Monte Carlo Simulation of Fluids in Curved Three-dimensional Space

Abstract

This work describes the methods required to perform computer simulations of three-dimensional fluids confined to the surface of a four-dimensional hypersphere. The use of such non-Euclidian spaces, or spherical boundary conditions, is convenient in cases where spatial inhomogeneities occur over length-scales comparable to that of the entire system. The form of the pressure equation in curved space is discussed, and the results of Monte Carlo simulations of hard spheres confined to the surface of a hypersphere are presented. Comparison of the simulation results to the Carnahan-Starling equation of state in flat space provides a basis for determining when curvature effects can be neglected.

Key Words:

• Curved space
• equation of state
• hard spheres
• Monte Carlo
• non-Euclidian space