Determination of the Box-Counting Fractal Dimension of Pore Distribution in Eggshell Based on Scanning Electron Microscopy Image Analysis

2011 ◽  
Vol 341-342 ◽  
pp. 776-779 ◽  
Author(s):  
Kai Zhang ◽  
Shu Cai Wang
Keyword(s):  
Fractal Dimensions ◽  
Negative Slope ◽  
Box Counting ◽  
Microscopy Image ◽  
Fractal Characteristics ◽  
Object Of Study ◽  
The Relationship ◽  
Microscopy Image Analysis ◽  
Electronic Microscope

The fractal characteristics of pore structures were investigated using duck eggshells as an object of study. The images of the sharp end, the equator and the blunt end of the eggshells were acquired by using scanning electronic microscope. The image processing operations were conducted for the preprocessing and the image converted into binary image. Then we developed programs based on the principle of changing megascopic degree and applied them to plot thelgN(δ)~lg(δ).The relationship betweenlgN(δ)andlg(δ)maintained linearity over a range [2,64] pixels. Therefore, the fractal dimensions of pore distributions were obtained from the negative slope by regression analysis. The experimental results showed that the fractal feature of the pore in eggshells was remarkable. The analysis confirmed that the blunt end of the eggshell in the pore distributions was more obvious than the sharp end and the equator.

Efficient box-counting determination of generalized fractal dimensions

1990 ◽  
Vol 42 (4) ◽  
pp. 1869-1874 ◽  
Author(s):  
A. Block ◽  
W. von Bloh ◽  
H. J. Schellnhuber
Keyword(s):  
Fractal Dimensions ◽  
Box Counting

Fractal Characteristics of Primary Phase Morphology in Semisolid A356 Alloy

2012 ◽  
Vol 535-537 ◽  
pp. 936-940
Author(s):  
Zheng Liu ◽  
Xiao Mei Liu
Keyword(s):  
Fractal Dimension ◽  
A356 Alloy ◽  
Fractal Dimensions ◽  
Processing Parameters ◽  
Primary Phase ◽  
Phase Morphology ◽  
Box Counting ◽  
Magnetic Stirring ◽  
Fractal Characteristics ◽  
Electro Magnetic

Semisolid A356 alloy was prepared by low superheat pouring and slightly electro- magnetic stirring(LSPSES). The fractal dimensions of primary phase morphology in semisolid A356 alloy were researched by the calculating program written to calculate the fractal dimensions of box-counting in the image of primary phase morphology in semisolid A356 alloy. The results indicated that the primary phase morphology in the alloy was characterized by fractal dimension, and the morphology obtained by the different processing parameters had the different fractal dimension. The morphology at the different position of ingot had the different fractal dimensions, which reflected the effect of solidified conditions at different position in the same ingot on the morphology in the alloy. Solidification of the alloy was a course of change in fractal dimension.

Fractal Characteristics of the Middle-Upper Ordovician Marine Shale Nano-Scale Porous Structure from the Ordos Basin, Northeast China

2021 ◽  
Vol 21 (1) ◽  
pp. 274-283
Author(s):  
Liang Liu ◽  
Wuling Mo ◽  
Min Wang ◽  
Nengwu Zhou ◽  
Yu Yan ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Ordos Basin ◽  
Fractal Dimensions ◽  
Upper Ordovician ◽  
Average Pore ◽  
Marine Shale ◽  
Fractal Characteristics ◽  
The Relationship

The fractal characteristics of marine shale from the Middle-Upper Ordovician Wulalike Formation (O2w) in the southwest margin of the Ordos Basin are studied. Based on low-temperature nitrogen adsorption experiments, the FHH (Frenkel-Halsey-Hill) model was employed to investigate the relationship between the marine shale composition, such as TOC, mineral content and shale gas content, and pore structure parameters, such as BET specific surface area, average pore diameter, porosity and fractal dimension. The results show that the pore size distribution curve of shale slowly decreased after the pore size was greater than 50 nm, the pore size distribution showed multiple peaks, and the peak value was mainly in the range of 2–10 nm. Most pores are nanopores, although the pore type and shape are different. Two different fractal dimensions D1 and D2 are obtained from the two segments with relative pressures of 0–0.5 and 0.5–1.0, respectively: the D1 range is 2.77–2.82, and the D2 range is 2.63–2.66. As D1 is larger than D2, the pore structure of small pores is more uniform than that of large pores in the shale samples. The relationship between the fractal dimensions D1 and D2 and the total organic carbon (TOC) content is a convex curve. Fractal dimension D reaches its maximum when TOC is 0.53 wt.%. Fractal dimension D decreases with increasing specific surface area, porosity and average pore size. The fractal dimension has a different influence on the gas storage and migration in shale; the larger the fractal dimension is, the stronger the heterogeneity and the more complex the pore structure, and this outcome is conducive to the storage of gas in shale but not beneficial to the permeability and production of gas.

scholarly journals Study on the Fractal Characteristics of Fracture Network Evolution Induced by Mining

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Tao Liang ◽  
Xiaoli Liu ◽  
Sijing Wang ◽  
Enzhi Wang ◽  
Quansheng Li
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Material Model ◽  
Fracture Network ◽  
Network Evolution ◽  
Rock Properties ◽  
Fracture Formation ◽  
Fractal Characteristics ◽  
Induced Fractures ◽  
The Relationship

The evolution and distribution of fracture network induced by mining is essential to determine the mechanical properties and permeability of disturbed rock mass. In this paper, the similar material model tests are employed to simulate the stress variation, cyclic breaking, and fracture formation and distribution status of the overlying strata with different loading conditions, rock properties, and mining process. The fractal dimension of mining-induced fracture network varied with mining advancing, and the evolvement laws of fracture network with mining advancing and different mining advancing footage are concerned and obtained. By establishing the relationship between the fractal dimension and the mining length in different horizontal and vertical zones, it demonstrates that the fractal dimensions in horizontal and vertical zones have a self-similar characteristic, and the distribution of the fractal dimension of the mining-induced fractures shows generally the “W”-type trend.

Experimental Research on the Relation between Processing Parameters and Fractal Dimensions of the Machined Surface

2012 ◽  
Vol 602-604 ◽  
pp. 2011-2016
Author(s):  
Zhi Xin Feng ◽  
Yu Jun Cai ◽  
Zhen Li
Keyword(s):  
Functional Relation ◽  
Fractal Dimensions ◽  
Processing Parameters ◽  
Experimental Sample ◽  
Machined Surface ◽  
Box Counting ◽  
Box Counting Method ◽  
The Relationship ◽  
Micro Topography

In the finishing machining, processing parameters directly affects the quality of machined surface. While the micro topography of the surface maps with the fractal dimensions. The paper researched the relation between processing parameters and fractal dimensions through the experiments in order to obtain the relationship. Through the design of orthogonal rotation experiment, determine the experimental parameters. Then measure the experimental sample for the surface and calculate the fractal dimensions using the box counting method. In the end, obtain the functional relation of processing parameters and fractal dimensions by regression method. The results show that the specific processing parameters of the surface can predict the fractal dimension by this formula. And this provides reference for selection of processing parameters.

scholarly journals CRIME AS AN OBJECT OF INQUIRY IN RUSSIAN CRIMINALISTICS ALEKSEY BESSONOV,

2018 ◽  
Vol 5 (2) ◽  
pp. 112-127
Author(s):  
A. Bessonov
Keyword(s):  
Criminal Activity ◽  
Criminal Cases ◽  
New Techniques ◽  
Crime Investigation ◽  
The Subject ◽  
Definition Of ◽  
Object Of Study ◽  
The Relationship ◽  
Modern Russian

This article deals with the definition of the subject and objects of modern Russian criminalistics. It is aimed at sensitizing world public opinion to the necessity of inquiry into the criminalistic essence of crime and encouraging criminalists to study new techniques of crime investigation in order to mitigate risks and reduce errors arising in the criminal investigation process.One of the main objects that is constantly undergoing research in Russian criminalistics is criminal activity. The subject of Russian criminalistics is the regularities of criminal activity. When investigating crimes scientists are interested in the information that allows the successful investigation of the crimes and determination of the offender. The information about different types of crimes, which is necessary for crime investigation, is accumulated in the criminalistic characteristic of crimes. The Criminalistic Characteristic of Crimes is a scientific theory of modern Russian criminalistics that makes it possible to fully examine the specific features of crimes of all kinds, i.e. the forensic nature (essence) of crime, the system of crime elements with their characteristics, and the relationship between those elements. In U.S. and European criminalistics, the regularities of criminal activity are not defined as an object of study of this science. Yet, in the U.S. and European countries criminal profilers investigating criminal cases study the criminal links between crimes to identify crime series and crimes committed by similar offenders (or to determine co-offenders).

Study on Fractal Characteristics of Primary Phase Morphology in Semi-Solid A356 Alloy

2010 ◽  
Vol 139-141 ◽  
pp. 653-656
Author(s):  
Zheng Liu ◽  
Xiao Mei Liu
Keyword(s):  
Fractal Dimension ◽  
A356 Alloy ◽  
Fractal Dimensions ◽  
Primary Phase ◽  
Phase Morphology ◽  
Fractal Characteristic ◽  
Box Counting ◽  
Compound Process ◽  
Fractal Characteristics ◽  
Semi Solid

Semi-solid A356 slurry was prepared by compound process, and the fractal characteristic of primary phase morphology was researched. The fractal dimensions of primary phase morphology in semi-solid A356 alloy were calculated by the calculating program written to calculate the fractal dimensions of box-counting in the imagine of morphology of semi-solid primary phase in A356 alloy. The results indicated that the primary phase morphology in semi-solid A356 prepared by compound process is characterized by fractal dimension, and the primary phase morphology prepared by the different technology parameters had different fractal dimensions. The primary phase morphology at the different position of ingot had the different fractal dimensions, which reflected the effect of solidified conditions at different position in the same ingot on the morphology of semi-solid primary phase

ON THE VISUAL COMPLEXITY OF BUILT AND NATURAL LANDSCAPES

Fractals ◽  
2014 ◽  
Vol 22 (04) ◽  
pp. 1450008
Author(s):  
ANDREI BOURCHTEIN ◽  
LUDMILA BOURCHTEIN ◽  
NATALIA NAOUMOVA
Keyword(s):  
Visual Complexity ◽  
Fractal Dimensions ◽  
Historical Buildings ◽  
Box Counting ◽  
Surrounding Environment ◽  
Natural Landscapes ◽  
Fractal Images ◽  
Box Counting Method ◽  
Natural Settings ◽  
The Relationship

In this study, we analyze some critical points of the application of the box-counting method to the evaluation of the fractal dimensions of the natural and built landscapes. A brief theoretical discussion of the eventual drawbacks of the method is supported by experimental results of two box-counting programs applied to classical fractals. The optimized version of the algorithm, based on the results of computations for the classical fractal images, is proposed and employed for the evaluation of the complexity level of the chosen historical buildings and surrounding environment in the well-known case of Amasya city. The hypothesis of the relationship between the visual complexity of built and natural settings is analyzed for the Amasya case and for two historical Brazilian cities.

scholarly journals Modifications and Statistical Analysis of Acoustic Emission Models Based on the Damage and Fractal Characteristics

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Jie Yang ◽  
Yanna Zheng ◽  
Huijing Wang
Keyword(s):  
Acoustic Emission ◽  
Damage Evolution ◽  
Fractal Dimensions ◽  
Homogeneous Material ◽  
Material Damage ◽  
Quasibrittle Materials ◽  
Damage Process ◽  
Emission Models ◽  
Fractal Characteristics ◽  
The Relationship

The damage process is accompanied by the acoustic emission for quasibrittle materials. And in the process of material damage evolution, the length of microcracks satisfies the fractal distribution. Research on their relationship in theory is helpful to reveal the law of material damage evolution and acoustic emission activities. Damage variable expressions are proposed based on the damage and fractal characteristics firstly. Then, the statistical models for acoustic emission considering damage and fractal characteristics are established by deducing the relationship between acoustic emission parameters and load cycles and fractal dimensions. The effects of damage and fractal effects on acoustic emission parameters are analyzed finally. The results show that the damage accelerates the AE activity to the rougher material, the opposite to the more homogeneous material. It can also be seen that the increase of the fractal dimension, the homogeneity constant m, will substantially increase the AE activities.

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