Random fractals built by diffusion and percolation: Intercalation, 1/f and invasion noise

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Abstract
Objects generated by diffusion have a natural fractal geometry. This geometry is closely related to the geometry of percolation clusters and may also show up in invasion patterns. The most general concept which permits a unique discussion of these structures is the concept of percolation in a gradient. The fractal interfaces which are obtained by diffusion will produce, besides anomalous electrical effects due to their static properties, an anomalous noise related to the fluctuation in time of their own geometry. These fluctuations occur at very high frequencies compared with the atomic jump rate. Fluctuations of diffused interfaces may then be a source of noise in heterogeneous systems or diffused contacts which can be otherwise considered as quenched. This ‘geometrical’ noise that we call ‘intercalation’ noise in D = 2 is calculated in the framework of gradient percolation theory. We predict a high-frequency power noise spectrum varying as l/f2 and a low-frequency spectrum varying as 1/f. The cross-over between the two regimes occurs at a frequency which exhibits a power-law dependence as a function of the diffusion length describing the diffusion state.