Skip to main content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.


The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Tabular Potentials for Monte Carlo Simulation of Supertoroids with Short-Range Interactions



Harold W. Hatch, Gordon W. McCann


We describe a methodology for constructing tabular potentials of supertoroids with short range interactions, which requires the calculation of the volume of overlap of these shapes for many relative positions and orientations. Recent advances in the synthesis of anisotropic colloids has made experimental realizations of such particles feasible and has increased the practical impact of fundamental simulation studies of these families of shapes. This extends our recent work on superquadric potentials to now include a family of ring-like shapes with a hole in the middle. Along with the addition of supertoroids, the ability to make tables for nonidentical particles and particle pairs with multiple, disconnected overlap volumes was added. Using newly developed extensions to a previously published algorithm, we produce tabular potentials for all of these new cases. The algorithmic developments in this work will enable Monte Carlo simulations of a wider variety of shapes to predict thermodynamic properties over a range of conditions.
Journal of Research of the National Institute of Standards and Technology
Created December 4, 2019, Updated February 4, 2020