Wavelet-based multiscaling in self-affine random media

Wavelet analysis is used to determine particular properties of self-affine random media, i.e. ones with homogeneous increments. When such media are filtered through introducing upper and lower cutoffs - corresponding to the domain and sample support scales -interesting properties result from wavelet analysis. In particular, we show that the filtered media can be used for transferring information along scales. Furthermore, we show that a wavelet-based approach for determining the underlying Hurst exponent is highly efficient. Examples relating to size and surface effects in materials demonstrate applications of the relevant multiscaling. Finally, we show that the wavelet-based approach and a method based on mode superposition complement each other nicely.