Applications of Multifractal Analysis in Surface Science

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: closed (1 June 2022) | Viewed by 4194

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Guest Editor
Institute of Aurel Stodola, Faculty of Electrical Engineering, University of Žilina, Nálepku 1390, 031 01 Liptovský Mikuláš, Slovakia
Interests: semiconductors; surface microstructure; material properties

Special Issue Information

Dear Colleagues,

The microstructural properties of natural or technologically shaped surfaces often have non-Euclidean properties and show a scale-invariant structure. Information about these structures can be experimentally obtained by atomic force microscopy or electron microscopy methods. Several characteristics estimated by the fractal analyses provide information about the particular kind of observed scale invariancy. These characteristics are strongly influenced by environmental effects or by applied technological operations. This is very important for the determination of the surface properties needed for an understanding of the influence of the surrounding environment, the development of surface features during the forming of structure, and the optimization of technological steps for preparing the resulting microstructure. Multifractal structures are a particular kind of scale-invariant structures. Spatial and temporal variation in the scale-invariant structure of the observed surface often appears. These spatial and temporal variations indicate the multifractal property of these studied surfaces, as described by a multifractal spectrum and several other characteristics important for a variety of applications.

 Topics that are invited for discussion include (but are not limited to):

  • Analysis of multifractal properties;
  • Multifractal properties of natural or technologically treated surfaces;
  • Implementation of multifractal methods;
  • Application of multifractal methods in the study of natural and technological surfaces;
  • Correlation between the multifractal and physical properties of observed surfaces.

Dr. Stanislav Jurečka
Guest Editor

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Published Papers (2 papers)

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Research

16 pages, 3684 KiB  
Article
A Novel Modeling Method of Micro-Topography for Grinding Surface Based on Ubiquitiform Theory
by Yue Liu, Qi An, Min Huang, Deyong Shang and Long Bai
Fractal Fract. 2022, 6(6), 341; https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract6060341 - 19 Jun 2022
Cited by 2 | Viewed by 1892
Abstract
In order to simulate the grinding surface more accurately, a novel modeling method is proposed based on the ubiquitiform theory. Combined with the power spectral density (PSD) analysis of the measured surface, the anisotropic characteristics of the grinding surface are verified. Based on [...] Read more.
In order to simulate the grinding surface more accurately, a novel modeling method is proposed based on the ubiquitiform theory. Combined with the power spectral density (PSD) analysis of the measured surface, the anisotropic characteristics of the grinding surface are verified. Based on the isotropic fractal Weierstrass–Mandbrot (W-M) function, the expression of the anisotropic fractal surface is derived. Then, the lower bound of scale invariance δmin is introduced into the anisotropic fractal, and an anisotropic W-M function with ubiquitiformal properties is constructed. After that, the influence law of the δmin on the roughness parameters is discussed, and the δmin for modeling the grinding surface is determined to be 10−8 m. When δmin = 10−8 m, the maximum relative errors of Sa, Sq, Ssk, and Sku of the four surfaces are 5.98%, 6.06%, 5.77%, and 4.53%, respectively. In addition, the relative errors of roughness parameters under the fractal method and the ubiquitiformal method are compared. The comparison results show that the relative errors of Sa, Sq, Ssk, and Sku under the ubiquitiformal modeling method are 5.36%, 6.06%, 5.84%, and 4.53%, while the maximum relative errors under the fractal modeling method are 23.21%, 7.03%, 83.10%, and 7.25%. The comparison results verified the accuracy of the modeling method in this paper. Full article
(This article belongs to the Special Issue Applications of Multifractal Analysis in Surface Science)
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13 pages, 2470 KiB  
Article
Correlating Morphology and Multifractal Spatial Patterns of the Leaf Surface Architecture of Anacardium occidentale L.
by Glenda Quaresma Ramos, Robert Saraiva Matos, Abhijeet Das, Sanjeev Kumar, Ştefan Ţălu and Henrique Duarte da Fonseca Filho
Fractal Fract. 2022, 6(6), 320; https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract6060320 - 07 Jun 2022
Cited by 5 | Viewed by 1788
Abstract
Plant leaf surfaces can contain interesting, reproducible spatial patterns that can be used for several industrial purposes. In this paper, the main goal was to analyze the surface microtexture of Amazon Anacardium occidentale L. using multifractal theory. AFM images were used to evaluate [...] Read more.
Plant leaf surfaces can contain interesting, reproducible spatial patterns that can be used for several industrial purposes. In this paper, the main goal was to analyze the surface microtexture of Amazon Anacardium occidentale L. using multifractal theory. AFM images were used to evaluate the multifractal spatial surface patterns of the adaxial and abaxial sides of the leaf. The 3D maps revealed that the abaxial side is dominated by stomach cells, while striated structures were observed on the adaxial side. The surface of the abaxial side is rougher than the adaxial side. The autocorrelation function calculations showed that the abaxial side has an isotropic surface compared to the adaxial side. Despite this, Minkowski functionals demonstrated that the morphological spatial patterns have robust statistical similarity. Both sides exhibit multifractal behavior, which was verified by the trend observed in the mass exponent and generalized dimension. However, the adaxial side exhibits stronger multifractality and increased vertical complexity compared to the abaxial side. Our findings show that the multifractal spatial patterns of the leaf surface depend on the rough dynamics of the topographic profile. The identification of the multifractal patterns of the structures present on the surface of plant leaves is useful for the fabrication of leaf-architecture-based materials. Full article
(This article belongs to the Special Issue Applications of Multifractal Analysis in Surface Science)
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