PyMembrane Tutorial#

This tutorial provides an introduction to the PyMembrane package, focusing on its applications in the physics of liquid and solid membranes. The package includes fully commented Python codes along with input files to facilitate understanding and usage (refer to Matoz, 2023).

Objective#

The demonstrations herein not only highlight PyMembrane’s capabilities but also guide users through a standard workflow for setting up a simulation. The examples follow a consistent layout, with code comments providing details on each step.

Key Steps#

  1. Step 1: Initialize the simulation box by creating an instance of the Box class.

  2. Step 2: Create an instance of the System() class to handle mesh, boundary conditions, and visualization outputs.

  3. Step 3: Create an instance of the Evolver() class, which is responsible for managing energy and force models, constraints, integrators, minimizers, and simulation runs (using methods like evolveMC(steps), evolveMD(steps), or minimize()).

Typical Use Case for System and Evolver Classes#

Force Potentials and Integrators#

Models#

Stretching Energy

The discrete stretching energy uses Hookean springs assigned to mesh edges and is modeled as: .. math:: E_{text{stretch}} = frac{1}{2} k (l_e - l_0)^2 In PyMembrane, this is implemented with the setting ‘Mesh>Harmonic’, using parameters ‘k’ for spring constant and ‘l0’ for rest length.

Bending Energy

The bending energy model is based on the dihedral angle between triangles sharing an edge: .. math:: E_{text{bend}} = frac{1}{2}kappa sum_{e} (1-hat{mathbf{n}}_{e}^{(1)}cdothat{mathbf{n}}_{e}^{(2)})

Edge Length Limit

To prevent deformed triangles causing numerical instability, PyMembrane restricts edge length: .. math:

E =
\begin{cases}
0 & l_{\text{min}} < l_e < l_{\text{max}}\\
\infty & \text{otherwise}
\end{cases},

You can set these limits using ‘Mesh>Limit’, with parameters ‘lmin’ and ‘lmax’.

Additional Details#

We have chosen the simplest models for demonstration purposes, although other combinations of stretching and bending energy models are available. Consult the full documentation Force Potentials in the main documentation for more information.

Please refer to the full documentation and examples provided in the package for further understanding and practical insights into using PyMembrane for your specific membrane physics simulations.