二维几何挫折：负曲率硬盘流体的理想化与实现
Geometrical Frustration in Two Dimensions: Idealizations and Realizations of a Hard Disc Fluid in Negative Curvature
摘要：
我们研究了一个简单的硬盘流体没有长程相互作用的常负高斯曲率的二维空间，双曲平面。这种几何形状提供了一个自然的机制，全球晶体秩序是受挫，使我们能够构建一个易于处理的模型无序单分散硬盘。我们扩展自由区理论和维里膨胀到这个政权，推导出系统的状态方程，并比较其预测与模拟附近的均衡包装在弯曲的空间。此外，我们调查包装和动力学三重周期性，负弯曲的表面，着眼于真正的生物和聚合物系统。
英文摘要：
We examine a simple hard disc 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 model of disordered monodisperse hard discs. 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 simulation 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.
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