Finite fractal analysis for Lennard-Jones liquids

Abstract

Results are given for the properties of the trajectories of atoms in a simulated Lennard-Jones 12-6 liquid at three states on the coexistence line. The trajectories are analysed by Richardson's method [1]. It is shown that the trajectories have a substantially different fractal behaviour even for these three states of this particular liquid. This is contrary to the recent assertion [7] that the finite-fractal properties of liquids have a ‘universal’ behaviour. However there may be ‘universality’ in a more limited sense for a certain function, f(ϵ), which was introduced elsewhere [8] and is used here to analyse the data. A satisfactory theory of the fractal properties of even this the simplest realistic liquid is still lacking.