m-thesis-introduction/simulations/01_travelling_1d_sine.ipynb

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 1D Travelling Signal (sine with linear dispersion)\n",
"\n",
"\n",
"$$\n",
"u(x, t) = \\sin\\left( \\frac{2 \\pi x}{\\lambda} -2\\pi f t\\right)\n",
"\\\\\n",
"= \\sin\\left( 2 \\pi f \\, ( \\frac{x}{v(f)} -t) \\right)\n",
"$$\n",
"\n",
"$\\lambda = \\dfrac{v}{f}$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.fft as ft\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import axes3d"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"class TravellingSine:\n",
" \"\"\"\n",
" Scalar Travelling Sine wave with a constant dispersion relation per frequency\n",
" \"\"\"\n",
" def __init__(self, x_0, t_0, frequencies):\n",
" self.x_0 = x_0\n",
" self.t_0 = t_0\n",
" self.freqs = np.array(frequencies).reshape(-1)\n",
"\n",
" def __call__(self, x_f, t_f, phase_velocities = None):\n",
" x_f = np.array(x_f)\n",
" t_f = np.array(t_f)\n",
" return self._signal(self.x_0, x_f, self.t_0, t_f, self.freqs, phase_velocities)\n",
"\n",
" def _signal(self, x_0, x_f, t_0, t_f, freqs, phase_velocities = None, debug = 0):\n",
"\n",
" # broadcasting between x_f and t_f\n",
" if np.ndim(x_f) != 0 or np.ndim(t_f) != 0:\n",
" if np.ndim(x_f) == 0:\n",
" x_f = x_f * np.ones(t_f.shape)\n",
" if np.ndim(t_f) == 0:\n",
" t_f = t_f * np.ones(x_f.shape)\n",
" \n",
" assert len(x_f) == len(t_f), \"x_f and t_f MUST have equal length: {} and {}\".format(len(x_f), len(t_f))\n",
" \n",
" # broadcasting between frequencies and phase velocities\n",
" if phase_velocities is None:\n",
" phase_velocities = 1\n",
" \n",
" if callable(phase_velocities):\n",
" phase_velocities = phase_velocities(freqs)\n",
"\n",
" if np.ndim(phase_velocities) == 0:\n",
" phase_velocities = phase_velocities * np.ones(self.freqs.shape)\n",
" \n",
" assert len(freqs) == len(phase_velocities), \"freqs and phase_velocities MUST have equal length: {} and {}\".format(len(freqs), len(phase_velocities))\n",
" \n",
" # get the wavelengths for each frequency\n",
" wavelengths = phase_velocities / freqs\n",
" \n",
" # make sure these are 1d arrays\n",
" time_diff = np.array(t_0 - t_f).reshape(-1) \n",
" space_diff = np.array(x_0 - x_f).reshape(-1) \n",
" \n",
" # ndarray of phase components\n",
" time_phase = np.outer(2*np.pi*freqs, time_diff)\n",
" space_phase = np.outer(2*np.pi/wavelengths, space_diff)\n",
" \n",
" if debug:\n",
" if debug > 1:\n",
" #print('time_diff', time_diff)\n",
" print('frequencies', freqs)\n",
" #print('time_phase', time_phase)\n",
"\n",
" #print('space_diff', space_diff)\n",
" print('wavelengths', wavelengths)\n",
" #print('space_phase', space_phase)\n",
" \n",
" print('time_phase shape', time_phase.shape)\n",
" print('space_phase shape', space_phase.shape)\n",
" \n",
" signal = np.sin( time_phase + space_phase )\n",
"\n",
" if freqs.shape:\n",
" signal = signal.sum(axis=0)\n",
" \n",
" return signal\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"frequencies = 1/np.array([2,-2])\n",
"velocities = np.array([1, 4])\n",
"signal = TravellingSine(0, 0, frequencies)\n",
"\n",
"zeros = np.zeros(500)\n",
"x = np.linspace(-10, 10, 500)\n",
"t = x\n",
"\n",
"x_mesh, t_mesh = np.meshgrid(x,t, sparse=True)\n",
"\n",
"fig = plt.figure()\n",
"plt.suptitle(\"Travelling sine wave\")\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.plot(x, zeros, signal(x, zeros, velocities), label='right moving')\n",
"ax.plot(x, t, signal(x, t, velocities), label='left moving')\n",
"ax.plot(x, t, signal(x, t, 1), label='flat line')\n",
"ax.set_xlabel(\"spatial distance\")\n",
"ax.set_ylabel('temporal distance')\n",
"ax.set_zlabel(\"amplitude\")\n",
"ax.legend()\n",
"plt.show();"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# animation\n",
"fig = plt.figure()\n",
"plt.suptitle(\"Travelling sine wave\")\n",
"ax = fig.add_subplot(111,projection='3d')\n",
"ax.set_xlabel(\"spatial distance\")\n",
"ax.set_ylabel('temporal distance')\n",
"ax.set_zlabel(\"amplitude\")\n",
"l1 = ax.plot(x[0], t[0], signal(x[0], t[0], velocities), label='right moving')\n",
"l2 = ax.plot(x[0], t[0], signal(x[0], t[0], velocities[::-1]), label='left moving')\n",
"l3 = ax.plot(x[0], t[0], signal(x[0], t[0], 1), label='flat line')\n",
"\n",
"lines = [l1, l2, l3]\n",
"\n",
"def update(i, fig, ax):\n",
" ax.view_init(elev=20., azim=i)\n",
" \n",
" \n",
" ax.legend()\n",
" return fig, ax\n",
" \n",
"anim = FuncAnimation(fig, update, frames=np.arange(0, 360, 2), repeat=True, fargs=(fig, ax))\n",
"anim.save('rgb_cube.gif', dpi=80, writer='imagemagick', fps=24)\n",
"plt.show();"
]
}
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