SENSITIVITY OF SAME OPTICAL-PROPERTIES OF FRACTALS TO THE CUTOFF FUNCTIONS

In physics, fractal objects are basically finite. This means that thei r geometrical features must be corrected by natural cut-offs. In the i mportant example of aggregates of small units, the scaling behaviours break down both for small length-scales (reflecting the typical size o f the monomers) and for large length-scales (due to the finite extent of the aggregate). These cut-off functions are either ignored in the t heoretical studies, or they are modelled by a simple exponential funct ion. In this paper we show that this simple form is not the generic ca se and that some physical properties depend quantitatively on the prec ise form of these cut-offs. Explicit analytical and numerical models, mainly connected to the cluster-cluster aggregation model, are studied from this perspective. All of them exhibit roughly the same form of c ut-off function. We discuss the sensitivity to these functions of some optical properties of importance in light scattering experiments.