{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## 2 COUPLED reactions of different speeds, forming a \"cascade\": \n", "### `A <-> B` (fast) and `B <-> C` (slow)\n", "All 1st order. Taken to equilibrium. Both reactions are mostly forward.\n", "The concentration of the intermediate product B manifests 1 oscillation (transient \"overshoot\")\n", "\n", "(Adaptive variable time resolution is used, with extensive diagnostics.)\n", "\n", "LAST REVISED: Feb. 5, 2023" ] }, { "cell_type": "markdown", "id": "c8763f25-9fab-4b36-89cc-388321a16be0", "metadata": {}, "source": [ "## Bathtub analogy:\n", "A is initially full, while B and C are empty. \n", "Tubs are progressively lower (reactions are mostly forward.) \n", "A BIG pipe connects A and B: fast kinetics. A small pipe connects B and C: slow kinetics. \n", "\n", "INTUITION: B, unable to quickly drain into C while at the same time being blasted by a hefty inflow from A, \n", "will experience a transient surge, in excess of its final equilibrium level.\n", "\n", "* [Compare with the final reaction plot (the red line is B)](#cascade_1_plot)" ] }, { "cell_type": "markdown", "id": "b11f68d6-d3bc-4908-93c0-eaee580acbc1", "metadata": {}, "source": [ "![2 Coupled Reactions](../../docs/2_coupled_reactions.png)" ] }, { "cell_type": "code", "execution_count": 1, "id": "13e55c1d-609f-4bf0-a004-6c45bcfcbc99", "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": "bdad128a-9214-46f5-aeb9-a7b77c81aa3e", "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": "83c3cc5f-de21-4f66-9988-2806fbf0666d", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'cascade_1.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_1\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "# Initialize the System\n", "Specify the chemicals and the reactions" ] }, { "cell_type": "code", "execution_count": 4, "id": "72b4245c-de4e-480d-a501-3495b7ed8bc4", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2\n" ] } ], "source": [ "# Specify the chemicals\n", "chem_data = chem(names=[\"A\", \"B\", \"C\"])\n", "\n", "# Reaction A <-> B (fast)\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"B\"],\n", " forward_rate=64., reverse_rate=8.) \n", "\n", "# Reaction B <-> C (slow)\n", "chem_data.add_reaction(reactants=[\"B\"], products=[\"C\"],\n", " forward_rate=12., reverse_rate=2.) \n", "\n", "print(\"Number of reactions: \", chem_data.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: 2 (at temp. 25 C)\n", "0: A <-> B (kF = 64 / kR = 8 / Delta_G = -5,154.85 / K = 8) | 1st order in all reactants & products\n", "1: B <-> C (kF = 12 / kR = 2 / Delta_G = -4,441.69 / K = 6) | 1st order in all reactants & products\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 6, "id": "cb582868-431c-4022-aa0e-a2f554f80d6c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `cascade_1.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions 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": "98a9fbe5-2090-4d38-9c5f-94fbf7c3eae2", "metadata": {}, "source": [ "# Start the simulation" ] }, { "cell_type": "code", "execution_count": 7, "id": "c2f4a554-807b-49f9-8ca2-8d929fe6eeef", "metadata": {}, "outputs": [], "source": [ "dynamics = ReactionDynamics(reaction_data=chem_data)" ] }, { "cell_type": "markdown", "id": "b0345d36-5702-4b40-9221-a765dfcb0bac", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals, in their index order" ] }, { "cell_type": "code", "execution_count": 8, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [], "source": [ "dynamics.set_conc([50., 0, 0.], snapshot=True)" ] }, { "cell_type": "code", "execution_count": 9, "id": "a605dacf-2c67-403e-9aa9-5be25fc9f481", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (C). Conc: 0.0\n" ] } ], "source": [ "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 10, "id": "0ff2c242-a15b-456d-ad56-0ba1041c0b4c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
00.050.00.00.0Initial state
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" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "0 0.0 50.0 0.0 0.0 Initial state" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "fc516ca2-e62d-4784-b826-5372ff7f4c75", "metadata": { "tags": [] }, "source": [ "## Run the reaction" ] }, { "cell_type": "code", "execution_count": 11, "id": "2502cd11-0df9-4303-8895-98401a1df7b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "single_compartment_react(): setting abs_fast_threshold to 95.0\n", "20 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "#dynamics.verbose_list = [1, 2, 3] # Uncomment for detailed run information (meant for debugging the adaptive variable time step)\n", "\n", "# The changes of concentrations vary very rapidly early on; \n", "# so, we'll be using the dynamic_substeps option to increase time resolution,\n", "# as long as the reaction remains \"fast\" (based on a threshold of % change, as specified by fast_threshold)\n", "dynamics.single_compartment_react(time_step=0.02, reaction_duration=0.4,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " dynamic_substeps=10, rel_fast_threshold=190)" ] }, { "cell_type": "markdown", "id": "99a9a4b2-a588-4ba5-85c9-0a5a5d1dbaad", "metadata": {}, "source": [ "### Note: the argument _dynamic_step=10_ splits the time steps in 10 for any reactions that are \"fast-changing\" (as determined using the given value of _fast_threshold_ )" ] }, { "cell_type": "code", "execution_count": 12, "id": "80fbaee3-bd6f-4197-9270-23374d46a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
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" ], "text/plain": [ " SYSTEM TIME A B C \\\n", "0 0.000 50.000000 0.000000 0.000000 \n", "1 0.002 43.600000 6.400000 0.000000 \n", "2 0.004 38.121600 11.724800 0.153600 \n", "3 0.006 33.429632 16.135987 0.434381 \n", "4 0.008 29.408815 19.771278 0.819907 \n", ".. ... ... ... ... \n", "88 0.320 0.970191 7.617998 41.411811 \n", "89 0.340 0.947226 7.469116 41.583658 \n", "90 0.360 0.929835 7.357265 41.712899 \n", "91 0.380 0.916809 7.273064 41.810127 \n", "92 0.400 0.906984 7.209759 41.883257 \n", "\n", " caption \n", "0 Initial state \n", "1 Interm. step, due to the fast rxns: [0, 1] \n", "2 Interm. step, due to the fast rxns: [0, 1] \n", "3 Interm. step, due to the fast rxns: [0, 1] \n", "4 Interm. step, due to the fast rxns: [0, 1] \n", ".. ... \n", "88 \n", "89 \n", "90 \n", "91 \n", "92 last reaction step \n", "\n", "[93 rows x 5 columns]" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = dynamics.get_history()\n", "df" ] }, { "cell_type": "code", "execution_count": 13, "id": "144d0388-a632-4165-a9c5-50bc7943fc88", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.16, in 80 substeps of 0.002 (each 1/10 of full step)\n", "From time 0.16 to 0.4, in 12 FULL steps of 0.02\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 14, "id": "18f6a225-20e0-41b7-8bd3-e28ab6fc934c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
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10.00243.6000006.4000000.000000Interm. step, due to the fast rxns: [0, 1]
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30.00633.42963216.1359870.434381Interm. step, due to the fast rxns: [0, 1]
40.00829.40881519.7712780.819907Interm. step, due to the fast rxns: [0, 1]
50.01025.96082722.7480351.291138Interm. step, due to the fast rxns: [0, 1]
60.01223.00181025.1662641.831926Interm. step, due to the fast rxns: [0, 1]
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80.01618.27510728.6553513.069543Interm. step, due to the fast rxns: [0, 1]
90.01816.39437929.8606283.744993Interm. step, due to the fast rxns: [0, 1]
100.02014.77366830.7796644.4466681st reaction step
110.02213.37511331.4572935.167593Interm. step, due to the fast rxns: [0, 1]
120.02412.16641531.9316875.901898Interm. step, due to the fast rxns: [0, 1]
130.02611.12002132.2353286.644651Interm. step, due to the fast rxns: [0, 1]
140.02810.21242432.3958567.391720Interm. step, due to the fast rxns: [0, 1]
150.0309.42356732.4367798.139654Interm. step, due to the fast rxns: [0, 1]
160.0328.73633932.3780838.885578Interm. step, due to the fast rxns: [0, 1]
170.0348.13613732.2367539.627110Interm. step, due to the fast rxns: [0, 1]
180.0367.61050032.02721710.362283Interm. step, due to the fast rxns: [0, 1]
190.0387.14879131.76172211.089487Interm. step, due to the fast rxns: [0, 1]
200.0406.74193331.45065611.807411
210.0426.38217631.10282712.514997Interm. step, due to the fast rxns: [0, 1]
220.0446.06290330.72569213.211405Interm. step, due to the fast rxns: [0, 1]
230.0465.77846330.32556213.895976Interm. step, due to the fast rxns: [0, 1]
240.0485.52402829.90776614.568205Interm. step, due to the fast rxns: [0, 1]
250.0505.29547729.47680415.227719Interm. step, due to the fast rxns: [0, 1]
260.0525.08928529.03646415.874251Interm. step, due to the fast rxns: [0, 1]
270.0544.90244028.58993116.507629Interm. step, due to the fast rxns: [0, 1]
280.0564.73236628.13987617.127757Interm. step, due to the fast rxns: [0, 1]
290.0584.57686127.68853517.734603Interm. step, due to the fast rxns: [0, 1]
300.0604.43404027.23777118.328190
310.0624.30228726.78913018.908583Interm. step, due to the fast rxns: [1]
320.0644.17053426.35357819.475888Interm. step, due to the fast rxns: [1]
330.0664.03878125.93074820.030470Interm. step, due to the fast rxns: [1]
340.0683.90702925.52028520.572687Interm. step, due to the fast rxns: [1]
350.0703.77527625.12184121.102883Interm. step, due to the fast rxns: [1]
360.0723.64352324.73508221.621395Interm. step, due to the fast rxns: [1]
370.0743.51177024.35967822.128552Interm. step, due to the fast rxns: [1]
380.0763.38001823.99531322.624670Interm. step, due to the fast rxns: [1]
390.0783.24826523.64167723.110059Interm. step, due to the fast rxns: [1]
400.0803.11651223.29846923.585019
410.0823.09037422.85978424.049842Interm. step, due to the fast rxns: [1]
420.0843.06423622.43348724.502277Interm. step, due to the fast rxns: [1]
430.0863.03809822.01923024.942672Interm. step, due to the fast rxns: [1]
440.0883.01196021.61667725.371363Interm. step, due to the fast rxns: [1]
450.0902.98582221.22550125.788677Interm. step, due to the fast rxns: [1]
460.0922.95968420.84538126.194935Interm. step, due to the fast rxns: [1]
470.0942.93354620.47601026.590444Interm. step, due to the fast rxns: [1]
480.0962.90740820.11708626.975507Interm. step, due to the fast rxns: [1]
490.0982.88127019.76831627.350415Interm. step, due to the fast rxns: [1]
500.1002.85513219.42941627.715453
510.1022.80054519.12855828.070897Interm. step, due to the fast rxns: [1]
520.1042.74595918.83634228.417698Interm. step, due to the fast rxns: [1]
530.1062.69137318.55252728.756100Interm. step, due to the fast rxns: [1]
540.1082.63678718.27687729.086336Interm. step, due to the fast rxns: [1]
550.1102.58220118.00916329.408636Interm. step, due to the fast rxns: [1]
560.1122.52761417.74916429.723221Interm. step, due to the fast rxns: [1]
570.1142.47302817.49666330.030308Interm. step, due to the fast rxns: [1]
580.1162.41844217.25145130.330107Interm. step, due to the fast rxns: [1]
590.1182.36385617.01332330.622821Interm. step, due to the fast rxns: [1]
\n", "
" ], "text/plain": [ " SYSTEM TIME A B C \\\n", "0 0.000 50.000000 0.000000 0.000000 \n", "1 0.002 43.600000 6.400000 0.000000 \n", "2 0.004 38.121600 11.724800 0.153600 \n", "3 0.006 33.429632 16.135987 0.434381 \n", "4 0.008 29.408815 19.771278 0.819907 \n", "5 0.010 25.960827 22.748035 1.291138 \n", "6 0.012 23.001810 25.166264 1.831926 \n", "7 0.014 20.460238 27.111173 2.428589 \n", "8 0.016 18.275107 28.655351 3.069543 \n", "9 0.018 16.394379 29.860628 3.744993 \n", "10 0.020 14.773668 30.779664 4.446668 \n", "11 0.022 13.375113 31.457293 5.167593 \n", "12 0.024 12.166415 31.931687 5.901898 \n", "13 0.026 11.120021 32.235328 6.644651 \n", "14 0.028 10.212424 32.395856 7.391720 \n", "15 0.030 9.423567 32.436779 8.139654 \n", "16 0.032 8.736339 32.378083 8.885578 \n", "17 0.034 8.136137 32.236753 9.627110 \n", "18 0.036 7.610500 32.027217 10.362283 \n", "19 0.038 7.148791 31.761722 11.089487 \n", "20 0.040 6.741933 31.450656 11.807411 \n", "21 0.042 6.382176 31.102827 12.514997 \n", "22 0.044 6.062903 30.725692 13.211405 \n", "23 0.046 5.778463 30.325562 13.895976 \n", "24 0.048 5.524028 29.907766 14.568205 \n", "25 0.050 5.295477 29.476804 15.227719 \n", "26 0.052 5.089285 29.036464 15.874251 \n", "27 0.054 4.902440 28.589931 16.507629 \n", "28 0.056 4.732366 28.139876 17.127757 \n", "29 0.058 4.576861 27.688535 17.734603 \n", "30 0.060 4.434040 27.237771 18.328190 \n", "31 0.062 4.302287 26.789130 18.908583 \n", "32 0.064 4.170534 26.353578 19.475888 \n", "33 0.066 4.038781 25.930748 20.030470 \n", "34 0.068 3.907029 25.520285 20.572687 \n", "35 0.070 3.775276 25.121841 21.102883 \n", "36 0.072 3.643523 24.735082 21.621395 \n", "37 0.074 3.511770 24.359678 22.128552 \n", "38 0.076 3.380018 23.995313 22.624670 \n", "39 0.078 3.248265 23.641677 23.110059 \n", "40 0.080 3.116512 23.298469 23.585019 \n", "41 0.082 3.090374 22.859784 24.049842 \n", "42 0.084 3.064236 22.433487 24.502277 \n", "43 0.086 3.038098 22.019230 24.942672 \n", "44 0.088 3.011960 21.616677 25.371363 \n", "45 0.090 2.985822 21.225501 25.788677 \n", "46 0.092 2.959684 20.845381 26.194935 \n", "47 0.094 2.933546 20.476010 26.590444 \n", "48 0.096 2.907408 20.117086 26.975507 \n", "49 0.098 2.881270 19.768316 27.350415 \n", "50 0.100 2.855132 19.429416 27.715453 \n", "51 0.102 2.800545 19.128558 28.070897 \n", "52 0.104 2.745959 18.836342 28.417698 \n", "53 0.106 2.691373 18.552527 28.756100 \n", "54 0.108 2.636787 18.276877 29.086336 \n", "55 0.110 2.582201 18.009163 29.408636 \n", "56 0.112 2.527614 17.749164 29.723221 \n", "57 0.114 2.473028 17.496663 30.030308 \n", "58 0.116 2.418442 17.251451 30.330107 \n", "59 0.118 2.363856 17.013323 30.622821 \n", "\n", " caption \n", "0 Initial state \n", "1 Interm. step, due to the fast rxns: [0, 1] \n", "2 Interm. step, due to the fast rxns: [0, 1] \n", "3 Interm. step, due to the fast rxns: [0, 1] \n", "4 Interm. step, due to the fast rxns: [0, 1] \n", "5 Interm. step, due to the fast rxns: [0, 1] \n", "6 Interm. step, due to the fast rxns: [0, 1] \n", "7 Interm. step, due to the fast rxns: [0, 1] \n", "8 Interm. step, due to the fast rxns: [0, 1] \n", "9 Interm. step, due to the fast rxns: [0, 1] \n", "10 1st reaction step \n", "11 Interm. step, due to the fast rxns: [0, 1] \n", "12 Interm. step, due to the fast rxns: [0, 1] \n", "13 Interm. step, due to the fast rxns: [0, 1] \n", "14 Interm. step, due to the fast rxns: [0, 1] \n", "15 Interm. step, due to the fast rxns: [0, 1] \n", "16 Interm. step, due to the fast rxns: [0, 1] \n", "17 Interm. step, due to the fast rxns: [0, 1] \n", "18 Interm. step, due to the fast rxns: [0, 1] \n", "19 Interm. step, due to the fast rxns: [0, 1] \n", "20 \n", "21 Interm. step, due to the fast rxns: [0, 1] \n", "22 Interm. step, due to the fast rxns: [0, 1] \n", "23 Interm. step, due to the fast rxns: [0, 1] \n", "24 Interm. step, due to the fast rxns: [0, 1] \n", "25 Interm. step, due to the fast rxns: [0, 1] \n", "26 Interm. step, due to the fast rxns: [0, 1] \n", "27 Interm. step, due to the fast rxns: [0, 1] \n", "28 Interm. step, due to the fast rxns: [0, 1] \n", "29 Interm. step, due to the fast rxns: [0, 1] \n", "30 \n", "31 Interm. step, due to the fast rxns: [1] \n", "32 Interm. step, due to the fast rxns: [1] \n", "33 Interm. step, due to the fast rxns: [1] \n", "34 Interm. step, due to the fast rxns: [1] \n", "35 Interm. step, due to the fast rxns: [1] \n", "36 Interm. step, due to the fast rxns: [1] \n", "37 Interm. step, due to the fast rxns: [1] \n", "38 Interm. step, due to the fast rxns: [1] \n", "39 Interm. step, due to the fast rxns: [1] \n", "40 \n", "41 Interm. step, due to the fast rxns: [1] \n", "42 Interm. step, due to the fast rxns: [1] \n", "43 Interm. step, due to the fast rxns: [1] \n", "44 Interm. step, due to the fast rxns: [1] \n", "45 Interm. step, due to the fast rxns: [1] \n", "46 Interm. step, due to the fast rxns: [1] \n", "47 Interm. step, due to the fast rxns: [1] \n", "48 Interm. step, due to the fast rxns: [1] \n", "49 Interm. step, due to the fast rxns: [1] \n", "50 \n", "51 Interm. step, due to the fast rxns: [1] \n", "52 Interm. step, due to the fast rxns: [1] \n", "53 Interm. step, due to the fast rxns: [1] \n", "54 Interm. step, due to the fast rxns: [1] \n", "55 Interm. step, due to the fast rxns: [1] \n", "56 Interm. step, due to the fast rxns: [1] \n", "57 Interm. step, due to the fast rxns: [1] \n", "58 Interm. step, due to the fast rxns: [1] \n", "59 Interm. step, due to the fast rxns: [1] " ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Expand the early part\n", "df.loc[:59]" ] }, { "cell_type": "code", "execution_count": 15, "id": "8a58aa99-fc9a-415f-b1ec-5536f3e8ab86", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
600.1202.30927016.78208030.908650
610.1222.28219616.53001831.187785Interm. step, due to the fast rxns: [1]
620.1242.25512316.28512231.459754Interm. step, due to the fast rxns: [1]
630.1262.22805016.04719231.724758Interm. step, due to the fast rxns: [1]
640.1282.20097715.81603131.982992Interm. step, due to the fast rxns: [1]
650.1302.17390415.59145232.234645Interm. step, due to the fast rxns: [1]
660.1322.14683015.37326932.479901Interm. step, due to the fast rxns: [1]
670.1342.11975715.16130332.718940Interm. step, due to the fast rxns: [1]
680.1362.09268414.95538132.951935Interm. step, due to the fast rxns: [1]
690.1382.06561114.75533333.179057Interm. step, due to the fast rxns: [1]
700.1402.03853714.56099433.400469
710.1422.01058014.37308933.616331Interm. step, due to the fast rxns: [1]
720.1441.98262414.19055733.826819Interm. step, due to the fast rxns: [1]
730.1461.95466714.01324834.032085Interm. step, due to the fast rxns: [1]
740.1481.92671013.84101534.232275Interm. step, due to the fast rxns: [1]
750.1501.89875313.67371734.427530Interm. step, due to the fast rxns: [1]
760.1521.87079613.51121534.617989Interm. step, due to the fast rxns: [1]
770.1541.84283913.35337434.803787Interm. step, due to the fast rxns: [1]
780.1561.81488213.20006534.985052Interm. step, due to the fast rxns: [1]
790.1581.78692513.05116135.161914Interm. step, due to the fast rxns: [1]
800.1601.75896912.90653735.334494
810.1801.57253511.40878237.018683
820.2001.38509510.33886138.276044
830.2201.2663919.50728039.226328
840.2401.1665758.89440239.939023
850.2601.0964638.42741940.476118
860.2801.0413778.07896940.879654
870.3001.0010497.81553041.183420
880.3200.9701917.61799841.411811
890.3400.9472267.46911641.583658
900.3600.9298357.35726541.712899
910.3800.9168097.27306441.810127
920.4000.9069847.20975941.883257last reaction step
\n", "
" ], "text/plain": [ " SYSTEM TIME A B C \\\n", "60 0.120 2.309270 16.782080 30.908650 \n", "61 0.122 2.282196 16.530018 31.187785 \n", "62 0.124 2.255123 16.285122 31.459754 \n", "63 0.126 2.228050 16.047192 31.724758 \n", "64 0.128 2.200977 15.816031 31.982992 \n", "65 0.130 2.173904 15.591452 32.234645 \n", "66 0.132 2.146830 15.373269 32.479901 \n", "67 0.134 2.119757 15.161303 32.718940 \n", "68 0.136 2.092684 14.955381 32.951935 \n", "69 0.138 2.065611 14.755333 33.179057 \n", "70 0.140 2.038537 14.560994 33.400469 \n", "71 0.142 2.010580 14.373089 33.616331 \n", "72 0.144 1.982624 14.190557 33.826819 \n", "73 0.146 1.954667 14.013248 34.032085 \n", "74 0.148 1.926710 13.841015 34.232275 \n", "75 0.150 1.898753 13.673717 34.427530 \n", "76 0.152 1.870796 13.511215 34.617989 \n", "77 0.154 1.842839 13.353374 34.803787 \n", "78 0.156 1.814882 13.200065 34.985052 \n", "79 0.158 1.786925 13.051161 35.161914 \n", "80 0.160 1.758969 12.906537 35.334494 \n", "81 0.180 1.572535 11.408782 37.018683 \n", "82 0.200 1.385095 10.338861 38.276044 \n", "83 0.220 1.266391 9.507280 39.226328 \n", "84 0.240 1.166575 8.894402 39.939023 \n", "85 0.260 1.096463 8.427419 40.476118 \n", "86 0.280 1.041377 8.078969 40.879654 \n", "87 0.300 1.001049 7.815530 41.183420 \n", "88 0.320 0.970191 7.617998 41.411811 \n", "89 0.340 0.947226 7.469116 41.583658 \n", "90 0.360 0.929835 7.357265 41.712899 \n", "91 0.380 0.916809 7.273064 41.810127 \n", "92 0.400 0.906984 7.209759 41.883257 \n", "\n", " caption \n", "60 \n", "61 Interm. step, due to the fast rxns: [1] \n", "62 Interm. step, due to the fast rxns: [1] \n", "63 Interm. step, due to the fast rxns: [1] \n", "64 Interm. step, due to the fast rxns: [1] \n", "65 Interm. step, due to the fast rxns: [1] \n", "66 Interm. step, due to the fast rxns: [1] \n", "67 Interm. step, due to the fast rxns: [1] \n", "68 Interm. step, due to the fast rxns: [1] \n", "69 Interm. step, due to the fast rxns: [1] \n", "70 \n", "71 Interm. step, due to the fast rxns: [1] \n", "72 Interm. step, due to the fast rxns: [1] \n", "73 Interm. step, due to the fast rxns: [1] \n", "74 Interm. step, due to the fast rxns: [1] \n", "75 Interm. step, due to the fast rxns: [1] \n", "76 Interm. step, due to the fast rxns: [1] \n", "77 Interm. step, due to the fast rxns: [1] \n", "78 Interm. step, due to the fast rxns: [1] \n", "79 Interm. step, due to the fast rxns: [1] \n", "80 \n", "81 \n", "82 \n", "83 \n", "84 \n", "85 \n", "86 \n", "87 \n", "88 \n", "89 \n", "90 \n", "91 \n", "92 last reaction step " ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Expand the last part\n", "df.loc[60:]" ] }, { "cell_type": "markdown", "id": "9fb5f6b8-dde3-415d-9e90-b8d102bfd748", "metadata": {}, "source": [ "### Notice:\n", "* the reaction proceeds in smaller steps in the earlier times (until t=0.160, in line 80), when the concentrations are changing much more rapidly \n", "\n", "* between lines 30 and 80 (time 0.060 to 0.160), only rection #1 (B <-> C) is regarded as fast-changing (based on the fast_threshold we specified in the _simulation run_); at earlier times, both reactions were regarded as fast-changing\n", "\n", "* \"fast-changing\" and \"slow-changing\" is NOT the same thing as \"fast\" and \"slow\" reaction kinetics. For example, reaction #1, though it has much slower kinetics than reaction #0, involves large concentration changes\n", "\n", "* after step 80, both reactions are regarded as slow-changing, and no more intermediate steps are used" ] }, { "cell_type": "markdown", "id": "c02a8f55-a671-4771-86c9-fc4d1b126bf8", "metadata": {}, "source": [ "### Check the final equilibrium" ] }, { "cell_type": "code", "execution_count": 16, "id": "b139f5e4-625f-4a5e-8f57-8f00244dced4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A <-> B\n", "Final concentrations: [B] = 7.21 ; [A] = 0.907\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 7.94916\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 8.0\n", "Discrepancy between the two values: 0.6355 %\n", "Reaction IS in equilibrium (within 4% tolerance)\n", "\n", "B <-> C\n", "Final concentrations: [C] = 41.88 ; [B] = 7.21\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.80925\n", " Formula used: [C] / [B]\n", "2. Ratio of forward/reverse reaction rates: 6.0\n", "Discrepancy between the two values: 3.179 %\n", "Reaction IS in equilibrium (within 4% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that all the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=4)" ] }, { "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": "f01115d6-ef3c-44cb-bb61-b5bf74dab532", "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(title=\"Coupled reactions A <-> B and B <-> C\",\n", " colors=['blue', 'red', 'green'])" ] }, { "cell_type": "code", "execution_count": 18, "id": "79fbeb16-2bbc-49b3-ad40-7795e4577c75", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at row: 6\n" ] }, { "data": { "text/plain": [ "(0.0111949581295586, 24.19287615172957)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(t_start=0, t_end=0.05, var1=\"A\", var2=\"B\")" ] }, { "cell_type": "code", "execution_count": 19, "id": "e696eba5-d0b3-4663-ab8b-39489c8093bb", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at row: 16\n" ] }, { "data": { "text/plain": [ "(0.031791733478898146, 8.807902395796198)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(t_start=0, t_end=0.05, var1=\"A\", var2=\"C\")" ] }, { "cell_type": "code", "execution_count": 20, "id": "db256c13-c587-4025-a8cb-4881f947c0bd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at row: 40\n" ] }, { "data": { "text/plain": [ "(0.07929953388136385, 23.418671833563117)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(t_start=0.05, t_end=0.1, var1=\"B\", var2=\"C\")" ] }, { "cell_type": "code", "execution_count": null, "id": "4d9b4808-b2ec-4b90-a604-f7fa69af39b8", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "5c3f8b4f-3a75-4a21-8579-13550bcebb3c", "metadata": {}, "source": [ "# EVERYTHING BELOW IS FOR DIAGNOSTIC INSIGHT\n", "\n", "### Perform some verification" ] }, { "cell_type": "code", "execution_count": 21, "id": "79b83c65-2b4f-4f36-b3bd-aa695311f9e4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the stoichiometry is respected at every reaction step/substep (NOTE: it requires earlier activation of saving diagnostic data)\n", "dynamics.stoichiometry_checker_entire_run()" ] }, { "cell_type": "markdown", "id": "07dd5aa4-9e71-40c1-9f15-a16a9333ed10", "metadata": {}, "source": [ "### Take a peek at the diagnostic data saved during the earlier reaction simulation" ] }, { "cell_type": "code", "execution_count": 22, "id": "53971f86-c702-485c-bf32-3b5858ddef1e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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93 rows × 9 columns

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" ], "text/plain": [ " TIME A B C is_primary primary_timestep \\\n", "0 0.000 50.000000 0.000000 0.000000 True 0.02 \n", "1 0.002 43.600000 6.400000 0.000000 False 0.02 \n", "2 0.004 38.121600 11.724800 0.153600 False 0.02 \n", "3 0.006 33.429632 16.135987 0.434381 False 0.02 \n", "4 0.008 29.408815 19.771278 0.819907 False 0.02 \n", ".. ... ... ... ... ... ... \n", "88 0.320 0.970191 7.617998 41.411811 True 0.02 \n", "89 0.340 0.947226 7.469116 41.583658 True 0.02 \n", "90 0.360 0.929835 7.357265 41.712899 True 0.02 \n", "91 0.380 0.916809 7.273064 41.810127 True 0.02 \n", "92 0.400 0.906984 7.209759 41.883257 True 0.02 \n", "\n", " n_substeps substep_number caption \n", "0 10 0 \n", "1 10 1 \n", "2 10 2 \n", "3 10 3 \n", "4 10 4 \n", ".. ... ... ... \n", "88 10 0 \n", "89 10 0 \n", "90 10 0 \n", "91 10 0 \n", "92 10 0 \n", "\n", "[93 rows x 9 columns]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# This table contains a subset of a typical system history\n", "dynamics.diagnostic_data_baselines.get()" ] }, { "cell_type": "code", "execution_count": 23, "id": "5ad64dc5-ba89-4f09-b7db-da40de1df4ed", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: A <-> B\n" ] }, { "data": { "text/html": [ "
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TIMEDelta ADelta BDelta Creactionsubsteptime_subdivisiondelta_timecaption
00.000-6.4000006.4000000.000100.002
10.002-5.4784005.4784000.001100.002
20.004-4.6919684.6919680.002100.002
30.006-4.0208174.0208170.003100.002
40.008-3.4479883.4479880.004100.002
50.010-2.9590172.9590170.005100.002
60.012-2.5415712.5415710.006100.002
70.014-2.1851322.1851320.007100.002
80.016-1.8807281.8807280.008100.002
90.018-1.6207101.6207100.009100.002
100.020-1.3985551.3985550.000100.002
110.022-1.2086981.2086980.001100.002
120.024-1.0463941.0463940.002100.002
130.026-0.9075970.9075970.003100.002
140.028-0.7888570.7888570.004100.002
150.030-0.6872280.6872280.005100.002
160.032-0.6002020.6002020.006100.002
170.034-0.5256370.5256370.007100.002
180.036-0.4617080.4617080.008100.002
190.038-0.4068580.4068580.009100.002
200.040-0.3597570.3597570.000100.002
210.042-0.3192730.3192730.001100.002
220.044-0.2844410.2844410.002100.002
230.046-0.2544340.2544340.003100.002
240.048-0.2285510.2285510.004100.002
250.050-0.2061920.2061920.005100.002
260.052-0.1868450.1868450.006100.002
270.054-0.1700730.1700730.007100.002
280.056-0.1555050.1555050.008100.002
290.058-0.1428220.1428220.009100.002
300.060-1.3175281.3175280.00010.020
310.080-0.2613800.2613800.00010.020
320.100-0.5458620.5458620.00010.020
330.120-0.2707320.2707320.00010.020
340.140-0.2795690.2795690.00010.020
350.160-0.1864340.1864340.00010.020
360.180-0.1874390.1874390.00010.020
370.200-0.1187040.1187040.00010.020
380.220-0.0998160.0998160.00010.020
390.240-0.0701120.0701120.00010.020
400.260-0.0550860.0550860.00010.020
410.280-0.0403280.0403280.00010.020
420.300-0.0308580.0308580.00010.020
430.320-0.0229650.0229650.00010.020
440.340-0.0173910.0173910.00010.020
450.360-0.0130270.0130270.00010.020
460.380-0.0098250.0098250.00010.020
\n", "
" ], "text/plain": [ " TIME Delta A Delta B Delta C reaction substep time_subdivision \\\n", "0 0.000 -6.400000 6.400000 0.0 0 0 10 \n", "1 0.002 -5.478400 5.478400 0.0 0 1 10 \n", "2 0.004 -4.691968 4.691968 0.0 0 2 10 \n", "3 0.006 -4.020817 4.020817 0.0 0 3 10 \n", "4 0.008 -3.447988 3.447988 0.0 0 4 10 \n", "5 0.010 -2.959017 2.959017 0.0 0 5 10 \n", "6 0.012 -2.541571 2.541571 0.0 0 6 10 \n", "7 0.014 -2.185132 2.185132 0.0 0 7 10 \n", "8 0.016 -1.880728 1.880728 0.0 0 8 10 \n", "9 0.018 -1.620710 1.620710 0.0 0 9 10 \n", "10 0.020 -1.398555 1.398555 0.0 0 0 10 \n", "11 0.022 -1.208698 1.208698 0.0 0 1 10 \n", "12 0.024 -1.046394 1.046394 0.0 0 2 10 \n", "13 0.026 -0.907597 0.907597 0.0 0 3 10 \n", "14 0.028 -0.788857 0.788857 0.0 0 4 10 \n", "15 0.030 -0.687228 0.687228 0.0 0 5 10 \n", "16 0.032 -0.600202 0.600202 0.0 0 6 10 \n", "17 0.034 -0.525637 0.525637 0.0 0 7 10 \n", "18 0.036 -0.461708 0.461708 0.0 0 8 10 \n", "19 0.038 -0.406858 0.406858 0.0 0 9 10 \n", "20 0.040 -0.359757 0.359757 0.0 0 0 10 \n", "21 0.042 -0.319273 0.319273 0.0 0 1 10 \n", "22 0.044 -0.284441 0.284441 0.0 0 2 10 \n", "23 0.046 -0.254434 0.254434 0.0 0 3 10 \n", "24 0.048 -0.228551 0.228551 0.0 0 4 10 \n", "25 0.050 -0.206192 0.206192 0.0 0 5 10 \n", "26 0.052 -0.186845 0.186845 0.0 0 6 10 \n", "27 0.054 -0.170073 0.170073 0.0 0 7 10 \n", "28 0.056 -0.155505 0.155505 0.0 0 8 10 \n", "29 0.058 -0.142822 0.142822 0.0 0 9 10 \n", "30 0.060 -1.317528 1.317528 0.0 0 0 1 \n", "31 0.080 -0.261380 0.261380 0.0 0 0 1 \n", "32 0.100 -0.545862 0.545862 0.0 0 0 1 \n", "33 0.120 -0.270732 0.270732 0.0 0 0 1 \n", "34 0.140 -0.279569 0.279569 0.0 0 0 1 \n", "35 0.160 -0.186434 0.186434 0.0 0 0 1 \n", "36 0.180 -0.187439 0.187439 0.0 0 0 1 \n", "37 0.200 -0.118704 0.118704 0.0 0 0 1 \n", "38 0.220 -0.099816 0.099816 0.0 0 0 1 \n", "39 0.240 -0.070112 0.070112 0.0 0 0 1 \n", "40 0.260 -0.055086 0.055086 0.0 0 0 1 \n", "41 0.280 -0.040328 0.040328 0.0 0 0 1 \n", "42 0.300 -0.030858 0.030858 0.0 0 0 1 \n", "43 0.320 -0.022965 0.022965 0.0 0 0 1 \n", "44 0.340 -0.017391 0.017391 0.0 0 0 1 \n", "45 0.360 -0.013027 0.013027 0.0 0 0 1 \n", "46 0.380 -0.009825 0.009825 0.0 0 0 1 \n", "\n", " delta_time caption \n", "0 0.002 \n", "1 0.002 \n", "2 0.002 \n", "3 0.002 \n", "4 0.002 \n", "5 0.002 \n", "6 0.002 \n", "7 0.002 \n", "8 0.002 \n", "9 0.002 \n", "10 0.002 \n", "11 0.002 \n", "12 0.002 \n", "13 0.002 \n", "14 0.002 \n", "15 0.002 \n", "16 0.002 \n", "17 0.002 \n", "18 0.002 \n", "19 0.002 \n", "20 0.002 \n", "21 0.002 \n", "22 0.002 \n", "23 0.002 \n", "24 0.002 \n", "25 0.002 \n", "26 0.002 \n", "27 0.002 \n", "28 0.002 \n", "29 0.002 \n", "30 0.020 \n", "31 0.020 \n", "32 0.020 \n", "33 0.020 \n", "34 0.020 \n", "35 0.020 \n", "36 0.020 \n", "37 0.020 \n", "38 0.020 \n", "39 0.020 \n", "40 0.020 \n", "41 0.020 \n", "42 0.020 \n", "43 0.020 \n", "44 0.020 \n", "45 0.020 \n", "46 0.020 " ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Concentration increments due to reaction 0 (A <-> B)\n", "# Note that [C] is not affected\n", "dynamics.get_diagnostic_data(rxn_index=0)" ] }, { "cell_type": "code", "execution_count": 24, "id": "71f62382-f07a-416d-876f-97832c1f79e5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: B <-> C\n" ] }, { "data": { "text/html": [ "
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TIMEDelta ADelta BDelta Creactionsubsteptime_subdivisiondelta_timecaption
00.0000.00.0000000.00000010100.002
10.0020.0-0.1536000.15360011100.002
20.0040.0-0.2807810.28078112100.002
30.0060.0-0.3855260.38552613100.002
40.0080.0-0.4712310.47123114100.002
..............................
870.3000.0-0.2283900.2283901010.020
880.3200.0-0.1718470.1718471010.020
890.3400.0-0.1292410.1292411010.020
900.3600.0-0.0972280.0972281010.020
910.3800.0-0.0731300.0731301010.020
\n", "

92 rows × 9 columns

\n", "
" ], "text/plain": [ " TIME Delta A Delta B Delta C reaction substep time_subdivision \\\n", "0 0.000 0.0 0.000000 0.000000 1 0 10 \n", "1 0.002 0.0 -0.153600 0.153600 1 1 10 \n", "2 0.004 0.0 -0.280781 0.280781 1 2 10 \n", "3 0.006 0.0 -0.385526 0.385526 1 3 10 \n", "4 0.008 0.0 -0.471231 0.471231 1 4 10 \n", ".. ... ... ... ... ... ... ... \n", "87 0.300 0.0 -0.228390 0.228390 1 0 1 \n", "88 0.320 0.0 -0.171847 0.171847 1 0 1 \n", "89 0.340 0.0 -0.129241 0.129241 1 0 1 \n", "90 0.360 0.0 -0.097228 0.097228 1 0 1 \n", "91 0.380 0.0 -0.073130 0.073130 1 0 1 \n", "\n", " delta_time caption \n", "0 0.002 \n", "1 0.002 \n", "2 0.002 \n", "3 0.002 \n", "4 0.002 \n", ".. ... ... \n", "87 0.020 \n", "88 0.020 \n", "89 0.020 \n", "90 0.020 \n", "91 0.020 \n", "\n", "[92 rows x 9 columns]" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Concentration increments due to reaction 1 (B <-> C)\n", "# Note that [A] is not affected\n", "dynamics.get_diagnostic_data(rxn_index=1)" ] }, { "cell_type": "code", "execution_count": 25, "id": "bc244857-c613-4736-8058-b17afa52d601", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: B <-> C\n" ] }, { "data": { "text/html": [ "
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TIMEDelta ADelta BDelta Creactionsubsteptime_subdivisiondelta_timecaption
600.1200.0-0.2791350.27913510100.002
610.1220.0-0.2719690.27196911100.002
620.1240.0-0.2650040.26500412100.002
630.1260.0-0.2582340.25823413100.002
640.1280.0-0.2516530.25165314100.002
650.1300.0-0.2452560.24525615100.002
660.1320.0-0.2390390.23903916100.002
670.1340.0-0.2329960.23299617100.002
680.1360.0-0.2271210.22712118100.002
690.1380.0-0.2214120.22141219100.002
700.1400.0-0.2158620.21586210100.002
710.1420.0-0.2104890.21048911100.002
720.1440.0-0.2052660.20526612100.002
730.1460.0-0.2001900.20019013100.002
740.1480.0-0.1952550.19525514100.002
750.1500.0-0.1904590.19045915100.002
760.1520.0-0.1857970.18579716100.002
770.1540.0-0.1812660.18126617100.002
780.1560.0-0.1768610.17686118100.002
790.1580.0-0.1725800.17258019100.002
800.1600.0-1.6841891.6841891010.020
810.1800.0-1.2573601.2573601010.020
820.2000.0-0.9502850.9502851010.020
830.2200.0-0.7126940.7126941010.020
840.2400.0-0.5370960.5370961010.020
850.2600.0-0.4035360.4035361010.020
860.2800.0-0.3037660.3037661010.020
870.3000.0-0.2283900.2283901010.020
880.3200.0-0.1718470.1718471010.020
890.3400.0-0.1292410.1292411010.020
900.3600.0-0.0972280.0972281010.020
910.3800.0-0.0731300.0731301010.020
\n", "
" ], "text/plain": [ " TIME Delta A Delta B Delta C reaction substep time_subdivision \\\n", "60 0.120 0.0 -0.279135 0.279135 1 0 10 \n", "61 0.122 0.0 -0.271969 0.271969 1 1 10 \n", "62 0.124 0.0 -0.265004 0.265004 1 2 10 \n", "63 0.126 0.0 -0.258234 0.258234 1 3 10 \n", "64 0.128 0.0 -0.251653 0.251653 1 4 10 \n", "65 0.130 0.0 -0.245256 0.245256 1 5 10 \n", "66 0.132 0.0 -0.239039 0.239039 1 6 10 \n", "67 0.134 0.0 -0.232996 0.232996 1 7 10 \n", "68 0.136 0.0 -0.227121 0.227121 1 8 10 \n", "69 0.138 0.0 -0.221412 0.221412 1 9 10 \n", "70 0.140 0.0 -0.215862 0.215862 1 0 10 \n", "71 0.142 0.0 -0.210489 0.210489 1 1 10 \n", "72 0.144 0.0 -0.205266 0.205266 1 2 10 \n", "73 0.146 0.0 -0.200190 0.200190 1 3 10 \n", "74 0.148 0.0 -0.195255 0.195255 1 4 10 \n", "75 0.150 0.0 -0.190459 0.190459 1 5 10 \n", "76 0.152 0.0 -0.185797 0.185797 1 6 10 \n", "77 0.154 0.0 -0.181266 0.181266 1 7 10 \n", "78 0.156 0.0 -0.176861 0.176861 1 8 10 \n", "79 0.158 0.0 -0.172580 0.172580 1 9 10 \n", "80 0.160 0.0 -1.684189 1.684189 1 0 1 \n", "81 0.180 0.0 -1.257360 1.257360 1 0 1 \n", "82 0.200 0.0 -0.950285 0.950285 1 0 1 \n", "83 0.220 0.0 -0.712694 0.712694 1 0 1 \n", "84 0.240 0.0 -0.537096 0.537096 1 0 1 \n", "85 0.260 0.0 -0.403536 0.403536 1 0 1 \n", "86 0.280 0.0 -0.303766 0.303766 1 0 1 \n", "87 0.300 0.0 -0.228390 0.228390 1 0 1 \n", "88 0.320 0.0 -0.171847 0.171847 1 0 1 \n", "89 0.340 0.0 -0.129241 0.129241 1 0 1 \n", "90 0.360 0.0 -0.097228 0.097228 1 0 1 \n", "91 0.380 0.0 -0.073130 0.073130 1 0 1 \n", "\n", " delta_time caption \n", "60 0.002 \n", "61 0.002 \n", "62 0.002 \n", "63 0.002 \n", "64 0.002 \n", "65 0.002 \n", "66 0.002 \n", "67 0.002 \n", "68 0.002 \n", "69 0.002 \n", "70 0.002 \n", "71 0.002 \n", "72 0.002 \n", "73 0.002 \n", "74 0.002 \n", "75 0.002 \n", "76 0.002 \n", "77 0.002 \n", "78 0.002 \n", "79 0.002 \n", "80 0.020 \n", "81 0.020 \n", "82 0.020 \n", "83 0.020 \n", "84 0.020 \n", "85 0.020 \n", "86 0.020 \n", "87 0.020 \n", "88 0.020 \n", "89 0.020 \n", "90 0.020 \n", "91 0.020 " ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Expand the last part of the above table\n", "dynamics.get_diagnostic_data(rxn_index=1).loc[60:]" ] }, { "cell_type": "code", "execution_count": null, "id": "520b3b44-7da9-49d3-9cfd-685607169f01", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "b4d987b6-fe56-408a-98f4-8dad3c14af1f", "metadata": {}, "source": [ "### Provide a detailed explanation of all the steps/substeps of the reactions, from the saved diagnostic data" ] }, { "cell_type": "code", "execution_count": 26, "id": "e8ed2965-1494-4efb-bba8-e51092b7644f", "metadata": {}, "outputs": [], "source": [ "# dynamics.explain_reactions() # Uncomment if desired" ] }, { "cell_type": "code", "execution_count": null, "id": "46fdcb5b-ed5f-43a9-9829-533039666d0c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "de51ec27-1d0f-4bfb-83f0-b1c79b436d75", "metadata": { "tags": [] }, "source": [ "# Re-run with very small constanst steps" ] }, { "cell_type": "markdown", "id": "ff9fffab-a1f5-4497-9d7b-c3db023d1bd2", "metadata": {}, "source": [ "We'll use constant steps of size 0.0005, which is 1/4 of the smallest steps (the \"substep\" size) previously used in the variable-step run" ] }, { "cell_type": "code", "execution_count": 27, "id": "93418d81-12fa-417d-9906-1dd24a40de48", "metadata": {}, "outputs": [], "source": [ "dynamics2 = ReactionDynamics(reaction_data=chem_data)" ] }, { "cell_type": "code", "execution_count": 28, "id": "ecf2029b-57a7-4db4-9b30-c854da91fb76", "metadata": { "tags": [] }, "outputs": [], "source": [ "dynamics2.set_conc([50., 0, 0.], snapshot=True)" ] }, { "cell_type": "code", "execution_count": 29, "id": "00777982-d633-4c12-8c92-2ece6bf00e5e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "800 total step(s) taken\n" ] } ], "source": [ "dynamics2.single_compartment_react(time_step=0.0005, reaction_duration=0.4,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " ) " ] }, { "cell_type": "code", "execution_count": 30, "id": "78ed4dee-870a-4517-8bd0-58122c10e663", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
SYSTEM TIME=%{x}
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SYSTEM TIMEABCcaption
00.000050.0000000.0000000.000000Initial state
10.000548.4000001.6000000.0000001st reaction step
20.001046.8576003.1328000.009600
30.001545.3706884.6009250.028387
40.002043.9372306.0068060.055964
..................
7960.39800.9254947.32915141.745354
7970.39850.9251957.32722141.747584
7980.39900.9248987.32530341.749800
7990.39950.9246027.32339641.752002
8000.40000.9243097.32150141.754190last reaction step
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801 rows × 5 columns

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" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "0 0.0000 50.000000 0.000000 0.000000 Initial state\n", "1 0.0005 48.400000 1.600000 0.000000 1st reaction step\n", "2 0.0010 46.857600 3.132800 0.009600 \n", "3 0.0015 45.370688 4.600925 0.028387 \n", "4 0.0020 43.937230 6.006806 0.055964 \n", ".. ... ... ... ... ...\n", "796 0.3980 0.925494 7.329151 41.745354 \n", "797 0.3985 0.925195 7.327221 41.747584 \n", "798 0.3990 0.924898 7.325303 41.749800 \n", "799 0.3995 0.924602 7.323396 41.752002 \n", "800 0.4000 0.924309 7.321501 41.754190 last reaction step\n", "\n", "[801 rows x 5 columns]" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2 = dynamics2.get_history()\n", "df2" ] }, { "cell_type": "markdown", "id": "45d5883d-c2c6-40a7-80b4-8a5976b8dfcd", "metadata": {}, "source": [ "## Notice that we now did 801 steps - vs. the 93 of the earlier variable-resolution run!" ] }, { "cell_type": "markdown", "id": "0f590255-1555-43d5-9adb-ace15ac80aa4", "metadata": {}, "source": [ "### Let's compare some entries with the coarser previous variable-time run" ] }, { "cell_type": "markdown", "id": "04ced99b-0e11-44ef-b7b4-1241f5b23189", "metadata": {}, "source": [ "**At time t=0.002:**" ] }, { "cell_type": "code", "execution_count": 35, "id": "4d0fccb4-eee5-4ce7-afe0-fdc5d1624319", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SYSTEM TIME 0.002\n", "A 43.6\n", "B 6.4\n", "C 0.0\n", "caption Interm. step, due to the fast rxns: [0, 1]\n", "Name: 1, dtype: object" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.loc[1]" ] }, { "cell_type": "code", "execution_count": 36, "id": "5b448232-3d8c-4a8b-95eb-9f0b3c9455f3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SYSTEM TIME 0.002\n", "A 43.93723\n", "B 6.006806\n", "C 0.055964\n", "caption \n", "Name: 4, dtype: object" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2.loc[4] # High-precision result from fine fixed-resolution run" ] }, { "cell_type": "code", "execution_count": 37, "id": "53f4400a-a0b9-45d0-ac42-db275d180b94", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([2.00e-03, 4.36e+01, 6.40e+00, 0.00e+00])" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "old = df.loc[1][['SYSTEM TIME', 'A', 'B', 'C']].to_numpy().astype(float)\n", "old" ] }, { "cell_type": "code", "execution_count": 38, "id": "9288a4de-587f-4bff-adf7-aea88d7a48fa", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([2.00000000e-03, 4.39372297e+01, 6.00680596e+00, 5.59643616e-02])" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "new = df2.loc[4][['SYSTEM TIME', 'A', 'B', 'C']].to_numpy().astype(float)\n", "new" ] }, { "cell_type": "code", "execution_count": 39, "id": "6a1268f3-0f2c-46a0-89de-95c65963674f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0. , 0.33722968, -0.39319404, 0.05596436])" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "new - old" ] }, { "cell_type": "code", "execution_count": null, "id": "0dd39e1b-893b-4497-a097-0970942281be", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "3c46fd0b-242a-4959-8988-2e9b1866bf9d", "metadata": {}, "source": [ "**At time t=0.032**, when [A] and [C] are almost equal:" ] }, { "cell_type": "code", "execution_count": 40, "id": "a1f1b452-7aa1-4f1b-8791-add4fafbbb6d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SYSTEM TIME 0.032\n", "A 8.736339\n", "B 32.378083\n", "C 8.885578\n", "caption Interm. step, due to the fast rxns: [0, 1]\n", "Name: 16, dtype: object" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.loc[16]" ] }, { "cell_type": "code", "execution_count": 41, "id": "d0aa1d4c-2455-46ce-bb98-7bfa50ebccb2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SYSTEM TIME 0.032\n", "A 9.282079\n", "B 31.85364\n", "C 8.864282\n", "caption \n", "Name: 64, dtype: object" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2.loc[64] # High-precision result from fine fixed-resolution run" ] }, { "cell_type": "code", "execution_count": null, "id": "a2682cb5-63fa-4d5e-8f4f-f9582e72870c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "30058776-552c-48a4-9f4a-b10823710e84", "metadata": {}, "source": [ "**At time t=0.14**:" ] }, { "cell_type": "code", "execution_count": 42, "id": "3bdd77e0-f6bb-4d1f-91b7-556bb4b5eb02", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SYSTEM TIME 0.14\n", "A 2.038537\n", "B 14.560994\n", "C 33.400469\n", "caption \n", "Name: 70, dtype: object" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.loc[70]" ] }, { "cell_type": "code", "execution_count": 43, "id": "b43496be-4aaf-4369-b9b6-df4754f95590", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SYSTEM TIME 0.14\n", "A 2.070976\n", "B 14.710086\n", "C 33.218938\n", "caption \n", "Name: 280, dtype: object" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2.loc[280] # High-precision result from fine fixed-resolution run" ] }, { "cell_type": "code", "execution_count": null, "id": "8cb95a1b-6e52-4490-ae3f-ea781b9d9696", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "a66a3b82-f705-40f1-b5b8-00923d4237c6", "metadata": {}, "source": [ "**At time t=0.26**:" ] }, { "cell_type": "code", "execution_count": 44, "id": "36cdb4fa-a4bd-4bc6-928f-20cb10d20cb3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SYSTEM TIME 0.26\n", "A 1.096463\n", "B 8.427419\n", "C 40.476118\n", "caption \n", "Name: 85, dtype: object" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.loc[85]" ] }, { "cell_type": "code", "execution_count": 45, "id": "0efd4b0d-e055-4579-a016-88c6f4f62107", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SYSTEM TIME 0.26\n", "A 1.145609\n", "B 8.749175\n", "C 40.105216\n", "caption \n", "Name: 520, dtype: object" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df2.loc[520] # High-precision result from fine fixed-resolution run" ] }, { "cell_type": "code", "execution_count": null, "id": "6b8e9c92-5190-4827-8761-fe39e30622db", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "bfef068e-d576-4c3c-bda8-b0b51c5f88da", "metadata": {}, "source": [ "## Let's compare the plots of [B] from the earlier (variable-step) run, and the latest (high-precision fixed-step) one" ] }, { "cell_type": "code", "execution_count": 46, "id": "ce76fb06-b0fa-486b-b1ce-78f5786d8a85", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Variable-step run=B
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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import plotly.graph_objects as go\n", "\n", "all_fig = go.Figure(data=fig1.data + fig2.data) # Note that the + is concatenating lists\n", "all_fig.update_layout(title=\"The 2 runs contrasted\")\n", "all_fig['data'][0]['name']=\"B (variable steps)\"\n", "all_fig['data'][1]['name']=\"B (fixed high precision)\"\n", "all_fig.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "a796af3e-a7cc-4faa-b425-f07ddaf33aa1", "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 }