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복잡계 이론물리 연구단
복잡계 이론물리 연구단
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small-angle scattering from the Cantor surface fractal on the plane and the Koch snowflake

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Title
small-angle scattering from the Cantor surface fractal on the plane and the Koch snowflake
Author(s)
A. Yu. Cherny; E. M. Anitas; V. A. Osipov; A. I. Kuklin
Publication Date
2017-01
Journal
PHYSICAL CHEMISTRY CHEMICAL PHYSICS, v.19, no.3, pp.2261 - 2268
Publisher
ROYAL SOC CHEMISTRY
Abstract
The small-angle scattering (SAS) from the Cantor surface fractal on the plane and Koch snowflake is considered. We develop the construction algorithm for the Koch snowflake, which makes possible the recurrence relation for the scattering amplitude. The surface fractals can be decomposed into a sum of surface mass fractals for arbitrary fractal iteration, which enables various approximations for the scattering intensity. It is shown that for the Cantor fractal, one can neglect with a good accuracy the correlations between the mass fractal amplitudes, while for the Koch snowflake, these correlations are important. It is shown that nevertheless, the correlations can be build in the mass fractal amplitudes, which explains the decay of the scattering intensity I(q) qDs−4 with 1 < Ds < 2 being the fractal dimension of the perimeter. The curve I(q)q4−Ds is found to be log-periodic in the fractal region with the period equal to the scaling factor of the fractal. The log-periodicity arises from the self-similarity of sizes of basic structural units rather than from correlations between their distances. A recurrence relation is obtained for the radius of gyration of Koch snowflake, which is solved in the limit of infinite iterations. The present analysis allows us to obtain additional information from SAS data, such as the edges of the fractal regions, the fractal iteration number and the scaling factor.
URI
https://pr.ibs.re.kr/handle/8788114/3632
ISSN
1463-9076
Appears in Collections:
Center for Theoretical Physics of Complex Systems(복잡계 이론물리 연구단) > Journal Papers (저널논문)
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