Sensitivity of some optical properties of fractals to the cut-off functions

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Abstract
In physics, fractal objects are basically finite. This means that their geometrical features must be corrected by natural cut-offs. In the important example of aggregates of small units, the scaling behaviours break down both for small length-scales (reflecting the typical size of the monomers) and for large length-scales (due to the finite extent of the aggregate). These cut-off functions are either ignored in the theoretical studies, or they are modelled by a simple exponential function. In this paper we show that this simple form is not the generic case and that some physical properties depend quantitatively on the precise 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 cut-off function. We discuss the sensitivity to these functions of some optical properties of importance in light scattering experiments.

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