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摘要翻译：
我们研究了一个在常负高斯曲率的二维空间--双曲平面上没有长程相互作用的简单硬盘流体。这种几何学提供了一种自然的机制，通过这种机制，我们可以构造一个无序单分散硬盘的易于处理的模型。我们将自由区域理论和维里展开推广到该区域，导出了系统的状态方程，并将其预测结果与弯曲空间中均衡填料附近的模拟结果进行了比较。此外，我们研究了三周期负曲面的填料和动力学，着眼于真实的生物和聚合物系统。
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英文标题：
《Geometrical Frustration in Two Dimensions: Idealizations and
Realizations of a Hard Disc Fluid in Negative Curvature》
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作者：
Carl D. Modes and Randall D. Kamien
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Soft Condensed Matter 软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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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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PDF链接：
https://arxiv.org/pdf/801.1166
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