From 0fb60f7113d64e8c7c31e30d7f9c4f3e3cc8fe34 Mon Sep 17 00:00:00 2001 From: Arthur Faria Date: Sat, 17 Jun 2023 07:38:33 +0200 Subject: [PATCH] upds --- FT_langevin.ipynb | 71 +++++++++++++++-------------------------------- README.md | 2 +- 2 files changed, 24 insertions(+), 49 deletions(-) diff --git a/FT_langevin.ipynb b/FT_langevin.ipynb index 278f32b..007d4ba 100644 --- a/FT_langevin.ipynb +++ b/FT_langevin.ipynb @@ -1,10 +1,11 @@ { "cells": [ { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "# Work Fluctuation Theorem for a gaussian Langevin eq." + "## Crooks fluctuation theorem for work considering a Gaussian Langevin dynamics" ] }, { @@ -20,6 +21,7 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -33,7 +35,6 @@ "outputs": [], "source": [ "# Gaussian estimator\n", - "\n", "def gaussian_func(x, M, V):\n", " denominator = np.sqrt(2*np.pi*V)\n", " numerator = np.exp(-((x-M)**2)/(2*V))\n", @@ -47,7 +48,6 @@ "outputs": [], "source": [ "#Harmonic force and internal energy\n", - "\n", "def energy_force(x, t, *args):\n", " v0 = args[0]\n", " ks = args[1]\n", @@ -58,7 +58,6 @@ "\n", "\n", "# Return the time length\n", - "\n", "def time_len(tMax, dt):\n", "\n", " t = 0\n", @@ -72,6 +71,7 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -137,7 +137,6 @@ " \n", " \n", " # work per trajectory calculation\n", - " \n", " F, _ = energy_force(x, t, v0, ks)\n", " dw = v0*F\n", " \n", @@ -158,6 +157,7 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -173,7 +173,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "1796.0150220394135\n" + "359.031445980072\n" ] } ], @@ -181,7 +181,6 @@ "###################### MAIN #############################\n", "\n", "# Parameters and time\n", - "\n", "v0 = 0.2\n", "ks = 2.0\n", "gamma = 5.0 \n", @@ -189,33 +188,24 @@ "dt = 0.01\n", "tMax = 100 \n", "\n", - "\n", "# Sample conditions\n", - "\n", "N = 10**4 #int(argv[1])\n", "x_init = 0.3\n", "v_init = 0.\n", "\n", - "\n", "# Work vector definition and extras\n", - "\n", "w = np.zeros(N)\n", - "\n", "start = tm.time()\n", "\n", "########### Work ###########\n", - "\n", - "# Stochastic evolution and work for each trajectory in a sample\n", - "\n", + "# Stochastic time-evolution for each trajectory in a sample\n", "for ii in range(N): \n", "\n", " time, dwork, dU = BAOAB_method(x_init, v_init, v0, tMax, dt, gamma, kBT, ks)\n", - "\n", + " # Computing work\n", " w[ii] = (1/kBT)*np.trapz(dwork, time)\n", " \n", - "\n", - "# Statistics\n", - "\n", + "# Work statistics\n", "mean_w = np.mean(w)\n", "var_w = np.var(w)\n", "\n", @@ -226,6 +216,7 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -262,6 +253,7 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -276,22 +268,10 @@ "execution_count": 7, "metadata": {}, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/tmp/ipykernel_19048/246970912.py:26: RuntimeWarning: divide by zero encountered in true_divide\n", - " n_d = n/reverse_n\n", - "/tmp/ipykernel_19048/246970912.py:26: RuntimeWarning: invalid value encountered in true_divide\n", - " n_d = n/reverse_n\n", - "/tmp/ipykernel_19048/246970912.py:27: RuntimeWarning: divide by zero encountered in log\n", - " div = np.log(n_d)\n" - ] - }, { "data": { "text/plain": [ - "
" + "
" ] }, "execution_count": 7, @@ -300,32 +280,28 @@ }, { "data": { - "image/png": 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\n", 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\n", 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", "text/plain": [ - "
" + "
" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -333,6 +309,9 @@ } ], "source": [ + "import warnings\n", + "warnings.filterwarnings('ignore')\n", + "\n", "n_bins = 100 \n", "\n", "########## Work Histogram and Analitical curve ##########\n", @@ -346,7 +325,6 @@ "\n", "\n", "# Settings\n", - "\n", "plt.xlabel(r'$W_{\\tau}$', fontsize = 12, labelpad = 4)\n", "plt.ylabel(r'$\\rho\\,(W_{\\tau})$', fontsize = 12, labelpad = 2)\n", "plt.legend(loc='upper right')\n", @@ -356,17 +334,14 @@ "########### W Division Histogram ###########\n", "\n", "#reversing the freq vector\n", - "\n", "reverse_n = n[::-1]\n", "n_d = n/reverse_n\n", "div = np.log(n_d)\n", "\n", - "\n", "plt.plot(bins[:-1], div, 'o', color = \"darkblue\", label = 'num')\n", "plt.plot(bins[:-1],bins[:-1], color = \"red\", linestyle = '--', linewidth = 2.0, label = 'an')\n", "\n", "# Settings\n", - "\n", "plt.xlabel(r'$W_{\\tau}$', fontsize = 12, labelpad = 4)\n", "plt.ylabel(r'$\\rho\\,(W_{\\tau})\\, /\\, \\rho\\,(-W_{\\tau})$', fontsize = 12, labelpad = 4)\n", "plt.xlim(-7.5,7.5)\n", @@ -392,7 +367,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.10" + "version": "3.9.16" } }, "nbformat": 4, diff --git a/README.md b/README.md index 9cf74d1..b82785d 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,6 @@ # Langevin dynamics: -This is a repository that sheds light on numerical results on fluctuation theorems for Gaussian Langevin dynamics. Codes are in `Python` +This repository offers numerical findings pertaining to fluctuation theorems concerning Gaussian Langevin dynamics. The code has been implemented using the `Python` programming language. ## Repository content