From 379ac336cabafde627b06b78f2a2d6b62834c9c2 Mon Sep 17 00:00:00 2001 From: emmetfrancis <99422170+emmetfrancis@users.noreply.github.com> Date: Mon, 22 Jun 2026 13:18:24 -0700 Subject: [PATCH 1/4] some mesh tools updates, but mostly changes to allow for species governed by CH aggregation-diffusion --- examples/example1/example1_CH.ipynb | 620 ++++++++++++++++++++++++++++ examples/example1/model_cur.pkl | Bin 0 -> 1864 bytes examples/example9/example9.ipynb | 299 ++++++++++++++ examples/example9/model_cur.pkl | Bin 0 -> 2388 bytes smart/mesh_tools.py | 209 ++++++++++ smart/model.py | 93 ++++- smart/model_assembly.py | 11 + 7 files changed, 1229 insertions(+), 3 deletions(-) create mode 100644 examples/example1/example1_CH.ipynb create mode 100644 examples/example1/model_cur.pkl create mode 100644 examples/example9/example9.ipynb create mode 100644 examples/example9/model_cur.pkl diff --git a/examples/example1/example1_CH.ipynb b/examples/example1/example1_CH.ipynb new file mode 100644 index 00000000..111a6730 --- /dev/null +++ b/examples/example1/example1_CH.ipynb @@ -0,0 +1,620 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "f65f18d7", + "metadata": {}, + "source": [ + "# Example 1-CH: Cahn Hilliard patterns for 2D aggregation-diffusion\n", + "\n", + "In this case, we consider a simple 2D geometry comprised of two compartments:\n", + "- surf - 2D surface\n", + "- edge - outer edges of the surface (1D)\n", + "\n", + "We implement a Cahn-Hilliard model with two species, one exhibiting aggregation-diffusion ($A$) and the other purely diffusive ($B$).\n", + "The equations governing their evolution are given by:\n", + "\n", + "$$\n", + "\\partial_t{u_A} = -k_{on} u_A + k_{off} u_B + D_A \\nabla \\cdot (\\hat{\\mu}_A \\nabla u_A) \\\\\n", + "\\partial_t{u_B} = k_{on} u_A - k_{off} u_B + D_B \\nabla \\cdot (\\nabla u_B),\n", + "$$\n", + "\n", + "where aggregation is accounted for through the chemical potential of $A$, whose nondimensional version ($\\hat{\\mu}_A = \\frac{\\mu_A}{k_B T}) is given by\n", + "\n", + "$$\n", + "\\hat{\\mu}_A = (\\ln \\phi_A - \\ln (1-\\phi_A)) - \\hat{A} (2 \\phi_A - 1) - \\hat{A} \\nabla^2 \\phi_A\n", + "$$\n", + "\n", + "in which $\\phi_A$ is the area fraction occupied by species A, which is proportional to its concentration; that is, $\\phi_A = \\frac{u_A}{u_{A,max}}$\n", + "\n", + "We solve these equations over a 1 by 1 square domain with no-flux boundary conditions." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "956a0fd1", + "metadata": {}, + "source": [ + "We begin with the necessary imports:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cc398816", + "metadata": {}, + "outputs": [], + "source": [ + "import dolfin as d\n", + "import sympy as sym\n", + "import numpy as np\n", + "import pathlib\n", + "import gmsh # must be imported before pyvista if dolfin is imported first\n", + "\n", + "from smart import config, common, mesh, model, mesh_tools, visualization\n", + "from smart.units import unit\n", + "from smart.model_assembly import (\n", + " Compartment,\n", + " Parameter,\n", + " Reaction,\n", + " Species,\n", + " SpeciesContainer,\n", + " ParameterContainer,\n", + " CompartmentContainer,\n", + " ReactionContainer,\n", + ")\n", + "import logging\n", + "from matplotlib import pyplot as plt" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "028bb85e", + "metadata": {}, + "source": [ + "We will set the logging level to `INFO`. This will display some output during the simulation. If you want to get even more output you could set the logging level to `DEBUG`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c6e826d7", + "metadata": {}, + "outputs": [], + "source": [ + "logger = logging.getLogger(\"smart\")\n", + "logger.setLevel(logging.INFO)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "c7fd3be3", + "metadata": {}, + "source": [ + "Futhermore, you could also save the logs to a file by attaching a file handler to the logger as follows.\n", + "\n", + "```\n", + "file_handler = logging.FileHandler(\"filename.log\")\n", + "file_handler.setFormatter(logging.Formatter(smart.config.base_format))\n", + "logger.addHandler(file_handler)\n", + "```" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "95b9d865", + "metadata": {}, + "source": [ + "We define the various units for use in the model. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4f4023cf", + "metadata": {}, + "outputs": [], + "source": [ + "# Aliases - base units\n", + "um = unit.um\n", + "molecule = unit.molecule\n", + "sec = unit.sec\n", + "dimensionless = unit.dimensionless\n", + "D_unit = um**2 / sec\n", + "flux_unit = molecule / (um * sec)\n", + "surf_unit = molecule / um**2\n", + "edge_unit = molecule / um" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "46582d26", + "metadata": {}, + "source": [ + "## Generate model\n", + "\n", + "### Compartments\n", + "As described above, the two compartments are the \"surf\" (2D) and edge (1D). These are initialized by calling:\n", + "```\n", + "compartment_var = Compartment(name, dimensionality, compartment_units, cell_marker)\n", + "```\n", + "where\n", + "- name: string naming the compartment\n", + "- dimensionality: topological dimensionality (e.g. 2 for surf, 1 for edge)\n", + "- compartment_units: length units for the compartment (um for both here)\n", + "- cell_marker: integer marker value identifying each compartment in the parent mesh" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "09079b17", + "metadata": {}, + "outputs": [], + "source": [ + "surf = Compartment(\"surf\", 2, um, 1)\n", + "edge = Compartment(\"edge\", 1, um, 3)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "2db8daf9", + "metadata": {}, + "source": [ + "Now we initialize a compartment container and add both compartments to it." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cc3393cb", + "metadata": {}, + "outputs": [], + "source": [ + "cc = CompartmentContainer()\n", + "cc.add([surf, edge])" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "8ee2332b", + "metadata": {}, + "source": [ + "### Species\n", + "In this case, we have a two species, \"A\" and \"B\", which exist in the 2D \"surf\" domain. Each is initialized by calling:\n", + "```\n", + "species_var = Species(\n", + " name, initial_condition, concentration_units,\n", + " D, diffusion_units, compartment_name, group (opt)\n", + " )\n", + "```\n", + "where\n", + "- name: string naming the species\n", + "- initial_condition: initial concentration for this species (can be an expression given by a string to be parsed by sympy - the only unknowns in the expression should be x, y, and z)\n", + "- concentration_units: concentration units for this species (molecules/μm2 here)\n", + "- D: diffusion coefficient\n", + "- diffusion_units: units for diffusion coefficient (μm2/sec here)\n", + "- compartment_name: each species should be assigned to a single compartment (\"surf\", here)\n", + "- group (opt): for larger models, specifies a group of species this belongs to;\n", + " for organizational purposes when there are multiple reaction modules\n", + "\n", + "With the added CH features, we also must provide the following for species A:\n", + "- `CH = True` - this tells SMART that we are considering both aggregation and diffusion for species A\n", + "- umax: maximum surface density of A\n", + "- A_hat: strength of aggregation\n", + "\n", + "Note that A_hat is dimensionless here and the chemical potential is a variable generated *internally* within this branch of SMART. Because only the nondimensional chemical potential appears in the dynamical equation for $u_A$, the chemical potential is always normalized to the thermal energy scale $k_B T$. (see equations up top for consistency on this point)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3f6f384b", + "metadata": {}, + "outputs": [], + "source": [ + "A = Species(\"A\", 10, surf_unit, 0.1, D_unit, \"surf\", CH=True, umax=100, A_hat = 25) # CH species\n", + "B = Species(\"B\", 90, surf_unit, 0.1, D_unit, \"surf\") # other stuff" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "f77d2d31", + "metadata": {}, + "source": [ + "Create a species container and add both species to it:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5c1df887", + "metadata": {}, + "outputs": [], + "source": [ + "sc = SpeciesContainer()\n", + "sc.add([A, B])" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "74d1d353", + "metadata": {}, + "source": [ + "### Parameters and Reactions\n", + "Parameters and reactions are generally defined together, although the order does not strictly matter. Parameters are specified as:\n", + "```\n", + "param_var = Parameter(name, value, unit, group (opt), notes (opt), use_preintegration (opt))\n", + "```\n", + "where\n", + "- name: string naming the parameter\n", + "- value: value of the given parameter\n", + "- unit: units associated with given value\n", + "- group (optional): optional string placing this reaction in a reaction group; for organizational purposes when there are multiple reaction modules\n", + "- notes (optional): string related to this parameter\n", + "- use_preintegration (optional): in the case of a time-dependent parameter, uses preintegration in the solution process\n", + "\n", + "Reactions are specified by a variable number of arguments (arguments are indicated by (opt) are either never\n", + "required or only required in some cases, for more details see notes below and API documentation):\n", + "```\n", + "reaction_var = Reaction(\n", + " name, lhs, rhs, param_map,\n", + " eqn_f_str (opt), eqn_r_str (opt), reaction_type (opt), species_map,\n", + " explicit_restriction_to_domain (opt), group (opt), flux_scaling (opt)\n", + " )\n", + "```\n", + "- name: string naming the reaction\n", + "- lhs: list of strings specifying the reactants for this reaction\n", + "- rhs: list of strings specifying the products for this reaction\n", + " ***NOTE: the lists \"reactants\" and \"products\" determine the stoichiometry of the reaction;\n", + " for instance, if two A's react to give one B, the reactants list would be [\"A\",\"A\"],\n", + " and the products list would be [\"B\"]\n", + "- param_map: relationship between the parameters specified in the reaction string and those given\n", + " in the parameter container. By default, the reaction parameters are \"kon\" and \"koff\" when\n", + " a system obeys simple mass action. If the forward rate is given by a parameter \"k1\" and the\n", + " reverse rate is given by \"k2\", then param_map = {\"on\":\"k1\", \"off\":\"k2\"}\n", + "- eqn_f_str: For systems not obeying simple mass action, this string specifies the forward reaction rate\n", + " By default, this string is \"on*{all reactants multiplied together}\"\n", + "- eqn_r_str: For systems not obeying simple mass action, this string specifies the reverse reaction rate\n", + " By default, this string is \"off*{all products multiplied together}\"\n", + "- reaction_type (opt): either \"custom\" or \"mass_action\" (default is \"mass_action\") [never a required argument]\n", + "- species_map: same format as param_map; required if other species not listed in reactants or products appear in the\n", + " reaction string\n", + "- explicit_restriction_to_domain: string specifying where the reaction occurs; required if the reaction is not\n", + " constrained by the reaction string (e.g., if production occurs only at the boundary,\n", + " as it does here, but the species being produced exists through the entire volume)\n", + "- group (opt): string placing this reaction in a reaction group; for organizational purposes when there are multiple reaction modules\n", + "- flux_scaling (opt): in certain cases, a given reactant or product may experience a scaled flux (for instance, if we assume that\n", + " some of the molecules are immediately sequestered after the reaction); in this case, to signify that this flux \n", + " should be rescaled, we specify ''flux_scaling = {scaled_species: scale_factor}'', where scaled_species is a\n", + " string specifying the species to be scaled and scale_factor is a number specifying the rescaling factor\n", + "\n", + "For this system, we do not define any reactions on the boundary (`edge`). This corresponds to assuming a no-flux boundary condition." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "df027853", + "metadata": {}, + "outputs": [], + "source": [ + "kon = Parameter(\"kon\", 10.0, 1/sec)\n", + "koff = Parameter(\"koff\", 1.0, 1/sec)\n", + "# Production of A\n", + "r1 = Reaction(\"r1\", [\"A\"], [\"B\"],\n", + " param_map={\"kon\": \"kon\", \"koff\": \"koff\"},\n", + " eqn_f_str=\"A*kon - B*koff\",\n", + " species_map={\"A\": \"A\", \"B\": \"B\"})" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "a0670e78", + "metadata": {}, + "source": [ + "Create parameter and reaction containers and add in associated objects." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1eb19fb6", + "metadata": {}, + "outputs": [], + "source": [ + "pc = ParameterContainer()\n", + "pc.add([kon, koff])\n", + "rc = ReactionContainer()\n", + "rc.add([r1])" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "15c35d39", + "metadata": {}, + "source": [ + "## Create/load in mesh\n", + "\n", + "In SMART we have different levels of meshes. Here we create a UnitSquare mesh defined by\n", + "\n", + "$$\n", + "\\Omega = [0, 1] \\times [0, 1] \\subset \\mathbb{R}^2\n", + "$$\n", + "\n", + "which will serve as our parent mesh\n", + "\n", + "For our two domains, we have two associated \"child meshes\", which are set by the marker functions `mf2` and `mf1`:\n", + "- surf: in this case, all cells (triangles) belong to this mesh; here, marked by `mf2 = 1`\n", + "- edge: 1D child mesh including all line elements along the edges of the domain; here, marked by `mf1 = 3`\n", + "\n", + "Note that the marker values must be chosen to match those given in the compartment definitions above." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fe56e162", + "metadata": {}, + "outputs": [], + "source": [ + "# define dimensions of domain\n", + "Shat = 200\n", + "x_size = np.sqrt(Shat/A.umax)\n", + "y_size = np.sqrt(Shat/A.umax)\n", + "# Create mesh\n", + "m = 30\n", + "n = int(x_size/y_size)*m\n", + "rect_mesh = d.RectangleMesh(d.Point(0.0, 0.0), d.Point(x_size, y_size), n, m)\n", + "mf2 = d.MeshFunction(\"size_t\", rect_mesh, 2, 1)\n", + "mf1 = d.MeshFunction(\"size_t\", rect_mesh, 1, 0)\n", + "class OuterEdge(d.SubDomain):\n", + " def inside(self, x, on_boundary):\n", + " return on_boundary\n", + "outerEdge = OuterEdge()\n", + "outerEdge.mark(mf1, 3)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "86c4b70c", + "metadata": {}, + "source": [ + "Now we write mesh and meshfunctions to file." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fe4d77ac", + "metadata": {}, + "outputs": [], + "source": [ + "mesh_folder = pathlib.Path(\"rect_mesh\")\n", + "mesh_folder.mkdir(exist_ok=True)\n", + "mesh_file = mesh_folder / \"rect_mesh.h5\"\n", + "mesh_tools.write_mesh(rect_mesh, mf1, mf2, mesh_file)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "173e5474", + "metadata": {}, + "source": [ + "Finally, we initialize the `mesh.ParentMesh` object, using the hdf5 file as input." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bcbd06cd", + "metadata": {}, + "outputs": [], + "source": [ + "parent_mesh = mesh.ParentMesh(\n", + " mesh_filename=str(mesh_file),\n", + " mesh_filetype=\"hdf5\",\n", + " name=\"parent_mesh\",\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "8f7ac819", + "metadata": {}, + "source": [ + "## Initialize model and solver\n", + "Now we are ready to set up the model. First we load the default configurations and set the solver config." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "43170d20", + "metadata": {}, + "outputs": [], + "source": [ + "config_cur = config.Config()\n", + "config_cur.flags.update({\"allow_unused_components\": True})\n", + "config_cur.solver.update(\n", + " {\n", + " \"final_t\": 1.0,\n", + " \"initial_dt\": 1e-3,\n", + " \"time_precision\": 8,\n", + " \"attempt_timestep_restart_on_divergence\": True,\n", + " }\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "96783316", + "metadata": {}, + "source": [ + "We create the model object initialize the model using the `initialize` function found in the `smart.model` module. We then save the model information to a .pkl file for later reference.\n", + "\n", + "Note that we could later load the model information from the pickle file using the line:\n", + "```\n", + "model_cur = model.from_pickle(model_cur.pkl)\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a86c7435", + "metadata": {}, + "outputs": [], + "source": [ + "model_cur = model.Model(pc, sc, cc, rc, config_cur, parent_mesh)\n", + "model_cur.initialize(initialize_solver=False)\n", + "model_cur.to_pickle('model_cur.pkl')" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "c0d464e3", + "metadata": {}, + "source": [ + "We then perturb the initial conditions by adding white noise to the dolfin vectors associated with each species." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4c42042c", + "metadata": {}, + "outputs": [], + "source": [ + "# add white noise perturbation to initial conditions\n", + "for sp_str in (\"A\", \"B\"):\n", + " sp = model_cur.sc[sp_str]\n", + " u = model_cur.cc[sp.compartment_name].u[\"u\"]\n", + " indices = sp.dof_map\n", + " uvec = u.vector()\n", + " values = uvec.get_local()\n", + " cur_seed = ord(sp_str) # set seed for reproducibility\n", + " generator_cur = np.random.default_rng(cur_seed)\n", + " values[indices] = np.multiply(values[indices],\n", + " generator_cur.normal(1, 0.01, len(indices)))\n", + " uvec.set_local(values)\n", + " uvec.apply(\"insert\")\n", + " nvec = model_cur.cc[sp.compartment_name].u[\"n\"].vector()\n", + " nvec.set_local(values)\n", + " nvec.apply(\"insert\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "79fbfad4", + "metadata": {}, + "source": [ + " Finally, we initialize the variational problem and solver." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ab27a38e", + "metadata": {}, + "outputs": [], + "source": [ + "model_cur.initialize_discrete_variational_problem_and_solver()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "b610b5b8", + "metadata": {}, + "source": [ + "## Solve the system and write output data\n", + "Now, we are ready to start the solution process. We store the initial conditions to output files and then solve the system at each time step using the `monolithic_solve` function. Once we pass the final time chosen above, we exit the loop." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ce499ef3", + "metadata": {}, + "outputs": [], + "source": [ + "# Write initial condition(s) to file\n", + "results = dict()\n", + "result_folder = pathlib.Path(\"resultsRect\")\n", + "result_folder.mkdir(exist_ok=True)\n", + "for species_name, species in model_cur.sc.items:\n", + " results[species_name] = d.XDMFFile(\n", + " model_cur.mpi_comm_world, str(result_folder / f\"{species_name}.xdmf\")\n", + " )\n", + " results[species_name].parameters[\"flush_output\"] = True\n", + " results[species_name].write(model_cur.sc[species_name].u[\"u\"], model_cur.t)\n", + "\n", + "# Set loglevel to warning in order not to pollute notebook output\n", + "logger.setLevel(logging.WARNING)\n", + "\n", + "# Solve\n", + "while True:\n", + " print(f\"Time is {model_cur.t}\")\n", + " # Solve the system\n", + " model_cur.monolithic_solve()\n", + " model_cur.adjust_dt()\n", + " # Save results for post processing\n", + " for species_name, species in model_cur.sc.items:\n", + " results[species_name].write(model_cur.sc[species_name].u[\"u\"], model_cur.t)\n", + " # End if we've passed the final time\n", + " if model_cur.t >= model_cur.final_t:\n", + " break" + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "main_language": "python", + "notebook_metadata_filter": "-all" + }, + "kernelspec": { + "display_name": "Python 3", + "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": "3.10.12" + }, + "vscode": { + "interpreter": { + "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1" + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/example1/model_cur.pkl b/examples/example1/model_cur.pkl new file mode 100644 index 0000000000000000000000000000000000000000..1b254aeb3c8809b6289c910d3dd1a373c8cc1264 GIT binary patch literal 1864 zcmbVNU2h{b6m8nHNxx~S7J)=5P*w%8sdzvFq-wWaMA?mqcKLckmNVmtO+5B=Y?t<7 zrR4$bM)Dix0sa9$fxp2ofp-KP&m?KuHyEiM&-JzMJ?Gwg^0fKWQERSxo`eJ6R5WM7 z&jr6y&=PCQN)x^b2iW8dzcAD)_{DQ79Sf)T_UnVb>6Ea+Hw&Tg+9pmFA{k0X&Ky-% z*vs%^@UO((PDT@EO{b7lsLpiTuRn^0$5-y%hF`7@I4flE8($%Uxv!Ol8!K_&+usMi z=@(rp5?g=zCBqV}((v#fJO($k`%XwJltIp!)HFIi3;k!|a~KAtc17Uxeo<-5Ok8a{ z!$?swB+3RQwE}2IeoGi)Mb1dd3Z_y9j3d7dqbUI9nzd~%bHXl)GTydX-$bUio?kaK zFQiZdl2S`U&+klpZrGdlvOpbnOioMN$#u#kp~kShFE0bwn$+gY=mv7z0B$VE4nIV2 zYgx%y4BXe!gr2Lb*Bt6B3%qrD_m8@8yvnIG{N*uI{8c{Bck%by zi0_T~>m&XKKHlu{{T_d-$8Ym@`JJ9)zGVuQ2oPC!3ur^h1eGM#1S@cP)iE!^n1IQe zWHbz_8*V0Z;M=*DEOC+rRC6U4NvW%r3=jWCi5)VZWa%3phts>i{T!cP{AMb$%o)U- zx%vwB6z%~(>ducbU%TyvMCTX)n66}GEip~#C?|uEWqLF_%PW+?TSp0aJ z20w`#{~;{@ls}jWP#0-#ZW>^k_Y82voBI9lc+9WO0FEWBI)*>+8!0+pMJB0?gWR3> zTQjaR^j>SDqizEOcvYR%gh@%z%tH)sx8bN?E*VW?S4^Y%`SQKs7bK4s-#8A`FO=ht z6MQUJiiAswD!V1V#1HwQ^Q+^=o9-yC_!&QQ7z61ph)IyT8dQhQdR+CKU!Mdg^_(pw z&RCrXzl-6OA`zC9%-9mz5_`yMlIk4F6UTZLO`8l!t$`!I%+3_a2%Mo($L~NO_wMYS z;EhqMH_K`hCtJ}qI`Sv6%DzP}1ZFf3Bk-{Ubg|iTW;n@&WOdiwDp^t+52vdRe;?9t z)4xX2GSaYE3N0X)F`I9d*$t z%=UA?8{bhR$8y97$Ym5DFO6lu;#VevpT;{L^*{Ul&tL!Y%QXEKBoi2WexuS;T#|^` zTA|zax2eVP!d6m?n~JIe7(s#pqyhj243dEi_E8!(sbo0@ Ha<20)Mgh%D literal 0 HcmV?d00001 diff --git a/examples/example9/example9.ipynb b/examples/example9/example9.ipynb new file mode 100644 index 00000000..4c6b7ccc --- /dev/null +++ b/examples/example9/example9.ipynb @@ -0,0 +1,299 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "f65f18d7", + "metadata": {}, + "source": [ + "# Example 9: Advection-diffusion in the case of confined migration\n", + "Here, we consider the binding or uptake of a molecule in the case of confined migration. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cc398816", + "metadata": {}, + "outputs": [], + "source": [ + "import dolfin as d\n", + "import sympy as sym\n", + "import numpy as np\n", + "import pathlib\n", + "import logging\n", + "import gmsh # must be imported before pyvista if dolfin is imported first\n", + "\n", + "from smart import config, mesh, model, mesh_tools, visualization\n", + "from smart.units import unit\n", + "from smart.model_assembly import (\n", + " Compartment,\n", + " Parameter,\n", + " Reaction,\n", + " Species,\n", + " SpeciesContainer,\n", + " ParameterContainer,\n", + " CompartmentContainer,\n", + " ReactionContainer,\n", + ")\n", + "\n", + "from matplotlib import pyplot as plt\n", + "import matplotlib.image as mpimg\n", + "from matplotlib import rcParams\n", + "\n", + "logger = logging.getLogger(\"smart\")\n", + "logger.setLevel(logging.INFO)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "95b9d865", + "metadata": {}, + "source": [ + "We define the relevant units here." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4f4023cf", + "metadata": {}, + "outputs": [], + "source": [ + "# Aliases - base units\n", + "uM = unit.uM\n", + "um = unit.um\n", + "molecule = unit.molecule\n", + "sec = unit.sec\n", + "dimensionless = unit.dimensionless\n", + "# Aliases - units used in model\n", + "D_unit = um**2 / sec\n", + "flux_unit = uM * um / sec\n", + "vol_unit = uM\n", + "surf_unit = molecule / um**2" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "46582d26", + "metadata": {}, + "source": [ + "## Model generation\n", + "\n", + "We define the compartments and species first, with their respective containers." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "02a000f2", + "metadata": {}, + "outputs": [], + "source": [ + "EC = Compartment(\"EC\", 2, um, 1)\n", + "Cyto = Compartment(\"Cyto\", 2, um, 2)\n", + "Tube = Compartment(\"Tube\", 1, um, 10)\n", + "PM = Compartment(\"PM\", 1, um, 12)\n", + " # vel=[\"0\",\"0\",\"100.0*[1-(x[0]**2 + x[1]**2//4)]\"])\n", + "\n", + "cc = CompartmentContainer()\n", + "cc.add([EC, Cyto, Tube, PM])\n", + "\n", + "A = Species(\"A\", 10.0, vol_unit, 1.0, D_unit, \"EC\")\n", + "Abound = Species(\"Abound\", 0.1, surf_unit, 0.1, D_unit, \"PM\")\n", + "B = Species(\"B\", 10.0, vol_unit, 0.1, D_unit, \"EC\")\n", + "Bcyto = Species(\"Bcyto\", 1.0, vol_unit, 0.1, D_unit, \"Cyto\")\n", + "sc = SpeciesContainer()\n", + "sc.add([A, Abound, B, Bcyto])" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "3c56e840", + "metadata": {}, + "source": [ + "Define parameters and reactions, then place in respective containers.\n", + "* r1: release of A from PM" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2e1f6882", + "metadata": {}, + "outputs": [], + "source": [ + "# reactions at PM\n", + "kon = Parameter(\"kon\", 0.0, flux_unit/vol_unit)\n", + "koff = Parameter(\"koff\", 0.0, 1/sec)\n", + "r1 = Reaction(\"r1\", [\"A\"], [\"Abound\"],\n", + " param_map={\"on\":\"kon\",\"off\":\"koff\"},\n", + " eqn_f_str=\"on*A - off*Abound\",\n", + " explicit_restriction_to_domain=\"PM\")\n", + "kin = Parameter(\"kin\", 0.01, flux_unit/vol_unit)\n", + "kout = Parameter(\"kout\", 0.01, flux_unit/vol_unit)\n", + "r2 = Reaction(\"r2\", [\"B\"], [\"Bcyto\"],\n", + " param_map={\"kin\":\"kin\",\"kout\":\"kout\"},\n", + " eqn_f_str=\"kin*B - kout*Bcyto\",\n", + " explicit_restriction_to_domain=\"PM\")\n", + "\n", + "pc = ParameterContainer()\n", + "pc.add([kon, koff, kin, kout])\n", + "rc = ReactionContainer()\n", + "rc.add([r1,r2])" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "15c35d39", + "metadata": {}, + "source": [ + "## Create and load in mesh\n", + "\n", + "Here, we consider cells embedded in a cube mesh. The source cell is located at (0,0,0) and 8 other cells are spread equidistant through the mesh." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fe56e162", + "metadata": {}, + "outputs": [], + "source": [ + "tubeRad = 5.0\n", + "gapSize = 1.0\n", + "cellVol = 1200.0\n", + "hEdge = 0.4\n", + "hInnerEdge = 0.1\n", + "domain, facet_markers, cell_markers = mesh_tools.create_confined(tubeRad, gapSize, cellVol, hEdge, hInnerEdge)\n", + "# Write mesh and meshfunctions to file\n", + "mesh_folder = pathlib.Path(\"mesh\")\n", + "mesh_folder.mkdir(exist_ok=True)\n", + "mesh_path = mesh_folder / \"cyl_mesh.h5\"\n", + "mesh_tools.write_mesh(\n", + " domain, facet_markers, cell_markers, filename=mesh_path\n", + ")\n", + "parent_mesh = mesh.ParentMesh(\n", + " mesh_filename=str(mesh_path),\n", + " mesh_filetype=\"hdf5\",\n", + " name=\"parent_mesh\",\n", + ")\n", + "# visualization.plot_dolfin_mesh(domain, cell_markers, facet_markers)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "0943588e", + "metadata": {}, + "source": [ + "Initialize model and solver." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ac88bdec", + "metadata": {}, + "outputs": [], + "source": [ + "config_cur = config.Config()\n", + "config_cur.flags.update({\"allow_unused_components\": True})\n", + "config_cur.flags.update({\"axisymmetric_model\": True})\n", + "model_cur = model.Model(pc, sc, cc, rc, config_cur, parent_mesh)\n", + "config_cur.solver.update(\n", + " {\n", + " \"final_t\": 1000.0,\n", + " \"initial_dt\": 0.01,\n", + " \"time_precision\": 8,\n", + " \"reset_timestep_for_negative_solution\": False,\n", + " }\n", + ")\n", + "model_cur.initialize()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "5d5aacbd", + "metadata": {}, + "source": [ + "Initialize XDMF files for saving results, save model information to .pkl file, then solve the system until `model_cur.t > model_cur.final_t`" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b54d28ca", + "metadata": {}, + "outputs": [], + "source": [ + "# Write initial condition(s) to file\n", + "results = dict()\n", + "result_folder = pathlib.Path(f\"results_largeGap\")\n", + "result_folder.mkdir(exist_ok=True)\n", + "for species_name, species in model_cur.sc.items:\n", + " results[species_name] = d.XDMFFile(\n", + " model_cur.mpi_comm_world, str(result_folder / f\"{species_name}.xdmf\")\n", + " )\n", + " results[species_name].parameters[\"flush_output\"] = True\n", + " results[species_name].write(model_cur.sc[species_name].u[\"u\"], model_cur.t)\n", + "model_cur.to_pickle(\"model_cur.pkl\")\n", + "\n", + "# Set loglevel to warning in order not to pollute notebook output\n", + "logger.setLevel(logging.WARNING)\n", + "# Solve\n", + "displayed = False\n", + "while True:\n", + " # Solve the system\n", + " model_cur.monolithic_solve()\n", + " model_cur.adjust_dt()\n", + " # Save results for post processing\n", + " for species_name, species in model_cur.sc.items:\n", + " results[species_name].write(model_cur.sc[species_name].u[\"u\"], model_cur.t)\n", + "\n", + " print(f\"Done with t={model_cur.t}\")\n", + " # End if we've passed the final time\n", + " if model_cur.t >= model_cur.final_t:\n", + " break\n", + "\n", + "# plt.plot(model_cur.tvec,)" + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "main_language": "python", + "notebook_metadata_filter": "-all" + }, + "kernelspec": { + "display_name": "Python 3", + "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": "3.10.12" + }, + "vscode": { + "interpreter": { + "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1" + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/example9/model_cur.pkl b/examples/example9/model_cur.pkl new file mode 100644 index 0000000000000000000000000000000000000000..a0e397017efbc3f253716434674dc2941648509e GIT binary patch literal 2388 zcmcImOK%)S5caOu_BwW)#IX`7hY%nH6Di9>LfrB)U=oWZJaa;=-kF}Q#`DTdcgQ9} z3KA$;QGp;jLgCE;<$%P66F-N4z%Ky4p4qiG4i{cKvUj?=y1MGCs;~BX>(06Psp|8d zTjf?N6Xkfy@vdAJcsHsj-P>*zo7CXx%`A01b6Lh#x%K+k)D*XDs*U4Tu2Xz13!COT z*o>99WMyi!8Mx0JAM(4MNCwK3ojjI0?QCuH?h9V<>bCkugXgOQ*67&r(wn%UT+31e zHC4dg6Yo3P!!tJ2fvK0PyerW`kyTDR7?>?pkfotJ{|7!6f_Bg9*yyxG3{jj(fAEIu z-Egl#&@VEZJ8JSwni*C4w`E%@krxV%t9~JkM)X78r%PdUqC}{2m4*s24|y5FGDmRt zN!#Th5$Z}_cx!uVOJYmb<=v%B@>r*R5lSOnmsiF*JLD}h$dQ+oGLePpBw46pAfJ2VlFt1u6PRw;&E{{?BU^&y~3fG^(O*1=IlQQOj8P0>c{$WBv5ex*>Q! zgaOK;t{8L!O4sc~c3iAkEDIFtB*NTy-mRbdZDegvsH4c1xMIT6*7kO)Jd(}7K$7Y!Pb3Tt%A*`>T`sJ?wd_gbm^m3KkNfxWX#tKf-f%CuDt+bt|SGG@I z@TdQVXY>{~FT6bI$QZ&cN6z`)qU7U<`gzA5J0k_r$Cac3xyf}gOxLl|~7kMcJ zXQV!lGWL|X(d2y-x)aF-(Ay1&_PDP$76KK=0yMA*8r*2qtxT2%NdDDP`mR-|UEiql z+n^A;jR$rYt>XDY$-tNIwyWGMo_0JPlNWL0jFUWF)Qj0Oz0878CAir$4&2BcxP+Ui zf12g#icg-hyfA8)u>#%3bBk_SFi~u;h%x{MY2Tlv+g-ZVwY+=miKwY=Hn641632(Z zpRo?K5rryE0lN3CU@{SA35J2AkQdNu!KSFk(vauXrBp-$%8vJ+IgXii#!;UaTj{ zXp0wLujFgBW;I>mJkLcM)hZ0g?UU0LA935y#4-gH-sHpn+YiXmC{hAhRT97sN~02t z#a&~b3}ItD1$bVD?;yJZ!Y(gWvlK=G?VH1GwE37cIG&qo%)(M$r5+R}koiy}fW895 z!v0azgqqNcvO=V)k5PRYUS=_VJ@}bzdw$@{K4|!7UU<>J?F{vxjN|NGbRpskLF-AL lr9j_@xttgH1t4&3FGKJ;jWRDCRf+O7DXNi-g6Ub?`4hmVj$;4- literal 0 HcmV?d00001 diff --git a/smart/mesh_tools.py b/smart/mesh_tools.py index e3b7335d..5eb54126 100644 --- a/smart/mesh_tools.py +++ b/smart/mesh_tools.py @@ -582,6 +582,215 @@ def meshSizeCallback(dim, tag, x, y, z, lc): return (dmesh, mf2, mf3) +def create_confined( + tubeRad: float = 10.0, + gapSize: float = 1.0, + cellVol: float = 1200.0, + hEdge: float = 0, + hInnerEdge: float = 0, + interface_marker: int = 12, + outer_marker: int = 10, + inner_vol_tag: int = 2, + outer_vol_tag: int = 1, + comm: MPI.Comm = d.MPI.comm_world, + verbose: bool = False, +) -> Tuple[d.Mesh, d.MeshFunction, d.MeshFunction]: + """ + Creates an axisymmetric mesh representing a cell within a cylindrical tube, + assuming axisymmetry about the r=0 axis. + + Args: + tubeRad: Radius of tube + gapSize: Gap between cell and tube wall + cellVol: volume of cell (constrains overall geometry) + hEdge: maximum mesh size at the outer edge + hInnerEdge: maximum mesh size at the edge + of the inner compartment + interface_marker: The value to mark facets on the interface with + outer_marker: The value to mark facets on the outer ellipsoid with + inner_vol_tag: The value to mark the inner ellipsoidal volume with + outer_vol_tag: The value to mark the outer ellipsoidal volume with + comm: MPI communicator to create the mesh with + verbose: If true print gmsh output, else skip + Returns: + Tuple (mesh, facet_marker, cell_marker) + """ + import gmsh + + if tubeRad <= 0: + raise ValueError("Tube radius must be greater than 0") + if gapSize <= 0 or gapSize >= tubeRad: + raise ValueError("Gap between cell membrane and wall must be between 0 and tubeRad") + if cellVol <= 0: + raise ValueError("Cell volume must be greater than 0") + + Lc = (cellVol - 4 * np.pi * (tubeRad - gapSize) ** 2) / (2 * np.pi * (tubeRad - gapSize)) + zmax = Lc / 2 + (tubeRad - gapSize) + 10.0 + rValsOuter = np.array([0.0, tubeRad, tubeRad, 0.0]) + zValsOuter = np.array([zmax, zmax, -zmax, -zmax]) + thetaVals = np.linspace(np.pi / 2, 0.0, 20) + rValsSphere = (tubeRad - gapSize) * np.cos(thetaVals) + zValsSphere = Lc / 2 + (tubeRad - gapSize) * np.sin(thetaVals) + maxOuterDim = zmax + maxInnerDim = Lc + (tubeRad - gapSize) + + if np.isclose(hEdge, 0): + hEdge = 0.1 * maxOuterDim + if np.isclose(hInnerEdge, 0): + hInnerEdge = 0.2 * maxInnerDim + # Create the two axisymmetric body mesh using gmsh + gmsh.initialize() + gmsh.option.setNumber("General.Terminal", int(verbose)) + gmsh.model.add("axisymm") + # first add outer body + outer_tag_list = [] + outer_line_list = [] + for i in range(len(rValsOuter)): + cur_tag = gmsh.model.occ.add_point(rValsOuter[i], 0, zValsOuter[i]) + outer_tag_list.append(cur_tag) + if i > 0: + outer_line_list.append(gmsh.model.occ.add_line(cur_tag, outer_tag_list[-2])) + # include symm axis + outer_line_list.append(gmsh.model.occ.add_line(outer_tag_list[0], outer_tag_list[-1])) + outer_loop_tag = gmsh.model.occ.add_curve_loop(outer_line_list) + cell_plane_tag = gmsh.model.occ.add_plane_surface([outer_loop_tag]) + + # Add inner shape + inner_tag_list1 = [] + for i in range(len(rValsSphere)): + cur_tag = gmsh.model.occ.add_point(rValsSphere[i], 0, zValsSphere[i]) + inner_tag_list1.append(cur_tag) + inner_spline1_tag = gmsh.model.occ.add_spline(inner_tag_list1) + inner_tag_list2 = [] + for i in range(len(rValsSphere)): + cur_tag = gmsh.model.occ.add_point(rValsSphere[-(i + 1)], 0, -zValsSphere[-(i + 1)]) + inner_tag_list2.append(cur_tag) + inner_spline2_tag = gmsh.model.occ.add_spline(inner_tag_list2) + inner_cyl_line = gmsh.model.occ.add_line(inner_tag_list1[-1], inner_tag_list2[0]) + symm_inner_tag = gmsh.model.occ.add_line(inner_tag_list1[0], inner_tag_list2[-1]) + inner_loop_tag = gmsh.model.occ.add_curve_loop( + [inner_spline1_tag, inner_cyl_line, inner_spline2_tag, symm_inner_tag] + ) + inner_plane_tag = gmsh.model.occ.add_plane_surface([inner_loop_tag]) + cell_plane_list = [cell_plane_tag] + inner_plane_list = [inner_plane_tag] + + outer_volume = [] + inner_volume = [] + all_volumes = [] + inner_marker_list = [] + outer_marker_list = [] + for i in range(len(cell_plane_list)): + cell_plane_tag = cell_plane_list[i] + inner_plane_tag = inner_plane_list[i] + # Create interface between 2 objects + two_shapes, (outer_shape_map, inner_shape_map) = gmsh.model.occ.fragment( + [(2, cell_plane_tag)], [(2, inner_plane_tag)] + ) + gmsh.model.occ.synchronize() + + # Get the outer boundary + outer_shell = gmsh.model.getBoundary(two_shapes, oriented=False) + for i in range(len(outer_shell)): + outer_marker_list.append(outer_shell[i][1]) + # Get the inner boundary + inner_shell = gmsh.model.getBoundary(inner_shape_map, oriented=False) + for i in range(len(inner_shell)): + inner_marker_list.append(inner_shell[i][1]) + for tag in outer_shape_map: + all_volumes.append(tag[1]) + for tag in inner_shape_map: + inner_volume.append(tag[1]) + + for vol in all_volumes: + if vol not in inner_volume: + outer_volume.append(vol) + + # Add physical markers for facets + # set symmetry axis to 0 (no flux) + xmin, ymin, zmin = (-hInnerEdge / 10, -hInnerEdge / 10, -1) + xmax, ymax, zmax = (hInnerEdge / 10, hInnerEdge / 10, max(zValsOuter) + 1) + all_symm_bound = gmsh.model.occ.get_entities_in_bounding_box( + xmin, ymin, zmin, xmax, ymax, zmax, dim=1 + ) + symm_bound_markers = [] + for i in range(len(all_symm_bound)): + symm_bound_markers.append(all_symm_bound[i][1]) + # note that this first call sets the symmetry axis to tag 0 and + # this is not overwritten by the next calls to add_physical_group + gmsh.model.add_physical_group(1, symm_bound_markers, tag=0) + gmsh.model.add_physical_group(1, outer_marker_list, tag=outer_marker) + gmsh.model.add_physical_group(1, inner_marker_list, tag=interface_marker) + + # Physical markers for "volumes" + gmsh.model.add_physical_group(2, outer_volume, tag=outer_vol_tag) + gmsh.model.add_physical_group(2, inner_volume, tag=inner_vol_tag) + + def meshSizeCallback(dim, tag, x, y, z, lc): + # mesh length is hEdge at the PM and hInnerEdge at the inner membrane + # between these, the value is interpolated based on the relative distance + # between the two membranes. + # Inside the inner shape, the value is interpolated between hInnerEdge + # and lc3, where lc3 = max(hInnerEdge, 0.2*maxInnerDim) + # if innerRad=0, then the mesh length is interpolated between + # hEdge at the PM and 0.2*maxOuterDim in the center + lc1 = hEdge + lc2 = hInnerEdge + lc3 = max(hInnerEdge, 0.3 * (tubeRad - gapSize)) + z_abs = np.abs(z) + if z_abs < Lc / 2: + if x > (tubeRad - gapSize): + in_outer = True + # dist_to_outer = tubeRad - x + dist_to_inner = x - (tubeRad - gapSize) + else: + in_outer = False + R_rel_inner = x / (tubeRad - gapSize) + else: + rTest = np.sqrt(x**2 + (z_abs - Lc / 2) ** 2) + if rTest > (tubeRad - gapSize): + in_outer = True + # dist_to_outer = tubeRad - x + dist_to_inner = rTest - (tubeRad - gapSize) + else: + in_outer = False + R_rel_inner = rTest / (tubeRad - gapSize) + + if in_outer: + lcTest = lc2 + (lc1 - lc2) * (1 - np.exp(-dist_to_inner / 1.0)) + else: + lcTest = lc2 + (lc3 - lc2) * (1 - R_rel_inner) + return lcTest + + gmsh.model.mesh.setSizeCallback(meshSizeCallback) + # set off the other options for mesh size determination + gmsh.option.setNumber("Mesh.MeshSizeExtendFromBoundary", 0) + gmsh.option.setNumber("Mesh.MeshSizeFromPoints", 0) + gmsh.option.setNumber("Mesh.MeshSizeFromCurvature", 0) + # this changes the algorithm from Frontal-Delaunay to Delaunay, + # which may provide better results when there are larger gradients in mesh size + gmsh.option.setNumber("Mesh.Algorithm", 5) + + gmsh.model.mesh.generate(2) + rank = MPI.COMM_WORLD.rank + tmp_folder = pathlib.Path(f"tmp_2DCell_{rank}") + tmp_folder.mkdir(exist_ok=True) + gmsh_file = tmp_folder / "2DCell.msh" + gmsh.write(str(gmsh_file)) + gmsh.finalize() + + # return dolfin mesh of max dimension (parent mesh) and marker functions mf2 and mf3 + dmesh, mf2, mf3 = gmsh_to_dolfin(str(gmsh_file), tmp_folder, 2, comm) + # ensure zero flux condition at r=0 axis + for f in d.facets(dmesh): + if np.isclose(f.midpoint().x(), 0.0): + mf2[f] = 0 + # remove tmp mesh and tmp folder + gmsh_file.unlink(missing_ok=False) + tmp_folder.rmdir() + return (dmesh, mf2, mf3) + + def create_cylinders( outerRad: float = 1.0, innerRad: float = 0.0, diff --git a/smart/model.py b/smart/model.py index 7964faff..03600512 100644 --- a/smart/model.py +++ b/smart/model.py @@ -255,6 +255,7 @@ def _init_1(self): logger.debug("Checking validity of model (step 1 of ZZ)", extra=dict(format_type="title")) self._init_1_1_check_mesh_dimensionality() + self._init_1_1b_CH_chem_potential_init() self._init_1_2_check_namespace_conflicts() self._init_1_3_check_parameter_dimensionality() logger.debug( @@ -372,6 +373,28 @@ def _init_1_1_check_mesh_dimensionality(self): for compartment in self.cc: compartment.is_volume = compartment.dimensionality == self.max_dim + def _init_1_1b_CH_chem_potential_init(self): + # all CH species require an additional species to be added to track chemical potential + # initial value is treated later + new_sp = [] + for species in self.sc: + if species.CH: + init_chem_potential = 0.0 + diff_units = self.cc[species.compartment_name].compartment_units ** 2 / unit.sec + chem_potential_sp = Species( + f"{species.name}_chem_potential", + init_chem_potential, + unit.dimensionless, + 0.0, + diff_units, + species.compartment_name, + ) + chem_potential_sp.is_chem_potential = True + new_sp.append(chem_potential_sp) + species.chem_potential = chem_potential_sp + for sp in new_sp: + self.sc.add(sp) + def _init_1_2_check_namespace_conflicts(self): """Namespace checks: @@ -584,6 +607,9 @@ def _init_2_4_check_for_unused_parameters_species_compartments(self): all_parameters = set(chain.from_iterable([r.parameters for r in self.rc])) all_species = set(chain.from_iterable([r.species for r in self.rc])) + for species in self.sc: + if species.is_chem_potential: + all_species.add(species.name) all_compartments = set(chain.from_iterable([r.compartments for r in self.rc])) if all_parameters != set(self.pc.keys): print_str = ( @@ -987,6 +1013,9 @@ def _init_4_7_set_initial_conditions(self): """ logger.debug("Set function values to initial conditions", extra=dict(format_type="log")) for species in self.sc: + if species.is_chem_potential: + species.D_dolfin = d.Constant(0.0) # set diffusion to zero (N/A) + continue # then initial condition is set to match concentration of assoc species # first, initialize diffusion coefficient if isinstance(species.D, float): species.D_dolfin = d.Constant(species.D) @@ -1024,6 +1053,21 @@ def _init_4_7_set_initial_conditions(self): values[species.dof_map] = values_new[species.dof_map] u_cur.vector().set_local(values) u_cur.vector().apply("insert") + if species.CH: + lagrange = species.compartment.deform_logic or species.alt_deform_logic + if lagrange: + logger.error("CH species are not compatible with Lagrange approach yet!") + for ckey in species.chem_potential.u.keys(): + A_hat = species.A_hat + phi_cur = species.u[ckey] / species.umax + cfunc = ( + d.ln(phi_cur) + - d.ln(1 - phi_cur) + - A_hat * (2 * phi_cur - 1) + + (A_hat / species.umax) * d.div(d.grad(phi_cur)) + ) + Vc = species.chem_potential.V + species.chem_potential.u[ckey].assign(d.project(cfunc, Vc)) species.alt_vel_logic = np.any([vel != 0.0 for vel in species.alt_vel]) species.alt_deform_logic = np.any([deform != 0.0 for deform in species.alt_deform]) if species.alt_vel_logic and species.alt_deform_logic: @@ -1339,8 +1383,53 @@ def _init_5_2_create_variational_forms(self): J = d.Constant(1.0) if self.config.flags["axisymmetric_model"]: J = x[0] * J + # catch CH case + if species.CH: + if species.is_chem_potential: + logger.debug( + "Chemical potential equation is defined with concentration," + "skipping to next species" + ) + continue + else: + u_c = species.chem_potential._usplit["u"] + v_c = species.chem_potential.v + A_hat = species.A_hat + phi_cur = u / species.umax + df_c = d.ln(phi_cur) - d.ln(1 - phi_cur) - A_hat * (2 * phi_cur - 1) + CForm = J * ( + (u_c - df_c) * v_c * dx + - (A_hat / species.umax) * d.inner(d.grad(phi_cur), d.grad(v_c)) * dx + ) + CForm_units = ( + species.compartment.compartment_units**species.compartment.dimensionality + ) + # chemical potential is in units of kBT for convenience + Dform = J * D * u * d.inner(d.grad(u_c), d.grad(v)) * dx + self.forms.add( + Form( + f"chem_potential_{species.name}", + CForm, + species.chem_potential, + "chem_potential", + CForm_units, + True, + linear_wrt_comp, + ) + ) + self.forms.add( + Form( + f"diffusion_{species.name}", + Dform, + species, + "diffusion", + Dform_units, + True, + linear_wrt_comp, + ) + ) # diffusion term - if species.D == 0: + elif species.D == 0: logger.debug( f"Species {species.name} has a diffusion coefficient of 0. " "Skipping creation of diffusive form.", @@ -1368,8 +1457,6 @@ def _init_5_2_create_variational_forms(self): ) else: Dform = J * D * d.inner(d.grad(u), d.grad(v)) * dx - # exponent is -2 because of two gradients - self.forms.add( Form( f"diffusion_{species.name}", diff --git a/smart/model_assembly.py b/smart/model_assembly.py index 55abd2b2..ffa79e54 100644 --- a/smart/model_assembly.py +++ b/smart/model_assembly.py @@ -988,6 +988,11 @@ class Species(ObjectInstance): alt_deform: list = dataclasses.field(default_factory=lambda: [0.0, 0.0, 0.0]) alt_vel: list = dataclasses.field(default_factory=lambda: [0.0, 0.0, 0.0]) alt_manual_update: bool = False + CH: bool = False + is_chem_potential: bool = False + A_hat: float = 0.0 + umax: float = 0.0 + # if this is a CH conc, then we also need fields: chem_potential, A_hat, umax def to_dict(self): "Convert to a dict that can be used to recreate the object." @@ -1061,6 +1066,12 @@ def __post_init__(self): else: raise TypeError("Diffusion coefficient must a float, int, or string") + if self.CH: + if not hasattr(self, "A_hat"): + raise ValueError("A_hat must be provided for CH species") + if not hasattr(self, "umax"): + raise ValueError("umax must be provided for CH variable") + self._convert_pint_quantity_to_unit() self._check_input_type_validity() self._convert_pint_unit_to_quantity() From 4fc9878d14f28ee0ae6596ab37a93e98cea100cc Mon Sep 17 00:00:00 2001 From: emmetfrancis <99422170+emmetfrancis@users.noreply.github.com> Date: Mon, 22 Jun 2026 13:21:20 -0700 Subject: [PATCH 2/4] remove pkl files --- examples/example1/model_cur.pkl | Bin 1864 -> 0 bytes examples/example9/model_cur.pkl | Bin 2388 -> 0 bytes 2 files changed, 0 insertions(+), 0 deletions(-) delete mode 100644 examples/example1/model_cur.pkl delete mode 100644 examples/example9/model_cur.pkl diff --git a/examples/example1/model_cur.pkl b/examples/example1/model_cur.pkl deleted file mode 100644 index 1b254aeb3c8809b6289c910d3dd1a373c8cc1264..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 1864 zcmbVNU2h{b6m8nHNxx~S7J)=5P*w%8sdzvFq-wWaMA?mqcKLckmNVmtO+5B=Y?t<7 zrR4$bM)Dix0sa9$fxp2ofp-KP&m?KuHyEiM&-JzMJ?Gwg^0fKWQERSxo`eJ6R5WM7 z&jr6y&=PCQN)x^b2iW8dzcAD)_{DQ79Sf)T_UnVb>6Ea+Hw&Tg+9pmFA{k0X&Ky-% z*vs%^@UO((PDT@EO{b7lsLpiTuRn^0$5-y%hF`7@I4flE8($%Uxv!Ol8!K_&+usMi z=@(rp5?g=zCBqV}((v#fJO($k`%XwJltIp!)HFIi3;k!|a~KAtc17Uxeo<-5Ok8a{ z!$?swB+3RQwE}2IeoGi)Mb1dd3Z_y9j3d7dqbUI9nzd~%bHXl)GTydX-$bUio?kaK zFQiZdl2S`U&+klpZrGdlvOpbnOioMN$#u#kp~kShFE0bwn$+gY=mv7z0B$VE4nIV2 zYgx%y4BXe!gr2Lb*Bt6B3%qrD_m8@8yvnIG{N*uI{8c{Bck%by zi0_T~>m&XKKHlu{{T_d-$8Ym@`JJ9)zGVuQ2oPC!3ur^h1eGM#1S@cP)iE!^n1IQe zWHbz_8*V0Z;M=*DEOC+rRC6U4NvW%r3=jWCi5)VZWa%3phts>i{T!cP{AMb$%o)U- zx%vwB6z%~(>ducbU%TyvMCTX)n66}GEip~#C?|uEWqLF_%PW+?TSp0aJ z20w`#{~;{@ls}jWP#0-#ZW>^k_Y82voBI9lc+9WO0FEWBI)*>+8!0+pMJB0?gWR3> zTQjaR^j>SDqizEOcvYR%gh@%z%tH)sx8bN?E*VW?S4^Y%`SQKs7bK4s-#8A`FO=ht z6MQUJiiAswD!V1V#1HwQ^Q+^=o9-yC_!&QQ7z61ph)IyT8dQhQdR+CKU!Mdg^_(pw z&RCrXzl-6OA`zC9%-9mz5_`yMlIk4F6UTZLO`8l!t$`!I%+3_a2%Mo($L~NO_wMYS z;EhqMH_K`hCtJ}qI`Sv6%DzP}1ZFf3Bk-{Ubg|iTW;n@&WOdiwDp^t+52vdRe;?9t z)4xX2GSaYE3N0X)F`I9d*$t z%=UA?8{bhR$8y97$Ym5DFO6lu;#VevpT;{L^*{Ul&tL!Y%QXEKBoi2WexuS;T#|^` zTA|zax2eVP!d6m?n~JIe7(s#pqyhj243dEi_E8!(sbo0@ Ha<20)Mgh%D diff --git a/examples/example9/model_cur.pkl b/examples/example9/model_cur.pkl deleted file mode 100644 index a0e397017efbc3f253716434674dc2941648509e..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 2388 zcmcImOK%)S5caOu_BwW)#IX`7hY%nH6Di9>LfrB)U=oWZJaa;=-kF}Q#`DTdcgQ9} z3KA$;QGp;jLgCE;<$%P66F-N4z%Ky4p4qiG4i{cKvUj?=y1MGCs;~BX>(06Psp|8d zTjf?N6Xkfy@vdAJcsHsj-P>*zo7CXx%`A01b6Lh#x%K+k)D*XDs*U4Tu2Xz13!COT z*o>99WMyi!8Mx0JAM(4MNCwK3ojjI0?QCuH?h9V<>bCkugXgOQ*67&r(wn%UT+31e zHC4dg6Yo3P!!tJ2fvK0PyerW`kyTDR7?>?pkfotJ{|7!6f_Bg9*yyxG3{jj(fAEIu z-Egl#&@VEZJ8JSwni*C4w`E%@krxV%t9~JkM)X78r%PdUqC}{2m4*s24|y5FGDmRt zN!#Th5$Z}_cx!uVOJYmb<=v%B@>r*R5lSOnmsiF*JLD}h$dQ+oGLePpBw46pAfJ2VlFt1u6PRw;&E{{?BU^&y~3fG^(O*1=IlQQOj8P0>c{$WBv5ex*>Q! zgaOK;t{8L!O4sc~c3iAkEDIFtB*NTy-mRbdZDegvsH4c1xMIT6*7kO)Jd(}7K$7Y!Pb3Tt%A*`>T`sJ?wd_gbm^m3KkNfxWX#tKf-f%CuDt+bt|SGG@I z@TdQVXY>{~FT6bI$QZ&cN6z`)qU7U<`gzA5J0k_r$Cac3xyf}gOxLl|~7kMcJ zXQV!lGWL|X(d2y-x)aF-(Ay1&_PDP$76KK=0yMA*8r*2qtxT2%NdDDP`mR-|UEiql z+n^A;jR$rYt>XDY$-tNIwyWGMo_0JPlNWL0jFUWF)Qj0Oz0878CAir$4&2BcxP+Ui zf12g#icg-hyfA8)u>#%3bBk_SFi~u;h%x{MY2Tlv+g-ZVwY+=miKwY=Hn641632(Z zpRo?K5rryE0lN3CU@{SA35J2AkQdNu!KSFk(vauXrBp-$%8vJ+IgXii#!;UaTj{ zXp0wLujFgBW;I>mJkLcM)hZ0g?UU0LA935y#4-gH-sHpn+YiXmC{hAhRT97sN~02t z#a&~b3}ItD1$bVD?;yJZ!Y(gWvlK=G?VH1GwE37cIG&qo%)(M$r5+R}koiy}fW895 z!v0azgqqNcvO=V)k5PRYUS=_VJ@}bzdw$@{K4|!7UU<>J?F{vxjN|NGbRpskLF-AL lr9j_@xttgH1t4&3FGKJ;jWRDCRf+O7DXNi-g6Ub?`4hmVj$;4- From b0b0c67a592e5b9d86e16ea5ceea1e0be8aa6fc7 Mon Sep 17 00:00:00 2001 From: emmetfrancis <99422170+emmetfrancis@users.noreply.github.com> Date: Mon, 22 Jun 2026 16:54:27 -0700 Subject: [PATCH 3/4] Implement cutoff and mass conservation in CH example --- .pre-commit-config.yaml | 3 +- examples/example1/example1_CH.ipynb | 186 ++++++++++++------- examples/example1/spheroid_ellipsoid_mesh.h5 | Bin 0 -> 2304688 bytes 3 files changed, 121 insertions(+), 68 deletions(-) create mode 100644 examples/example1/spheroid_ellipsoid_mesh.h5 diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml index b9ff80d5..9541779f 100644 --- a/.pre-commit-config.yaml +++ b/.pre-commit-config.yaml @@ -11,7 +11,8 @@ repos: exclude: | (?x)^( joss-paper/JOSS_Fig2.png| - examples/example2-3d/spine_mesh.xml + examples/example2-3d/spine_mesh.xml| + examples/example1/spheroid_ellipsoid_mesh.h5 )$ - id: check-docstring-first - id: debug-statements diff --git a/examples/example1/example1_CH.ipynb b/examples/example1/example1_CH.ipynb index 111a6730..96e1af3c 100644 --- a/examples/example1/example1_CH.ipynb +++ b/examples/example1/example1_CH.ipynb @@ -12,23 +12,24 @@ "- surf - 2D surface\n", "- edge - outer edges of the surface (1D)\n", "\n", - "We implement a Cahn-Hilliard model with two species, one exhibiting aggregation-diffusion ($A$) and the other purely diffusive ($B$).\n", + "We implement a Cahn-Hilliard model with two species, one exhibiting aggregation-diffusion ($B$) and the other purely diffusive ($X$).\n", "The equations governing their evolution are given by:\n", "\n", "$$\n", - "\\partial_t{u_A} = -k_{on} u_A + k_{off} u_B + D_A \\nabla \\cdot (\\hat{\\mu}_A \\nabla u_A) \\\\\n", - "\\partial_t{u_B} = k_{on} u_A - k_{off} u_B + D_B \\nabla \\cdot (\\nabla u_B),\n", + "\\partial_t{u_X} = -k_{on} u_X + k_{off} u_B + D_X \\nabla \\cdot (\\hat{\\mu}_X \\nabla u_X) \\\\\n", + "\\partial_t{u_B} = k_{on} u_X - k_{off} u_B + D_B \\nabla \\cdot (\\hat{\\mu}_B \\nabla u_B),\n", "$$\n", "\n", - "where aggregation is accounted for through the chemical potential of $A$, whose nondimensional version ($\\hat{\\mu}_A = \\frac{\\mu_A}{k_B T}) is given by\n", + "where aggregation is accounted for through the chemical potential of $B$, whose nondimensional version ($\\hat{\\mu}_B = \\frac{\\mu_B}{k_B T}$) is given by\n", "\n", "$$\n", - "\\hat{\\mu}_A = (\\ln \\phi_A - \\ln (1-\\phi_A)) - \\hat{A} (2 \\phi_A - 1) - \\hat{A} \\nabla^2 \\phi_A\n", + "\\hat{\\mu}_B = (\\ln \\phi_B - \\ln (1-\\phi_B)) - \\hat{A} (2 \\phi_B - 1) - \\frac{\\hat{A}}{u_{B,max}} \\nabla^2 \\phi_B\n", "$$\n", "\n", - "in which $\\phi_A$ is the area fraction occupied by species A, which is proportional to its concentration; that is, $\\phi_A = \\frac{u_A}{u_{A,max}}$\n", + "in which $\\phi_B$ is the area fraction occupied by species B, which is proportional to its concentration; that is, $\\phi_B = \\frac{u_B}{u_{B,max}}$.\n", + "The chemical potential is defined similarly for X, but with $\\hat{A}=0$; that is, $\\hat{\\mu}_X = (\\ln \\phi_X - \\ln (1-\\phi_X))$\n", "\n", - "We solve these equations over a 1 by 1 square domain with no-flux boundary conditions." + "We solve these equations over a square domain with no-flux boundary conditions." ] }, { @@ -158,8 +159,7 @@ "metadata": {}, "outputs": [], "source": [ - "surf = Compartment(\"surf\", 2, um, 1)\n", - "edge = Compartment(\"edge\", 1, um, 3)" + "surf = Compartment(\"surf\", 2, um, 10)" ] }, { @@ -179,7 +179,7 @@ "outputs": [], "source": [ "cc = CompartmentContainer()\n", - "cc.add([surf, edge])" + "cc.add([surf])" ] }, { @@ -189,7 +189,7 @@ "metadata": {}, "source": [ "### Species\n", - "In this case, we have a two species, \"A\" and \"B\", which exist in the 2D \"surf\" domain. Each is initialized by calling:\n", + "In this case, we have a two species, \"X\" and \"B\", which exist in the 2D \"surf\" domain. Each is initialized by calling:\n", "```\n", "species_var = Species(\n", " name, initial_condition, concentration_units,\n", @@ -206,9 +206,9 @@ "- group (opt): for larger models, specifies a group of species this belongs to;\n", " for organizational purposes when there are multiple reaction modules\n", "\n", - "With the added CH features, we also must provide the following for species A:\n", - "- `CH = True` - this tells SMART that we are considering both aggregation and diffusion for species A\n", - "- umax: maximum surface density of A\n", + "With the added CH features, we also must provide the following for Cahn-Hilliard type species:\n", + "- `CH = True` - this tells SMART that we are considering both aggregation and diffusion\n", + "- umax: maximum surface density of X or B\n", "- A_hat: strength of aggregation\n", "\n", "Note that A_hat is dimensionless here and the chemical potential is a variable generated *internally* within this branch of SMART. Because only the nondimensional chemical potential appears in the dynamical equation for $u_A$, the chemical potential is always normalized to the thermal energy scale $k_B T$. (see equations up top for consistency on this point)" @@ -221,8 +221,8 @@ "metadata": {}, "outputs": [], "source": [ - "A = Species(\"A\", 10, surf_unit, 0.1, D_unit, \"surf\", CH=True, umax=100, A_hat = 25) # CH species\n", - "B = Species(\"B\", 90, surf_unit, 0.1, D_unit, \"surf\") # other stuff" + "X = Species(\"X\", 10, surf_unit, 0.1, D_unit, \"surf\", CH=True, umax=100, A_hat = 0) \n", + "B = Species(\"B\", 90, surf_unit, 0.1, D_unit, \"surf\", CH=True, umax=100, A_hat = 25)" ] }, { @@ -242,7 +242,7 @@ "outputs": [], "source": [ "sc = SpeciesContainer()\n", - "sc.add([A, B])" + "sc.add([X, B])" ] }, { @@ -309,13 +309,13 @@ "metadata": {}, "outputs": [], "source": [ - "kon = Parameter(\"kon\", 10.0, 1/sec)\n", - "koff = Parameter(\"koff\", 1.0, 1/sec)\n", + "kon = Parameter(\"kon\", 0.0, 1/sec)\n", + "koff = Parameter(\"koff\", 0.0, 1/sec)\n", "# Production of A\n", - "r1 = Reaction(\"r1\", [\"A\"], [\"B\"],\n", + "r1 = Reaction(\"r1\", [\"X\"], [\"B\"],\n", " param_map={\"kon\": \"kon\", \"koff\": \"koff\"},\n", - " eqn_f_str=\"A*kon - B*koff\",\n", - " species_map={\"A\": \"A\", \"B\": \"B\"})" + " eqn_f_str=\"X*kon - B*koff\",\n", + " species_map={\"X\": \"X\", \"B\": \"B\"})" ] }, { @@ -370,43 +370,31 @@ "metadata": {}, "outputs": [], "source": [ - "# define dimensions of domain\n", - "Shat = 200\n", - "x_size = np.sqrt(Shat/A.umax)\n", - "y_size = np.sqrt(Shat/A.umax)\n", - "# Create mesh\n", - "m = 30\n", - "n = int(x_size/y_size)*m\n", - "rect_mesh = d.RectangleMesh(d.Point(0.0, 0.0), d.Point(x_size, y_size), n, m)\n", - "mf2 = d.MeshFunction(\"size_t\", rect_mesh, 2, 1)\n", - "mf1 = d.MeshFunction(\"size_t\", rect_mesh, 1, 0)\n", - "class OuterEdge(d.SubDomain):\n", - " def inside(self, x, on_boundary):\n", - " return on_boundary\n", - "outerEdge = OuterEdge()\n", - "outerEdge.mark(mf1, 3)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "86c4b70c", - "metadata": {}, - "source": [ - "Now we write mesh and meshfunctions to file." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "fe4d77ac", - "metadata": {}, - "outputs": [], - "source": [ - "mesh_folder = pathlib.Path(\"rect_mesh\")\n", - "mesh_folder.mkdir(exist_ok=True)\n", - "mesh_file = mesh_folder / \"rect_mesh.h5\"\n", - "mesh_tools.write_mesh(rect_mesh, mf1, mf2, mesh_file)" + "useSpheroid = True\n", + "if useSpheroid:\n", + " vol = Compartment(\"vol\", 3, um, 1) # SMART just needs to know its a 3d mesh\n", + " cc.add(vol)\n", + " mesh_file = pathlib.Path(\"spheroid_ellipsoid_mesh.h5\")\n", + "else:\n", + " # define dimensions of domain\n", + " Shat = 200\n", + " x_size = np.sqrt(Shat/B.umax)\n", + " y_size = np.sqrt(Shat/B.umax)\n", + " # Create mesh\n", + " m = 30\n", + " n = int(x_size/y_size)*m\n", + " rect_mesh = d.RectangleMesh(d.Point(0.0, 0.0), d.Point(x_size, y_size), n, m)\n", + " mf2 = d.MeshFunction(\"size_t\", rect_mesh, 2, 10)\n", + " mf1 = d.MeshFunction(\"size_t\", rect_mesh, 1, 0)\n", + " class OuterEdge(d.SubDomain):\n", + " def inside(self, x, on_boundary):\n", + " return on_boundary\n", + " outerEdge = OuterEdge()\n", + " outerEdge.mark(mf1, 3)\n", + " mesh_folder = pathlib.Path(\"rect_mesh\")\n", + " mesh_folder.mkdir(exist_ok=True)\n", + " mesh_file = mesh_folder / \"rect_mesh.h5\"\n", + " mesh_tools.write_mesh(rect_mesh, mf1, mf2, mesh_file)" ] }, { @@ -483,7 +471,7 @@ "outputs": [], "source": [ "model_cur = model.Model(pc, sc, cc, rc, config_cur, parent_mesh)\n", - "model_cur.initialize(initialize_solver=False)\n", + "model_cur.initialize()\n", "model_cur.to_pickle('model_cur.pkl')" ] }, @@ -504,7 +492,7 @@ "outputs": [], "source": [ "# add white noise perturbation to initial conditions\n", - "for sp_str in (\"A\", \"B\"):\n", + "for sp_str in (\"X\", \"B\"):\n", " sp = model_cur.sc[sp_str]\n", " u = model_cur.cc[sp.compartment_name].u[\"u\"]\n", " indices = sp.dof_map\n", @@ -522,22 +510,59 @@ ] }, { - "attachments": {}, "cell_type": "markdown", - "id": "79fbfad4", + "id": "fbe592a7", "metadata": {}, "source": [ - " Finally, we initialize the variational problem and solver." + "Define other functions to be used for mass conservation and cutoffs here" ] }, { "cell_type": "code", "execution_count": null, - "id": "ab27a38e", + "id": "8aa0f4cf", "metadata": {}, "outputs": [], "source": [ - "model_cur.initialize_discrete_variational_problem_and_solver()" + "def _set_clipped_sum_c_tmp_scalar(sp, xi1_scalar, dt_val, epsilon):\n", + " \"\"\"clip(c + dt*xi_1) on all DOFs; xi_1 is a global scalar.\"\"\"\n", + " lo = sp.umax*(epsilon)\n", + " hi = sp.umax*(1.0 - epsilon)\n", + " c_tmp = d.Function(sp.V)\n", + " d.assign(c_tmp, sp.sol)\n", + " cvec = c_tmp.vector()[:]\n", + " cvec = np.clip(cvec + float(dt_val) * xi1_scalar, float(lo), float(hi))\n", + " c_tmp.vector().set_local(cvec)\n", + " c_tmp.vector().apply(\"insert\")\n", + " return c_tmp\n", + "\n", + "Xfunc = model_cur.sc[\"X\"].sol\n", + "Xdof = model_cur.sc[\"X\"].dof_map\n", + "Bfunc = model_cur.sc[\"B\"].sol\n", + "Bdof = model_cur.sc[\"B\"].dof_map\n", + "dx = d.Measure(\"dx\", model_cur.cc[\"surf\"].dolfin_mesh)\n", + "c_mass_init = d.assemble_mixed((Xfunc+Bfunc)*dx)\n", + "def F_mass(xi_arg1, epsilon, c_mass_init):\n", + " \"\"\"F(xi_1) = int clip(phi_X + dt*xi_1) + int clip(phi_B + dt*xi_1) minus previous X+B.\"\"\"\n", + " dt_val = float(model_cur.dt)\n", + " Xtemp = _set_clipped_sum_c_tmp_scalar(\n", + " model_cur.sc[\"X\"], xi_arg1, dt_val, epsilon)\n", + " Btemp = _set_clipped_sum_c_tmp_scalar(\n", + " model_cur.sc[\"B\"], xi_arg1, dt_val, epsilon)\n", + " dx = d.Measure(\"dx\", Xtemp.function_space().mesh())\n", + " mass_err = d.assemble_mixed((Xtemp+Btemp)*dx) - c_mass_init\n", + " return mass_err\n", + "\n", + "def assign_from_sub(subfunc, func, dofmap):\n", + " fullvec = func.vector()[:]\n", + " subvec = subfunc.vector()[:]\n", + " fullvec[dofmap] = subvec\n", + " func.vector().set_local(fullvec)\n", + " func.vector().apply(\"insert\")\n", + "\n", + "# check that the above functions are consistent\n", + "if F_mass(0.0, 0.01, c_mass_init) > 0.0:\n", + " raise ValueError(\"This should not be possible\")" ] }, { @@ -571,13 +596,40 @@ "# Set loglevel to warning in order not to pollute notebook output\n", "logger.setLevel(logging.WARNING)\n", "\n", + "epsilon = 0.01\n", + "xi_secant_max_iter = 500\n", + "\n", "# Solve\n", "while True:\n", " print(f\"Time is {model_cur.t}\")\n", " # Solve the system\n", " model_cur.monolithic_solve()\n", " model_cur.adjust_dt()\n", - " # Save results for post processing\n", + " # Secant on global scalar xi_1: initial guesses (0, -dt).\n", + " xi_secant_iter = 0\n", + " xi_guess_prev = 0.0\n", + " xi_guess = -float(model_cur.dt)\n", + " secant_tol = 1e-12\n", + " F1 = F_mass(xi_guess, epsilon, c_mass_init)\n", + " F0 = F_mass(xi_guess_prev, epsilon, c_mass_init)\n", + " while xi_secant_iter < xi_secant_max_iter and abs(F1) > secant_tol:\n", + " xi_secant_iter += 1\n", + " denom = F1 - F0\n", + " if abs(denom) < 1e-30 or xi_guess == xi_guess_prev:\n", + " break\n", + " xi_guess_next = xi_guess - F1 * (xi_guess - xi_guess_prev) / denom\n", + " xi_guess_prev = float(xi_guess)\n", + " xi_guess = float(xi_guess_next)\n", + " F1 = F_mass(xi_guess, epsilon, c_mass_init)\n", + " F0 = F_mass(xi_guess_prev, epsilon, c_mass_init)\n", + " print(f\"Secant approach converged in {xi_secant_iter} iterations\")\n", + " # now assign corrected values\n", + " Xnew = _set_clipped_sum_c_tmp_scalar(model_cur.sc[\"X\"], xi_guess, model_cur.dt, epsilon)\n", + " assign_from_sub(Xnew, Xfunc, Xdof)\n", + " Bnew = _set_clipped_sum_c_tmp_scalar(model_cur.sc[\"B\"], xi_guess, model_cur.dt, epsilon)\n", + " assign_from_sub(Bnew, Bfunc, Bdof)\n", + "\n", + "\n", " for species_name, species in model_cur.sc.items:\n", " results[species_name].write(model_cur.sc[species_name].u[\"u\"], model_cur.t)\n", " # End if we've passed the final time\n", diff --git a/examples/example1/spheroid_ellipsoid_mesh.h5 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example1_CH for consistency with nondimensional parameters, apply weighting to variational form for mu in model.py --- examples/example1/example1_CH.ipynb | 37 +++++++++++++++++++---------- smart/model.py | 8 +++---- 2 files changed, 29 insertions(+), 16 deletions(-) diff --git a/examples/example1/example1_CH.ipynb b/examples/example1/example1_CH.ipynb index 96e1af3c..08f60a2a 100644 --- a/examples/example1/example1_CH.ipynb +++ b/examples/example1/example1_CH.ipynb @@ -221,8 +221,13 @@ "metadata": {}, "outputs": [], "source": [ - "X = Species(\"X\", 10, surf_unit, 0.1, D_unit, \"surf\", CH=True, umax=100, A_hat = 0) \n", - "B = Species(\"B\", 90, surf_unit, 0.1, D_unit, \"surf\", CH=True, umax=100, A_hat = 25)" + "l0 = np.sqrt(4*np.pi) # reference length scale\n", + "Shat = 10.0\n", + "phi0_X = 0.1\n", + "phi0_B = 0.1\n", + "sigma_s = Shat/l0**2\n", + "X = Species(\"X\", phi0_X*sigma_s, surf_unit, 1.0, D_unit, \"surf\", CH=True, umax=sigma_s, A_hat = 0) \n", + "B = Species(\"B\", phi0_B*sigma_s, surf_unit, 1.0, D_unit, \"surf\", CH=True, umax=sigma_s, A_hat = 50)" ] }, { @@ -309,13 +314,15 @@ "metadata": {}, "outputs": [], "source": [ - "kon = Parameter(\"kon\", 0.0, 1/sec)\n", - "koff = Parameter(\"koff\", 0.0, 1/sec)\n", - "# Production of A\n", + "kon_hat = 1.0\n", + "koff_hat = 1.0\n", + "tref = l0**2 / float(X.D)\n", + "kon = Parameter(\"kon\", kon_hat*sigma_s**(3/2)/tref, 1/sec)\n", + "koff = Parameter(\"koff\", koff_hat*sigma_s**(3/2)/tref, 1/sec)\n", + "# Conversion of X to B\n", "r1 = Reaction(\"r1\", [\"X\"], [\"B\"],\n", " param_map={\"kon\": \"kon\", \"koff\": \"koff\"},\n", - " eqn_f_str=\"X*kon - B*koff\",\n", - " species_map={\"X\": \"X\", \"B\": \"B\"})" + " eqn_f_str=\"X*kon - B*koff\")" ] }, { @@ -372,9 +379,14 @@ "source": [ "useSpheroid = True\n", "if useSpheroid:\n", + " # rOuter = [0.6849, 0.4365, 2.1896]\n", + " # rInner = [0.0,0.0,0.0]\n", + " # domain, facet_markers, cell_markers = mesh_tools.create_ellipsoids(rOuter, rInner, hEdge=0.05)\n", " vol = Compartment(\"vol\", 3, um, 1) # SMART just needs to know its a 3d mesh\n", " cc.add(vol)\n", " mesh_file = pathlib.Path(\"spheroid_ellipsoid_mesh.h5\")\n", + " # mesh_file = pathlib.Path(\"spheroid_ellipsoid_mesh_new.h5\")\n", + " # mesh_tools.write_mesh(domain, facet_markers, cell_markers, filename=mesh_file)\n", "else:\n", " # define dimensions of domain\n", " Shat = 200\n", @@ -441,8 +453,8 @@ "config_cur.flags.update({\"allow_unused_components\": True})\n", "config_cur.solver.update(\n", " {\n", - " \"final_t\": 1.0,\n", - " \"initial_dt\": 1e-3,\n", + " \"final_t\": 100.0,\n", + " \"initial_dt\": 0.001,\n", " \"time_precision\": 8,\n", " \"attempt_timestep_restart_on_divergence\": True,\n", " }\n", @@ -492,7 +504,7 @@ "outputs": [], "source": [ "# add white noise perturbation to initial conditions\n", - "for sp_str in (\"X\", \"B\"):\n", + "for sp_str in (\"B\"):#(\"X\", \"B\"):\n", " sp = model_cur.sc[sp_str]\n", " u = model_cur.cc[sp.compartment_name].u[\"u\"]\n", " indices = sp.dof_map\n", @@ -596,7 +608,7 @@ "# Set loglevel to warning in order not to pollute notebook output\n", "logger.setLevel(logging.WARNING)\n", "\n", - "epsilon = 0.01\n", + "epsilon = 0.001\n", "xi_secant_max_iter = 500\n", "\n", "# Solve\n", @@ -612,7 +624,8 @@ " secant_tol = 1e-12\n", " F1 = F_mass(xi_guess, epsilon, c_mass_init)\n", " F0 = F_mass(xi_guess_prev, epsilon, c_mass_init)\n", - " while xi_secant_iter < xi_secant_max_iter and abs(F1) > secant_tol:\n", + " while (xi_secant_iter < xi_secant_max_iter and \n", + " abs(F1) > secant_tol and abs(F0) > secant_tol):\n", " xi_secant_iter += 1\n", " denom = F1 - F0\n", " if abs(denom) < 1e-30 or xi_guess == xi_guess_prev:\n", diff --git a/smart/model.py b/smart/model.py index 03600512..2a25a1b1 100644 --- a/smart/model.py +++ b/smart/model.py @@ -1397,13 +1397,12 @@ def _init_5_2_create_variational_forms(self): A_hat = species.A_hat phi_cur = u / species.umax df_c = d.ln(phi_cur) - d.ln(1 - phi_cur) - A_hat * (2 * phi_cur - 1) + # CForm scaling factor + CScale = (float(species.D) * species.umax) / (4 * np.pi) # assuming l^2 = 4*pi CForm = J * ( (u_c - df_c) * v_c * dx - (A_hat / species.umax) * d.inner(d.grad(phi_cur), d.grad(v_c)) * dx ) - CForm_units = ( - species.compartment.compartment_units**species.compartment.dimensionality - ) # chemical potential is in units of kBT for convenience Dform = J * D * u * d.inner(d.grad(u_c), d.grad(v)) * dx self.forms.add( @@ -1412,9 +1411,10 @@ def _init_5_2_create_variational_forms(self): CForm, species.chem_potential, "chem_potential", - CForm_units, + Dform_units, True, linear_wrt_comp, + form_scaling=CScale, ) ) self.forms.add(