{ "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." ] }, { "cell_type": "markdown", "id": "80a01d7f-0788-46bb-97da-735fb5ddedc3", "metadata": {}, "source": [ "### TAGS : \"diffusion 1D\", \"under-the-hood\"" ] }, { "cell_type": "code", "execution_count": 1, "id": "55a8c3db-d88b-4859-9726-ea72351ac8db", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"May 3, 2025\"\n", "LIFE123_VERSION = \"1.0.0rc3\" # Library version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "cd32c72b-8bcb-43a5-940f-84f2159de2de", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!" ] }, { "cell_type": "code", "execution_count": 3, "id": "5725ccb7-c5d8-4b34-92c6-23d7ff376950", "metadata": {}, "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", "from life123 import BioSim1D, ChemData, CollectionArray, Numerical, check_version\n", "\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 4, "id": "5a8a805e-7dc4-4ef3-9c73-3c77f4be0e94", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION)" ] }, { "cell_type": "code", "execution_count": null, "id": "00eb98e2-432a-4a37-a171-a51b6cc71ebf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 5, "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": 6, "id": "53d302cc-b017-4104-8689-96a038234be9", "metadata": {}, "outputs": [], "source": [ "chem_data = ChemData(diffusion_rates=diffusion_rate, names=\"A\")" ] }, { "cell_type": "code", "execution_count": null, "id": "0b514690-b0ba-4519-a7e4-e87f6accf19e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "82504138-da32-486a-930d-bc9419cb1dc2", "metadata": {}, "source": [ "# ALGORITHM 1" ] }, { "cell_type": "code", "execution_count": 7, "id": "e7a18dc8-1ae7-48d4-b557-0c7512f651c6", "metadata": {}, "outputs": [], "source": [ "algorithm = None # \"Explicit, with 3+1 stencil\"" ] }, { "cell_type": "code", "execution_count": 8, "id": "696122b0-c8c4-4d43-a4fc-319f95221602", "metadata": { "tags": [] }, "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(chem_label=\"A\", number_cycles=1, amplitude=12, bias=40)\n", "bio.inject_sine_conc(chem_label=\"A\", number_cycles=2, amplitude=10)\n", "bio.inject_sine_conc(chem_label=\"A\", number_cycles=16, amplitude=5)" ] }, { "cell_type": "code", "execution_count": 9, "id": "3b521b5f-20c0-499f-9130-f47ac813340e", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Bin number=%{x}
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System snapshot at time t=0" }, "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": "[A]" }, "type": "linear" } } }, "image/png": 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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Show as heatmap\n", "bio.system_heatmaps(title_prefix=\"Initial System State (for the tiny system)\")" ] }, { "cell_type": "code", "execution_count": null, "id": "8cd8b184-89e6-4bff-9824-31f39c4b1fc6", "metadata": {}, "outputs": [], "source": [] }, { "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": 11, "id": "28e46cc9-4ddf-4d9c-8ab2-20c08bb3106e", "metadata": { "tags": [] }, "outputs": [], "source": [ "history = CollectionArray() # All the system state will get collected in this object\n", "# Store the initial state\n", "arr = bio.lookup_species(chem_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": 12, "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(chem_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": 13, "id": "a77b0423-fd2b-4219-8dc0-4f2fa65813be", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "(5, 5000)" ] }, "execution_count": 13, "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": 14, "id": "128ff22d-0ce2-45ed-8ec0-2a067a613990", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "(5000,)" ] }, "execution_count": 14, "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(Numerical.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": 15, "id": "398588e7-2066-4171-b95c-089b83126034", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "(5000,)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Computer the second spacial derivative, using 5-point stencils\n", "gradient_x_at_t2 = Numerical.gradient_order4_1d(arr=f_at_t2, dx=delta_x)\n", "second_gradient_x_at_t2 = Numerical.gradient_order4_1d(arr=gradient_x_at_t2, dx=delta_x)\n", "second_gradient_x_at_t2.shape" ] }, { "cell_type": "code", "execution_count": 16, "id": "19514cd4-ceb5-450d-8c3e-9b43456f02c0", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "0.0017647994920801059" ] }, "execution_count": 16, "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", "Numerical.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": "code", "execution_count": null, "id": "aaaa268d-21d7-440d-8927-04f588a488f2", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "57ecca6a-b32c-4461-b342-94435214fe9c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "e7441a0b-832d-444d-8be0-8f20cb77c361", "metadata": {}, "source": [ "# ALGORITHM 2" ] }, { "cell_type": "code", "execution_count": 17, "id": "0b35d2f4-82db-42bd-8c62-84c6639a2339", "metadata": { "tags": [] }, "outputs": [], "source": [ "algorithm = \"5_1_explicit\" # \"Explicit, with 5+1 stencil\"" ] }, { "cell_type": "code", "execution_count": 18, "id": "a8188968-e2bb-4111-b727-dc4b2aebc550", "metadata": { "tags": [] }, "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(chem_label=\"A\", number_cycles=1, amplitude=12, bias=40)\n", "bio.inject_sine_conc(chem_label=\"A\", number_cycles=2, amplitude=10)\n", "bio.inject_sine_conc(chem_label=\"A\", number_cycles=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": 19, "id": "8d0d637c-c42b-49e0-9cce-f5790c6c8c8b", "metadata": { "tags": [] }, "outputs": [], "source": [ "history = CollectionArray() # All the system state will get collected in this object\n", "# Store the initial state\n", "arr = bio.lookup_species(chem_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": 20, "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(chem_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": 21, "id": "b7621bf0-7208-4219-afb8-98c2a437a084", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "(5, 5000)" ] }, "execution_count": 21, "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": 22, "id": "cbb1db99-ad35-4c29-8bad-3646e6d83631", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "(5000,)" ] }, "execution_count": 22, "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(Numerical.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": 23, "id": "82893b7f-1080-40a8-aeb5-f6f789ed6260", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "(5000,)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Computer the second spacial derivative, using 5-point stencils\n", "gradient_x_at_t2 = Numerical.gradient_order4_1d(arr=f_at_t2, dx=delta_x)\n", "second_gradient_x_at_t2 = Numerical.gradient_order4_1d(arr=gradient_x_at_t2, dx=delta_x)\n", "second_gradient_x_at_t2.shape" ] }, { "cell_type": "code", "execution_count": 24, "id": "b8a220b2-d795-45c0-b786-c5174e4768ea", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "0.003517310789846865" ] }, "execution_count": 24, "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", "Numerical.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": "f7ae7f19", "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": "3.9.13" }, "toc-autonumbering": false, "toc-showcode": true, "toc-showmarkdowntxt": false }, "nbformat": 4, "nbformat_minor": 5 }