Add files via upload (FlorisCalkoen#85)

notebooks/initialize/init_3b.ipynb

@@ -0,0 +1,351 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fd978930-bbc5-4c62-9218-96af5c11320f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "import panel as pn\n",
+    "pn.extension(\"ipywidgets\", 'katex', 'mathjax')\n",
+    "import ipywidgets as ipw\n",
+    "from matplotlib.animation import FuncAnimation\n",
+    "from matplotlib.figure import Figure\n",
+    "\n",
+    "from random import shuffle, uniform\n",
+    "\n",
+    "import sys\n",
+    "from inspect import signature\n",
+    "print(\"Packages successfully loaded\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4a18b5d0-538b-45b9-a552-1a6c4865090b",
+   "metadata": {},
+   "source": [
+    "# Functions from cookbook"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "81c22d90-98ad-4367-a297-7cf650f73c13",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "try:\n",
+    "    %run Initialize/init_cookbook.ipynb # valid when running the cookbook in the main file\n",
+    "except:\n",
+    "    %run init_cookbook.ipynb # valid when running the cookbook from this file."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "add2043c-b3cd-4ef8-9da6-9310aee3f2bc",
+   "metadata": {},
+   "source": [
+    "# Commonly used functions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "74b6ba94-f4a6-46f4-8277-8b2e83d9266d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def wave_length(T, h):\n",
+    "    d = h\n",
+    "\n",
+    "    # based on waveNumber_Fenton(T,d) from Jaime in computerlab\n",
+    "    g=9.81\n",
+    "    omega = 2*np.pi/T\n",
+    "    k0 = omega*omega/g\n",
+    "    alpha = k0*d\n",
+    "    beta = alpha * (np.tanh(alpha))**-0.5 \n",
+    "    k = (alpha + beta**2 * np.cosh(beta)**-2) / (np.tanh(beta)+ beta*np.cosh(beta)**-2) / d\n",
+    "\n",
+    "    L = 2*np.pi/k\n",
+    "            \n",
+    "    return L\n",
+    "\n",
+    "def group_stats(k1,k2,w1,w2):\n",
+    "    Delta_k = np.abs(k2-k1)\n",
+    "    Delta_w = np.abs(w2-w1)\n",
+    "    L = 2*np.pi/Delta_k\n",
+    "    T = 2*np.pi/Delta_w\n",
+    "    cg = Delta_w/Delta_k\n",
+    "    return L,T, cg"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fba1b418-519b-485f-82ac-88d44eac8c32",
+   "metadata": {},
+   "source": [
+    "# Part 1B"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4a9a7a70-b3eb-4b11-915a-1c4ff62091e1",
+   "metadata": {},
+   "source": [
+    "## Second order waves"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4aaf78cd-a30a-421e-99e6-90f298fa0095",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def second_order_waves():# second-order_Stokes_waves\n",
+    "    a1 = ipw.FloatText(value=1, min=0, max=20, step=0.01, description='a1 [m]')\n",
+    "    a2 = ipw.FloatText(value=0, min=0, max=20, step=0.01, description='a2 [m]')\n",
+    "    phi1 = ipw.FloatText(value=0, min=0, max=20, step=0.01, description='phi [2 pi rad]')\n",
+    "    phi2 = ipw.FloatText(value=0, min=0, max=20, step=0.01, description='phi [2 pi rad]')\n",
+    "\n",
+    "    # Setup widget layout (User Interface)\n",
+    "    vbox1 = ipw.VBox([ipw.Label('Wave 1', layout=ipw.Layout(align_self='center')),a1, phi1])\n",
+    "    vbox2 = ipw.VBox([ipw.Label('Wave 2', layout=ipw.Layout(align_self='center')),a2, phi2])\n",
+    "    ui = ipw.HBox([vbox1, vbox2])\n",
+    "    \n",
+    "    def update_graph(a1, a2, phi1, phi2):\n",
+    "        S_min = -0.25*np.pi\n",
+    "        S_max = 2.25*np.pi\n",
+    "        \n",
+    "        S = np.linspace(S_min, S_max,60)\n",
+    "        S1 = S   - phi1*np.pi\n",
+    "        S2 = S*2 - phi2*np.pi\n",
+    "        \n",
+    "        eta1 = a1*np.cos(S1)\n",
+    "        eta2 = a2*np.cos(S2)\n",
+    "        eta = eta1 + eta2\n",
+    "        \n",
+    "        fig, axs = plt.subplots(nrows=1,ncols=1,figsize=(5,4), sharex=False, sharey = False)\n",
+    "        axs.plot(S, eta1, label = '$\\eta_1$', color = 'gray', linestyle = 'dashed')\n",
+    "        axs.plot(S, eta2, label = '$\\eta_2$', color = 'gray', linestyle = 'dashdot')\n",
+    "        axs.plot(S, eta, label = '$\\eta_{1+2}$', color = 'k')\n",
+    "        axs.legend(loc = 'best')\n",
+    "        axs.set_ylabel('$\\eta$ [m]')\n",
+    "        axs.set_xlabel('phase [rad]')\n",
+    "        axs.set_xlim(S_min,S_max)\n",
+    "\n",
+    "        x_tick_min = S_min//(0.5*np.pi)*0.5*np.pi+0.5*np.pi\n",
+    "        x_ticks = np.arange(x_tick_min, S_max, 0.5*np.pi)\n",
+    "        x_ticks_labels = [f\"{angle/np.pi:.1f}π\" for angle in x_ticks]\n",
+    "        axs.set_xticks(x_ticks, x_ticks_labels)\n",
+    "\n",
+    "    graph = ipw.interactive_output(update_graph, {'a1': a1,'a2': a2, 'phi1':phi1, 'phi2':phi2})\n",
+    "\n",
+    "    question1 = ['What are the values of eta1, eta2 and phi2 to make figure 5.13 of the book, if we assume phi1 = 0 and a cosinus function, as in equation 1']\n",
+    "    answer1 = [[1, 0.2, 0]]\n",
+    "    subquestions1 = [['eta1', 'eta2', 'phi2 [pi rad]']]\n",
+    "    Q1_unit = 'm'\n",
+    "\n",
+    "    question2 = ['What are the values of eta1, eta2 and phi2 to make figure 5.16 of the book, if we assume phi1 = 0 and a cosinus function, as in equation 1']\n",
+    "    answer2 = [[1, 0.2, -0.5]]\n",
+    "    subquestions2 = [['eta1', 'eta2', 'phi2 [pi rad]']]\n",
+    "    Q2_unit = 'm'\n",
+    "    \n",
+    "    Q1 = nummerical_subquestions(question1, answer1, subquestions1, Q1_unit)\n",
+    "    Q2 = nummerical_subquestions(question2, answer2, subquestions2, Q2_unit)\n",
+    "    \n",
+    "    display(ui, graph, *Q1,*Q2)\n",
+    "\n",
+    "#second_order_waves()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "0b556916-ca5d-44a7-ac17-399b7727ef65",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# wt = 0 and k = 2 pi/L, with k = k1, the first harmonic component is the basis.\n",
+    "def show_second_order_waves_x_L():\n",
+    "    # define the name of the function that the students will make\n",
+    "    function_name = \"second_order_waves_x_L\"\n",
+    "\n",
+    "    # define the name of the parameter plotted on the horizontal axis\n",
+    "    parameter_x_axis = 'x_L'\n",
+    "\n",
+    "    # set the horizontal axis of the graph\n",
+    "    horizontal_axis = np.arange(0,3 +1/30,1/30)\n",
+    "\n",
+    "    # define the correct function and its values along the x-axis.\n",
+    "    def correct_function(x_L, eta1, eta2, phi1, phi2):\n",
+    "        eta = eta1 * np.cos(-2*np.pi*x_L-phi1) + eta2*np.cos(-4*np.pi*x_L-phi2)\n",
+    "        return eta\n",
+    "\n",
+    "    # set the acceptable computational error (ratio)\n",
+    "    f_margin = 0.001 # 0.001 = 0.01%\n",
+    "\n",
+    "    fig = Figure((6,3))\n",
+    "    xlabel = 'x/L'\n",
+    "    ylabel = 'y [m]'\n",
+    "    check_code_function(fig, horizontal_axis, function_name, correct_function, parameter_x_axis, f_margin, xlabel = xlabel, ylabel = ylabel)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e6a88191-8120-40f8-90d4-7cccb0d65f8f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def show_second_order_waves_t_T():\n",
+    "    # define the name of the function that the students will make\n",
+    "    function_name = \"second_order_waves_t_T\"\n",
+    "\n",
+    "    # define the name of the parameter plotted on the horizontal axis\n",
+    "    parameter_x_axis = 't_T'\n",
+    "\n",
+    "    # set the horizontal axis of the graph\n",
+    "    horizontal_axis = np.arange(0,3 +1/30,1/30)\n",
+    "\n",
+    "    # define the correct function and its values along the x-axis.\n",
+    "    def correct_function(t_T, eta1, eta2, phi1, phi2):\n",
+    "        eta = eta1 * np.cos(2*np.pi*t_T-phi1) + eta2*np.cos(4*np.pi*t_T-phi2)\n",
+    "        return eta\n",
+    "\n",
+    "    # set the acceptable computational error (ratio)\n",
+    "    f_margin = 0.001 # 0.001 = 0.01%\n",
+    "\n",
+    "    fig = Figure((6,3))\n",
+    "    xlabel = 't/T'\n",
+    "    ylabel = 'y [m]'\n",
+    "    check_code_function(fig, horizontal_axis, function_name, correct_function, parameter_x_axis, f_margin, xlabel = xlabel, ylabel = ylabel)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a3264d4c-6d5c-4d98-b8ff-780ba68f98da",
+   "metadata": {},
+   "source": [
+    "## second order waves and powers of eta"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7535b9a3-7603-42c6-8b62-cac16547eeba",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def Skewed_assymetric_waves():\n",
+    "    a1 = ipw.FloatText(value=1, min=0, max=20, step=0.01, description='a1 [m]')\n",
+    "    a2_1 = ipw.FloatText(value=0, min=0, max=20, step=0.01, description='a2 [m]')\n",
+    "    a2_2 = ipw.FloatText(value=0, min=0, max=20, step=0.01, description='a2 [m]')\n",
+    "    phi1 = ipw.FloatText(value=0, min=0, max=20, step=0.01, description='phi [2 pi rad]')\n",
+    "    phi2_1 = ipw.FloatText(value=0, min=0, max=20, step=0.01, description='phi [2 pi rad]')\n",
+    "    phi2_2 = ipw.FloatText(value=0, min=0, max=20, step=0.01, description='phi [2 pi rad]')\n",
+    "    \n",
+    "    # Setup widget layout (User Interface)\n",
+    "    vbox1 = ipw.VBox([ipw.Label('Wave 1', layout=ipw.Layout(align_self='center')),a1, phi1])\n",
+    "    vbox2 = ipw.VBox([ipw.Label('Wave 2 (left panel)', layout=ipw.Layout(align_self='center')),a2_1, phi2_1])\n",
+    "    vbox3 = ipw.VBox([ipw.Label('Wave 2 (right panel)', layout=ipw.Layout(align_self='center')),a2_2, phi2_2])\n",
+    "    ui = ipw.HBox([vbox1, vbox2, vbox3])\n",
+    "    \n",
+    "    def update_graph(a1, a2_1, a2_2, phi1, phi2_1, phi2_2):\n",
+    "        S_min = -0.25*np.pi\n",
+    "        S_max = 2.25*np.pi\n",
+    "        S = np.linspace(S_min, S_max,100)\n",
+    "\n",
+    "        # left panel\n",
+    "        eta_L = a1*np.cos(S-phi1) + a2_1*np.cos(S*2-phi2_1*np.pi)\n",
+    "        eta_3_L = eta_L**3\n",
+    "\n",
+    "        # right panel\n",
+    "        eta_R = a1*np.cos(S-phi1) + a2_2*np.cos(S*2-phi2_2*np.pi)\n",
+    "        eta_3_R = eta_R**3\n",
+    "  \n",
+    "        # set structure for graph\n",
+    "        fig, axs = plt.subplots(nrows=1,ncols=2,figsize=(10,4), sharex=False, sharey = True)\n",
+    "        fig.subplots_adjust(hspace=0)\n",
+    "        fig.subplots_adjust(wspace=0.06)\n",
+    "\n",
+    "        # plot lines\n",
+    "        axs[0].plot(S, eta_L, label = '$\\eta$', color = 'gray', linestyle = '--')\n",
+    "        axs[0].plot(S, eta_3_L, label = '$\\eta^3$', color = 'k', linestyle = '-')\n",
+    "        axs[0].plot([S_min, S_max],[0,0], color = 'k', linewidth = 1, linestyle = 'dashed')\n",
+    "        \n",
+    "        axs[1].plot(S, eta_R, label = '$\\eta$', color = 'gray', linestyle = '--')\n",
+    "        axs[1].plot(S, eta_3_R, label = '$\\eta^3$', color = 'k', linestyle = '-')\n",
+    "        axs[1].plot([S_min, S_max],[0,0], color = 'k', linewidth = 1, linestyle = 'dashed')\n",
+    "\n",
+    "        # set legend and labels\n",
+    "        axs[0].legend(loc = 'best')\n",
+    "        axs[0].set_ylabel('$\\eta$ [m]')\n",
+    "        axs[0].set_xlabel('phase [rad]') \n",
+    "        axs[0].set_xlim(S_min,S_max)\n",
+    "\n",
+    "        axs[1].legend(loc = 'best')\n",
+    "        axs[1].set_xlabel('phase [rad]') \n",
+    "        axs[1].set_xlim(S_min,S_max)\n",
+    "        \n",
+    "        x_tick_min = S_min//(0.5*np.pi)*0.5*np.pi+0.5*np.pi\n",
+    "        x_ticks = np.arange(x_tick_min, S_max, 0.5*np.pi)\n",
+    "        x_ticks_labels = [f\"{angle/np.pi:.1f}π\" for angle in x_ticks]\n",
+    "        axs[0].set_xticks(x_ticks, x_ticks_labels)\n",
+    "        axs[1].set_xticks(x_ticks, x_ticks_labels)\n",
+    "\n",
+    "    graph = ipw.interactive_output(update_graph, {'a1': a1, 'a2_1': a2_1, 'a2_2':a2_2, 'phi1': phi1, 'phi2_1':phi2_1, 'phi2_2':phi2_2})\n",
+    "\n",
+    "    question1 = ['What are the values of eta1, phi1, eta2 (left and right pane), phi2 (left and right pane) to make the skewed waves shown in figure 5.14 of the book?']\n",
+    "    answer1 = [[1, 0, 0, 0, 0.2, 0]]\n",
+    "    subquestions1 = [['eta1 [m]', 'phi1 [phi rad]', 'eta2 (left) [m]', 'phi2 (left) [pi rad]', 'eta2 (right) [m]', 'phi2 (right) [pi rad]']]\n",
+    "    Q1_unit = ' '\n",
+    "\n",
+    "    question2 = ['What are the values of eta1, phi1, eta2 (left and right pane), phi2 (left and right pane) to make the assymetric waves shown in figure 5.17 of the book?']\n",
+    "    answer2 = [[1, 0, 0.2, 0, 0.2, -0.5]]\n",
+    "    subquestions2 = [['eta1 [m]', 'phi1 [phi rad]', 'eta2 (left) [m]', 'phi2 (left) [pi rad]', 'eta2 (right) [m]', 'phi2 (right) [pi rad]']]\n",
+    "    Q2_unit = ' '\n",
+    "\n",
+    "    Q1 = nummerical_subquestions(question1, answer1, subquestions1, Q1_unit)\n",
+    "    Q2 = nummerical_subquestions(question2, answer2, subquestions2, Q2_unit)\n",
+    "    \n",
+    "    display(ui, graph, *Q1, *Q2)\n",
+    "\n",
+    "#Skewed_assymetric_waves()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "32b7cebf-fa50-4122-816d-a9d7fe7877dc",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.11.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}