The fractal nature of a diffusion front and the relation to percolation
J. Physique Lett., 46 4 (1985) 149-156
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https://doi.org/10.1103/PhysRevE.81.041108
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https://doi.org/10.1088/1742-5468/2010/03/P03004
6521 (2009)
https://doi.org/10.1007/978-0-387-30440-3_386
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https://doi.org/10.1088/1742-5468/2009/08/P08007
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https://doi.org/10.1103/PhysRevE.80.051123
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https://doi.org/10.1086/599292
3847 (2009)
https://doi.org/10.1007/978-0-387-30440-3_227
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https://doi.org/10.1080/00018730300741518
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