
|
|
"The estimate for $n_{relax}$ comes from the contribution of each star-star encounter to the velocity dispersion. This depends on the perpendicular force\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"The full integration of the force along the path of the star reduces to the main contribution at the closest approach (distance $b$):\n",
|
|
"$$\n",
|
|
"\\delta v \\approx \\frac{2 G m}{b} \\to \\delta v \\approx \\frac{2 G m}{b + \\varepsilon}\n",
|
|
"$$\n",
|
|
"$\\implies$ a bigger softening length leads to a smaller $\\delta v$.\n",
|
|
"\n",
|
|
"Using $n_{relax} = \\frac{\\delta v^2}{v^2}$, and knowing that the value of $v^2$ is derived from the Virial theorem (i.e. unaffected by the softening length), we can see that $n_{relax}$ scales like $\\varepsilon^{-2}$.\n",
|
|
"\n",
|
|
"##### Effect\n",
|
|
"- The relaxation time decreases with increasing softening length\n",
|
|
"- From the integration over all impact parameters $b$ even $b_{min}$ is chosen to be larger than $\\varepsilon$ $\\implies$ expect only a small effect on the relaxation time\n",
|
|
"\n",
|
|
"#TODO : The softening dampens the change of velocity => time to relax is longer"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 102,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"import inspect\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"tags": [
|
|
"function_density_distribution"
|
|
]
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"print(inspect.getsource(utils.density_distribution))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 103,
|
|
"metadata": {
|
|
"tags": [
|
|
"function_analytical_forces"
|
|
]
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"def analytical_forces(particles: np.ndarray):\n",
|
|
" \"\"\"\n",
|
|
" Computes the interparticle forces without computing the n^2 interactions.\n",
|
|
" This is done by using newton's second theorem for a spherical mass distribution.\n",
|
|
" The force on a particle at radius r is simply the force exerted by a point mass with the enclosed mass.\n",
|
|
" Assumes that the particles array has the following columns: x, y, z, m.\n",
|
|
" \"\"\"\n",
|
|
"\n",
|
|
" n = particles.shape[0]\n",
|
|
" forces = np.zeros((n, 3))\n",
|
|
"\n",
|
|
" logger.debug(f\"Computing forces for {n} particles using spherical approximation\")\n",
|
|
"\n",
|
|
" r_particles = np.linalg.norm(particles[:, :3], axis=1)\n",
|
|
" for i in range(n):\n",
|
|
" r_current = np.linalg.norm(particles[i, 0:3])\n",
|
|
" m_current = particles[i, 3]\n",
|
|
"\n",
|
|
" m_enclosed = np.sum(particles[r_particles < r_current, 3])\n",
|
|
"\n",
|
|
" # the force is the same as the force exerted by a point mass at the center\n",
|
|
" f = - m_current * m_enclosed / r_current**2\n",
|
|
" forces[i] = f\n",
|
|
"\n",
|
|
" if i % 5000 == 0:\n",
|
|
" logger.debug(f\"Particle {i} done\")\n",
|
|
"\n",
|
|
" return forces\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(inspect.getsource(utils.analytical_forces))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 104,
|
|
"metadata": {
|
|
"tags": [
|
|
"function_n2_forces"
|
|
]
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"def n_body_forces(particles: np.ndarray, G: float, softening: float = 0):\n",
|
|
" \"\"\"\n",
|
|
" Computes the gravitational forces between a set of particles.\n",
|
|
" Assumes that the particles array has the following columns: x, y, z, m.\n",
|
|
" \"\"\"\n",
|
|
" if particles.shape[1] != 4:\n",
|
|
" raise ValueError(\"Particles array must have 4 columns: x, y, z, m\")\n",
|
|
"\n",
|
|
" x_vec = particles[:, 0:3]\n",
|
|
" masses = particles[:, 3]\n",
|
|
"\n",
|
|
" n = particles.shape[0]\n",
|
|
" forces = np.zeros((n, 3))\n",
|
|
" logger.debug(f\"Computing forces for {n} particles using n^2 algorithm (using {softening=:.2g})\")\n",
|
|
"\n",
|
|
" for i in range(n):\n",
|
|
" # the current particle is at x_current\n",
|
|
" x_current = x_vec[i, :]\n",
|
|
" m_current = masses[i]\n",
|
|
"\n",
|
|
" # first compute the displacement to all other particles (and its magnitude)\n",
|
|
" r_vec = x_vec - x_current\n",
|
|
" r = np.linalg.norm(r_vec, axis=1)\n",
|
|
"\n",
|
|
" # add softening to the denominator\n",
|
|
" r_adjusted = r**2 + softening**2\n",
|
|
" # usually with a square root: r' = sqrt(r^2 + softening^2) and then cubed, but we combine that below\n",
|
|
"\n",
|
|
" # the numerator is tricky:\n",
|
|
" # m is a list of scalars and r_vec is a list of vectors (2D array)\n",
|
|
" # we only want row_wise multiplication\n",
|
|
" num = G * (masses * r_vec.T).T\n",
|
|
" # a zero value is expected where we have the same particle\n",
|
|
" r_adjusted[i] = 1\n",
|
|
" num[i] = 0\n",
|
|
"\n",
|
|
" f = - np.sum((num.T / r_adjusted**1.5).T, axis=0) * m_current\n",
|
|
" forces[i] = f\n",
|
|
"\n",
|
|
" if i!= 0 and i % 5000 == 0:\n",
|
|
" logger.debug(f\"Particle {i} done\")\n",
|
|
"\n",
|
|
" return forces\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(inspect.getsource(utils.n_body_forces))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 105,
|
|
"metadata": {
|
|
"tags": [
|
|
"function_interparticle_distance"
|
|
]
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"def mean_interparticle_distance(particles: np.ndarray):\n",
|
|
" \"\"\"\n",
|
|
" Computes the mean interparticle distance of a set of particles.\n",
|
|
" Assumes that the particles array has the following columns: x, y, z ...\n",
|
|
" \"\"\"\n",
|
|
" if particles.shape[1] < 3:\n",
|
|
" raise ValueError(\"Particles array must have at least 3 columns: x, y, z\")\n",
|
|
" \n",
|
|
"\n",
|
|
" r_half_mass = half_mass_radius(particles)\n",
|
|
" r = np.linalg.norm(particles[:, :3], axis=1)\n",
|
|
"\n",
|
|
" n_half_mass = np.sum(r < r_half_mass)\n",
|
|
" logger.debug(f\"Number of particles within half mass radius: {n_half_mass} of {particles.shape[0]}\")\n",
|
|
"\n",
|
|
" rho = n_half_mass / (4/3 * np.pi * r_half_mass**3)\n",
|
|
" # the mean distance between particles is the inverse of the density\n",
|
|
"\n",
|
|
" epsilon = (1 / rho)**(1/3)\n",
|
|
" logger.info(f\"Found mean interparticle distance: {epsilon}\")\n",
|
|
" return epsilon\n",
|
|
" # TODO: check if this is correct\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(inspect.getsource(utils.mean_interparticle_distance))"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "projects-X-9bmgL6",
|
|
"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": "3.13.1"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|