硬椭球：精确重叠距离的解析逼近
Hard ellipsoids: analytically approaching the exact overlap distance
摘要：
根据先前的工作（JCP 134，201103（2011）），副本交换蒙特卡罗技术被用来产生硬1：5的高宽比扁椭球的状态方程的一个广泛的密度范围。在这里，除了由伯尔尼和Pechukas（BP）给出的重叠距离的解析近似和Perram和Wertheim的精确数值解之外，我们还测试了对原始BP近似（MBP）的简单修改，该修改纠正了所有纵横比的BP的已知T形失配。我们发现MBP状态方程与精确解有很好的定量一致性。MBP的分析表达式，使我们能够研究以前报道的结果的大小的影响。在热力学极限下，我们估计了在体积分数为0.343（3）时的1：5硬椭球各向同性-非晶相变，以及在体积分数为0.592（6）-0.634（8）时的向列相-固体相变。
英文摘要：
Following previous work (JCP 134, 201103 (2011)), the replica exchange Monte Carlo technique is used to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. Here, in addition to the analytical approximation of the overlap distance given by Berne and Pechukas (BP) and the exact numerical solution of Perram and Wertheim, we tested a simple modification of the original BP approximation (MBP) which corrects the known T-shape mismatch of BP for all aspect-ratios. We found that the MBP equation of state shows a very good quantitative agreement with the exact solution. The MBP analytical expression allowed us to study size effects on the previously reported results. For the thermodynamic limit, we estimated the exact 1:5 hard ellipsoid isotropic-nematic transition at the volume fraction 0.343(3), and the nematic-solid transition in the volume fraction interval 0.592(6)-0.634(8).
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