The relation between diffusion along fractal surfaces and observable diffusion

Fractal solid surfaces are presented as being built up from repeating fractal units of size xi equal to the surface upper self-similarity cutoff. Taking into account the difference between real diffusion pathways of particles of size lambda and their observable projections the authors distinguish three types of observable diffusion: (i) the classical law for lambda > xi , (ii) anomalous time dependence for lambda << xi and short times; (iii) normal time dependence but anomalous behaviour of the observable diffusion coefficient for lambda << xi and long times. Crossovers occur from (iii) to (i) with increasing lambda and from (ii) to (iii) with increasing time.