UNC-CH Physics and Astronomy Thesis Defense

Christopher Moakler

“The Hydra String Method and its Application to High Dimensional Potential Energy Surfaces Arising from Granular Systems”

Granular materials are a ubiquitous yet ill-understood class of media. Different approaches and techniques have been developed to understand the many complex behaviors they exhibit, but none have been completely successful. I have instituted a novel means to understand granular materials. This novel method, the Hydra String Method (HSM), is an efficient and autonomous way to trawl the potential energy surfaces (PESs) to enumerate the saddles, minima, and connections between them. I have applied the Hydra String Method to bi-disperse configurations of soft spheres to map out ensembles of pathways between stable packings of the system. These transition pathways are a low-dimensional projection of the larger PES. By understanding these pathways and how they connect to one another may allow for the prediction of the dynamics of a granular system as it moves between stable packings.

In this thesis, I show some interesting results about the PESs that arise from systems of Hertzian disks. For example, the basins of attraction around the minima of these PESs possess “tentacles” that twist and curl through configuration space and the profile of these basins have a characteristic shape, Energy ~ x^1.7. I have also found novel results about the networks formed by these minima such as: the networks appear to be small-world networks, gamma distribution of the minimum/saddle energies, and the separation in energy space of the various branches of the network.

The Hydra String Method is also a useful tool to visualize high dimensional PESs. These surfaces are vast and complex and have not been the subject of much study. This leads me to propose natural extensions of the Climbing String Method and the HSM: the Climbing Kite String Method and the Flying Hydra Method. These two methods enable one to explore more fully the PESs of an arbitrary system. This can potentially be used to study chemical and granular systems that possess too much kinetic energy to be well described as gradient systems.

The defense will take place remotely via Zoom.