diff --git a/Lyapage/High-Order_NLSE.ipynb b/Lyapage/High-Order_NLSE.ipynb new file mode 100644 index 0000000..14edd49 --- /dev/null +++ b/Lyapage/High-Order_NLSE.ipynb @@ -0,0 +1,772 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###### Content under Creative Commons Attribution license CC-BY 4.0, code under MIT license (c)2014 L.A. Barba, C. Cooper, G.F. Forsyth, A. Krishnan.\n", + "\n", + "# Application of Schrödinger equation in micropropulsion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Introduction\n", + "### 1.1 Background for micropropulsion engine\n", + "

“ Where did we get that (equation) from? Nowhere. It is not possible to derive it from\n", + "anything you know. It came out of the mind of Schrödinger. ”

\n", + "

--Richard Feynman [1]

\n", + "\n", + "Schrödinger equation can be used to explain the dynamics of solition which is highly related to optical fiber communication performance. Besides, this magic equation plays a perfect tool in micropropulsion (powered by energized plama) to represent the dynamics of waves creaed by plasma (neutral combination of ions and electrons) associated with thrust which based on the mechanism of utilizing eletromanetic coil to produce and accelerate plasma.\n", + "\n", + "\n", + "

Figure 1.Micropropulsion engine

\n", + "\n", + "

Figure 2.Micropropulsion engine cross-section

\n", + "\n", + "The Figure 1 shows the part of micropropulsion engine included the plasma injecting chamber and nozzle.The Figure 2 highlihted the plasma chamber as blue part which can be easily distinguished. In this project, nonlinear Schrödinger equation (NLSE) will be treated as 1D and the spatial coordinates correspond to the length of chamber.\n", + "\n", + "### 1.2 Selection of proper NLSE for micropropulsion Engine\n", + "\n", + "Then,it is the time to select the most appropriate schrödinger equation to depict this problem from various types. Original Inhomogeneous higher order nonlinear schrödinger equation (IHNLSE) by **Zhang** [2]:\n", + "\n", + "$$\\Psi_x = i( a_1(x)\\Psi_{tt} + a_2(x)|\\Psi|^2\\Psi ) + a_3(x)\\Psi_{ttt} + a_4(x)(|\\Psi|^2\\Psi)_t \\\\\n", + " a_5(x)\\Psi(|\\Psi|^2)_t + \\Gamma(x)\\Psi\\qquad\\qquad(1)$$\n", + " \n", + "For numerical solution, Eq (1) contains a third order time derivatives term which causing the problem of chosing schemes. An interesting thing is that if one let $a_3(x) = a_4(x) = a_5(x) = \\Gamma (x) = 0$, this equation will become a perturbed nonlinear schrödinger equation:\n", + "\n", + "$$\\Psi_x = i(a_1(x)\\Psi_{tt} + a_2(x)|\\Psi|^2\\Psi)\\qquad\\qquad(2)$$\n", + "\n", + "Eq (2) is similar to derivative nonlinear schrödinger type 1 solved by **David J. kaup** [3] and type 2 derived by **Hassan** [4]: \n", + "\n", + "$$i\\Psi_t = -\\Psi_{xx} + i(\\Psi \\Psi^2)_x\\qquad type~1\\\\\n", + " i\\Psi_t + \\dfrac{1}{2}\\Psi_{xx}+|\\Psi|^2\\Psi + i\\epsilon\\beta_2|\\Psi|^2\\Psi_x = 0\\qquad type~2\\qquad(3)$$\n", + "\n", + "However, for above three equations, they hold one common defficiency: lack of dissipation term which is required for describing working status of plasma injecting chamber.Then,a dissipative NLSE by **Hilmi Demiray** [5] introduced:\n", + "\n", + "$$i\\Psi_t + \\mu_1\\Psi_{xx} + \\mu_2|\\Psi|^2\\Psi + i\\mu_3\\Psi = 0\\qquad\\qquad(4)$$\n", + "\n", + "For above equation $\\mu_1-dispersion, \\mu_2-nonlinearity, \\mu_3-dissipation$ when dissipasive are weak which means $\\mu_3=0$, then this equation have almost the same expression of **S.M.Hoseini etc** model [6]." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2 Solving NLSE\n", + "\n", + "### 2.1 Analytical solution \n", + "\n", + "For Eq (4), **Hilmi Demiray** also derive the exact analytical solution in [5]. Due the complex expression of analytical solution, sympy will be used here to presents the expression clearly.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/latex": [ + "$$\\Psi{\\left (t,x \\right )} = a_{0} e^{i \\left(- K^{2} \\mu_{1} t + K \\zeta - \\frac{3 a_{0}^{2} \\mu_{2}}{4 \\mu_{3}} \\left(-1 + e^{- \\frac{4 \\mu_{3}}{3} t}\\right)\\right)} e^{- \\frac{2 \\mu_{3}}{3} t} \\tanh{\\left (\\zeta \\right )}$$" + ], + "text/plain": [ + " ⎛ ⎛ -4⋅μ₃⋅t ⎞⎞ \n", + " ⎜ ⎜ ────────⎟⎟ \n", + " ⎜ 2 ⎜ 3 ⎟⎟ \n", + " ⎜ 2 3⋅a₀ ⋅μ₂⋅⎝-1 + ℯ ⎠⎟ -2⋅μ₃⋅t \n", + " i⋅⎜- K ⋅μ₁⋅t + K⋅ζ - ─────────────────────────⎟ ──────── \n", + " ⎝ 4⋅μ₃ ⎠ 3 \n", + "Ψ(t, x) = a₀⋅ℯ ⋅ℯ ⋅tanh(ζ\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + ")" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import sympy\n", + "from fractions import Fraction\n", + "sympy.init_printing()\n", + "\n", + "'''\n", + "define three variables actually zata is the intermediate variables depend on t and x\n", + "'''\n", + "(i, Psi, K, a_0,mu_1,mu_2,mu_3,t,x,zeta) = sympy.symbols('i Psi K a_0 mu_1 mu_2 mu_3 t x zeta') \n", + "\n", + "eq1 = sympy.Eq(Psi(t,x),a_0*sympy.exp(Fraction(-2,3)*mu_3*t)*sympy.tanh(zeta)\\\n", + " *sympy.exp(i*(K*zeta-mu_1*K**2*t\\\n", + " -Fraction(3,4)*mu_2/mu_3*a_0**2*(sympy.exp(Fraction(-4,3)*mu_3*t)-1))))\n", + "\n", + "eq2 = sympy.Eq(zeta(t,x),(-mu_2/(2*mu_1))**(Fraction(1,2))*a_0*sympy.exp(-Fraction(2,3)*mu_3\\\n", + " *t)*(x-2*mu_1*K*t))\n", + "eq1" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/latex": [ + "$$\\zeta\\left(t, x\\right) = \\frac{\\sqrt{2} a_{0}}{2} \\sqrt{- \\frac{\\mu_{2}}{\\mu_{1}}} \\left(- 2 K \\mu_{1} t + x\\right) e^{- \\frac{2 \\mu_{3}}{3} t}$$" + ], + "text/plain": [ + " -2⋅μ₃⋅t \n", + " ______ ────────\n", + " ╱ -μ₂ 3 \n", + " √2⋅a₀⋅ ╱ ──── ⋅(-2⋅K⋅μ₁⋅t + x)⋅ℯ \n", + " ╲╱ μ₁ \n", + "ζ(t, x) = ──────────────────────────────────────────\n", + " 2 " + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "eq2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Above two equations consists of the exact anlytical solution system among these two equations, $a_0,K-constants$" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def NLSE_analytical(t,x,mu_1,mu_2,mu_3,a_0,K):\n", + " \n", + " '''\n", + " 1. using code: print(eq1) print(eq2) will obtain analytical solution just copy and paste\n", + " them and add prefix:numpy for each operator. \n", + " \n", + " mu_1: dispersion coefficient\n", + " \n", + " mu_2: nonlinearity coefficient\n", + " \n", + " mu_3: dissipation coefficient\n", + " \n", + " a_0,K - arbitrary constants for solution\n", + " \n", + " '''\n", + " if mu_1*mu_2 > 0: #numpy.sqrt() cannot calculate negative number so make some changes:\n", + " # ex) numpy.sqrt(-5) = 1j*numpy.sqrt(numpy.abs(5))\n", + " \n", + " zeta= numpy.sqrt(2.0)*a_0*numpy.sqrt(numpy.abs(-mu_2/mu_1))*1j*(-2*K*mu_1*t + x)\\\n", + " *numpy.exp(-2*mu_3*t/3)/2\n", + " \n", + " \n", + " else:\n", + " \n", + " zeta= numpy.sqrt(2.0)*a_0*numpy.sqrt(-mu_2/mu_1)*(-2*K*mu_1*t + x)\\\n", + " *numpy.exp(-2*mu_3*t/3)/2\n", + " \n", + " \n", + " psi = a_0*numpy.exp(1j*(-K**2*mu_1*t + K*zeta - 3*a_0**2*mu_2\\\n", + " *(-1 + numpy.exp(-4*mu_3*t/3))/(4*mu_3)))\\\n", + " *numpy.exp(-2*mu_3*t/3)*numpy.tanh(zeta)\n", + " \n", + " \n", + " return psi" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import numpy\n", + "#Specific impulse for micropropulsion is short, so 5s is an acceptable value.\n", + "#According to Professor Michael Keidar's design, length of plasma injecting chamber is 50cm.\n", + "\n", + "tmin = 0.0\n", + "tmax = 5.0\n", + "nt = 101 #number of steps for time\n", + "dt = (tmax-tmin)/(nt-1)\n", + "\n", + "xmin = 0.0\n", + "xmax = 0.5\n", + "nx = 101 #number of steps for space\n", + "dx = (xmax-xmin)/(nx-1)\n", + "\n", + "t = numpy.linspace(tmin,tmax,nt)\n", + "x = numpy.linspace(xmin,xmax,nx)\n", + "t,x = numpy.meshgrid(t,x)\n", + "\n", + "#mu_1,2,3 coefficients for function \n", + "#a_0,K arbitrary constants for analytical solution \n", + "mu_1 = 1\n", + "mu_2 = 1\n", + "mu_3 = 1\n", + "a_0 = 1\n", + "K = 1\n", + "#obtain the anlytical solution:\n", + "psi_analy = NLSE_analytical(t,x,mu_1,mu_2,mu_3,a_0,K)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from matplotlib import pyplot\n", + "%matplotlib inline\n", + "from matplotlib import rcParams\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "from matplotlib import cm\n", + "rcParams['font.family'] = 'serif'\n", + "rcParams['font.size'] = 16\n", + "\n", + "\n", + "def plot_3D(t, x, psi):\n", + " \n", + " '''Creates 3D plot for real and imaginary part of psi(t,x)\n", + " \n", + " Parameters:\n", + " ----------\n", + " t: time array\n", + " \n", + " x: space array\n", + " \n", + " psi: wave array\n", + " \n", + " '''\n", + " fig = pyplot.figure(figsize=(16,10), dpi=100)\n", + " \n", + " ax1 = fig.add_subplot(121, projection='3d')\n", + " ax1.plot_surface(t,x,numpy.real(psi), rstride=1, cstride=1, cmap=cm.viridis,\n", + " linewidth=0, antialiased=False)\n", + " ax1.set_title('$Analytical\\;solution\\;for\\;NLSE:real\\;part$')\n", + " ax1.set_xlabel('$t$',fontsize = 30)\n", + " ax1.set_ylabel('$x$',fontsize = 30)\n", + " ax1.set_zlabel('$z$',fontsize = 30)\n", + " ax1.ticklabel_format(style='sci', axis='z', scilimits=(0,0))\n", + " \n", + " ax2 = fig.add_subplot(122, projection='3d')\n", + " ax2.plot_surface(t,x,numpy.imag(psi), rstride=1, cstride=1, cmap=cm.viridis,\n", + " linewidth=0, antialiased=False)\n", + " ax2.set_title('$Analytical\\;solution\\;for\\;NLSE:imaginary\\;part$')\n", + " ax2.set_xlabel('$t$',fontsize = 30)\n", + " ax2.set_ylabel('$x$',fontsize = 30)\n", + " ax2.set_zlabel('$z$',fontsize = 30)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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S4XAYyWRSXUE0gxtHPnOpFadYLAZZljMSp7///e+orKzEq6++issuu0xNpiaI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2ebz2ZT22RkZWVhwoQJOHHihF1crCbViiaLxLQtW7Zg/PjxWLBgATw8PPjjZ8+eRcOGDTFn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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_3D(t,x,psi_analy)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "### 2.2 Numerical solution\n", + "S.M.Hoeini in his paper [6] introduces two implicit schemes--Crank-nicolson scheme and Taha schemes(based on inverse scatterig transform) to calculate this function. \n", + "\n", + "Crank-nilson scheme recommended here, since this method is popular for second-order parabolic PDE:\n", + "\n", + "$$i(\\Psi_i^{n+1} - \\Psi_i^{n}) + \n", + "\\frac{i\\Delta t }{2}\\mu_3(\\Psi_{i}^{n+1} + \\Psi_{i}^{n})\n", + "+\\frac{\\Delta t }{2}\\mu_2(\\Psi_i^n~{|\\Psi_i^{n}|}^2 + \\Psi_i^{n+1}~|\\Psi_i^{n+1}|^2) \n", + "\\\\+\\dfrac{\\Delta t}{2\\Delta x^2}\\mu_1(\\Psi_{i+1}^{n+1} - 2\\Psi_{i}^{n+1}+\\Psi_{i-1}^{n+1}+\\Psi_{i+1}^n - 2\\Psi_{i}^n + \\Psi_{i-1}^n) = 0$$\n", + "\n", + "This system is unconditionally stable and this is one of the main advantages of implicit method.\n", + "\n", + "Now it is time to provide the Taha scheme:\n", + "\n", + "$$\\Psi_i^{n+1} - \\Psi_i^n+(\\Psi_{i+2}^n+\\Psi_{i-2}^n)A^{(4)}-(\\Psi_{i+2}^{n+1}+\\Psi_{i-2}^{n+1})D^{(4)} + (\\Psi_{i+1}^n + \\Psi_{i-1}^n)A^{(2)}-(\\Psi_{i+1}^{n+1}+\\Psi_{i-1}^{n+1})D^{(2)}\\\\\n", + "+\\Psi_{i}^{n}A^{(0)} - \\Psi_{i}^{n+1}D^{(0)}+\\Delta x^2[((\\Psi_{i+1}^{n}~\\Psi_{i+2}^{n+1}~\\Psi_{i+1}^{n+1})+\\Psi_{i+1}^{n+1}\\Psi_{i}^{n+1}\\Psi_{i+1}^{n})...)]$$\n", + "\n", + "It is beyond complicated, I will remove Taha scheme or apply this fancy scheme later. Rearrange terms in Crank scheme put unknown terms on the left whereas place known terms on the right:\n", + "\n", + "\n", + "\n", + "$$ i\\Psi_i^{n+1} + \\frac{i\\Delta t}{2}\\mu_3\\Psi_i^{n+1} +\\frac{\\Delta t}{2}\\mu_2|\\Psi_i^{n+1}|^2\\Psi_i^{n+1} + \\frac{\\Delta t}{2\\Delta x^2}\\mu_1(\\Psi_{i+1}^{n+1} - 2\\Psi_i^{n+1} - \\Psi_{i-1}^{n+1}) = \\\\ i\\Psi_{i}^{n}-\\frac{i\\Delta t}{2}\\mu_3\\Psi_{i}^{n} - \\frac{\\Delta t}{2}\\mu_2|\\Psi_{i}^{n}|^2\\Psi_{i}^{n} -\\frac{\\Delta t}{2\\Delta x^2}\\mu_1(\\Psi_{i+1}^{n} - 2\\Psi_i^{n} + \\Psi_{i-1}^n) $$\n", + "\n", + "Taking condition of inlet and outlet of injecting plasma chamber into account, the left side of this equation satisfy Dirichlet boundary condition: $\\Psi(t,0) = 0$ and the right side satisfy Dirichlet condition$\\Psi(t,L=0.5) = 0$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "solving the equations: $[A][\\Psi_i^{n+1}] = [b] + [b]_{b.c} + a_2[~|\\Psi_i^n|^2\\Psi_i^n~]$, then Coefficient matrix A:\n", + "\n", + "\\begin{bmatrix}\n", + " i+a_1-2a_3 & a_3 &\\cdots &\\cdots &0 \\\\\n", + " -a_3 & i+a_1-2a_3 & a_3 &\\cdots &0 \\\\\n", + " 0 & -a_3 & i+a_1-2a_3 & a_3 &\\cdots\\\\\n", + " \\cdots\\\\\n", + " \\cdots\\\\\n", + " \\cdots &\\cdots & \\cdots &-a_3 & i+a_1-2a_3 \\\\\n", + "\\end{bmatrix}\n", + "\n", + "matrix $[\\Psi_i^{n+1}]$, and $[b] + [b]_{b.c} + a_2[~|\\Psi_i^n|^2\\Psi_i^n~]$ should be: \n", + "\n", + " \\begin{bmatrix} \\Psi_1^{n+1}\\\\ \\Psi_2^{n+1} \\\\ \\vdots \\\\ \\Psi_{nx-2}^{n+1} \\end{bmatrix}\n", + " \n", + " \\begin{bmatrix}a_3\\Psi_0^{n+1} -a_3\\Psi_0^{n} + (i+2a_3-a_1)\\Psi_1^{n} - a_2(|\\Psi_1^{n}|^2\\Psi_1^n+|\\Psi_1^{n+1}|^2\\Psi_1^{n+1}) + a_3\\Psi_2^n \\\\ \n", + " -a_3\\Psi_1^n + (i+2a_3-a_1)\\Psi_2^{n} - a_2(|\\Psi_2^{n}|^2\\Psi_2^n+|\\Psi_2^{n+1}|^2\\Psi_2^{n+1}) - a_3\\Psi_3^n \\\\ \n", + " \\vdots \\\\ \n", + " -a_3\\Psi_{nx-3}^n + (i+2a_3-a_1)\\Psi_{nx-2}^{n} - a_2(|\\Psi_{nx-2}^{n}|^2\\Psi_{nx-2}^n+|\\Psi_{nx-2}^{n+1}|^2\\Psi_{nx-2}^{n+1}) - a_3(\\Psi_{nx-1}^n+\\Psi_{nx-1}^{nx+1})\n", + " \\end{bmatrix}\n", + "\n", + "$a_1 = \\frac{i\\Delta t}{2}\\mu_3,~ a_2 = \\frac{\\Delta t}{2}\\mu_2,~a_3 = \\frac{\\Delta t}{2\\Delta x^2}\\mu_1$. **Mark J. Ablowitz** in his paper [7] states that it is rational to assume (only in the right side): $\\Psi_i^{n} = \\Psi_i^{n+1}$. Therefore, the right-hand side becomes known." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import numpy\n", + "from scipy.linalg import solve" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def Coefficient_Matrix(nx,dt,dx,mu_1,mu_3):\n", + " \n", + " '''\n", + " This is function aims at finding the matrix of coefficient\n", + " \n", + " '''\n", + " \n", + " a1 = 1j*dt/2*mu_3\n", + " a3 = dt/(2*dx**2)*mu_1\n", + " \n", + " #setup the diagonal \n", + " d = numpy.diag(numpy.ones(nx-2)*(1j - 2*a3+a1))\n", + "\n", + " #setup upper diagonal\n", + " ud = numpy.diag(numpy.ones(nx-3)*a3,1)\n", + "\n", + " #setup the lower diagonal\n", + " ld = numpy.diag(numpy.ones(nx-3)*-a3,-1)\n", + "\n", + " A = d + ud + ld \n", + "\n", + " return A" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-2000.+1.025j, 1000.+0.j , 0.+0.j , ..., 0.+0.j ,\n", + " 0.+0.j , 0.+0.j ],\n", + " [-1000.+0.j , -2000.+1.025j, 1000.+0.j , ..., 0.+0.j ,\n", + " 0.+0.j , 0.+0.j ],\n", + " [ 0.+0.j , -1000.+0.j , -2000.+1.025j, ..., 0.+0.j ,\n", + " 0.+0.j , 0.+0.j ],\n", + " ..., \n", + " [ 0.+0.j , 0.+0.j , 0.+0.j , ..., -2000.+1.025j,\n", + " 1000.+0.j , 0.+0.j ],\n", + " [ 0.+0.j , 0.+0.j , 0.+0.j , ..., -1000.+0.j ,\n", + " -2000.+1.025j, 1000.+0.j ],\n", + " [ 0.+0.j , 0.+0.j , 0.+0.j , ..., 0.+0.j ,\n", + " -1000.+0.j , -2000.+1.025j]])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = Coefficient_Matrix(nx,dt,dx,mu_1,mu_3)\n", + "A" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def generateRHS(dx,dt,mu_1,mu_2,mu_3,psi):\n", + " \n", + " '''\n", + " compute the right-hand side for NLSE\n", + " ------------------\n", + " psi: wave at current time step\n", + " \n", + " dx,dt: space and time step size\n", + " \n", + " mu_1,2,3: equation coefficients\n", + " \n", + " b: right hand side\n", + " \n", + " |psi|^2 = psi*numpy.conj(psi) due to psi is complex array\n", + " '''\n", + " b = numpy.empty_like(numpy.zeros(nx-2),dtype=complex)\n", + " a1 = 1j*dt/2*mu_3\n", + " a2 = dt/2*mu_2\n", + " a3 = dt/(2*dx**2)*mu_1\n", + " \n", + " b = -a3*psi[:-2] + (1j-a1+2*a3)*psi[1:-1] -\\\n", + " 2*a2*psi[1:-1]*numpy.conj(psi[1:-1])*psi[1:-1] -a3*psi[2:]\n", + " \n", + " boundary condition:\n", + " b[0] += psi[0]\n", + " \n", + " \n", + " return b" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def NLSE_crank_nicolson(psi,A):\n", + " \n", + " '''\n", + " A: coefficient matrix\n", + " \n", + " other parameters explained in above function\n", + " \n", + " psi_t: an array of wave contained time and space \n", + " '''\n", + " b = numpy.empty_like(numpy.zeros(nx-2),dtype=complex)\n", + " psi_t = numpy.empty_like( numpy.zeros((nt,nx)),dtype = complex)\n", + "\n", + " for i in range(nt):\n", + " psi_n = psi.copy()\n", + " b = generateRHS(dx,dt,mu_1,mu_2,mu_3,psi_n)\n", + "\n", + " psi_interior = solve(A,b)\n", + " psi[1:-1] = psi_interior\n", + " psi_t[i,:] = psi\n", + " \n", + " return psi_t" + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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XewAVwG3lHgBRnWhpM4/0MavN8Xgc69evx5133pmjl0ptTqVSRWkz4W5SqRSS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pTzpB23lUXCWWedhbPOOstxm4cfftj2e1deeaXrc/khXU+eEdNut9FoNLryUZhQHCOthjYEY0QG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\nRUhIo0P3IDLKymazti70I5EIFj51YcVjTjifEkYDxWp4ZWjjd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b6J53m0trai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\nOXPm4MCBA3rHVCoVrl27hr///e9mGhUhhBD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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "'''In Yaan Yee Choy paper [8], initial wave for NLSE was explained that\n", + " initial condition for psi should equals the derivation in [5]\n", + "\n", + " Therefore, in numerical solution initial condition of analytical solution will\n", + " be adopted here. \n", + "\n", + "t,x: time and space already provided in above context\n", + "'''\n", + "#initial condition of wave:\n", + "psi_i = psi_analy[0]\n", + "#attain the numerical solution: \n", + "psi_numerical = NLSE_crank_nicolson(psi_i.copy(),A)\n", + "\n", + "def plot_3D_n(t, x, psi):\n", + " \n", + " '''Creates 3D plot for numerical solution of real and imaginary part of psi(t,x)\n", + " \n", + " Parameters:\n", + " ----------\n", + " t: time array\n", + " \n", + " x: space array\n", + " \n", + " psi: wave array\n", + " \n", + " '''\n", + " fig = pyplot.figure(figsize=(16,10), dpi=100)\n", + " \n", + " ax1 = fig.add_subplot(121, projection='3d')\n", + " ax1.plot_surface(t,x,numpy.real(psi), rstride=1, cstride=1, cmap=cm.viridis,\n", + " linewidth=0, antialiased=False)\n", + " ax1.set_title('$Numerical\\;solution\\;for\\;NLSE:real\\;part$')\n", + " ax1.set_xlabel('$t$',fontsize = 30)\n", + " ax1.set_ylabel('$x$',fontsize = 30)\n", + " ax1.set_zlabel('$z$',fontsize = 30)\n", + " ax1.ticklabel_format(style='sci', axis='z', scilimits=(0,0))\n", + " \n", + " ax2 = fig.add_subplot(122, projection='3d')\n", + " ax2.plot_surface(t,x,numpy.imag(psi), rstride=1, cstride=1, cmap=cm.viridis,\n", + " linewidth=0, antialiased=False)\n", + " ax2.set_title('$Numerical\\;solution\\;for\\;NLSE:imaginary\\;part$')\n", + " ax2.set_xlabel('$t$',fontsize = 30)\n", + " ax2.set_ylabel('$x$',fontsize = 30)\n", + " ax2.set_zlabel('$z$',fontsize = 30)\n", + "\n", + "plot_3D_n(t,x,psi_numerical)" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def NLSE_FTCS(dt,dx,psi):\n", + " \n", + " '''\n", + " This is Forward time and central space (explicit method)\n", + " \n", + " let me consider the stability: dt/dx**2 >> 1 (not stable)\n", + " so this method should not be applied!!!!!!!!\n", + " '''\n", + " \n", + " psi_n = numpy.empty_like(numpy.zeros((nt,nx)),dtype = complex)\n", + " for i in range(nt):\n", + " psin = psi.copy()\n", + " psi[1:-1] = psin[1:-1] +\\\n", + " 1j*dt*dx**2*(psin[2:] - 2*psin[1:-1] + psin[0:-2])+\\\n", + " psin[1:-1]*numpy.conj(psin[1:-1])*psin[1:-1]-psin[1:-1]\n", + "\n", + " psi_n[i,:] = psi\n", + " \n", + " return psi_n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "### 2.3 Comparison of analytical and numerical solution\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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YtmwaP9/mfaPxAEVFMGoU9O7lYGj2F1SVVnL9V9fL/L5CGOSBN6+n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ry8vNCpUydER0dj5cqVJktpqlevbvzMS0lJMfnaACAwMBC1a9fGwYMFV7o7duwYQkNDAcDk2XYR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\n8UREREREdub/AXqke1GMMyiDAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#real part for analytical solution:\n", + "psi_analy_r = numpy.real(psi_analy)\n", + "#Imaginary part for analytical solution:\n", + "psi_analy_i = numpy.imag(psi_analy)\n", + "\n", + "#real part for numerical solution:\n", + "psi_numerical_r = numpy.real(psi_numerical)\n", + "#real part for numerical solution:\n", + "psi_numerical_i = numpy.imag(psi_numerical)\n", + "\n", + "pyplot.figure(figsize = (12,8))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('$x(m)$',fontsize = 16)\n", + "pyplot.ylabel('$\\Psi$',fontsize = 16)\n", + "pyplot.plot(x,psi_analy_r[10],ls='-',color='purple')\n", + "pyplot.plot(x,psi_numerical_r[10],ls='--',color='blue')\n", + "\n", + "pyplot.plot(x,psi_analy_i[10],ls='-',color='green')\n", + "pyplot.plot(x,psi_numerical_i[10],ls='--',color='brown')\n", + "pyplot.legend(['Re-Anlytical','Re-Numerical','Im-Anlytical','Im-Numerical'],loc=4,fontsize = 16)\n", + "pyplot.title('$Comparison$');" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def L2_error(psi_analy,psi_numerical):\n", + " '''\n", + " this function is to find the realtive error between analytical and numerical\n", + " \n", + " psi_analy: exact analytical solution of psi\n", + " \n", + " psi_numerical: numerical solution of psi\n", + " \n", + " e_r: L2 norm of error for real part\n", + " \n", + " e_i: L2 norm of error for imaginary part\n", + " \n", + " '''\n", + " #Finding the real and imaginary part for psi\n", + " psi_analy_r = numpy.real(psi_analy)\n", + " psi_analy_i = numpy.imag(psi_analy)\n", + " psi_numerical_r = numpy.real(psi_numerical)\n", + " psi_numerical_i = numpy.imag(psi_numerical)\n", + " \n", + " e_r = numpy.sqrt(numpy.sum((psi_analy_r-psi_numerical_r)**2)\\\n", + " /numpy.sum(psi_analy_r)**2)\n", + "\n", + " e_i = numpy.sqrt(numpy.sum((psi_analy_i-psi_numerical_i)**2)\\\n", + " /numpy.sum(psi_analy_i)**2)\n", + " \n", + " return e_r, e_i" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.00586200079894\n", + "0.0139251328871\n" + ] + } + ], + "source": [ + "e_r,e_i = L2_error(psi_analy[10],psi_numerical[10])\n", + "print(e_r)\n", + "print(e_i)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "##

Reference

\n", + "\n", + "[1]Section I.11 of Part I of Quantum Theory and Measurement by J.A. Wheeler and W.H. Zurek, eds., Princeton University Press, New Jersey 1983.\n", + "\n", + "[2]Li, Qi, Qiu-yuan Duan, and Jian-bing Zhang. \"Exact multisoliton solutions of general nonlinear Schrödinger equation with derivative.\" The Scientific World Journal 2014 (2014).\n", + "\n", + "[3]Kaup, David J., and Alan C. Newell. \"An exact solution for a derivative nonlinear Schrödinger equation.\" Journal of Mathematical Physics 19.4 (1978): 798-801.\n", + "\n", + "[4]Zedan, Hassan A., and Seham Sh Tantawy. \"Exact solutions for a perturbed nonlinear Schrödinger equation by using Bäcklund transformations.\" Mathematical Methods in the Applied Sciences 32.9 (2009): 1068-1081.\n", + "\n", + "[5]Demiray, Hilmi. \"An analytical solution to the dissipative nonlinear Schrödinger equation.\" Applied mathematics and computation 145.1 (2003): 179-184.\n", + "\n", + "[6]Hoseini, S. M., and Timothy R. Marchant. \"The analytical evolution of NLS solitons due to the numerical discretization error.\" Journal of Physics A: Mathematical and Theoretical 44.50 (2011): 505205.\n", + "\n", + "[7]Taha, Thiab R., and Mark I. Ablowitz. \"Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation.\" Journal of Computational Physics 55.2 (1984): 203-230." + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "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": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +}