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In collaboration with J.Casademunt, M.Lopez-Salvan and F. Sagues we proposed a phenomenologi- cal model to describe the dynamics of fingering patterns recently observed in quasi-twodimensional electrodeposition experiments. The effects of hydrodynamic convection are introduced through an effective drift. We study the role of the new length scale in the crossover between a Laplacian growth regime and a weak competition regime. A stabilization of the finger array morphology is obtained as a consequence of the external drift. The interplay between the velocity selection problem and the wavelength selection of a cellular array is discussed within the general context of diffusion-limited growth problems. The dynamics of the model is studied numerically with boundary-integral meth- ods in the quasistatic approximation and, complementarily, using a biased random walk Monte Carlo simulation. Results are in qualitative agreement with the physical picture proposed. In collaboration with A.Lange, C. Volts, M. Schroter, M.A.Scherer, A. Engel and I.Reberg, we investigated experimentally the temporal evolution of water-sand interface driven by gravity. By means of a Fourier analysis of the evolutving interface the growth rates are determined for the different modes appearing in the developing front. To model the observed bahaviour we apply the idea of the Rayleight-Taylor instability for two stratified fluids. Carrying out a linear stability analysis we calculate the growth rates from the corresponding dispersion relations for finite and infinite cell sizes and compose those results with the experimental data. Alternatively, the situation of the sedimenting sand has been modeled by a two-dimentional cellular automaton. A qualitative similarity between the model and the experimental situation is obtained.