Poisson-Nernst-Planck equation on rough surfaces

Snakemake workflow for solving system of Poisson-Nernst-Planck equations on 2d domains with one rough boundary.

This workflow uses

• F. Mlder et al., Sustainable data analysis with Snakemake, Apr. 19, 2021, F1000Research: 10:33. doi: 10.12688/f1000research.29032.2.

to stitch together

• I. A. Baratta et al., DOLFINx: the next generation FEniCS problem solving environment. 2023. doi: 10.5281/zenodo.10447666.
• J. S. Dokken, ADIOS4DOLFINx: A framework for checkpointing in FEniCS, Journal of Open Source Software, vol. 9, no. 96, p. 6451, Apr. 2024, doi: 10.21105/joss.06451.
• C. Geuzaine and J.-F. Remacle, Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities, International Journal for Numerical Methods in Engineering, vol. 79, no. 11, pp. 13091331, 2009, doi: 10.1002/nme.2579.
• P. Grigorev et al., matscipy: materials science at the atomic scale with Python, Journal of Open Source Software, vol. 9, no. 93, p. 5668, Jan. 2024, doi: 10.21105/joss.05668.
• M. C. Rttger et al., Contact.engineeringCreate, analyze and publish digital surface twins from topography measurements across many scales, Surf. Topogr.: Metrol. Prop., vol. 10, no. 3, p. 035032, Sep. 2022, doi: 10.1088/2051-672X/ac860a.

for modeling and analyzing the electrochemical double layer on rough line profiles.

Input

Raw profiles are found within in/profiles.

Profile-specific configuration and assignment of unique labels happens within workflow/config.yml.

Output

Content of output directory:

all.csv # homogenized global properties of all systems figures # publication-quality figures of global properties geometries # 2d geometries generated from line scan profiles global_properties_plots # plots of global properties meshes # meshes generated from geometries potential_0.005 # sweep across potential values potential_0.01 ... potential_0.18 potential_0.2 profiles # homogenized line scan profiles

Within each potential_* subfolder, the following folders contain polished figures:

• plot_solution_1d: illustration of 1d double layer
• plot_solution_2d_global: color maps of potential and concentrations on whole domain

• plot_solution_2d_local: color maps of potential and concentrations on small subdomain

• surface_excess_global_plots: surface excess on whole domain

• surface_excess_local_plots: surface excess on small subdomain

• comparative_plots: plots comparing global scalar profile-specific properties

Other folders contain intermediate or final results.

• checkpoint: immediate, dimensionless solution of PNP system
• comparative_properties: global scalar profile-specific properties with respect to reference profile
• derived_properties: global scalar profile-specific properties derived from FEM solution
• geometries: domain geometries generated from profiles
• interpolation: dimensionless solution of PNP system interpolated down to 1st order Lagrange elements for visualization
• profile_properties: global scalar profile-specific properties derived from profiles alone
• surface_charge: results from surface charge compuaton
• surface_integrals: results from integration of variables in z direction
• volume_integrals: results from integration over whole domain

Container

To build a container image based on the fenicsx tutorials container that includes additional packages necessary to run this workflow, run

docker build -t imteksim/dolfinx-tutorial-extended -f container/dolfinx-tutorial-extended/Dockerfile .

from within the repository root.

The container runs in the same manner as the tutorial container itself,

docker run -v $(pwd):/tmp/data --init -ti -p 8888:8888 imteksim/dolfinx-tutorial-extended

Installation

To install development versions of git repositories within container, mark dirctory as safe, i.e. with

git config --global --add safe.directory /tmp/data/matscipy

before running

pip install .

For an editable install of matscipy, use

pip install meson-python
pip install --no-build-isolation -e .

Run with snakemake

Use

bash snakemake --cores all --verbose

to run all analysis.

Create directed acyclic graphs of the workflow with

bash snakemake --dag | dot -Tsvg > dag_all.svg snakemake --rulegraph | dot -Tsvg > rulegraph.svg snakemake --filegraph | dot -Tsvg > filegraph.svg

Snakemake interactive notebook editing

To be able to interactively edit a notebook with a command like

bash snakemake --cores 1 --edit-notebook out/figures/surplus_surface_excess_potential_bias.svg --notebook-listen 0.0.0.0:8889

launch the conainer embedding snakemake with additional ports open first, e.g.

bash docker run -v $(pwd):/tmp/data --init -ti -p 8888:8888 -p 8889:8889 imteksim/dolfinx-tutorial-extended

Generate a jupyter configuration with

```console

jupyter notebook --generate-config

Writing default config to: /root/.jupyter/jupyternotebookconfig.py ```

and append the lines

```bash echo "c.ServerApp.allowroot = True" >> /root/.jupyter/jupyternotebook_config.py

echo "c.NotebookApp.ip = '0.0.0.0'" >> /root/.jupyter/jupyternotebookconfig.py

```

to the config file.

Plot with pyvista

Launch a display server before running snakemake, e.g. with

bash export DISPLAY=:99.0 export PYVISTA_OFF_SCREEN=true Xvfb :99 -screen 0 1024x768x24 > /dev/null 2>&1 &

Plot with matplotlib

Use matplotlibrc in repository with

bash export MATPLOTLIBRC="$(pwd)/matplotlibrc"

before running plotting scripts.

Install Arial with

bash apt update apt install ttf-mscorefonts-installer