Diffusion-limited-aggregation model for Poisson growth

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Abstract
We propose an extension of the diffusion-limited-aggregation model for fractal growth. In our model, the Poisson equation is statistically simulated through the use of diffusive particles generated everywhere outside the aggregate. We relate the model to our experiments on viscous fingering in a Hele-Shaw cell in which flow is forced by separating the plates. Our simulations yield nonstationary fractal patterns which exhibit multiscaling and look much like the experimental patterns. We discuss features of the growth measure.

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