Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation

TL;DR

This paper develops heuristic analytic approximations for the radial distribution function, structure factor, and equation of state of hard-core fluids in fractal dimensions, validated against Monte Carlo simulations and Percus-Yevick solutions.

Contribution

It introduces new heuristic interpolation formulas for hard-core fluids in fractal dimensions, bridging exact and Percus-Yevick results, and validates them with numerical data.

Findings

Good agreement with Monte Carlo simulations

Effective interpolation between known solutions

Provides practical tools for fractal dimension fluids

Abstract

Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension $d$ ($1 \leq d \leq 3$) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for fractal dimension [M. Heinen et al., Phys. Rev. Lett. \textbf{115}, 097801 (2015)], a good agreement being observed.