Modeling atomic interactions with graphs
https://www.sciencedaily.com/releases/2019/04/190418141601.htm
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0213262
Throughout the course we have discussed graphs in great detail, particularly in their connections to social networks. Graph theory has also found its applications in modeling macroscopic behavior. This article discusses research currently being done at Florida State University using graph theory to learn more about the composition of different materials. There are electrons and ions within each atom that impact how they interact with other atoms. These researchers modeled the interactions between atoms using a graph by letting the atoms be nodes, and the forces be directed edges with certain weights. When they modeled the atoms in a graph, they implemented spectral sparsification, an algorithm that reduces the edges in the graph while keeping the same number of nodes. This algorithm helped to sparsify the graph while retaining important information, decreasing the computational complexity of analyzing the graph itself and allowing simulations to run much faster.
I thought that this research showed an interesting application of modeling with graph theory; in our course, we have certainly used graphs to model connections between people/things or between different groups, but using graphs to model the forces between atoms is quite different. According to the article, the research was mainly a proof of concept, but it would be intriguing to see where it goes — perhaps this interesting application of network theory could be taken further in the field, allowing us to gain more insight into what makes certain materials efficient or into how materials transport energy.