Piastra Marco, Virga Epifanio G
Dipartimento di Ingegneria Industriale e dell'Informazione, Università di Pavia, Via Ferrata 1, I-27100 Pavia, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Sep;88(3):032507. doi: 10.1103/PhysRevE.88.032507. Epub 2013 Sep 25.
We propose a simply computable formula for the excluded volume of convex, axially symmetric bodies, based on the classical Brunn-Minkoski theory for convex bodies, which is briefly outlined in an Appendix written in a modern mathematical language. This formula is applied to cones and spherocones, which are regularized cones; a shape-reconstruction algorithm is able to generate the region in space inaccessible to them and to compute their excluded volume, which is found to be in good agreement with our approximate analytical formula. Finally, for spherocones with an appropriately tuned amplitude, we predict the occurrence of a relative deep minimum of the excluded volume in a configuration lying between the parallel alignment (where the excluded volume is maximum) and the antiparallel alignment (where the excluded volume is minimum).
基于凸体的经典布伦-闵可夫斯基理论，我们提出了一个用于计算凸轴对称体排斥体积的简单可计算公式，该理论在附录中用现代数学语言简要概述。此公式应用于圆锥体和球锥（即正则化圆锥体）；一种形状重建算法能够生成它们在空间中无法到达的区域，并计算其排斥体积，结果发现与我们的近似解析公式吻合良好。最后，对于振幅经过适当调整的球锥，我们预测在平行排列（此时排斥体积最大）和反平行排列（此时排斥体积最小）之间的一种构型中，排斥体积会出现相对较深的最小值。
