diff --git a/schwarzschild-geodesics_bc.ipynb b/schwarzschild-geodesics_bc.ipynb new file mode 100644 index 0000000..e3d95d2 --- /dev/null +++ b/schwarzschild-geodesics_bc.ipynb @@ -0,0 +1,259 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem set 2: Schwarzschild geodesics" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.integrate import ode" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Hint:** This is how you define a function:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def square(x, a):\n", + " return a * x**2" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def V_eff(r, L, kappa):\n", + " return 1/2*(1 - 2/r)*(kappa + L**2/r**2)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "def V_eff_deriv(r, L, kappa=1):\n", + " return (r**2 - r*L**2 + 3*L**2)/(r**4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the expression we obtained at 2.1 (a), we find that $r = \\frac{1}{2}L(L\\pm\\sqrt{L^2-12})$" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + " def r_orbit (L, sign):\n", + " return 0.5*L*(L+sign*math.sqrt(L**2-12))\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Hint:** This is how you can plot a function:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Generate 100 numbers between 0 and 10 for the x-axis of the plot\n", + "r_space = np.linspace(start=2, stop=10, num=300)\n", + "# Make a list of a few values of `a` to plot\n", + "L_list = np.linspace(start=1, stop=5, num=10)\n", + "\n", + "for L in L_list:\n", + " plt.plot(r_space, V_eff(r_space, L, kappa=1))\n", + "\n", + "# Limit the axes to these ranges\n", + "#plt.ylim(0, 310)\n", + "#plt.xlim(-10, 10)\n", + "# Add axis labels\n", + "plt.xlabel(r'Coordinate $r$')\n", + "plt.ylabel(r'V_eff ');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Hint**: This is how you can integrate a coupled system of ODEs $\\dot{\\vec{x}}(\\tau,\\vec{x})$, where $\\vec{x}$ is a collection of variables like $\\vec{x}=(r,s,\\ldots)$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def r_dot(tau, x, a):\n", + " r = x[0] # `r` is the first variable in `x`\n", + " s = x[1] # `s` is the second variable in `s`\n", + " return r * s + a\n", + "\n", + "def s_dot(tau, x, a):\n", + " r, s = x # This is a faster way to unpack the variables in `x`\n", + " return r + a * s\n", + "\n", + "def integrate_something(r0, s0, a, step):\n", + " # Set up lists to store the values of the integration variable `tau`\n", + " # and the integrated values `x(tau)=[r(tau), s(tau)]`.\n", + " # Initially, they contain only the initial values `tau_0` and `[r_0, s_0]`.\n", + " tau_history = [ 0. ]\n", + " x_history = [ [r0, s0] ]\n", + " # Set up the integration. The `lambda` function returns `x_dot` as a list `[r_dot, s_dot, ...]`.\n", + " x = ode(lambda tau, x: [\n", + " r_dot(tau, x, a),\n", + " s_dot(tau, x, a),\n", + " ]).set_integrator('zvode', method='bdf').set_initial_value(x_history[0], tau_history[0])\n", + " # Integrate while these conditions are met. We stop when `r` exceeds `3 * r0`\n", + " # or when `s` exceeds `10`.\n", + " while x.successful() and x_history[-1][0] < 3 * r0 and x_history[-1][1] < 10:\n", + " x_history.append(x.integrate(x.t + step))\n", + " tau_history.append(x.t)\n", + " # Return the history as Numpy arrays, instead of simple lists, so that we can do slicing\n", + " return np.asarray(tau_history), np.asarray(x_history)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# Perform the integration\n", + "r0 = 1\n", + "s0 = 0\n", + "tau, x = integrate_something(r0=r0, s0=s0, a=3, step=0.02)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Hint**: If the it takes too long, you can stop a running simulation by selecting `Kernel > Interrupt Kernel` in the menu bar above, or typing `Esc, I, I`. Adjust the integration step to make sure the simulation finishes in a reasonable time." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\Bogdan\\Anaconda3\\lib\\site-packages\\numpy\\core\\numeric.py:501: ComplexWarning: Casting complex values to real discards the imaginary part\n", + " return array(a, dtype, copy=False, order=order)\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the results. You can retrieve the history of a particular\n", + "# variable by \"slicing\" the array `x`. For example, `x[:,0]`\n", + "# selects all rows of the array, but only the first value of each\n", + "# row. This corresponds to all values of the variable `r`.\n", + "# We make a polar plot here by treating `s` as an angle (in radians) and\n", + "# `r` as the radius corresponding to that angle.\n", + "plt.figure(figsize=(8, 8))\n", + "plt.polar(x[:,1], x[:,0], marker='.', ls='dotted');" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "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": "3.7.0" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}