由维里展开式导出Rosenfeld泛函
Deriving the Rosenfeld Functional from the Virial Expansion
摘要：
在这篇文章中，我们取代了硬凸粒子的Rosenfeld泛函的半启发式推导与迈耶集团的系统计算。结果表明，每个集群积分进一步分解成图的交叉模式，我们分类的循环数。这扩展了维里膨胀的自由能的循环顺序的扩展，罗森菲尔德功能作为其主要贡献。Rosenfeld的权重函数则是通过推广Blaschke、Santalo和Chern的方程而从相交概率的推导中得出的。结果表明，0-loop阶可以被精确地导出，并且再现了Rosenfeld泛函。我们进一步讨论了粒子的尺寸，拓扑结构和几何形状的影响的数学结构的计算。
英文摘要：
In this article we replace the semi-heuristic derivation of the Rosenfeld functional of hard convex particles with the systematic calculation of Mayer clusters. It is shown that each cluster integral further decomposes into diagrams of intersection patterns that we classify by their loop number. This extends the virial expansion of the free-energy by an expansion in the loop order, with the Rosenfeld functional as its leading contribution. Rosenfeld's weight functions follow then from the derivation of the intersection probability by generalizing the equation of Blaschke, Santalo, and Chern. It is found that the 0-loop order can be derived exactly and reproduces the Rosenfeld functional. We further discuss the influence of particle dimensions, topologies, and geometries on the mathematical structure of the calculation.
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