scholarly journals FRACTAL GEOMETRY OF THE RIVER NETWORK AND NEOTECTONICS OF THE SOUTHERN SIKHOTE-ALIN

2020 ◽  
Vol 39 (6) ◽  
pp. 48-64
Author(s):  
V. S. Zakharov ◽  
◽  
D. A. Simonov ◽  
G. Z. Gilmanova ◽  
A. N. Didenko ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Shuttle Radar Topography Mission ◽  
River Network ◽  
The Self ◽  
Sikhote Alin ◽  
Self Similarity ◽  
Vertical Movements ◽  
Crustal Earthquakes ◽  
Fractal Analyses ◽  
Comparison Of The Results

A new complex parameter is proposed to characterize the self-similarity of a river network, that is, the parameter of river networks self-similarity (PRNS), which is a combination of the exponent in the distribution of channels along the lengths, fractal dimension of channels, and fractal dimension of points of channel order change, which is more correct when compared with neotectonic movements. A comprehensive analysis of the self-similarity of the river network model for the southern Sikhote-Alin derived from the Digital Elevation Model (DEM) based on the Shuttle Radar Topography Mission (SRTM) image was performed. Comparison of the results of morphostructural and fractal analyses showed a good correlation of these two methods. PRNS relative maxima coincide with areas where ascending neotectonic movements are of the largest amplitude (increment of relief), while minima coincide with areas either of the least increment of relief or where erosion rates are the greatest. At the same time, most epicenters of crustal earthquakes are confined to the boundary zones between PRNS relative maxima and minima, that is, uplifts are flanked by elongated seismic areas, which is related to the block nature of neotectonic vertical movements.

scholarly journals CHARACTERISTICS OF SELF‐SIMILARITY OF SEISMICITY AND THE FAULT NETWORK OF THE SIKHOTE ALIN OROGENIC BELT AND THE ADJACENT AREAS

2019 ◽  
Vol 10 (2) ◽  
pp. 541-559
Author(s):  
V. S. Zakharov ◽  
A. N. Didenko ◽  
G. Z. Gil’manova ◽  
T. V. Merkulova
Keyword(s):  
Fractal Dimension ◽  
Quantitative Characteristic ◽  
Recurrence Plot ◽  
Orogenic Belt ◽  
Sikhote Alin ◽  
Self Similarity ◽  
Crustal Earthquakes ◽  
Self Similar ◽  
Fault Network ◽  
Bureya Massif

We performed a comprehensive analysis of the characteristics of self‐similarity of seismicity and the fault network within the Sikhote Alin orogenic belt and the adjacent areas. It has been established that the main features of seismicity are controlled by the crustal earthquakes. Differentiation of the study area according to the density of earthquake epicenters and the fractal dimension of the epicentral field of earthquakes (De) shows that the most active crustal areas are linked to the Kharpi‐Kur‐Priamurye zone, the northern Bureya massif and the Mongol‐Okhotsk folded system. The analysis of the earthquake recurrence plot slope values reveals that the highest b‐values correlate with the areas of the highest seismic activity of the northern part of the Bureya massif and, to a less extent, of the Mongol‐Okhotsk folded system. The increased fractal dimension values for the fault network (Df) correlate with the folded systems (Sikhote Alin and Mongol‐Okhotsk), while the decreased values conform to the depressions and troughs (Middle Amur, Uda and Torom). A comparison of the fractal analysis results for the fault network with the recent stress‐strain data gives evidence of their general confineness to the contemporary areas of intense compression. The correspondence between the field of the parameter b‐value for the upper crustal earthquakes and the fractal dimension value for the fault network (Df) suggests a general consistency between the self‐similar earthquake magnitude (energy) distribution and the fractal distribution of the fault sizes. The analysis results demonstrate that the selfsimilarity parameters provide an important quantitative characteristic in seismotectonics and can be used for the neotectonic and geodynamic analyses.

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.

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%.

Neotectonic vertical movements of the South Sikhote-Alin and characteristics of self-similarity of the stream network

2020 ◽  
pp. 25-36
Author(s):  
D. A. Simonov ◽  
V. S. Zakharov ◽  
G. Z. Gilmanova ◽  
A. N. Didenko
Keyword(s):  
Fractal Analysis ◽  
Orogenic Belt ◽  
Complex Parameter ◽  
Sikhote Alin ◽  
The South ◽  
Self Similarity ◽  
Stream Network ◽  
Vertical Movements ◽  
Stage Of Development ◽  
Network Pattern

Morphostructural analysis of the relief and fractal analysis of the stream network of the South of the Sikhote-Alin orogenic belt were carried out. The formation of the relief at the neotectonic stage occurred in several stages, which was reflected in the stream network pattern: 1) during pre-Oligocene time there was a general uplift of Sikhote-Alin; 2) in the Pliocene there was an activation of vertical neotectonic movements, most intense to the East of the Central Sikhote-Alin fault and synchronous whith basalt volcanism; 3) in the Pleistocene vertical movements of significant amplitude did not occur, at this time the modern erosion-denudation relief of the region was formed; 4) at the end of the Pleistocene and in Holocene there was a slight activation of vertical movements to the East of the Central Sikhote-Alin fault, which was reflected in the peculiarities of residual relief. Comparison of morphological and fractal analysis results showed, that the maximum of complex parameter of self-similarity PRNS coincide with the areas of greatest increments in elevation and the minima is the smallest increment of relief or whith the areas whith most significant erosion. In regions with the stage character of neotectonic development during fractal analysis of stream network it is necessary to consider additional factors due to the peculiarities of development of the stream network at each stage of development, and conservative of its pattern, reflecting features of the development of the relief in different stages.

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.

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 Fingerprints Authentication Using Grayscale Fractal Dimension

2019 ◽  
Vol 29 (3) ◽  
pp. 106
Author(s):  
Nadia. M. G. Alsaidi ◽  
Arkan J. Mohammed ◽  
Wael J. Abdulaal
Keyword(s):  
Pattern Recognition ◽  
Fractal Dimension ◽  
Shape Analysis ◽  
Relevant Information ◽  
The Self ◽  
Fingerprint Recognition ◽  
Self Similarity ◽  
Visual Objects ◽  
Box Counting ◽  
Box Counting Dimension

Characterizing of visual objects is an important role in pattern recognition that can be performed through shape analysis. Several approaches have been introduced to extract relevant information of a shape. The complexity of the shape is the most widely used approach for this purpose where fractal dimension and generalized fractal dimension are methodologies used to estimate the complexity of the shapes. The box counting dimension is one of the methods that used to estimate fractal dimension. It is estimated basically to describe the self-similarity in objects. A lot of objects have the self-similarity; fingerprint is one of those objects where the generalized box counting dimension is used for recognizing of the fingerprints to be utilized for authentication process. A new fractal dimension method is proposed in this paper. It is verified by the experiment on a set of natural texture images to show its efficiency and accuracy, and a satisfactory result is found. It also offers promising performance when it is applied for fingerprint recognition.

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