I am a PhD student who is struggling to implement a 3D vertex model. Vertex model are commonly used by physicists in biology to understand how biological cells in a tissue coordinate together. In the model, the cells are represented by vertices and neighbouring cells are joined together through these vertices forming a network of polyhedra (shown below).
The vertices of the network can move in space according to the following model (please see equation 1). The problem that I have been facing is how to do numerical integration for moving the vertices in space. More specifically, how can I compute the gradient of potential energy (U) at a given vertex i in the network? The author has performed improved euler integration to evolve the network; how can this be done given these equations?
The value of eta is 1 and therefore can be ignored in equation 1.
Any help will be much appreciated. Thanks !
