Fractal analysis of brownian trajectories in fluids

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Abstract
Fractal analysis of molecular brownian motion in liquids was carried out in two and three dimensions. It was observed that the trajectories are self-affine and can be characterized by a differential fractal dimension, which varies with the trajectory length. The analysis of the brownian motion by different kinds of coverings, and the comparison of this motion with diffusion-limited processes, allows us to deduce that the ensemble of all trajectories has a multifractal structure. Finally, the brownian motion in disordered media was studied. Significant differences were found depending on the euclidean dimension in which the motions were performed.