Department of Physics Papers

Document Type

Journal Article

Date of this Version

4-28-2008

Comments

Suggested Citation:
C.D. Modes and R.D. Kamien. (2008). "Geometrical frustration in two dimensions: Idealizations and realizations of a hard-disk fluid in negative curvature." Physical Review E. 77, 041125.

© 2008 The American Physical Society
http://dx.doi.org/10.1103/PhysRevE.77.041125

Abstract

We examine a simple hard-disk fluid with no long-range interactions on the two-dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable, one-parameter model of disordered monodisperse hard disks. We extend free-area theory and the virial expansion to this regime, deriving the equation of state for the system, and compare its predictions with simulations near an isostatic packing in the curved space. Additionally, we investigate packing and dynamics on triply periodic, negatively curved surfaces with an eye toward real biological and polymeric systems.

Date Posted: 25 January 2011

This document has been peer reviewed.