Fractal Characteristic of Electrical Trees Grown in Silicone Rubber under Environmental Stress

2017 ◽  
Vol 7 (3) ◽  
pp. 1628
Author(s):  
M. S. Mohd Fua’ad ◽  
M.H. Ahmad ◽  
Y. Z. Arief ◽  
N. A. Ahmad
Keyword(s):  
Fractal Dimension ◽  
Fractal Structure ◽  
The Self ◽  
Fractal Structures ◽  
Self Similarity ◽  
Fractal Characteristic ◽  
Electrical Tree ◽  
Breakdown Phenomenon ◽  
Electrical Trees ◽  
Electrical Treeing

<div class="WordSection1"><p>One of the degradations of insulation is in the form of electrical treeing in which classified as a pre-breakdown phenomenon of electrical insulation. The electrical tree is commonly forming in the shape of tree-like or root-like which may have fractal structures. Due to this fractal structure, electrical treeing formation and patterns are analysed via fractal dimension and lacunarity to study the self-similarity patterns of electrical treeing. Many types of research have been conducted to study the fractal dimension and lacunarity of electrical treeing to fully understand the electrical tree mechanism and characteristics. However, fractal and lacunarity structures of</p></div>

scholarly journals After notes on self-similarity exponent for fractal structures

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 440-448 ◽  
Author(s):  
Manuel Fernández-Martínez ◽  
Manuel Caravaca Garratón
Keyword(s):  
Fractal Dimension ◽  
Broad Spectrum ◽  
Fractal Structure ◽  
Similarity Index ◽  
Random Processes ◽  
The Self ◽  
Sample Function ◽  
Fractal Structures ◽  
Self Similarity ◽  
Image Set

AbstractPrevious works have highlighted the suitability of the concept of fractal structure, which derives from asymmetric topology, to propound generalized definitions of fractal dimension. The aim of the present article is to collect some results and approaches allowing to connect the self-similarity index and the fractal dimension of a broad spectrum of random processes. To tackle with, we shall use the concept of induced fractal structure on the image set of a sample curve. The main result in this paper states that given a sample function of a random process endowed with the induced fractal structure on its image, it holds that the self-similarity index of that function equals the inverse of its fractal dimension.

SELF-SIMILARITY IN COMPLEX NETWORKS: FROM THE VIEW OF THE HUB REPULSION

2013 ◽  
Vol 27 (28) ◽  
pp. 1350201 ◽  
Author(s):  
HAIXIN ZHANG ◽  
XIN LAN ◽  
DAIJUN WEI ◽  
SANKARAN MAHADEVAN ◽  
YONG DENG
Keyword(s):  
Fractal Dimension ◽  
Complex Systems ◽  
Complex Networks ◽  
Fractal Structure ◽  
The Self ◽  
New Method ◽  
Self Similarity ◽  
Nature And Society ◽  
Real Complex

Complex networks are widely used to model the structure of many complex systems in nature and society. Recently, fractal and self-similarity of complex networks have attracted much attention. It is observed that hub repulsion is the key principle that leads to the fractal structure of networks. Based on the principle of hub repulsion, the metric in complex networks is redefined and a new method to calculate the fractal dimension of complex networks is proposed in this paper. Some real complex networks are investigated and the results are illustrated to show the self-similarity of complex networks.

scholarly journals A Community-Structure-Based Method for Estimating the Fractal Dimension, and its Application to Water Networks for the Assessment of Vulnerability to Disasters

2021 ◽  
Vol 35 (4) ◽  
pp. 1197-1210
Author(s):  
C. Giudicianni ◽  
A. Di Nardo ◽  
R. Greco ◽  
A. Scala
Keyword(s):  
Fractal Dimension ◽  
Community Structure ◽  
Distribution Systems ◽  
Water Distribution ◽  
Scaling Law ◽  
Vulnerability Index ◽  
The Self ◽  
Node Degree ◽  
Specific Response ◽  
Self Similarity

AbstractMost real-world networks, from the World-Wide-Web to biological systems, are known to have common structural properties. A remarkable point is fractality, which suggests the self-similarity across scales of the network structure of these complex systems. Managing the computational complexity for detecting the self-similarity of big-sized systems represents a crucial problem. In this paper, a novel algorithm for revealing the fractality, that exploits the community structure principle, is proposed and then applied to several water distribution systems (WDSs) of different size, unveiling a self-similar feature of their layouts. A scaling-law relationship, linking the number of clusters necessary for covering the network and their average size is defined, the exponent of which represents the fractal dimension. The self-similarity is then investigated as a proxy of recurrent and specific response to multiple random pipe failures – like during natural disasters – pointing out a specific global vulnerability for each WDS. A novel vulnerability index, called Cut-Vulnerability is introduced as the ratio between the fractal dimension and the average node degree, and its relationships with the number of randomly removed pipes necessary to disconnect the network and with some topological metrics are investigated. The analysis shows the effectiveness of the novel index in describing the global vulnerability of WDSs.

A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions

2018 ◽  
Vol 33 (10) ◽  
pp. 1850057 ◽  
Author(s):  
I. Zborovský
Keyword(s):  
Conservation Law ◽  
Fractal Structure ◽  
Fractal Dimensions ◽  
The Self ◽  
Hadron Structure ◽  
Self Similarity ◽  
Similarity Variable ◽  
Variable Formula ◽  
Entropy Principle ◽  
Fragmentation Processes

Fractal self-similarity of hadron interactions demonstrated by the [Formula: see text]-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable [Formula: see text] is a function of the momentum fractions [Formula: see text] and [Formula: see text] of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions [Formula: see text] and [Formula: see text] of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the [Formula: see text]-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.

scholarly journals Study on the Fractal Dimension and Growth Time of the Electrical Treeing Degradation at Different Temperature and Moisture

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Youping Fan ◽  
Dai Zhang ◽  
Jingjiao Li
Keyword(s):  
Fractal Dimension ◽  
Tree Growth ◽  
Fractal Dimensions ◽  
Moisture Level ◽  
Growth Time ◽  
Counting Method ◽  
Box Counting ◽  
Electrical Trees ◽  
Box Counting Method ◽  
Electrical Treeing

The paper aims to understand how the fractal dimension and growth time of electrical trees change with temperature and moisture. The fractal dimension of final electrical trees was estimated using 2-D box-counting method. Four groups of electrical trees were grown at variable moisture and temperature. The relation between growth time and fractal dimension of electrical trees were summarized. The results indicate the final electrical trees can have similar fractal dimensions via similar tree growth time at different combinations of moisture level and temperature conditions.

scholarly journals Rock Mechanical Property Influenced by Inhomogeneity

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yunliang Tan ◽  
Dongmei Huang ◽  
Ze Zhang
Keyword(s):  
Mechanical Property ◽  
Fractal Dimension ◽  
Rock Type ◽  
Fractal Dimensions ◽  
Rock Material ◽  
The Self ◽  
Self Similarity ◽  
Red Sandstone ◽  
Variation Patterns ◽  
Rock Microstructure

In order to identify the microstructure inhomogeneity influence on rock mechanical property, SEM scanning test and fractal dimension estimation were adopted. The investigations showed that the self-similarity of rock microstructure markedly changes with the scanned microscale. Different rocks behave in different fractal dimension variation patterns with the scanned magnification, so it is conditional to adopt fractal dimension to describe rock material. Grey diabase and black diabase have high suitability; red sandstone has low suitability. The suitability of fractal-dimension-describing method for rocks depends on both investigating scale and rock type. The homogeneities of grey diabase, black diabase, grey sandstone, and red sandstone are 7.8, 5.7, 4.4, and 3.4, separately; their average fractal dimensions of microstructure are 2.06, 2.03, 1.72, and 1.40 correspondingly, so the homogeneity is well consistent with fractal dimension. For rock material, the stronger brittleness is, the less profile fractal dimension is. In a sense, brittleness is an image of rock inhomogeneity in macroscale, while profile fractal dimension is an image of rock inhomogeneity in microscale. To combine the test of brittleness with the estimation of fractal dimension with condition will be an effective approach for understanding rock failure mechanism, patterns, and behaviours.

A Modified Box-Counting Method to Estimate the Fractal Dimensions

2011 ◽  
Vol 58-60 ◽  
pp. 1756-1761 ◽  
Author(s):  
Jie Xu ◽  
Giusepe Lacidogna
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
The Self ◽  
Whole Body ◽  
Counting Method ◽  
Border Effect ◽  
Self Similarity ◽  
Box Counting ◽  
Self Similar ◽  
Box Counting Method

A fractal is a property of self-similarity, each small part of the fractal object is similar to the whole body. The traditional box-counting method (TBCM) to estimate fractal dimension can not reflect the self-similar property of the fractal and leads to two major problems, the border effect and noninteger values of box size. The modified box-counting method (MBCM), proposed in this study, not only eliminate the shortcomings of the TBCM, but also reflects the physical meaning about the self-similar of the fractal. The applications of MBCM shows a good estimation compared with the theoretical ones, which the biggest difference is smaller than 5%.

scholarly journals Ameliorated Electrical-Tree Resistant Characteristics of UV-Initiated Cross-Linked Polyethylene Nanocomposites with Surface-Functionalized Nanosilica

Processes ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 313 ◽  
Author(s):  
Yong-Qi Zhang ◽  
Ping-Lan Yu ◽  
Wei-Feng Sun ◽  
Xuan Wang
Keyword(s):  
Fractal Dimension ◽  
Electric Fields ◽  
Tree Growth ◽  
Electrical Resistance ◽  
Dielectric Breakdown ◽  
Breakdown Strength ◽  
Sio2 Nanoparticles ◽  
Polyethylene Matrix ◽  
Electrical Tree ◽  
Electrical Trees

Given the high interest in promoting crosslinking efficiency of ultraviolet-initiated crosslinking technique and ameliorating electrical resistance of crosslinked polyethylene (XLPE) materials, we have developed the funcionalized-SiO2/XLPE nanocomposites by chemically grafting auxiliary crosslinkers onto nanosilica surfaces. Trimethylolpropane triacrylate (TMPTA) as an effective auxiliary crosslinker for polyethylene is grafted successfully on nanosilica surfaces through thiolene-click chemical reactions with coupling agents of sulfur silanes and 3-mercaptopropyl trimethoxy silane (MPTMS), as characterized by nuclear magnetic resonance and Fourier transform infrared spectroscopy. The functionalized SiO2 nanoparticles could be dispersively filled into polyethylene matrix even at a high filling content that would generally produce agglomerations of neat SiO2 nanofillers. Ultraviolet-initiated polyethylene crosslinking reactions are efficiently stimulated by TMPTA grafted onto surfaces of SiO2 nanofillers, averting thermal migrations out of polyethylene matrix. Electrical-tree pathways and growth mechanism are specifically investigated by elucidating the microscopic tree-morphology with fractal dimension and simulating electric field distributions with finite-element method. Near nano-interfaces where the shielded-out electric fluxlines concentrate, the highly enhanced electric fields will stimulate partial discharging and thus lead to the electrical-trees being able to propagate along the routes between nanofillers. Surface-modified SiO2 nanofillers evidently elongate the circuitous routes of electrical-tree growth to be restricted from directly developing toward ground electrode, which accounts for the larger fractal dimension and shorter length of electrical-trees in the functionlized-SiO2/XLPE nanocomposite compared with XLPE and neat-SiO2/XLPE nanocomposite. Polar-groups on the modified nanosilica surfaces inhibit electrical-tree growth and simultaneously introduce deep traps impeding charge injections, accounting for the significant improvements of electrical-tree resistance and dielectric breakdown strength. Combining surface functionalization and nanodielectric technology, we propose a strategy to develop XLPE materials with high electrical resistance.

scholarly journals Investigation of electrical treeing in perspex material

2021 ◽  
Vol 2 (1) ◽  
pp. 1-7
Author(s):  
Mohammad Abderrahman
Keyword(s):  
Growth Speed ◽  
Equal Area ◽  
Electrical Tree ◽  
Tree Construction ◽  
Long Time ◽  
Electrical Trees ◽  
Dry Conditions ◽  
Dry And Wet Conditions ◽  
Electrical Treeing ◽  
Tree Development

Perspex has been known for a long time as a polymeric material, and it has been used for a large number of electrical and non-electrical applications. The present work was carried out to investigates the ageing mechanism of perspex material under a high electric field. The electrical treeing phenomenon was studied using perspex samples with electrodes of a pin-to-plane configuration. The growth of an electrical tree in Perspex was measured and analysed with the aid of an advanced microscope, equipped with a high-resolution camera and connected to a personal computer. Several distinct stages were assigned to characterise the electrical tree development. The area occupied by the electrical tree channels was calculated using equal-area squares. This approach was employed to measure the growth rate of electrical trees under dry and wet conditions. The tree construction, shape and growth speed were studied and analysed to distinguish between treeing phenomenon under wet and dry conditions of fabricated perspex specimens. The absorption of water has increased the tree growth inside the samples, and ions with water have accelerated the breakdown process. The findings of this study are essential to improve the performance of perspex material, which is widely used in a variety of applications for both energy and non-energy purposes.

SELF SIMILARITY IN SWELLING SYSTEMS: FRACTAL PROPERTIES OF PEAT

Fractals ◽  
1994 ◽  
Vol 02 (01) ◽  
pp. 45-52 ◽  
Author(s):  
A. V. NEIMARK ◽  
E. ROBENS ◽  
K. K. UNGER ◽  
Yu. M. VOLFKOYICH
Keyword(s):  
Fractal Dimension ◽  
Water Adsorption ◽  
The Self ◽  
Self Similarity ◽  
Sphagnum Peat ◽  
Fractal Properties ◽  
Wide Range ◽  
Capillary Equilibrium ◽  
Scale Range ◽  
Self Similar

Sphagnum peat gives an example of a swelling system with a self-similar structure in sufficiently wide range of scales. The surface fractal dimension, dfs, has been calculated by means of thermodynamic method on the basis of water adsorption and capillary equilibrium measurements. This method makes possible the exploration of the self-similarity in the scale range over at least 4 decimal orders of magnitude from 1 nm to 10 μm. In a sample explored, two ranges of fractality have been observed: dfs ≈ 2.55 in the range 1.5–80 nm and dfs ≈ 2.42 in the range 0.25–9 µm.

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