Analyzing Local Structure in Atomic Systems

Many physical and chemical systems are modeled as large sets of atom-like particles.  Understanding how these particles are arranged is thus a very natural problem, though describing this ``structure'' in an insightful yet tractable manner can be tricky.  We consider several conventional methods for describing local structure and their limitations, theoretical and practical.  We then introduce a topological approach more naturally suited for structure analysis and highlight its versatility and robustness.  In particular, the proposed method can aid in analyzing materials at high temperatures, close to melting, without uncontrolled modification of raw data.  Several short applications to materials science are considered.