{ "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: July 14, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "cd32c72b-8bcb-43a5-940f-84f2159de2de", "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": "7593be7e", "metadata": {}, "outputs": [], "source": [ "\n", "from src.life_1D.bio_sim_1d import BioSim1D\n", "from src.modules.chemicals.chem_data import ChemData 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" ] }, { "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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" ] }, "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": "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": "3.8.10" }, "toc-autonumbering": false, "toc-showcode": true, "toc-showmarkdowntxt": false }, "nbformat": 4, "nbformat_minor": 5 }