{ "cells": [ { "cell_type": "markdown", "id": "4f93ae47", "metadata": {}, "source": [ "# Compression, pressure and jamming\n", "\n", "This notebook follows a compression from a dilute gas to a jammed packing, compares the stopping criteria, and checks that the result is really jammed: a well-defined network of contacts that carries all the force." ] }, { "cell_type": "markdown", "id": "2956a2dd", "metadata": { "spheropack-header": true }, "source": [ "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/computational-chemical-engineering/spheropack/blob/main/docs/notebooks/02_compression_and_jamming.ipynb) [![Download notebook](https://img.shields.io/badge/download-notebook-orange?logo=jupyter)](https://computational-chemical-engineering.github.io/spheropack/notebooks/02_compression_and_jamming.ipynb)" ] }, { "cell_type": "code", "execution_count": null, "id": "af224718", "metadata": { "spheropack-header": true }, "outputs": [], "source": [ "# Install spheropack when it is not available (for example on Google Colab).\n", "import importlib.util\n", "\n", "if importlib.util.find_spec(\"spheropack\") is None:\n", " %pip install -q spheropack" ] }, { "cell_type": "code", "execution_count": 1, "id": "17c10c39", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T15:37:33.248637Z", "iopub.status.busy": "2026-10-01T15:37:33.248419Z", "iopub.status.idle": "2026-10-01T15:37:33.552485Z", "shell.execute_reply": "2026-10-01T15:37:33.551825Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import spheropack as sp\n", "from spheropack import analysis" ] }, { "cell_type": "markdown", "id": "dda43986", "metadata": {}, "source": [ "## The course of a compression\n", "\n", "`density=\"max\"` grows the spheres until they jam. `history` holds one record per measurement window (10 collisions per sphere): the radius scale, the mean and median reduced pressure $Z = PV/(Nk_BT)$, the temperature and the phase of the jamming protocol." ] }, { "cell_type": "code", "execution_count": 2, "id": "9f5f43da", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T15:37:33.555521Z", "iopub.status.busy": "2026-10-01T15:37:33.555290Z", "iopub.status.idle": "2026-10-01T15:38:04.388334Z", "shell.execute_reply": "2026-10-01T15:38:04.387376Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Packing(n=2000, dim=3, density=0.640406, status='jammed', reduced_pressure=1.21e+09, n_collisions=8451446, seed=1)\n", "394 windows, 4226 collisions per sphere, 30.8 s\n" ] } ], "source": [ "p = sp.pack(n=2000, density=\"max\", seed=1)\n", "print(p)\n", "h = p.history\n", "phi = p.density * (h[\"scale\"] / h[\"scale\"][-1]) ** 3\n", "print(f\"{len(phi)} windows, {p.n_collisions / p.n:.0f} collisions per sphere, {p.wall_time:.1f} s\")" ] }, { "cell_type": "markdown", "id": "f36ade57", "metadata": {}, "source": [ "At low density the pressure follows the equilibrium equation of state of hard spheres (Carnahan-Starling): the compression is slow compared with the collision rate. Near jamming the pressure diverges as $Z \\approx 3/(1-\\phi/\\phi_J)$." ] }, { "cell_type": "code", "execution_count": 3, "id": "22743dbc", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T15:38:04.390786Z", "iopub.status.busy": "2026-10-01T15:38:04.390643Z", "iopub.status.idle": "2026-10-01T15:38:04.737887Z", "shell.execute_reply": "2026-10-01T15:38:04.737089Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def carnahan_starling(phi):\n", " return (1 + phi + phi**2 - phi**3) / (1 - phi) ** 3\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n", "ax = axes[0]\n", "grow = h[\"phase\"] == 0\n", "ax.semilogy(phi[grow], h[\"reduced_pressure\"][grow], \".\", label=\"growing\")\n", "ax.semilogy(phi[~grow], h[\"median_pressure\"][~grow], \".\", label=\"jamming protocol (median)\")\n", "x = np.linspace(0.05, 0.55, 100)\n", "ax.semilogy(x, carnahan_starling(x), \"k-\", lw=1, label=\"Carnahan-Starling\")\n", "ax.set_xlabel(r\"$\\phi$\"); ax.set_ylabel(\"Z\"); ax.legend()\n", "\n", "ax = axes[1]\n", "phi_j = p.density\n", "ax.loglog(1 - phi / phi_j, h[\"median_pressure\"], \".\")\n", "d = np.logspace(-10, -1, 10)\n", "ax.loglog(d, 3 / d, \"k--\", lw=1, label=r\"$3/(1-\\phi/\\phi_J)$\")\n", "ax.set_xlabel(r\"$1 - \\phi/\\phi_J$\"); ax.set_ylabel(\"median Z\"); ax.legend();" ] }, { "cell_type": "markdown", "id": "f590a615", "metadata": {}, "source": [ "## Is it jammed? Contacts and rattlers\n", "\n", "Two spheres are in contact when their gap is below a tolerance. In a jammed packing at pressure $Z$ the gaps between touching spheres are of order $d/Z$, and much larger between spheres that do not touch, so the number of contacts has a plateau as a function of the tolerance.\n", "\n", "The per-sphere pressure is the time-averaged contact force on a sphere. Spheres without force are *rattlers*: they sit loose in a cage of jammed neighbours. A frictionless jammed packing is *isostatic*: the force-bearing spheres have exactly as many contacts as needed for rigidity, $D(N_\\mathrm{nr}-1)$ in a periodic box, so their mean coordination number is close to $2D = 6$." ] }, { "cell_type": "code", "execution_count": 4, "id": "661b9023", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T15:38:04.740659Z", "iopub.status.busy": "2026-10-01T15:38:04.740526Z", "iopub.status.idle": "2026-10-01T15:38:05.022590Z", "shell.execute_reply": "2026-10-01T15:38:05.021772Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rattlers: 80 of 2000 (4.0%)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n", "axes[0].hist(np.log10(p.sphere_pressure / p.median_pressure), bins=60)\n", "axes[0].set_xlabel(r\"$\\log_{10}(Z_i / Z_\\mathrm{median})$\"); axes[0].set_ylabel(\"spheres\")\n", "axes[0].set_title(\"per-sphere pressure: rattlers on the left\")\n", "\n", "tols = np.logspace(-11, -2, 19)\n", "iso = [analysis.isostaticity(p, t) for t in tols]\n", "axes[1].semilogx(tols, iso, \"o-\")\n", "axes[1].axhline(1, color=\"k\", lw=0.8)\n", "axes[1].set_xlabel(\"contact tolerance\"); axes[1].set_ylabel(\"contacts / isostatic number\")\n", "rat = analysis.rattlers(p)\n", "print(f\"rattlers: {rat.sum()} of {p.n} ({100 * rat.mean():.1f}%)\")" ] }, { "cell_type": "markdown", "id": "d1e62eda", "metadata": {}, "source": [ "Below a tolerance of about $10^{-8}$ (the gap scale $d/Z$ at $Z=10^9$) contacts are missed; above about $10^{-4}$ near neighbours that do not touch are counted. In between lies the plateau, slightly below the isostatic number: a compression at a finite rate leaves a few percent of the contacts unformed. A slower protocol comes closer to 1 (see the user guide on stopping criteria)." ] }, { "cell_type": "markdown", "id": "700e0c20", "metadata": {}, "source": [ "## Pressure versus Jammed\n", "\n", "`Pressure(value)` stops as soon as the mean pressure exceeds `value`, while the spheres keep growing. The density is almost the same, but the contact network is not yet formed: there is no plateau." ] }, { "cell_type": "code", "execution_count": 5, "id": "d19f3915", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T15:38:05.025229Z", "iopub.status.busy": "2026-10-01T15:38:05.025095Z", "iopub.status.idle": "2026-10-01T15:38:14.067770Z", "shell.execute_reply": "2026-10-01T15:38:14.067001Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Packing(n=2000, dim=3, density=0.640188, status='pressure', reduced_pressure=1.04e+06, n_collisions=2452045, seed=1)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q = sp.pack(n=2000, density=\"max\", stop=sp.stop.Pressure(1e6), seed=1)\n", "print(q)\n", "z_q = [analysis.contact_numbers(q, t).mean() for t in tols]\n", "z_p = [analysis.contact_numbers(p, t).mean() for t in tols]\n", "plt.semilogx(tols, z_p, \"o-\", label=f\"Jammed: phi = {p.density:.4f}\")\n", "plt.semilogx(tols, z_q, \"s-\", label=f\"Pressure(1e6): phi = {q.density:.4f}\")\n", "plt.xlabel(\"contact tolerance\"); plt.ylabel(\"mean contacts per sphere\"); plt.legend();" ] }, { "cell_type": "markdown", "id": "0bcfaa77", "metadata": {}, "source": [ "## Budgets and failures\n", "\n", "Limit criteria bound the cost. When one fires before the goal is reached, `success` is False and a `PackingWarning` is issued; with `strict=True` a `PackingError` is raised that carries the partial packing." ] }, { "cell_type": "code", "execution_count": 6, "id": "cea710d7", "metadata": { "execution": { "iopub.execute_input": "2026-10-01T15:38:14.070061Z", "iopub.status.busy": "2026-10-01T15:38:14.069876Z", "iopub.status.idle": "2026-10-01T15:38:24.240683Z", "shell.execute_reply": "2026-10-01T15:38:24.239765Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "collisions False Collisions(total=None, per_particle=200)\n", "packing stopped with status 'collisions' at density 0.5529 (reduced pressure 19.8)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "PackingError: packing stopped with status 'pressure' at density 0.64019 (reduced pressure 1.04e+06) | partial density 0.6402\n" ] } ], "source": [ "import warnings\n", "with warnings.catch_warnings(record=True) as w:\n", " warnings.simplefilter(\"always\")\n", " r = sp.pack(n=2000, density=0.7, stop=[sp.stop.Pressure(1e6), sp.stop.Collisions(per_particle=200)], seed=1)\n", "print(r.status, r.success, r.stopped_by)\n", "print(w[0].message)\n", "\n", "try:\n", " sp.pack(n=2000, density=0.7, seed=1, strict=True)\n", "except sp.PackingError as err:\n", " print(\"PackingError:\", err, \"| partial density\", round(err.packing.density, 4))" ] } ], "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": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 5 }