Many physical systems can be studied as collections of particles embedded in space, often evolving in time. Natural questions arise concerning how to characterize these arrangements-are they ordered or disordered? If they are ordered, how are they ordered and what kinds of defects do they possess? Voronoi tessellations, originally introduced to study problems in pure mathematics, have become a powerful and versatile tool for analyzing countless problems in pure and applied physics. We explain the basics of Voronoi tessellations and the shapes that they produce and describe how they can be used to characterize many physical systems.
Bibliographical noteFunding Information:
This research was supported by a grant from the United States—Israel Binational Science Foundation (BSF), Jerusalem, Israel through Grant No. 2018/170. C. H. Rycroft was partially supported by the Applied Mathematics Program of the U.S. DOE Office of Science Advanced Scientific Computing Research under Contract No. DEAC02-05CH11231.
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