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Created April 8, 2018 13:07
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Shallow water with bathymetry"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this notebook we study the Riemann problem for the shallow water equations in the presence of varying bathymetry. Specifically, we consider the case in which the elevation of the bottom is piecewise constant with a jump at $x=0$. Thus the Riemann problem consists of the shallow water equations, including an additional term in the momentum equation (corresponding to the bathymetry):\n",
"\\begin{align}\n",
" h_t + (hu)_x & = 0 \\\\\n",
" (hu)_t + \\left(hu^2 + \\frac{1}{2}gh^2\\right)_x & = -ghb_x,\n",
"\\end{align}\n",
"together with initial data\n",
"\\begin{align}\n",
" (h(x,0),u(x,0)) & = \\begin{cases} (h_l, u_l) & x<0 \\\\ (h_r, u_r) & x>0 \\end{cases}\n",
"\\end{align}\n",
"and bathymetry\n",
"$$b(x) = \\begin{cases} b_l & x<0 \\\\ b_r & x>0 \\end{cases}.$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Stationary wave at $x=0$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The source term owing to the bathymetry is (like that introduced to represent traffic flow from an on-ramp) singular: since the bathymetry $b(x)$ is discontinuous at $x=0$, the term $b_x$ is given by a delta-function: \n",
"$$b_x = (b_r-b_l)\\delta(x) = \\Delta b \\delta(x).$$ \n",
"Based on what we have learned in earlier chapters, it is natural to expect that the Riemann solution will include a stationary jump at $x=0$, due to this singular source term. What are the appropriate jump conditions for thiw wave? As usual, we would like to impose continuity of the flux at $x=0$, which for the first equation gives \n",
"$$h_- u_- = h_+ u_+.$$ \n",
"where e.g. $h_\\pm$ denote the limiting values of $h$ as $x\\to0$ from the right and left.\n",
"The other appropriate condition is evidently\n",
"\\begin{align} \\label{h_ave}\n",
" h_+ u_+^2 - h_- u_-^2 + \\frac{1}{2}g(h_+^2-h_-^2) = -g\\Delta b \\tilde{h},\n",
"\\end{align}\n",
"but it is unclear what value should be used for $\\tilde{h}$.\n",
"The source term involves the product of a delta function ($b_x$) and a discontinuous function ($h$). The product of these two functions has no clear definition. What is the second jump condition that should be imposed at $x=0$?\n",
"\n",
"The answer is still a matter of debate, and is unclear from both a mathematical perspective (as just mentioned) and from a physical perspective, since the shallow water assumption that a column of fluid has a single uniform velocity must break down near a bathymetry jump."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Hydrostatic approach"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we will take a natural condition that has been proposed in the literature. That is that the momentum flux on either side of $x=0$ should be equal, after taking into account the fact that the bathymetry on the higher side supports part of the pressure of the water on the lower side. For concreteness, suppose that $b_r > b_l$. Then we impose\n",
"$$h_- u_-^2 + \\frac{1}{2}g(h_- - (b_r-b_l))^2 = h_+ u_+^2 + \\frac{1}{2}gh_+^2.$$\n",
"This expression can also be written\n",
"$$h_+ u_+^2 - h_- u_-^2 + \\frac{1}{2}g(h_+^2-h_-^2) = -g(h_- - \\Delta b/2)\\Delta b ,$$\n",
"which has the form of \\eqref{h_ave} above with $\\tilde{h} = h_- - \\Delta b/2$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Approach of Alcrudo et. al."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$h_+ - h_- + \\frac{1}{2g}(u_+^2 - u_-^2) + \\Delta b = 0$$\n",
"This can also be written\n",
"$$ \\frac{\\tilde{h}}{2}(u_+^2 - u_-^2) + \\frac{g}{2} (h_+^2 - h_-^2) = - g \\tilde{h}\\Delta b$$\n",
"where $\\tilde{h}$ is the arithmetic average $(h_++h_-)/2$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Smooth steady state approach (George)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"D. George (citation) showed that any two steady states in a smooth steady state solution satisfy \n",
"$$h_+ u_+^2 - h_- u_-^2 + \\frac{1}{2}g(h_+^2-h_-^2) = -g\\Delta b \\tilde{h},$$ \n",
"where\n",
"$$\\tilde{h} = \\frac{h_+ + h_-}{2} \\frac{\\widetilde{\\lambda^+ \\lambda^-}}{\\overline{\\lambda^+ \\lambda^-}}$$\n",
"with\n",
"$$\\overline{\\lambda^+ \\lambda^-} = \\left(\\frac{u_+ + u_-}{2}\\right)^2 - g \\frac{h_+ + h_-}{2}$$\n",
"and\n",
"$$\\widetilde{\\lambda^+ \\lambda^-} = \\max(0,u_+ u_-) - g \\frac{h_+ + h_-}{2}.$$\n",
"This is equivalent to the approach of Alcrudo above (I think)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Resonance"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We expect that the Riemann solution will consist of two genuinely nonlinear waves (as in the case of the shallow water equations with flat bathymetry) and the stationary wave just described. However, as we have seen in the chapter on traffic with a variable speed limit, these waves can interact in more interesting ways. Note that we can write the SW with bathymetry system as a system of three equations:\n",
"\\begin{align}\n",
" h_t + (hu)_x & = 0 \\\\\n",
" (hu)_t + \\left(hu^2 + \\frac{1}{2}gh^2\\right)_x & = \\frac{1}{2}ghb_x \\\\\n",
" b_t & = 0.\n",
"\\end{align}\n",
"Here we have added the bathymetry as a third conserved quantity. The above system can be written as a homogeneous quasilinear hyperbolic system $q_t + A(q)q_x = 0$, with $q=[h,hu,b]^T$. The eigenvalues of $A(q)$ are then\n",
"$$\\lambda = u-\\sqrt{gh}, 0, u+\\sqrt{gh}.$$\n",
"This is exactly what we'd expect: the non-zero eigenvalues are the characteristic speeds present in the homogeneous shallow water system, while the zero eigenvalue corresponds to the stationary wave. However, notice that the ordering of the eigenvalues is not fixed, since the values $u\\pm\\sqrt{gh}$ can be positive or negative depending on the nature of the flow. In particular, these values can pass through zero, in which case the quasilinear system is not strictly hyperbolic -- it has a repeated eigenvalue. This leads to the phenomenon of resonance, in which a transcritical rarefaction wave is split by the stationary wave into two waves. One of them is a rarefaction, while the other may be a rarefaction or a shock (just as we saw in the case of the traffic flow model with varying speed limit).\n",
"\n",
"Thus in general the Riemann solution may consist of as many as four waves."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Examples"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"from exact_solvers import shallow_water_bathymetry as swb\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from utils import riemann_tools"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def c1(q, xi, g=1.):\n",
" \"Characteristic speed for shallow water 1-waves.\"\n",
" h = q[0]\n",
" if h > 0:\n",
" u = q[1]/q[0]\n",
" return u - np.sqrt(g*h)\n",
" else:\n",
" return 0\n",
"\n",
"def c2(q, xi, g=1.):\n",
" \"Characteristic speed for shallow water 2-waves.\"\n",
" h = q[0]\n",
" if h > 0:\n",
" u = q[1]/q[0]\n",
" return u + np.sqrt(g*h)\n",
" else:\n",
" return 0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Subcritical cases"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 1008x288 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"b_l = 0.\n",
"b_r = 1.\n",
"h_l = 2.-b_l\n",
"h_r = 1.5-b_r\n",
"u_l = 1.\n",
"u_r = -1.\n",
"g=1.\n",
"\n",
"q_l = np.array([h_l,h_l*u_l])\n",
"q_r = np.array([h_r,h_r*u_r])\n",
"states, speeds, reval, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='hydrostatic')\n",
"states, speeds, reval_d, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='alcrudo')\n",
"fig, axes = plt.subplots(1,2,figsize=(14,4))\n",
"riemann_tools.plot_waves(states,speeds,reval,wave_types,t_pointer=False,ax=axes[0])\n",
"xi = np.linspace(-5,5,500)\n",
"axes[1].plot(xi,reval(xi)[0]+(xi>0),xi,reval_d(xi)[0]+(xi>0));\n",
"plt.legend(['Hydrostatic','Alcrudo']);"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1008x288 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"b_l = 0.\n",
"b_r = 1.\n",
"h_l = 1.3-b_l\n",
"h_r = 1.2-b_r\n",
"u_l = 0.\n",
"u_r = 0.2\n",
"g=1.\n",
"\n",
"q_l = np.array([h_l,h_l*u_l])\n",
"q_r = np.array([h_r,h_r*u_r])\n",
"states, speeds, reval, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='hydrostatic')\n",
"states, speeds, reval_d, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='alcrudo')\n",
"fig, axes = plt.subplots(1,2,figsize=(14,4))\n",
"riemann_tools.plot_waves(states,speeds,reval,wave_types,t_pointer=False,ax=axes[0])\n",
"xi = np.linspace(-5,5,500)\n",
"axes[1].plot(xi,reval(xi)[0]+(xi>0),xi,reval_d(xi)[0]+(xi>0));\n",
"plt.legend(['Hydrostatic','Alcrudo']);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Resonant cases"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1008x288 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"b_l = 0.\n",
"b_r = 1.\n",
"h_l = 2.-b_l\n",
"h_r = 2.-b_r\n",
"u_l = 0.\n",
"u_r = 2.\n",
"g = 1.\n",
"\n",
"q_l = np.array([h_l,h_l*u_l])\n",
"q_r = np.array([h_r,h_r*u_r])\n",
"states, speeds, reval, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='hydrostatic')\n",
"states, speeds, reval_d, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='alcrudo')\n",
"fig, axes = plt.subplots(1,2,figsize=(14,4))\n",
"riemann_tools.plot_waves(states,speeds,reval,wave_types,t_pointer=False,ax=axes[0])\n",
"xi = np.linspace(-5,5,500)\n",
"axes[1].plot(xi,reval(xi)[0]+(xi>0),xi,reval_d(xi)[0]+(xi>0));\n",
"plt.legend(['Hydrostatic','Alcrudo']);"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x113a77d10>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1008x288 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"b_l = 0.\n",
"b_r = 1.\n",
"h_l = 2.-b_l\n",
"h_r = 1.5-b_r\n",
"u_l = 1.4\n",
"u_r = 2.0\n",
"g=1.\n",
"\n",
"q_l = np.array([h_l,h_l*u_l])\n",
"q_r = np.array([h_r,h_r*u_r])\n",
"states, speeds, reval, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='hydrostatic')\n",
"states, speeds, reval_d, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='alcrudo')\n",
"fig, axes = plt.subplots(1,2,figsize=(14,4))\n",
"riemann_tools.plot_waves(states,speeds,reval,wave_types,t_pointer=False,ax=axes[0])\n",
"xi = np.linspace(-5,5,500)\n",
"axes[1].plot(xi,reval(xi)[0]+(xi>0),xi,reval_d(xi)[0]+(xi>0));\n",
"plt.legend(['Hydrostatic','Alcrudo'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Supercritical cases"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1008x288 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"b_l = 0.\n",
"b_r = 1.\n",
"h_l = 2.-b_l\n",
"h_r = 2.-b_r\n",
"u_l = 3.\n",
"u_r = 0.\n",
"g=1.\n",
"\n",
"q_l = np.array([h_l,h_l*u_l])\n",
"q_r = np.array([h_r,h_r*u_r])\n",
"states, speeds, reval, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='hydrostatic')\n",
"states, speeds, reval_d, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='alcrudo')\n",
"fig, axes = plt.subplots(1,2,figsize=(14,4))\n",
"riemann_tools.plot_waves(states,speeds,reval,wave_types,t_pointer=False,ax=axes[0])\n",
"xi = np.linspace(-5,5,500)\n",
"axes[1].plot(xi,reval(xi)[0]+(xi>0),xi,reval_d(xi)[0]+(xi>0));\n",
"plt.legend(['Hydrostatic','Alcrudo']);"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1008x288 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"b_l = 0.\n",
"b_r = 1.\n",
"h_l = 2.-b_l\n",
"h_r = 5.-b_r\n",
"u_l = 3.\n",
"u_r = 2.\n",
"g=1.\n",
"\n",
"q_l = np.array([h_l,h_l*u_l])\n",
"q_r = np.array([h_r,h_r*u_r])\n",
"states, speeds, reval, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='hydrostatic')\n",
"states, speeds, reval_d, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='alcrudo')\n",
"fig, axes = plt.subplots(1,2,figsize=(14,4))\n",
"riemann_tools.plot_waves(states,speeds,reval,wave_types,t_pointer=False,ax=axes[0])\n",
"xi = np.linspace(-5,5,500)\n",
"axes[1].plot(xi,reval(xi)[0]+(xi>0),xi,reval_d(xi)[0]+(xi>0));\n",
"plt.legend(['Hydrostatic','Alcrudo']);"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(0.0, 1.6036822533546014, 4.0531719961377792)\n"
]
}
],
"source": [
"b_l = 0.\n",
"b_r = 1.\n",
"h_l = 2.-b_l\n",
"h_r = 2.-b_r\n",
"u_l = 2.\n",
"u_r = 4.\n",
"g = 1.\n",
"\n",
"states, speeds, wave_types = swb.predictor(h_l, h_r, u_l, u_r, b_l, b_r, g=1.)\n",
"print(speeds)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A problematic case"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First solution; this seems to violate the energy condition (see Rosetti) when the hydrostatic interface condition is used."
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1008x288 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"b_l = 0.\n",
"b_r = 1.\n",
"h_l = 2.-b_l\n",
"h_r = 1.5-b_r\n",
"u_l = 3.\n",
"u_r = 3.\n",
"g=1.\n",
"\n",
"q_l = np.array([h_l,h_l*u_l])\n",
"q_r = np.array([h_r,h_r*u_r])\n",
"states, speeds, reval, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='hydrostatic')\n",
"states, speeds, reval_d, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, which='alcrudo')\n",
"fig, axes = plt.subplots(1,2,figsize=(14,4))\n",
"riemann_tools.plot_waves(states,speeds,reval,wave_types,t_pointer=False,ax=axes[0])\n",
"xi = np.linspace(-5,5,500)\n",
"axes[1].plot(xi,reval(xi)[0]+(xi>0),xi,reval_d(xi)[0]+(xi>0));\n",
"plt.legend(['Hydrostatic','Alcrudo']);"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State just to left of x=0\n",
"('lambda 1: ', 1.5857864376269049)\n",
"('E :', 6.5)\n",
"('u :', 3.0)\n"
]
}
],
"source": [
"h, hu = reval([-0.01])\n",
"h = h[0]; hu=hu[0]\n",
"u = hu/h\n",
"c1 = u-np.sqrt(g*h)\n",
"print('State just to left of x=0')\n",
"print('lambda 1: ',c1)\n",
"print('E :', 0.5*u**2+h+b_l)\n",
"print('u :', u)"
]
},
{
"cell_type": "code",
"execution_count": 127,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State just to right of x=0\n",
"('lambda 1: ', 1.1568806242466438)\n",
"('E :', 5.791686534329747)\n",
"('u :', 2.6590323867226497)\n"
]
}
],
"source": [
"h, hu = reval([0.01])\n",
"h = h[0]; hu=hu[0]\n",
"u = hu/h\n",
"c1 = u-np.sqrt(g*h)\n",
"print('State just to right of x=0')\n",
"print('lambda 1: ',c1)\n",
"print('E :', 0.5*u**2+h+b_l)\n",
"print('u :', u)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Second solution: this seems to satisfy the energy condition of Rosetti."
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1008x288 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"states, speeds, reval, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, \n",
" which='hydrostatic',perturb_guess=True)\n",
"states, speeds, reval_d, wave_types = swb.exact_riemann_solution(q_l, q_r, b_l, b_r, g=g, \n",
" which='alcrudo',perturb_guess=True)\n",
"fig, axes = plt.subplots(1,2,figsize=(14,4))\n",
"riemann_tools.plot_waves(states,speeds,reval,wave_types,t_pointer=False,ax=axes[0])\n",
"xi = np.linspace(-5,5,500)\n",
"axes[1].plot(xi,reval(xi)[0]+(xi>0),xi,reval_d(xi)[0]+(xi>0));\n",
"plt.legend(['Hydrostatic','Alcrudo']);"
]
},
{
"cell_type": "code",
"execution_count": 128,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State just to left of x=0\n",
"('lambda 1: ', 1.5857864376269049)\n",
"('E :', 6.5)\n",
"('u :', 3.0)\n"
]
}
],
"source": [
"h, hu = reval([-0.01])\n",
"h = h[0]; hu=hu[0]\n",
"u = hu/h\n",
"c1 = u-np.sqrt(g*h)\n",
"print('State just to left of x=0')\n",
"print('lambda 1: ',c1)\n",
"print('E :', 0.5*u**2+h+b_l)\n",
"print('u :', u)"
]
},
{
"cell_type": "code",
"execution_count": 129,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State just to right of x=0\n",
"('lambda 1: ', 1.1568806242466438)\n",
"('E :', 5.791686534329747)\n",
"('u :', 2.6590323867226497)\n"
]
}
],
"source": [
"h, hu = reval([0.01])\n",
"h = h[0]; hu=hu[0]\n",
"u = hu/h\n",
"c1 = u-np.sqrt(g*h)\n",
"print('State just to right of x=0')\n",
"print('lambda 1: ',c1)\n",
"print('E :', 0.5*u**2+h+b_l)\n",
"print('u :', u)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that both solutions seem fine from the Alcrudo/George perspective (as far as I understand)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.13"
},
"toc": {
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"toc_cell": false,
"toc_position": {},
"toc_section_display": "block",
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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