Material from the UMass Amherst Summer School

From June 2–6, 2024 Chris Rycroft was a lecturer at the 16th UMass Amherst Summer School on Soft Solids and Complex Fluids. His lectures were on Computational geometry for soft matter, and covered both discrete and continuum approaches for analyzing geometry. Photos from the event are available on Flickr.

The talk has an associated GitHub repository, which contains analysis scripts and C++ code for making some of the graphics and movies covered in the lectures. The GitHub repository also provides links to many of the software packages that were discussed in the lectures.

Slides from the lectures are here:

• Lecture 1 – a model of dense granular drainage; Voronoi analysis of granular flow; neighbor relations
• Lecture 2 – development of the Voro++ library; network analysis for carbon dioxide capture; alternative models and methods
• Lecture 3 – topological Voronoi analysis; Lloyd's algorithm and meshing; insect wing structure
• Lecture 4 – continuum representations of deformation; the reference map technique; fluid–structure interaction

Associated movies from the lectures are here:

• Creation of a small granular packing via pouring in LAMMPS
• Drainage of particles thin rectangular silo using LAMMPS
• Illustration of computing density by counting particle centers in a scanning box
• Illustration of computing density by counting the fraction of particle areas in a scanning box
• Illustration of computing the Voronoi tessellation by adding particles incrementally
• Lloyd's algorithm for particles in a spiral
• Lloyd's algorithm for particles clustered in a corner
• Lloyd's algorithm for particles in a spiral with associated Delaunay triangulation mesh
• Finding the initial wing pad shape via circularity maximization
• Modeling insect wing patterning by running Lloyd's algorithm on the initial wing pad

Most of these movies are provided in the QuickTime movie format using the H.265/HEVC codec. Movies from lecture 4 on the reference map technique were taken from a previous seminar given by Chris Rycroft.

Chris Rycroft's work on materials science and the development of computational tools is partially supported by the National Science Foundation under Grant No. DMREF 2323719.