Symmetry and Fractals: Theory and Applications

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 June 2025 | Viewed by 1943

Special Issue Editors


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Guest Editor
1. School of Mathematics and Statistic, Nanjing University of Information Science and Technology, Nanjing 210044, China
2. Center for Applied Mathematics of Jiangsu Province, Nanjing University of Information Science and Technology, Nanjing 210044, China
3. Jiangsu International Joint Laboratory on System Modeling and Data Analysis, Nanjing University of Information Science and Technology, Nanjing 210044, China
Interests: fractals; image processing; time series; feature extraction; pattern recognition; 3D modeling; topology optimization; machine learning
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
1. School of Mathematics and Statistic, Nanjing University of Information Science and Technology, Nanjing 210044, China
2. Jiangsu International Joint Laboratory on System Modeling and Data Analysis, Nanjing University of Information Science and Technology, Nanjing 210044, China
Interests: stochastic partial differential equations; stochastic control; mathematical biology; dynamic system
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetry and fractals are two concepts that are abundant in mathematics, physics, and nature.  They provide new mathematical tools for studying complex systems and are important for understanding and describing physical phenomena. These tools can extract useful information hidden in complex data, providing strong support for scientific research and engineering applications. They both hold important positions and values in the field of science, providing us with new perspectives and methods for understanding and describing complex phenomena in nature.

This Special Issue aims to explore the basic principles and applications of symmetry and fractal theory in fields such as mathematics, physics, chemistry, biology, sociology, and engineering; promote the research and development of symmetry and fractal theory; discover new theories and methods; develop new numerical and experimental methods to validate and expand symmetry and fractal theory; and apply the theories of symmetry and fractals to solve practical problems and promote scientific and technological progress.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but are not limited to) the following:

  • symmetry;
  • fractals;
  • theoretical research;
  • interdisciplinary applications;
  • numerical methods;
  • mathematical models.

I look forward to receiving your contributions.

Prof. Dr. Jian Wang
Prof. Dr. Guangying Lv
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • symmetry
  • fractals
  • theoretical research
  • interdisciplinary applications
  • numerical methods
  • mathematical models

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Published Papers (2 papers)

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Research

14 pages, 712 KiB  
Article
Correlation between Temperature and the Posture of Transmission Line Towers
by Minzhen Wang, Haihang Gao, Zhigang Wang, Keyu Yue, Caiming Zhong, Guangxin Zhang and Jian Wang
Symmetry 2024, 16(10), 1270; https://doi.org/10.3390/sym16101270 - 26 Sep 2024
Viewed by 674
Abstract
Ensuring the safety of transmission line towers is vital for human safety, power supply, economic development, and environmental protection. This study specifically examines how temperature affects tower inclination. Multifractal detrended cross-correlation analysis (MF-DCCA) is a combination of multifractal detrended fluctuation analysis (MF-DFA) and [...] Read more.
Ensuring the safety of transmission line towers is vital for human safety, power supply, economic development, and environmental protection. This study specifically examines how temperature affects tower inclination. Multifractal detrended cross-correlation analysis (MF-DCCA) is a combination of multifractal detrended fluctuation analysis (MF-DFA) and DCCA that reveals the multifractal features of two cross-correlated non-stationary signals. This paper adopts the MF-DCCA tool to investigate the cross-correlations between the internal temperature of an inclination sensor device and the posture of a transmission line tower. The tilt angle data in the x- and y-axes are used to measure the posture of the transmission line tower. We start by using Pearson correlation to assess the relationship between temperature and two inclination angles, followed by verifying their correlation with a p-value below 0.05 using first-order linear fitting. We initially assess the multifractal features of three time series using MF-DFA before MF-DCCA analysis. All exhibit multifractal traits with H(2)<0.5, indicating negative persistence, especially notable in the temperature series. Finally, we adopt the MF-DCCA approach to examine the multifractal cross-correlation between tilt-angle time series and temperature time series, and the results indicate the negative persistence of the cross-correlation between the time series. Furthermore, the multifractal cross-correlation of temperature and inclination data on the y-axis was also found to be stronger than on the x-axis based on features of the scaling exponent and symmetry exponent. Full article
(This article belongs to the Special Issue Symmetry and Fractals: Theory and Applications)
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21 pages, 5433 KiB  
Article
A Novel Detection Algorithm for the Icing Status of Transmission Lines
by Dongxu Dai, Yan Hu, Hao Qian, Guoqiang Qi and Yan Wang
Symmetry 2024, 16(10), 1264; https://doi.org/10.3390/sym16101264 - 25 Sep 2024
Viewed by 786
Abstract
As more and more transmission lines need to pass through areas with heavy icing, the problem of transmission line faults caused by ice and snow disasters frequently occurs. Existing ice coverage monitoring methods have defects such as the use of a single monitoring [...] Read more.
As more and more transmission lines need to pass through areas with heavy icing, the problem of transmission line faults caused by ice and snow disasters frequently occurs. Existing ice coverage monitoring methods have defects such as the use of a single monitoring type, low accuracy of monitoring results, and an inability to obtain ice coverage data over time. Therefore, this study proposes a new algorithm for detecting the icing status of transmission lines. The algorithm uses two-dimensional multifractal detrended fluctuation analysis (2D MF-DFA) to determine the optimal sliding-window size and wave function and accurately segment and extract local feature areas. Based on the local Hurst exponent (Lh(z)) and the power-law relationship between the fluctuation function and the scale at multiple continuous scales, the ice-covered area of a transmission conductor was accurately detected. By analyzing and calculating the key target pixels, the icing thickness was accurately measured, achieving accurate detection of the icing status of the transmission lines. The experimental results show that this method can accurately detect ice-covered areas and the icing thickness of transmission lines under various working conditions, providing a strong guarantee for the safe and reliable operation of transmission lines under severe weather conditions. Full article
(This article belongs to the Special Issue Symmetry and Fractals: Theory and Applications)
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