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"cells": [
{
"cell_type": "markdown",
"id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0",
"metadata": {},
"source": [
"## Association/Dissociation reaction `2A <-> C`\n",
"#### with 2nd-order kinetics for `A`, \n",
"#### and 1-st order kinetics for `C`\n",
"\n",
"Taken to equilibrium. (Adaptive variable time teps are used)\n",
"\n",
"_See also the experiment \"1D/reactions/reaction_7\"_ \n",
"\n",
"LAST REVISED: July 14, 2023"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "e6cefd48-5909-4cc0-a48f-ef016a2ee1cf",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n"
]
}
],
"source": [
"import set_path # Importing this module will add the project's home directory to sys.path"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "b708df90",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"from experiments.get_notebook_info import get_notebook_basename\n",
"\n",
"from src.modules.chemicals.chem_data import ChemData as chem\n",
"from src.modules.reactions.reaction_dynamics import ReactionDynamics\n",
"\n",
"from src.modules.visualization.graphic_log import GraphicLog"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "83c3cc5f-de21-4f66-9988-2806fbf0666d",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-> Output will be LOGGED into the file 'react_4.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: 1 (at temp. 25 C)\n",
"0: 2 A <-> C (kF = 3 / kR = 2 / Delta_G = -1,005.13 / K = 1.5) | 2-th order in reactant A\n"
]
}
],
"source": [
"# Specify the chemicals\n",
"chem_data = chem(names=[\"A\", \"C\"])\n",
"\n",
"# Reaction 2A <-> C , with 2nd-order kinetics for A, and 1st-order kinetics for C\n",
"chem_data.add_reaction(reactants=[(2, \"A\", 2)], products=[\"C\"],\n",
" forward_rate=3., reverse_rate=2.) \n",
"# Note: the first 2 in (2, \"A\", 2) is the stoichiometry coefficient, while the other one is the order\n",
"\n",
"chem_data.describe_reactions()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "cb582868-431c-4022-aa0e-a2f554f80d6c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[GRAPHIC ELEMENT SENT TO LOG FILE `react_4.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": 6,
"id": "c2f4a554-807b-49f9-8ca2-8d929fe6eeef",
"metadata": {},
"outputs": [],
"source": [
"dynamics = ReactionDynamics(chem_data=chem_data)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef",
"metadata": {},
"outputs": [],
"source": [
"# Initial concentrations of all the chemicals, in index order\n",
"dynamics.set_conc([200., 40.], snapshot=True)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a605dacf-2c67-403e-9aa9-5be25fc9f481",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"2 species:\n",
" Species 0 (A). Conc: 200.0\n",
" Species 1 (C). Conc: 40.0\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "0ff2c242-a15b-456d-ad56-0ba1041c0b4c",
"metadata": {},
"outputs": [
{
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"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
" C | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.0 | \n",
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" 40.0 | \n",
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"cell_type": "markdown",
"id": "fc516ca2-e62d-4784-b826-5372ff7f4c75",
"metadata": {
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"source": [
"## Run the reaction"
]
},
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"cell_type": "code",
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"id": "2502cd11-0df9-4303-8895-98401a1df7b8",
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"\n",
"*** CAUTION: negative concentration in chemical `A` in step starting at t=0. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n",
" INFO: the tentative time step (0.002) leads to a NEGATIVE concentration of `A` from reaction 2 A <-> C (rxn # 0): \n",
" Baseline value: 200 ; delta conc: -479.68\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.001) [Step started at t=0, and will rewind there]\n",
"\n",
"*** CAUTION: negative concentration in chemical `A` in step starting at t=0. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n",
" INFO: the tentative time step (0.001) leads to a NEGATIVE concentration of `A` from reaction 2 A <-> C (rxn # 0): \n",
" Baseline value: 200 ; delta conc: -239.84\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.0005) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.0005) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.00025) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.00025) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.000125) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.000125) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 6.25e-05) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (6.25e-05) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 3.125e-05) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (3.125e-05) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 1.5625e-05) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (1.5625e-05) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 7.8125e-06) [Step started at t=0, and will rewind there]\n",
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"103 total step(s) taken\n"
]
}
],
"source": [
"dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n",
"\n",
"# All of these settings are currently close to the default values... but subject to change; set for repeatability\n",
"dynamics.set_thresholds(norm=\"norm_A\", low=1.0, high=2.0, abort=3.5)\n",
"dynamics.set_thresholds(norm=\"norm_B\", low=0.1, high=0.5, abort=3.0)\n",
"dynamics.set_step_factors(upshift=1.5, downshift=0.5, abort=0.5)\n",
"dynamics.set_error_step_factor(0.5)\n",
"\n",
"dynamics.single_compartment_react(initial_step=0.002, reaction_duration=0.04,\n",
" snapshots={\"initial_caption\": \"1st reaction step\",\n",
" \"final_caption\": \"last reaction step\"},\n",
" variable_steps=True, explain_variable_steps=False)"
]
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{
"cell_type": "markdown",
"id": "99a9a4b2-a588-4ba5-85c9-0a5a5d1dbaad",
"metadata": {},
"source": [
"### Note how the (tentative) original time step that we provide, 0.002, turned out to be so large that the simulation backtracks several times, because of \"hard\" aborts (negative concentrations) or \"soft\" aborts (concentration changes surpassing the thresholds we provided)"
]
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_curves(colors=['red', 'green'],\n",
" title=\"Reaction 2A <-> C (2nd order in A). Changes in concentrations with time\")"
]
},
{
"cell_type": "markdown",
"id": "b1366038-2dea-4d69-a655-ae464ca22922",
"metadata": {},
"source": [
"## Note: \"A\" (now largely depleted) is the limiting reagent"
]
},
{
"cell_type": "markdown",
"id": "39cb26e8-c061-41ab-a91a-77df6f431efa",
"metadata": {},
"source": [
"#### Let's take a look at time t=0.002, which in our simulation run had proposed as the first step:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "232349ed-fa23-4ebf-b4ba-d5bddcc8902c",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" search_value | \n",
" SYSTEM TIME | \n",
" A | \n",
" C | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 74 | \n",
" 0.002 | \n",
" 0.002044 | \n",
" 57.328404 | \n",
" 111.335798 | \n",
" | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" search_value SYSTEM TIME A C caption\n",
"74 0.002 0.002044 57.328404 111.335798 "
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Locate the value closest to the original time step we had requested\n",
"dynamics.get_history(t=0.002)"
]
},
{
"cell_type": "markdown",
"id": "b03c9994-cade-48cf-8b14-4b894cc755cf",
"metadata": {},
"source": [
"### Because of the very large changes happening between t=0 and 0.002, the simulation automatically slowed down and opted to actually take 74 steps in lieu of the 1 step we had proposed.\n",
"The number of variable steps actually taken can be modulated by changing the \"norm thresholds\" and \"step factors\" that we can optionally specify"
]
},
{
"cell_type": "markdown",
"id": "ce3cd198-de57-4e0f-80f2-8e07f2cd7f96",
"metadata": {},
"source": [
"### Notice how, later in the simulation, the step sizes get BIGGER than the 0.002 we had originally proposed:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "071a9544-639a-40f7-92bc-3a20050c9c00",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"From time 0 to 3.125e-05, in 4 steps of 7.81e-06\n",
"From time 3.125e-05 to 4.297e-05, in 1 step of 1.17e-05\n",
"From time 4.297e-05 to 4.883e-05, in 1 step of 5.86e-06\n",
"From time 4.883e-05 to 8.398e-05, in 4 steps of 8.79e-06\n",
"From time 8.398e-05 to 9.717e-05, in 1 step of 1.32e-05\n",
"From time 9.717e-05 to 0.0001038, in 1 step of 6.59e-06\n",
"From time 0.0001038 to 0.0001433, in 4 steps of 9.89e-06\n",
"From time 0.0001433 to 0.0001581, in 1 step of 1.48e-05\n",
"From time 0.0001581 to 0.0001656, in 1 step of 7.42e-06\n",
"From time 0.0001656 to 0.0001989, in 3 steps of 1.11e-05\n",
"From time 0.0001989 to 0.0002156, in 1 step of 1.67e-05\n",
"From time 0.0002156 to 0.000224, in 1 step of 8.34e-06\n",
"From time 0.000224 to 0.0002615, in 3 steps of 1.25e-05\n",
"From time 0.0002615 to 0.0002803, in 1 step of 1.88e-05\n",
"From time 0.0002803 to 0.0002897, in 1 step of 9.39e-06\n",
"From time 0.0002897 to 0.0003319, in 3 steps of 1.41e-05\n",
"From time 0.0003319 to 0.000353, in 1 step of 2.11e-05\n",
"From time 0.000353 to 0.0003636, in 1 step of 1.06e-05\n",
"From time 0.0003636 to 0.0003952, in 2 steps of 1.58e-05\n",
"From time 0.0003952 to 0.000419, in 1 step of 2.38e-05\n",
"From time 0.000419 to 0.0004309, in 1 step of 1.19e-05\n",
"From time 0.0004309 to 0.0004665, in 2 steps of 1.78e-05\n",
"From time 0.0004665 to 0.0004932, in 1 step of 2.67e-05\n",
"From time 0.0004932 to 0.0005066, in 1 step of 1.34e-05\n",
"From time 0.0005066 to 0.0005467, in 2 steps of 2e-05\n",
"From time 0.0005467 to 0.0005768, in 1 step of 3.01e-05\n",
"From time 0.0005768 to 0.0005918, in 1 step of 1.5e-05\n",
"From time 0.0005918 to 0.0006369, in 2 steps of 2.26e-05\n",
"From time 0.0006369 to 0.0006707, in 1 step of 3.38e-05\n",
"From time 0.0006707 to 0.0006876, in 1 step of 1.69e-05\n",
"From time 0.0006876 to 0.0007384, in 2 steps of 2.54e-05\n",
"From time 0.0007384 to 0.001081, in 9 steps of 3.81e-05\n",
"From time 0.001081 to 0.001138, in 1 step of 5.71e-05\n",
"From time 0.001138 to 0.001166, in 1 step of 2.85e-05\n",
"From time 0.001166 to 0.001209, in 1 step of 4.28e-05\n",
"From time 0.001209 to 0.001659, in 7 steps of 6.42e-05\n",
"From time 0.001659 to 0.002237, in 6 steps of 9.63e-05\n",
"From time 0.002237 to 0.002959, in 5 steps of 0.000144\n",
"From time 0.002959 to 0.003826, in 4 steps of 0.000217\n",
"From time 0.003826 to 0.004801, in 3 steps of 0.000325\n",
"From time 0.004801 to 0.006264, in 3 steps of 0.000488\n",
"From time 0.006264 to 0.007727, in 2 steps of 0.000731\n",
"From time 0.007727 to 0.009922, in 2 steps of 0.0011\n",
"From time 0.009922 to 0.01321, in 2 steps of 0.00165\n",
"From time 0.01321 to 0.01568, in 1 step of 0.00247\n",
"From time 0.01568 to 0.02309, in 2 steps of 0.0037\n",
"From time 0.02309 to 0.02864, in 1 step of 0.00555\n",
"From time 0.02864 to 0.03697, in 1 step of 0.00833\n",
"From time 0.03697 to 0.04947, in 1 step of 0.0125\n",
"(103 steps total)\n"
]
}
],
"source": [
"dynamics.explain_time_advance()"
]
},
{
"cell_type": "markdown",
"id": "9fb5f6b8-dde3-415d-9e90-b8d102bfd748",
"metadata": {},
"source": [
"### Notice how the reaction proceeds in far-smaller steps in the early times, when the concentrations are changing much more rapidly"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "12118fdd-5e81-42e5-b271-818f8d686b79",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([200., 40.], dtype=float32),\n",
" array([198.12625 , 40.936874], dtype=float32))"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Let's look at the first two arrays of concentrations, from the run's history\n",
"arr0 = dynamics.get_historical_concentrations(0) # The initial concentrations\n",
"arr1 = dynamics.get_historical_concentrations(1) # After the first actual step\n",
"arr0, arr1"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "a2450ae8-e342-4adf-9330-ce86a1dfcbeb",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Let's verify that the reaction's stoichiometry is being respected\n",
"dynamics.stoichiometry_checker(rxn_index=0, \n",
" conc_arr_before = arr0, \n",
" conc_arr_after = arr1)"
]
},
{
"cell_type": "markdown",
"id": "bf6dc3ed-5999-4379-8ae1-05f73e2a670d",
"metadata": {},
"source": [
"#### Indeed, it can be easy checked that the drop in [A] is twice the increase in [C], as dictated by the stoichiometry"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "4ccfa79c-0bd4-40f0-be82-2da19523cd40",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reaction: 2 A <-> C\n"
]
},
{
"data": {
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"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" START_TIME | \n",
" Delta A | \n",
" Delta C | \n",
" time_step | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" NaN | \n",
" NaN | \n",
" 0.002000 | \n",
" aborted: neg. conc. in `A` | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.000000 | \n",
" NaN | \n",
" NaN | \n",
" 0.001000 | \n",
" aborted: neg. conc. in `A` | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.000000 | \n",
" -119.920000 | \n",
" 59.960000 | \n",
" 0.000500 | \n",
" aborted: excessive norm value(s) | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.000000 | \n",
" -59.960000 | \n",
" 29.980000 | \n",
" 0.000250 | \n",
" aborted: excessive norm value(s) | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.000000 | \n",
" -29.980000 | \n",
" 14.990000 | \n",
" 0.000125 | \n",
" aborted: excessive norm value(s) | \n",
"
\n",
" \n",
" | 5 | \n",
" 0.000000 | \n",
" -14.990000 | \n",
" 7.495000 | \n",
" 0.000063 | \n",
" aborted: excessive norm value(s) | \n",
"
\n",
" \n",
" | 6 | \n",
" 0.000000 | \n",
" -7.495000 | \n",
" 3.747500 | \n",
" 0.000031 | \n",
" aborted: excessive norm value(s) | \n",
"
\n",
" \n",
" | 7 | \n",
" 0.000000 | \n",
" -3.747500 | \n",
" 1.873750 | \n",
" 0.000016 | \n",
" aborted: excessive norm value(s) | \n",
"
\n",
" \n",
" | 8 | \n",
" 0.000000 | \n",
" -1.873750 | \n",
" 0.936875 | \n",
" 0.000008 | \n",
" | \n",
"
\n",
" \n",
" | 9 | \n",
" 0.000008 | \n",
" -1.838752 | \n",
" 0.919376 | \n",
" 0.000008 | \n",
" | \n",
"
\n",
" \n",
" | 10 | \n",
" 0.000016 | \n",
" -1.804729 | \n",
" 0.902364 | \n",
" 0.000008 | \n",
" | \n",
"
\n",
" \n",
" | 11 | \n",
" 0.000023 | \n",
" -1.771643 | \n",
" 0.885821 | \n",
" 0.000008 | \n",
" | \n",
"
\n",
" \n",
" | 12 | \n",
" 0.000031 | \n",
" -2.609190 | \n",
" 1.304595 | \n",
" 0.000012 | \n",
" | \n",
"
\n",
" \n",
" | 13 | \n",
" 0.000043 | \n",
" -1.269449 | \n",
" 0.634725 | \n",
" 0.000006 | \n",
" | \n",
"
\n",
" \n",
" | 14 | \n",
" 0.000049 | \n",
" -1.878784 | \n",
" 0.939392 | \n",
" 0.000009 | \n",
" | \n",
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\n",
" \n",
"
\n",
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"
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" START_TIME Delta A Delta C time_step \\\n",
"0 0.000000 NaN NaN 0.002000 \n",
"1 0.000000 NaN NaN 0.001000 \n",
"2 0.000000 -119.920000 59.960000 0.000500 \n",
"3 0.000000 -59.960000 29.980000 0.000250 \n",
"4 0.000000 -29.980000 14.990000 0.000125 \n",
"5 0.000000 -14.990000 7.495000 0.000063 \n",
"6 0.000000 -7.495000 3.747500 0.000031 \n",
"7 0.000000 -3.747500 1.873750 0.000016 \n",
"8 0.000000 -1.873750 0.936875 0.000008 \n",
"9 0.000008 -1.838752 0.919376 0.000008 \n",
"10 0.000016 -1.804729 0.902364 0.000008 \n",
"11 0.000023 -1.771643 0.885821 0.000008 \n",
"12 0.000031 -2.609190 1.304595 0.000012 \n",
"13 0.000043 -1.269449 0.634725 0.000006 \n",
"14 0.000049 -1.878784 0.939392 0.000009 \n",
"\n",
" caption \n",
"0 aborted: neg. conc. in `A` \n",
"1 aborted: neg. conc. in `A` \n",
"2 aborted: excessive norm value(s) \n",
"3 aborted: excessive norm value(s) \n",
"4 aborted: excessive norm value(s) \n",
"5 aborted: excessive norm value(s) \n",
"6 aborted: excessive norm value(s) \n",
"7 aborted: excessive norm value(s) \n",
"8 \n",
"9 \n",
"10 \n",
"11 \n",
"12 \n",
"13 \n",
"14 "
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dynamics.get_diagnostic_rxn_data(rxn_index=0, head=15) # Easily seen in the diagnostic data"
]
},
{
"cell_type": "markdown",
"id": "a2f4d0e3-b259-4bd1-a94e-5751264775f7",
"metadata": {},
"source": [
"### From the diagnostic data, it can be seen that the first step had several false starts - and was automatically repeatedly shrunk - but finally happened. `Delta A` indeed equals - 2 * `Delta C`, satisfying the stoichiometry"
]
},
{
"cell_type": "markdown",
"id": "c02a8f55-a671-4771-86c9-fc4d1b126bf8",
"metadata": {},
"source": [
"### Check the final equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "765f6f39-4b2e-4a86-b6a9-ace9d1941663",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: 2 A <-> C\n",
"Final concentrations: [C] = 135.3 ; [A] = 9.493\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.50075\n",
" Formula used: [C] / [A]^2 \n",
"2. Ratio of forward/reverse reaction rates: 1.5\n",
"Discrepancy between the two values: 0.05016 %\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 the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium()"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "014c9870-1e91-4979-a24b-6e9f1c216640",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dynamics.stoichiometry_checker_entire_run()"
]
},
{
"cell_type": "markdown",
"id": "6ac3dd4e-9dd0-4d3a-aa83-76102bd79524",
"metadata": {
"tags": []
},
"source": [
"## Display the variable time steps"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "21e4814e-5603-4d38-acc8-549b1d59ec93",
"metadata": {},
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_curves(colors=['red', 'green'], show_intervals=True,\n",
" title=\"Reaction 2A <-> C (2nd order in A). Changes in concentrations with time\")"
]
},
{
"cell_type": "markdown",
"id": "fde6184c-b365-4ef3-aac7-ad7561671f2d",
"metadata": {},
"source": [
"### The intersection of the two lines may be found as follows:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "e5370c40-4812-4bcd-aac0-949757513454",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Min abs distance found at data row: 56\n"
]
},
{
"data": {
"text/plain": [
"(0.0009405253857178681, 93.33333333333333)"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dynamics.curve_intersection('A', 'C', t_start=0, t_end=0.01)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f288907f-4305-43c9-80f2-38f35d19fc56",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "5c3f8b4f-3a75-4a21-8579-13550bcebb3c",
"metadata": {},
"source": [
"#### For diagnostic insight, uncomment the following lines:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "10af1095-a320-4fa4-a45e-e1f3f87203c9",
"metadata": {},
"outputs": [],
"source": [
"#dynamics.get_diagnostic_decisions_data()\n",
"\n",
"#dynamics.get_diagnostic_rxn_data(rxn_index=0)\n",
"\n",
"#dynamics.get_diagnostic_conc_data()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c75e9ff2",
"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
}