mirror of
https://gitlab.science.ru.nl/mthesis-edeboone/m-thesis-introduction.git
synced 2024-11-13 01:53:31 +01:00
163 lines
93 KiB
Text
163 lines
93 KiB
Text
{
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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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"# 1D Travelling Signal (sine with linear dispersion)\n",
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"\n",
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"\n",
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"$$\n",
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"A(x, t) = \\sin\\left( \\frac{2 \\pi x}{\\lambda} -2\\pi f t\\right)\n",
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"\\\\\n",
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"= \\sin\\left( 2 \\pi f \\, ( \\frac{x}{v(f)} -t) \\right)\n",
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"$$\n",
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"\n",
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"$\\lambda = \\dfrac{v}{f}$"
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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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"source": [
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"import numpy as np\n",
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"import scipy.fft as ft\n",
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"import matplotlib.pyplot as plt\n",
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"from mpl_toolkits.mplot3d import axes3d"
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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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"source": [
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"class TravellingSine:\n",
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" \"\"\"\n",
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" Scalar Travelling Sine wave with a constant dispersion relation per frequency\n",
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" \"\"\"\n",
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" def __init__(self, x_0, t_0, frequencies):\n",
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" self.x_0 = x_0\n",
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" self.t_0 = t_0\n",
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" self.freqs = np.array(frequencies).reshape(-1)\n",
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"\n",
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" def __call__(self, x_f, t_f, phase_velocities = None):\n",
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" x_f = np.array(x_f)\n",
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" t_f = np.array(t_f)\n",
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" return self._signal(self.x_0, x_f, self.t_0, t_f, self.freqs, phase_velocities)\n",
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"\n",
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" def _signal(self, x_0, x_f, t_0, t_f, freqs, phase_velocities = None, debug = 0):\n",
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" \n",
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" 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",
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" \n",
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" if phase_velocities is None:\n",
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" phase_velocities = 1\n",
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" \n",
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" if callable(phase_velocities):\n",
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" phase_velocities = phase_velocities(freqs)\n",
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"\n",
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" if np.ndim(phase_velocities) == 0:\n",
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" phase_velocities = phase_velocities * np.ones(self.freqs.shape)\n",
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" \n",
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" assert len(freqs) == len(phase_velocities), \"freqs and phase_velocities MUST have equal length: {} and {}\".format(len(freqs), len(phase_velocities))\n",
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" \n",
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" # get the wavelengths for each frequency\n",
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" wavelengths = phase_velocities / freqs\n",
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" \n",
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" # make sure these are 1d arrays\n",
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" time_diff = np.array(t_0 - t_f).reshape(-1) \n",
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" space_diff = np.array(x_0 - x_f).reshape(-1) \n",
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" \n",
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" # ndarray of phase components\n",
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" time_phase = np.outer(2*np.pi*freqs, time_diff)\n",
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" space_phase = np.outer(2*np.pi/wavelengths, space_diff)\n",
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" \n",
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" if debug:\n",
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" if debug > 1:\n",
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" #print('time_diff', time_diff)\n",
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" print('frequencies', freqs)\n",
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" #print('time_phase', time_phase)\n",
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"\n",
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" #print('space_diff', space_diff)\n",
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" print('wavelengths', wavelengths)\n",
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" #print('space_phase', space_phase)\n",
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" \n",
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" print('time_phase shape', time_phase.shape)\n",
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" print('space_phase shape', space_phase.shape)\n",
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" \n",
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" signal = np.sin( time_phase + space_phase )\n",
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"\n",
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" if freqs.shape:\n",
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" signal = signal.sum(axis=0)\n",
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" \n",
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" return signal\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": 3,
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"metadata": {},
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"outputs": [
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{
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"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, 8])\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",
|
|
"\n",
|
|
"fig = plt.figure()\n",
|
|
"plt.suptitle(\"Travelling sine wave\")\n",
|
|
"ax = fig.add_subplot(111,projection='3d')\n",
|
|
"ax.plot(x, t, signal(x, t, velocities), label='right moving')\n",
|
|
"ax.plot(x, t, signal(x, t, velocities[::-1]), 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();"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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