{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Special Case Solution for Riemannian Manifold B\n", "\n", "## Background and Introduction:\n", "\n", "This section provides a solution for a special case of the problem related to Riemannian manifold B, as discussed in Chapter 3. The solution is particularly related to the calculations in Exercise 1.41 (page 58) and Appendix B, offering a parametric version of those calculations.\n", "\n", "### Subset Definition\n", "\n", "Consider the subset $A^2$ defined as:\n", "\n", "$$\n", "A^2 = \\{\\alpha \\in \\mathcal{B}^2(B^1(0)) : \\alpha \\in A\\}\n", "$$\n", "\n", "where:\n", "\n", "$$\n", "A = \\{\\alpha \\in \\mathcal{B}^1(B^1(0)): \\alpha(a) = x, \\alpha(b) = y \\in B^1(0) \\}.\n", "$$\n", "\n", "In this context, we assume $\\alpha \\in C^2([a,b] \\rightarrow B^1(0))$ minimizes the following expression:\n", "\n", "$$\n", "\\int_a^b \\frac{4}{4+|\\alpha|^2} |\\alpha'| d\\alpha.\n", "$$\n", "\n", "## Calculation\n", "\n", "Given an admissible vector-valued perturbation $\\phi \\in C^2([a,b] \\rightarrow \\mathbb{R}^2)$ with $\\phi(a) = \\phi(b) = 0$, the calculation proceeds as:\n", "\n", "$$\n", "\\left. \\frac{d}{dt} \\right|_{t=0} \\int_a^b \\frac{4|\\alpha' + t\\phi'|}{4 + |\\alpha + t\\phi|^2} dt = \\int_a^b \\left( -\\frac{8\\langle\\alpha, \\phi\\rangle}{(4 +|\\alpha|^2)^2} |\\alpha'| + \\frac{4\\langle\\alpha' , \\phi'\\rangle}{|\\alpha'| (4 +|\\alpha|^2)^2} \\right).\n", "$$\n", "\n", "This leads to the parametric Euler-Lagrange equation for geodesics in $B^1$:\n", "\n", "$$\n", "N[\\alpha] = (4 + |\\alpha|^2) \\alpha'' - \\frac{(4 + |\\alpha|^2) \\langle \\alpha', \\alpha'' \\rangle \\alpha'}{|\\alpha'|^2} - 2\\langle \\alpha, \\alpha' \\rangle \\alpha' + 2|\\alpha'|^2 \\alpha = 0.\n", "$$\n", "\n", "## Special Case and Parametric Euler-Lagrange Equation\n", "\n", "For the special case of a nonparametric minimizer $\\alpha(x) = (x, h(x))$, the system simplifies to:\n", "\n", "$$\n", "\\frac{(4 + x^2 + h^2)}{(1 + h'^2)} h'' + 2(h - xh') = 0.\n", "$$\n", "\n", "## Circular Arcs as Geodesics\n", "\n", "It may be recalled that we have found a nominally two-parameter family of solutions of (D.2) given by\n", "$$\n", "h(x) = y + \\sqrt{(y_a - y)^2 - x^2}\n", "$$\n", "corresponding to points $(a, y_a)$ in the second quadrant of $B_1(0)$ for the particular values\n", "$$\n", "y = \\frac{-4 - a^2 - y^2}{2y_a}.\n", "$$\n", "Recall also that the point $(0,y)$ gives the center of the circular arc determined by these solutions. The radii of the circular arcs determined by these solutions may also be determined and is found to be given by\n", "$$\n", "\\left| (a, y_a) - (0,y) \\right| = \\sqrt{a^2 + \\frac{\\left(4 - a^2 + y_a^2\\right)^2}{4y_a^2}} = \\left| (\\pm 2,0) - (0,y) \\right|.\n", "$$\n", "\n", "\n", "## Rotation Argument\n", "Argue that if an arc of a circle passing through four points $x = (x_1,x_2)$ and $y = (y_1,y_2)$ in $B_1(0)$ and $(\\pm 2,0)$, and parameterized by $\\alpha = (\\alpha_1,\\alpha_2) : [a,b] \\rightarrow B_1(0)$ is a minimizer for $lengthB[\\alpha]$ among paths connecting $x$ to $y$ in $B_1(0)$, then for any fixed $\\theta \\in \\mathbb{R}$ the path $\\beta : [a,b] \\rightarrow B_1(0)$ by\n", "$$\n", "\\beta(t) = (\\cos\\theta \\alpha_1(t) - \\sin\\theta \\alpha_2(t), \\sin\\theta \\alpha_1(t) + \\cos\\theta \\alpha_2(t))\n", "$$\n", "demonstrates that by rotating the geodesic arc $\\Gamma$ with respect to $(0,0)$ so the point of intersection rotates to coincide with $(0,b)$, one obtains a geodesic circular arc $\\Gamma'$ passing through $(0,b)$ and making an angle $\\theta$ with $\\partial B_b(0)$ and hence with the geodesic arc $\\Gamma_0$ which is horizontal at $(0,b)$. This gives the desired geodesic ray passing through $(0,b)$ and gives a one-to-one correspondence between the rays in the \"geodesic star\" and the rotations of the foliation of $B_1(0)$ given by circular arcs passing through $(\\pm 2,0)$.\n", "\n", "The alternative approach, which we will attempt to discuss in detail, is illustrated in the middle and right in Figure D.4. Here we begin directly with an initial direction $(\\cos\\theta,\\sin\\theta)$ at $(0,b)$ and consider the family of circles tangent to the line generated by the direction. The circle with curvature $k > 0$ has center\n", "$$\n", "(0, b) + \\frac{1}{k}(\\sin\\theta,-\\cos\\theta)\n", "$$\n", "and may be parameterized by\n", "$$\n", "p = (0,b) + \\frac{1}{k}(\\sin\\theta,-\\cos\\theta) + \\frac{1}{k}(\\cos t,\\sin t) = \\frac{1}{k}(\\sin\\theta + \\cos t), b + \\frac{1}{k}(-\\cos\\theta + \\sin t).\n", "$$\n", "\n", "So here our code provide discussion about how to obtain the different situation of the above equation in a numerical way.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.optimize import brentq\n", "# Parameters corresponds to the given theta and b but trying different t.\n", "b=1.0\n", "theta = np.pi/4\n", "t=np.linspace(0, 2*np.pi, 100)\n", "\n", "# Plotting the ball B2(0) of radius 2\n", "fig, ax = plt.subplots(figsize=(10, 8))\n", "circle = plt.Circle((0, 0), 2, color='blue', fill=False, label='Ball B2(0)')\n", "ax.add_artist(circle)\n", "\n", "# Parametrization of p for different values of k\n", "k_values = [0.1, 0.5, 1, 2] \n", "\n", "# Plot parametrization of p for different values of k on the ball\n", "for k in k_values:\n", " p_x = (1/k) * (np.sin(theta) + np.cos(t))\n", " p_y = b + (1/k) * (-np.cos(theta) + np.sin(t))\n", " ax.plot(p_x, p_y, label=f'k={k}')\n", "\n", "# Plot the points (±2, 0)\n", "ax.plot([2, -2], [0, 0], 'go', label='Points (±2, 0)')\n", "\n", "# Setting the same scale for both axes and other plot settings\n", "ax.set_xlim([-3, 3])\n", "ax.set_ylim([-3, 3])\n", "ax.set_aspect('equal', 'box')\n", "ax.legend()\n", "ax.grid(True)\n", "ax.set_title('Parametrization of p for different k values and Arc through (±2, 0) on Ball B2(0)')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you trying to obtain the dynamical changes of different k, try this" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "import os\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import imageio\n", "from scipy.optimize import brentq\n", "os.makedirs('tmp', exist_ok=True)\n", "\n", "# Define parametrization functions\n", "def p_x(t, k, theta):\n", " return (1/k) * (np.sin(theta) + np.cos(t))\n", "\n", "def p_y(t, k, theta, b):\n", " return b + (1/k) * (-np.cos(theta) + np.sin(t))\n", "\n", "# Define the distance function from the origin\n", "def distance_from_origin(t, k, theta, b):\n", " return np.sqrt(p_x(t, k, theta)**2 + p_y(t, k, theta, b)**2) - 2\n", "\n", "# Check for sign changes in the distance function across the interval [0, 2pi]\n", "def find_intersections(k, theta, b):\n", " t_values = np.linspace(0, 2 * np.pi, 1000)\n", " distances = distance_from_origin(t_values, k, theta, b)\n", " sign_changes = np.where(np.diff(np.sign(distances)))[0] # Indices where sign changes\n", " intersections = []\n", " for idx in sign_changes:\n", " try:\n", " t_intersection = brentq(distance_from_origin, t_values[idx], t_values[idx + 1], args=(k, theta, b))\n", " intersections.append(t_intersection)\n", " except ValueError:\n", " pass \n", " return intersections\n", "\n", "\n", "\n", "# Function to plot parametrization of p for a given k on the ball B2(0)\n", "def plot_for_k(k, filename, b, theta):\n", " intersections = find_intersections(k, theta, b)\n", " fig, ax = plt.subplots(figsize=(10, 8))\n", " circle = plt.Circle((0, 0), 2, color='blue', fill=False)\n", " ax.add_artist(circle)\n", " t = np.linspace(0, 2 * np.pi, 100)\n", " \n", " ax.plot(p_x(t, k, theta), p_y(t, k, theta, b), label=f'k={k}')\n", "\n", " # Points (±2, 0)\n", " ax.plot([2, -2], [0, 0], 'go')\n", "\n", " for t_int in intersections:\n", " P_int = (p_x(t_int, k, theta), p_y(t_int, k, theta, b))\n", " ax.plot(P_int[0], P_int[1], 'ro')\n", " # Additional elements for k=0.05\n", " # Calculate and plot line for k=0.05\n", " # This is an example and needs actual calculation based on your model\n", " line_x = np.linspace(-3, 3, 100)\n", " line_y = np.tan(theta) * (line_x - 0) + b\n", " ax.plot(line_x, line_y, 'r--', label='Line for k=0.05')\n", " \n", " # Calculate and plot tangent at (0,b) for k\n", " # Placeholder tangent, replace with actual calculation\n", " tangent_y = np.tan(theta) * (line_x - 0) + b\n", " ax.plot(line_x, tangent_y, 'g--', label=f'Tangent at (0,{b}) for k={k}')\n", "\n", " ax.set_xlim([-3, 3])\n", " ax.set_ylim([-3, 3])\n", " ax.set_aspect('equal', 'box')\n", " ax.legend()\n", " plt.close(fig)\n", " fig.savefig(filename)\n", " return filename\n", "\n", "def arc_equation(t, k, theta, b):\n", " p_x = (1/k) * (np.sin(theta) + np.cos(t))\n", " p_y = b + (1/k) * (-np.cos(theta) + np.sin(t))\n", " return p_x, p_y\n", "\n", "\n", "# Generate plots for a series of k values and create a GIF\n", "theta = np.pi/4 #0\n", "b=1\n", "k_values = list(np.linspace(0.05, 0.86, 20) )+ list(np.linspace(0.86, 0.87, 50) )+list(np.linspace(0.87, 4, 30))\n", "filenames = []\n", "for k in k_values:\n", " filename = f'tmp/plot_k_{k:.4f}.png'\n", " plot_for_k(k, filename,b, theta)\n", " filenames.append(filename)\n", "\n", "# Create a GIF from the saved images\n", "with imageio.get_writer('parameterized_theta=0.gif', mode='I', duration=0.5) as writer:\n", " for filename in filenames:\n", " image = imageio.imread(filename)\n", " writer.append_data(image)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "quantnn2024", "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": "3.8.0" } }, "nbformat": 4, "nbformat_minor": 2 }