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Volumn 56, Issue 3, 1997, Pages 2817-2828

Scaling range and cutoffs in empirical fractals

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0000012899     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.56.2817     Document Type: Article
Times cited : (161)

References (160)
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    • Z. R. Struzik, E. H. Dooijes, and F. C. A. Groen, Fractal Frontiers, edited by M. M. Novak and T. G. Dewey (World Scientific, Singapore, 1997), p. 189
    • Z. R. Struzik, E. H. Dooijes, and F. C. A. Groen, Fractal Frontiers, edited by M. M. Novak and T. G. Dewey (World Scientific, Singapore, 1997), p. 189.
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    • The search was done using the command “find kw fractal or fractals and date 199n and jo physical review and pt experimental” for (Formula presented). The numbers of papers obtained were (Formula presented), (Formula presented), (Formula presented), (Formula presented), (Formula presented), (Formula presented), and (Formula presented) for (Formula presented), respectively, a total of 165 papers
    • The search was done using the command “find kw fractal or fractals and date 199n and jo physical review and pt experimental” for (Formula presented). The numbers of papers obtained were (Formula presented), (Formula presented), (Formula presented), (Formula presented), (Formula presented), (Formula presented), and (Formula presented) for (Formula presented), respectively, a total of 165 papers.
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    • Conventionally, log of base 10 is used for both horizontal and vertical axes and the width of the linear range is given in decades. In cases where a different base was used we converted it to base 10. It is also important to realize that the property presented in the horizontal axis should have a linear dimension (such as length, time, etc.) as fractal dimension relates some generalized volume to a linear stick size. If the feature presented has dimensions of area, for example, the apparent width of the linear range will double. In a number of cases we had to correct the width measurements to avoid such effects
    • Conventionally, log of base 10 is used for both horizontal and vertical axes and the width of the linear range is given in decades. In cases where a different base was used we converted it to base 10. It is also important to realize that the property presented in the horizontal axis should have a linear dimension (such as length, time, etc.) as fractal dimension relates some generalized volume to a linear stick size. If the feature presented has dimensions of area, for example, the apparent width of the linear range will double. In a number of cases we had to correct the width measurements to avoid such effects.
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    • where the fractal dimension of a strange attractor in turbulent plasma was measured
    • where the fractal dimension of a strange attractor in turbulent plasma was measured.
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    • (1994) Scale Invariance, Interfaces, and Non-Equilibrium Dynamics
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    • the present analysis we focus on the case (Formula presented) and (Formula presented). In systems for which (Formula presented) there are unstable or mobile islands of size (Formula presented). Such systems exhibit mobility along island edges or detachment moves that modify the morphology from fractal to more compact even at the time scale of single atom hopping, and therefore are not relevant for our considerations
    • In the present analysis we focus on the case (Formula presented) and (Formula presented). In systems for which (Formula presented) there are unstable or mobile islands of size (Formula presented). Such systems exhibit mobility along island edges or detachment moves that modify the morphology from fractal to more compact even at the time scale of single atom hopping, and therefore are not relevant for our considerations.
  • 149
    • 85037199760 scopus 로고    scopus 로고
    • This is achieved by starting with a high deposition rate and gradually reducing it as the coverage increases. The large number of islands nucleated in the early stages are stable and keep aggregating more atoms in spite of the reduced deposition rate. For the purpose of growing larger DLA-like islands in a shorter time one may want to use a slow deposition rate in the early stages and increase it gradually. However, in this case new islands will continue to nucleate and the low island density of the initial low deposition rate will not be maintained
    • This is achieved by starting with a high deposition rate and gradually reducing it as the coverage increases. The large number of islands nucleated in the early stages are stable and keep aggregating more atoms in spite of the reduced deposition rate. For the purpose of growing larger DLA-like islands in a shorter time one may want to use a slow deposition rate in the early stages and increase it gradually. However, in this case new islands will continue to nucleate and the low island density of the initial low deposition rate will not be maintained.


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