{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This simple Python example uses the stationary phase approximation to evaluate the integral:\n", "\\begin{equation}\n", "f(x,t) = \\int_{-\\infty}^\\infty dk\\, e^{-\\frac{(k-k_0)^2}{\\Delta k^2}}e^{\\frac{i}{\\lambda}\\left[kx - k^2 t\\right]}\n", "\\end{equation}\n", "\n", "The points of stationary phase obey:\n", "$$\n", " x = 2k_0t\n", "$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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BAsOaJI2RYU3S+FXBq52wVh1nWJOkMTGsSRo/w5okdZxhTdL43XlnsYzUwoXtHV+FtczO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\nWAGLF8OsWXVXUo+TToING2D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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import quad\n", "import math\n", "Dk2 = 0.01\n", "lmda = 0.01\n", "k0 = 1.0\n", "kmax = 0.4\n", "T = 1.0\n", "N = 400\n", "X_len = 10.0\n", "\n", "def I(k,x,t):\n", " return (np.exp(-(k-k0)**2/Dk2)*np.exp(1j*(k*x-k**2*t)/lmda))\n", "def I_real(k,x,t):\n", " return (I(k,x,t)).real\n", "def I_imag(k,x,t):\n", " return (I(k,x,t)).imag\n", "def F(x,t):\n", " return quad(I_real,-kmax+k0,+kmax+k0,args=(x,t,),limit=100)[0] \\\n", " +1j*quad(I_imag,-5,+5,args=(x,t,),limit=100)[0]\n", "X = np.zeros(N+1,)\n", "FF = np.zeros(N+1,)\n", "for n in range(0,N+1):\n", " X[n]=X_len*n/N\n", "def F_array(t):\n", " for n in range(0,N+1):\n", " FF[n] = abs(F(X[n],t))\n", " return FF\n", "\n", "#plot result\n", "fig, (ax) = plt.subplots(nrows=1, figsize=(10, 8))\n", "ax.plot(X,F_array(T),'r-') # determine what is shown in ax. Choose the first \n", " # curve red solid.\n", "ax.set(xlabel='position (x)', ylabel='|F(x)', \n", " title='Stationary Phase Approximation') # add a tile and axis labels.\n", "#ax.set_ylim(-20000,0000)\n", "#ax.set_xlim(47,53)\n", "#ax.grid() #superimpose a grid\n", "fig.savefig(\"test.pdf\") # save the figure as a png file.\n", "plt.show(fig) # Plot the figure here." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }