{ "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: Nov. 28, 2022" ] }, { "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": [ "# Extend the sys.path variable, to contain the project's root directory\n", "import set_path\n", "set_path.add_ancestor_dir_to_syspath(3) # The number of levels to go up \n", " # to reach the project's home, from the folder containing this notebook" ] }, { "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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", "text/html": [ "
" ] }, "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(pars=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(pars=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(pars=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(pars=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 }