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{
"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: June 4, 2023"
]
},
{
"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": [
"import set_path # Importing this module will add the project's home directory to sys.path"
]
},
{
"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 ChemData 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 '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(reaction_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",
" 200.0 | \n",
" 40.0 | \n",
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"cell_type": "markdown",
"id": "fc516ca2-e62d-4784-b826-5372ff7f4c75",
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"source": [
"## Run the reaction"
]
},
{
"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": {
"text/html": [
"\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",
"
\n",
" \n",
"
\n",
"
"
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"text/plain": [
" 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"
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],
"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",
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"source": [
"### Check the final equilibrium"
]
},
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"cell_type": "code",
"execution_count": 18,
"id": "765f6f39-4b2e-4a86-b6a9-ace9d1941663",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"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"
]
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"data": {
"text/plain": [
"True"
]
},
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"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",
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"tags": []
},
"source": [
"## Display the variable time steps"
]
},
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"execution_count": 20,
"id": "21e4814e-5603-4d38-acc8-549b1d59ec93",
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"title": {
"standoff": 15
},
"zerolinecolor": "white",
"zerolinewidth": 2
},
"yaxis": {
"automargin": true,
"gridcolor": "white",
"linecolor": "white",
"ticks": "",
"title": {
"standoff": 15
},
"zerolinecolor": "white",
"zerolinewidth": 2
}
}
},
"title": {
"text": "Reaction 2A <-> C (2nd order in A). Changes in concentrations with time (time steps shown in dashed lines)"
},
"xaxis": {
"anchor": "y",
"autorange": true,
"domain": [
0,
1
],
"range": [
-2.8237832656611064e-05,
0.0495009206470392
],
"title": {
"text": "SYSTEM TIME"
},
"type": "linear"
},
"yaxis": {
"anchor": "x",
"autorange": true,
"domain": [
0,
1
],
"range": [
-1.090353777283104,
210.58370283038332
],
"title": {
"text": "concentration"
},
"type": "linear"
}
}
},
"image/png": 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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": "e6cefd48-5909-4cc0-a48f-ef016a2ee1cf",
"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": "f288907f-4305-43c9-80f2-38f35d19fc56",
"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
}