{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "6391b058-8273-4208-a2f4-c467ffa0b5fa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 74998.22213794 366.04271268 -364.26485061]\n", " [ 74983.98070068 1104.02743475 -1088.00813543]\n", " [ 74969.72843243 1521.68159847 -1491.4100309 ]\n", " ...\n", " [ 51430.15568009 51430.15568009 -27860.31136019]\n", " [ 51436.305844 51436.305844 -27872.61168801]\n", " [ 51442.45232458 51442.45232458 -27884.90464915]]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_64970/1840589270.py:24: ComplexWarning: Casting complex values to real discards the imaginary part\n", " roots[i] = np.roots([alpha, beta, gamma, delta])\n" ] } ], "source": [ "import numpy as np\n", "\n", "import matplotlib.pyplot as plt\n", "from scipy.optimize import root_scalar\n", "\n", "# Parameters\n", "alpha = 4e-7\n", "beta = -0.03\n", "gamma = 0\n", "N_0 = 40000\n", "\n", "# Define s_dot function\n", "def s_dot(s, delta):\n", " return alpha * s**2 + beta * s + gamma + delta / s\n", "\n", "# Delta values to evaluate\n", "delta_values = np.linspace(0.1, 800, 1000) * N_0\n", "roots_positive = []\n", "roots_negative = []\n", "\n", "# Find roots for each delta\n", "roots = np.zeros([1000,3])\n", "for i, delta in enumerate(delta_values):\n", " roots[i] = np.roots([alpha, beta, gamma, delta])\n", "\n", "print(roots)" ] }, { "cell_type": "code", "execution_count": 2, "id": "0c80e43c-d9f6-419c-8eac-803b425a5ab9", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "<>:11: SyntaxWarning: invalid escape sequence '\\g'\n", "<>:12: SyntaxWarning: invalid escape sequence '\\s'\n", "<>:20: SyntaxWarning: invalid escape sequence '\\d'\n", "<>:21: SyntaxWarning: invalid escape sequence '\\s'\n", "<>:11: SyntaxWarning: invalid escape sequence '\\g'\n", "<>:12: SyntaxWarning: invalid escape sequence '\\s'\n", "<>:20: SyntaxWarning: invalid escape sequence '\\d'\n", "<>:21: SyntaxWarning: invalid escape sequence '\\s'\n", "/tmp/ipykernel_64970/2098390987.py:11: SyntaxWarning: invalid escape sequence '\\g'\n", " ax1.set_xlabel('$\\gamma$')\n", "/tmp/ipykernel_64970/2098390987.py:12: SyntaxWarning: invalid escape sequence '\\s'\n", " ax1.set_ylabel('$s^\\star$')\n", "/tmp/ipykernel_64970/2098390987.py:20: SyntaxWarning: invalid escape sequence '\\d'\n", " ax2.set_xlabel('$\\delta / N_0$')\n", "/tmp/ipykernel_64970/2098390987.py:21: SyntaxWarning: invalid escape sequence '\\s'\n", " ax2.set_ylabel('$s^\\star$')\n", "/tmp/ipykernel_64970/2098390987.py:6: RuntimeWarning: invalid value encountered in sqrt\n", " s_1 = -beta / (2 * alpha) * (1 + np.sqrt(1 - 4 * gamma_values * alpha / beta**2))\n", "/tmp/ipykernel_64970/2098390987.py:7: RuntimeWarning: invalid value encountered in sqrt\n", " s_2 = -beta / (2 * alpha) * (1 - np.sqrt(1 - 4 * gamma_values * alpha / beta**2))\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot results\n", "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 6))\n", "\n", "# Gamma values and roots\n", "gamma_values = np.linspace(0, 800, 10000)\n", "s_1 = -beta / (2 * alpha) * (1 + np.sqrt(1 - 4 * gamma_values * alpha / beta**2))\n", "s_2 = -beta / (2 * alpha) * (1 - np.sqrt(1 - 4 * gamma_values * alpha / beta**2))\n", "ax1.plot(gamma_values, s_1, 'r', label='Unstable Mode')\n", "ax1.plot(gamma_values, s_2, 'b', label='Stable Mode')\n", "ax1.set_title('(A)')\n", "ax1.set_xlabel('$\\gamma$')\n", "ax1.set_ylabel('$s^\\star$')\n", "ax1.legend()\n", "ax1.grid('on')\n", "\n", "# Delta vs Roots\n", "ax2.plot(delta_values / N_0, roots[:,0], 'r', label='Unstable Mode')\n", "ax2.plot(delta_values / N_0, roots[:,1], 'b', label='Stable mode')\n", "ax2.set_title('(B)')\n", "ax2.set_xlabel('$\\delta / N_0$')\n", "ax2.set_ylabel('$s^\\star$')\n", "ax2.legend()\n", "ax2.grid('on')\n", "plt.tight_layout()\n", "plt.show()\n", "fig.savefig('figure4.png')" ] }, { "cell_type": "code", "execution_count": 3, "id": "4e8800fc-0016-4fea-891f-eaa789e7e751", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.622701743303522e-07 0.024743415176937383\n" ] } ], "source": [ "N_total = 68301\n", "N_average = N_total/65*10 #Fudged. the paper is missing factor of 10\n", "#Define parametrs\n", "alpha = 40/N_average**2\n", "beta = 260/N_average\n", "print(alpha, beta)\n", "gamma = 0\n", "delta = 0\n", "N_0 = 40000\n", "\n", "# Define s_dot function\n", "def s_dot(t, s, beta, gamma, delta):\n", " return alpha * s**2 + beta * s + gamma + delta / s\n", "\n", "def reach_sk(t, s):\n", " s_k = 1/alpha\n", " return s_k-s[0]\n", "\n", "reach_sk.terminal = True" ] }, { "cell_type": "code", "execution_count": 4, "id": "87f6e940-844a-4511-ae68-124ab128d501", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "<>:47: SyntaxWarning: invalid escape sequence '\\g'\n", "<>:74: SyntaxWarning: invalid escape sequence '\\d'\n", "<>:47: SyntaxWarning: invalid escape sequence '\\g'\n", "<>:74: SyntaxWarning: invalid escape sequence '\\d'\n", "/tmp/ipykernel_64970/3632696374.py:47: SyntaxWarning: invalid escape sequence '\\g'\n", " ax1.plot(np.array(beta_vals) * N_0, t_values, label=f'$\\gamma$ = {name}')\n", "/tmp/ipykernel_64970/3632696374.py:74: SyntaxWarning: invalid escape sequence '\\d'\n", " ax2.plot(np.array(beta_vals) * N_0, t_values, label=f'$\\delta / N_0$ = {name}')\n", "Processing gamma values: 0%| | 0/4 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.integrate import solve_ivp\n", "from concurrent.futures import ThreadPoolExecutor, as_completed\n", "from tqdm import tqdm\n", "import matplotlib.pyplot as plt\n", "\n", "# Assuming these variables and functions are defined elsewhere in your code\n", "# N_0, s_dot, reach_sk\n", "\n", "t_span = (0, 400)\n", "\n", "beta_values = np.linspace(-1500, 0, 2000) / N_0 # Adjust the range and number as needed\n", "delta_values = np.asarray([0, 100, 500, 1000])*N_0\n", "gamma_values = [0, 100, 500, 1000]\n", "\n", "# Function to solve ODE for a single (beta, gamma, delta) combination\n", "def solve_single_case(beta, gamma, delta):\n", " sol = solve_ivp(\n", " fun=lambda t, s: s_dot(t, s, beta, gamma, delta),\n", " t_span=t_span,\n", " y0=[N_0],\n", " method='RK45',\n", " events=reach_sk\n", " )\n", " return sol.t[-1] # Replace with `sol[-1, 0]` if needed\n", "\n", "# Multithreading with progress tracking for the first graph\n", "max_ts_gamma = {}\n", "for gamma in tqdm(gamma_values, desc=\"Processing gamma values\"):\n", " with ThreadPoolExecutor() as executor:\n", " futures = {executor.submit(solve_single_case, beta, gamma, 0): beta for beta in beta_values}\n", " t_betas = []\n", " for future in tqdm(as_completed(futures), total=len(futures), desc=f\"Gamma = {gamma}\", leave=False):\n", " beta = futures[future] # Retrieve the associated beta value\n", " t_value = future.result()\n", " t_betas.append((beta, t_value)) # Store as tuple\n", " # Filter and sort by beta\n", " t_betas = [(beta, t_value) for beta, t_value in t_betas if t_value <= 399.9]\n", " t_betas.sort(key=lambda x: x[0])\n", " max_ts_gamma[f'{gamma}'] = t_betas\n", "\n", "# Plotting the first graph\n", "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6))\n", "for name in max_ts_gamma:\n", " if max_ts_gamma[name]: # Skip empty data\n", " beta_vals, t_values = zip(*max_ts_gamma[name]) # Unpack filtered and sorted tuples\n", " ax1.plot(np.array(beta_vals) * N_0, t_values, label=f'$\\gamma$ = {name}')\n", "\n", "ax1.set_xlabel(r\"$\\beta N_0$\")\n", "ax1.set_ylabel(\"$t_k$ (yrs)\")\n", "ax1.set_title(\"(a)\")\n", "ax1.legend()\n", "\n", "# Multithreading with progress tracking for the second graph\n", "max_ts_delta = {}\n", "gamma = 0\n", "for delta in tqdm(delta_values, desc=\"Processing delta values\"):\n", " with ThreadPoolExecutor() as executor:\n", " futures = {executor.submit(solve_single_case, beta, gamma, delta): beta for beta in beta_values}\n", " t_betas = []\n", " for future in tqdm(as_completed(futures), total=len(futures), desc=f\"Delta = {delta/N_0}\", leave=False):\n", " beta = futures[future] # Retrieve the associated beta value\n", " t_value = future.result()\n", " t_betas.append((beta, t_value)) # Store as tuple\n", " # Filter and sort by beta\n", " t_betas = [(beta, t_value) for beta, t_value in t_betas if t_value <= 399.9]\n", " t_betas.sort(key=lambda x: x[0])\n", " max_ts_delta[f'{delta/N_0}'] = t_betas\n", "\n", "# Plotting the second graph\n", "for name in max_ts_delta:\n", " if max_ts_delta[name]: # Skip empty data\n", " beta_vals, t_values = zip(*max_ts_delta[name]) # Unpack filtered and sorted tuples\n", " ax2.plot(np.array(beta_vals) * N_0, t_values, label=f'$\\delta / N_0$ = {name}')\n", "\n", "ax2.set_xlabel(r\"$\\beta N_0$\")\n", "ax2.set_ylabel(\"$t_k$ (yrs)\")\n", "ax2.set_title(\"(b)\")\n", "ax2.legend()\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "id": "09b68327-d3a3-434a-8996-f30d83cff3a6", "metadata": {}, "outputs": [], "source": [ "fig.savefig('figure5.png')" ] } ], "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }