Self‐similar (fractal) structures are present at every scale ranging from galaxies down to aggregates of atoms to elementary particles. For surface fractals, the self‐similarity is inherited from the superposition of non‐overlapping mass fractal...
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https://www.riss.kr/link?id=O114251453
2018년
-
0003-3804
1521-3889
SCI;SCIE;SCOPUS
학술저널
n/a-n/a [※수록면이 p5 이하이면, Review, Columns, Editor's Note, Abstract 등일 경우가 있습니다.]
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
Self‐similar (fractal) structures are present at every scale ranging from galaxies down to aggregates of atoms to elementary particles. For surface fractals, the self‐similarity is inherited from the superposition of non‐overlapping mass fractal...
Self‐similar (fractal) structures are present at every scale ranging from galaxies down to aggregates of atoms to elementary particles. For surface fractals, the self‐similarity is inherited from the superposition of non‐overlapping mass fractals. Despite long‐standing theoretical investigations, no generic framework exists yet to describe the nature and generation of surface fractal systems. Here, cellular automata (CA) are identified as a generic mathematical system and, by exploring the associated small‐angle scattering (neutrons, X‐rays, light) intensity curves, the emergence of surface fractals is reported. The observed decay of scattering intensity manifesting as a non‐coherent sum of scattering amplitudes of objects composing the surface fractal is in agreement with theoretical predictions and is a manifestation of the power‐law distribution of object's sizes. The non‐coherent sum of intensities of a randomly distributed system of objects provides an approximation to the surface fractal scattering intensity, which is expected from the interplay of distances between objects and their size. The finding on the emergence of surface fractals in CA will enrich the understanding of their structural properties while the approximation of independent objects can provide a route toward testing randomness generated by CA.
Theoretical investigations on small‐angle scattering (SAS) show the emergence of surface fractals in several classes of cellular automata (CA). It is shown that SAS can distinguish between exact and self‐similar structures and thus it can provide a route toward testing of randomness in CA‐based structures at nano‐ and microscales.
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