{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## `A` down-regulates `B` , \n", "### by being the *limiting reagent* in reaction `A + 2 B <-> Y` (mostly forward)\n", "1st-order kinetics. \n", "If [A] is low and [B] is high, then [B] remains high. If [A] goes high, [B] goes low. However, at that point, A can no longer bring B up to any substantial extent.\n", "\n", "See also 1D/reactions/down_regulation_1\n", "\n", "LAST REVISED: Feb. 5, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "d9efa3fd-e95d-4e1c-878a-81ae932b2709", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "# Extend the sys.path variable, to contain the project's root directory\n", "import set_path\n", "set_path.add_ancestor_dir_to_syspath(2) # The number of levels to go up \n", " # to reach the project's home, from the folder containing this notebook" ] }, { "cell_type": "code", "execution_count": 2, "id": "01bae555-3dcf-42c1-bddc-9477a37f49f8", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.reactions.reaction_data import ReactionData as chem\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "import numpy as np\n", "import plotly.express as px\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "cc53849f-351d-49e0-bfa8-22f8d8e22f8e", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'down_regulate_2.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging\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_1\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "markdown", "id": "d6d3ca49-589d-49b7-8424-37c7b01bcacf", "metadata": {}, "source": [ "### Initialize the system" ] }, { "cell_type": "code", "execution_count": 4, "id": "23c15e66-52e4-495b-aa3d-ecddd8d16942", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A + 2 B <-> Y (kF = 8 / kR = 2 / Delta_G = -3,436.56 / K = 4) | 1st order in all reactants & products\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `down_regulate_2.log.htm`]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"A\", \"B\", \"Y\"])\n", "\n", "# Reaction A + 2 B <-> Y , with 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=[(\"A\") , (2, \"B\")], products=[(\"Y\")],\n", " forward_rate=8., reverse_rate=2.)\n", "\n", "chem_data.describe_reactions()\n", "\n", "# Send the plot of the reaction network to the HTML log file\n", "graph_data = chem_data.prepare_graph_network()\n", "GraphicLog.export_plot(graph_data, \"vue_cytoscape_1\")" ] }, { "cell_type": "markdown", "id": "d1d0eabb-b5b1-4e15-846d-5e483a5a24a7", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals" ] }, { "cell_type": "code", "execution_count": 5, "id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 5.0\n", " Species 1 (B). Conc: 100.0\n", " Species 2 (Y). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(reaction_data=chem_data)\n", "dynamics.set_conc(conc={\"A\": 5., \"B\": 100., \"Y\": 0.},\n", " snapshot=True) # A is scarce, B is plentiful, Y is absent\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "0b46b395-3f68-4dbd-b0c5-d67a0e623726", "metadata": { "tags": [] }, "source": [ "### Take the initial system to equilibrium" ] }, { "cell_type": "code", "execution_count": 6, "id": "bcf652b8-e0dc-438e-bdbe-02216c1d52a0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "single_compartment_react(): setting abs_fast_threshold to 300.0\n", "30 total step(s) taken\n" ] }, { "data": { "text/html": [ "
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SYSTEM TIMEABYcaption
00.000005.000000100.0000000.000000Initial state
10.000254.00000098.0000001.000000Interm. step, due to the fast rxns: [0]
20.000503.21650096.4330001.783500
30.000752.59703895.1940772.402962Interm. step, due to the fast rxns: [0]
40.001002.10379494.2075892.896206
50.001251.70885693.4177113.291144Interm. step, due to the fast rxns: [0]
60.001501.39122792.7824533.608773
70.001751.13486892.2697363.865132Interm. step, due to the fast rxns: [0]
80.002000.92737391.8547454.072627
90.002250.75904291.5180844.240958Interm. step, due to the fast rxns: [0]
100.002500.62223091.2444604.377770
110.002750.51086991.0217384.489131Interm. step, due to the fast rxns: [0]
120.003000.42011390.8402264.579887
130.003250.34607790.6921544.653923Interm. step, due to the fast rxns: [0]
140.003500.28563190.5712624.714369
150.003750.23624890.4724964.763752Interm. step, due to the fast rxns: [0]
160.004000.19588290.3917644.804118
170.004250.16287290.3257444.837128Interm. step, due to the fast rxns: [0]
180.004500.13586790.2717354.864133
190.005000.09167290.1833434.908328
200.005500.06351190.1270224.936489
210.006000.04555190.0911024.954449
220.006500.03409190.0681814.965909
230.007000.02677590.0535494.973225
240.007500.02210390.0442064.977897
250.008000.01912090.0382404.980880
260.008500.01721590.0344304.982785
270.009000.01599890.0319964.984002
280.009500.01522190.0304414.984779
290.010000.01472490.0294484.985276
300.010500.01440790.0288144.985593
310.011000.01420490.0284094.985796
320.011500.01407590.0281504.985925
330.012000.01399290.0279854.986008
340.012500.01394090.0278794.986060
350.013000.01390690.0278124.986094
360.013500.01388490.0277694.986116
370.014000.01387190.0277414.986129
380.014500.01386290.0277234.986138
390.015000.01385690.0277124.986144
\n", "
" ], "text/plain": [ " SYSTEM TIME A B Y \\\n", "0 0.00000 5.000000 100.000000 0.000000 \n", "1 0.00025 4.000000 98.000000 1.000000 \n", "2 0.00050 3.216500 96.433000 1.783500 \n", "3 0.00075 2.597038 95.194077 2.402962 \n", "4 0.00100 2.103794 94.207589 2.896206 \n", "5 0.00125 1.708856 93.417711 3.291144 \n", "6 0.00150 1.391227 92.782453 3.608773 \n", "7 0.00175 1.134868 92.269736 3.865132 \n", "8 0.00200 0.927373 91.854745 4.072627 \n", "9 0.00225 0.759042 91.518084 4.240958 \n", "10 0.00250 0.622230 91.244460 4.377770 \n", "11 0.00275 0.510869 91.021738 4.489131 \n", "12 0.00300 0.420113 90.840226 4.579887 \n", "13 0.00325 0.346077 90.692154 4.653923 \n", "14 0.00350 0.285631 90.571262 4.714369 \n", "15 0.00375 0.236248 90.472496 4.763752 \n", "16 0.00400 0.195882 90.391764 4.804118 \n", "17 0.00425 0.162872 90.325744 4.837128 \n", "18 0.00450 0.135867 90.271735 4.864133 \n", "19 0.00500 0.091672 90.183343 4.908328 \n", "20 0.00550 0.063511 90.127022 4.936489 \n", "21 0.00600 0.045551 90.091102 4.954449 \n", "22 0.00650 0.034091 90.068181 4.965909 \n", "23 0.00700 0.026775 90.053549 4.973225 \n", "24 0.00750 0.022103 90.044206 4.977897 \n", "25 0.00800 0.019120 90.038240 4.980880 \n", "26 0.00850 0.017215 90.034430 4.982785 \n", "27 0.00900 0.015998 90.031996 4.984002 \n", "28 0.00950 0.015221 90.030441 4.984779 \n", "29 0.01000 0.014724 90.029448 4.985276 \n", "30 0.01050 0.014407 90.028814 4.985593 \n", "31 0.01100 0.014204 90.028409 4.985796 \n", "32 0.01150 0.014075 90.028150 4.985925 \n", "33 0.01200 0.013992 90.027985 4.986008 \n", "34 0.01250 0.013940 90.027879 4.986060 \n", "35 0.01300 0.013906 90.027812 4.986094 \n", "36 0.01350 0.013884 90.027769 4.986116 \n", "37 0.01400 0.013871 90.027741 4.986129 \n", "38 0.01450 0.013862 90.027723 4.986138 \n", "39 0.01500 0.013856 90.027712 4.986144 \n", "\n", " caption \n", "0 Initial state \n", "1 Interm. step, due to the fast rxns: [0] \n", "2 \n", "3 Interm. step, due to the fast rxns: [0] \n", "4 \n", "5 Interm. step, due to the fast rxns: [0] \n", "6 \n", "7 Interm. step, due to the fast rxns: [0] \n", "8 \n", "9 Interm. step, due to the fast rxns: [0] \n", "10 \n", "11 Interm. step, due to the fast rxns: [0] \n", "12 \n", "13 Interm. step, due to the fast rxns: [0] \n", "14 \n", "15 Interm. step, due to the fast rxns: [0] \n", "16 \n", "17 Interm. step, due to the fast rxns: [0] \n", "18 \n", "19 \n", "20 \n", "21 \n", "22 \n", "23 \n", "24 \n", "25 \n", "26 \n", "27 \n", "28 \n", "29 \n", "30 \n", "31 \n", "32 \n", "33 \n", "34 \n", "35 \n", "36 \n", "37 \n", "38 \n", "39 " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.single_compartment_react(time_step=0.0005, n_steps=30,\n", " dynamic_substeps=2, rel_fast_threshold=15)\n", "\n", "df = dynamics.get_history()\n", "df" ] }, { "cell_type": "markdown", "id": "7dc56592-179d-4e4c-b75a-8eb81dcafe71", "metadata": {}, "source": [ "A, as the scarse limiting reagent, stops the reaction. \n", "When A is low, B is also low." ] }, { "cell_type": "markdown", "id": "962acf15-3b50-40e4-9daa-3dcca7d3291a", "metadata": {}, "source": [ "### Equilibrium" ] }, { "cell_type": "code", "execution_count": 7, "id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + 2 B <-> Y\n", "Final concentrations: [Y] = 4.986 ; [A] = 0.01386 ; [B] = 90.03\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99712\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.07189 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "cbf6c9c7-8cec-400f-9e70-49ff1a9f485c", "metadata": { "tags": [] }, "source": [ "## Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 8, "id": "665dfff9-e943-44e1-b76d-af363d94c9f8", "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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'darkorange', 'green'],\n", " title=\"Changes in concentrations (reaction A + 2 B <-> Y)\")" ] }, { "cell_type": "markdown", "id": "448ec7fa-6529-438b-84ba-47888c2cd080", "metadata": { "tags": [] }, "source": [ "# Now, let's suddenly increase [A]" ] }, { "cell_type": "code", "execution_count": 9, "id": "7245be7a-c9db-45f5-b033-d6c521237a9c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.015:\n", "3 species:\n", " Species 0 (A). Conc: 40.0\n", " Species 1 (B). Conc: 90.0277121942094\n", " Species 2 (Y). Conc: 4.986143902895314\n" ] } ], "source": [ "dynamics.set_chem_conc(species_name=\"A\", conc=40., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 10, "id": "007161ef-f4d0-4623-92c5-0fe3d2bda98a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABYcaption
360.01350.01388490.0277694.986116
370.01400.01387190.0277414.986129
380.01450.01386290.0277234.986138
390.01500.01385690.0277124.986144
400.015040.00000090.0277124.986144Set concentration of `A`
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "36 0.0135 0.013884 90.027769 4.986116 \n", "37 0.0140 0.013871 90.027741 4.986129 \n", "38 0.0145 0.013862 90.027723 4.986138 \n", "39 0.0150 0.013856 90.027712 4.986144 \n", "40 0.0150 40.000000 90.027712 4.986144 Set concentration of `A`" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.history.get(tail=5)" ] }, { "cell_type": "markdown", "id": "24455d58-a0ea-43fa-b6ad-95c42a8b34b2", "metadata": {}, "source": [ "### Again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 11, "id": "c06fd8d8-d550-4e35-a239-7b91bee32be9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "single_compartment_react(): setting abs_fast_threshold to 150.0\n", "40 total step(s) taken\n" ] }, { "data": { "text/html": [ "
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SYSTEM TIMEABYcaption
00.000005.000000100.0000000.000000Initial state
10.000254.00000098.0000001.000000Interm. step, due to the fast rxns: [0]
20.000503.21650096.4330001.783500
30.000752.59703895.1940772.402962Interm. step, due to the fast rxns: [0]
40.001002.10379494.2075892.896206
..................
960.051001.00630612.04032443.979838
970.052000.99733512.02238343.988808
980.053000.98939012.00649343.996754
990.054000.98235111.99241444.003793
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" ], "text/plain": [ " SYSTEM TIME A B Y \\\n", "0 0.00000 5.000000 100.000000 0.000000 \n", "1 0.00025 4.000000 98.000000 1.000000 \n", "2 0.00050 3.216500 96.433000 1.783500 \n", "3 0.00075 2.597038 95.194077 2.402962 \n", "4 0.00100 2.103794 94.207589 2.896206 \n", ".. ... ... ... ... \n", "96 0.05100 1.006306 12.040324 43.979838 \n", "97 0.05200 0.997335 12.022383 43.988808 \n", "98 0.05300 0.989390 12.006493 43.996754 \n", "99 0.05400 0.982351 11.992414 44.003793 \n", "100 0.05500 0.976112 11.979937 44.010031 \n", "\n", " caption \n", "0 Initial state \n", "1 Interm. step, due to the fast rxns: [0] \n", "2 \n", "3 Interm. step, due to the fast rxns: [0] \n", "4 \n", ".. ... \n", "96 \n", "97 \n", "98 \n", "99 \n", "100 \n", "\n", "[101 rows x 5 columns]" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.single_compartment_react(time_step=0.001, n_steps=40,\n", " dynamic_substeps=2, rel_fast_threshold=15)\n", "\n", "df = dynamics.history.get()\n", "df" ] }, { "cell_type": "code", "execution_count": 12, "id": "2783a665-fca0-44e5-8d42-af2a96eae392", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + 2 B <-> Y\n", "Final concentrations: [Y] = 44.01 ; [A] = 0.9761 ; [B] = 11.98\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.76355\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 5.911 %\n", "Reaction IS in equilibrium (within 6% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=6)" ] }, { "cell_type": "code", "execution_count": 13, "id": "58f4f09c-8af6-46b7-bd85-2f6ca194c42a", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'darkorange', 'green'],\n", " title=\"Changes in concentrations (reaction A + 2 B <-> Y)\")" ] }, { "cell_type": "markdown", "id": "158e3787-f2d5-4a01-aaa9-6066e93e584c", "metadata": {}, "source": [ "**A**, still the limiting reagent, is again stopping the reaction. \n", "The (transiently) high value of [A] led to a high value of [B]" ] }, { "cell_type": "markdown", "id": "f6619731-c5ea-484c-af3e-cea50d685361", "metadata": { "tags": [] }, "source": [ "# Let's again suddenly increase [A]" ] }, { "cell_type": "code", "execution_count": 14, "id": "d3618eba-a673-4ff5-85d0-08f5ea592361", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.055:\n", "3 species:\n", " Species 0 (A). Conc: 30.0\n", " Species 1 (B). Conc: 11.979937031950595\n", " Species 2 (Y). Conc: 44.010031484024715\n" ] } ], "source": [ "dynamics.set_chem_conc(species_name=\"A\", conc=30., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 15, "id": "61eead55-fcef-41cd-b29e-f2d5ad5c6078", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "97 0.052 0.997335 12.022383 43.988808 \n", "98 0.053 0.989390 12.006493 43.996754 \n", "99 0.054 0.982351 11.992414 44.003793 \n", "100 0.055 0.976112 11.979937 44.010031 \n", "101 0.055 30.000000 11.979937 44.010031 Set concentration of `A`" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.history.get(tail=5)" ] }, { "cell_type": "markdown", "id": "0974480d-ca45-46fe-addd-c8d394780fdb", "metadata": {}, "source": [ "### Yet again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 16, "id": "8fe20f9c-05c4-45a4-b485-a51005440200", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "single_compartment_react(): setting abs_fast_threshold to 150.0\n", "35 total step(s) taken\n" ] }, { "data": { "text/html": [ "
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SYSTEM TIMEABYcaption
00.000005.000000100.0000000.000000Initial state
10.000254.00000098.0000001.000000Interm. step, due to the fast rxns: [0]
20.000503.21650096.4330001.783500
30.000752.59703895.1940772.402962Interm. step, due to the fast rxns: [0]
40.001002.10379494.2075892.896206
..................
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'darkorange', 'green'],\n", " title=\"Changes in concentrations (reaction A + 2 B <-> Y)\")" ] }, { "cell_type": "markdown", "id": "81a8be4a-f374-494e-b647-184e35707295", "metadata": {}, "source": [ "**A**, again the scarse limiting reagent, stops the reaction yet again" ] }, { "cell_type": "code", "execution_count": null, "id": "cb4749d0-dc12-44ba-a032-8068c80d9c4c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "d40258c5-5520-44a2-8dca-c28864386742", "metadata": {}, "source": [ "## A can down-regulate B, but it cannot bring it up to any significant amount\n", "#### Even if A is completely taken out (i.e., [A] set to 0), [B] can only slightly increase, from the reverse reaction (\"Le Chatelier's principle\".) \n", "Let's try it:" ] }, { "cell_type": "code", "execution_count": 19, "id": "84e83a01-76b1-4a6c-92e3-3f540cb47b1e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.09:\n", "3 species:\n", " Species 0 (A). Conc: 0.0\n", " Species 1 (B). Conc: 0.5124787710943272\n", " Species 2 (Y). Conc: 49.74376061445283\n" ] } ], "source": [ "dynamics.set_chem_conc(species_name=\"A\", conc=0., snapshot=True) # Completely eliminate A\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 20, "id": "31f1e4d5-8027-41de-90cc-f0492c88a9d9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "single_compartment_react(): setting abs_fast_threshold to 150.0\n", "70 total step(s) taken\n" ] }, { "data": { "text/html": [ "
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SYSTEM TIMEABYcaption
00.000005.000000100.0000000.000000Initial state
10.000254.00000098.0000001.000000Interm. step, due to the fast rxns: [0]
20.000503.21650096.4330001.783500
30.000752.59703895.1940772.402962Interm. step, due to the fast rxns: [0]
40.001002.10379494.2075892.896206
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" ], "text/plain": [ " SYSTEM TIME A B Y \\\n", "0 0.00000 5.000000 100.000000 0.000000 \n", "1 0.00025 4.000000 98.000000 1.000000 \n", "2 0.00050 3.216500 96.433000 1.783500 \n", "3 0.00075 2.597038 95.194077 2.402962 \n", "4 0.00100 2.103794 94.207589 2.896206 \n", ".. ... ... ... ... \n", "224 0.15600 2.291779 5.096036 47.451982 \n", "225 0.15700 2.293251 5.098980 47.450510 \n", "226 0.15800 2.294606 5.101691 47.449155 \n", "227 0.15900 2.295853 5.104185 47.447907 \n", "228 0.16000 2.297001 5.106481 47.446759 \n", "\n", " caption \n", "0 Initial state \n", "1 Interm. step, due to the fast rxns: [0] \n", "2 \n", "3 Interm. step, due to the fast rxns: [0] \n", "4 \n", ".. ... \n", "224 \n", "225 \n", "226 \n", "227 \n", "228 \n", "\n", "[229 rows x 5 columns]" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.single_compartment_react(time_step=0.001, n_steps=70,\n", " dynamic_substeps=2, rel_fast_threshold=15)\n", "\n", "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 21, "id": "88f744d6-17fb-4d03-b8cc-bb22b12555e0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + 2 B <-> Y\n", "Final concentrations: [Y] = 47.45 ; [A] = 2.297 ; [B] = 5.106\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.04505\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 1.126 %\n", "Reaction IS in equilibrium (within 2% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=2)" ] }, { "cell_type": "code", "execution_count": 22, "id": "cc34ca51-8ec3-4170-abc9-f9bccdd7ce00", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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FAhCAAAQgAAEIQAACEEgfAaQtfW3KGUEAAhCAAAQgAAEIQAACKSKAtKWoMTkVCEAAAhCAAAQgAAEIQCB9BJC29LUpZwQBCEAAAhCAAAQgAAEIpIgA0paixuRUIAABCEAAAhCAAAQgAIH0EUDa0temnBEEIAABCEAAAhCAAAQgkCICSFuKGpNTgQAEIAABCEAAAhCAAATSRwBpS1+bckYQgAAEIAABCEAAAhCAQIoIIG0pakxOBQIQgAAEIAABCEAAAhBIHwGkLX1tyhlBAAIQgAAEIAABCEAAAikigLSlqDE5FQhAAAIQgAAEIAABCEAgfQSQtvS1KWcEAQhAAAIQgAAEIAABCKSIANKWosbkVCAAAQhAAAIQgAAEIACB9BFA2tLXppwRBCAAAQhAAAIQgAAEIJAiAkhbihqTU4EABCAAAQhAAAIQgAAE0kcAaUtfm3JGEIAABCAAAQhAAAIQgECKCCBtKWpMTgUCEIAABCAAAQhAAAIQSB8BpC19bcoZQQACEIAABCAAAQhAAAIpIoC0pagxORUIQAACEIAABCAAAQhAIH0EkLb0tSlnBAEIQAACEIAABCAAAQikiADSlqLG5FQgAAEIQAACEIAABCAAgfQRQNrS16acEQQgAAEIQAACEIAABCCQIgJIW4oak1OBAAQgAAEIQAACEIAABNJHAGlLX5tyRhCAAAQgAAEIQAACEIBAigggbSlqTE4FAhCAAAQgAAEIQAACEEgfAaQtfW3KGUEAAhCAAAQgAAEIQAACKSKAtKWoMTkVCEAAAhCAAAQgAAEIQCB9BJC29LUpZwQBCEAAAhCAAAQgAAEIpIgA0paixuRUIAABCEAAAhCAAAQgAIH0EUDa0temnBEEIAABCEAAAhCAAAQgkCICSFsCjbm8YWMCUQiRSWD86BpZvbZNOru6gZMwgeoh5TJ86BBpWNeWcGTCGQKjhlfJpvZO2dDWCRAFAlvVDxU+dxXAOiGHVVdI1ZAKWdO8SaeAEo9aP7Jamje2S1t7V4mTSP70K8rLZGxdtaxsak0+OBFdAuazl2PwCCBtCbDn4iEBiAEhkDYdriYq0qbHFmnTZetdOPC5q8MZadPh6kVF2vT4Im16bL3ISJs+41wlIG0J8OfiIQGISJsOxCxRkTZd3Iy06fJlpE2PL9Kmx9ZERtr0+CJtemyRNn22NiUgbTaUQtIgbQlARNp0ICJtA8rVKwxp08WOtOnxRdr02CJtumyRNl2+JjojbfqMc5VQMtK2aMlSOenMi+W2ay6SaVOn9GFyzJwL5fU3l7l/22HyRFlw0yWRXkfadDox0yN1uJqojLTpsTWRkTZdvkibHl+kTY8t0qbLFmnT5Yu06fMNK6EkpG3G7LnSuGa9yyJT2k495wppaFzXK2pG4OrHjJQbrzrPTR/2ukmDtIV1s3ivI23xuNnkQtpsKMVPg7TFZ2eTE2mzoRQvDdIWj5ttLqZH2pKKng5pi84sag5G2qISSzZ9SUibQZZtpM0I3TfOOFFmz9rfJXvvAwvlyvm3y2P3znN/D3sdaUu2Q/qjIW16bJE2PbYmMtKmyxdp0+OLtOmxNZGRNj2+SJseWy8y0qbPOFcJJS1tQSLn/5sBlzmlMigPI206nRhp0+FqoiJtemyRNl22JjrSpscYadNji7TpskXadPl6n736pfSUkDnzbaDKTaKcXEuy8omPtGWsc4ssbauel/XDdhYpr8ynHcgbQKB2aKVsaO2U7m6e05Z0B6moKJOqygrZ2NaRdGjiOQRqqirc5wu2d/AsJo0OMWLYEFm/oV0jdMnHHFJZLubit3UTzxjU6AxDqytlU0endHbyvZY037KyMhlWUyEtG/leS5qtF8989iZ1mOVHTz27pE+4MaNG9M50GwxpM7PtLrz8ernk/NN7Z+DFOV+kLQ41X56wUTVvc5LI0nZlmWycdZd0bHd0njUkeyYBpE2vTyBtemxNZKRNly/SpscXadNjayIjbXp8kTY9tklL224z54hf0Lz4RuTGjx0tl337S4y0BTRnSY+0GR5Ba9aMZS9+5CYXV9jrYqRtu+Ol6cBb9N8tJVYC0yP1GpzpkXpsTWTWtOnyZXqkHl+mR+qxNZFZ06bHl+mRemy9yEmsaTNi9trSd3pH1LLV2htpM697I3LZRM8/YuffcNBcw++/9zRZ+PSi3g0JzzjlaNlm4jh3RM07vDxBAzyZI4Im/9zTjnM3KswcKfTcgZG2PPtiNoBhu0OGvS437Cjdzcul8eN3SduWM/OsJdn9BJA2vf6AtOmxRdp02ZroSJseY6RNjy3SpssWadPl63325luKGWU7+tD93NG0XIf3OC5PkkxaI2E7Ttk66w7v8264W+bfcl+fgReze7wnZd7rmdMwTWzzuK9MV8gUTPP61dfd6ZZvXvv6Fz/V+xgxU99scfJl5uUviZE2/5b/5sQzTT2v57Q9/DWRZ38kzbvNlXUfuSKpdiGOQwBp0+sGSJseW6RNly3SpssXadPly0ibHl+kTY+tFznfkTZPimzWjAWtabvg0p/LS6++FShYXh3NNf8JRx3kjoZ5I22eIAYN4JiYZiTO7BoftETKpq6mbCOEd9z/cL84mc+GzqeVSkLa8gEUmveth6T77iOlc/g27mhbR91OoVlIYEcAabPjFCcV0haHmn0epkfas4qTkpG2ONTs8iBtdpzipkLa4pILz4e0hTPKN0UhSZu3aUjQOXmjc9mkzS9i2WTrjbeWu1MovSmPQeVkDgqZNCY90yPz7WmK+Vvvmi01by1wRtouc0bczlYsqbRCI2167Y206bE1kZE2Xb5Imx5fpE2PrYmMtOnxRdr02HqR85U2EyfK9Mj6MSN7p0KavP6RNk/awqTKrGnLHGlLQtrMeUzfc2pv/fxTM5E2/b4Yu4Q1T14ro/5+hrRNOMAdbeseMjx2LDJuJoC06fUGpE2PLdKmy9ZER9r0GCNtemyRNl22SJsuX++zN99SwjYiMWKWbffIoOmRuaYv5jPSZs7TPKs5KH6QMCJt+faMAcq//L31MuHOHaV840ppmvlr2Tj52AEqOd3FIG167Yu06bFF2nTZIm26fJE2Xb6MtOnxRdr02HqRkxhpM7GCtvz3RMjbpCRsTZuJ4+3g6B9tM2I3fc9d3ees5SNtZi2aqUPjmnW9O116G5GYDUgyhc6ckzmYHqnfD/MqYXnDRqldMl/qnjpHuoaOl1VHP+n+y5EfAaQtP365ciNtemyRNl22SJsuX6RNly/SpscXadNjm7S0+YXLX2v/qJaNtGWL439sV9zpkd4GIv7NCk15Xh2NHN7358d7q2/W0Xk7VzI9Ur8vxi7BSJs56h+YJdUrHnU2I9lZVs96AHGLTbQnI9KWJ8Ac2ZE2PbZImy5bpE2XL9Kmyxdp0+OLtOmx1ZA2/dqmrwR2j0ygTT1pK9+0Vsb85XipWvm4s5vkJGk45F5X4DjiEUDa4nGzyYW02VCKn4aNSOKzs8nJmjYbSvHSIG3xuNnmQtpsSUVPh7RFZxY1R1LTI6OWS/oeAkhbAj3BkzYXaEez1D842xU3M0Wy4ZAF0j5mjwRKKb0QSJtemyNtemxNZKRNly/SpscXadNjayIjbXp8kTY9tl5kpE2fca4SkLYE+PulLVPcpLxSWnY+3dmc5JOyafx+CZRWOiGQNr22Rtr02CJtumxNdKRNjzHSpscWadNli7Tp8vU+e/VLoYRsBJC2BPpGprR54jbymW9L7SvX95bQWTtRNuxwirROms3omwV3pM0CUswkSFtMcJbZGGmzBBUzGdIWE5xFNqTNAlIeSRhpywNeSFakTY+tF5mRNn3GuUpA2hLgHyRtXtghq5+VYf++TWrevEcqWpZtFjhnzZuZNtlVNcpZ/7atdFfWSld1vXQOnSDd1XXSWTPemV5Z7/y9dJ/5hrQl0DmzhEDa9NiayEibLl+kTY8v0qbH1kRG2vT4Im16bJE2fbY2JSBtNpRC0uSSNn9Ws85t6Nv39hM4myp01RS2wJmpn00zbrA5Fes0SJs1qsgJkbbIyCJlQNoi4YqcGGmLjMw6A9JmjSpWQqQtFjarTEibFaa8EjHSlhe+vDMjbXkjFLGVNn9RQxpflMq1r0hZe4tUbFgm5e1rpaxtrVQ0vyXlzmYm5a0N7sO6yzpbE6ihfoi2CQdIg/OYgyQPpC1Jmn1jIW16bE1kpE2XL9Kmxxdp02NrIiNtenyRNj22XmSkTZ9xrhKQtgT4x5G2qMW6AtdReAI3ZO1LMuah492pnu85DxVP8kDakqSJtOnR7B8ZadOljbTp8UXa9NgibbpskTZdviY60qbPGGlTZjwQ0qZ8CrHDV655Wcbdu6f7PLpVxz4XO05QRqQtUZx9gjHSpsfWREbadPkibXp8kTY9tkibLlukTZcv0qbPN6wERtrCCFm8XsrSVtHyjoy/cyfpHDZRVp7wmgUt+yRImz2rqCmRtqjEoqVH2qLxipoaaYtKzD490mbPKk5KpkfGoWaXB2mz45RPqlIYadtt5hzZYfJEWXDTJfmgUsmLtCWAtZSlrbytSSbcOtHZ+XKUrDh5eQI0N4dA2hLF2ScY0qbH1kRG2nT5Im16fJE2PbYmMtKmxxdp02PrRU67tM274W556LF/SuOadfKzy74u06ZO0YcaoQSkLQKsbElLWdrKOjfJhF9v4aJZ8Zn3pLuiKgGiPSGQtsRQ9guEtOmxRdp02ZroSJseY6RNjy3SpssWadPl63326pcyeCUcM+dCOXjGXvLc4tdk/NjRctm3vzR4lQkoGWlLoDlKWdoMvgm/2VLKN62VFZ9e7j53LqkDaUuKZP84SJseW6RNly3SpssXadPly0ibHl+kTY+tFznRkbZHHtGvcFAJM2cGlrtoyVI56cyL5bZrLpI33louV86/XR67d97g1DFLqUhbAs1R6tI2/s4d3QeHr/zUq9JZu3UCRHtCIG2JoewXCGnTY4u06bJF2nT5Im26fJE2Pb5Imx5bFWkbPVpkzRr9SmeW0NTkrGHoP8DgTY301rKZtW1G4AppiiTSlkB3KXVpG3f3B6Vy3avu7pFmF8mkDqQtKZL94yBtemyRNl22SJsuX6RNly/SpscXadNjqyJtBx2kX+GgEh5+OLBcb2rk3NOOc18/9ZwrCm6KJNKWQJcpdWnb4v6PypCG5+S9IxdK+9g9EyDaEwJpSwxlv0BImx5bpE2XLdKmyxdp0+WLtOnxRdr02KpIm351rUvwpkZmZhgzakRBTZFE2qybNHvCUpe2sX88VKpWLpTVh/1JNo2fkQBRpC0xiFkCIW26hNk9UpcvG5Ho8UXa9NiayEibHl+kTY9t2qUtc2qkd75miuQl558us2ftrw/XogSkzQJSWJJSl7YxDx0rNe/8SRoPuUdaJ34iDJf164y0WaOKnBBpi4wsUgakLRKuyImRtsjIrDMgbdaoYiVE2mJhs8qEtFlhyitRohuR5FWTZDPPmD1XTjjqIPGmRnrRzRRJc9x41XnJFhgzGtIWE5w/W6lL2+hHPitD37xbmg68RTZud3wCRHtCIG2JoewXCGnTY2siI226fJE2Pb5Imx5bExlp0+OLtOmx9SKnVdr0ySVTAtKWAMdSl7ZRC78sw16/RdZ8dL5s2PFzCRBF2hKDmCUQ0qZLGGnT5Yu06fFF2vTYIm26bJE2Xb4mOtKmzzhXCUhbAvxLXdrqnjpHapfMl7XTr5SWqWcmQBRpSwwi0qaNMjA+0qaLHWnT44u06bFF2nTZIm26fJE2fb5hJSBtYYQsXi91aRv5z+/I8EVXyrq9Lpbmad+0IGaXhOmRdpzipGKkLQ41+zxImz2rOCmRtjjU7PIgbXac4qZiemRccuH5kLZwRvmmYKQtX4L55Ufa8uPn5i51aRvxwuUy4rmLZf0Hzpf1H7ooAaI9IZC2xFD2C4S06bE1kZE2Xb5Imx5fpE2PrYmMtOnxRdr02HqRkTZ9xrlKQNoS4F/q0kPYli0AACAASURBVDZ88TwZ+cx50rLrWbJ27/9NgCjSlhjELIGQNl3CSJsuX6RNjy/SpscWadNli7Tp8jXRkTZ9xgMubWbrzMY16wPLXfzITYN7xgqll7q0DXv1Rhn1+FmyYacvyJr9fpoYYUbaEkPZLxDSpsfWREbadPkibXp8kTY9tkibLlukTZcv0qbPN6yExEfajplzodSPGVkwzzQIA5DE66UubUOX3i6jH/2Cs93/Cc62/8lJOdKWRO8MjoG06bFF2nTZehcOpf65q0UZadMi2xOX6ZF6fJE2PbZeZEba9BnnKiFxaSu0p4cPBN5Sv3ioeft3MuavJ0jrNkdI48fvTAw50pYYyn6BkDY9tkibLlukTZcv0qbLF2nT44u06bFF2vTZ2pSAtNlQCklT6tJW/e7DUv+nI6Rty5nS8Ik/JEC0JwTSlhhKpE0PZWBkpkfqAmd6pB5fpE2PrYmMtOnxRdr02CJt+mxtSkhc2sz0yINn7CVzTzvOpvxUpCl1aat672kZ+/uZsmmLj8jqI/6WWJsibYmhRNr0UCJtA8zWFIe06UFH2vTYIm26bJE2Xb7eZ69+KQNfwqIlS+WkMy/uV/Al558us2ftP/AVylJi4tJ27wML5cr5t8tj984rmJPUrkipS1tl00sybsGHpWP0rrLqmH8khhtpSwwl0qaHEmkbYLZImy5wpE2XLyNtenyRNj22XuS0rmnzpO22ay6SaVOnuKd7waU/l4VPLyoon0lc2syatlwHu0fqv6kGuoSK9W/K+N/uKp3DJ8nKTy5JrHikLTGUSJseSqRtgNkibbrAkTZdvkibHl+kTY9tKUqbGYS68PLrpZC8JXFp0+8yhVdCqY+0lbe+JxNumyRdNWNlxUlvJ9ZASFtiKJE2PZRI2wCzRdp0gSNtunyRNj2+SJseWxVp+88j+hUOKmGbmf3+GjTSduo5V7jpbrzqvMGpZ0CpSFsCTVHq0lbWuUG2vGUL6a6okXc/+55IWXkCVNmIJBGIWYKwe6QmXZ7TpkuXNW2afJE2TbpsRKJJF2nTpNsTO9HpkT8ZLdK2Rr/SmSWc1SRSParPX7OtaTvjlKMLao8OFWnzhhT9RAptMV+SvaTUpc2w3PLX46Wsfb28++kV0l01MhG8jLQlgjEwCNKmx9ZEZvdIXb5sRKLHF2nTY2siM9Kmxxdp02PrRU5U2u44SL/CQSWc8HC/vwaNtJXE9Mh5N9wt82+5T/yL+TwYhWasSfUWpE1kwu3bSfnGlbLyxKXSOXRCImiRtkQwIm16GLNGRtp0oSNtenyRNj22SJsuW6RNl6+Jnqi06VfXuoQgaTOZzT4dfp+xDqiUMPGRthmz58oJRx3UbzjRyNwd9z9cULuwJMUUaRMZ99vdpXL9Ull1/CLpGLF9ImiRtkQwIm16GJG2QWDrXTjwuasDH2nT4epFZaRNjy/SpsfWi1xK0uYNQqV6IxJjpUFTIQtxmDGp7s3Fg8gWC6bLkKZF8t7RT0r7mD0SQYu0JYIRadPDiLQNAlukTRc60qbLF2nT44u06bEtFWnLJFhIwmbqxkhbAn0caRMZ+4ePSdWqJ2X1YX+RTeP3TYAqG5EkAjFLENa0adJlTZsuXTYi0eSLtGnSZU2bJl2kTZNuT+y0jrTpk0umhMSljTVtyTRMsUWpf/BoqV72kDQccp+0TTw4keoz0pYIxsAgSJseWxOZNW26fFnTpscXadNjayIz0qbHF2nTY+tFRtr0GecqIXFpM4Wxe+TgNupglD7mrydJzdv3SeNBt0rrpGMSqQLSlghGpE0PY9bISJsudKRNjy/SpscWadNli7Tp8jXRkTZ9xgMubYN7SgNfOtMjRUY/droMfeM30jTjetm4/acTaQSkLRGMSJseRqRtENh6Fw587urAR9p0uHpRGWnT44u06bH1IiNt+oyRNmXGXDyI1D3xVal95XpZu++PpGXnLyZCHGlLBCPSpocRaRsEtkibLnSkTZcv0qbHF2nTY4u06bO1KSGx6ZFm10jzHDbzjLZcR6HtxGIDKSwN0iYy8pkLZPjiH8m6j1wqzbt9LQyZ1etImxWmWIlY0xYLm3Umpkdao4qVkOmRsbBZZULarDDFToS0xUYXmhFpC0WUdwJG2vJGmFeAxKQtr1oUeWakTWTE85e4P+s/eKH7k8SBtCVBMTgG0qbH1kRG2nT5Im16fJE2PbYmMtKmxxdp02PrRUba9BnnKiFxacv2nDYerj24Da1d+vB/XS0j/3GhO8pmRtuSOJC2JCgibXoUs0dG2nSpI216fJE2PbZImy5bpE2Xr4mOtOkzLghp4+Hag9vQ2qXXvnKds67tbGc92+nOurYfJ1Ic0pYIxsAgjLTpsTWRkTZdvkibHl+kTY8t0qbLFmnT5Yu06fMNK2HARtouuPTnsvDpRfLYvfPC6lR0rzM9UmTYG7+WUY990d050uwgmcSBtCVBMTgG0qbHFmnTZetdOPC5q8MZadPh6kVleqQeX6RNj60XmZE2fca5SkhE2oKeyxZU6CXnny6zZ+0/uGesUDoXDyI1by2QMQ+f7D6jzTyrLYkDaUuCItKmRzF7ZEbadKkz0qbHF2nTY2siI216fJE2PbZpl7YZs+fK/ntPk8u+/aVeiJ7b3HbNRTJt6hR9uBYlJCJt/nKyrWmzqEvRJkHaRKqXPST1Dx4tbVsdLA2H5t5B1LahkTZbUtHTMdIWnVmUHEhbFFrR0yJt0ZnZ5kDabEnFS4e0xeNmkwtps6GUX5q0jrQtWrJUTjrzYvHvcG9E7htnnFhQg02JS1t+3aE4cyNtIlUrH5exfzxYNo3fV1Yf9pdEGhJpSwRjYBCkTY+tiYy06fJF2vT4Im16bE1kpE2PL9Kmx9aLnFZpM+d36jlXuKd541XniVnStXJ1k/v/QjqQtgRaA2kTGdL4omxx3z7SPnqavHfMUwlQFUHaEsGItOlhzBoZadOFjrTp8UXa9NgibbpskTZdviZ6ktL2yJuP6Fc4oISZk2dmLdf/zOlCfK504tLmDTFmI1KIEPLtNUibSOW612Xc3XtIx4jtZdXxi/JF6uZH2hLBiLTpYUTaBoGtd+HA564OfKRNh6sXlZE2Pb5Imx5bL3KS0jb6itGypnWNfqUzSmg6r0lG1YwKLNeMsN3358fljFOOlrmnHTfgdQsrMHFp8xbzTd9zV7ly/u29u0UeM+dCOXjGXgUJIQxS2OtcPIhUrH9Lxv92qnQNHS8rTvx3GDKr15E2K0yxEjE9MhY260yMtFmjipWQkbZY2KwyIW1WmGInQtpiowvNiLSFIso7QZLSdtAvD8q7PnECPPz5h7Nm8waeCmnzEX9lE5c2byOS7SdtJV+54OpeaTO7sPglLg7oQs2DtImUta+XCbdvL9LdISsdaeuqqsu7uZC2vBFmDYC06bE1kZE2Xb5Imx5fpE2PrYmMtOnxRdr02HqRk5Q2/dpGL6Fkpc1s7W8EzpsOycO1o3eeYsthpkeaaZKrjn1WOup2ybv6SFveCJE2PYQ5IyNtuuCRNj2+SJseW6RNly3SpsvXREfa9BnnKiHxkTYzDXLXnSa5zzrw/5+Haw9uQw9E6WP/eKizi+RCafjEH6Rty5l5F4m05Y0QadNDiLQNElvvwoEZDjoNgLTpcPWiMtKmxxdp02PrRUba9BkPqLRlFmZG27yjUOeI5tsEXDz0EBz96Odk6NK7pOmAG2XjlJPyxcpGJHkTzB6A6ZGKcJ3QjLTp8mWkTY8v0qbH1kRG2vT4Im16bEtF2vQJ5ldC4iNt+VWnOHMjbT3tVvf0uVL70k9l3UculebdvpZ3YzLSljfCrAGQNj22JjLSpssXadPji7TpsUXadNkibbp8TfS0j7TpE8yvhMSlzduIxKxpK5UDaetp6eGLrpSR//yOI2xfdcTt8rybH2nLGyHSpocwZ2SkTRc80qbHF2nTY4u06bJF2nT5Im36fMNKQNrCCFm8jrT1QBr2+q9l1MIvysbtTpCmA2+yIJc7CdKWN0KkTQ8h0jZIbL0LBz53dRoAadPh6kVleqQeX6RNj60XmZE2fca5Skhc2tL8PLZsILl46CFTvfwvUv/no6RtwgHSMOuBvHs20pY3QqRNDyHSNkhskTZd8EibLl+kTY8v0qbHFmnTZ2tTQuLSZp5x4H8+m00lij0N0tbTgpVNL8m4BR92tvvf2dn2/7m8mxVpyxsh0qaHEGkbJLZImy54pE2XL9Kmxxdp02OLtOmztSkhcWnz7xYZVAHvuW02lSuWNEhbT0uVtzbK+DunSHdFjfOA7aXOv8PyakKkLS98OTOzEYkeWxOZNW26fFnTpscXadNjayIjbXp8kTY9tkibPlubEhKXNptC05YGadvcouPv2kUqmt+WVcf/SzpGTMmrqZG2vPAhbXr4QiMjbaGI8kqAtOWFL2dmpE2PLdKmyxZp0+VrorOmTZ9xrhISl7Zsu0fOu+FuueP+h+Wxe+cN7hkrlI60bYY69vcHStV7z8jqwx6STeP3y4s20pYXPqRND19oZKQtFFFeCZC2vPAhbXr4QiMz0haKKHYCpC02OuuMSJs1KpWEAyZt9z6wUC68/HpheqRKOxZM0DF/PVFq3r7f2T3yV84uksflVS+kLS98SJsevtDISFsoorwSIG154UPa9PCFRkbaQhHFToC0xUZnnRFps0alknDApO2CS38uC59eVHAjbZ5MZtL1y6XZEfP1N5e5SXaYPFEW3HRJn+SMtG3GUffE2VL7ynWydu8fSsuuX8mr0yJteeFD2vTwhUZG2kIR5ZUAacsLH9Kmhy80MtIWiih2AqQtNjrrjEibNSqVhIlIWzbxyazxJeefLoX20G1T9yvn355VJk895wppaFzXK2pG4OrHjJQbrzqv9/SQts0tPeKFy2TEc/8jzXucK+v2/H5enRZpywsf0qaHLzQy0haKKK8ESFte+JA2PXyhkZG2UESxEyBtsdFZZ0TarFGpJExE2vw1y7amTaX2CQQNk7YZs+fKN844sVc2g9IjbZsbYtirN8mox78iG3Y4Rdbsf21eLYS05YUPadPDFxoZaQtFlFcCpC0vfEibHr7QyEhbKKLYCZC22OisMyJt1qhUEiYubSq1VAwaNEroTY00z5w76cyL5bZrLpJpU3t2Qgz6G9K2uYFq3nlAxjx0nLRNPFgaDrkvr5ZD2vLCh7Tp4QuNjLSFIsorAdKWFz6kTQ9faGSkLRRR7ARIW2x01hmRNmtUKglLXtoyqfqnQ9pK2/oN7SqNU4xBK1Y/J8PunC5d9dOk5YR/5nUKtUMrZUNrp3R3d+cVh8z9CVRUlElVZYVsbOsAjwKBmqoK6ezqlvaOrn7RO7o6ZPn6ZdLc3iwNG1dLW0errGxZmWgtWjY5sVsbEo25tm2trG1d0xuzsrxSthoxMXYZtUNqpX7o2Fj5Dd+6IWOlurImVn6TadLIybHz1lbFr3vsQgco45DKcjEXv62bOgeoxNIqZmh1pWzq6JTOTr7Xkm75srIyGVZTIS0b+V5Lmq0Xb8SwIVqhiWtBQEXazJTCxjXrA4sv9N0jPVEz9UTaLHpQRpKylndl+M2TpLtmC2n+/FvOE7crowd5PwfSFhtdaEakLRSRdYKlTW/IsuZ3pGFDg7Q4IrZs/TvSJe3yn3XvyPq29e7fjZwZSTOyZqSNo7QJGFk14hf3yBTO2qrhjgDX9wlXVzNK6qrr+vytvqbeKXd4n78Z8TYC7h2VFeUyZfRkadu0+YZDhfP6xDwEPe55pjEf0qbXqkibHlukTZ+tTQmJS1vQRh02FSmUNJmPJgha05b56AKmR/ZtvS1/NU7KOpplxUn/kS7nIiHuwfTIuOTC81UPKZfhQ4dIw7q28MSk6CVgpOzp5U/Ik8sfk8eXPSrPrng6Mp1xw8bLsCHDZcvhPaNU5oLZ+3/kYFkymFGsMXm894LCjqiq6yMBHV2dsqKlZ1fdOEdLe4s0xhwNNA+AfqtpmbR2xO+/76x3birFPEw/aNyY7EhmzKoMWrZapw+PyRDFkU4fGVk9qk+dTBqT1n+Y90B1RXWfv209Yts+vxtR3Or994j3QnVFjWzh5PUfdU55IzPkdNCgWBTM9EgLSDGTMD0yJrgI2ZgeGQGWQtLEpa3YNiIxUuZ/4HemdLJ7ZPReN27Bh6Wy6SVZfcQjsmmLvaMHeD8H0hYbXWhGpC0UUW8CI2aPvP2gPPbOw66kZY6UmYvSyXXbu+JlLk63cS4+62tHOoIzRoZXjnH+Vitbj5jkvpZ5kWtfC1L6CRT7mjYjfEb84h6ZwukKsDOa6z/MdNb1m9b2+ZuRZJPWf7zb3Hf01xloc0aJ35Yu37R00+dNumI5MkUxSPZsz8W9ARJzGq+5cWLy+w/bkTYjp5lia1vnbUZOsk3aJ11FWfwbSGaqspHxwTyQNn36SJs+41wllLy0+Z/BZkBN33Nqn+38zd94Tlu0Tjpq4Zdk2Ou/krX7XC0tu3w5WmZfaqQtNrrQjEhbbkRtna3y25dvk5sWzZfFq1/sTWxGxfYYt6fsN/EA2WerGbL3Vvv2G0UwidmIJLQL5pWg2KUtr5NXzmxGMauGVMia5k05SwoabVznSOK6ts3rHk2AIEE1AtjZ3XfN3H/Wv92nvE6z9jNDFDeYEc6M0dm1TnnrHEHlgEC+BOLKbr7lFlP+t7/+ZjFVN3V1TVzajOAcPGMvmXvacamDle2EmB7Zl8zwRf8nI//5XWmZeqasnX5l7H6AtMVGF5oRacuOyIymff0vX5bXm15xE5kv8llTjnIlbcY2BwVKWmY0pC20C+aVAGnLC1/OzLbSpleD/COv2rDS3eDHO8xNmPecv8U5gkYxbeMYwdyQMbJpO9LmnkNnvOm//1kXb+pvZ3f8EVXD29SZI90Eur/LBjqD2cKJS1vYc88G82S1ykba+pKtefNeGfPIp/Pe9h9p0+qxIkhbf7Zm5OCyJy6SX7w4v1fWvrf//8rBkw/rs1GDTasgbTaU4qdB2uKzC8uZBmkLO8fBfJ01bXr0850eGVd29c6o8CJP326XwqtUCdUocWkza9pyHYW+e2Sctkfa+lIz69nMurbO4dvKquOel+7yeNtyI21xeqNdHqStL6cnnE1F5j54mrtux0yBPP0DZ8m39rnIWVMSr+8ibXb9MG4qpC0uufB8SFs4o3xSIG350MudN19p06tZeiKzpm1w2zJxaRvc0xmc0pG2vtzLutpl3N0flIrmf8t7xzwl7aOnxWoYpC0WNqtMSNtmTE8vf1w+e/9sd2OI3cbuIf/3sZ/JB5x1a/kcSFs+9MLzIm3hjOKmQNrikrPLh7TZcYqTCmmLQy1aHqQtGq+kUyNtCRBF2vpDrH9otlS/82dpOvAW2bjd8bEoI22xsFllGmxp09yNzqxBaWrtu5NeNihmDca5f/0vV9i+sMcZYqZD+p9ZZQUzIBHSFpecXT6kzY5TnFRIWxxq9nmQNntWUVMibVGJRU+PtEVnlmQOFWnz77Z4yfmny+xZ+4uZNhm0M2OSJzNYsZC2/uTrnvmW1C7+iaz/0Hdk/QcuiNU0pSJtQburmUXzZvG8/zA7qZkd1fzHOxk7rnU4O7Jlbs0dtAtbe5dZmL+qz7bepfzsqS9+8CxX2JI6kLakSAbHQdr0+CJtemxNZKRNjy/SpsfWi4y06TPOVULi0uZ/zpn/wdTzbrhb7rj/4T7PRBvcU0+udKStP8val6+TuifPlo1TTpKmA26MBbtQpc3bmcw8K8k83Pe9DSvEeyaSt+OXWdActGMZ21P3dAWNB0p7ncw8F2l0zVjrPmemQn7no5dap7dJiLTZUIqfBmmLzy4sJ9IWRii/15G2/Pjlyo206bFF2vTZ2pSQuLSZEbXbrrlIpk2dIn5pM7tKXnj59cJGJDbNUvxpqt99ROr/dLi0j91T3jtyYawTGghpM6NS5sdIV5h8aQlX5oNgDayeB6v23QTDPLjUPMDUf5gHOleWVfT529bOw539R4WzscZWTjr/Mbx6mGxXP1Ga1m9+FhMPf47VTQMzIW3JsQyKhLTp8UXa9NiayEibHl+kTY8t0qbP1qaExKXNiNrPLvt6P2ljpM2mOdKTpmLDcnczEikrk1XHPi+dw7aMfHJJSZsZ8fr3mqXyhvPcrVcaX5KXnZ8317zhPIfr1X5TEG0q6UmWESYjVuZfM7ozpqbeGeGpd//vf80fs656lIysrrMpRjXNYK9pUz25AgiOtOk2AtKmxxdp02OLtOmyRdp0+ZroTI/UZ5yrhMSl7YJLfy4Ln17kToP0Rtq2n7SVnHTmxXL0ofvJZd/+0uCesULpTI8Mhjrung9J5dpX3JE2M+IW9YgqbWZNlhGxVxoWyxtrXnMfjmx+9x6SHFS+EbAtayfKmKFjQ+UrTSNRSFvU3hgtPdIWjVfU1EhbVGL26ZE2e1ZxUjLSFoeaXR6kzY5TPqmQtnzo5Z83cWkzVfKmQvqrd8YpR8vc047Lv8YFGAFpC26U0Y+dJkPfuFXWTr9KWqaeEbnlwqRt8eoX5fF3HpUnlz8m5v+5Hoy5w+idZYfRO8nkuu1l+1E7yS71uzq/71wQo16RwSSQAWlLAGKOEEibLl+kTY8v0qbH1kRG2vT4Im16bL3ISJs+41wlqEjb4J7SwJeOtAUzH7r0Vhn96GnSuu3R0vix2yI3TJC0GTn7/Rv3yoJX75Q3177RJ6aZdridI2VGxnYaM9X910iakbUktnGPfAIFnAFp020cpE2XL9Kmxxdp02OLtOmyRdp0+ZroSJs+4wGVtlPPuUKeenZJvw1H2PJ/cBtaq/Qh/3pR6r75VekaN14ab769TzEVzW/J2D98XMq6Nsnqwx6UjrqdI1XDk7YXV70QKGpmuuKsKUfJgdseLHtvuZ9sM3JSpPilnBhp0219pE2XL9Kmxxdp02OLtOmyRdp0+SJt+nzDSkh8pM2sYzvhqIP6TYVkI5KwpijO16v//qjUHzNLOredJCsdWc88Rv/tczL033fJmv1+Jht2mmN9kmZHx3ve+KX8ZtGtziYim0fUPFE7fPvZctCkQ/rtsGhdQIknRNp0OwDSpssXadPji7TpsUXadNkibbp8kTZ9vmElJC5tZkTNe6C2v3C2/A9riuJ83ZM2qayU5SvW9TuJ2pfnO89rO0c2bP8ZWTPjutCTNLJ22RMXyYLX7pSO9x8kbTYLMSNqR+/wSdl34gFMdQylGJ4AaQtnlE8KpC0feuF5kbZwRnFTIG1xydnlY02bHac4qZC2ONSi5WF6ZDReSadOXNoYaUu6iQo7Xq+0OdVc8ca70lXXdzv7IY0vOFMkD5aumnGy+vAHna3/t8p6QncsuUW+u/Bbss55ZppZg/aZaZ+VI6Z8SqZvOQNRS7gbIG0JA80Ih7Tp8kXa9PgibXpsTWSkTY8v0qbH1ouMtOkzzlVC4tJmpkHOv+W+3gdsm8IXLVnqbvmf1h0kS3kjEr+0rXriOenYsf+6tfoHj5bqZQ9J04E3y8btPtmvPzZubJBzH/6KPLD0fve1I3Y4Vn5wwFUybeIkWb22TTq7ugf3XZLC0pE23UZF2nT5Im16fJE2PbZImy5bpE2Xr4mOtOkzHlBpM4UFbfkfNGVycE89udKRtlkuzIYFD0jbRw/oB3bE85fJiOf/R1p2+bKs3efqPq/f+tJNcsu/rpcXVj0ru43dQ07Z/XT3xxxhW/4n14KlFwlp021zpE2XL9Kmxxdp02OLtOmyRdp0+SJt+nzDSkh8pC2swDS+jrT1SFvTNTfIxk+d3K+Jq1f8TeofOEzaR09zp0h2DxkprzQucWTtOrll8Q3S0dkun9rls/I5R9b2nLB3b36kTe/dgrTpsTWRkTZdvkibHl+kTY8t0qbLFmnT5Yu06fMNKwFpCyNk8TrS1iNta3/wv9Jyxln9iJV1tUu9s/V/1ep/SOPBd8vbYz4kR981030YttkN8jsfvbR3dM2fGWmz6HwxkyBtMcFZZkPaLEHFTIa0xQRnkQ1ps4CURxLWtOUBLyQr0qbH1ovM9Eh9xrlKUJE2sxlJ45r1geUufuSmwT1jhdKRth5paz77m7LuOxcHEh75zPkyfPGP5Y1dzpRZb/xVXm96xR1V+9mhv8z6fDWkTaGzvh8SadNjayIjbbp8kTY9vkibHlsTGWnT44u06bFF2vTZ2pSQuLQdM+dCqR8zUm686jyb8lORBmnrkbYNJ58ia+ZdG9imNW/fJ+V/OUn22TRUXmnf6Arbbcf8zh1py3YgbXpvD6RNjy3SpsvWREfa9BgjbXpskTZdtkibLl/vs1e/FErIRiBxacv2nLY0NwHS1iNtbQd+TBp++7vApi5vfU++e+s0+XnLOtlxxDZyx6celXHDxufsFkib3rsGadNji7TpskXadPkibbp8GWnT44u06bH1IjM9Up9xrhKQtgT4I2090ta++x7y3iNPBhL9879/L+c88FkZ2tUmP939FNn7wOAROX9mpC2BzpklBNKmxxZp02WLtOnyRdp0+SJtenyRNj22SJs+W5sSEpc2Mz3y4Bl7ydzTjrMpPxVpkLYeaesaN15WvPTvfm1qHpb99b98yX0O239XiVw0wZG7o4PlDmkbmLcE0qbLmTVtunyZHqnHF2nTY2siI216fJE2PbZImz5bmxISlzbzjLYr598uj907z6b8VKRB2nqkzRzLV2/o16bXPT9PvrfwPNl3y73lFxVtsvOaF2TN/tfJhh0+k7P9GWnTe3sgbXpsTWSkTZcv0qbHF2nTY4u06bJF2nT5muhMj9RnnKuExKXNrGnLdbB75OA2eNKlV//9Uak/ZrO0rXzxNencamJvMS++95yc85cvy8urF8vVB18rX+h4T0b+40Jp3eZIaTzoVpHyiqxVQtqSbq3N8ZA2PbZImy5b78KhlG+WaRJG2jTpMtKmSRdp06TbExtp02c8oNI2uKczOKWX8sVDw1ox8gAAIABJREFUprSZNW1mbZt3/Pej58gvXpwvJ+82R3540M+kovnfMuYvJ8uQphelaeavZePkY5G2Qei2SNtm6JVLXpKOqbsm2gqMtCWKs18wRtr0+CJtemxNZKZH6vFF2vTYepGRNn3GSJsyY6Rt80hbw+0LpO3jh7jEn17+uBx798Hutv5/+8xzsuXwnhG4Ec9f4v60TThAGmY9gLQp98+g8EhbD5UtDt5fhjz/rLTMOV3WXn6VSGVlIq2BtCWCMWsQpE2PL9KmxxZp02WLtOnyNdGRNn3GAy5tZl3bhZdf36fcS84/XWbP2n9wz1apdKRts7SZ57SZ57WZ46i7ZsqzK56W73z0UjnjQ1/rpV++aa2Mu2sXMf+u+aiTfsee9JkH0yOVOqwTFmnrYbvV2GG9kFsPP0qarrlBumuzPzvQtkWQNltS8dIhbfG42eRC2mwoxU/DSFt8dmE5kbYwQvm/jrTlzzCfCImvaZt3w90y/5b75LZrLpJpU6e4dVu0ZKmcdObFcsYpR6dyV0mkbbO0rb/gIln/jfPlmXefkBPuOVy2Hrmt+xDtic6z2fxH7cs/l7onvybtY3aTtfv8RDaNm4605fNOjpgXaesrbUbUylqaZdM++0njjb92d0LN50Da8qEXnhdpC2cUNwXSFpecXT6kzY5TnFRIWxxq0fIgbdF4JZ06cWmbMXuunHDUQf3kzMjcHfc/nMpdJZG2zdLWcsZZsvYH/ytXPX2JXOn8fG73L8plM3/Ur9+WdbVL3RNzZdhrNzu7SJ4ia/edJ90VzvMAfAcjbUm/3TfHQ9r6Stuqx/4hY48/QspXrZSOHXeWNVf/1BW4uAfSFpecXT6kzY5TnFRIWxxq9nmQNntWUVMibVGJRU+PtEVnlmSOxKXN7B4ZNBXSmzLJ7pFJNt/gx8rciGTjsZ+SVfOvkxPvPUKeevfvct1ht8rh2x8TWNGqVU854naWsynJYlk7/SppmXoG0jZATYq09ZU286iKiuXLpP74I6XytVfcF810yeavnB1L3pA23Y6MtOnxRdr02JrISJseX6RNj60XGWnTZ5yrhMSljZG2wW3QgS49U9raPnqA3Pnjc+SU+2fLB8ftJbfN/r2MqBqZtVq1S66Ruqe+Ie2jnWmS+znTJLfYPE2SkTa91kTa+kub+Uv52rUy/KorZPi1PxHp6HATmUdYtB59rGw8cra1wCFten3XREba9PgibXpskTZdtkibLl/vs1e/FErIRiBxaWNNW2l1Nk/azBogd2rZdtvLWVcfKdc+/yOZu9e5cv6+388JpKyrTer+fpYMe+PXPdMk93OmSZb3TJNE2vT6EtIWLG0e8cp/vyG1N1wrNffd447AeYcncK2HzJL2D+4lXXV1gY2EtOn1XaRNly3SpsuXkTY9vkibHlsvMiNt+oxzlZC4tJnC2D1ycBt1IEv3pM2sAzLTysyGDhO+WyurNqyUP5ywUD4wbs/Q6lS0LJMtFnzY3U1y3Ycvlebde3aaRNpC0cVOgLTlljY/2KonH5ehv7tXav5wv1S8/VYf5kbiOredJJ3OTQtz46JrTL10brOtDJ20tWyq30JaRm+R96YmsRs5xRkZadNrXKRNj62JjLTp8UXa9NgibfpsbUpQkTabgtOUho1IZomZFjnEkbbnK1bKXl8W2XbkZHno5KfdZ7TZHMNeu0VG/d3J6BxNB/5SNm73KaTNBlzMNEibvbT5EQ/514sy9J67pPpvf3VuUrzq7jhpcxi5c6XOuanR7YzOddWNCs1m5C/s6BpZ58aLenSOmyBSUx01W8GkNxe+DevaCqY+NhVp3/0DWUdmbfIPVBqkTZc00qbHF2nTY4u06bO1KSFxaTv1nCvkqWeXSOaGI2aDkul7TpUbrzrPpl5FlQZp65E2c/F42/L75QuzRQ7d7gj5xRF3RmrHES9cLiOeu9hZWFQpTTNukJF7niKr17ZJZ1d3pDgkDieAtMWTtkyyZuSt8j9vSbkzhbK8oUEq3lvlThOuXva2yOrVUrZyhft3Dgg0LHjA/Zws9ANp020hpE2PL9KmxxZp02drU0Li0sZGJDbY05PGmx5pLkbaPnawfP/pi+SqfUXO/sj58q3pF0U+0bqnzpHaJfPdfN3T/1tWTT1POqUichwy5CaAtCUjbdko91nT5mxoYtbFVTgyV9bW6kpc6Ahdh9Pr3928li5bOeWNJlZL5O5esWqFsz1mcY1U+U/S9N+29q7I5z0YGYb86wV3gxukbTDoF16ZSJtemyBtemyRNn22NiUkLm1s+W+DPT1p/NLW/K1vy8m/nSUPOs9Un/+JW+SoHY+PfqJdHTL8pXkyfPGPpXzjStm442elede5zu6S06LHIkdWAkjbAEob/TBxAsW0pq3+mFliPieRtsS7QVEGRNr0mg1p02OLtOmztSkhcWljpM0Ge3rS+KXt1RvmyyHX7yqNw0QeOv7vssPED8U+0aH/vkNGvfwTZ3rZP6Rty4OkZbe50rr15od4xw5MRpcA0oa0FfNbAWnTaz2mR+qxNZGRNj2+SJseW6RNn61NCYlLG1v+22BPTxq/tC346XnuQ7X3fFfkwQPuktZPHJ7XiU5oeUban/6hVL91v3SM3FFadv+qtOx0Wl4xydxDAGlD2or5vVBM0jbmcye6O4823ny7+8D2Qj+QNt0WQtr0+CJtemyRNn22NiUkLm2mULb8t0GfjjR+abv8+0fK9xZ+Sz7/vMiPd/ueNH/9W3mdpNnyv6HRedjx378qw16/xY3VPO2bsu5Dzlo5Z7MSjvgEkDakLX7vGfycSJteGyBtemxNZKRNjy/SpscWadNna1OCirTZFJymNOwe2bN75Oe/OlluX3KzXPknkTMnfFKarrs5r2b2P6fNbE5S94wjgc6at466nWXt9CulbauP5RW/lDMjbUhbMfd/pE2v9ZA2PbZImy5bpE2Xr4nOw7X1GecqAWlLgD/S1iNt0z/TLC+selb+7AyKHVQ5VVY9+rRIRfydHzMfrl39zoMy6smvSkVzzwOO28fsIc27ne0+042Rt2gdGWlD2qL1mMJKjbTptQfSpscWadNli7Tp8kXa9PmGlYC0hRGyeB1pmyXLD9pXJh74hFRX1EjTDytl6NpmWfXEc9Kx484WBIOTZEqbSVXW2SrD//X/pPbla93dJc3RNXS8s8Pkf8mGnb8oXVXRHzQcu4JFnBFpQ9qKuPu6d3uL5XOX3SOLuaclX3emRybP1IuItOmx9SIz0qbPOFcJSFsC/Ivl4iGBU+0XwlvT9s9P7Ckf3vdZ2WnMVHn2uf2l9hfXSfNXzpZ1F18Wu9ggaev9cN6wXGr+83vn53diRuDM0Tl8O2nd9gjn50hpm1D4D7GNDSaBjEgb0pZANxq0EMUkbWxEMmjdpCALRtr0mgVp02OLtOmztSkBabOhFJIGaZslfzxqmhy+1yLZd+IBcv+Ic6T+M8dLx+Qp0vibu6Rj+x1jUc4lbf6A1cv/KrUv/VRq3vlj759btz3K2WnydGfd20FMnQygj7QhbbHelAWSCWnTawimR+qxNZGRNj2+SJseW6RNn61NCUibDSWkLSsBb6Tt5uN3kc9Pe9l9oLZ5sLZ3d9mMtJkRtziHrbR5sSvXv+HK27BXb3KnUZqjq6beeb7b4bJp/P7u6FvniElxqpK6PEgb0lbMnRpp02s9pE2PLdKmyxZp0+VrojM9Up9xrhKQtgT4M9I2S3548vZy7s5vyBf2OEN+cMBVMuzXv5RRZ58pm/abIQ3OaFv38BGRSUeVNq+A8k1rpXbJNVLz1r0ypPHFPuV2Dp/kylupSxzShrRFfkMWUAakTa8xkDY9tkibLlukTZcv0qbPN6wEpC2MkMXrSNssOX/OtnLF5Lfl3Onfka995AIpX/2ejPnMJ6Xqn89I07W/kI3Hn2hBsm+SuNLmj1K59hV3zVv1ysekasWjYoTOf3TWTpRN4/aTTRNmODI3w32cQCkcSBvSVsz9HGnTaz2kTY8t0qbLFmnT5Yu06fMNKwFpCyNk8TrSNktO/eIE+cXEFXLFQfPks7ud5lIbceXlMuKyi2XjsZ9yntn2SwuSyUtbZqFm5K3q3UezSpyZTtk+dk9X3jqGT3GnU3bUTnL+3Va6K4dHPodCzYC0IW2F2jdt6oW02VCKlwZpi8fNNhdr2mxJRU+HtEVnFjUH0yOjEks2PdKWAE+kbZYcdVa9/G5sg1x/+G1y2JSjXapDFi9yR9vKm5qk8dd3Stv+B0aincRIW1iBlU0vSfWqx51RuMek2ozEvf8YgaB8Rug6Rmzv7FLpSJz7s22P0NVNcf8tpmfFIW1IW9h7o5BfR9r0Wgdp02NrIiNtenyRNj22XmSkTZ9xrhKQtgT4I22zZJ+vj5Sn6tbJPcc9JHtvtV8v1bpvfU1qb/y5NJ85V9b9zxWRaA+EtGVWqKJlmQxpeFaGNC2Wipa3nQd5Oz/r35LKFueB3l0dOetvplp6Qtcxwhmlq93WHanrrB7rjNLVStew8dLtPMeuEA6kDWkrhH4Ytw5IW1xy4fmQtnBG+aRA2vKhlzsv0qbHFmnTZ2tTAtJmQykkDdI2S6acN1T+PXSjPPbZF2TKqM1b/Ff/5cGe7f+3neyOtkV52PZgSFuupjZCZ3aoNBLnCZ37e7P5fZl1TzIjdmaqZfeQWlfopLJaOmsmuPnN6J3777CJzpPEK5wHh78vfFWjpGtInZOvxn2YeL4H0oa05duHBjM/0qZHH2nTY2siI216fJE2PbZImz5bmxKQNhtKSFtWAmbL/6GfnCXjz6+QtqoKefHUt2RkdV2f9GOPPFiqnnxc1n3nYmk++5vWxAtN2nJW3BmFM6Nx7qjc+qU9I3SOzJnplhXOj3kEQcUGR+xCRuus4ZRX9oidETxnhK+7rNKVOTOS1+3wN4LX81qPBHY76bucdN4xpLJchlZVyroNm3r/5k7xzHGYcoppCqgNy63GDnOTLV+9wSa5dZpRw6tkU3unbGjrtM5DQnsCxSRt9cfMEvM52bDgAWn76AH2JzlIKZE2XfBImx5fpE2PrReZ6ZH6jHOVgLQlwL/UR9qaPz9LJn9NZMvhE+Ufc17rR7T6b3+V+uOPdEaUKuW9Bx6R9g/uaUW9qKTN6ox6EhmRK+tolfL2tc5ulmuc/7c4f1vtmFVnj9g5h5E+99/WFSIdbVLRtlrK2luctM1S3toQobSBS+pJY7YSO9+XymyveyOQ2V73y2hgGmdk0hNZ27MeNffLIs6GosufQNpsmRVCOqRNrxWQNj22JjLSpscXadNji7Tps7UpAWmzoRSSptSlbelXZsneXxSZtsUH5YETHw+kNfJ/LpLhP/qhtB1wkKy94iqraZJplbYEupw7cle+YaUbyl1v5xzlzhTNMmckr7ytwRVBV/rel7+ybufvvimc5WXOaxVl0t7R3VudSmdkMNdhRg5TebSJrPjCu9JV1XeEOJ9zZaQtH3rheYtJ2sZ87kSp+cP90njz7dJ6+FHhJzfIKZA23QZA2vT4Im16bJE2fbY2JSBtNpSQtqwEzLSfJ8+dJUd+WuSgSYfIr45aEJi2rK1Vxn5ipgz514uyaZ/9pOH2e6W7NvcW+khbAp0zSwiNNW3uur4c0z8rWnumiWY7vBHIrK/7ZDQwjRmpjLC20MQYtvAWEWc54foPXuj+JHUgbUmRDI5TTNLG9EjdvlBs0ZE2vRZD2vTYIm36bG1KQNpsKCFtOaXtvu85z2k7RuSTO39afnTI9VnTVi55ScYef4SUr1ppJW5IWwKdcwClTa+2epG3+qizpu3zzgzUcVOlceavpGPU1EQKQ9oSwZg1CNKmx5eRNj22JjLSpscXadNji7Tps7UpAWmzoYS05ZS26/9vlpx/sMiXP3i2XLT/ZTlp1Tz4gAy/6gqpeuYpaT3sSFn/jfOzrnFD2hLonEhbTojuRiQnOUk+7Iy2feg7sv4DFyQCHWlLBGMqpI3pkbp9odiiI216LYa06bFF2vTZ2pSAtNlQQtpyStulP5slV+0rcuF+P5Cv7HlOKNHqRx+W4Vde4e6o1vaxg2X9Oee7I2+ZB9IWijJ2Ao3pkbErM4gZXWnbyqmA023NmrZVxz6fyCMVkDbdRi2mkTakTbcvFFt0pE2vxZA2PbZImz5bmxKQNhtKSFtOafvaL2fJr/YQufrj18oJU0+xImqmSI51tsKufO0V6dx2kqyZd22/7bCRNiuUsRIhbT3YvC3/237zMale/ldpm3CANBz6u7wfbYC0xeqW1pmKSdpY02bdrCWREGnTa2akTY8t0qbP1qYEpM2GEtKWU9o+c9cs+dP2IrccdY98bNInrIkacas/4Rh3cxJztMw5XdZ/60LpGtfz8GikzRpl5IRIW19pW734z1L31LkypPEFad7jW7Juz+9FZurPgLTlhS80M9IWiih2Ata0xUZnlRFps8IUKxHSFgtbpEw8py0SrsQTI20JIC31Lf8P+eMsec7Zge8PJyyUD4yzewZbL/aODhnhrHEzP+L8v7u6RjZ84XRp/srZMna37WX12jbp7Nq8LX0CzUUIhwDS1lfazMO1h712i4x85lznsQmdsnbv/5MNO82J3VeQttjorDIibVaYYiVC2mJhs86EtFmjipwQaYuMLHIGpC0yskQzIG0J4Cx1afvA32bJspEiT33uZdl65LaxiJrRthH/e4n7PCP3cB7E3f2Zz0rD3G/KpslTYsUkU3YCSFt/aTN/GfH8D5yfS6Vj9K6OuDnPFdxyZqxuhLTFwmadCWmzRhU5IdIWGVmkDEhbJFyREiNtkXDFSoy0xcKWWCakLQGUpSxtG//2B5n6/CelprtCnj9rldRUDs2LqJG32mt/KsPuvNUdeTPy1nroYdJy2pd71rw5v3PkTwBpC5a28rYmqXv6XBn6xm+kdZsj3BG3zhGTIwNH2iIji5QBaYuEK1JipC0SrsiJkbbIyKwzIG3WqGInRNpio0skI9KWAMZikbY258HGq1pWJnDGm0OsfuIPcuRr35CJrdXy9DebEotd+e83ZIubrhW5/noxD+Y2R1d9vWw86ljZdMBB0ubsNumtfUus0BIKhLQFS5v5a3lrg2xx/z7ug7pbtz1Kmg64Qborcz8IPrPrIG26byakTY8v0qbH1kRG2vT4utJWtV5Wv9egV0iBRa5oXSllzrXdQB31u9nvWzBQdSqlcpC2fFt7/nxZceAsK4Ew0vRu8zL5z7q3nJ+35Z1m58f5/3Lnbxvam6XRuViMchgBMzEL4dhr3Qi579vJCqHZiKTxtbdl6Lz/J0PvuVMqli/rc6pm10kz+ta+10ekbfp+0jF110JAURR1QNqyS5t5peq9p2XMX0+U8o0rpX3MHtL48d9KZ+1E67ZF2qxRxUqItMXCZpUJabPCZJ+oq8O9AeQdo4d1SWvTMmnv6AqNUbZprZS3rQlN509Q3tYgZR0tkfJUbHDq56zljXJUNL8VJbkrFhXO52mUo6yj2b2JxlFABL7BHgOD2RpIW770y8pk04f3loYFD7ibaPgPI2e/WnyDPL7sUVfOVm2I9oGVb9Uy81eWV8qWw+0vPG3KL2ttFbML5N6tW8jVP4j2IR4WP3P3yKonH5eqpx6X6scfk6onn5CyluY+Ibrq6mSTI2+bpu/r/tv+oT37tUlYmaXyOtLW09Lelv9mI5J+75f1b8iYhz4plWtfke4KZ4OcXZzdTXf/htVz3JA23XcS0qbHN43SZi78y5wbo95hxKbcEYLe3x2ZKOvYfAO03B29aOt9PVNqMoWl0i8w3X0lTa+liBxIYOhY6ayoLRk4nUPHu99PA3VUf+ZvA1UU5QQQQNry7RY77ijy+uuy8VMnS9M1N7jRnl3xtMx//kfyp6X3S4dzl807aocMd6XJ+9lmxLaytfNjfh9ZPUrG1NRHqs242vFSPYBv1qDKmQdkm+cQmREvI65JHjm3/HfWuw15+SWpWvhoj8Q5MlfekHFHzln/1rHjTtK+y27SNX68dG65lXRuNdEdFe3YZpL7/1JdI4e0hUubSVHu3Omue/wrMvTNe9wMtvKGtCX5SdA/FtKmx3cgpM2TKL88mVFtT5zKutrcUW7vMALV5/eMEZjyTWvc92pv+ozf9WhZRHZulnYO23yztHzIUOmoGSc2myJ3V9ZKV81Yi0I2J+lyriNMvihHl7nwL6+OksVZ6zspUvrusr4cbDJ3O9dM5nxsD9a02ZKKn441bfHZJZETacuX4ssvS9c++0j52rXy5wvnyAXbvORKmznMyNYnphwlp+x2mrMV/l6OmNXlW1rB5R80aQsgYR7UXf13I3BPuBJX8Xb4yJ8RuE7z4wicJ3Sd22zr+32CmBG8tB1IW0+L5hpp87f5kEZnd9Pnnd1N3+7Z3TRM3pA23XcM0qbH10baMqXL/7uZmudO0Wt3/m1d7U7Vq2hz/nV/N1P3+s6Q0DsTn8hU1Ul31ajePxgR6PKtU+0Rnc3rVl2JqdgsMa50lVX05nenSjvf797RUdtXYHIJDWva9FocadNj60VG2vQZ5yoBabPgf8ycC+X1N3vmpO8weaIsuOmSPrka7vuT3HrZ4fL1Q7uko1ycEbMx8undTpU5076c+HREi+oOaJJCkrbMEzcibUTO/JgpnBXvLu/511kb5/3YwOquHd4jcY7cGcnrrqmRrjHOl3xtz91M92/VPV/wZp1dz0W9c1fRjOSZ/5v07z8w3Ka8gUiDtPVQtpU2r00y5c1cuLVNOMDZafJIaR+7p7Q7jwowF39Im24vRtry45tLuqpko1RuapRNG9apSVfX+xJl/u16X6b6iFN5RZ/RKSNQXTXje0+6u9L5THXEyjuMgHVVbx6R6XZmrpjYhXhkSpu7VtvslBzhqPxP+A3JPuFa26Ri1YoIJTiO6nx/lq/bPHoZKfMgJS5zlqsMq6mQlo39eZrv/rK2zVNeB6mKRV/ssN/cXPTnUMwngLSFtN6p51whDY3rekXNCFz9mJFy41Xn9ea8+Z93y2m/P0E6ujvlvx8V+fY/nS+Qk+e429R3bLd9MfeP0LoXsrSFVt5J4Be4PmLnjNJ5r3m7V9rEC0tjBNDsgmmOrpHOBUtdz91fTwbN/13Zq+i5q2tG/bzDnzdbOZ1jxvbKZK66VA0pl9qaSmlav0m6nTqkcTQxrC3M61GlzYvZT958hXUOd8R93AelfdSusnHk7tJet7P73DeO5AiUurSZqYBlzgYV5e3OhbUzFdDbsML91/zN+Slr8732/nTBsoSmDWZKV/f78tXtzCbpGtLz4/7NkSfvNfdvOWQqc2ZEeaOz7sy3brmsxRmpa1i9uRN1dDo34vpuTuX+7vw98zDrn/tNnw/pjuVrHb4RpcWUkbnWOrleTyQIFACBbjYiGcxWQNpC6M+YPVe+ccaJMnvW/m7Kex9YKFfOv10eu3ee+/uCVxbIOQ+cK0vXvCbnbf0FuXj+Yqn6R8/0SO8ZYxtO+qy7s6FZR5W2NVTFLm02bz4zYlduRucaV7v/ljl3Rf137fwXCt6FR1mnsxj9/d0u41ww2NRrMNPYCGRm/cxGPWa0MtLhrEv0Riwj5bNMPOzWW9yUQRuR2IQwIxbVy/4s1e8+IkMaX3A2LXk1cPtlM53SiJsZVfDWt7hTrN6fcmVGCbx1KJmjCP6pV13DBnbRuQ2DwUhT7NJWMNI1ZKR0y1Cn7410pguOkG7n98q2MikvHyatnc7fzYYOzY4EtZZJd9kw90dausQIlf+o+M/bfX83ozrO6I53ZAqQt4HVYPSdQiszztpq91oiylFT7Xz2ToiSw735Z2aUFNORa6TNPyOmmM6p0Oo66qwvFVqVSqo+SFuO5l60ZKmcdObFcts1F8m0qVPclJl/2/8X+8vf3/67OxXyO/tfKjUVQ2XI88/KcOcB0TX33dP7jDGvGHcTDGcKnbt+yky5M5tjOB/A3uhLUHWifkDHuaCO2+tLQdrisgnKZwSwzLmDaw7/nWRXAp2dOM3RewHU6dxJ9j3mwFz4mCkruQ4jluaOdNhR5iQwX3Bdzl0zUx9Tr1I+4kpbP2bOxkNG3Ora3pDu1f9yf4Y0veTuQJn0YaZhRlmkn3T5gxnPrF3ptNnJYTAr+X7Z5SvNtKxWdzS9TFoSWdPV3VUj3V1VIu3OiHxHlXR3Oj/Ov2Vrnc+Q9krp3uSst3L+LVu9Xsoc6epuc+btOz/m9/KV6wqASt8qBH1nZX7vme9Ik847zJT0zGnnnVuazaU2rz3rTRtjirqZBWFmQ0Q5MusYlJc1bVGIRkvLmrZovOKkZk1bHGrJ5UHacrC0kbay75fJPlvvIw9//mGpcebZ9zlWOHcbf/UrkT/9ScTZsETeeSe5liu0SDNnijz8cKHVivpoEWh2NhNY7ZuqZFOOkVLznohymLUeA/G+mTMnSq2ipzXbia/8h3Ph7Aj7hve5NTufB86UavfY6Pxt0/sbNJityc3v5jC7z673fW5scPj5tiaPXhFyFASBjabNnR9zn8b7f5TfkziJ4Y4Ajc3YmXDy5L6RzesmnXc48iMTMkZsJmbswjvKmfJtfrzDGS2XrbfuG9fEMLE4IAABCEDAmgDSlgOVjbTd9PxNMmuHWTJhuOXUgzffFDE/5kLU/Cxz5uCbf9dkeYBmnItWEytbPOuuETEh0hYRGMkhkCcBI4Ct0R68m2eJZI9D4OSTRZ58sifnEGe64bAt+kZBlOJQJQ8EIACBkiOAtIU0edCatgsvv14WP3JTb87lDeYWKUfSBHI+py3pwkosHrtH6jY4u0fq8i2mNW26JJKPbrPlf/Kllk5EpkfqtTXTI/XYepGZHqnPOFcJSFsIf5vdI5E2nU6MtOlwNVGRNj22JjLSpssXadPji7TpsTWRkTY9vkibHlukTZ+tTQlImwWlsOe0IW0WEGMkQdpiQLPMgrRZgoqZDGmLCc4yG9JmCSpGMqQtBrTroTxMAAAN7klEQVQIWZC2CLAiJkXaIgKLkZyRthjQEsyCtCUAE2lLAGJACKRNh6uJirTpsTWRkTZdvkibHl+kTY+tiYy06fFF2vTYepGRNn3GuUpA2hLgj7QlABFp04GYJSrSposbadPli7Tp8UXa9NgibbpskTZdviY60qbPGGlTZoy06QBmpE2Hq4mKtOmxNZGRNl2+SJseX6RNjy3SpssWadPli7Tp8w0rgZG2MEIWryNtFpBiJEHaYkCzzIK0WYKKmQxpiwnOMhvSZgkqRjKkLQa0CFmYHhkBVsSkSFtEYDGSM9IWA1qCWZC2BGAibQlADAiBtOlwNVGRNj22JjLSpssXadPji7TpsTWRkTY9vkibHlsvMtKmzzhXCUjb4PKndAhAAAIQgAAEIAABCEAAAjkJIG10EAhAAAIQgAAEIAABCEAAAgVMAGkr4MahahCAAAQgAAEIQAACEIAABJA2+gAEIAABCEAAAhCAAAQgAIECJoC0xWycY+ZcKK+/uczNvcPkibLgpktiRiqtbFG55Up/6jlXyFPPLukDcPEjN5UWUN/ZJsnWD/GCS38u9/35cbntmotk2tQp8LV8z9u0x24z5/TyPOOUo2XuacfBNyG+M2bPlcY163t5lvJnQ2ansumbmXkWLVkqJ515ccl/DgS9QZPkyfdaX8JJsuV7rX/v1eDL95re1zjSFoOt+VBtaFzXK2qm09ePGSk3XnVejGilkyUqt7D05qLssXvn9QI0crHw6UV9/lYqdMNYZXKwTX/vAwvlF7f90b1BUcrSZsvL4xyW3rsAvuT802X2rP1LpZtmPc8wXlH7r/lM3nWnSXLZt7/kZs2MX8rAo7I2rPwCXMqfA0H9JmmefK9tppw0Wy8y32s9JJLmy/ea/jcL0haDsflQ/cYZJ/ZebJkPgCvn316SshAFX1RuUdOX8p3gqKxs05s7ZuYirdTvsNvy8t4PYemNVBw8Y6+SHlnzf3aE8cr8nAlLH/Z6lM+ttKWNy6aUP19z9QFtnqXMXYst32s9PTppvnyv6X9bIG0RGQd9gJbyh6otvqjcoqY39Zh3w91yx/0Pl5w8R2Vlm958AH/hpMNk+0lblbS02fLy3gs26c1Fw5hRI/pM3yvVEQwbXv7PGZv03pReb0okFxM9BG3YZftM53uuP5mB4Mn32uZp+bZ9MFc6vtf0Pgv4XrO9Io6fDmmLyC6fD+mIRaUqeVRucdOX4nSzuKz8kpAZw1z0rlzd5E75tf2iTFWH9Z1M0nxNaDNy6e+rmZKRVpZB55U0X7Pu0ovpL481bUhb0u+rqH037OZDZv1KebqZBlu+1zb3sKT5BvXVUv5eS/qzxouHtEUkm09Hj1hUqpJH5RYlvZe2VDdyiMLK5m77G28t7zPdF2nrvwFDLiZh7eFJW+bImrlLyU2Hno1u8uFrpM2b/uRtnGNGK+bfcp+UuriF9c1cGw2V+udAEjccokgb32vRPnfD2GYuYyn1/pz0Z0E2nqX6vaZ1AY+0xSAbNA/4wsuvL/kLgjCUUbnZpDcfxIZ9qU4t85jbsPK3T670HtOg9ixVMU6Sr+Ea9EVWyl9uSfL1Lh78glbqF2i27/1cn+EwDKYTte96UXLx5Huth1KSbPle699/k+TL91rYFXAyryNtMTjG2XEnRjGpyxLGzcw1N4f3+ISw9GwAs7mLhLGKyjbsrmXqOmfICSXN18R7bek7vesvS3nnU4M+ab5GgKfvObV3R99S5+vv3lFZ20hGqX0eaPLkey3+91qUvspNiOifu2F8+V7T/yRE2mIyjvNsi5hFpSpbLm6ZYmFOPFv6oDUrHqhSnGKWi5X3ml+Iw9Ijbf3fdkn1XS+yP57ZlMT/+IpUvektTyZpvv5nBcG3byNEZZ35zDt46vDkey3/z13bvoq09bBO+rOA7zXLL7yYyZC2mODIBgEIQAACEIAABCAAAQhAYCAIIG0DQZkyIAABCEAAAhCAAAQgAAEIxCSAtMUERzYIQAACEIAABCAAAQhAAAIDQQBpGwjKlAEBCEAAAhCAAAQgAAEIQCAmAaQtJjiyQQACEIAABCAAAQhAAAIQGAgCSNtAUKYMCEAAAhCAAAQgAAEIQAACMQkgbTHBkQ0CEIAABCAAAQhAAAIQgMBAEEDaBoIyZUAAAhCAAAQgAAEIQAACEIhJAGmLCY5sEIAABCAAAQhAAAIQgAAEBoIA0jYQlCkDAhCAAAQgAAEIQAACEIBATAJIW0xwZIMABCAAAQhAAAIQgAAEIDAQBJC2gaBMGRCAAAQgAAEIQAACEIAABGISQNpigiMbBCAAAQhAAAIQgAAEIACBgSCAtA0EZcqAAAQgAAEIQAACEIAABCAQkwDSFhMc2SAAAQhAAAIQgAAEIAABCAwEAaRtIChTBgQgAAEIQAACEIAABCAAgZgEkLaY4MgGAQhAAAIQgAAEIAABCEBgIAggbQNBmTIgAAEIQAACEIAABCAAAQjEJIC0xQRHNghAAAIQgAAEIAABCEAAAgNBAGkbCMqUAQEIQKAACcy74W6Zf8t9/Wp2xilHy9zTjpMZs+e6rz1277x+acxrY0aNlAU3XeK+FhZrt5lzchIYM2qEW86p51whTz27JDDtJeefLrNn7S/HzLlQXn9zmXi/e4nvfWChXHj59bLD5Im99coMZFOP/feeJvf9+fHerEcfup9c9u0vRSrX5jwKsEtQJQhAAAIQKFACSFuBNgzVggAEIKBJwJOK2665SKZNndJblJGvhx77Z6/0GMmZvudUufGq83rTXHDpz2Xh04t6Zc42VqZcZUqXed3Eamhcl1W6TBpP2jLr5f09l7T5mXqSF1SPoNeilGtzHprtS2wIQAACEEgXAaQtXe3J2UAAAhCwImBkzBtBypUhU14WLVkqJ515cZ9RLttYSUpb/ZiR7oicJ51evYzIhUmfTT2ySZttuUibVTckEQQgAAEIWBJA2ixBkQwCEIBAmgiY6Y07Ttm6zwhatvMzAvLa0nfckTUz2mTExT/yFiWWKSPXCJeN7Jg67LrTJFm5uknGjx3tTl00o3/mMH/TlDbbcm3OI039iXOBAAQgAAFdAkibLl+iQwACEChIAp44eZXz1pRlq6x/LdjiR27qkyxqrDBps1nTZuRp+p67umvYTH1M/cyo29XX3akubTblsqatILs9lYIABCBQtASQtqJtOioOAQhAIBkC3tRCL1rQtElPtLxNSrKVHCVWPmvajLR5m4OYunijf1FGuOKsabMtN0o9kmlFokAAAhCAQJoJIG1pbl3ODQIQgEBEAmaaodk5MXM0LWgtW1jobLHCRtrCpjd60yONtHm7VnoCGEWW8pG2sHKj1COMI69DAAIQgAAEkDb6AAQgAIESI2AE7Df3POSOVGUenoxk7iqZTdrixEpS2kz9zZo677EEUWQpH2kLKzdKPUqs+3G6EIAABCAQgwDSFgMaWSAAAQgUMwH/FEb/iJp/B0b/RiPmXHNJm9lN0hy2sZKWNn9bRJGlfKUtV7lR6lHMfYm6QwACEIDAwBBA2gaGM6VAAAIQKDgCQQ+azrZmLWx6ZJRYYdJmuxFJ0EhhFFnKVg9vWqfXYP6Ha3tr2jIbM7NcNiIpuO5OhSAAAQgUNQGkraibj8pDAAIQgAAEIAABCEAAAmkngLSlvYU5PwhAAAIQgAAEIAABCECgqAkgbUXdfFQeAhCAAAQgAAEIQAACEEg7AaQt7S3M+UEAAhCAAAQgAAEIQAACRU0AaSvq5qPyEIAABCAAAQhAAAIQgEDaCSBtaW9hzg8CEIAABCAAAQhAAAIQKGoCSFtRNx+VhwAEIAABCEAAAhCAAATSTgBpS3sLc34QgAAEIAABCEAAAhCAQFETQNqKuvmoPAQgAAEIQAACEIAABCCQdgJIW9pbmPODAAQgAAEIQAACEIAABIqaANJW1M1H5SEAAQhAAAIQgAAEIACBtBNA2tLewpwfBCAAAQhAAAIQgAAEIFDUBJC2om4+Kg8BCEAAAhCAAAQgAAEIpJ0A0pb2Fub8IAABCEAAAhCAAAQgAIGiJoC0FXXzUXkIQAACEIAABCAAAQhAIO0EkLa0tzDnBwEIQAACEIAABCAAAQgUNQGkraibj8pDAAIQgAAEIAABCEAAAmkngLSlvYU5PwhAAAIQgAAEIAABCECgqAkgbUXdfFQeAhCAAAQgAAEIQAACEEg7AaQt7S3M+UEAAhCAAAQgAAEIQAACRU0AaSvq5qPyEIAABCAAAQhAAAIQgEDaCSBtaW9hzg8CEIAABCAAAQhAAAIQKGoCSFtRNx+VhwAEIAABCEAAAhCAAATSTgBpS3sLc34QgAAEIAABCEAAAhCAQFETQNqKuvmoPAQgAAEIQAACEIAABCCQdgJIW9pbmPODAAQgAAEIQAACEIAABIqaANJW1M1H5SEAAQhAAAIQgAAEIACBtBNA2tLewpwfBCAAAQhAAAIQgAAEIFDUBJC2om4+Kg8BCEAAAhCAAAQgAAEIpJ0A0pb2Fub8IAABCEAAAhCAAAQgAIGiJoC0FXXzUXkIQAACEIAABCAAAQhAIO0EkLa0tzDnBwEIQOD/t18HRQAAAAQE+7eW48w2YL0QIECAAAECBNICTlt6PuEJECBAgAABAgQIEHgXcNreF9aPAAECBAgQIECAAIG0gNOWnk94AgQIECBAgAABAgTeBZy294X1I0CAAAECBAgQIEAgLeC0pecTngABAgQIECBAgACBdwGn7X1h/QgQIECAAAECBAgQSAsMdRcaARFvZo8AAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'darkorange', 'green'],\n", " title=\"Changes in concentrations (reaction A + 2 B <-> Y)\")" ] }, { "cell_type": "markdown", "id": "92c82a23-3c8e-4cff-9efc-7cd708f0f9ad", "metadata": {}, "source": [ "#### As expected, even the complete withdrawal of A (red), brings about only a modest increase of B's concentration, from the reverse reaction (i.e. [B] slightly increases at the expense of [Y].) \n", "#### The change is modest because our reaction A + 2 B <-> Y is mostly in the forward direction (K = 4)\n", "*Le Chatelier's principle* in action: \"A change in one of the variables that describe a system at equilibrium produces a shift in the position of the equilibrium that counteracts the effect of this change.\"" ] }, { "cell_type": "code", "execution_count": null, "id": "162ae075-48c4-4d55-ba15-1f19e3b75b9b", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "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 }