{ "cells": [ { "cell_type": "markdown", "id": "df00d243", "metadata": {}, "source": [ "# Molecular dynamics: depinning under applied force and torque\n", " \n", " This notebook drives a rigid cluster with an applied external force $F_x$\n", " or torque $\\tau_\\text{ext}$ and finds the depinning transition: the critical force $F_c$\n", " (or critical torque $\\tau_c$) above which the cluster begins to slide.\n", " \n", " The dynamics follow the overdamped Langevin (Euler–Maruyama) equations:\n", " \n", " $$\\eta_t \\dot{x}_\\text{cm} = F_x + F_x^\\text{sub} + \\xi_x$$\n", " \n", " $$\\eta_t \\dot{y}_\\text{cm} = F_y + F_y^\\text{sub} + \\xi_y$$\n", " \n", " $$\\eta_r \\dot{\\theta} = \\tau_\\text{ext} + \\tau^\\text{sub} + \\xi_\\theta$$\n", " \n", " where $\\eta_t$ and $\\eta_r$ are the translational and rotational drag coefficients\n", " (computed from $N$ and the moment of inertia), and the noise satisfies the\n", " fluctuation-dissipation theorem:\n", " \n", " $$\\langle \\xi_i(t) \\xi_j(t') \\rangle = 2 k_B T \\eta_i \\, \\delta_{ij} \\delta(t - t')$$\n", " \n", " `sweep_md` runs one MD trajectory per grid point (here: per $F_x$ or $\\tau$ value)\n", " in parallel, then applies a post-processing function to extract a scalar metric\n", " (drift velocity or angular velocity). The depinning appears as a sharp onset\n", " in that metric.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "151b451e", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from numpy import sqrt\n", "import matplotlib.pyplot as plt\n", "from time import time\n", "\n", "from flake.substrate import substrate_from_params, get_ks\n", "from flake.cluster import cluster_from_params, calc_cluster_langevin\n", "from flake.dynamics import run_md\n", "from flake.sweep import sweep_md, grid_sweep, drift_velocity, mean_velocity" ] }, { "cell_type": "markdown", "id": "b07ab28e", "metadata": {}, "source": [ "## System definition\n", " \n", " Commensurate cluster on a sinusoidal triangular substrate ($\\rho = 1$).\n", " You can setup the same geometry as the barrier notebook so the depinning force $F_c$ is\n", " directly comparable to the static friction $F_s$ computed from the MEP.\n", " \n", " `kBT = 1e-8` instead of `0` avoids saddle-point ambiguity in the Euler–Maruyama\n", " integrator. At $\\epsilon = 1$ this is thermally negligible (effectively $T = 0$).\n", " " ] }, { "cell_type": "code", "execution_count": 3, "id": "6b34c491", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "N=223 E=-223 eta_t=223 eta_r=6.86e+03 eta_r/eta_t=30.8\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ks = get_ks(1, 3, 4./3., 0.) # triangular substrate wave vectors\n", "\n", "params = {\n", " 'sub_basis': [[0, 0]],\n", " 'epsilon': 1,\n", " 'well_shape': 'sin',\n", " 'ks': ks,\n", " 'a1': np.array([1., 0.]),\n", " 'a2': np.array([0.5, -sqrt(3.)/2.]),\n", " 'cl_basis': [[0, 0]],\n", " 'cluster_shape': 'circle',\n", " 'N1': 15, 'N2': 15,\n", " 'theta': 0.0, 'pos_cm': [0., 0.],\n", "}\n", "\n", "pen_func, en_func, en_inputs = substrate_from_params(params)\n", "pos = cluster_from_params(params)\n", "N = pos.shape[0]\n", "\n", "# Translational and rotational drag coefficients.\n", "# eta_r / eta_t ~ / 1 sets the ratio of rotational to translational\n", "# relaxation times -- larger clusters relax rotationally more slowly.\n", "eta = 1.0\n", "eta_t, eta_r = calc_cluster_langevin(eta, pos)\n", "pen = pen_func(pos + params['pos_cm'], params['pos_cm'])[0]\n", "print('N=%i E=%.3g eta_t=%.3g eta_r=%.3g eta_r/eta_t=%.3g'\n", " % (N, np.sum(pen), eta_t, eta_r, eta_r/eta_t))\n", "\n", "fig, ax = plt.subplots(dpi=120, figsize=(4, 4))\n", "sc = ax.scatter(pos[:, 0], pos[:, 1], c=pen, vmin=-params['epsilon'], vmax=0)\n", "plt.colorbar(sc, ax=ax, label=r'$E_i$ [$\\epsilon$]')\n", "ax.set_xlabel('x [a.u.]')\n", "ax.set_ylabel('y [a.u.]')\n", "ax.set_title('Cluster reference frame, N=%d' % N)\n", "ax.set_aspect('equal')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "31f10ffc", "metadata": {}, "source": [ "## Single trajectory: below and above depinning\n", " \n", " Before running the full sweep it is instructive to watch individual\n", " trajectories at $F_x$ just below and just above the depinning threshold.\n", " This gives physical intuition for what the sweep is measuring:\n", " - **Pinned** ($F_x < F_c$): the CM is stuck at fixed point.\n", " - **Sliding** ($F_x > F_c$): the CM drifts with a finite average velocity.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "4b828046", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "base_kw = dict(\n", " eta=1.0, kBT=1e-8, dt=1e-3, n_steps=20000,\n", " Tau=0., print_every=10,\n", " pos_cm0=params['pos_cm'],\n", ")\n", "\n", "fig, axes = plt.subplots(1, 2, dpi=150, figsize=(8, 3))\n", "for ax, Fx_test, label in [\n", " (axes[0], 200., 'below Fc (pinned)'),\n", " (axes[1], 630., 'above Fc (sliding)'),\n", "]:\n", " traj = run_md(pos, en_func, Fx=Fx_test, **base_kw)\n", " t, xcm, ycm = traj['t'], traj['pos_cm'][:, 0], traj['pos_cm'][:, 1]\n", " ax.plot(t, xcm, label=r'$x_\\mathrm{cm}$')\n", " ax.plot(t, ycm, label=r'$y_\\mathrm{cm}$', ls='--')\n", " ax.set_xlabel('time [a.u.]')\n", " ax.set_ylabel('position [a.u.]')\n", " ax.set_title('Fx=%.0f — %s' % (Fx_test, label))\n", " ax.legend(fontsize=8)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f63e59fd", "metadata": {}, "source": [ " ## Force sweep: translational depinning\n", " \n", " `grid_sweep({'Fx': ...})` generates one parameter set per $F_x$ value.\n", " `drift_velocity()` post-processes each trajectory to extract\n", " $\\langle v_x \\rangle = (x_f - x_0)/(t_f - t_0)$ — a scalar that is $\\approx 0$\n", " in the pinned state and grows linearly above depinning.\n", " \n", " `n_jobs=-1` uses all available CPUs; each trajectory is independent." ] }, { "cell_type": "code", "execution_count": 5, "id": "1b5e78e7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Done: 0.2min\n" ] } ], "source": [ "t0 = time()\n", "\n", "spec = grid_sweep({'Fx': np.linspace(0., 1000., 50)})\n", "\n", "results = sweep_md(\n", " pos, en_func, spec,\n", " base_md_kwargs={\n", " 'eta': 1.0,\n", " 'kBT': 1e-8,\n", " 'dt': 1e-3,\n", " 'n_steps': 10000,\n", " 'Tau': 0.,\n", " 'print_every': 10,\n", " 'pos_cm0': params['pos_cm'],\n", " },\n", " post_fn=drift_velocity(),\n", " n_jobs=-1,\n", " save=False,\n", " verbose=False,\n", ")\n", "\n", "Fx_vals = np.array([r['params']['Fx'] for r in results])\n", "vdrift = np.array([r['result'] for r in results])\n", "\n", "print('Done: %.1fmin' % ((time() - t0) / 60.))" ] }, { "cell_type": "markdown", "id": "62b72536", "metadata": {}, "source": [ "The depinning transition appears as a sharp onset in drift velocity.\n", " \n", " - **Pinned** ($F_x < F_c$): $\\langle v_x \\rangle \\approx 0$\n", " - **Sliding** ($F_x > F_c$): $\\langle v_x \\rangle$ grows linearly with $F_x - F_c$\n", " \n", " The orange band brackets the transition region $[F_c^\\text{lo},\\, F_c^\\text{hi}]$.\n", " The threshold `1e-1` is appropriate in this coarse example because `kBT=1e-8`, so thermal drift is\n", " negligible — any $v_x > 10^{-2}$ is genuine sliding." ] }, { "cell_type": "code", "execution_count": 6, "id": "d69d2282", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120, figsize=(5, 3.5))\n", "\n", "pinned = vdrift[:, 0] < 1e-1\n", "sliding = ~pinned\n", "\n", "ax.scatter(Fx_vals[pinned], vdrift[pinned, 0], color='tab:blue',\n", " label='pinned', zorder=3)\n", "ax.scatter(Fx_vals[sliding], vdrift[sliding, 0], color='tab:red',\n", " marker='^', label='sliding', zorder=3)\n", "\n", "if sliding.any() and pinned.any():\n", " Fc_lo = Fx_vals[pinned].max()\n", " Fc_hi = Fx_vals[sliding].min()\n", " ax.axvspan(Fc_lo, Fc_hi, alpha=0.15, color='orange',\n", " label=r'$F_c \\in [%.3f,\\, %.3f]$' % (Fc_lo, Fc_hi))\n", "\n", "ax.set_xlabel(r'$F_x$')\n", "ax.set_ylabel(r'$\\langle v_x \\rangle$')\n", "ax.legend(fontsize=8)\n", "ax.set_title('Translational depinning N=%i' % N)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f57df9b8", "metadata": {}, "source": [ "## Torque sweep: rotational depinning\n", " \n", " Same idea, but driving the cluster with an applied torque $\\tau_\\text{ext}$\n", " instead of $F_x$.\n", " `drift_omega` extracts $\\langle \\omega \\rangle = (\\theta_f - \\theta_0)/(t_f - t_0)$,\n", " the angular drift velocity.\n", " A sharp onset in $\\langle \\omega \\rangle$ marks the rotational depinning threshold $\\tau_c$.\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "34bfa70f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Done: 0.5min\n" ] } ], "source": [ "def drift_omega():\n", " \"\"\"Post-processing: return angular drift velocity dtheta/dt in deg/time.\"\"\"\n", " def _post_fn(traj_dict, run_params):\n", " theta = traj_dict['theta']\n", " t = traj_dict['t']\n", " dt_tot = float(t[-1] - t[0])\n", " if dt_tot == 0.:\n", " return 0.\n", " return (theta[-1] - theta[0]) / dt_tot\n", " return _post_fn\n", "\n", "\n", "t0 = time()\n", "\n", "spec_tau = grid_sweep({'Tau': np.linspace(0., 6000., 50)})\n", "\n", "results_tau = sweep_md(\n", " pos, en_func, spec_tau,\n", " base_md_kwargs={\n", " 'eta': 1.0,\n", " 'kBT': 1e-8,\n", " 'dt': 1e-3,\n", " 'n_steps': 50000,\n", " 'print_every': 10,\n", " },\n", " post_fn=drift_omega(),\n", " n_jobs=-1,\n", " save=False,\n", " verbose=False,\n", ")\n", "\n", "Tau_vals = np.array([r['params']['Tau'] for r in results_tau])\n", "odrift = np.array([r['result'] for r in results_tau])\n", "\n", "print('Done: %.1fmin' % ((time() - t0) / 60.))" ] }, { "cell_type": "code", "execution_count": 9, "id": "7f73f59b", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(dpi=120, figsize=(5, 3.5))\n", "\n", "pinned = odrift < 1e-1\n", "rotating = ~pinned\n", "\n", "ax.scatter(Tau_vals[pinned], odrift[pinned], color='tab:blue',\n", " label='pinned', zorder=3)\n", "ax.scatter(Tau_vals[rotating], odrift[rotating], color='tab:red',\n", " marker='^', label='rotating', zorder=3)\n", "\n", "if rotating.any() and pinned.any():\n", " Tau_lo = Tau_vals[pinned].max()\n", " Tau_hi = Tau_vals[rotating].min()\n", " ax.axvspan(Tau_lo, Tau_hi, alpha=0.15, color='orange',\n", " label=r'$\\tau_c \\in [%.3f,\\, %.3f]$' % (Tau_lo, Tau_hi))\n", "\n", "ax.set_xlabel(r'$\\tau$')\n", "ax.set_ylabel(r'$\\langle \\omega \\rangle$ [deg/time]')\n", "ax.legend(fontsize=8)\n", "ax.set_title('Rotational depinning N=%i' % N)\n", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "DRIFT2", "language": "python", "name": "drift" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.13" } }, "nbformat": 4, "nbformat_minor": 5 }