{ "cells": [ { "cell_type": "markdown", "id": "4e50d971", "metadata": {}, "source": [ "### `A <-> 3B` reaction, taken to equilibrium.\n", "### Examine State Space trajectory, using [A] and [B] as state variables\n", "\n", "1st-order kinetics in both directions\n", "\n", "Based on experiment \"1D/reaction/reaction_2\"\n", "\n", "LAST REVISED: July 14, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "84bf7d8f-3ad4-4b5a-8b26-321122660f41", "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": "8f60b9ca", "metadata": {}, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.chemicals.chem_data import ChemData\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "import plotly.express as px\n", "import plotly.graph_objects as go\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "180bfbdd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'state_space_1.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging\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": "code", "execution_count": 4, "id": "610ce687-64a0-4ad8-a7df-a7d204b94684", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> 3 B (kF = 5 / kR = 2 / Delta_G = -2,271.45 / K = 2.5) | 1st order in all reactants & products\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = ChemData(names=[\"A\", \"B\"])\n", "\n", "\n", "# Reaction A <-> 3B , with 1st-order kinetics in both directions\n", "chem_data.add_reaction(reactants=\"A\", products=[(3,\"B\")], forward_rate=5., reverse_rate=2.)\n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 5, "id": "0423bb64-0481-4ea8-a566-f2d10d82574a", "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" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc(conc={\"A\": 10., \"B\": 50.},\n", " snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 6, "id": "4b5e75e5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `state_space_1.log.htm`]\n" ] } ], "source": [ "# Send the plot 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": "dfb4e9e3", "metadata": { "tags": [] }, "source": [ "### To equilibrium" ] }, { "cell_type": "code", "execution_count": 7, "id": "c3ed24bd-c237-491f-a2b9-676fc666b087", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.05, n_steps=10, variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 8, "id": "56e68446-bc47-4b0d-b772-bc206bacaec4", "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", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SYSTEM TIMEABcaption
00.0010.00000050.000000Initial state
10.0512.50000042.500000
20.1013.62500039.125000
30.1514.13125037.606250
40.2014.35906336.922812
50.2514.46157836.615266
60.3014.50771036.476870
70.3514.52847036.414591
80.4014.53781136.386566
90.4514.54201536.373955
100.5014.54390736.368280
\n", "
" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.00 10.000000 50.000000 Initial state\n", "1 0.05 12.500000 42.500000 \n", "2 0.10 13.625000 39.125000 \n", "3 0.15 14.131250 37.606250 \n", "4 0.20 14.359063 36.922812 \n", "5 0.25 14.461578 36.615266 \n", "6 0.30 14.507710 36.476870 \n", "7 0.35 14.528470 36.414591 \n", "8 0.40 14.537811 36.386566 \n", "9 0.45 14.542015 36.373955 \n", "10 0.50 14.543907 36.368280 " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = dynamics.get_history()\n", "df" ] }, { "cell_type": "code", "execution_count": 9, "id": "968e0c7f-4fef-4dbf-b055-96168432aecb", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> 3 B\n", "Final concentrations: [B] = 36.37 ; [A] = 14.54\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.50059\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 2.5\n", "Discrepancy between the two values: 0.02341 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": 10, "id": "af88741e-72cc-41be-98d4-3e95f8a90a10", "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
SYSTEM TIME=%{x}
concentration=%{y}", "legendgroup": "A", "line": { "color": "navy", "dash": "solid" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "A", "orientation": "v", "showlegend": true, "type": "scatter", "x": [ 0, 0.05, 0.1, 0.15000000000000002, 0.2, 0.25, 0.3, 0.35, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994 ], "xaxis": "x", "y": [ 10, 12.5, 13.625, 14.13125, 14.3590625, 14.461578125, 14.50771015625, 14.5284695703125, 14.537811306640625, 14.54201508798828, 14.543906789594727 ], "yaxis": "y" }, { "hovertemplate": "Chemical=B
SYSTEM TIME=%{x}
concentration=%{y}", "legendgroup": "B", "line": { "color": "orange", "dash": "solid" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "B", "orientation": "v", "showlegend": true, "type": "scatter", "x": [ 0, 0.05, 0.1, 0.15000000000000002, 0.2, 0.25, 0.3, 0.35, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994 ], "xaxis": "x", "y": [ 50, 42.5, 39.125, 37.60625, 36.9228125, 36.615265625, 36.47686953125, 36.4145912890625, 36.386566080078126, 36.37395473603516, 36.36827963121582 ], "yaxis": "y" } ], "layout": { "autosize": true, "legend": { "title": { "text": "Chemical" }, "tracegroupgap": 0 }, "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "baxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "type": "carpet" } ], "choropleth": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "choropleth" } ], "contour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "contour" } ], "contourcarpet": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "contourcarpet" } ], "heatmap": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "heatmap" } ], "heatmapgl": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "heatmapgl" } ], "histogram": [ { "marker": { "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "histogram" } ], "histogram2d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "histogram2d" } ], "histogram2dcontour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "histogram2dcontour" } ], "mesh3d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "mesh3d" } ], "parcoords": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "parcoords" } ], "pie": [ { "automargin": true, "type": "pie" } ], "scatter": [ { "fillpattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 }, "type": "scatter" } ], "scatter3d": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatter3d" } ], "scattercarpet": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattercarpet" } ], "scattergeo": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergeo" } ], "scattergl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergl" } ], "scattermapbox": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattermapbox" } ], "scatterpolar": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolar" } ], "scatterpolargl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolargl" } ], "scatterternary": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterternary" } ], "surface": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "surface" } ], "table": [ { "cells": { "fill": { "color": "#EBF0F8" }, "line": { "color": "white" } }, "header": { "fill": { "color": "#C8D4E3" }, "line": { "color": "white" } }, "type": "table" } ] }, "layout": { "annotationdefaults": { "arrowcolor": "#2a3f5f", "arrowhead": 0, "arrowwidth": 1 }, "autotypenumbers": "strict", "coloraxis": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "colorscale": { "diverging": [ [ 0, "#8e0152" ], [ 0.1, "#c51b7d" ], [ 0.2, "#de77ae" ], [ 0.3, "#f1b6da" ], [ 0.4, "#fde0ef" ], [ 0.5, "#f7f7f7" ], [ 0.6, "#e6f5d0" ], [ 0.7, "#b8e186" ], [ 0.8, "#7fbc41" ], [ 0.9, "#4d9221" ], [ 1, "#276419" ] ], "sequential": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "sequentialminus": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ] }, "colorway": [ "#636efa", "#EF553B", "#00cc96", "#ab63fa", "#FFA15A", "#19d3f3", "#FF6692", "#B6E880", "#FF97FF", "#FECB52" ], "font": { "color": "#2a3f5f" }, "geo": { "bgcolor": "white", "lakecolor": "white", "landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "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": "Reaction `A <-> 3 B` . Changes in concentrations with time" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 0.49999999999999994 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": "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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['navy', 'orange'])" ] }, { "cell_type": "code", "execution_count": null, "id": "c4e0120d-1541-4552-a2d0-8100a3fea8d9", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "70994860-4cde-45ba-b3a2-2ada1c541bf5", "metadata": {}, "source": [ "## Same data, but shown differently" ] }, { "cell_type": "code", "execution_count": 11, "id": "85b3c06f", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "A=%{x}
B=%{y}", "legendgroup": "", "line": { "color": "#C83778", "dash": "solid" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "", "orientation": "v", "showlegend": false, "type": "scatter", "x": [ 10, 12.5, 13.625, 14.13125, 14.3590625, 14.461578125, 14.50771015625, 14.5284695703125, 14.537811306640625, 14.54201508798828, 14.543906789594727 ], "xaxis": "x", "y": [ 50, 42.5, 39.125, 37.60625, 36.9228125, 36.615265625, 36.47686953125, 36.4145912890625, 36.386566080078126, 36.37395473603516, 36.36827963121582 ], "yaxis": "y" } ], "layout": { "autosize": true, "legend": { "tracegroupgap": 0 }, "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "baxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "type": "carpet" } ], "choropleth": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "choropleth" } ], "contour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "contour" } ], "contourcarpet": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "contourcarpet" } ], "heatmap": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "heatmap" } ], "heatmapgl": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "heatmapgl" } ], "histogram": [ { "marker": { "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "histogram" } ], "histogram2d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "histogram2d" } ], "histogram2dcontour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "histogram2dcontour" } ], "mesh3d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "mesh3d" } ], "parcoords": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "parcoords" } ], "pie": [ { "automargin": true, "type": "pie" } ], "scatter": [ { "fillpattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 }, "type": "scatter" } ], "scatter3d": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatter3d" } ], "scattercarpet": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattercarpet" } ], "scattergeo": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergeo" } ], "scattergl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergl" } ], "scattermapbox": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattermapbox" } ], "scatterpolar": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolar" } ], "scatterpolargl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolargl" } ], "scatterternary": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterternary" } ], "surface": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "surface" } ], "table": [ { "cells": { "fill": { "color": "#EBF0F8" }, "line": { "color": "white" } }, "header": { "fill": { "color": "#C8D4E3" }, "line": { "color": "white" } }, "type": "table" } ] }, "layout": { "annotationdefaults": { "arrowcolor": "#2a3f5f", "arrowhead": 0, "arrowwidth": 1 }, "autotypenumbers": "strict", "coloraxis": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "colorscale": { "diverging": [ [ 0, "#8e0152" ], [ 0.1, "#c51b7d" ], [ 0.2, "#de77ae" ], [ 0.3, "#f1b6da" ], [ 0.4, "#fde0ef" ], [ 0.5, "#f7f7f7" ], [ 0.6, "#e6f5d0" ], [ 0.7, "#b8e186" ], [ 0.8, "#7fbc41" ], [ 0.9, "#4d9221" ], [ 1, "#276419" ] ], "sequential": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "sequentialminus": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ] }, "colorway": [ "#636efa", "#EF553B", "#00cc96", "#ab63fa", "#FFA15A", "#19d3f3", "#FF6692", "#B6E880", "#FF97FF", "#FECB52" ], "font": { "color": "#2a3f5f" }, "geo": { "bgcolor": "white", "lakecolor": "white", "landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "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": "State space of reaction A <-> 3B : [A] vs. [B]" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 10, 14.543906789594727 ], "title": { "text": "A" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 35.61096183295003, 50.75731779826579 ], "title": { "text": "B" }, "type": "linear" } } }, "image/png": "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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig0 = px.line(data_frame=dynamics.get_history(), x=\"A\", y=\"B\", \n", " title=\"State space of reaction A <-> 3B : [A] vs. [B]\",\n", " color_discrete_sequence = ['#C83778'],\n", " labels={\"value\":\"concentration\", \"variable\":\"Chemical\"})\n", "fig0.show()" ] }, { "cell_type": "code", "execution_count": 12, "id": "50b08a83-7a05-4fa7-bbde-93d3d6402df9", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "customdata": [ [ 0 ], [ 0.05 ], [ 0.1 ], [ 0.15 ], [ 0.2 ], [ 0.25 ], [ 0.3 ], [ 0.35 ], [ 0.4 ], [ 0.45 ], [ 0.5 ] ], "hovertemplate": "A=%{x}
B=%{y}
SYSTEM TIME=%{customdata[0]}", "legendgroup": "", "marker": { "color": "#2FAC74", "size": 6, "symbol": "circle" }, "mode": "markers", "name": "", "orientation": "v", "showlegend": false, "type": "scatter", "x": [ 10, 12.5, 13.625, 14.13125, 14.3590625, 14.461578125, 14.50771015625, 14.5284695703125, 14.537811306640625, 14.54201508798828, 14.543906789594727 ], "xaxis": "x", "y": [ 50, 42.5, 39.125, 37.60625, 36.9228125, 36.615265625, 36.47686953125, 36.4145912890625, 36.386566080078126, 36.37395473603516, 36.36827963121582 ], "yaxis": "y" } ], "layout": { "annotations": [ { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 0, "ay": 20, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "t=0.0", "x": 10, "y": 50 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 16, "ay": 28, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.05", "x": 12.5, "y": 42.5 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 32, "ay": 36, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.1", "x": 13.625, "y": 39.125 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 48, "ay": 44, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.15", "x": 14.13125, "y": 37.60625 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 64, "ay": 52, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.2", "x": 14.3590625, "y": 36.9228125 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 96, "ay": 68, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.3", "x": 14.50771015625, "y": 36.47686953125 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 128, "ay": 84, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.4", "x": 14.537811306640625, "y": 36.386566080078126 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 160, "ay": 100, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.5", "x": 14.543906789594727, "y": 36.36827963121582 } ], "autosize": true, "legend": { "tracegroupgap": 0 }, "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "baxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "type": "carpet" } ], "choropleth": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "choropleth" } ], "contour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "contour" } ], "contourcarpet": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "contourcarpet" } ], "heatmap": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "heatmap" } ], "heatmapgl": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "heatmapgl" } ], "histogram": [ { "marker": { "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "histogram" } ], "histogram2d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "histogram2d" } ], "histogram2dcontour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "histogram2dcontour" } ], "mesh3d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "mesh3d" } ], "parcoords": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "parcoords" } ], "pie": [ { "automargin": true, "type": "pie" } ], "scatter": [ { "fillpattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 }, "type": "scatter" } ], "scatter3d": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatter3d" } ], "scattercarpet": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattercarpet" } ], "scattergeo": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergeo" } ], "scattergl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergl" } ], "scattermapbox": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattermapbox" } ], "scatterpolar": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolar" } ], "scatterpolargl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolargl" } ], "scatterternary": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterternary" } ], "surface": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "surface" } ], "table": [ { "cells": { "fill": { "color": "#EBF0F8" }, "line": { "color": "white" } }, "header": { "fill": { "color": "#C8D4E3" }, "line": { "color": "white" } }, "type": "table" } ] }, "layout": { "annotationdefaults": { "arrowcolor": "#2a3f5f", "arrowhead": 0, "arrowwidth": 1 }, "autotypenumbers": "strict", "coloraxis": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "colorscale": { "diverging": [ [ 0, "#8e0152" ], [ 0.1, "#c51b7d" ], [ 0.2, "#de77ae" ], [ 0.3, "#f1b6da" ], [ 0.4, "#fde0ef" ], [ 0.5, "#f7f7f7" ], [ 0.6, "#e6f5d0" ], [ 0.7, "#b8e186" ], [ 0.8, "#7fbc41" ], [ 0.9, "#4d9221" ], [ 1, "#276419" ] ], "sequential": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "sequentialminus": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ] }, "colorway": [ "#636efa", "#EF553B", "#00cc96", "#ab63fa", "#FFA15A", "#19d3f3", "#FF6692", "#B6E880", "#FF97FF", "#FECB52" ], "font": { "color": "#2a3f5f" }, "geo": { "bgcolor": "white", "lakecolor": "white", "landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "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": "Trajectory in State space: [A] vs. [B]" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 9.667412977766867, 15.77571057564337 ], "title": { "text": "A" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 11.520586807102884, 52.93340818062445 ], "title": { "text": "B" }, "type": "linear" } } }, "image/png": "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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Now show the individual data points\n", "\n", "df['SYSTEM TIME'] = round(df['SYSTEM TIME'], 2) # To avoid clutter from too many digits, in the column\n", "\n", "fig1 = px.scatter(data_frame=df, x=\"A\", y=\"B\",\n", " title=\"Trajectory in State space: [A] vs. [B]\",\n", " hover_data=['SYSTEM TIME'])\n", "\n", "fig1.update_traces(marker={\"size\": 6, \"color\": \"#2FAC74\"}) # Modify the style of the dots\n", "\n", "# Add annotations (showing the System Time value) to SOME of the points, to avoid clutter\n", "for ind in df.index: # for each row in the Pandas dataframe\n", " label = df[\"SYSTEM TIME\"][ind]\n", " if ind == 0:\n", " label = f\"t={label}\"\n", " \n", " label_x = ind*16\n", " label_y = 20 + ind*8 # A greater y value here means further DOWN!!\n", " \n", " if (ind <= 3) or (ind%2 == 0):\n", " fig1.add_annotation(x=df[\"A\"][ind], y=df[\"B\"][ind],\n", " text=label,\n", " font=dict(\n", " size=10,\n", " color=\"grey\"\n", " ),\n", " showarrow=True, arrowhead=0, ax=label_x, ay=label_y, arrowcolor=\"#b0b0b0\",\n", " bordercolor=\"#c7c7c7\")\n", "\n", "fig1.show()" ] }, { "cell_type": "code", "execution_count": 13, "id": "f3c287ce-9a33-43bd-8473-f81f22ff9e81", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "A=%{x}
B=%{y}", "legendgroup": "", "line": { "color": "#C83778", "dash": "solid" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "", "orientation": "v", "showlegend": false, "type": "scatter", "x": [ 10, 12.5, 13.625, 14.13125, 14.3590625, 14.461578125, 14.50771015625, 14.5284695703125, 14.537811306640625, 14.54201508798828, 14.543906789594727 ], "xaxis": "x", "y": [ 50, 42.5, 39.125, 37.60625, 36.9228125, 36.615265625, 36.47686953125, 36.4145912890625, 36.386566080078126, 36.37395473603516, 36.36827963121582 ], "yaxis": "y" }, { "customdata": [ [ 0 ], [ 0.05 ], [ 0.1 ], [ 0.15 ], [ 0.2 ], [ 0.25 ], [ 0.3 ], [ 0.35 ], [ 0.4 ], [ 0.45 ], [ 0.5 ] ], "hovertemplate": "A=%{x}
B=%{y}
SYSTEM TIME=%{customdata[0]}", "legendgroup": "", "marker": { "color": "#2FAC74", "size": 6, "symbol": "circle" }, "mode": "markers", "name": "", "orientation": "v", "showlegend": false, "type": "scatter", "x": [ 10, 12.5, 13.625, 14.13125, 14.3590625, 14.461578125, 14.50771015625, 14.5284695703125, 14.537811306640625, 14.54201508798828, 14.543906789594727 ], "xaxis": "x", "y": [ 50, 42.5, 39.125, 37.60625, 36.9228125, 36.615265625, 36.47686953125, 36.4145912890625, 36.386566080078126, 36.37395473603516, 36.36827963121582 ], "yaxis": "y" } ], "layout": { "annotations": [ { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 0, "ay": 20, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "t=0.0", "x": 10, "y": 50 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 16, "ay": 28, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.05", "x": 12.5, "y": 42.5 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 32, "ay": 36, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.1", "x": 13.625, "y": 39.125 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 48, "ay": 44, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.15", "x": 14.13125, "y": 37.60625 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 64, "ay": 52, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.2", "x": 14.3590625, "y": 36.9228125 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 96, "ay": 68, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.3", "x": 14.50771015625, "y": 36.47686953125 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 128, "ay": 84, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.4", "x": 14.537811306640625, "y": 36.386566080078126 }, { "arrowcolor": "#b0b0b0", "arrowhead": 0, "ax": 160, "ay": 100, "bordercolor": "#c7c7c7", "font": { "color": "grey", "size": 10 }, "showarrow": true, "text": "0.5", "x": 14.543906789594727, "y": 36.36827963121582 } ], "autosize": true, "legend": { "tracegroupgap": 0 }, "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "baxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "type": "carpet" } ], "choropleth": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "choropleth" } ], "contour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "contour" } ], "contourcarpet": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "contourcarpet" } ], "heatmap": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "heatmap" } ], "heatmapgl": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "heatmapgl" } ], "histogram": [ { "marker": { "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "histogram" } ], "histogram2d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "histogram2d" } ], "histogram2dcontour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "histogram2dcontour" } ], "mesh3d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "mesh3d" } ], "parcoords": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "parcoords" } ], "pie": [ { "automargin": true, "type": "pie" } ], "scatter": [ { "fillpattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 }, "type": "scatter" } ], "scatter3d": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatter3d" } ], "scattercarpet": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattercarpet" } ], "scattergeo": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergeo" } ], "scattergl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergl" } ], "scattermapbox": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattermapbox" } ], "scatterpolar": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolar" } ], "scatterpolargl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolargl" } ], "scatterternary": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterternary" } ], "surface": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "type": "surface" } ], "table": [ { "cells": { "fill": { "color": "#EBF0F8" }, "line": { "color": "white" } }, "header": { "fill": { "color": "#C8D4E3" }, "line": { "color": "white" } }, "type": "table" } ] }, "layout": { "annotationdefaults": { "arrowcolor": "#2a3f5f", "arrowhead": 0, "arrowwidth": 1 }, "autotypenumbers": "strict", "coloraxis": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "colorscale": { "diverging": [ [ 0, "#8e0152" ], [ 0.1, "#c51b7d" ], [ 0.2, "#de77ae" ], [ 0.3, "#f1b6da" ], [ 0.4, "#fde0ef" ], [ 0.5, "#f7f7f7" ], [ 0.6, "#e6f5d0" ], [ 0.7, "#b8e186" ], [ 0.8, "#7fbc41" ], [ 0.9, "#4d9221" ], [ 1, "#276419" ] ], "sequential": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ], "sequentialminus": [ [ 0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1, "#f0f921" ] ] }, "colorway": [ "#636efa", "#EF553B", "#00cc96", "#ab63fa", "#FFA15A", "#19d3f3", "#FF6692", "#B6E880", "#FF97FF", "#FECB52" ], "font": { "color": "#2a3f5f" }, "geo": { "bgcolor": "white", "lakecolor": "white", "landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "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": "Trajectory in State space: [A] vs. [B]" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 9.667412977766867, 15.77571057564337 ], "title": { "text": "A" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 11.520586807102884, 52.93340818062445 ], "title": { "text": "B" }, "type": "linear" } } }, "image/png": "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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Combine the two above plots, while using the layout of fig1 (which includes the title and annotations)\n", "all_fig = go.Figure(data=fig0.data + fig1.data, layout = fig1.layout)\n", "all_fig.show()" ] }, { "cell_type": "markdown", "id": "4fe369cf-d2c0-454c-a3f9-9794008be8d8", "metadata": {}, "source": [ "#### Note how the trajectory is progressively slowing down towards the dynamical system's \"attractor\" (equilibrium state of the reaction)" ] }, { "cell_type": "code", "execution_count": null, "id": "62004ee1", "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 }