{ "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", "Taken to equilibrium. Both reactions are mostly forward. All 1st order. \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", "and finally compared to a new run using fixed time intervals, with the same initial data.\n", "\n", "In part2, some diagnostic insight is explored. \n", "\n", "In part3, two identical runs (\"adaptive variable steps\" vs. \"fixed small steps\") are compared. " ] }, { "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 orange 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": "f5f1e6a4-2d9c-4638-bde7-09cb56e995a3", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"Oct. 11, 2024\"\n", "LIFE123_VERSION = \"1.0.0.beta.39\" # Library version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "8ef47cb2-812a-4cd1-87d3-0a6573ab0a5c", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!" ] }, { "cell_type": "code", "execution_count": 3, "id": "3924c013", "metadata": { "tags": [] }, "outputs": [], "source": [ "#import sys\n", "#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n", "# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path\n", "\n", "import ipynbname\n", "\n", "from life123 import check_version, ChemData, UniformCompartment, PlotlyHelper, GraphicLog" ] }, { "cell_type": "code", "execution_count": 4, "id": "e96579d6-e07a-4d62-9655-aab230e6f186", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION)" ] }, { "cell_type": "code", "execution_count": 5, "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 = ipynbname.name() + \".log.htm\" # Use the notebook base filename for the log file\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "# Initialize the System\n", "Specify the chemicals and the reactions" ] }, { "cell_type": "code", "execution_count": 6, "id": "72b4245c-de4e-480d-a501-3495b7ed8bc4", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2\n" ] } ], "source": [ "# Specify the chemicals and the reactions; this data structure will get re-used in \n", "# the various simulations below\n", "chem = ChemData()\n", "\n", "# Reaction A <-> B (fast)\n", "chem.add_reaction(reactants=\"A\", products=\"B\",\n", " forward_rate=64., reverse_rate=8.) \n", "\n", "# Reaction B <-> C (slow)\n", "chem.add_reaction(reactants=\"B\", products=\"C\",\n", " forward_rate=12., reverse_rate=2.) \n", "\n", "print(\"Number of reactions: \", chem.number_of_reactions())" ] }, { "cell_type": "code", "execution_count": 7, "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 = -5,154.8 / K = 8) | 1st order in all reactants & products\n", "1: B <-> C (kF = 12 / kR = 2 / delta_G = -4,441.7 / K = 6) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'C', 'A', 'B'}\n" ] } ], "source": [ "chem.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 8, "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", "chem.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "code", "execution_count": null, "id": "74a1e2bd-4e82-4aaa-a68f-7cee52b2ebbf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "98a9fbe5-2090-4d38-9c5f-94fbf7c3eae2", "metadata": {}, "source": [ "## Run the simulation" ] }, { "cell_type": "code", "execution_count": 9, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "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", "Set of chemicals involved in reactions: {'C', 'A', 'B'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem, preset=\"fast\")\n", "\n", "dynamics.set_conc({\"A\": 50.}, snapshot=True) # Set the initial concentrations of all the chemicals, in their index order\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 10, "id": "0ff2c242-a15b-456d-ad56-0ba1041c0b4c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SYSTEM TIMEABCcaption
00.050.00.00.0Initialized state
\n", "
" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "0 0.0 50.0 0.0 0.0 Initialized 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": [ "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "48 total step(s) taken\n", "Number of step re-do's because of negative concentrations: 1\n", "Number of step re-do's because of elective soft aborts: 5\n", "Norm usage: {'norm_A': 25, 'norm_B': 17, 'norm_C': 16, 'norm_D': 16}\n" ] } ], "source": [ "dynamics.enable_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "dynamics.single_compartment_react(initial_step=0.02, duration=0.4,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " variable_steps=True)" ] }, { "cell_type": "markdown", "id": "199b6238-f6ed-44a8-8130-a003444d7658", "metadata": {}, "source": [ "### Plots of changes of concentration with time\n", "Notice the variable time steps (vertical dashed lines)" ] }, { "cell_type": "code", "execution_count": 12, "id": "a2c0e793-5457-46a5-9150-388c9f562cf0", "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_history(title=\"Coupled reactions A <-> B and B <-> C\",\n", " colors=['darkturquoise', 'orange', 'green'], show_intervals=True)" ] }, { "cell_type": "code", "execution_count": 13, "id": "844183a6-e61f-4b7a-8aa6-013f4530a74b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.011857732428358053, 24.047031609298816)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersect(\"A\", \"B\", t_start=0, t_end=0.05)" ] }, { "cell_type": "code", "execution_count": 14, "id": "025c387b-5bd2-4666-a140-9c66630da072", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.031934885008449314, 8.852813807230596)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersect(\"A\", \"C\", t_start=0, t_end=0.05)" ] }, { "cell_type": "code", "execution_count": 15, "id": "86f3a798-4a5b-4016-b4d1-121f9fb48506", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.07740303497735611, 23.285274847029168)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersect(\"B\", \"C\", t_start=0.05, t_end=0.1)" ] }, { "cell_type": "code", "execution_count": 16, "id": "80fbaee3-bd6f-4197-9270-23374d46a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
00.00000050.0000000.0000000.000000Initialized state
10.00077847.5116802.4883200.0000001st reaction step
20.00140045.6324754.3489500.018575
30.00202243.8373476.1116360.051017
40.00251942.4654387.4470970.087465
50.00301741.1425428.7256060.131851
60.00351539.8668719.9493000.183829
70.00401238.63670311.1202340.243063
80.00451037.45037812.2403910.309231
90.00500836.30629813.3116800.382022
100.00550535.20292214.3359390.461139
110.00600334.13876715.3149390.546294
120.00650133.11240416.2503860.637210
130.00699832.12245517.1439220.733623
140.00749631.16759517.9971300.835276
150.00824329.78601819.2187360.995246
160.00898928.47774220.3563371.165921
170.00973627.23876421.4147051.346531
180.01048226.06530022.3983471.536353
190.01160224.39801023.7681131.833877
200.01272222.86247424.9883862.149140
210.01384121.44791126.0719942.480095
220.01496120.14442827.0307042.824868
230.01664118.34220428.2976033.360193
240.01832016.75073429.3300123.919255
250.02000015.34421230.1585424.497247
260.02251913.47792031.1357085.386372
270.02503911.93225031.7671906.300559
280.02755810.64853732.1222317.229232
290.0313379.04418632.3244918.631323
300.0351167.83398632.13402610.031989
310.0388966.91073231.67583811.413430
320.0445645.84002630.72121113.438763
330.0502335.11447829.50932715.376196
340.0587364.33855727.53570318.125740
350.0655383.94821925.92491920.126862
360.0757423.48612923.62339322.890478
370.0839053.20756821.96162724.830805
380.0961492.84524019.70514827.449612
390.1059452.60569918.16619029.228112
400.1206382.29074516.13700631.572249
410.1353322.03344214.47684233.489716
420.1573711.71770812.43997635.842316
430.1794111.48819510.95929937.552505
440.2124711.2379299.34477139.417300
450.2455311.0901758.39154340.518282
460.2951210.9593157.54737141.493315
470.3695060.8836537.05906142.057286
480.4810830.8745847.00183542.123581last reaction step
\n", "
" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "0 0.000000 50.000000 0.000000 0.000000 Initialized state\n", "1 0.000778 47.511680 2.488320 0.000000 1st reaction step\n", "2 0.001400 45.632475 4.348950 0.018575 \n", "3 0.002022 43.837347 6.111636 0.051017 \n", "4 0.002519 42.465438 7.447097 0.087465 \n", "5 0.003017 41.142542 8.725606 0.131851 \n", "6 0.003515 39.866871 9.949300 0.183829 \n", "7 0.004012 38.636703 11.120234 0.243063 \n", "8 0.004510 37.450378 12.240391 0.309231 \n", "9 0.005008 36.306298 13.311680 0.382022 \n", "10 0.005505 35.202922 14.335939 0.461139 \n", "11 0.006003 34.138767 15.314939 0.546294 \n", "12 0.006501 33.112404 16.250386 0.637210 \n", "13 0.006998 32.122455 17.143922 0.733623 \n", "14 0.007496 31.167595 17.997130 0.835276 \n", "15 0.008243 29.786018 19.218736 0.995246 \n", "16 0.008989 28.477742 20.356337 1.165921 \n", "17 0.009736 27.238764 21.414705 1.346531 \n", "18 0.010482 26.065300 22.398347 1.536353 \n", "19 0.011602 24.398010 23.768113 1.833877 \n", "20 0.012722 22.862474 24.988386 2.149140 \n", "21 0.013841 21.447911 26.071994 2.480095 \n", "22 0.014961 20.144428 27.030704 2.824868 \n", "23 0.016641 18.342204 28.297603 3.360193 \n", "24 0.018320 16.750734 29.330012 3.919255 \n", "25 0.020000 15.344212 30.158542 4.497247 \n", "26 0.022519 13.477920 31.135708 5.386372 \n", "27 0.025039 11.932250 31.767190 6.300559 \n", "28 0.027558 10.648537 32.122231 7.229232 \n", "29 0.031337 9.044186 32.324491 8.631323 \n", "30 0.035116 7.833986 32.134026 10.031989 \n", "31 0.038896 6.910732 31.675838 11.413430 \n", "32 0.044564 5.840026 30.721211 13.438763 \n", "33 0.050233 5.114478 29.509327 15.376196 \n", "34 0.058736 4.338557 27.535703 18.125740 \n", "35 0.065538 3.948219 25.924919 20.126862 \n", "36 0.075742 3.486129 23.623393 22.890478 \n", "37 0.083905 3.207568 21.961627 24.830805 \n", "38 0.096149 2.845240 19.705148 27.449612 \n", "39 0.105945 2.605699 18.166190 29.228112 \n", "40 0.120638 2.290745 16.137006 31.572249 \n", "41 0.135332 2.033442 14.476842 33.489716 \n", "42 0.157371 1.717708 12.439976 35.842316 \n", "43 0.179411 1.488195 10.959299 37.552505 \n", "44 0.212471 1.237929 9.344771 39.417300 \n", "45 0.245531 1.090175 8.391543 40.518282 \n", "46 0.295121 0.959315 7.547371 41.493315 \n", "47 0.369506 0.883653 7.059061 42.057286 \n", "48 0.481083 0.874584 7.001835 42.123581 last reaction step" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 17, "id": "144d0388-a632-4165-a9c5-50bc7943fc88", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.0007776, in 1 step of 0.000778\n", "From time 0.0007776 to 0.002022, in 2 steps of 0.000622\n", "From time 0.002022 to 0.007496, in 11 steps of 0.000498\n", "From time 0.007496 to 0.01048, in 4 steps of 0.000746\n", "From time 0.01048 to 0.01496, in 4 steps of 0.00112\n", "From time 0.01496 to 0.02, in 3 steps of 0.00168\n", "From time 0.02 to 0.02756, in 3 steps of 0.00252\n", "From time 0.02756 to 0.0389, in 3 steps of 0.00378\n", "From time 0.0389 to 0.05023, in 2 steps of 0.00567\n", "From time 0.05023 to 0.05874, in 1 step of 0.0085\n", "From time 0.05874 to 0.06554, in 1 step of 0.0068\n", "From time 0.06554 to 0.07574, in 1 step of 0.0102\n", "From time 0.07574 to 0.08391, in 1 step of 0.00816\n", "From time 0.08391 to 0.09615, in 1 step of 0.0122\n", "From time 0.09615 to 0.1059, in 1 step of 0.0098\n", "From time 0.1059 to 0.1353, in 2 steps of 0.0147\n", "From time 0.1353 to 0.1794, in 2 steps of 0.022\n", "From time 0.1794 to 0.2455, in 2 steps of 0.0331\n", "From time 0.2455 to 0.2951, in 1 step of 0.0496\n", "From time 0.2951 to 0.3695, in 1 step of 0.0744\n", "From time 0.3695 to 0.4811, in 1 step of 0.112\n", "(48 steps total)\n" ] } ], "source": [ "dynamics.diagnostics.explain_time_advance()" ] }, { "cell_type": "markdown", "id": "c02a8f55-a671-4771-86c9-fc4d1b126bf8", "metadata": {}, "source": [ "### Check the final equilibrium" ] }, { "cell_type": "code", "execution_count": 18, "id": "b139f5e4-625f-4a5e-8f57-8f00244dced4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [A] = 0.8746 ; [B] = 7.002\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 8.0059\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 8\n", "Discrepancy between the two values: 0.07378 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: B <-> C\n", "Final concentrations: [B] = 7.002 ; [C] = 42.12\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 6.01608\n", " Formula used: [C] / [B]\n", "2. Ratio of forward/reverse reaction rates: 6\n", "Discrepancy between the two values: 0.268 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that all the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "c279c0b2-754e-4574-95a6-ffbe8e162463", "metadata": {}, "source": [ "### Let's look at the final concentrations of `A` and `C` (i.e., the reactant and product of the composite reaction)" ] }, { "cell_type": "code", "execution_count": 19, "id": "c093910f-62f2-43cf-88ef-d5df935a44b8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.8745841244150234" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A_final = dynamics.get_chem_conc(\"A\")\n", "A_final" ] }, { "cell_type": "code", "execution_count": 20, "id": "22636dc7-fd18-468f-8ddb-8152891eb9b5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "42.123581082850514" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C_final = dynamics.get_chem_conc(\"C\")\n", "C_final" ] }, { "cell_type": "markdown", "id": "420e0075-6b81-4836-8641-b0ccdeacf550", "metadata": {}, "source": [ "#### Their ratio:" ] }, { "cell_type": "code", "execution_count": 21, "id": "8280c0be-2f8d-4f4c-adc0-9ca7f5d5060e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "48.16412727709344" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C_final / A_final" ] }, { "cell_type": "markdown", "id": "07fe7c6c-f8dd-4460-aa08-d7c61d60bd62", "metadata": {}, "source": [ "### As expected the equilibrium constant for the overall reaction `A <-> C` (approx. 48) is indeed the product of the equilibrium constants of the two elementary reactions (K = 8 and K = 6, respectively) that we saw earlier." ] }, { "cell_type": "code", "execution_count": null, "id": "587c2018-e781-43c1-aee8-e78b7b6dc9bf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "520b3b44-7da9-49d3-9cfd-685607169f01", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "5c3f8b4f-3a75-4a21-8579-13550bcebb3c", "metadata": {}, "source": [ "# PART 2 - DIAGNOSTIC INSIGHT\n", "\n", "Perform some verification" ] }, { "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": "5ad64dc5-ba89-4f09-b7db-da40de1df4ed", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: A <-> B\n" ] }, { "data": { "text/html": [ "
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START_TIMEtime_stepabortedDelta ADelta Bcaptionrate
00.0000000.020000TrueNaNNaNaborted: neg. conc. in `A`NaN
10.0000000.010000True-32.00000032.000000aborted: excessive norm value(s)3200.000000
20.0000000.006000True-19.20000019.200000aborted: excessive norm value(s)3200.000000
30.0000000.003600True-11.52000011.520000aborted: excessive norm value(s)3200.000000
40.0000000.002160True-6.9120006.912000aborted: excessive norm value(s)3200.000000
50.0000000.001296True-4.1472004.147200aborted: excessive norm value(s)3200.000000
60.0000000.000778False-2.4883202.4883203200.000000
70.0007780.000622False-1.8792051.8792053020.840960
80.0014000.000622False-1.7951281.7951282885.686820
90.0020220.000498False-1.3719091.3719092756.697133
100.0025190.000498False-1.3228961.3228962658.211272
110.0030170.000498False-1.2756711.2756712563.317851
120.0035150.000498False-1.2301681.2301682471.885360
130.0040120.000498False-1.1863251.1863252383.787110
140.0045100.000498False-1.1440801.1440802298.901050
150.0050080.000498False-1.1033761.1033762217.109600
160.0055050.000498False-1.0641551.0641552138.299488
170.0060030.000498False-1.0263631.0263632062.361590
180.0065010.000498False-0.9899490.9899491989.190778
190.0069980.000498False-0.9548610.9548611918.685776
200.0074960.000746False-1.3815771.3815771850.749018
210.0082430.000746False-1.3082751.3082751752.555256
220.0089890.000746False-1.2389781.2389781659.724818
230.0097360.000746False-1.1734641.1734641571.963289
240.0104820.001120False-1.6672901.6672901488.992431
250.0116020.001120False-1.5355361.5355361371.327721
260.0127220.001120False-1.4145631.4145631263.291238
270.0138410.001120False-1.3034831.3034831164.090351
280.0149610.001680False-1.8022241.8022241072.997749
290.0166410.001680False-1.5914701.591470947.520208
300.0183200.001680False-1.4065221.406522837.406853
310.0200000.002519False-1.8662921.866292740.761211
320.0225190.002519False-1.5456701.545670613.501217
330.0250390.002519False-1.2837131.283713509.526499
340.0275580.003779False-1.6043511.604351424.528524
350.0313370.003779False-1.2102001.210200320.231977
360.0351160.003779False-0.9232540.923254244.302890
370.0388960.005669False-1.0707061.070706188.880147
380.0445640.005669False-0.7255490.725549127.992002
390.0502330.008503False-0.7759200.77592091.251951
400.0587360.006802False-0.3903380.39033857.382032
410.0655380.010204False-0.4620900.46209045.286669
420.0757420.008163False-0.2785610.27856134.125104
430.0839050.012244False-0.3623280.36232829.591334
440.0961490.009796False-0.2395410.23954124.454162
450.1059450.014693False-0.3149530.31495321.435190
460.1206380.014693False-0.2573040.25730417.511654
470.1353320.022040False-0.3157330.31573314.325526
480.1573710.022040False-0.2295130.22951310.413518
490.1794110.033060False-0.2502660.2502667.570088
500.2124710.033060False-0.1477540.1477544.469280
510.2455310.049590False-0.1308600.1308602.638855
520.2951210.074385False-0.0756620.0756621.017172
530.3695060.111577False-0.0090680.0090680.081275
\n", "
" ], "text/plain": [ " START_TIME time_step aborted Delta A Delta B \\\n", "0 0.000000 0.020000 True NaN NaN \n", "1 0.000000 0.010000 True -32.000000 32.000000 \n", "2 0.000000 0.006000 True -19.200000 19.200000 \n", "3 0.000000 0.003600 True -11.520000 11.520000 \n", "4 0.000000 0.002160 True -6.912000 6.912000 \n", "5 0.000000 0.001296 True -4.147200 4.147200 \n", "6 0.000000 0.000778 False -2.488320 2.488320 \n", "7 0.000778 0.000622 False -1.879205 1.879205 \n", "8 0.001400 0.000622 False -1.795128 1.795128 \n", "9 0.002022 0.000498 False -1.371909 1.371909 \n", "10 0.002519 0.000498 False -1.322896 1.322896 \n", "11 0.003017 0.000498 False -1.275671 1.275671 \n", "12 0.003515 0.000498 False -1.230168 1.230168 \n", "13 0.004012 0.000498 False -1.186325 1.186325 \n", "14 0.004510 0.000498 False -1.144080 1.144080 \n", "15 0.005008 0.000498 False -1.103376 1.103376 \n", "16 0.005505 0.000498 False -1.064155 1.064155 \n", "17 0.006003 0.000498 False -1.026363 1.026363 \n", "18 0.006501 0.000498 False -0.989949 0.989949 \n", "19 0.006998 0.000498 False -0.954861 0.954861 \n", "20 0.007496 0.000746 False -1.381577 1.381577 \n", "21 0.008243 0.000746 False -1.308275 1.308275 \n", "22 0.008989 0.000746 False -1.238978 1.238978 \n", "23 0.009736 0.000746 False -1.173464 1.173464 \n", "24 0.010482 0.001120 False -1.667290 1.667290 \n", "25 0.011602 0.001120 False -1.535536 1.535536 \n", "26 0.012722 0.001120 False -1.414563 1.414563 \n", "27 0.013841 0.001120 False -1.303483 1.303483 \n", "28 0.014961 0.001680 False -1.802224 1.802224 \n", "29 0.016641 0.001680 False -1.591470 1.591470 \n", "30 0.018320 0.001680 False -1.406522 1.406522 \n", "31 0.020000 0.002519 False -1.866292 1.866292 \n", "32 0.022519 0.002519 False -1.545670 1.545670 \n", "33 0.025039 0.002519 False -1.283713 1.283713 \n", "34 0.027558 0.003779 False -1.604351 1.604351 \n", "35 0.031337 0.003779 False -1.210200 1.210200 \n", "36 0.035116 0.003779 False -0.923254 0.923254 \n", "37 0.038896 0.005669 False -1.070706 1.070706 \n", "38 0.044564 0.005669 False -0.725549 0.725549 \n", "39 0.050233 0.008503 False -0.775920 0.775920 \n", "40 0.058736 0.006802 False -0.390338 0.390338 \n", "41 0.065538 0.010204 False -0.462090 0.462090 \n", "42 0.075742 0.008163 False -0.278561 0.278561 \n", "43 0.083905 0.012244 False -0.362328 0.362328 \n", "44 0.096149 0.009796 False -0.239541 0.239541 \n", "45 0.105945 0.014693 False -0.314953 0.314953 \n", "46 0.120638 0.014693 False -0.257304 0.257304 \n", "47 0.135332 0.022040 False -0.315733 0.315733 \n", "48 0.157371 0.022040 False -0.229513 0.229513 \n", "49 0.179411 0.033060 False -0.250266 0.250266 \n", "50 0.212471 0.033060 False -0.147754 0.147754 \n", "51 0.245531 0.049590 False -0.130860 0.130860 \n", "52 0.295121 0.074385 False -0.075662 0.075662 \n", "53 0.369506 0.111577 False -0.009068 0.009068 \n", "\n", " caption rate \n", "0 aborted: neg. conc. in `A` NaN \n", "1 aborted: excessive norm value(s) 3200.000000 \n", "2 aborted: excessive norm value(s) 3200.000000 \n", "3 aborted: excessive norm value(s) 3200.000000 \n", "4 aborted: excessive norm value(s) 3200.000000 \n", "5 aborted: excessive norm value(s) 3200.000000 \n", "6 3200.000000 \n", "7 3020.840960 \n", "8 2885.686820 \n", "9 2756.697133 \n", "10 2658.211272 \n", "11 2563.317851 \n", "12 2471.885360 \n", "13 2383.787110 \n", "14 2298.901050 \n", "15 2217.109600 \n", "16 2138.299488 \n", "17 2062.361590 \n", "18 1989.190778 \n", "19 1918.685776 \n", "20 1850.749018 \n", "21 1752.555256 \n", "22 1659.724818 \n", "23 1571.963289 \n", "24 1488.992431 \n", "25 1371.327721 \n", "26 1263.291238 \n", "27 1164.090351 \n", "28 1072.997749 \n", "29 947.520208 \n", "30 837.406853 \n", "31 740.761211 \n", "32 613.501217 \n", "33 509.526499 \n", "34 424.528524 \n", "35 320.231977 \n", "36 244.302890 \n", "37 188.880147 \n", "38 127.992002 \n", "39 91.251951 \n", "40 57.382032 \n", "41 45.286669 \n", "42 34.125104 \n", "43 29.591334 \n", "44 24.454162 \n", "45 21.435190 \n", "46 17.511654 \n", "47 14.325526 \n", "48 10.413518 \n", "49 7.570088 \n", "50 4.469280 \n", "51 2.638855 \n", "52 1.017172 \n", "53 0.081275 " ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Concentration increments due to reaction 0 (A <-> B)\n", "# Note that [C] is not affected\n", "dynamics.diagnostics.get_rxn_data(rxn_index=0)" ] }, { "cell_type": "code", "execution_count": 23, "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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START_TIMEtime_stepabortedDelta BDelta Cratecaption
00.0000000.010000True0.0000000.0000000.000000aborted: excessive norm value(s)
10.0000000.006000True0.0000000.0000000.000000aborted: excessive norm value(s)
20.0000000.003600True0.0000000.0000000.000000aborted: excessive norm value(s)
30.0000000.002160True0.0000000.0000000.000000aborted: excessive norm value(s)
40.0000000.001296True0.0000000.0000000.000000aborted: excessive norm value(s)
50.0000000.000778False0.0000000.0000000.000000
60.0007780.000622False-0.0185750.01857529.859840
70.0014000.000622False-0.0324420.03244252.150244
80.0020220.000498False-0.0364480.03644873.237598
90.0025190.000498False-0.0443870.04438789.190237
100.0030170.000498False-0.0519780.051978104.443575
110.0035150.000498False-0.0592340.059234119.023938
120.0040120.000498False-0.0661680.066168132.956683
130.0045100.000498False-0.0727910.072791146.266235
140.0050080.000498False-0.0791170.079117158.976118
150.0055050.000498False-0.0851550.085155171.108992
160.0060030.000498False-0.0909170.090917182.686681
170.0065010.000498False-0.0964130.096413193.730206
180.0069980.000498False-0.1016530.101653204.259814
190.0074960.000746False-0.1599700.159970214.295006
200.0082430.000746False-0.1706750.170675228.634342
210.0089890.000746False-0.1806100.180610241.944203
220.0097360.000746False-0.1898220.189822254.283393
230.0104820.001120False-0.2975240.297524265.707463
240.0116020.001120False-0.3152630.315263281.549606
250.0127220.001120False-0.3309540.330954295.562349
260.0138410.001120False-0.3447730.344773307.903744
270.0149610.001680False-0.5353250.535325318.718715
280.0166410.001680False-0.5590620.559062332.850855
290.0183200.001680False-0.5779920.577992344.121633
300.0200000.002519False-0.8891250.889125352.908006
310.0225190.002519False-0.9141880.914188362.855756
320.0250390.002519False-0.9286730.928673368.605168
330.0275580.003779False-1.4020911.402091371.008309
340.0313370.003779False-1.4006661.400666370.631249
350.0351160.003779False-1.3814421.381442365.544329
360.0388960.005669False-2.0253332.025333357.283191
370.0445640.005669False-1.9374331.937433341.777002
380.0502330.008503False-2.7495442.749544323.359530
390.0587360.006802False-2.0011232.001123294.176957
400.0655380.010204False-2.7636152.763615270.845299
410.0757420.008163False-1.9403271.940327237.699766
420.0839050.012244False-2.6188072.618807213.877913
430.0961490.009796False-1.7785001.778500181.562555
440.1059450.014693False-2.3441372.344137159.538054
450.1206380.014693False-1.9174671.917467130.499569
460.1353320.022040False-2.3526002.352600106.742678
470.1573710.022040False-1.7101891.71018977.595076
480.1794110.033060False-1.8647951.86479556.406583
490.2124710.033060False-1.1009821.10098233.302648
500.2455310.049590False-0.9750330.97503319.661952
510.2951210.074385False-0.5639720.5639727.581818
520.3695060.111577False-0.0662950.0662950.594162
\n", "
" ], "text/plain": [ " START_TIME time_step aborted Delta B Delta C rate \\\n", "0 0.000000 0.010000 True 0.000000 0.000000 0.000000 \n", "1 0.000000 0.006000 True 0.000000 0.000000 0.000000 \n", "2 0.000000 0.003600 True 0.000000 0.000000 0.000000 \n", "3 0.000000 0.002160 True 0.000000 0.000000 0.000000 \n", "4 0.000000 0.001296 True 0.000000 0.000000 0.000000 \n", "5 0.000000 0.000778 False 0.000000 0.000000 0.000000 \n", "6 0.000778 0.000622 False -0.018575 0.018575 29.859840 \n", "7 0.001400 0.000622 False -0.032442 0.032442 52.150244 \n", "8 0.002022 0.000498 False -0.036448 0.036448 73.237598 \n", "9 0.002519 0.000498 False -0.044387 0.044387 89.190237 \n", "10 0.003017 0.000498 False -0.051978 0.051978 104.443575 \n", "11 0.003515 0.000498 False -0.059234 0.059234 119.023938 \n", "12 0.004012 0.000498 False -0.066168 0.066168 132.956683 \n", "13 0.004510 0.000498 False -0.072791 0.072791 146.266235 \n", "14 0.005008 0.000498 False -0.079117 0.079117 158.976118 \n", "15 0.005505 0.000498 False -0.085155 0.085155 171.108992 \n", "16 0.006003 0.000498 False -0.090917 0.090917 182.686681 \n", "17 0.006501 0.000498 False -0.096413 0.096413 193.730206 \n", "18 0.006998 0.000498 False -0.101653 0.101653 204.259814 \n", "19 0.007496 0.000746 False -0.159970 0.159970 214.295006 \n", "20 0.008243 0.000746 False -0.170675 0.170675 228.634342 \n", "21 0.008989 0.000746 False -0.180610 0.180610 241.944203 \n", "22 0.009736 0.000746 False -0.189822 0.189822 254.283393 \n", "23 0.010482 0.001120 False -0.297524 0.297524 265.707463 \n", "24 0.011602 0.001120 False -0.315263 0.315263 281.549606 \n", "25 0.012722 0.001120 False -0.330954 0.330954 295.562349 \n", "26 0.013841 0.001120 False -0.344773 0.344773 307.903744 \n", "27 0.014961 0.001680 False -0.535325 0.535325 318.718715 \n", "28 0.016641 0.001680 False -0.559062 0.559062 332.850855 \n", "29 0.018320 0.001680 False -0.577992 0.577992 344.121633 \n", "30 0.020000 0.002519 False -0.889125 0.889125 352.908006 \n", "31 0.022519 0.002519 False -0.914188 0.914188 362.855756 \n", "32 0.025039 0.002519 False -0.928673 0.928673 368.605168 \n", "33 0.027558 0.003779 False -1.402091 1.402091 371.008309 \n", "34 0.031337 0.003779 False -1.400666 1.400666 370.631249 \n", "35 0.035116 0.003779 False -1.381442 1.381442 365.544329 \n", "36 0.038896 0.005669 False -2.025333 2.025333 357.283191 \n", "37 0.044564 0.005669 False -1.937433 1.937433 341.777002 \n", "38 0.050233 0.008503 False -2.749544 2.749544 323.359530 \n", "39 0.058736 0.006802 False -2.001123 2.001123 294.176957 \n", "40 0.065538 0.010204 False -2.763615 2.763615 270.845299 \n", "41 0.075742 0.008163 False -1.940327 1.940327 237.699766 \n", "42 0.083905 0.012244 False -2.618807 2.618807 213.877913 \n", "43 0.096149 0.009796 False -1.778500 1.778500 181.562555 \n", "44 0.105945 0.014693 False -2.344137 2.344137 159.538054 \n", "45 0.120638 0.014693 False -1.917467 1.917467 130.499569 \n", "46 0.135332 0.022040 False -2.352600 2.352600 106.742678 \n", "47 0.157371 0.022040 False -1.710189 1.710189 77.595076 \n", "48 0.179411 0.033060 False -1.864795 1.864795 56.406583 \n", "49 0.212471 0.033060 False -1.100982 1.100982 33.302648 \n", "50 0.245531 0.049590 False -0.975033 0.975033 19.661952 \n", "51 0.295121 0.074385 False -0.563972 0.563972 7.581818 \n", "52 0.369506 0.111577 False -0.066295 0.066295 0.594162 \n", "\n", " caption \n", "0 aborted: excessive norm value(s) \n", "1 aborted: excessive norm value(s) \n", "2 aborted: excessive norm value(s) \n", "3 aborted: excessive norm value(s) \n", "4 aborted: excessive norm value(s) \n", "5 \n", "6 \n", "7 \n", "8 \n", "9 \n", "10 \n", "11 \n", "12 \n", "13 \n", "14 \n", "15 \n", "16 \n", "17 \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 \n", "40 \n", "41 \n", "42 \n", "43 \n", "44 \n", "45 \n", "46 \n", "47 \n", "48 \n", "49 \n", "50 \n", "51 \n", "52 " ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Concentration increments due to reaction 1 (B <-> C) \n", "# Also notice that the 0-th row from the A <-> B reaction isn't seen here (start time 0 and step 0.02), \n", "# because that step was aborted early on, BEFORE even getting to THIS reaction\n", "dynamics.diagnostics.get_rxn_data(rxn_index=1)" ] }, { "cell_type": "code", "execution_count": null, "id": "46fdcb5b-ed5f-43a9-9829-533039666d0c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "a539f288-e9bc-44c3-a03a-982174b2babf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "de51ec27-1d0f-4bfb-83f0-b1c79b436d75", "metadata": { "tags": [] }, "source": [ "# PART 3 : Re-run with very small constant steps, and compare with original run" ] }, { "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": 24, "id": "93418d81-12fa-417d-9906-1dd24a40de48", "metadata": {}, "outputs": [], "source": [ "dynamics2 = UniformCompartment(chem_data=chem) # Re-use the same chemicals and reactions of the previous simulation" ] }, { "cell_type": "code", "execution_count": 25, "id": "ecf2029b-57a7-4db4-9b30-c854da91fb76", "metadata": { "tags": [] }, "outputs": [], "source": [ "dynamics2.set_conc({\"A\": 50.}, snapshot=True)" ] }, { "cell_type": "code", "execution_count": 26, "id": "00777982-d633-4c12-8c92-2ece6bf00e5e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "800 total step(s) taken\n" ] } ], "source": [ "# Notice that we're using FIXED steps this time\n", "dynamics2.single_compartment_react(initial_step=0.0005, duration=0.4,\n", " variable_steps=False,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " )" ] }, { "cell_type": "code", "execution_count": 27, "id": "6bb61113-a081-4366-893d-f94894c44ec2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (801) - only showing 1 every 6 lines\n" ] }, { "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": [ "dynamics2.plot_history(title=\"Coupled reactions A <-> B and B <-> C , re-run with CONSTANT STEPS\",\n", " colors=['darkturquoise', 'orange', 'green'], show_intervals=True)" ] }, { "cell_type": "markdown", "id": "3e27e613-21d9-4e99-ba9a-87b3a5393a44", "metadata": {}, "source": [ "_(Notice that the vertical steps are now equally spaced - and that there are so many of them that we're only showing 1 every 6)_" ] }, { "cell_type": "code", "execution_count": 28, "id": "e884f562-a723-4208-88e5-ba0bf36e5e3a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.011934802021672202, 24.03028826511689)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics2.curve_intersect(t_start=0, t_end=0.05, chem1=\"A\", chem2=\"B\")" ] }, { "cell_type": "code", "execution_count": 29, "id": "5b01f35a-17ac-4965-8a21-f300783c1e2c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.03259520587890533, 9.081194286771336)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics2.curve_intersect(t_start=0, t_end=0.05, chem1=\"A\", chem2=\"C\")" ] }, { "cell_type": "code", "execution_count": 30, "id": "5dae6925-3f3b-49ca-81f9-3cb8f19fdd55", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.07932921476313338, 23.238745930657448)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics2.curve_intersect(t_start=0.05, t_end=0.1, chem1=\"B\", chem2=\"C\")" ] }, { "cell_type": "code", "execution_count": 31, "id": "4fd2ea95-76e3-4cdf-9ea0-ecd37a515cb5", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
00.000050.0000000.0000000.000000Initialized 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
\n", "

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 Initialized 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": 31, "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 800 steps - vs. the 48 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": "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": 32, "id": "b2917e15-1c3a-4597-bc9b-22f0a83b3e08", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "SYSTEM TIME=%{x}
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", 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", 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"white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "The 2 runs, contrasted together" }, "xaxis": { "autorange": true, "range": [ 0, 0.4810828075200001 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "autorange": true, "range": [ -1.795805069078828, 34.120296312497736 ], "title": { "text": "[B]" }, "type": "linear" } } }, "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.combine_plots(fig_list=[fig1, fig2], title=\"The 2 runs, contrasted together\", \n", " curve_labels=[\"B (adaptive variable steps)\", \"B (fixed small steps)\"])" ] }, { "cell_type": "markdown", "id": "791e4d10-3173-4139-8216-09209acdfe6a", "metadata": {}, "source": [ "#### They overlap fairly well! The 800 fixed-timestep points vs. the 48 adaptable variable-timestep ones.\n", "The adaptive algorithms avoided 752 extra steps of limited benefit..." ] }, { "cell_type": "code", "execution_count": null, "id": "893df3ce-7cb3-4eec-b8a4-397334f65dd4", "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": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 5 }