{ "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: June 23, 2024 (using v. 1.0 beta34.1)" ] }, { "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 life123 import BioSim1D\n", "from life123 import ChemData as chem\n", "from life123 import MovieArray\n", "from life123 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": "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": 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": "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": 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 }