Statistical Network Representations of Energy Landscapes in Soft-Sphere Models

Just as a ball rolls downhill and comes to rest at the lowest point of potential energy, many physical and biological systems approach equilibrium at an energy-minimizing state. Sand is an example of such a system: being poured in a container it comes to rest in a randomly arranged state, but can transition to an even lower energy state through the addition of energy in the form of tapping the container. This research project seeks to predict how such granular materials respond to applied forces from the viewpoint of their underlying energy landscape, which like a mountain range is a vast expanse of valleys and peaks. Of particular interest is the effect of microgravity environments on granular systems, such as rubble-pile asteroids composed of loosely held-together dust and fractured rock. Like the sand sitting in a container, the weak gravitational force loosely holds the asteroid together in its shape. How the asteroid responds to the forces of probing or digging is important for developing mining techniques for such near-earth asteroids.

The project aims at developing new techniques for quantifying the relationship between high-dimensional complex energy-landscapes and the dynamics of the system. This relies on a new computational method for extracting the dominate features of the energy landscape by forming a low-dimensional bipartite graph representation; a network with two types of nodes, energy minimizers and accessible saddle points, connected by edges weighted by the energy barrier heights. The graph and dynamics taking place on the graph are then used to explain the behavior of large stochastic systems of interacting spheres, a model for granular materials in microgravity.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.