Modes Carl D, Kamien Randall D
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Apr;77(4 Pt 1):041125. doi: 10.1103/PhysRevE.77.041125. Epub 2008 Apr 28.
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.
我们研究了一种简单的硬磁盘流体，它在具有恒定负高斯曲率的二维空间——双曲面上不存在长程相互作用。这种几何结构提供了一种使全局晶体有序受挫的自然机制，使我们能够构建一个易于处理的、单参数的无序单分散硬磁盘模型。我们将自由面积理论和维里展开扩展到这个体系，推导出系统的状态方程，并将其预测结果与弯曲空间中接近等静堆积的模拟结果进行比较。此外，我们着眼于实际的生物和聚合物体系，研究了三重周期负曲率表面上的堆积和动力学。
