diff --git a/lectures/03_ResistiveCompanion/Lecture_SimExample_ResistiveCompanion.ipynb b/lectures/03_ResistiveCompanion/Lecture_SimExample_ResistiveCompanion.ipynb deleted file mode 100644 index ba58796f590294810f550f8d85724f06216f601b..0000000000000000000000000000000000000000 --- a/lectures/03_ResistiveCompanion/Lecture_SimExample_ResistiveCompanion.ipynb +++ /dev/null @@ -1,349 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# MSP Simulation Example - Resistive Companion" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Sample Circuit" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "<img src=\"VS_R2L3.png\" width=\"500\" align=\"left\">" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$R_1$=$1 \\Omega$, $R_2$=$2 \\Omega$ \n", - "$L_1$=$20 mH$, $L_2$=$100 mH$, $L_3$=$50 mH$ \n", - "$V_{in}(t)$=$10 Vsin(\\omega t)$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Circuit and Simulation Setup" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Total simulation time: 0.05\n", - "Simulation time step: 1e-06\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "np.set_printoptions(sign=' ')\n", - "\n", - "# Circuit parameters\n", - "R1 = 1\n", - "R2 = 2\n", - "L1 = 20e-3\n", - "L2 = 100e-3\n", - "L3 = 50e-3\n", - "Emax = 10\n", - "\n", - "G1 = 1/R1\n", - "G2 = 1/R2\n", - "\n", - "# Simulation parameters\n", - "# Note: Euler forward is numerically unstable for Ts>7.51e-6\n", - "T_total = 0.05\n", - "Ts = 1e-6\n", - "npoint = int(np.round(T_total/Ts))\n", - "\n", - "print('Total simulation time: ' + str(T_total))\n", - "print('Simulation time step: ' + str(Ts))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Euler Backward Integration Method" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "GL1_back = Ts/(L1)\n", - "GL2_back = Ts/(L2)\n", - "GL3_back = Ts/(L3)\n", - "\n", - "# Conductance matrix\n", - "Gn = np.array([ [G1+GL1_back, -GL1_back, 0],\n", - " [-GL1_back, GL1_back+GL2_back+GL3_back, -GL3_back],\n", - " [0, -GL3_back, GL3_back+G2]])\n", - " \n", - "# Node voltage vector\n", - "vn_back = np.zeros((3,npoint))\n", - "\n", - "# Current vector in the 3 inductances\n", - "in_back = np.zeros((3,npoint))\n", - " \n", - "# Intial conditions\n", - "# Voltage source at E(t=0)=0;\n", - "# i_L(t=0)=0 -> e1 = E(t=0) =0; e2 = 0; e3 = 0;\n", - "in_back[:,0] = np.zeros(3)\n", - "vn_back[:,0] = np.zeros(3) \n", - "\n", - "# Enter Loop\n", - "# tic %Start a timer\n", - "for i in np.arange(1,npoint):\n", - " # Update source vector\n", - " AL1_back = in_back[0,i-1]\n", - " AL2_back = in_back[1,i-1]\n", - " AL3_back = in_back[2,i-1]\n", - " E = Emax*np.sin(2*np.pi*60*i*Ts)\n", - " Jn = np.array([E/R1-AL1_back, AL1_back-AL2_back-AL3_back, AL3_back])\n", - "\n", - " # Matrix inversion and solution of the equation G*e=J;\n", - " vn_back[:,i] = np.linalg.solve(Gn, Jn)\n", - "\n", - " # post step\n", - " in_back[0,i] = AL1_back+GL1_back*(vn_back[0,i]-vn_back[1,i])\n", - " in_back[1,i] = AL2_back+GL2_back*(vn_back[1,i])\n", - " in_back[2,i] = AL3_back+GL3_back*(vn_back[1,i]-vn_back[2,i])\n", - "\n", - "# toc %stop the timer " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Euler Forward Integration Method" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "# Large resistor added in parallel with inductors (3 current sources coincide at a node)\n", - "Gadd = 1e-4\n", - "# Conductance matrix\n", - "Gn = np.array( [[G1+Gadd, -Gadd, 0],\n", - " [-Gadd, 3*Gadd, -Gadd],\n", - " [ 0, -Gadd, Gadd+G2]])\n", - " \n", - "# Node voltage vector\n", - "vn_forw = np.zeros((3,npoint))\n", - "\n", - "# Current vector in the 3 inductances\n", - "in_forw = np.zeros((3,npoint))\n", - "\n", - "# Intial conditions\n", - "# Voltage source at E(t=0)=0;\n", - "# i_L(t=0)=0 -> e1 = E(t=0) =0; e2 = 0; e3 = 0;\n", - "in_forw[:,0] = np.zeros(3)\n", - "vn_forw[:,0] = np.zeros(3) \n", - "\n", - "#Enter Loop\n", - "# tic % Start a timer\n", - "for i in np.arange(1,npoint):\n", - " # Update source vector\n", - " AL1_forw = in_forw[0,i-1]+(vn_forw[0,i-1]-vn_forw[1,i-1])*Ts/L1\n", - " AL2_forw = in_forw[1,i-1]+(vn_forw[1,i-1])*Ts/L2\n", - " AL3_forw = in_forw[2,i-1]+(vn_forw[1,i-1]-vn_forw[2,i-1])*Ts/L3\n", - " E = Emax*np.sin(2*np.pi*60*i*Ts)\n", - " Jn = np.array([E/R1-AL1_forw, AL1_forw-AL2_forw-AL3_forw, AL3_forw])\n", - "\n", - " # Matrix inversion and solution of the equation G*e=J \n", - " vn_forw[:,i] = np.linalg.solve(Gn, Jn)\n", - "\n", - " # post step\n", - " in_forw[0,i]= AL1_forw\n", - " in_forw[1,i]= AL2_forw\n", - " in_forw[2,i]= AL3_forw" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Trapezoidal Integration Method" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "GL1_trap = Ts/(2*L1)\n", - "GL2_trap = Ts/(2*L2)\n", - "GL3_trap = Ts/(2*L3)\n", - "\n", - "# Conductance matrix\n", - "Gn = np.array( [[G1+GL1_trap, -GL1_trap, 0],\n", - " [-GL1_trap, GL1_trap+GL2_trap+GL3_trap, -GL3_trap],\n", - " [0, -GL3_trap, GL3_trap+G2]])\n", - " \n", - "# Node voltage vector\n", - "vn_trap = np.zeros((3,npoint))\n", - "\n", - "# Current vector in the 3 inductances\n", - "in_trap = np.zeros((3,npoint))\n", - "\n", - "# Intial conditions\n", - "# Voltage source at E(t=0)=0\n", - "# i_L(t=0)=0 -> e1 = E(t=0) =0; e2 = 0; e3 = 0;\n", - "in_trap[:,0] = np.zeros(3)\n", - "vn_trap[:,0] = np.zeros(3)\n", - " \n", - "#Enter Loop\n", - "#tic\n", - "for i in np.arange(1,npoint):\n", - " # Update source vector\n", - " AL1 = in_trap[0,i-1]+(vn_trap[0,i-1]-vn_trap[1,i-1])*Ts/(2*L1)\n", - " AL2 = in_trap[1,i-1]+(vn_trap[1,i-1])*Ts/(2*L2)\n", - " AL3 = in_trap[2,i-1]+(vn_trap[1,i-1]-vn_trap[2,i-1])*Ts/(2*L3)\n", - " E = Emax*np.sin(2*np.pi*60*i*Ts)\n", - " Jn = np.array([E/R1-AL1, AL1-AL2-AL3, AL3])\n", - "\n", - " # Matrix inversion and solution of the equation G*e=J\n", - " vn_trap[:,i] = np.linalg.solve(Gn, Jn)\n", - "\n", - " # post step\n", - " in_trap[0,i]= AL1+GL1_trap*(vn_trap[0,i]-vn_trap[1,i])\n", - " in_trap[1,i]= AL2+GL2_trap*(vn_trap[1,i])\n", - " in_trap[2,i]= AL3+GL3_trap*(vn_trap[1,i]-vn_trap[2,i])\n", - "#toc" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Result Comparison for different Integration Methods" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Considering current through inductors $L_1$ and $L_2$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " ### Euler Backward vs Trapezoidal" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "<Figure size 576x432 with 1 Axes>" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "t = np.arange(0, npoint)*Ts\n", - "plt.figure(figsize=(8,6))\n", - "plt.xlabel('Time [s]')\n", - "plt.ylabel('Current [A]')\n", - "plt.plot(t,in_trap[0,:], t, in_trap[2,:], linewidth=2)\n", - "plt.plot(t,in_back[0,:], ':', t, in_back[2,:],':', linewidth=2)\n", - "plt.xlim([0, (npoint-1)*Ts])\n", - "plt.legend(['Trapezoidal $I_{L1}$(t)', 'Trapezoidal $I_{L2}$(t)','E. Backward $I_{L1}$(t)', 'E. Backward $I_{L2}$(t)'])\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Euler Forward vs Trapezoidal" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "<Figure size 576x432 with 1 Axes>" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=(8,6))\n", - "plt.xlabel('Time [s]')\n", - "plt.ylabel('Current [A]')\n", - "plt.plot(t,in_trap[0,:], t, in_trap[2,:], linewidth=2)\n", - "plt.plot(t,in_forw[0,:], ':', t, in_forw[2,:],':', linewidth=2)\n", - "plt.xlim([0, (npoint-1)*Ts])\n", - "plt.legend(['Trapezoidal $I_{L1}$(t)', 'Trapezoidal $I_{L2}$(t)','E. Forward $I_{L1}$(t)', 'E. Forward $I_{L2}$(t)'])\n", - "plt.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "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": "3.7.3" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/lectures/03_ResistiveCompanion/Lecture_SimExample_ResistiveCompanion_automated.ipynb b/lectures/03_ResistiveCompanion/Lecture_SimExample_ResistiveCompanion_automated.ipynb index 33e26e1cb2596b62372ccc5b06d340904ba02068..65092a0224c4b7eeaa6dcc930251c168b8e0df15 100644 --- a/lectures/03_ResistiveCompanion/Lecture_SimExample_ResistiveCompanion_automated.ipynb +++ b/lectures/03_ResistiveCompanion/Lecture_SimExample_ResistiveCompanion_automated.ipynb @@ -39,28 +39,16 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "1ce06daf45f447e197aaaf31c6fa2434", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "interactive(children=(SelectionSlider(continuous_update=False, description='Time step', layout=Layout(height='…" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "import numpy as np\n", "import ipywidgets as widget\n", "import matplotlib.pyplot as plt\n", + "import warnings\n", + "warnings.filterwarnings('ignore')\n", + "%matplotlib inline\n", "np.set_printoptions(sign=' ')\n", "\n", "# Circuit parameters\n", @@ -76,7 +64,22 @@ "\n", "#default start values for Ts and T_total\n", "Ts=1e-7\n", - "T_total=1\n", + "T_total=0.05" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Euler Backward Integration Method" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ "\n", "#function to perform the euler backward integration \n", "def int_EB(Ts, T_total, npoint):\n", @@ -121,12 +124,24 @@ " in_back[2,i] = AL3_back+GL3_back*(vn_back[1,i]-vn_back[2,i])\n", "\n", " # toc %stop the timer \n", - " \n", - " #Plot results\n", - " plot_fun(in_back, Ts, npoint, 'E. Backward')\n", - " \n", - " return in_back\n", "\n", + " \n", + " return in_back" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Euler Forward Integration Method" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ "#function to perform the euler forward integration \n", "def int_EF(Ts, T_total, npoint):\n", " \n", @@ -167,11 +182,23 @@ " in_forw[1,i]= AL2_forw\n", " in_forw[2,i]= AL3_forw\n", " \n", - " #Plot results\n", - " plot_fun(in_forw, Ts, npoint, 'E. Forward')\n", " \n", - " return in_forw\n", - "\n", + " return in_forw" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Trapezoidal Integration Method" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ "#function to perform the trapezoidal integration \n", "def int_TR(Ts, T_total, npoint):\n", " \n", @@ -215,58 +242,7 @@ " in_trap[2,i]= AL3+GL3_trap*(vn_trap[1,i]-vn_trap[2,i])\n", " #toc\n", " \n", - " #Plot results \n", - " plot_fun(in_trap, Ts, npoint, 'Trapezoidal')\n", - " \n", - " return in_trap\n", - "\n", - "#Plot function \n", - "def plot_fun(input_data, Ts, npoint, in_method):\n", - " #Plot results\n", - " t = np.arange(0, npoint)*Ts\n", - " plt.figure(figsize=(4,3))\n", - " plt.xlabel('Time [s]')\n", - " plt.ylabel('Current [A]')\n", - " #plot current through L1 and L3\n", - " plt.plot(t,input_data[0,:], t, input_data[2,:], linewidth=2)\n", - " plt.xlim([0, (npoint-1)*Ts])\n", - " plt.legend([in_method +' $I_{L1}$(t)', in_method + ' $I_{L2}$(t)'])\n", - " plt.show()\n", - " \n", - " \n", - "#Slider function to forward the selected values to the simulation functions\n", - "def slider_fun(time_step, total_time):\n", - " \n", - " global in_back , in_forw , in_trap, npoint \n", - " \n", - " if time_step==0 or total_time==0:\n", - " print('\\n \\n \\n' + 'Simulation time step is set to: ' + str(time_step) + ' seconds')\n", - " print('Total simulation time: ' + str(total_time) + ' seconds' + '\\n \\n')\n", - " \n", - " else:\n", - " print('\\n \\n \\n' + 'Simulation time step is set to: ' + str(time_step) + ' seconds')\n", - " print('Total simulation time: ' + str(total_time) + ' seconds' + '\\n \\n')\n", - " \n", - " npoint = int(np.round(total_time/time_step))\n", - "\n", - " in_back=int_EB(time_step, total_time, npoint)\n", - "\n", - " in_forw=int_EF(time_step, total_time, npoint)\n", - "\n", - " in_trap=int_TR(time_step, total_time, npoint)\n", - "\n", - " return time_step, total_time\n", - "\n", - "#Values range for the simulation steps\n", - "values=[round(i*10**-7, 7) for i in range(101)]\n", - "\n", - "#It is important to set the argument continous_update to 'false' so that the slider_fun is called after the user finishes dragging the slider. \n", - "#Otherwise the function will be continuously called for several values in the dragging interval and the expected results will take alot of time to appear \n", - "slider= widget.interactive(slider_fun, time_step=widget.SelectionSlider(description=\"Time step\", continuous_update=False, options=[(\"%g\"%i,i) for i in values], layout=widget.Layout(width='50%', height='80px')), \n", - " total_time=widget.FloatSlider(description=\"Total time\", continuous_update=False, min=0.0, max=0.1, step=0.001, layout=widget.Layout(width='50%', height='80px')));\n", - "\n", - "display(slider)\n", - "#inspect.getmembers(widget.SelectionSlider)" + " return in_trap" ] }, { @@ -276,34 +252,20 @@ "## Result Comparison for different Integration Methods" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Considering current through inductors $L_1$ and $L_2$" - ] - }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Please select the integration methods you want to compare:\n" - ] - }, { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "be28341ba95142f8a59b99b6d49c2e33", + "model_id": "96f4a5e1a0f44fec8446ca1b2a713e72", "version_major": 2, "version_minor": 0 }, "text/plain": [ - "interactive(children=(Checkbox(value=False, description='Euler_Forward'), Checkbox(value=False, description='E…" + "interactive(children=(SelectionSlider(continuous_update=False, description='Time step', layout=Layout(height='…" ] }, "metadata": {}, @@ -311,38 +273,85 @@ } ], "source": [ - "#Assign slider values to simulation parameters\n", - "Ts, T_total = slider.result\n", - "npoint = int(np.round(T_total/Ts))\n", - "\n", - "def plot_vs(Euler_Forward,Euler_Backward,Trapezoidal_Rule):\n", + "#Plot function\n", + "def plot_fun(time_step, npoint):\n", " \n", - " flags= [int(Euler_Forward), int(Euler_Backward) , int(Trapezoidal_Rule)]\n", + " #Number of subplots (1*3) and size of the figure where the subplots will appear\n", + " fig, ax = plt.subplots(1,3, figsize=(16, 5))\n", " \n", + " #Calculate time values\n", + " t = np.arange(0, npoint)*Ts\n", " \n", - " graphs={'E. Forward ': in_forw*flags[0], \n", - " 'E. Backward ': in_back*flags[1],\n", - " 'Trapezoidal ': in_trap*flags[2]}\n", + " #Transform time values to milliseconds for better representation\n", + " t= np.multiply(t, 10e+3)\n", + " \n", + " #Plot results E. Backward\n", + " ax[0].set_title('E. Backward')\n", + " ax[0].set_xlim([0, (npoint-1)*Ts*10e+3])\n", + " ax[0].set_xlabel('Time [ms]')\n", + " ax[0].set_ylabel('Current [A]')\n", + " ax[0].plot(t,in_back[0,:], 'r', t, in_back[2,:], 'r:')\n", + " leg = ax[0].legend(['$I_{L1}$(t)','$I_{L2}$(t)'])\n", " \n", - " t = np.arange(0, npoint)*Ts\n", - " plt.figure(figsize=(8,6))\n", - " plt.xlabel('Time [s]')\n", - " plt.ylabel('Current [A]')\n", + " #Plot results E. Forward\n", + " ax[1].set_title('E. Forward')\n", + " #Set axis limite and transform to milliseconds\n", + " ax[1].set_xlim([0, (npoint-1)*Ts*10e+3])\n", + " ax[1].set_xlabel('Time [ms]')\n", + " ax[1].set_ylabel('Current [A]')\n", + " ax[1].plot(t, in_forw[0,:] ,'g', t, in_forw[2,:], 'g:', linewidth=2)\n", + " leg = ax[1].legend(['$I_{L1}$(t)','$I_{L2}$(t)'])\n", + " \n", + " #Plot results Trapezoidal\n", + " ax[2].set_title('Trapezoidal')\n", + " ax[2].set_xlim([0, (npoint-1)*Ts*10e+3])\n", + " ax[2].set_xlabel('Time [ms]')\n", + " ax[2].set_ylabel('Current [A]')\n", + " ax[2].plot(t,in_trap[0,:], 'b', t, in_trap[2,:], 'b:', linewidth=2)\n", + " leg = ax[2].legend(['$I_{L1}$(t)','$I_{L2}$(t)'])\n", " \n", - " for key,val in graphs.items(): \n", - " if np.all(val==0):\n", - " continue\n", - "\n", - " plt.plot(t,val[0,:], label= key + '$I_{L1}$(t)') \n", - " plt.plot(t, val[2,:], label= key +'$I_{L2}$(t)')\n", " \n", - " plt.legend(loc='upper right')\n", - " plt.show()\n", + "#Slider function to forward the selected values to the simulation functions\n", + "def slider_fun(time_step):\n", + " \n", + " global in_back , in_forw , in_trap, npoint \n", + " \n", + " if time_step==0 or T_total==0:\n", + " print('\\n \\n \\n' + 'Simulation time step is set to: ' + str(time_step) + ' seconds')\n", + " print('Total simulation time: ' + str(T_total) + ' seconds' + '\\n \\n')\n", + " \n", + " else:\n", + " print('\\n \\n \\n' + 'Simulation time step is set to: ' + str(time_step) + ' seconds')\n", + " print('Total simulation time: ' + str(T_total) + ' seconds' + '\\n \\n')\n", + " \n", + " npoint = int(np.round(T_total/time_step))\n", + "\n", + " in_back=int_EB(time_step, T_total, npoint)\n", + "\n", + " in_forw=int_EF(time_step, T_total, npoint)\n", "\n", - "print('Please select the integration methods you want to compare:')\n", - "widget.interact(plot_vs, Euler_Forward =False,\n", - " Euler_Backward=False,\n", - " Trapezoidal_Rule=False);\n" + " in_trap=int_TR(time_step, T_total, npoint)\n", + " \n", + " plot_fun(time_step, npoint)\n", + "\n", + " return time_step, T_total\n", + "\n", + "#Values range for the simulation steps\n", + "values=[round(i*10**-7, 7) for i in range(101)]\n", + "\n", + "#It is important to set the argument continous_update to 'false' so that the slider_fun is called after the user finishes dragging the slider. \n", + "#Otherwise the function will be continuously called for several values in the dragging interval and the expected results will take alot of time to appear \n", + "slider= widget.interactive(slider_fun, time_step=widget.SelectionSlider(description=\"Time step\", continuous_update=False, options=[(\"%g\"%i,i) for i in values], layout=widget.Layout( width='50%', height='50px',)));\n", + "\n", + "display(slider)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Critical time step: \n", + "$7,6 \\cdot 10^{-6} s < T_{critical} $" ] }, {