Dynamic scaling behavior of the Ziff-Gulari-Barshad model on regular fractal lattices: The influence of lacunarity

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 59, Issue 3, 1999, Pages 2795-2800

  Gao, Zhuo ^b   Yang, Z R ^a,b  

^a CCAST WORLD LABORATORY   (China)

^b BEIJING NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008951530     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.2795     Document Type: Article

References (34)

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30. For the concept of lacunarity, it was originally proposed by B. B. Mandelbrot for explaining the galaxy distributions in his famous book [B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982)]. Then lacunarity was introduced to describe the degree of inhomogeneity of a fractal in fractal geometry. The lacunarity of a fractal which is nearly translationally invariant should be small, and vice versa. So far, a general and exact expression of lacunarity has still not been found. However, for a kind of fractal, such as Sierpiński carpets, several approximate expressions have been suggested. These expressions may measure the extent of deviation of Sierpiński carpets of different structure from translationally invariant lattices. For a recent review on lacunarity, see
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34. Since the lattices are not homogeneous, different sites are not equivalent. So it is important to choose the initial vacant site randomly.