diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div')
24 files changed, 969 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file10_gauss.png b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file10_gauss.png Binary files differnew file mode 100644 index 0000000..74e2723 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file10_gauss.png diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file10_gauss.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file10_gauss.py new file mode 100644 index 0000000..d77f92e --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file10_gauss.py @@ -0,0 +1,51 @@ +import sys +import numpy as np +import matplotlib.pyplot as plt +from matplotlib.patches import Circle + +def E(q, r0, x, y): + """Return the electric field vector E=(Ex,Ey) due to charge q at r0.""" + den = np.hypot(x-r0[0], y-r0[1])**3 + return q * (x - r0[0]) / den, q * (y - r0[1]) / den + +# Grid of x, y points +nx, ny = 64, 64 +x = np.linspace(-2, 2, nx) +y = np.linspace(-2, 2, ny) +X, Y = np.meshgrid(x, y) + +# Create a multipole with nq charges of alternating sign, equally spaced +# on the unit circle. +nq = 2**int(sys.argv[1]) +charges = [] +for i in range(nq): + q = i%2 * 2 - 1 + charges.append((q, (np.cos(2*np.pi*i/nq), np.sin(2*np.pi*i/nq)))) + +# Electric field vector, E=(Ex, Ey), as separate components +Ex, Ey = np.zeros((ny, nx)), np.zeros((ny, nx)) +for charge in charges: + ex, ey = E(*charge, x=X, y=Y) + Ex += ex + Ey += ey + +fig = plt.figure() +plt.rcParams['axes.facecolor'] = 'black' +ax = fig.add_subplot(111) + +# Plot the streamlines with an appropriate colormap and arrow style +color = 2 * np.log(np.hypot(Ex, Ey)) +ax.streamplot(x, y, Ex, Ey, color=color, linewidth=1, cmap=plt.cm.inferno, + density=2, arrowstyle='->', arrowsize=1.5) + +# Add filled circles for the charges themselves +charge_colors = {True: '#aa0000', False: '#0000aa'} +for q, pos in charges: + ax.add_artist(Circle(pos, 0.05, color=charge_colors[q>0])) + +ax.set_xlabel('$x$') +ax.set_ylabel('$y$') +ax.set_xlim(-2,2) +ax.set_ylim(-2,2) +ax.set_aspect('equal') +plt.show() diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file11_gravitational-field.png b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file11_gravitational-field.png Binary files differnew file mode 100644 index 0000000..129e51b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file11_gravitational-field.png diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file11_gravitational-filed.ipynb b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file11_gravitational-filed.ipynb new file mode 100644 index 0000000..4ad8c27 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file11_gravitational-filed.ipynb @@ -0,0 +1,119 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "%gui qt" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from mayavi import mlab\n", + "import scipy\n", + "import time" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/padmapriya/mohyavi/lib/python3.6/site-packages/ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in true_divide\n", + " This is separate from the ipykernel package so we can avoid doing imports until\n", + "/home/padmapriya/mohyavi/lib/python3.6/site-packages/ipykernel_launcher.py:4: RuntimeWarning: invalid value encountered in true_divide\n", + " after removing the cwd from sys.path.\n", + "/home/padmapriya/mohyavi/lib/python3.6/site-packages/ipykernel_launcher.py:5: RuntimeWarning: invalid value encountered in true_divide\n", + " \"\"\"\n" + ] + } + ], + "source": [ + "x, y, z = np.mgrid[-2:3, -2:3, -2:3]\n", + "r = np.sqrt(x**2 + y**2 + z**2)\n", + "u = x/r**3\n", + "v = y/r**3\n", + "w = z/r**3\n", + "\n", + "a = mlab.quiver3d(x, y, z, u, v, w)\n", + "mlab.axes(a)\n", + "mlab.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x, y, z = np.mgrid[-2:3, -2:3, -2:3]\n", + "u = y**3 - 9*y\n", + "v = x**3 - 9*x\n", + "w = x\n", + "\n", + "a = mlab.quiver3d(x, y, z, u, v, w, colormap = 'gist_earth')\n", + "mlab.fig(bgcolor = (0,0,0))\n", + "\n", + "for i in range(50):\n", + " mlab.view(65, -65)\n", + " mlab.view(azimuth= 3.6*i, elevation=-60, distance=10)\n", + " mlab.process_ui_events()\n", + " time.sleep = 0.005\n", + " mlab.savefig('curl_%02d.png' % i)\n", + " \n", + "\n", + "x, y, z = np.mgrid[-2:3, -2:3, -2:3]\n", + "p = x\n", + "q = y\n", + "r = 4.5*(x**2 - y**2)\n", + "\n", + "b = mlab.quiver3d(x, y, z, p, q, r, colormap = 'gist_earth')\n", + "for j in range(25):\n", + " mlab.view(65, -65)\n", + " mlab.view(azimuth= 3.6*j, elevation=-60, distance=10)\n", + " mlab.process_ui_events()\n", + " time.sleep = 0.005\n", + " mlab.savefig('curl2_%02d.png' % j)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.6.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file12_ponder-curl.png b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file12_ponder-curl.png Binary files differnew file mode 100644 index 0000000..2e7fc79 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file12_ponder-curl.png diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file12_ponder-curl.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file12_ponder-curl.py new file mode 100644 index 0000000..be8a17a --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file12_ponder-curl.py @@ -0,0 +1,17 @@ +from manimlib.imports import * +import numpy as np + +def curl(coordinate): + x,y = coordinate[:2] + return np.array([ + y, + 0, + 0 + ]) + +class Ponder_curl(Scene): + def construct(self): + vf = VectorField(curl) + self.add(vf) + self.wait() + diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file1_sources-and-sinks.gif b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file1_sources-and-sinks.gif Binary files differnew file mode 100644 index 0000000..dcc0843 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file1_sources-and-sinks.gif diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file1_sources-and-sinks.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file1_sources-and-sinks.py new file mode 100644 index 0000000..d26525e --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file1_sources-and-sinks.py @@ -0,0 +1,76 @@ +from manimlib.imports import * +import numpy as np + +def divergence(coordinate): + x,y = coordinate[:2] + return np.array([ + np.sin(x), + np.cos(y), + 0 + ]) + +def curl(coordinate): + x,y = coordinate[:2] + return np.array([ + np.sin(y), + np.cos(x), + 0 + ]) + +class fluid_flow(Scene): + def construct(self): + + + + ball_a = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([-6,-1,0])).fade(0.2).scale(1.2) + ball_b = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([0.1,3,0])).fade(0.2).scale(1.2) + ball_c = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([-0.5,-1, 0])).fade(0.2).scale(1.2) + ball_d = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([4.5,-1.2,0])).fade(0.2).scale(1.2) + ball2 = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([-0.5,0,0])).fade(0.2).scale(1.2) + ball3 = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([-1.5,1.2,0])).fade(0.2).scale(1.2) + ball4 = Dot().set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).move_to(np.array([-1.5,-1.2,0])).fade(0.2).scale(1.2) + ball5 = Sphere(radius = 0.2, chekerboard_colors =["#F87666", "#F53A23", PURPLE_E]).set_color_by_gradient(["#F87666", "#F53A23", PURPLE_E]).fade(0.2).move_to(np.array([-4.7,0,0])) + + flow_one = StreamLines( + divergence, + virtual_time=3, + min_magnitude=0, + max_magnitude=1, + ).set_color_by_gradient(["#003853", "#0478A1","#04AED9", WHITE]) + flow_div =(AnimatedStreamLines( + flow_one, + line_anim_class=ShowPassingFlashWithThinningStrokeWidth + )) + + flow_two = StreamLines( + curl, + + virtual_time=3, + min_magnitude=0, + max_magnitude=1, + ).set_color_by_gradient(["#003853", "#0478A1","#04AED9", WHITE]) + flow_curl =(AnimatedStreamLines( + flow_two, + line_anim_class=ShowPassingFlashWithThinningStrokeWidth + )) + + label_div = TexMobject(r"\textit{Fluid flows out from }", r"\textit{sources }", r"\textit{and into }", r"\textit{sinks}" ).move_to(np.array([0,3.5, 0])).set_stroke(width = 1.5).scale(0.7) + label_div[1].set_color("#F87666") + label_div[3].set_color("#F87666") + title_div = TexMobject(r"Divergence").set_stroke(width = 1.5).move_to(3*DOWN).set_color("#F87666").scale(1.2) + label_curl = TexMobject(r"\textit{Fluid also rotates }", r"\textit{clockwise }", r"\textit{and }", r"\textit{counter-clockwise}" ).move_to(np.array([0,3.5, 0])).set_stroke(width = 1.5).scale(0.7) + label_curl[1].set_color("#F87666") + label_curl[3].set_color("#F87666") + title_curl = TexMobject(r"Curl").set_stroke(width = 1.5).move_to(3*DOWN).set_color("#F87666").scale(1.2) + + + + + self.add(flow_div, label_div) + self.play(Write(title_div)) + self.wait(5) + self.remove(flow_div) + self.wait() + self.add(flow_curl) + self.play(ReplacementTransform(label_div, label_curl), ReplacementTransform(title_div, title_curl)) + self.wait(6) diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file2_div-curl-types.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file2_div-curl-types.py new file mode 100644 index 0000000..e8e1a83 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file2_div-curl-types.py @@ -0,0 +1,162 @@ +from manimlib.imports import * +import numpy as np + +def pos_div(coordinate): + x,y = coordinate[:2] + return np.array([ + x, + y, + 0 + ]) + +def neg_div(coordinate): + x,y = coordinate[:2] + return np.array([ + -x, + -y, + 0 + ]) + +def zero_div(coordinate): + x,y = coordinate[:2] + y = 1.0 + return np.array([ + y, + 0, + 0 + ]) + +def curl_c(coordinate): + x,y = coordinate[:2] + return np.array([ + y, + -x, + 0 + ]) + +def curl_ac(coordinate): + x,y = coordinate[:2] + return np.array([ + -y, + x, + 0 + ]) + + + + +class Examples(Scene): + def construct(self): + + vf1 = VectorField(pos_div, x_min = -1.5, x_max = 1.5, y_min = -1.5, y_max = 1.5).shift(2.5*UP, 4*LEFT) + vf3 = VectorField(neg_div, x_min = -1.5, x_max = 1.5, y_min = -1.5, y_max = 1.5).shift(2.5*UP, 4*RIGHT) + vf2 = VectorField(zero_div, x_min = -1.5, x_max = 1.5, y_min = -1.5, y_max = 1.5).move_to(np.array([0, 0.5, 0])) + vf4 = VectorField(curl_c, x_min = -1.5, x_max = 1.5, y_min = -1.5, y_max = 1.5).shift(2*DOWN, 4*RIGHT) + vf5 = VectorField(curl_ac, x_min = -1.5, x_max = 1.5, y_min = -1.5, y_max = 1.5).shift(2*DOWN, 4*LEFT) + dot = Dot().move_to(vf1.get_center()) + label3 = TexMobject(r"\textit{Sink}", r"\textrm{div} F < 0").set_color(BLUE_E).scale(0.6).shift(3*DOWN + 0.7*RIGHT) + label1 = TexMobject(r"\textit{Source}", r"\textrm{div} F > 0").set_color(YELLOW_E).scale(0.6).shift(2.8*DOWN + 0.7*RIGHT) + label2 = TexMobject(r"\textrm{div} F =0", r"\textrm{ curl} F = 0").scale(0.6).shift(3*DOWN + 0.7*RIGHT) + label4 = TexMobject(r"\textit{Clockwise rotation}", r"\textrm{curl} F < 0").set_color(BLUE_E).scale(0.6).shift(3*DOWN + 0.7*RIGHT) + label5 = TexMobject(r"\textit{Counter-clockwise rotation}", r"\textrm{curl} F > 0").set_color(YELLOW_E).scale(0.6).shift(3*DOWN + 0.7*RIGHT) + + label1[1].next_to(label1[0], DOWN, buff = SMALL_BUFF).set_color(WHITE) + label2[1].next_to(label2[0], DOWN, buff = SMALL_BUFF).set_color(WHITE) + label3[1].next_to(label3[0], DOWN, buff = SMALL_BUFF).set_color(WHITE) + + label4[1].next_to(label4[0], DOWN, buff = SMALL_BUFF).set_color(WHITE) + label5[1].next_to(label5[0], DOWN, buff = SMALL_BUFF).set_color(WHITE) + + lines_a = StreamLines( + pos_div, + virtual_time=1.5, + min_magnitude=0, + max_magnitude=1.5, + x_min = -1, x_max = 1, y_min = -1, y_max = 1 + ).shift(2.5*UP, 4*LEFT) + lines1 = AnimatedStreamLines( + lines_a, + line_anim_class=ShowPassingFlashWithThinningStrokeWidth + ) + + lines_b = StreamLines( + zero_div, + virtual_time=1.5, + min_magnitude=0, + max_magnitude=1.5, + x_min = -0.5, x_max = 0.5, y_min = -0.5, y_max = 0.5 + ).move_to(np.array([-0.2, 0.5, 0])) + lines2 = AnimatedStreamLines( + lines_b, + line_anim_class=ShowPassingFlashWithThinningStrokeWidth + ) + + lines_c = StreamLines( + neg_div, + virtual_time=1.5, + min_magnitude=0, + max_magnitude=1.5, + x_min = -1, x_max = 1, y_min = -1, y_max = 1 + ).shift(2.5*UP, 4*RIGHT) + lines3 =(AnimatedStreamLines( + lines_c, + line_anim_class=ShowPassingFlashWithThinningStrokeWidth + )) + + lines_d = StreamLines( + curl_c, + virtual_time=1.5, + min_magnitude=0, + max_magnitude=1.5, + x_min = -1, x_max = 1, y_min = -1, y_max = 1 + ).shift(2*DOWN, 4*RIGHT) + lines4 =(AnimatedStreamLines( + lines_d, + line_anim_class=ShowPassingFlashWithThinningStrokeWidth + )) + + lines_e = StreamLines( + curl_ac, + virtual_time=1.5, + min_magnitude=0, + max_magnitude=1.5, + x_min = -1, x_max = 1, y_min = -1, y_max = 1 + ).shift(2*DOWN, 4*LEFT) + lines5 =(AnimatedStreamLines( + lines_e, + line_anim_class=ShowPassingFlashWithThinningStrokeWidth + )) + self.play(Write(vf1)) + self.wait() + self.add(lines1) + self.play(ShowCreation(label1[0]), ShowCreation(label1[1])) + self.wait(4) + self.remove(lines1) + self.play(Write(vf2)) + self.add(lines2) + self.play(ReplacementTransform(label1, label2)) + self.play(Indicate(label2)) + self.wait(4) + self.remove(lines2) + self.play(Write(vf3)) + self.add(lines3) + self.play(ReplacementTransform(label2, label3)) + self.play(Indicate(label3)) + self.wait(4) + self.remove(lines3) + self.play(Write(vf4)) + self.add(lines4) + self.play(ReplacementTransform(label3, label4)) + self.play(Indicate(label4)) + self.wait(4) + self.remove(lines4) + self.play(Write(vf5)) + self.add(lines5) + self.play(ReplacementTransform(label4, label5)) + self.play(Indicate(label5)) + self.wait(4) + self.remove(lines5) + self.wait() + + + diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file2_div_curl-types.gif b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file2_div_curl-types.gif Binary files differnew file mode 100644 index 0000000..9d60f45 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file2_div_curl-types.gif diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file3_threed-vec-field.gif b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file3_threed-vec-field.gif Binary files differnew file mode 100644 index 0000000..ad331a3 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file3_threed-vec-field.gif diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file3_threed-vec-field.ipynb b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file3_threed-vec-field.ipynb new file mode 100644 index 0000000..8d41df4 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file3_threed-vec-field.ipynb @@ -0,0 +1,67 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "%gui qt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from mayavi import mlab" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x, y, z = np.mgrid[-2:3, -2:3, -2:3]\n", + "u = y**3 - 9*y\n", + "v = x**3 - 9*x\n", + "w = x\n", + "\n", + "a = mlab.quiver3d(x, y, z, u, v, w)\n", + "mlab.axes(a)\n", + "mlab.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.6.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file4_output-curl.gif b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file4_output-curl.gif Binary files differnew file mode 100644 index 0000000..956458b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file4_output-curl.gif diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file4_output-curl.ipynb b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file4_output-curl.ipynb new file mode 100644 index 0000000..0f8b326 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file4_output-curl.ipynb @@ -0,0 +1,67 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "%gui qt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from mayavi import mlab" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x, y, z = np.mgrid[-2:3, -2:3, -2:3]\n", + "u = x\n", + "v = y\n", + "w = 4.5*(x**2 - y**2)\n", + "\n", + "a = mlab.quiver3d(x, y, z, u, v, w)\n", + "mlab.axes(a)\n", + "mlab.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.6.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file5_neg-div.gif b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file5_neg-div.gif Binary files differnew file mode 100644 index 0000000..7634acf --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file5_neg-div.gif diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file5_neg-div.ipynb b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file5_neg-div.ipynb new file mode 100644 index 0000000..7fec515 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file5_neg-div.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file6_macro-micro-curl.gif b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file6_macro-micro-curl.gif Binary files differnew file mode 100644 index 0000000..9b30ce5 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file6_macro-micro-curl.gif diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file6_macro-micro-curl.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file6_macro-micro-curl.py new file mode 100644 index 0000000..02c75a3 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file6_macro-micro-curl.py @@ -0,0 +1,42 @@ +from manimlib.imports import * +import numpy as np + +def curl(coordinate): + x,y = coordinate[:2] + return np.array([ + -y, + x, + 0 + ]) + + +class Subtle(Scene): + def construct(self): + vf1 = VectorField(curl) + pinwheel = SVGMobject("geo").move_to(np.array([2, 0, 0])).scale(0.3).set_stroke(width = 0.3).set_color_by_gradient(["#adf802", YELLOW_C]).move_to(np.array([2.3, 0, 0])) + self.add(pinwheel) + + label1 = TexMobject(r"\textit{Microscopic curl}").shift(3*DOWN).add_background_rectangle() + label2 = TexMobject(r"\textit{Macroscopic curl}").shift(3*DOWN) + + ball1 = Dot(checkerboard_colors = [BLUE_E, PURPLE_E], resolution = [2,2], radius = 0.4).move_to(np.array([-1, -1, 0])) + ball2 = Sphere(checkerboard_colors = [BLUE_E, TEAL], resolution = [16, 16], radius = 0.3).move_to(np.array([2, 0, 0])) + circ = Circle(radius = 2) + + + self.add(vf1) + self.wait() + self.play(ShowCreation(pinwheel)) + self.bring_to_front(pinwheel) + self.play(Rotating(pinwheel), ShowCreation(label1)) + self.wait(2) + #self.add(ball1) + move_submobjects_along_vector_field(pinwheel, curl) + self.play(FadeOut(label1), ShowCreation(label2)) + self.play(Indicate(label2)) + + self.wait(5) + + + + diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file7_div-formula.gif b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file7_div-formula.gif Binary files differnew file mode 100644 index 0000000..4910d2f --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file7_div-formula.gif diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file7_div-formula.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file7_div-formula.py new file mode 100644 index 0000000..4e1eab2 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file7_div-formula.py @@ -0,0 +1,225 @@ +from manimlib.imports import * +import numpy as np + +def div(coordinate): + x,y = coordinate[:2] + return np.array([ + x, + y, + 0 + ]) + + + + +class Grid(VMobject): + CONFIG = { + "height": 6.0, + "width": 6.0, + } + + def __init__(self, rows, columns, **kwargs): + digest_config(self, kwargs, locals()) + VMobject.__init__(self, **kwargs) + + def generate_points(self): + x_step = self.width / self.columns + y_step = self.height / self.rows + + for x in np.arange(0, self.width + x_step, x_step): + self.add(Line( + [x - self.width / 2., -self.height / 2., 0], + [x - self.width / 2., self.height / 2., 0], + )) + for y in np.arange(0, self.height + y_step, y_step): + self.add(Line( + [-self.width / 2., y - self.height / 2., 0], + [self.width / 2., y - self.height / 2., 0] + )) + + +class ScreenGrid(VGroup): + CONFIG = { + "rows":8, + "columns":14, + "height": FRAME_Y_RADIUS*2, + "width": 14, + "grid_stroke":0.5, + "grid_color":WHITE, + "axis_color":RED, + "axis_stroke":2, + "show_points":False, + "point_radius":0, + "labels_scale":0.5, + "labels_buff":0, + "number_decimals":2 + } + + def __init__(self,**kwargs): + VGroup.__init__(self,**kwargs) + rows=self.rows + columns=self.columns + grilla=Grid(width=self.width,height=self.height,rows=rows,columns=columns).set_stroke(self.grid_color,self.grid_stroke) + + vector_ii=ORIGIN+np.array((-self.width/2,-self.height/2,0)) + vector_id=ORIGIN+np.array((self.width/2,-self.height/2,0)) + vector_si=ORIGIN+np.array((-self.width/2,self.height/2,0)) + vector_sd=ORIGIN+np.array((self.width/2,self.height/2,0)) + + ejes_x=Line(LEFT*self.width/2,RIGHT*self.width/2) + ejes_y=Line(DOWN*self.height/2,UP*self.height/2) + + ejes=VGroup(ejes_x,ejes_y).set_stroke(self.axis_color,self.axis_stroke) + + divisiones_x=self.width/columns + divisiones_y=self.height/rows + + direcciones_buff_x=[UP,DOWN] + direcciones_buff_y=[RIGHT,LEFT] + dd_buff=[direcciones_buff_x,direcciones_buff_y] + vectores_inicio_x=[vector_ii,vector_si] + vectores_inicio_y=[vector_si,vector_sd] + vectores_inicio=[vectores_inicio_x,vectores_inicio_y] + tam_buff=[0,0] + divisiones=[divisiones_x,divisiones_y] + orientaciones=[RIGHT,DOWN] + puntos=VGroup() + leyendas=VGroup() + + + for tipo,division,orientacion,coordenada,vi_c,d_buff in zip([columns,rows],divisiones,orientaciones,[0,1],vectores_inicio,dd_buff): + for i in range(1,tipo): + for v_i,direcciones_buff in zip(vi_c,d_buff): + ubicacion=v_i+orientacion*division*i + punto=Dot(ubicacion,radius=self.point_radius) + coord=round(punto.get_center()[coordenada],self.number_decimals) + leyenda=TextMobject("%s"%coord).scale(self.labels_scale) + leyenda.next_to(punto,direcciones_buff,buff=self.labels_buff) + puntos.add(punto) + leyendas.add(leyenda) + + self.add(grilla,ejes,leyendas) + if self.show_points==True: + self.add(puntos) + + + + + + +class ExpDiv(Scene): + def construct(self): + + #all the text + field_text = TexMobject(r"\vec F = P\hat i + Q\hat j").shift(3*UP+5*RIGHT) + field_text_2 = TexMobject(r"\vec F = 2x\hat i + 2y\hat j").shift(3*UP+5*RIGHT) + p = TexMobject(r"P = 2x").scale(0.8) + q = TexMobject(r"Q = 2y").next_to(p, RIGHT).scale(0.8) + pq = VGroup(p, q) + pq.next_to(field_text_2, DOWN, buff = SMALL_BUFF) + dpq = TexMobject(r"\frac{\partial P}{\partial x}", r" \frac{\partial Q}{\partial y}").scale(0.8).next_to(pq, DOWN, buff = LARGE_BUFF) + + + dp_dq = TexMobject(r"\frac{\partial P}{\partial x} + \frac{\partial Q}{\partial y}", r" = \textrm{div} \vec F").scale(0.8).next_to(pq, DOWN, buff = LARGE_BUFF) + #dp_dq1 = TexMobject(r" = \textrm{div} \vec F").scale(0.8) + #dp_dq1.next_to(dp_dq[0], DOWN, buff = SMALL_BUFF) + dp_text = TexMobject(r"\frac{\partial P}{\partial x}\textit{: the rate of change of the horizontal component as x increases}").shift(3*DOWN).scale(0.8) + dq_text = TexMobject(r"\frac{\partial Q}{\partial y}\textit{: the rate of change of the vertical component as y increases}").shift(3*DOWN).scale(0.8) + + + vector_field = VectorField(div, x_min = -4, x_max = 4, y_min = -4, y_max = 4).shift(1.5*LEFT) + + x_comps=VGroup() + y_comps=VGroup() + for vector in vector_field: + x = Vector(RIGHT, color = BLUE_E) + y = Vector(UP, color= YELLOW_E) + x.put_start_and_end_on(vector.points[0], np.array([vector.get_end()[0],vector.points[0][1],0])) + y.put_start_and_end_on(vector.points[0], np.array([vector.points[0][0],vector.get_end()[1],0])) + x_comps.add(x) + y_comps.add(y) + + line1 = Arrow(4*LEFT, 4*RIGHT).shift(3.5*DOWN+1.5*LEFT) + line2 = Arrow(4*DOWN, 4*UP).shift(3*RIGHT) + + + + + # f(x) = x**2 + fx = lambda x: x.get_value()/10 + # ValueTrackers definition + x_value = ValueTracker(-4) + fx_value = ValueTracker(fx(x_value)) + # DecimalNumber definition + x_tex = DecimalNumber(x_value.get_value()).add_updater(lambda v: v.set_value(x_value.get_value())) + fx_tex = DecimalNumber(fx_value.get_value()).add_updater(lambda v: v.set_value(fx(x_value))) + # TeX labels definition + x_label = TexMobject("x = ") + fx_label = TexMobject("P = ") + # Grouping of labels and numbers + group = VGroup(x_tex,fx_tex,x_label,fx_label).scale(0.8) + VGroup(x_tex, fx_tex).arrange_submobjects(DOWN,buff=0.3) + # Align labels and numbers + x_label.next_to(x_tex,LEFT, buff=0.1,aligned_edge=x_label.get_bottom()) + fx_label.next_to(fx_tex,LEFT, buff=0.1,aligned_edge=fx_label.get_bottom()) + + + fy = lambda y: y.get_value()/10 + # ValueTrackers definition + y_value = ValueTracker(-4) + fy_value = ValueTracker(fy(y_value)) + # DecimalNumber definition + y_tex = DecimalNumber(y_value.get_value()).add_updater(lambda v: v.set_value(y_value.get_value())) + fy_tex = DecimalNumber(fy_value.get_value()).add_updater(lambda v: v.set_value(fy(y_value))) + # Tey labels definition + y_label = TexMobject("y = ") + fy_label = TexMobject("Q = ") + # Grouping of labels and numbers + group_2 = VGroup(y_tex,fy_tex,y_label,fy_label).scale(0.8) + VGroup(y_tex, fy_tex).arrange_submobjects(DOWN,buff=0.3) + # Align labels and numbers + y_label.next_to(y_tex,LEFT, buff=0.1,aligned_edge=y_label.get_bottom()) + fy_label.next_to(fy_tex,LEFT, buff=0.1,aligned_edge=fy_label.get_bottom()) + + + self.play(ShowCreation(field_text)) + self.wait() + self.play(ShowCreation(vector_field), ReplacementTransform(field_text, field_text_2)) + self.wait() + self.play(ShowCreation(p), ShowCreation(q), FadeOut(vector_field)) + self.wait() + self.play(ShowCreation(dpq[0]), ShowCreation(x_comps)) + self.play(Indicate(dpq[0])) + self.wait() + self.play(ShowCreation(dp_text)) + self.wait() + self.play(Uncreate(dp_text)) + + self.add(group.move_to(5*RIGHT+3*DOWN)) + self.play(Write(line1), + x_value.set_value,4, + rate_func=linear, + run_time=3 + ) + self.wait(2) + self.play(FadeOut(group), FadeOut(line1), ApplyFunction(lambda a:a.fade(), x_comps)) + + self.play(ShowCreation(dpq[1]), ShowCreation(y_comps)) + self.play(Indicate(dpq[1])) + self.wait(2) + self.play(ShowCreation(dq_text)) + self.wait() + self.play(Uncreate(dq_text)) + + self.add(group_2.move_to(5*RIGHT+3*DOWN)) + self.play(Write(line2), + y_value.set_value,4, + rate_func=linear, + run_time=3 + ) + self.wait(2) + self.play(ReplacementTransform(dpq, dp_dq), FadeOut(line2), ReplacementTransform(x_comps, vector_field), ReplacementTransform(y_comps, vector_field), FadeOut(group_2)) + + self.play(Indicate(dp_dq)) + self.wait() + diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file8_curl-paddle.gif b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file8_curl-paddle.gif Binary files differnew file mode 100644 index 0000000..41db451 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file8_curl-paddle.gif diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file8_curl-paddle.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file8_curl-paddle.py new file mode 100644 index 0000000..7a11992 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file8_curl-paddle.py @@ -0,0 +1,55 @@ +from manimlib.imports import * + +def field_func(coordinate): + x,y = coordinate[:2] + return np.array([ + -y, + x, + 0 + ]) + +class Paddlewheel(ThreeDScene): + def construct(self): + axes = ThreeDAxes() + #self.add(axes) + text = TextMobject("Insert the paddle into the flow of water").shift(3*DOWN).add_background_rectangle() + text_a = TextMobject("The rotation of the wheel is proportional to the component of curl in the direction of the axle").shift(3*DOWN).scale(0.7) + + vec_field = VectorField(field_func, x_min =-4, x_max = 4, y_min =-4, y_max =4) + + self.set_camera_orientation(phi=0*DEGREES,theta=0*DEGREES,distance=40) + lines_a = StreamLines( + field_func, + virtual_time=3, + min_magnitude=0, + max_magnitude=3, + ).set_color_by_gradient([WHITE, BLUE_E]) + flow = AnimatedStreamLines( + lines_a, + line_anim_class=ShowPassingFlashWithThinningStrokeWidth + ) + + paddle = VGroup(Line(np.array([3, 0, 0]), np.array([-3, 0, 0])), + Line(np.array([0, 3, 0]), np.array([0, -3, 0]))).set_stroke(width = 8).set_color(YELLOW_E) + cylinder = ParametricSurface( + lambda u, v: np.array([ + 0.1*np.cos(u), + 0.1*np.sin(u), + v, + ]), + u_min = 0, u_max = 2*np.pi, v_min = -0.2, v_max = 3.5, checkerboard_colors = [YELLOW_E, YELLOW_E]).fade(0.5) + plane = ParametricSurface(lambda u, v: np.array([u, v, 0]), checkerboard_colors = [WHITE, WHITE]).fade(0.9) + + self.add(paddle, cylinder, flow) + self.add_fixed_in_frame_mobjects(text) + self.play(Rotating(paddle)) + self.wait() + self.play(FadeIn(vec_field)) + self.remove(flow, text) + self.bring_to_front(cylinder) + #self.play(Rotating(paddle)) + self.wait() + self.add_fixed_in_frame_mobjects(text_a) + #self.play(ReplacementTransform(text, text_a)) + self.move_camera(phi=60*DEGREES,theta=30*DEGREES) + self.wait() diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file9_formal-def.gif b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file9_formal-def.gif Binary files differnew file mode 100644 index 0000000..6247aea --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file9_formal-def.gif diff --git a/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file9_formal-def.py b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file9_formal-def.py new file mode 100644 index 0000000..ecafca4 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/div-curl-grad-and-all-that/Curl and Div/DivCurl_file9_formal-def.py @@ -0,0 +1,82 @@ +from manimlib.imports import * +import numpy as np + + + +def func(coordinate): + x,y = coordinate[:2] + return np.array([ + 1.9*np.cos(x+2*y), + 1.5*np.sin(x-2*y), + 0 + ]) + +def coord(x,y,z=0): + return np.array([x,y,z]) + +class Instrument(Scene): + CONFIG = { + "x_coords": ([1, 2.2, 3.9, 3, -0, -0.2, 1]), + "y_coords": ([1.5, 1, -0.5, -2.0, -1.4, 0.5, 1.5]), + } + + def setup(self): + self.tuples = list(zip(self.x_coords,self.y_coords)) + dots = self.get_all_mobs() + + def get_dots(self, coords): + dots = VGroup(*[Dot(coord(x,y)) for x,y in coords]) + return dots + + def get_all_mobs(self): + dots = self.get_dots(self.tuples) + return dots + + +class Curl_one(MovingCameraScene, Instrument): + def setup(self): + MovingCameraScene.setup(self) + Instrument.setup(self) + + + def construct(self): + vec = VectorField(func) + + + frame_one = Circle(radius = 0.5).move_to(np.array([4, 2, 0])) + dot = Dot(frame_one.get_center()).scale(0.5) + surface = VMobject() + surface.set_points_smoothly([*[coord(x,y) for x,y in self.tuples]]) + surface.move_to(dot.get_center()).set_stroke(width = 0.5) + + label = TexMobject(r"A").scale(0.5).next_to(dot, LEFT+UP, buff = SMALL_BUFF) + #self.add(frame_one) + self.camera_frame.save_state() + self.play( + self.camera_frame.set_width,frame_one.get_width()*7.0, + self.camera_frame.move_to,frame_one) + + + + + self.add(vec, dot, label) + lines = StreamLines( + func, + virtual_time=7, + min_magnitude=0, + max_magnitude=8, + ) + lines1 = AnimatedStreamLines( + lines, + line_anim_class=ShowPassingFlashWithThinningStrokeWidth + ) + + self.add(lines1) + self.wait(3) + self.play(Restore(self.camera_frame)) + self.wait(2) + self.add(surface) + self.wait(3) + self.play(ApplyMethod(surface.scale, 0.01), run_time = 2) + self.remove(surface) + self.wait(2) |
