A few minor improvements to pyclaw notebooks.

clawpack · Nov 19, 2023 · 219daee · 219daee
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diff --git a/notebooks/pyclaw/Stegotons.ipynb b/notebooks/pyclaw/Stegotons.ipynb
@@ -4,7 +4,21 @@
  "cell_type": "markdown",
  "metadata": {},
  "source": [
- "# Stegotons: solitary waves arising in non-dispersive periodic media\n",
+ "# Stegotons: solitary waves arising in non-dispersive periodic media"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Author: [David I. Ketcheson](http:https://www.davidketcheson.info/) \n",
+ "License: CC-BY"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
  "A fascinating new class of solitary waves was discovered in [a 2003 paper by R.J. LeVeque and D. Yong](http:https://faculty.washington.edu/rjl/pubs/solitary/40815.pdf). Solitary waves usually appear as solutions of nonlinear dispersive wave equations, like the KdV or NLS equations. But the waves discovered by LeVeque and Yong arise in a system of nonlinear wave equations **with no dispersion!** The nonlinear elasticity equations they investigated are:\n",
  "\n",
  "\\begin{align}\n",
@@ -14,7 +28,7 @@
  "\n",
  "They took the density $\\rho(x)$ and bulk modulus $K(x)$ to be periodic functions and the stress strain relation $\\sigma(\\epsilon,x)$ nonlinear (they used an exponential function, but any nonlinear function will work).\n",
  "\n",
- "If $\\rho$ and $K$ are chosen so that the impedance $Z = \\sqrt{\\rho K}$ varies in space, then waves undergo reflection on the fine scale. Remarkably, the effect of these reflections is an effective behavior that mimics dispersion -- as [predicted already by Santosa & Symes in 1993](http:https://epubs.siam.org/doi/abs/10.1137/0151049).\n",
+ "If $\\rho$ and $K$ are chosen so that the impedance $Z = \\sqrt{\\rho K}$ varies in space, then waves undergo reflection on the fine scale. Remarkably, the effect of these reflections is an effective behavior that mimics dispersion -- as [predicted already by Santosa & Symes in 1991](http:https://epubs.siam.org/doi/abs/10.1137/0151049).\n",
  "\n",
  "Here we reproduce some of their original experiments in PyClaw. If you're interested in the simulations, all of the code is provided here and you can run it yourself. If you're only interested in the results, feel free to just skip over the code.\n",
  "\n",
@@ -92,7 +106,7 @@
  "plt.figure(figsize=(10,6))\n",
  "plt.plot(xc,state.q[0,:])\n",
  "plt.xlim(460,540)\n",
- "plt.title('Strain at t=0')"
+ "plt.title('Strain at t=0');"
  ]
  },
  {
@@ -441,5 +455,5 @@
  }
  },
  "nbformat": 4,
- "nbformat_minor": 1
+ "nbformat_minor": 4
 }
diff --git a/notebooks/pyclaw/beach.ipynb b/notebooks/pyclaw/beach.ipynb
@@ -186,7 +186,6 @@
  " surface = np.maximum(b,h+b)\n",
  "\n",
  " x, y = frame.state.grid.p_centers \n",
- " save_plots = True\n",
  " slice = 1\n",
  " #line, = ax1.plot(x[:,0],surface[:,slice],'-k',linewidth=3)\n",
  " fill = ax1.fill_between(x[:,0],b[:,slice],surface[:,slice],facecolor='blue')\n",
@@ -214,8 +213,15 @@
  "\n",
  " anim = animation.FuncAnimation(fig, fplot, frames=len(claw.frames), interval=100, repeat=False)\n",
  " plt.close()\n",
- " return HTML(anim.to_jshtml())\n",
- "\n",
+ " return HTML(anim.to_jshtml())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
  "plot_waves(claw)"
  ]
  },
@@ -250,7 +256,7 @@
  ],
  "metadata": {
  "kernelspec": {
- "display_name": "Python 3",
+ "display_name": "Python 3 (ipykernel)",
  "language": "python",
  "name": "python3"
  },
@@ -264,7 +270,7 @@
  "name": "python",
  "nbconvert_exporter": "python",
  "pygments_lexer": "ipython3",
- "version": "3.6.5"
+ "version": "3.11.4"
  },
  "toc": {
  "nav_menu": {},
@@ -278,5 +284,5 @@
  }
  },
  "nbformat": 4,
- "nbformat_minor": 1
+ "nbformat_minor": 4
 }
diff --git a/notebooks/pyclaw/pyclaw_geometry.ipynb b/notebooks/pyclaw/pyclaw_geometry.ipynb
@@ -309,7 +309,7 @@
  "metadata": {},
  "outputs": [],
  "source": [
- "grid.plot(num_ghost=2);"
+ "grid.plot(num_ghost=4);"
  ]
  },
  {
@@ -355,6 +355,8 @@
  "outputs": [],
  "source": [
  "x.upper = 1.\n",
+ "x.num_cells = 30\n",
+ "y.num_cells = 30\n",
  "\n",
  "grid.mapc2p = square2circle\n",
  "grid.plot(num_ghost=1);"
@@ -363,7 +365,7 @@
  ],
  "metadata": {
  "kernelspec": {
- "display_name": "Python 3",
+ "display_name": "Python 3 (ipykernel)",
  "language": "python",
  "name": "python3"
  },
@@ -377,7 +379,7 @@
  "name": "python",
  "nbconvert_exporter": "python",
  "pygments_lexer": "ipython3",
- "version": "3.6.5"
+ "version": "3.11.4"
  },
  "toc": {
  "nav_menu": {},
@@ -391,5 +393,5 @@
  }
  },
  "nbformat": 4,
- "nbformat_minor": 1
+ "nbformat_minor": 4
 }