add flux_3d.png

examples/jupyter/expansion-filters.ipynb

@@ -151,7 +151,7 @@
     {
      "data": {
       "text/plain": [
-       "PosixPath('/mnt/d/MIT_CRPG/openmc_develop/openmc/examples/jupyter/statepoint.210.h5')"
+       "0.30282347701347406+/-0.0006325501096712208"
       ]
      },
      "execution_count": 7,
@@ -160,7 +160,7 @@
     }
    ],
    "source": [
-    "model.run(output=False)"
+    "sp_file = model.run(output=False)"
    ]
   },
   {
@@ -176,7 +176,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "with openmc.StatePoint('statepoint.210.h5') as sp:\n",
+    "with openmc.StatePoint(sp_file) as sp:\n",
     "    df = sp.tallies[flux_tally.id].get_pandas_dataframe()"
    ]
   },
@@ -444,15 +444,18 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Alternatively, Zernike polynomials provided in OepnMC to represent continuous functions of space or angle can be reconstructed from the tallied moments.\n",
+    "## Zernike polynomials\n",
     "\n",
-    "In this example, we will determine the spatial dependence of the flux along the radial direction $r'$ and / or azimuthal angle $\\theta$ by making a Zernike polynomial expansion. Let us represent the flux along the radial and azimuthal direction, $\\phi(r', \\theta)$, by the function\n",
+    "Now let's look at an example of functional expansion tallies using Zernike polynomials as the basis functions.\n",
+    "\n",
+    "In this example, we will determine the spatial dependence of the flux along the radial direction $r'$ and $/$ or azimuthal angle $\\theta$ by making a Zernike polynomial expansion. Let us represent the flux along the radial and azimuthal direction, $\\phi(r', \\theta)$, by the function\n",
     "\n",
     "$$ \\phi(r', \\theta) = \\sum\\limits_{n=0}^N \\sum\\limits_{m=-n}^n a_n^m Z_n^m(r', \n",
     "\\theta) $$\n",
     "\n",
     "where $r'$ is the position normalized to the range [0, r], and the azimuthal lies within the range [0, $ 2\\pi$]. \n",
-    "Since $Z_n^m(r', \\theta)$ are known functions, what we need to do is to determine the expansion coefficients, $a_n^m$. By the orthogonality properties of the Zernike polynomials, one can deduce that the coefficients, $a_n^m$, are given by\n",
+    "\n",
+    "Since $Z_n^m(r', \\theta)$ are known functions, we need to determine the expansion coefficients, $a_n^m$. By the orthogonality properties of the Zernike polynomials, one can deduce that the coefficients, $a_n^m$, are given by\n",
     "\n",
     "$$ a_n^m = k_n^m \\int_{0}^r dr' \\int_{0}^{2\\pi} d\\theta Z_n^m(r',\\theta) \\phi(r', \\theta).$$\n",
     "$$ k_n^m = \\frac{2n + 2}{\\pi}, m \\ne 0. $$\n",
@@ -465,7 +468,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "To begin, let us first create a simple model. The model will be a pin-cell fuel material with vacuum boundary condition in both radial direction and axial direction."
+    "To begin with, let us first create a simple model. The model will be a pin-cell fuel material with vacuum boundary condition in both radial direction and axial direction."
    ]
   },
   {
@@ -596,7 +599,7 @@
     }
    ],
    "source": [
-    "model.run(output=False)"
+    "sp_file = model.run(output=False)"
    ]
   },
   {
@@ -612,7 +615,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "with openmc.StatePoint('statepoint.100.h5') as sp:\n",
+    "with openmc.StatePoint(sp_file) as sp:\n",
     "    df1 = sp.tallies[flux_tally_legendre.id].get_pandas_dataframe()"
    ]
   },
@@ -789,7 +792,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Since the scaling factors for expansion coefficients will be given in Python API, thus, we do not need to multiply the moments by scaling factors."
+    "Since the scaling factors for expansion coefficients will be provided by the Python API, thus, we do not need to multiply the moments by scaling factors."
    ]
   },
   {
@@ -864,7 +867,7 @@
    "metadata": {},
    "source": [
     "A rough cosine shape is obtained. \n",
-    "One can also conduct numerically integrating using the trapezoidal rule."
+    "One can also numerically integrate the function using the trapezoidal rule."
    ]
   },
   {
@@ -900,7 +903,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "with openmc.StatePoint('statepoint.100.h5') as sp:\n",
+    "with openmc.StatePoint(sp_file) as sp:\n",
     "    df2 = sp.tallies[flux_tally_zernike.id].get_pandas_dataframe()"
    ]
   },
@@ -1166,7 +1169,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "with openmc.StatePoint('statepoint.100.h5') as sp:\n",
+    "with openmc.StatePoint(sp_file) as sp:\n",
     "    df3 = sp.tallies[flux_tally_zernike1d.id].get_pandas_dataframe()"
    ]
   },
@@ -1437,7 +1440,7 @@
     "    phi = np.arctan2(y, x)\n",
     "    return(rho, phi)\n",
     "\n",
-    "# reconstruct 3-D flux based on azimuthal Zernike and Legendre polynomials\n",
+    "# Reconstruct 3-D flux based on azimuthal Zernike and Legendre polynomials\n",
     "z_n = np.array(df2['mean'])\n",
     "zz = openmc.Zernike(z_n, radius=radius) \n",
     "#\n",
@@ -1539,7 +1542,7 @@
     }
    ],
    "source": [
-    "f1 = plt.imread('flux3d.png')\n",
+    "f1 = plt.imread('./images/flux3d.png')\n",
     "plt.imshow(f1, cmap='jet')"
    ]
   },