Geometrical frustration in two dimensions: Idealizations and realizations of a hard-disk fluid in negative curvature

被引：20

作者：

Modes, Carl D. ^{[1
]}

Kamien, Randall D. ^{[1
]}

机构：

[1] Univ Penn, Dept Phys & Astron, Philadelphia, PA 19104 USA

来源：

PHYSICAL REVIEW E | 2008年 / 77卷 / 04期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1103/PhysRevE.77.041125

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

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.

引用

页数：14

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