Abstract
We discuss a model for the development of discharge patterns in dielectric breakdown based on the Laplace equation associated with a probability field. The model gives rise to random fractals with well-defined Hausdorff dimensions. The relations of this model with the diffusion-limited aggregation are discussed in detail. The possibility of application to other stochastic phenomena like fracture propagation is proposed.
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Pietronero, L., Wiesmann, H.J. Stochastic model for dielectric breakdown. J Stat Phys 36, 909–916 (1984). https://doi.org/10.1007/BF01012949
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DOI: https://doi.org/10.1007/BF01012949