Colloidal suspensions are important industrially relevant materials, from milk, to paints, to advanced manufacturing inks. Unstable colloids will eventually aggregate and crash out of solution, so it is essential to understand the thermodynamic stability of colloids used for specific applications. In this work we consider a model of nanoparticle flakes that are suspended in solution with linear copolymers. In experiments, the flakes are observed to crash out of solution above a weight percentage of about 7%. Here we develop a phenomenological model to represent the shape, size, concentration, and molecular interaction components of the experimental system. We investigate the aggregation behavior of the flakes as a function of their shape, size, concentration, and interactions relative to the copolymers with the aim of mapping a phase diagram of thermodynamic stability. En route to that we report on successes and challenges deploying our model on laptop and high performance cluster hardware and summarize the aggregation behaviors observed thus far.

Macaulay2 (M2) is a Computer Algebra System utilized in several fields of mathematics for computations involving commutative rings. The primary research goal is to develop an algorithm for calculating the invariants of finite group actions on skew commutative polynomials. The research group initially focused on the study of invariant theory to form a research basis to explore Dr. Francesca Gandini’s work on degree bounds for skew commutative invariants. This study can then be used to develop the respective algorithm in M2 for the InvariantRings 3.0 package. Particularly for finite groups, there are known degree bounds for invariant skew polynomials in the exterior algebra which inevitably results in termination of our computational recipe. The algorithm has a planned release for the October 2025 release of M2.