Stokes Flow of an Evolving Fluid Film with Arbitrary Shape and Topology

This repository provides a minimal MATLAB implementation of a fluid membrane undergoing Helfrich-Stokes relaxation, as described in the paper:

Stokes Flow of an Evolving Fluid Film with Arbitrary Shape and Topology

Cuncheng Zhu, David Saintillan, and Albert Chern

Getting Started

This implementation relies on the following key components:

• Mesh.m: Constructs the halfedge data structure for a triangular manifold mesh.
• Geometry.m: Computes geometric attributes of the $\mathbb{R}^3$-embedded mesh and the spatial differential operators for an evolving surface.
• main.m: The main executable that performs the variational time integration.

Prerequisites

To run this code, you will need:

• MATLAB
• The sptensor library for efficient storage and manipulation of sparse multidimensional arrays.

Running the Code

1. Clone this repository:

git clone https://github.com/CunchengZhu/Evolving-Stokes-flow-2024.git

2. Open main.m in MATLAB and execute it to start the simulation.

Visualization

• MATLAB Visualization: Use the built-in trisurf function to visualize the triangular mesh and the quiver function to display the fluid velocity.
• External Tools: For advanced visualization, export the mesh data and use tools like Houdini. Learn more about Houdini with this Introduction to Houdini.

Resources and Attribution

If you use this code in your academic projects or wish to learn more about the underlying methodology, please refer to and cite our papers:

Main Paper

@article{zhu2024stokesflowevolvingfluid,
    title={Stokes flow of an evolving fluid film with arbitrary shape and topology},
    author={Zhu, Cuncheng and Saintillan, David and Chern, Albert},
    journal={arXiv preprint arXiv:2407.14025},
    year={2024}
}

Helfrich Energy

The discretization of the Helfrich energy is based on the following paper:

@article{Zhu_Mem3DG_Modeling_Membrane_2022,
    author = {Zhu, Cuncheng and Lee, Christopher T. and Rangamani, Padmini},
    doi = {10.1016/j.bpr.2022.100062},
    journal = {Biophysical Reports},
    title = {{Mem3DG: Modeling Membrane Mechanochemical Dynamics in 3D using Discrete Differential Geometry}},
    year = {2022}
}