{ "cells": [ { "cell_type": "markdown", "id": "a40f6857", "metadata": {}, "source": [ "## Carry out a few single indivual steps of diffusion, \n", "### and directly verify that the values satisfy the diffusion equation\n", "\n", "In this \"PART 3\", we perform all the steps done in part2,\n", "with an even finer resolution, and more complex initial concentrations,\n", "repeated for 2 different diffusion algorithms.\n", "\n", "LAST REVISED: May 27, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "d142d450-f2af-42fa-9026-2b44919c5b40", "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": "9897632a-191c-4cdc-9bc2-a1143c2f0d36", "metadata": {}, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.life_1D.bio_sim_1d import BioSim1D\n", "from src.modules.reactions.reaction_data import ReactionData as chem\n", "from src.modules.movies.movies import MovieArray\n", "from src.modules.numerical.numerical import Numerical as num\n", "\n", "import numpy as np\n", "\n", "import plotly.express as px\n", "import plotly.graph_objects as go" ] }, { "cell_type": "code", "execution_count": 3, "id": "0c291bcf-fd3a-443d-9df1-1b8ce9fefcae", "metadata": {}, "outputs": [], "source": [ "# Parameters of the simulation run. We'll be considering just 1 chemical species, \"A\"\n", "diffusion_rate = 10.\n", "delta_t = 0.01\n", "n_bins = 5000\n", "delta_x = 2 # Note that the number of bins also define the fraction of the sine wave cycle in each bin" ] }, { "cell_type": "code", "execution_count": 4, "id": "53d302cc-b017-4104-8689-96a038234be9", "metadata": {}, "outputs": [], "source": [ "chem_data = chem(diffusion_rates=[diffusion_rate], names=[\"A\"])" ] }, { "cell_type": "markdown", "id": "82504138-da32-486a-930d-bc9419cb1dc2", "metadata": {}, "source": [ "# ALGORITHM 1" ] }, { "cell_type": "code", "execution_count": 5, "id": "e7a18dc8-1ae7-48d4-b557-0c7512f651c6", "metadata": {}, "outputs": [], "source": [ "algorithm = None # \"Explicit, with 3+1 stencil\"" ] }, { "cell_type": "code", "execution_count": 6, "id": "696122b0-c8c4-4d43-a4fc-319f95221602", "metadata": {}, "outputs": [], "source": [ "# Initialize the system\n", "bio = BioSim1D(n_bins=n_bins, chem_data=chem_data)\n", "\n", "# Initialize the concentrations to 2 superposed sine waves\n", "bio.inject_sine_conc(species_name=\"A\", frequency=1, amplitude=12, bias=40)\n", "bio.inject_sine_conc(species_name=\"A\", frequency=2, amplitude=10)\n", "bio.inject_sine_conc(species_name=\"A\", frequency=16, amplitude=5)" ] }, { "cell_type": "code", "execution_count": 7, "id": "338bd51c-6b12-4cf0-8526-797389fbc55c", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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"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": "Initial System State (for the tiny system)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 4999 ], "title": { "text": "Bin number" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 13.234405989521976, 66.76559401047801 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = px.line(data_frame=bio.system_snapshot(), y=[\"A\"], \n", " title= \"Initial System State (for the tiny system)\",\n", " color_discrete_sequence = ['red'],\n", " labels={\"value\":\"concentration\", \"variable\":\"Chemical\", \"index\":\"Bin number\"})\n", "fig.show()" ] }, { "cell_type": "markdown", "id": "2ba3f95a-2d63-4a11-a150-c5f1ea4a7716", "metadata": {}, "source": [ "#### Now do 4 rounds of single-step diffusion, to collect the system state at a total of 5 time points: t0 (the initial state), plus t1, t2, t3 and t4" ] }, { "cell_type": "code", "execution_count": 8, "id": "28e46cc9-4ddf-4d9c-8ab2-20c08bb3106e", "metadata": {}, "outputs": [], "source": [ "history = MovieArray() # All the system state will get collected in this object\n", "# Store the initial state\n", "arr = bio.lookup_species(species_index=0, copy=True)\n", "history.store(par=bio.system_time, data_snapshot=arr, caption=f\"State at time {bio.system_time}\")" ] }, { "cell_type": "code", "execution_count": 9, "id": "45c018bc-5f69-4da2-b8c2-4c412e10bc5e", "metadata": { "tags": [] }, "outputs": [], "source": [ "# Do the 4 rounds of single-step diffusion; accumulate all data in the history object\n", "for _ in range(4):\n", " bio.diffuse(time_step=delta_t, n_steps=1, delta_x=delta_x , algorithm=algorithm)\n", "\n", " arr = bio.lookup_species(species_index=0, copy=True)\n", " history.store(par=bio.system_time, data_snapshot=arr, caption=f\"State at time {bio.system_time}\")" ] }, { "cell_type": "code", "execution_count": 10, "id": "a77b0423-fd2b-4219-8dc0-4f2fa65813be", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5, 5000)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Now, let's examine the data collected at the 5 time points\n", "all_history = history.get_array()\n", "all_history.shape " ] }, { "cell_type": "code", "execution_count": 11, "id": "128ff22d-0ce2-45ed-8ec0-2a067a613990", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5000,)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Compute time derivatives (for each bin), using 5-point stencils\n", "df_dt_all_bins = np.apply_along_axis(num.gradient_order4_1d, 0, all_history, delta_t)\n", "\n", "# Let's consider the state at the midpoint in time (t2)\n", "f_at_t2 = all_history[2] # The middle of the 5 time snapshots\n", "f_at_t2.shape" ] }, { "cell_type": "code", "execution_count": 12, "id": "398588e7-2066-4171-b95c-089b83126034", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5000,)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Computer the second spacial derivative, using 5-point stencils\n", "gradient_x_at_t2 = num.gradient_order4_1d(arr=f_at_t2, dx=delta_x)\n", "second_gradient_x_at_t2 = num.gradient_order4_1d(arr=gradient_x_at_t2, dx=delta_x)\n", "second_gradient_x_at_t2.shape" ] }, { "cell_type": "code", "execution_count": 13, "id": "19514cd4-ceb5-450d-8c3e-9b43456f02c0", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "0.0017647994920801059" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Compare the left and right hand sides of the diffusion equation\n", "lhs = df_dt_all_bins[2] # t2 is the middle point of the 5\n", "rhs = diffusion_rate*second_gradient_x_at_t2\n", "\n", "num.compare_vectors(lhs, rhs, trim_edges=2) # Euclidean distance, ignoring 2 edge points at each end" ] }, { "cell_type": "markdown", "id": "258e81c8-0720-4a70-a7e0-af06167490d8", "metadata": {}, "source": [ "The above number is a measure of the discrepancy from the perfect match (zero distance) that an ideal solution would provide. " ] }, { "cell_type": "markdown", "id": "e7441a0b-832d-444d-8be0-8f20cb77c361", "metadata": {}, "source": [ "# ALGORITHM 2" ] }, { "cell_type": "code", "execution_count": 14, "id": "0b35d2f4-82db-42bd-8c62-84c6639a2339", "metadata": {}, "outputs": [], "source": [ "algorithm = \"5_1_explicit\" # \"Explicit, with 5+1 stencil\"" ] }, { "cell_type": "code", "execution_count": 15, "id": "a8188968-e2bb-4111-b727-dc4b2aebc550", "metadata": {}, "outputs": [], "source": [ "# Initialize the system\n", "bio = BioSim1D(n_bins=n_bins, chem_data=chem_data)\n", "\n", "# Initialize the concentrations to 2 superposed sine waves\n", "bio.inject_sine_conc(species_name=\"A\", frequency=1, amplitude=12, bias=40)\n", "bio.inject_sine_conc(species_name=\"A\", frequency=2, amplitude=10)\n", "bio.inject_sine_conc(species_name=\"A\", frequency=16, amplitude=5)" ] }, { "cell_type": "markdown", "id": "7ac884d5-4dee-4c67-bb4b-6fec1c68aea4", "metadata": {}, "source": [ "#### Now do 4 rounds of single-step diffusion, to collect the system state at a total of 5 time points: t0 (the initial state), plus t1, t2, t3 and t4" ] }, { "cell_type": "code", "execution_count": 16, "id": "8d0d637c-c42b-49e0-9cce-f5790c6c8c8b", "metadata": {}, "outputs": [], "source": [ "history = MovieArray() # All the system state will get collected in this object\n", "# Store the initial state\n", "arr = bio.lookup_species(species_index=0, copy=True)\n", "history.store(par=bio.system_time, data_snapshot=arr, caption=f\"State at time {bio.system_time}\")" ] }, { "cell_type": "code", "execution_count": 17, "id": "49ab1f19-7c57-4c0b-a9e7-07e1534877c6", "metadata": { "tags": [] }, "outputs": [], "source": [ "# Do the 4 rounds of single-step diffusion; accumulate all data in the history object\n", "for _ in range(4):\n", " bio.diffuse(time_step=delta_t, n_steps=1, delta_x=delta_x , algorithm=algorithm)\n", "\n", " arr = bio.lookup_species(species_index=0, copy=True)\n", " history.store(par=bio.system_time, data_snapshot=arr, caption=f\"State at time {bio.system_time}\")" ] }, { "cell_type": "code", "execution_count": 18, "id": "b7621bf0-7208-4219-afb8-98c2a437a084", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5, 5000)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Now, let's examine the data collected at the 5 time points\n", "all_history = history.get_array()\n", "all_history.shape " ] }, { "cell_type": "code", "execution_count": 19, "id": "cbb1db99-ad35-4c29-8bad-3646e6d83631", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5000,)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Compute time derivatives (for each bin), using 5-point stencils\n", "df_dt_all_bins = np.apply_along_axis(num.gradient_order4_1d, 0, all_history, delta_t)\n", "\n", "# Let's consider the state at the midpoint in time (t2)\n", "f_at_t2 = all_history[2] # The middle of the 5 time snapshots\n", "f_at_t2.shape" ] }, { "cell_type": "code", "execution_count": 20, "id": "82893b7f-1080-40a8-aeb5-f6f789ed6260", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5000,)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Computer the second spacial derivative, using 5-point stencils\n", "gradient_x_at_t2 = num.gradient_order4_1d(arr=f_at_t2, dx=delta_x)\n", "second_gradient_x_at_t2 = num.gradient_order4_1d(arr=gradient_x_at_t2, dx=delta_x)\n", "second_gradient_x_at_t2.shape" ] }, { "cell_type": "code", "execution_count": 21, "id": "b8a220b2-d795-45c0-b786-c5174e4768ea", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "0.003517310789846865" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Compare the left and right hand sides of the diffusion equation\n", "lhs = df_dt_all_bins[2] # t2 is the middle point of the 5\n", "rhs = diffusion_rate*second_gradient_x_at_t2\n", "\n", "num.compare_vectors(lhs, rhs, trim_edges=2) # Euclidean distance, ignoring 2 edge points at each end" ] }, { "cell_type": "markdown", "id": "775dae05-aacf-4b3c-b28a-8e531435676a", "metadata": {}, "source": [ "# Both algorithms show good measures of accuracy" ] }, { "cell_type": "code", "execution_count": null, "id": "cd32c72b-8bcb-43a5-940f-84f2159de2de", "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" }, "toc-autonumbering": false, "toc-showcode": true, "toc-showmarkdowntxt": false }, "nbformat": 4, "nbformat_minor": 5 }