Anomalous multifractal spectrum of aggregating Lennard-Jones particles with Brownian dynamics

We perform a Brownian Dynamics simulation of Lennard-Jones particles at low density and temperature. From an initially homogeneous but random configuration the system flocculates into a fractal gel. We have found that the bicontinous structures formed can be characterized by a fractal dimensionality, but the fractal regime is only very small, and the scaling depends upon the volume fraction of the particles. In this paper we investigate a possibly more universal multifractal spectrum of the aggregates. Because of the small scaling regime of less than a decade, we cannot extrapolate the box counting results for the partition function to zero box size. As a consequence we observe a multifractal spectrum Dq which is an increasing function of q. We show that within a multifractal model a similar anomalous result can be obtained. Because in practice the scaling regime of any physical system will always be bounded from below, it appears necessary to either redefine the notion of a multifractal spectrum, or accept the existence of the anomalous spectra and assess their relevance.