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Morphological characteristics of self-assembled aggregate textures using multifractal analysis: Interpretation of Multifractal τ(q) Using Simulations

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  • Sato, Yoshihiro
  • Munakata, Fumio

Abstract

In recent years, multifractal analysis has been used in various fields, such as medicine and urban development. In particular, multifractal analysis is expected to offer an understanding of the distribution of the morphology, arrangement, and dispersibility of dispersed particles due to the process of particle self-assembly. However, the numerical values obtained by multifractal analysis have not been quantitatively mapped to the filler arrangement, dispersion, and morphology. In this study, we generate simulated images that mimic self-assembled aggregates and clarify the interpretation of local (micro) and global (macro) changes in the system using multifractal analysis results τ(q). The results show that q < 0 in the τ(q)−q graph can be quantitatively evaluated as macro characteristics (aggregate network structure), whereas q > 0 can be quantitatively evaluated as micro characteristics (aggregate morphology and arrangement). Additionally, the occurrence and signs of percolation can be confirmed using macro- and micro-level internal energies. The same trend is observed from a comparison of a multifractal analysis of actual composite materials with the simulation results. The results of this study can also serve as an indicator in various fields where multifractal analysis is performed.

Suggested Citation

  • Sato, Yoshihiro & Munakata, Fumio, 2022. "Morphological characteristics of self-assembled aggregate textures using multifractal analysis: Interpretation of Multifractal τ(q) Using Simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    • Handle: RePEc:eee:phsmap:v:603:y:2022:i:c:s0378437122005118
    DOI: 10.1016/j.physa.2022.127771
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    References listed on IDEAS

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    1. He, Ling-Yun & Chen, Shu-Peng, 2010. "Are crude oil markets multifractal? Evidence from MF-DFA and MF-SSA perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3218-3229.
    2. Sato, Yoshihiro & Mizukami, Yuka & Takeda, Mariko & Okubo, Kazuya & Kobayashi, Ryota & Munakata, Fumio, 2021. "Quantitative evaluation of morphological characteristics of self-assembled aggregates using multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    3. Jalan, Sarika & Yadav, Alok & Sarkar, Camellia & Boccaletti, Stefano, 2017. "Unveiling the multi-fractal structure of complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 11-14.
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