The Hydra String Method: A Novel Means to Explore Potential Energy Surfaces and its Application to Granular Materials

TL;DR

The paper introduces the Hydra String Method (HSM), an autonomous technique for exploring high-dimensional potential energy surfaces, specifically applied to granular materials, to identify saddle points, minima, and transition pathways.

Contribution

The Hydra String Method (HSM) is a novel, efficient approach for mapping potential energy surfaces and transition pathways in complex systems like granular materials.

Findings

Successfully applied HSM to granular systems of soft spheres.

Generated a network of transition pathways for granular energy landscapes.

Optimized parameters for effective application of HSM.

Abstract

Granular materials are a ubiquitous yet ill-understood class of media. Many different approaches and techniques have been developed to understand the many complex behaviors they exhibit but none have been completely successful. We present a novel means to understand granular materials, the Hydra String Method (HSM). This is an efficient and autonomous way to trawl an arbitrary potential energy surface (or any similarly high dimensional function) that enumerates the saddle points, minima, and minimum energy paths between them. In doing so, it creates a reduced dimensional network representation of this function. We also present a series of tests to choose optimized parameters for the application of the HSM. We apply this to the potential energy function of a granular system consisting of a bidisperse configuration of frictionless soft spheres. Future work will make use of the found ensemble of transition pathways to statistically predict the dynamics of a system of grains.