{
"cells": [
{
"cell_type": "markdown",
"id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0",
"metadata": {},
"source": [
"## `A <-> B` elementary unimolecular reaction \n",
"with 1st-order kinetics in both directions, taken to equilibrium,\n",
"using a simple, **coarse fixed-timestep simulation.** \n",
"\n",
"In Part 2, below, we perform some analysis of the results: in particular, we examine the **reaction rates**. \n",
"\n",
"(See also the experiment _\"1D/reactions/reaction_1\"_ for a multi-compartment version) \n",
"\n",
"#### This experiment gets repeated in _\"react_2_b\"_ , with a more sophisticated approach, \n",
"#### involving adaptive variable time steps"
]
},
{
"cell_type": "markdown",
"id": "c9b76274-719e-491c-b70e-cbf3e167f10a",
"metadata": {
"tags": []
},
"source": [
"### TAGS : \"basic\", \"uniform compartment\""
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "0fac88df-1c44-4419-8479-a20369b06499",
"metadata": {},
"outputs": [],
"source": [
"LAST_REVISED = \"Feb. 16, 2026\"\n",
"LIFE123_VERSION = \"1.0.0rc7\" # Library version this experiment is based on"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "e2d818e7-05d8-4624-b9de-2ff263b879be",
"metadata": {},
"outputs": [],
"source": [
"#import set_path # Using MyBinder? Uncomment this before running the next cell!"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "b0ce3cdd",
"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 numpy as np\n",
"import ipynbname\n",
"\n",
"from life123 import check_version, UniformCompartment, ThermoDynamics, PlotlyHelper"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "4f75ae66-3d5c-474c-8d88-bd8a7ca92aef",
"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": [],
"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",
" # IN CASE OF PROBLEMS, set manually to any desired name"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "46703103-a97d-426c-bf6e-ad6e397a7ddb",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "66400086-eaa7-427c-9bdd-fb1de0346596",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "83eb30cd-1a3f-4732-8927-f5240c255d85",
"metadata": {},
"source": [
"# PART 1 - simulation of the reaction"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "72b4245c-de4e-480d-a501-3495b7ed8bc4",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"add_reaction(): detected reaction type `ReactionUnimolecular`\n",
"Number of reactions: 1\n"
]
}
],
"source": [
"# Instantiate the simulator and specify the chemicals\n",
"uc = UniformCompartment()\n",
"\n",
"# Reaction A <-> B , with 1st-order kinetics in both directions\n",
"uc.add_reaction(reactants=\"A\", products=\"B\", kF=3., kR=2.)\n",
"\n",
"print(\"Number of reactions: \", uc.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: 1\n",
"0: A <-> B Elementary Unimolecular reaction (kF = 3 / kR = 2 / delta_G = -1,005.1 / K = 1.5 / Temp = 25 C)\n",
"Chemicals involved in the above reactions: ['A', 'B']\n"
]
}
],
"source": [
"uc.describe_reactions()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "cb582868-431c-4022-aa0e-a2f554f80d6c",
"metadata": {
"lines_to_next_cell": 2
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[GRAPHIC ELEMENT SENT TO FILE `react_2_a.log.htm`]\n"
]
}
],
"source": [
"# Send a plot of the network of reactions to the HTML log file\n",
"uc.plot_reaction_network(log_file=log_file)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b5a0bc1d-2638-4eeb-bdec-0090906b5c5d",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 9,
"id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef",
"metadata": {},
"outputs": [],
"source": [
"# Initial concentrations of all the chemicals\n",
"uc.set_conc({\"A\": 10., \"B\": 50.})"
]
},
{
"cell_type": "code",
"execution_count": 10,
"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: 10.0\n",
" Species 1 (B). Conc: 50.0\n",
"Chemicals involved in reactions: ['B', 'A']\n"
]
}
],
"source": [
"uc.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "0ff2c242-a15b-456d-ad56-0ba1041c0b4c",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
" B | \n",
" step | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.0 | \n",
" 10.0 | \n",
" 50.0 | \n",
" | \n",
" Set concentration | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" SYSTEM TIME A B step caption\n",
"0 0.0 10.0 50.0 Set concentration"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"uc.get_history()"
]
},
{
"cell_type": "markdown",
"id": "ab7147fe-712c-4c92-b61f-20ff51675ab8",
"metadata": {},
"source": [
"### Test your intuition: \n",
"#### given that this reaction operates mostly in the forward direction (kF = 3 , kR = 2 , K = 1.5), \n",
"#### do you think that A will be consumed and B will be produced??\n",
"We can take a sneak preview at the final equilibrium concentrations without actually running the simulation:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "12cac04d-dd61-4646-9339-8b70e22139e8",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'A': 24.0, 'B': 36.0}"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"uc.find_equilibrium_conc(rxn_index=0) # This is an EXACT equilibrium solution, \n",
" # for 1 reaction (the only reaction)"
]
},
{
"cell_type": "markdown",
"id": "690cc5bd-2e57-43da-8a1b-292ca6e37ea1",
"metadata": {},
"source": [
"That's consistent with the 3/2 ratio of forward/reverse rate constants (and the 1st order of the reaction)"
]
},
{
"cell_type": "markdown",
"id": "ee5b9d1c-3ebe-497a-a0e9-bfb02dcd0693",
"metadata": {},
"source": [
"#### Considering that our initial state is {\"A\": 10., \"B\": 50.}, the reaction will actually proceed IN REVERSE (decreasing product), because of the large initial concentration of `B`, relative to the small initial concentration of `A`\n",
"More precisely, it's because the **reaction quotient Q**, at the current initial concentrations, is larger than our **equilibrium constant K**, which is 1.5 :"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "3f46ea3f-e8e8-4b9b-9b56-ed144661d24e",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"5.0"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ThermoDynamics.compute_reaction_quotient(reactant_data=[\"A\"], product_data=[\"B\"],\n",
" conc={\"A\": 10., \"B\": 50.})"
]
},
{
"cell_type": "markdown",
"id": "92d79bbd-a538-4437-96bd-fb7dc8c3a7e2",
"metadata": {},
"source": [
"Now, let's see the reaction in action!"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7862d1a6-c731-4e08-a497-7abd6f20bf5f",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "7c0f5358-01f8-444b-a6b5-2ce3806af143",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "fc516ca2-e62d-4784-b826-5372ff7f4c75",
"metadata": {
"tags": []
},
"source": [
"### Run the reaction"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "50c7e478-ad0e-4aeb-9cea-dfed47cded21",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 total fixed step(s) taken in 0.005 sec\n"
]
}
],
"source": [
"# First step of reaction\n",
"uc.single_compartment_react(initial_step=0.1, n_steps=1, variable_steps=False) # NOT using variable steps!"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "c9115720-e66e-44f3-bb0a-fabec5b96673",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
" B | \n",
" step | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.0 | \n",
" 10.0 | \n",
" 50.0 | \n",
" | \n",
" Set concentration | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.1 | \n",
" 17.0 | \n",
" 43.0 | \n",
" 1 | \n",
" last reaction step | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" SYSTEM TIME A B step caption\n",
"0 0.0 10.0 50.0 Set concentration\n",
"1 0.1 17.0 43.0 1 last reaction step"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"uc.get_history()"
]
},
{
"cell_type": "markdown",
"id": "98ec8a03-7a9b-403a-8dcd-d9e19c49d656",
"metadata": {},
"source": [
"We can already see the reaction proceeding in reverse..."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "2502cd11-0df9-4303-8895-98401a1df7b8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10 total fixed step(s) taken in 0.020 sec\n"
]
}
],
"source": [
"# Numerous more fixed steps\n",
"uc.single_compartment_react(initial_step=0.1, n_steps=10, variable_steps=False) # Again, fixed steps used"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "80fbaee3-bd6f-4197-9270-23374d46a4a7",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
" B | \n",
" step | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.0 | \n",
" 10.000000 | \n",
" 50.000000 | \n",
" | \n",
" Set concentration | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.1 | \n",
" 17.000000 | \n",
" 43.000000 | \n",
" 1 | \n",
" last reaction step | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.2 | \n",
" 20.500000 | \n",
" 39.500000 | \n",
" 1 | \n",
" 1st reaction step | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.3 | \n",
" 22.250000 | \n",
" 37.750000 | \n",
" 2 | \n",
" | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.4 | \n",
" 23.125000 | \n",
" 36.875000 | \n",
" 3 | \n",
" | \n",
"
\n",
" \n",
" | 5 | \n",
" 0.5 | \n",
" 23.562500 | \n",
" 36.437500 | \n",
" 4 | \n",
" | \n",
"
\n",
" \n",
" | 6 | \n",
" 0.6 | \n",
" 23.781250 | \n",
" 36.218750 | \n",
" 5 | \n",
" | \n",
"
\n",
" \n",
" | 7 | \n",
" 0.7 | \n",
" 23.890625 | \n",
" 36.109375 | \n",
" 6 | \n",
" | \n",
"
\n",
" \n",
" | 8 | \n",
" 0.8 | \n",
" 23.945312 | \n",
" 36.054688 | \n",
" 7 | \n",
" | \n",
"
\n",
" \n",
" | 9 | \n",
" 0.9 | \n",
" 23.972656 | \n",
" 36.027344 | \n",
" 8 | \n",
" | \n",
"
\n",
" \n",
" | 10 | \n",
" 1.0 | \n",
" 23.986328 | \n",
" 36.013672 | \n",
" 9 | \n",
" | \n",
"
\n",
" \n",
" | 11 | \n",
" 1.1 | \n",
" 23.993164 | \n",
" 36.006836 | \n",
" 10 | \n",
" last reaction step | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" SYSTEM TIME A B step caption\n",
"0 0.0 10.000000 50.000000 Set concentration\n",
"1 0.1 17.000000 43.000000 1 last reaction step\n",
"2 0.2 20.500000 39.500000 1 1st reaction step\n",
"3 0.3 22.250000 37.750000 2 \n",
"4 0.4 23.125000 36.875000 3 \n",
"5 0.5 23.562500 36.437500 4 \n",
"6 0.6 23.781250 36.218750 5 \n",
"7 0.7 23.890625 36.109375 6 \n",
"8 0.8 23.945312 36.054688 7 \n",
"9 0.9 23.972656 36.027344 8 \n",
"10 1.0 23.986328 36.013672 9 \n",
"11 1.1 23.993164 36.006836 10 last reaction step"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"uc.get_history()"
]
},
{
"cell_type": "markdown",
"id": "c7650ed4-365e-43c2-b001-280297c68ece",
"metadata": {},
"source": [
"## NOTE: for demonstration purposes, we're using FIXED time steps... \n",
"## Typically, one would use the option for adaptive variable time steps (see experiment `react_2_b`)"
]
},
{
"cell_type": "markdown",
"id": "c034956a-683c-4c3d-8134-ecac9e19a45c",
"metadata": {},
"source": [
"### Check the final equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "b139f5e4-625f-4a5e-8f57-8f00244dced4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([23.99316406, 36.00683594])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"uc.get_system_conc() # The current concentrations, in the order the chemicals were added "
]
},
{
"cell_type": "markdown",
"id": "d25eedf3-89f8-4f8c-a49a-d2689103528b",
"metadata": {},
"source": [
"That's very close to the values we previewed earlier: {'A': 24.0, 'B': 36.0}\n"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "765f6f39-4b2e-4a86-b6a9-ace9d1941663",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: A <-> B\n",
"Current concentrations: [A] = 23.99 ; [B] = 36.01\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.50071\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 1.5\n",
"Discrepancy between the two values: 0.04749 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"uc.is_in_equilibrium()"
]
},
{
"cell_type": "markdown",
"id": "905adfdd-6d70-4dfc-bb34-c547c4d604b9",
"metadata": {},
"source": [
"### As noted earlier, because of the high initial concentration of B relative to A, the overall reaction has proceeded IN REVERSE"
]
},
{
"cell_type": "markdown",
"id": "6ac3dd4e-9dd0-4d3a-aa83-76102bd79524",
"metadata": {
"tags": []
},
"source": [
"## Plots of changes of concentration with time"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "86976e6f-f453-41c3-9553-b27b1328db6b",
"metadata": {},
"outputs": [
{
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" \n",
" "
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"uc.plot_history(colors=['darkturquoise', 'green'], show_intervals=True)"
]
},
{
"cell_type": "markdown",
"id": "dffad4cb-ec16-4ded-9766-b609244f4496",
"metadata": {},
"source": [
"### Note the raggedness of the left-side (early times) of the curves. \n",
"### In experiment `react_2_b` this simulation gets repeated with an _adaptive variable time resolution_ that takes smaller steps at the beginning, when the reaction is proceeding faster \n",
"#### By contrast, here we used _FIXED_ time steps (shown in dashed lines), which generally gives poor results, unless taking a very large number of very small steps! In particular, the early steps we took were too large, and the later steps were unnecessarily small"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e73955b7-21c5-4147-96f1-55bdad8092ba",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "3f3556f4-2474-4233-b6f9-d05ec856dd13",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "f72f4988-4e4b-4268-9f4a-e36300c9dcf1",
"metadata": {},
"source": [
"# PART 2 - Now investigate A_dot, i.e. d[A]/dt"
]
},
{
"cell_type": "markdown",
"id": "0ddc7f18-dcc7-4563-b6f7-75049d944669",
"metadata": {},
"source": [
"There's no need to compute this; it is automatically saved during the reaction simulations"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "3b77582e-514d-42bc-9ecd-b7c98b7043df",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" rxn0_rate | \n",
" step | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.0 | \n",
" -70.000000 | \n",
" 0 | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.1 | \n",
" -35.000000 | \n",
" 0 | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.2 | \n",
" -17.500000 | \n",
" 1 | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.3 | \n",
" -8.750000 | \n",
" 2 | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.4 | \n",
" -4.375000 | \n",
" 3 | \n",
"
\n",
" \n",
" | 5 | \n",
" 0.5 | \n",
" -2.187500 | \n",
" 4 | \n",
"
\n",
" \n",
" | 6 | \n",
" 0.6 | \n",
" -1.093750 | \n",
" 5 | \n",
"
\n",
" \n",
" | 7 | \n",
" 0.7 | \n",
" -0.546875 | \n",
" 6 | \n",
"
\n",
" \n",
" | 8 | \n",
" 0.8 | \n",
" -0.273438 | \n",
" 7 | \n",
"
\n",
" \n",
" | 9 | \n",
" 0.9 | \n",
" -0.136719 | \n",
" 8 | \n",
"
\n",
" \n",
" | 10 | \n",
" 1.0 | \n",
" -0.068359 | \n",
" 9 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" SYSTEM TIME rxn0_rate step\n",
"0 0.0 -70.000000 0\n",
"1 0.1 -35.000000 0\n",
"2 0.2 -17.500000 1\n",
"3 0.3 -8.750000 2\n",
"4 0.4 -4.375000 3\n",
"5 0.5 -2.187500 4\n",
"6 0.6 -1.093750 5\n",
"7 0.7 -0.546875 6\n",
"8 0.8 -0.273438 7\n",
"9 0.9 -0.136719 8\n",
"10 1.0 -0.068359 9"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rates_df = uc.get_rate_history()\n",
"rates_df"
]
},
{
"cell_type": "markdown",
"id": "7e469e8a-b8dc-47f9-a6f2-60688f192357",
"metadata": {},
"source": [
"Note that **reaction rates** are defined for the reaction _products_; since `A` is a reactant (in reaction 0, our only reaction), we must flip its sign; since the stoichiometry of A is simply 1, no further adjustment needed."
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "4a78121a-b08f-4c8c-8163-4138e0dd41a1",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" rxn0_rate | \n",
" step | \n",
" A_dot | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.0 | \n",
" -70.000000 | \n",
" 0 | \n",
" 70.000000 | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.1 | \n",
" -35.000000 | \n",
" 0 | \n",
" 35.000000 | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.2 | \n",
" -17.500000 | \n",
" 1 | \n",
" 17.500000 | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.3 | \n",
" -8.750000 | \n",
" 2 | \n",
" 8.750000 | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.4 | \n",
" -4.375000 | \n",
" 3 | \n",
" 4.375000 | \n",
"
\n",
" \n",
" | 5 | \n",
" 0.5 | \n",
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" 4 | \n",
" 2.187500 | \n",
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"text/plain": [
" SYSTEM TIME rxn0_rate step A_dot\n",
"0 0.0 -70.000000 0 70.000000\n",
"1 0.1 -35.000000 0 35.000000\n",
"2 0.2 -17.500000 1 17.500000\n",
"3 0.3 -8.750000 2 8.750000\n",
"4 0.4 -4.375000 3 4.375000\n",
"5 0.5 -2.187500 4 2.187500\n",
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"10 1.0 -0.068359 9 0.068359"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"rates_df['A_dot'] = - rates_df['rxn0_rate'] # Add a column to the Pandas dataframe\n",
"rates_df"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "c78e828d-583a-45d0-b7d2-4fb979bdb586",
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"0 0.0 10.000000 50.000000 Set concentration\n",
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"2 0.2 20.500000 39.500000 1 1st reaction step\n",
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},
"execution_count": 23,
"metadata": {},
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"source": [
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},
{
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"id": "50bfe622-cd5f-46ea-a433-db3a9901ce8d",
"metadata": {},
"source": [
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]
},
{
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"execution_count": 24,
"id": "cda9afb7-4e99-493f-a420-3109455e8534",
"metadata": {},
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"source": [
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},
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"execution_count": 25,
"id": "4b4f3495-bab5-4c07-a569-d4b96a14bf04",
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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": "Concentration of A with time, and its rate of change (A_dot)"
},
"xaxis": {
"autorange": true,
"range": [
0,
1.0999999999999999
],
"title": {
"text": "SYSTEM TIME"
},
"type": "linear"
},
"yaxis": {
"autorange": true,
"range": [
-3.816731770833333,
73.88509114583333
],
"title": {
"text": "[A] (turquoise) /
A_dot (brown)"
},
"type": "linear"
}
}
},
"image/png": 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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"PlotlyHelper.combine_plots([p1, p2], \n",
" title=\"Concentration of A with time, and its rate of change (A_dot)\",\n",
" y_label=\"[A] (turquoise) /
A_dot (brown)\",\n",
" legend_title=\"Plot\",\n",
" curve_labels=[\"A\", \"A_dot\"])"
]
},
{
"cell_type": "markdown",
"id": "85d87078-8fc1-4166-95e1-343b546f9971",
"metadata": {},
"source": [
"### At t=0 : \n",
"[A]=10 and [A] has a high rate of change (70)\n",
"### As the system approaches equilibrium : \n",
"[A] approaches a value of 24, and its rate of change decays to zero."
]
},
{
"cell_type": "markdown",
"id": "99cd0942-555b-444e-9c6f-ee1481a2a980",
"metadata": {},
"source": [
"#### **NOTE:** The above curves are jagged because of _the large time steps taken_ (especially in the early times, when there's a lot of change.) \n",
"## In experiment `react_2_b`, we revisit the same reaction using a better approach that employs **_adaptive variable time steps_**."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "531ce53b-7336-440e-bce4-716aafa6c692",
"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": "3.11.9"
}
},
"nbformat": 4,
"nbformat_minor": 5
}