{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## An `A <-> B` reaction \n", "with 1st-order kinetics in both directions, taken to equilibrium,\n", "using a simple, coarse fixed-timestep simulation. \n", "\n", "Afterwards, perform some analysis of the results\n", "\n", "See also the experiment _\"1D/reactions/reaction_1\"_ for a multi-compartment version. \n", "\n", "This experiment gets continued in _\"react_2_b\"_ , with a more sophisticated approach, \n", "involving adaptive variable time steps.\n", "\n", "LAST REVISED: June 14, 2024 (using v. 1.0 beta33)" ] }, { "cell_type": "code", "execution_count": 1, "id": "1f552123-2456-42fa-9fea-42582e096c0f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "import set_path # Importing this module will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 2, "id": "b0ce3cdd", "metadata": { "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.reactions.uniform_compartment import UniformCompartment\n", "from src.modules.visualization.plotly_helper import PlotlyHelper\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "83c3cc5f-de21-4f66-9988-2806fbf0666d", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'react_2_a.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging (for the graphics)\n", "log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "code", "execution_count": null, "id": "eed9fe97-872a-44de-93ba-c499a6f1191b", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "# Initialize the System" ] }, { "cell_type": "code", "execution_count": 4, "id": "72b4245c-de4e-480d-a501-3495b7ed8bc4", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1\n" ] } ], "source": [ "# Instantiate the simulator and specify the chemicals\n", "dynamics = UniformCompartment(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B , with 1st-order kinetics in both directions\n", "dynamics.add_reaction(reactants=[\"A\"], products=[\"B\"], \n", " forward_rate=3., reverse_rate=2.)\n", "\n", "print(\"Number of reactions: \", dynamics.number_of_reactions())" ] }, { "cell_type": "code", "execution_count": 5, "id": "00ea560d-9a49-4041-b119-6de11bfcc7af", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 3 / kR = 2 / delta_G = -1,005.1 / K = 1.5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 6, "id": "cb582868-431c-4022-aa0e-a2f554f80d6c", "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `react_2_a.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions to the HTML log file\n", "dynamics.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "code", "execution_count": 7, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [], "source": [ "# Initial concentrations of all the chemicals, in index order\n", "dynamics.set_conc([10., 50.])" ] }, { "cell_type": "code", "execution_count": 8, "id": "a605dacf-2c67-403e-9aa9-5be25fc9f481", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 10.0\n", " Species 1 (B). Conc: 50.0\n", "Set of chemicals involved in reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 9, "id": "0ff2c242-a15b-456d-ad56-0ba1041c0b4c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.010.050.0Initialized state
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.0 50.0 Initialized state" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "ab7147fe-712c-4c92-b61f-20ff51675ab8", "metadata": {}, "source": [ "### Test your intuition: \n", "#### given that this reaction operates mostly in the forward direction (kF = 3 , kR = 2 , K = 1.5), \n", "#### do you think that A will be consumed and B will be produced??\n", "We can take a sneak preview at the final equilibrium concentrations without actually running the simulation:" ] }, { "cell_type": "code", "execution_count": 10, "id": "12cac04d-dd61-4646-9339-8b70e22139e8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'A': 24.0, 'B': 36.0}" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.find_equilibrium_conc(rxn_index=0) # This is an EXACT solution" ] }, { "cell_type": "markdown", "id": "ee5b9d1c-3ebe-497a-a0e9-bfb02dcd0693", "metadata": {}, "source": [ "#### The reaction will actually proceed IN REVERSE, because of the large initial concentration of B (which we had set to 50), relative to the small initial concentration of A (10)\n", "Now, let's see the reaction in action!" ] }, { "cell_type": "code", "execution_count": null, "id": "d748df77-1b71-4d16-9e24-212d74a93ff4", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "fc516ca2-e62d-4784-b826-5372ff7f4c75", "metadata": { "tags": [] }, "source": [ "### Run the reaction" ] }, { "cell_type": "code", "execution_count": 11, "id": "50c7e478-ad0e-4aeb-9cea-dfed47cded21", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 total step(s) taken\n" ] } ], "source": [ "# First step of reaction\n", "dynamics.single_compartment_react(initial_step=0.1, n_steps=1, variable_steps=False, \n", " snapshots={\"initial_caption\": \"first reaction step\"})" ] }, { "cell_type": "code", "execution_count": 12, "id": "c9115720-e66e-44f3-bb0a-fabec5b96673", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SYSTEM TIMEABcaption
00.010.050.0Initialized state
10.117.043.0first reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.0 50.0 Initialized state\n", "1 0.1 17.0 43.0 first reaction step" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "98ec8a03-7a9b-403a-8dcd-d9e19c49d656", "metadata": {}, "source": [ "We can already see the reaction proceeding in reverse..." ] }, { "cell_type": "code", "execution_count": 13, "id": "2502cd11-0df9-4303-8895-98401a1df7b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10 total step(s) taken\n" ] } ], "source": [ "# Numerous more fixed steps\n", "dynamics.single_compartment_react(initial_step=0.1, n_steps=10, variable_steps=False, \n", " snapshots={\"initial_caption\": \"2nd reaction step\",\n", " \"final_caption\": \"last reaction step\"})" ] }, { "cell_type": "code", "execution_count": 14, "id": "80fbaee3-bd6f-4197-9270-23374d46a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.010.00000050.000000Initialized state
10.117.00000043.000000first reaction step
20.220.50000039.5000002nd reaction step
30.322.25000037.750000
40.423.12500036.875000
50.523.56250036.437500
60.623.78125036.218750
70.723.89062536.109375
80.823.94531236.054688
90.923.97265636.027344
101.023.98632836.013672
111.123.99316436.006836last reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.000000 50.000000 Initialized state\n", "1 0.1 17.000000 43.000000 first reaction step\n", "2 0.2 20.500000 39.500000 2nd reaction step\n", "3 0.3 22.250000 37.750000 \n", "4 0.4 23.125000 36.875000 \n", "5 0.5 23.562500 36.437500 \n", "6 0.6 23.781250 36.218750 \n", "7 0.7 23.890625 36.109375 \n", "8 0.8 23.945312 36.054688 \n", "9 0.9 23.972656 36.027344 \n", "10 1.0 23.986328 36.013672 \n", "11 1.1 23.993164 36.006836 last reaction step" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "c7650ed4-365e-43c2-b001-280297c68ece", "metadata": {}, "source": [ "## NOTE: for demonstration purposes, we're using FIXED time steps... \n", "## Typically, one would use the option for adaptive variable time steps (see experiment `react_2_b`)" ] }, { "cell_type": "markdown", "id": "c034956a-683c-4c3d-8134-ecac9e19a45c", "metadata": {}, "source": [ "### Check the final equilibrium" ] }, { "cell_type": "code", "execution_count": 15, "id": "b139f5e4-625f-4a5e-8f57-8f00244dced4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([23.99316406, 36.00683594])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_system_conc() # The current concentrations, in the order the chemicals were added " ] }, { "cell_type": "markdown", "id": "d25eedf3-89f8-4f8c-a49a-d2689103528b", "metadata": {}, "source": [ "NOTE: Consistent with the 3/2 ratio of forward/reverse rates (and the 1st order of the reactions), the systems settles in the following equilibrium:\n", "\n", "[A] = 23.99316406\n", " \n", "[B] = 36.00683594\n" ] }, { "cell_type": "code", "execution_count": 16, "id": "765f6f39-4b2e-4a86-b6a9-ace9d1941663", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [A] = 23.99 ; [B] = 36.01\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.50071\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 1.5\n", "Discrepancy between the two values: 0.04749 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "905adfdd-6d70-4dfc-bb34-c547c4d604b9", "metadata": {}, "source": [ "### As noted earlier, because of the high initial concentration of B relative to A, the overall reaction has proceeded IN REVERSE" ] }, { "cell_type": "markdown", "id": "6ac3dd4e-9dd0-4d3a-aa83-76102bd79524", "metadata": { "tags": [] }, "source": [ "## Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 17, "id": "86976e6f-f453-41c3-9553-b27b1328db6b", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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Changes in concentrations with time" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 1.0999999999999999 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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BCEAAAhCAAAQgAAEnCCCrTqSRRkAAAhCAAAQgAAEIQAACEHCLALLqVj5pDQQgAAEIQAACEIAABCAAAScIIKtOpJFGQAACEIAABCAAAQhAAAIQcIsAsupWPmkNBCAAAQhAAAIQgAAEIAABJwggq06kkUZAAAIQgAAEIAABCEAAAhBwiwCy6lY+aQ0EIAABCEAAAhCAAAQgAAEnCCCrTqSRRkAAAhCAAAQgAAEIQAACEHCLALLqVj5pDQQgAAEIQAACEIAABCAAAScIIKtOpJFGQAACEIAABCAAAQhAAAIQcIsAsupWPmkNBCAAAQhAAAIQgAAEIAABJwggq06kkUZAAAIQgAAEIAABCEAAAhBwiwCy6lY+aQ0EIAABCEAAAhCAAAQgAAEnCCCrTqSRRkAAAhCAAAQgAAEIQAACEHCLALLqVj5pDQQgAAEIQAACEIAABCAAAScIIKtOpJFGQAACEIAABCAAAQhAAAIQcIsAsupWPmkNBCAAAQhAAAIQgAAEIAABJwggq06kkUZAAAIQgAAEIAABCEAAAhBwiwCy6lY+aQ0EIAABCEAAAhCAAAQgAAEnCCCrTqSRRkAAAhCAAAQgAAEIQAACEHCLALLqVj5pDQQgAAEIQAACEIAABCAAAScIIKtOpJFGQAACEIAABCAAAQhAAAIQcIsAsupWPmkNBCAAAQhAAAIQgAAEIAABJwggq06kkUZAAAIQgAAEIAABCEAAAhBwiwCy6lY+aQ0EIAABCEAAAhCAAAQgAAEnCCCrTqSRRkAAAhCAAAQgAAEIQAACEHCLALLqVj5pDQQgAAEIQAACEIAABCAAAScIIKtOpJFGQAACEIAABCAAAQhAAAIQcIsAsupWPmkNBCAAAQhAAAIQgAAEIAABJwggq06kkUZAAAIQgAAEIAABCEAAAhBwiwCy6lY+aQ0EIAABCEAAAhCAAAQgAAEnCCCrTqSRRkAAAhCAAAQgAAEIQAACEHCLALLqVj5pDQQgAAEIQAACEIAABCAAAScIIKtOpJFGQAACEIAABCAAAQhAAAIQcIsAsupWPmkNBCAAAQhAAAIQgAAEIAABJwggq06kkUZAAAIQgAAEIAABCEAAAhBwiwCy6lY+aQ0EIAABCEAAAhCAAAQgAAEnCCCrTqSRRkAAAhCAAAQgAAEIQAACEHCLALLqVj5pDQQgAAEIQAACEIAABCAAAScIIKsG0vjb948ZKIUiXCbwoXVj6p39k2puft7lZtK2ggSWjbbVyHBbHTg8VbAkLnedwEmrR9WBI9NqembO9abSvgIExkbaSt5X9h3iPaUARi8uXb9qVB0+Nq0mp3lPiSb8tPXjXuTf5kYiqwayg6wagOh4Eciq4wk21Dxk1RBID4pBVj1IsoEmIqsGIHpSBLKanGhktf4XALJqIAfIqgGIjheBrDqeYEPNQ1YNgfSgGGTVgyQbaCKyagCiJ0Ugq8iqrV0dWTWQGWTVAETHi0BWHU+woeYhq4ZAelAMsupBkg00EVk1ANGTIpBVZNXWru69rD7+1Atq290PnZCf3c/t7D125bXb1KuvvRn8+5yzTldP7Ny+6Hxk1dbubU9cyKo9ubA5EmTV5uzYFRuyalc+bI0GWbU1M/bFhawiq/b1ym5EyKqW1XsfeFQ9//iOxBxdd8s96v19B3uCKuK6ft0q9fB9t/bOR1Zt7d72xIWs2pMLmyNBVm3Ojl2xIat25cPWaJBVWzNjX1zIKrJqX69EVgMCMrK6lKxu2rJVfemmz6stmy/tez6yamv3ticuZNWeXNgcCbJqc3bsig1ZtSsftkaDrNqaGfviQlaRVft6JbLak8/4NOBwCvCuPXvVNTffqR65/w51wcazg/OTHkNWbe3e9sSFrNqTC5sjQVZtzo5dsSGrduXD1miQVVszY19cyKodspo0g9O+3pIcUZIjmYjd+2nAcYjRab+pZPXFP1OTY+eo6TOvU/PDa0zkhDIcJLBivKOOTMyqee6z6mB2zTVpuNNS7daQmpiaNVcoJTlJYNlYJ+gnc3Pcu9nJBBtqVKfdUsOdIXVskvcUQ0idLWZ8tKOmZmbV7CzvKdEkr1w2bDTn4hnff2nPojLXrVnZW45Yh6yG+/dsv+2G3kzSPI1GVvNQy3FNCFpGV1PJ6n8a6tbSHlPTp1+tps/6MzW77pIcNXOJywSQVZeza65tyKo5lq6XhKy6nmEz7UNWzXD0oRRkNTnLJmX1/E9fq6JiGtYoAnvKhrXqK1++UdUhq6b6N7JqiuSAcsJvF8KpwElrVmXacG+34Nf+ozr237+pRt99SrVmPghKn9zwt9XEhs1q8qS/o2aWdacPc/hNgGnAfuc/beuZBpyWFOcxDZg+kIYA04DTUOIcIcA04OR+cNr6cSMdRIT0lb1v9N3QNawklFX5dzgC209woyO00SWL4i6XXnyBeuHFXWrfgUNB0Td94Qr14dNPXnQHlPCaJMmMjwDL9Vuvv0oljQwvtXzSBDzvpwFLQqM7Ace/0Ui7G/DI/v+mRt/7thrT0jp86CdBbmaWn6smtLBObtA/6y8zkS/KaCgBZLWhias4bGS1YuANrg5ZbXDyKgwdWa0QdsOrQlbLlVUZVb3iTz4VjJ4udYS3ywzlUM4VV/no2Wf07kQSd5MdX/uGeuDrT/YG0uR8kdRQRsPn49ONpWy5HWdcVuNiLc9/9d/9ZVC/PPfFP/u7vb18JN5+5Zh6SXgvq9F7qArUSy7cuOi2NPJYlvustid/F4yyjmlxHX3322pobkLNt0YCYZ04SY+26t+zY6eZyh/lNIQAstqQRNUcJrJacwIaVD2y2qBk1Rgqsloj/IZVjayWJ6uhDKZZE5o0Dfj2ux5UP3/59USxDKMWQb36c58JRj/DkdVQjJNGTqVMGXmVAbvo81KebC6bJlY5V0T4sW8+e0I54ca0Jl4G3suqCYj9dgMe3fdcIKwirp3Dvwiqml5xgZ4evDkYcZ1a+ykT1VNGAwggqw1IkgUhIqsWJKEhISCrDUlUzWEiqzUnoEHVI6vNkNVwuWJStOFobD9ZjQpoP8n81eu/DaYK95Y7JlQUjtxGn+q314+JlwCyaoDioFvXtI+9FkwPlp/R974T1DjfWaXXtcpoq0wT3qzmRtYZiIQibCWArNqaGbviQlbtyofN0SCrNmfHntiQVXtyYXskyGp5siolZ5kGvH7dqkWzPKMjq/G9dZKiLlNWpR3RWajRKchssGTxq3yQrPZC17ct6U4P7k4Tbh97PXhqavUne9OEp1dfaHFLCS0vAWQ1Lzm/rkNW/cp3kdYiq0Xo+XMtsupProu2FFktV1YHbbAkQtpvN+CkacBLTdMtIqtCod804CRRRlaLvvIquj61rEbi6Rze01vXOrrvvwbPzI2c1FvXKiOu8+3lFbWAasomgKyWTdiN8pFVN/JYRSuQ1SooN78OZLX5OayqBchqubIqpSfduiYUwHDzpUFrVqWccEfe6FRdEdpLLjwvuE9qEVmVtaYSw74DB3sb0IYbLMnGSnGRlTbJwTTgql6pOevJI6thVUNzx3rrWmWacGvy7eCpqbWbginCcgucmZXn5YyMy2whgKzakgm740BW7c6PTdEhqzZlw95YkFV7c2NbZMhq+bIaFc1obdFR0jSy2q+c6G035dY18Q2W0qxZDTdGim9AG14rUvzkd77XC1/WyYY7ETMN2LZXdSSeIrIabdbwoR9317XqTZlGDnw/eGp27MPB2tbJk/WmTPq3GmpbTILQ+hFAVukbaQggq2kocY4QQFbpB2kIIKtpKHGOEEBWq5FVelt2AmywlJ3ZCVeYktWw4NbUfr0Rk2zIpNe36t+tmYPBU5MbLg9GWif1iOvMso8YiJwiqiKArFZFutn1IKvNzl+V0SOrVdJubl3IanNzV3XkyCqyWnWfS1sfspqW1BLnmZbVaFUj+/+qtynT8KGfBk/NLPtoIKzBiOuGzxpoAUWUTQBZLZuwG+Ujq27ksYpWIKtVUG5+Hchq83NYVQuQVWS1qr6WtR5kNSuxhPPLlNWwuvbkWwtrW7vThIfmJtV8a7i3i/CkFtfZsdMNtIYiyiCArJZB1b0ykVX3clpWi5DVssi6VS6y6lY+y2wNsoqsltm/ipSNrBaht3BtFbIaDXN037N6evC31dg731adI78Mnppe+fHgfq2yKdPU2r9hoFUUYZIAsmqSprtlIavu5tZ0y5BV00TdLA9ZdTOvZbQKWUVWy+hXJspEVg1QrFpWw5A7R/ceH219778ED8+3VwbC2p0mvFnfDme9gRZSRFECyGpRgn5cj6z6kWcTrURWTVB0vwxk1f0cm2ohsoqsmupLpstBVg0QrUtWe6HPz/XWtY7pEdf2sV8HT02t/uu9acLTqy8y0FKKyEsAWc1Lzq/rkFW/8l2ktchqEXr+XIus+pProi1FVpHVon2orOuRVQNka5fVSBs6h/doce2uax3d9/8Ez8wNb9CjrXoXYb2uVUZd5zsrDLSaIrIQQFaz0PL3XGTV39xnbTmympWYn+cjq37mPU+rkVVkNU+/qeIaZNUAZZtkNWzO0NzR7q1v9I/cu7U19U7w1NTaS7vThPUU4emV5xtoPUWkIYCspqHEOcgqfSAtAWQ1LSm/z0NW/c5/ltYjq8hqlv5S5bnIqgHaNspqtFnDH7wUCKtsyjTywQ+Cp2bHzuje+kaPuMpv1eoYIEER/Qggq/SNNASQ1TSUOEcIIKv0gzQEkNU0lDhHCCCryKqtrwRk1UBmbJfVsImtqX1aWJ8KRlxlbevQzMHgqcn1l/c2ZZpZdo4BIhQRJ4Cs0ifSEEBW01DiHGSVPpCWALKalhTnIat+y+r5n75WnXPW6eqJndutezEgqwZS0hRZjTZ1ZP/3epsyDR/aFTwlotrdRVimCV9ugAxFhASQVfpCGgLIahpKnIOs0gfSEkBW05LiPGTVX1nd8bVvqO8+/0O178BB9W+/8kV1wcazrXpBIKsG0tFEWQ2b3Z787cI9W7vThIfmppQa6iyaIjw7foYBSn4Xgaz6nf+0rUdW05LiPKYB0wfSEEBW01DiHCGArPorq1deu01dvuki9aPdr6hTNqxVX/nyjVa9KJBVA+losqxGmz/63tMLo63fVp2jrwRPySZMshmTbMokmzNx5COArObj5ttVyKpvGc/fXmQ1PzufrkRWfcp2sbYiq9XI6o+PHVMHZmaLJSvH1X+4bFytabdPuHLXnr3qmpvvVI/cf4f61eu/Vfc+8Kh6/vEdOWoo7xJk1QBbV2Q1RNE5+qvuLsJyC5z3vhs8PN9esbCLsNz+ZrOaG9lggJw/RSCr/uS6SEuR1SL0/LoWWfUr33lbi6zmJeffdchqNbL6mVf2qucOH668gz17ztnq0ytPvHVlOAU4XKsqa1dFXG2aCoysGugurslqD8n8bG9dq2zI1D72m+Cp6VUXqYmTu/dtnVr91w0QdL8IZNX9HJtoIbJqgqIfZSCrfuS5aCuR1aIE/bkeWa1GVr/45lvqx0ePVd6xvnrGqeoPx8dPqDecArz1+quC56675R7rpgIjqwa6i7OyGmHTOfzzYKR17B19+5v9zwfPzI2s12tbu9Iq04TnOysN0HSzCGTVzbyabhWyapqou+Uhq+7m1mTLkFWTNN0uC1mtRlZt6kXhFOB4TOvWrLRqKjCyaqDX+CCrIaah2SPBrW9kM6axd76lWtPvBU9NrfkbC7e/2azXuX7cAFW3ikBW3cpnWa1BVssi6165yKp7OS2jRchqGVTdLBNZ9U9W41OAQwIyFXj7bTeoLZvt2KsGWTXwnuOTrEZxtSbfVst/85Ba9uZO1Z54M3hqvjWmpwh/Tm/G9Md6ivDFamblecFjvh/Iqu89IF37kdV0nDhLKWSVXpCGALKahhLnCAFk1T9Z3bRlq7r6c59R4RTgkIBMBZbj4ftuteLFgawaSIOvstpDNz+jR1u/pZa/8ZDemOm/LCaqb4MzveI8NVeuxPAAACAASURBVL3mQjW18uLgt/xbbo/j04Gs+pTt/G1FVvOz8+1KZNW3jOdrL7Kaj5uPVyGr/slqU/o5smogU97LaoRh+9jravzt/6yGP/iBGj74U30LnF+dQFhGWme0sE6tuViPvn5STxv+RDAC6/KBrLqcXXNtQ1bNsXS9JGTV9QybaR+yaoajD6Ugq8iqrf0cWTWQGWS1P0SR1c7hPfrn52r40M9V50j3t96eadFFs2NnBMI6vfw8LbIbg/u7yu/51ok7lxlIWeVFIKuVI29khchqI9NWS9DIai3YG1cpstq4lNUWMLKKrNbW+QZUjKwayAyymg1i5/Av1PCRrsAGEhvI7C9OKGR2/K9paRV51RKrxbX7u5lTiJHVbH3E17ORVV8zn73dyGp2Zj5egaz6mPV8bUZWkdV8Paf8q5BVA4yR1YIQ9f1cA2FdGHXtSqz+d8IU4pnl53ZHYLW0zizXI7DyW4us7QeyanuG7IgPWbUjD02IAlltQpbqjxFZrT8HTYkAWUVWbe2rtciq7D6178ChRCa7n9tpK6u+cSGr5lM2NDcRCOvwod3HpxFriW1P/CZW2VB32vCK7rThUF5nln/UfFAFSkRWC8Dz6FJk1aNkF2wqsloQoCeXI6ueJNpAM5FVZNVANyqliMpl9cprt6n161ZZsx2yCarIqgmKg8sYmjnUHYHVa16Hjy6MvmqZbU/+btHF862RYNQ1mDYcTiPW/55ddtbgSko6A1ktCaxjxSKrjiW0xOYgqyXCdahoZNWhZJbcFGQVWS25i+UuvnJZte1Gs7nJRS5EVk1QzFdGa3q/HnndvbDu9fgmTq2p9xcLbHt5b91ruPZVRmJnx07PV3HGq5DVjMA8PR1Z9TTxOZqNrOaA5uElyKqHSc/ZZGQVWc3ZdUq/DFmNIL79rgfVk9/5nnrk/jvUBRvP7j0jo8GvvvZm8O9zzjpdPbFz+6LEIKul99NMFbSm3ulNHx5e2MRJ1sG2Zg4uKmdueHUw+hqsfV3YfVimEc+NnJypvjQnI6tpKHEOskofSEsAWU1Lyu/zkFW/85+l9cgqspqlv1R5buWyKuJ3+aaL1Nbrr6qynQPrevypF9S/f+RbgZRGZfW6W+5R7+872BPUpGnMyOpAvLWf0D72ht7ASa+B1Zs4BdOIFzZxGpo9ulhgRzYcX/eq18EGuxDr2+nMjawt1AZktRA+by5GVr1JdeGGIquFEXpRALLqRZqNNBJZRVaNdKQSCqlcVkUK733gUfX84ztKaE7+ImV6skjqNTffuUhWZTOoL930ebVl86VB4UnxI6v5udd5ZfvYf188fVgEVgvt0Nz0orBmR0/tjsD2NnDq3kpnvrMydfjIampUXp+IrHqd/kyNR1Yz4fL2ZGTV29Rnbjiy6p+s7tqzN/Ce+LH9tht63pO5I5VwQeWyKlK41FHHbsAyWvqPrvlT9ZEzT1skq2ESoyOtSY8hqyX0zJqK7Bx5+fguxDISuzACGw9ndvz31PTCJk69W+mIwLbGEiNHVmtKaMOqRVYblrAaw0VWa4TfoKqR1QYlq+ZQkVV/ZTXqObIk8oUXd1k1qFi5rNb8WjyheknK2+/tD3YnjotoWlm1rU3EY5DA/LxSH+xe+PnZ8f8/+PKJlaw8R6nV53d/1nz8+P8PtQ0GRFEQgAAEIAABCEAAAhAoRiDJc2QG6ba7H1J1DB72a43Xshqf0ptXVhlZLfZiaeLVnaO/UsMHf6qGP/iB3sxJ/z74Q9Wa/uCEpsyNrFdTqy9Wo6dcrA4Onalmxk4LdiCeHT1FzbdXNLHpxFwiAUZWS4TrWNGMrDqW0JKaw8hqSWAdLJaR1YpGVvf/WKmpA9X3oLV/qNTImkX1Jsmq7NUjhwzi2XLUIquhtUch1DE/OimOMKabvnBFsAlU0prV+DcOyKot3bneOIKNmw79RI0c+pGW2JcCmR2aPdw3KJFVkdZAXsfPVHPy/8Mnq7mxU/SGTqeoGf1YcGudoU69DaP2ygggq5WhbnxFyGrjU1hJA5DVSjA7UQmyWpGsPv0Zpd5+rvo+89lnlTrl04myGg8mdKDqg0yusXJZ3fG1b6gHvv7kok2MQrOvG06/bxjYDdiW7tqwOOZngjWvwwdeUqvnXlaTH7yphibfVp1jr6v2hL4Vkn4+zSGjs4HIjnyoK7b6Z25Uj9Dqx0RqA+HVYsvRfALIavNzWFULkNWqSDe7HmS12fmrMnpktSJZfemLSsnoatXHhV9VSkZXIwfTgPskQUYqr/7cZ064dY1I7GPffLbWBb1JSZNmcJ/Vql9R7tUX32BJdhxuaXFtTb+j2vJb/7Snur/lPrHtiePPDcXuD5tEZ769LLg/bCCwgdjqEVotssH/h1Irj+lR2/nWuHuAHWkRsupIIitoBrJaAWQHqkBWHUhiRU1AViuS1Yrymaaaft4T3iHlgo1npymm9HMqH1kVAElTfm1c0JuWPtOA05Ly97y8uwHLfWBbk1peRWRFYhfEtqX/Hfy/PCbPabkdmjs2EPB8Z5UW2VBitbyKyOqpx4HQjumRW5mGHMjtyVpqhweWxwlmCSCrZnm6XBqy6nJ2zbUNWTXH0vWSkFVkVQiEM2C93mDJ5pHVvG9EyGpecv5cl1dW0xKS0ddAXmWkVkZloyIro7YLz8nj8fvIJtUxN7KuO8U4Krbh/8tvPUIbim3aGDlvMAFkdTAjzugSQFbpCWkIIKtpKHGOEEBW/ZXVeMttElWJrfKRVZvXrOZ9u0JW85Lz57qyZTUtydbUPj0auzDlOJxu3JuO/Lvjo7j6sTRHdFOoUGy762i7I7TBY8HPujTFeX8Osup9F0gNAFlNjcrrE5FVr9OfqfHIqn+ymqmD1Hhy5bIqbbVlN2BT3JFVUyTdLccWWU1LWHYxltFY2QiqpX/kd1uP2sp0Y5Fd2SSqO0o7karIxE2iZKpxe3lvx+O54TVqrrM6KM/XDaOQ1VTdiZM0AWSVbpCGALKahhLnCAFkFVm19ZVQi6zaCiNvXMhqXnL+XNc0WU2bmdbU+wubQ/2uK7Qit8GIrfzuTj9ua7HNe4jkyi1+5vXte4Lb+OhDRmrn22OB6M4Nr+/K7ah+rtXW/16j5heEV2790z2/W0YTDmS1CVmyI0Zk1Y482B4Fsmp7huyJD1lFVu3pjYsjQVYNZAZZNQDR8SJcldW0aQt3O+6O1IrEarGd0rfvmZvtyWxr+oBqzXwQ3NInuLWP6SMivLKh1HxrTKn2aHBLoEB4Axlua9mNSPCC8M4Obwgel3vehtJsOjwpD1ktg6qbZSKrbubVdKuQVdNE3S0PWUVWbe3dlcmq7AIs91GVe6wuddi2qDdN4pDVNJT8Psd3Wc2T/aHZI2po5rBq6SnJ8ntoTv+//Jafhcd6zyX8uzVzSJ+ny5jVv2f077nJPGEkXiOjujJaOyejvh39I/8vv4Ofld1R34XfJ/w7OFef09JlyG8twfOt0aAeZNVYipwvCFl1PsVGGoisGsHoRSHIKrJqa0evTFZtBWAiLmTVBEW3y0BW68+vrK+VEV45ZOR2SI/gisy2pt7rPnbs18Hv1uwHamha/+jnZb1u8Nz0e13hndVl6OnNpg8Z5ZUNqYYCYz1DTc+3F1Uxp0d9ZSp09Jgd+70TwpgdX/yYXCPXRo/olOre4yWPGJvmRXmsWaUPpCOArKbjxFmsWe3XB05bz73p6359VC6r/e6zKrsEP/bNZ9Xzj++om0nm+pHVzMi8uwBZdS/l4QZTIrEis4HULqzPFdkNpjQrPc15QXhFioORXi3NspZXjiybVFVNMBToRaKrpVqmUC96TEaRRzac+NjCeuLwiej06vCx6Brj6GPhRlu9xxq07riqPDGyWhXpZteDrDY7f1VGz8hqMm1ktcpemFyXNbIa7hDMNOD6OwURmCeArJpn6lKJMq1ZNqsaH22rkem31JEjxxY1T0Z4ZaQ3eoQjwYsem+iODodHdHQ4+lh8TXBZI8ZV5yjcfGtQvbLuOD5SnXRN0oh20nlJo9wnnDfUTrXeWTYPk3YMOlavXqsOzq1R0zNzg04t5flg6rv+EoHDbgLIqt35sSk6ZDU5G8hq/b3UGlm9/a4H1Qsv7mJktf4+QQQlEEBWS4DqYJE2rVmNTpvuiW5kVLj3WGQq9eLH3l+UoXB6dfRB2VRrKBiBPn6EU64XnadFXoSeAwIhgbplWWYKyMZrdR3BuvjYjIakWNqtIdVpD6nJabNfaswPr9Zr9ru3GqvjkNkXEgOHOQIrxofVxNSsmpk121fMRVhPSWv+4MZ6KqbWHoFKZDXpvqpJOdh+2w1qy+ZLG5cepgE3LmWVB4ysVo68kRXaJKtNBJh2WnW4ZnlQG5NGtBOFYGG989LlHZ8SvtR5aUe5R+aPqrmJdwc1obTnw9kApVVAwRCAAARsIPD3522IwusYKpHVKOF+a1abnAVktcnZqyZ2ZLUazk2vBVltegari9/3Nat1y3J0rXp1WT9eU3RzuKXqH+601Ij+OTKxeBlB0ZiPr8svWlK+65NmauQriatCAqPDrWBUlYHVxX1i2d/6D3SSmglULqs1t7eU6pHVUrA6VSiy6lQ6S2sMsloaWucK9l1WnUtoSQ1izWpJYB0sljWryUllzWr9nR1ZNZADZNUARMeLQFYdT7Ch5iGrhkB6UAyy6kGSDTQRWTUA0ZMikFVk1dauXrms7tqzV11z8519ebAbsK1dhbiKEEBWi9Dz51pk1Z9cF20pslqUoB/XI6t+5NlEK5FVZNVEPyqjjMplddOWrerSiy9Ql1x4nrr3gUd7u/9eee02dfmmi9TW668qo52llsnIaql4nSgcWXUijaU3AlktHbEzFSCrzqSy1IYgq6XidapwZBVZtbVDVy6r4QZLHznzNPU/3v7VnqzKjsFRebUVWFJcyGqTslVPrMhqPdybViuy2rSM1Rcvslof+ybVjKw2KVv1xoqsIqv19sD+tdcmq3KLGhHXcNpveHsbpgHb2lWIqwgBZLUIPX+uRVb9yXXRliKrRQn6cT2y6keeTbQSWUVWTfSjMsqoXFZluu95556pvvLlG1X0/2+/60H1wou7eiOtZTS2rDIZWS2LrDvlIqvu5LLMliCrZdJ1q2xk1a18ltUaZLUssu6Vi6wiq7b26splNQ5CRlfD45H771AXbDzbVlZ940JWG5eyygNGVitH3sgKkdVGpq2WoJHVWrA3rlJktXEpqy1gZBVZra3zDai4dlm1FUyWuJDVLLT8PBdZ9TPvWVuNrGYl5u/5yKq/uc/ScmQ1Cy2/z0VWkVVbXwGVy2q4wZKsWXXlQFZdyWR57UBWy2PrUsnIqkvZLLctyGq5fF0pHVl1JZPltwNZRVbL72X5akBW83FbdBWyagCi40Ugq44n2FDzkFVDID0oBln1IMkGmoisGoDoSRHIKrJqa1evXFabfD/VfklEVm3t3vbEhazakwubI0FWbc6OXbEhq3blw9ZokFVbM2NfXMgqsmpfr+xGVLms7tqzd9H9VW0FkyUuZDULLT/PRVb9zHvWViOrWYn5ez6y6m/us7QcWc1Cy+9zkVVk1dZXQOWyGt39NwkK91m1tasQVxECyGoRev5ci6z6k+uiLUVWixL043pk1Y88m2glsoqsmuhHZZRRuayW0Yi6y2Rkte4M2F8/smp/jmyIEFm1IQvNiAFZbUae6o4SWa07A82pH1lFVm3trZXLar/dgHd87RvqsW8+q55/fIetrPrGhaw2LmWVB4ysVo68kRUiq41MWy1BI6u1YG9cpchq41JWW8DIKrJaW+cbULE1svr4Uy+obXc/pJgGbGtXIa4iBJDVIvT8uRZZ9SfXRVuKrBYl6Mf1yKofeTbRSmQVWTXRj8oowxpZvf2uB9ULL+5iZLWMLFNm7QSQ1dpT0IgAkNVGpMmKIJFVK9JgfRDIqvUpsiZAZBVZtaYzxgKpRFbDUdNBELbfdoPasvnSQacZfV4k+cnvfG9RmfHRXbndzquvvRmcc85Zp6sndm5fdD7TgI2mxMnCkFUn02q8UciqcaTOFoisOptaow1DVo3idLowZBVZtbWDVyKr0cb3W7NaFyAR0b+49Xp1wcazgxDia2evu+Ue9f6+gz1BlfPXr1ulHr7v1l7IyGpd2WtOvchqc3JVZ6TIap30m1U3stqsfNUVLbJaF/nm1YusIqu29trKZdVWEGFcch/Ya26+Uz1y/x2BwG7aslV96abP90Z8ZZT43gceXTRdGVm1Pav1x4es1p+DJkSArDYhS3bEiKzakQfbo0BWbc+QPfEhq8iqPb1xcSTIaiwzMpL6yt43AhmNi6ucmvQYsmpr97YnLmTVnlzYHAmyanN27IoNWbUrH7ZGg6zamhn74kJWkVX7emU3olpkVUYr9x04lMikrt2AozGFMaSV1UNHp23NL3FZQmDFeEcdmZhV8/PzlkREGDYSGO60VLs1pCamZm0Mj5gsIrBsrBP0k7k53lMsSot1oXTaLTXcGVLHJnlPsS45lgU0PtpRUzOzanaW95RoalYuG7YsU/6FU7msJq35tAm7rFl94OtPBrfQQVZtykyzY0FWm52/qqJHVqsi3fx6kNXm57CKFiCrVVB2ow5kNTmPyGr9/btyWbVtg6WkFEiMS61Zjd8PlmnA9Xdk2yNgGrDtGbIjPqYB25GHJkTBNOAmZKn+GJkGXH8OmhIB04CTM3Xa+vGmpNDZOL2XVZn+K+tTwyN+v1d2A3a271faMGS1UtyNrQxZbWzqKg8cWa0ceSMrRFYbmbZagkZWkdVaOl6KSiuXVZkGfPmmi9TW669KEV75p0TvoRrWxn1Wy+fuWw3Iqm8Zz9deZDUfNx+vQlZ9zHr2NiOr2Zn5egWyiqza2vcrl9WkW7/YCidtXEwDTkvK3/OQVX9zn6XlyGoWWn6fi6z6nf+0rUdW05LiPGQVWbX1VVC5rMp60KWOunYDLpIgZLUIPT+uRVb9yHPRViKrRQn6cz2y6k+ui7QUWS1Cz69rkVVk1dYeX7ms2gqiSFzIahF6flyLrPqR56KtRFaLEvTnemTVn1wXaSmyWoSeX9ciq8iqrT0eWTWQGWTVAETHi0BWHU+woeYhq4ZAelAMsupBkg00EVk1ANGTIpBVZNXWrl6LrEY3Ndp+2w1qy+ZLlUwPvuTCjerh+261lVXfuJDVxqWs8oCR1cqRN7JCZLWRaaslaGS1FuyNqxRZbVzKagsYWUVWa+t8AyquXFZFVNevWxVIqdw25ks3fT6Q1R1f+4Z67JvPLrqNjK3Q4nEhq03JVH1xIqv1sW9Szchqk7JVb6zIar38m1I7stqUTNUfJ7KKrNbfC5MjqFxWZQT1kfvvUBdsPHuRrMouwdvufkixwZKtXYW4ihBAVovQ8+daZNWfXBdtKbJalKAf1yOrfuTZRCuRVWTVRD8qo4zKZVVGU//tV754gqwyslpGeinTFgLIqi2ZsDsOZNXu/NgUHbJqUzbsjQVZtTc3tkWGrCKrtvXJMJ7KZfX2ux5UL7y4K5juG04D/siZp6lrbr5TXfEnn1Jf+fKNtrLqGxfTgBuXssoDRlYrR97ICpHVRqatlqCR1VqwN65SZLVxKastYGQVWa2t8w2ouHJZlXjCKb/R2G76whVq6/VX2cppybiQ1UamrdKgkdVKcTe2MmS1samrPHBktXLkjawQWW1k2moJGllFVmvpeCkqrUVWU8TVqFOQ1Ualq5ZgkdVasDeuUmS1cSmrLWBktTb0jaoYWW1UumoNFllFVmvtgEtUXrmsXnfLPer7L+05YSMlbl1jaxchLhMEkFUTFN0vA1l1P8emWoismiLpdjnIqtv5Ndk6ZBVZNdmfTJZVuazKOtWrP/eZE6b8ssGSybRSlm0EkFXbMmJnPMiqnXmxMSpk1cas2BcTsmpfTmyNCFlFVm3tm5XLqoygbr/thuDeqtGDW9fY2kWIywQBZNUERffLQFbdz7GpFiKrpki6XQ6y6nZ+TbYOWUVWTfYnk2VVLquMrJpMH2U1hQCy2pRM1Rsnslov/ybVjqw2KVv1xYqs1se+aTUjq8iqrX22clmV6b4PfP1J9cj9dwT3WpVj1569wa1rmrojMBss2dq97YkLWbUnFzZHgqzanB27YkNW7cqHrdEgq7Zmxr64kFVk1b5e2Y2oclmVSpNuXZM0NdhWaPG4kNWmZKq+OJHV+tg3qWZktUnZqjdWZLVe/k2pHVltSqbqjxNZRVbr74XJEdQiq7bCyBsXspqXnD/XIav+5LpIS5HVIvT8uhZZ9SvfeVuLrOYl5991yCqyamuvR1YNZAZZNQDR8SKQVccTbKh5yKohkB4Ug6x6kGQDTURWDUD0pAhkFVm1tavXIquyydK+A4cSmex+bqetrPrGhaw2LmWVB4ysVo68kRUiq41MWy1BI6vFsB+Zn1P7ZmeLFVLg6iNz82r/3EyBEtJdOtJpq9GRljp0dHrRBR/MzamDc/W1X+o/pHNQ13Fwfl5JDBzHCYwOt9TM7JzS/3FECDz60TPhUTOBymX1ymu3qfXrVqmH77u15qabqx5ZNcfS1ZKQVVcza7ZdyKpZnlLaO1pIJlN8KH5rZkbNqvmBAfxmZvGH/qQLZuaH1O/mUpynhtRbs4OFZVJ/qJZ2RI+RzpD+YDmvtPPkOo6KrNUoK3XLYi5oXAQBCHhHYP6P/sC7NtvW4Mpltd99Vm0DkyUeZDULLT/PRVb9zHvWVtsqq0nClyR3v9XiNatHLKLHGwky9puEEa3fTC+Wu9mheSV19DtkVEyEhwMCeQgsH2qpde12nkuNXLO8NaTWDnWMlLVUIa2WUu2hITWtv9iIHqvbLbWqVV/7V+vAVum46jpW6vxLDBzHCawYH1YTU7PB6CrHcQL/85kfAkfNBJBVAwlAVg1AdLwIZNXxBBto3oyWvAOdeTXcaamDR6ZV0jTBpKl7SdPp9umRuCMxadynpVHKjB7750987B193mTsWgPNq62Ik7WQjOoPpoOOUzsd1dYjooOODw8PDzpFdbRon9oaLCKiCqe2B583qj9UnxwTi9XLR9ThCf3lQM4Plst0metqlJW6ZXFgEh05gTWrjiSygmawZjUZ8mnrxyugTxVLEahcVmUa8OWbLlJbr7/Kmcwgq86ksrSGIKuloa214HB0T6aPhqOA7+iplTJtc1JH9u7CqOJbem2aTA2VNWIfLMjFG7PdkcQmjBAmCd9JIoFqsQSeJsIXGy0RGevEpteekSBoH+6cKIFnJDwWJlxGxUR4fD1Ys+pr5rO1G1nNxsvns5FVZNXW/l+5rMo9Vu994FH1/OM7bGWSOS5kNTMy7y5AVu1JebjmUNbrHdVSORMTzSk9qjipByBFOuV4S69RnNH/FtE8uDDtNM26xTwt/j0tZ0Na9uZ0DEnTBJOm7iVNp0ua4rZOC+LymEiu1aN/Uk/0SDsSmad9XGOOALJqjqXLJSGrLmfXbNuQVWTVbI8yV1rlsiprVpc62A3YXHIpyR4CyGq+XExoOZTprEdkWquewiprFA8HU1zl393nDs9r6ZTfWiaPaKmU37J5THCeXLNwvvx7IsUGOmkjHdOjeiJ/K/R0ymVa+FboKZXy7+XyW2+cI4/LyN+yhXO657b1v1vd5/Q1yxfOkX+P6WtsXbOalgnnVUcAWa2OdZNrQlabnL1qY0dWkdVqe1z62iqX1fShNedMRlabk6u6IvVdVmU9pux6KlNlZUrsO/r3e7LD6cLo5bt6SuyE3tMhukOpnC/XmT7C6aartDTKBiN6U1V16sJ003WBPA6pEf0TrhE8qT2sxvQ50TV+wdTWEjYHQVZNZ9vd8pBVd3NrsmXIqkmabpeFrCKrtvZwZNVAZpBVAxAdL8JlWZUpse/qnVllY553tXzKOk3Z7VWmz74rYqr/v8j9DKMbsZyhxVGOcDpsdCObtQsjm9HNaE7SUjkqo5017/yZtnsjq2lJcR6ySh9IQwBZTUOJc4QAsoqs2vpKqEVWZd3qtrsfWsRk+203qC2bL7WV05JxIauNTFulQTdRVkUyA9mcEfGcCe4b2R0VFSHtymmae0SGoGVEUzblOVkL5ElaLE/V/x/uhBqOXsqurXKOHGWNXlaa+IyVIasZgXl8OrLqcfIzNB1ZzQDL81ORVWTV1pdA5bK642vfUA98/Un1yP13qAs2nh1w2bVnr7rm5jvVTV+4opG7BCOrtnZve+KyRVZlWq2I5rt6nWcgnMHoZ/f/g99aSkNJPaSn6Q46ZN3myZ222jAkEqp/awk9WUtp7/9FTPXj8jPu8c6tgziGzyOraUlxHrJKH0hDAFlNQ4lzhACyiqza+kqoXFY3bdmqrv7cZ06QUpHYx775bCN3CUZWbe3e9sRVhayGU3AD8dSjnt1puXOBgIbPyWP7U0io3PlRptDKKOgGucdjMCoqI6L6/+WxYIRUS6jeTXYlN1Y31tGQVWMonS8IWXU+xUYaiKwawehFIcgqsmprR69cVmU34KQpv+HUYHYDtrWrEFcRAkVkdX846hmuCdXTcHvrQ/W03ONy2r3VyqDjuICKiIqQdqfmhgK6YagrqWvb/t7DchDDsp5HVssi6165yKp7OS2jRchqGVTdLBNZRVZt7dmVy6ptI6vX3XKP+v5LexblJy7MV167Tb362pvBOeecdbp6Yuf2Reczsmpr97YnriRZlWm2MgIanYYbSOjCyGj3Ob1jbspdcUUuuyLaFdBgSu7CaKisCT25szBKqh/jsJMAsmpnXmyMClm1MSv2xYSs2pcTWyNCVpFVW/tm5bJq25pVkefnH9/Ry8/tdz2oXnhxV+8xkdn39x3sCaqI6/p1q9TD993auwZZtbV71x/XQS2bP5k6pn7d1r8PH1Nvy5Rc2SlX36pF1oamPaKbE8nGQzIdV36fqgX0pFZ3jei6hY2J0pbJefYRQFbty4mtESGrtmbGrriQVbvyYXM0czEOkgAAHOJJREFUyCqyamv/rFxWBYTNuwGHmz2FG0CJzH7pps/3diqW2O994NFFgous2tq9q43ryPyc2j05qeV0Qu2anlI/nJxQr81MLRmESOapetQz2CVXb1R0qh4V/ZDIp/x/IKLdUVIOPwggq37k2UQrkVUTFN0vA1l1P8emWoisIqum+pLpcmqRVdONMFledKOnuLhKPUmPIasmM9CMsia1mP5CC+lLWkh/NDWpdk9PqF9MnSimcn/P80dH1R+vWqFOmxk6PjVXC6iMlnJAIEoAWaU/pCWArKYl5fd5yKrf+c/SemQVWc3SX6o8F1mN0A5FNNwAKq2sVpkw6qqegOymu3tiQu0+pqVUfk9Mqp8dO6b2xabxyprQj4+PqfPH5GdU//948HsNI6PVJ40aIQABCEAAAhCAAAQaT6AyWQ3XqibdS3Wp56oinHSv17SyyshqVVkqvx5ZY/oLPVL6sp6++0s9cio/L09PButMo8dqvWb094dH1bnDI+pj+uf3R7r/v15vapR0FNkNuPxWU4MtBBhZtSUT9sfByKr9ObIhQkZWbchCM2JgZDU5T6etH29GAh2OsjJZTdqYKMo1vpFRlczDNbThOtVo3UlrVrfd/ZCK7hiMrFaZLXN1yRrTl7WMipz+Usvpy1PTWk4n1e/07rvRQ6byfmxEpHRUfUxP3f2YFlMR1FMy7KqLrJrLm8slIasuZ9ds25BVszxdLQ1ZdTWz5tuFrCKr5nuVmRIrk9V+91cNm1HXfVaTNkxaSqLZDdhMx6u6lMn5+d4oqawtFSl9eWZavaF/oseIGtKjpCN6lFSEdFj//5g6VwvqGQXXlyKrVWe8mfUhq83MWx1RI6t1UG9enchq83JWV8TIKrJaV98bVK/XshpO802CFK5blee4z+qgbmTX8zNaTMNpvL2RUz2C+npMTFs67GDEtNMV049pMZXfZ3VGjDcIWTWO1MkCkVUn01pKo5DVUrA6Vyiy6lxKS2sQsoqslta5ChZcmazGp9PG4x40wlmwnaVezjTgUvEOLDxYVxpM5Z0O1pfKyOmvEm4Z81E9dVfWlf5+sM5U1pgOq4/q31UcyGoVlJtfB7La/BxW1QJktSrSza4HWW12/qqMHllFVqvsb1nqqkxWb7/rQfXzl19XT+zcnhjfoDWtWRpV9bnIanXEfxXZ9Cgqp/EIZHQ0Olr6Mfm3Xmsqo6l1HMhqHdSbVyey2ryc1RUxsloX+WbVi6w2K191RousIqt19r+l6q5MViUIGV2V4/nHdyyKSR7fd+DQok2LbAWWFBeyWk62Xp/VGx6F60uD3/pHj5jKNN/oIetJZV2prC8VQZX1prLuVNaf2nIgq7Zkwu44kFW782NTdMiqTdmwNxZk1d7c2BYZsoqs2tYnw3gqlVWpVEZYn/zO9xbxuOTCjerh+261ldHAuJDVgYgGnvCmvpdp91Yxejrvwu1ifjk9rSb0jr3RQ3bglZ14gx15ZWde2QhJi6ns2GvzgazanB17YkNW7cmF7ZEgq7ZnyI74kFU78tCEKJBVZNXWflq5rNoKokhcyGo2em/rW8OE9zDtyakeOT0cE1O5Z2mwxnThVjHd9aajSu5x2rQDWW1axuqJF1mth3sTa0VWm5i16mNGVqtn3tQakVVk1da+i6wayAyy2h/ie3Oz3c2P9ChpV0y7I6cfzC0eMV2lBTQYMQ1uGSO/u6OnG7SwunAgqy5ksfw2IKvlM3alBmTVlUyW2w5ktVy+LpWOrCKrtvZnZNVAZpDV4xDfmZ1V3z16RP18ZlK9NDmhfqHlVO5xGj9kTen5w2PqAi2ln9BrTc8fHbV+Km+RroKsFqHnz7XIqj+5LtpSZLUoQT+uR1b9yLOJViKryKqJflRGGciqAarIqlJ/NXFUff3wQfV/HTt8wgZIsjPv+VpOLxQp1b8/MTKuZCTVpwNZ9Snb+duKrOZn59uVyKpvGc/XXmQ1Hzcfr0JWkVVb+z2yaiAzvsrqQT2V9/88clDtPPyBelVP7ZWjMzSkNo2Nq08GYjqmLh71T0yTuhSyauCF5kERyKoHSTbURGTVEEjHi0FWHU+wweYhq8iqwe5ktChk1QBO32T1GT2K+rQeQX3m2FH165npgOAFen3pZePL1WfHlquLRscMUHWrCGTVrXyW1RpktSyy7pWLrLqX0zJahKyWQdXNMpFVZNXWno2sGsiMD7IqUipyGkiqllU5xvTtYj47vkxdNqZ/xleok9tubIZkoEucUASyWgZV98pEVt3LaVktQlbLIutWuciqW/ksszXIKrJaZv8qUjayWoTewrUuy+r/G4yiHgkE9ZWFqb7n6h17RVBFVD+lf3MMJoCsDmbEGUohq/SCtASQ1bSk/D4PWfU7/1laj6wiq1n6S5XnIqsGaLsmq+/o2808I4Kqf57Wo6kT+v6nQ5pTIKjLVgS/P9wZNkDOnyKQVX9yXaSlyGoRen5di6z6le+8rUVW85Lz7zpkFVm1tdcjqwYy44qs/lDfauZpPYL6jJ7qu0vfG1WOM9vD6rJlMtVXS6oeSeXIRwBZzcfNt6uQVd8ynr+9yGp+dj5diaz6lO1ibUVWkdViPai8q5FVA2ybLKuyo+/TE3oUVd8bVX5/oP8tx6UyihqsRV2uztH3QuUoRgBZLcbPl6uRVV8yXbydyGpxhj6UgKz6kGUzbURWkVUzPcl8KciqAaZNlNWf6ZHTYJqvFtT/T4+oynFKu7OwYZLe1XfZcjUSTP7lMEEAWTVB0f0ykFX3c2yqhciqKZJul4Osup1fk61DVpFVk/3JZFnIqgGaTZHVKTUfrEGVHX2f1iOpsjZVjk/qe6HKFN/P6lHU8/XmSRzmCSCr5pm6WCKy6mJWy2kTsloOV9dKRVZdy2h57UFWkdXyelexkpHVYvyCq22X1Vf1Lr7BbWf0KOoLC7edWdOS285016HKvVFX6n9zlEcAWS2PrUslI6suZbPctiCr5fJ1pXRk1ZVMlt8OZBVZLb+X5asBWc3HbdFVtsqqCOozsh5VT/d9Xd8nVY4/GNG3ndGSKutRLxwdM9B6ikhDAFlNQ4lzkFX6QFoCyGpaUn6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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0007227332457293035, 1.1007227332457292 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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SYSTEM TIMEABcaption
00.010.00000050.000000Initialized state
10.117.00000043.000000first reaction step
20.220.50000039.5000002nd reaction step
30.322.25000037.750000
40.423.12500036.875000
50.523.56250036.437500
60.623.78125036.218750
70.723.89062536.109375
80.823.94531236.054688
90.923.97265636.027344
101.023.98632836.013672
111.123.99316436.006836last reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.000000 50.000000 Initialized state\n", "1 0.1 17.000000 43.000000 first reaction step\n", "2 0.2 20.500000 39.500000 2nd reaction step\n", "3 0.3 22.250000 37.750000 \n", "4 0.4 23.125000 36.875000 \n", "5 0.5 23.562500 36.437500 \n", "6 0.6 23.781250 36.218750 \n", "7 0.7 23.890625 36.109375 \n", "8 0.8 23.945312 36.054688 \n", "9 0.9 23.972656 36.027344 \n", "10 1.0 23.986328 36.013672 \n", "11 1.1 23.993164 36.006836 last reaction step" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = dynamics.get_history() # Revisited from earlier\n", "df" ] }, { "cell_type": "markdown", "id": "f72f4988-4e4b-4268-9f4a-e36300c9dcf1", "metadata": {}, "source": [ "## Now investigate A_dot, i.e. d[A]/dt" ] }, { "cell_type": "code", "execution_count": 20, "id": "5ee8ec14-442f-4e76-bc86-26b8791f7e70", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[10.0,\n", " 17.0,\n", " 20.5,\n", " 22.25,\n", " 23.125,\n", " 23.5625,\n", " 23.78125,\n", " 23.890625,\n", " 23.9453125,\n", " 23.97265625,\n", " 23.986328125,\n", " 23.9931640625]" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = list(df.A)\n", "A" ] }, { "cell_type": "code", "execution_count": 21, "id": "a390ed46-f014-414f-9b14-69f6da95dc41", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(A)" ] }, { "cell_type": "code", "execution_count": 22, "id": "b3b1b169-bae2-493b-b652-ce9e82b2ddab", "metadata": {}, "outputs": [], "source": [ "A_dot = np.gradient(A, 0.1) # 0.1 is the constant step size" ] }, { "cell_type": "code", "execution_count": 23, "id": "35c7be1f-95ce-4bac-9fb3-02745a505f92", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([7.00000000e+01, 5.25000000e+01, 2.62500000e+01, 1.31250000e+01,\n", " 6.56250000e+00, 3.28125000e+00, 1.64062500e+00, 8.20312500e-01,\n", " 4.10156250e-01, 2.05078125e-01, 1.02539062e-01, 6.83593750e-02])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A_dot" ] }, { "cell_type": "code", "execution_count": 24, "id": "f5fa1f8e-517f-4fd1-b3bf-51c12ab883f0", "metadata": {}, "outputs": [], "source": [ "df['A_dot'] = A_dot # Add a column to the Pandas dataframe" ] }, { "cell_type": "code", "execution_count": 25, "id": "e3773cfc-88ed-4565-a760-e90fa050d5b9", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaptionA_dot
00.010.00000050.000000Initialized state70.000000
10.117.00000043.000000first reaction step52.500000
20.220.50000039.5000002nd reaction step26.250000
30.322.25000037.75000013.125000
40.423.12500036.8750006.562500
50.523.56250036.4375003.281250
60.623.78125036.2187501.640625
70.723.89062536.1093750.820312
80.823.94531236.0546880.410156
90.923.97265636.0273440.205078
101.023.98632836.0136720.102539
111.123.99316436.006836last reaction step0.068359
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" ], "text/plain": [ " SYSTEM TIME A B caption A_dot\n", "0 0.0 10.000000 50.000000 Initialized state 70.000000\n", "1 0.1 17.000000 43.000000 first reaction step 52.500000\n", "2 0.2 20.500000 39.500000 2nd reaction step 26.250000\n", "3 0.3 22.250000 37.750000 13.125000\n", "4 0.4 23.125000 36.875000 6.562500\n", "5 0.5 23.562500 36.437500 3.281250\n", "6 0.6 23.781250 36.218750 1.640625\n", "7 0.7 23.890625 36.109375 0.820312\n", "8 0.8 23.945312 36.054688 0.410156\n", "9 0.9 23.972656 36.027344 0.205078\n", "10 1.0 23.986328 36.013672 0.102539\n", "11 1.1 23.993164 36.006836 last reaction step 0.068359" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df" ] }, { "cell_type": "code", "execution_count": 26, "id": "91db31bd-0f5d-48d5-90b8-6d584ca32046", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(chemicals=[\"A\", \"A_dot\"], colors=['navy', 'brown'], \n", " ylabel=\"concentration (darkturquoise) /
concentration change per unit time (brown)\",\n", " title=\"Concentration of A with time (darkturquoise), and its rate of change (brown)\")" ] }, { "cell_type": "markdown", "id": "85d87078-8fc1-4166-95e1-343b546f9971", "metadata": {}, "source": [ "### At t=0 : \n", "[A]=10 and [A] has a high rate of change (70)\n", "### As the system approaches equilibrium : \n", "[A] approaches a value of 24, and its rate of change decays to zero." ] }, { "cell_type": "markdown", "id": "99cd0942-555b-444e-9c6f-ee1481a2a980", "metadata": {}, "source": [ "#### **NOTE:** The curves are jagged because of limitations of numerically estimating derivatives, as well as _the large time steps taken_ (especially in the early times, when there's a lot of change.) \n", "## In experiment \"react_2_b\", we revisit the same reaction using a better simulator that employs **_adaptive variable time steps_**" ] }, { "cell_type": "code", "execution_count": null, "id": "531ce53b-7336-440e-bce4-716aafa6c692", "metadata": {}, "outputs": [], "source": [] } ], "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }