Structure of noise generated on diffusion fronts

We show in this paper the characteristic behavior of the noise generated by the fluctuation of diffusion fronts. We predict a 1/$f^2$ noise at high frequency and a 1/f noise at low frequency. A crossover frequency $f_c$ separates the two regimes. This crossover frequency $f_c$ has a power-law behavior as a function of the diffusion length. To relate the static properties of the fronts represented by a problem of percolation in a gradient to the dynamical behavior, we assume that the probability of disconnecting a finite cluster is proportional to the number of red bonds present in a disk with a radius equal to the cluster radius. A scaling of the different fluctuation regimes as well as a scaling of the density of events of a given size is proposed. The various critical exponents are compared with those extracted from numerical simulations performed in the two-dimensional case. We also point out the close relation of these results to noise in invasion experiments in the presence of a gravity field.