scholarly journals Fractal evolution of a crack network in overburden rock rtratum

2000 ◽  
Vol 5 (1) ◽  
pp. 47-52 ◽  
Author(s):  
Guangming Yu ◽  
Heping Xie ◽  
Jianfeng Zhoa ◽  
Lun Yang
Keyword(s):  
Spatial Distribution ◽  
Fractal Dimension ◽  
Fundamental Problem ◽  
Quantitative Description ◽  
Surface Subsidence ◽  
Physical Models ◽  
Overburden Rock ◽  
Crack Network ◽  
Rock Stratum ◽  
Mining Width

A quantitative description for the spatial distribution and the evolution of a crack network in mining rock stratum is one of the most difficult and fundamental problem in the subject of surface subsidence. In this paper, the physical models are employed to simulate the spatial distribution of a crack network. By using the fractal geometry, the self-similarity of spatial distribution of crack network is discovered. As a result, the conception of fractal crack network is proposed. Furthermore, the evolution of a crack network with the increasing of mining width is investigated. It is shown that (1) the spatial distribution of a crack network displays the fractal behavior, so, the fractal dimension can be used to describe quantitatively the evolution of the crack network, (2) the fractal dimension of the crack network increases with increasing of mining width, (3) the surface subsidence increases with the increasing of fractal dimension of crack network.

Modeling of spatial distribution of passenger traffi c on interurban bus routes

Innotrans ◽  
2020 ◽  
pp. 31-36
Author(s):  
Alexander V. Martynenko ◽  
◽  
Alexander A. Shevtsov ◽  
Keyword(s):  
Spatial Distribution ◽  
Quantitative Description ◽  
Point Of View ◽  
Practical Point ◽  
Ticket Price ◽  
Passenger Traffic ◽  
Correlation And Regression Analysis ◽  
Classical Gravity ◽  
Bus Service

This paper is devoted to the quantitative description of the spatial distribution of passenger traffic based on the classical gravity model on the example of interurban bus service between Yekaterinburg and other cities of the Sverdlovsk region. The influence of factors such as population, distance between localities, and ticket price on the volume of passenger traffic was studied. As a result of the correlation and regression analysis, it was found that both the distance between localities and the ticket price can be used as a measure of the remoteness of localities. However, the quality of the resulting regression model does not change. The spatial distribution of interurban bus passenger traffic depends on the measure of distance of localities from each other and the size of their population. Moreover, the size of the population is a much more significant factor than the measure of distance. From a practical point of view, this means that when predicting passenger traffic, demographic factors must first be taken into account.

INVESTIGATION OF DYNAMIC TEXTURE AND FLOW CHARACTERISTICS OF FOAM TRANSPORT IN POROUS MEDIA BASED ON FRACTAL THEORY

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940013 ◽  
Author(s):  
FEI WANG ◽  
HAIFENG LI ◽  
DONGXING DU ◽  
XU DONG
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Quantitative Description ◽  
Flow Characteristics ◽  
Transport In Porous Media ◽  
Steady Stage ◽  
Profile Control ◽  
Fractal Characteristics

Foam fluid has found wide applications in oilfield development, such as profile control, water plugging, gas channeling control, fracturing, and so on. As a non-Newtonian fluid, the successful application of foam is significantly influenced by its structure. The foam texture, however, is complex and irregular, and becomes even more complicated in porous media by the boundary effects. Therefore, the description of dynamic foam structure is crucial and a quantitative description method for foam fluid is worth exploring. In this paper, the fractal characteristics of foam in porous media are verified and combined with foam microdisplacement experiment, and the fractal rule of foam is found. The relationship between fractal dimension and pressure is also discussed. The results show that foam has dynamic fractal characteristics during transport in porous media and the box-counting fractal dimension ranges from 1 to 2. Furthermore, the dynamic change of foam fractal dimension during transport in porous media could be divided into three stages. In the first stage when no foam forms, the fractal dimension is about 2; in the second unsteady foam stage, the fractal dimension is reduced from 1.9 to 1.6; the last one is the steady stage and the fractal dimension is almost constant (about 1.6). Besides, the fractal dimension of foam fluid is closely related to displacement pressure. Low pressure corresponds to higher fractal dimension, and high pressure corresponds to lower fractal dimension. Pressure is negatively linearly correlated with fractal dimension. These results are expected to enrich the understanding of the foam dynamic characteristics in their advanced applications.

Spatial Distribution and Fractal Properties of Aggregating Magnetic and Non-Magnetic Particles

Fractals ◽  
1998 ◽  
Vol 06 (03) ◽  
pp. 219-230 ◽  
Author(s):  
A. Provata ◽  
K. N. Trohidou
Keyword(s):  
Spatial Distribution ◽  
Fractal Dimension ◽  
Magnetic Particles ◽  
Composite System ◽  
System Size ◽  
Real Space ◽  
Magnetic Clusters ◽  
Self Similarity ◽  
Fractal Properties ◽  
Simple Connectivity

We study the spatial distribution in aggregating systems of mixtures of magnetic and non-magnetic particles using Monte-Carlo simulations together with scaling arguments. In particular, we show that (a) as the system size grows, the fractal dimension of the composite system is dominated by the smaller fractal dimension, (b) the system is realized as a back-bone consisting of magnetic particles (lower fractal dimension) with denser regions of non-magnetic particles attached to it at random positions. Using simple connectivity features observed in pure magnetic and non-magnetic clusters and self-similarity arguments we predict, via Real-Space-Renormalization, fractal exponents Dm = 1.25 ± 0.05 for the magnetic clusters and Dnm = 1.4 ± 0.1 for the non-magnetic clusters.

Fractal and Multifractal Analyses of the Porosity Degree of Ceramics Used in Biomedicine

2020 ◽  
Vol 12 (4) ◽  
pp. 450-456
Author(s):  
Wiktoria Sapota ◽  
Patrycja Szczepanik ◽  
Sebastian Stach ◽  
Zygmunt Wróbel
Keyword(s):  
Fractal Dimension ◽  
Cellular Response ◽  
Quantitative Description ◽  
Ceramic Coatings ◽  
Quantitative Fractography ◽  
Porous Surfaces ◽  
Scale Properties ◽  
New Generation ◽  
The Impact ◽  
Area Development

Designing a new generation of biomaterials is based on the assumption that the appropriate chemical composition of a material, the chemical state of its surface and the surface structure in nanoand micrometer scales are the elements which selected in a planned way decide on the type of cellular response to the material. The use of quantitative fractography enables a quantitative description of the surface. The parameter most frequently used in surface stereometry is the area development coefficient Sdr. Attempts are being made to use other tools for determining additional parameters. One of them may be fractal analysis, in which fractal dimension D is the measure of surface complexity. For the purposes of the study, comparative fractal and multifractal analyses of images showing porous surfaces of Al2O3 ceramic coatings were performed. The analyses were carried out for three lenses, namely 20×, 50× and 100×, and the impact of magnification (scale properties) on the obtained results was examined.

scholarly journals Study on the Development Height of Overburden Water-Flowing Fracture Zone of the Working Face

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ke Ding ◽  
Lianguo Wang ◽  
Wenmiao Wang ◽  
Kai Wang ◽  
Bo Ren ◽  
...  
Keyword(s):  
Coal Seam ◽  
Fracture Zone ◽  
Tensile Deformation ◽  
Drainage Water ◽  
Future Research ◽  
Overburden Rock ◽  
Material Transfer ◽  
Rock Stratum ◽  
Working Face ◽  
Sandstone Rock

Mining-induced fractures in underground coal mining face affect the stability of overburdens and provide preferential channels for water and material transfer in the underground environment. Therefore, to study the development of water-flowing fracture zones in overburdens of working face and goaf is of great significance for roof control, gas drainage, water resistance, disaster reduction, and efficient mining from the mining. In this study, a new method for predicting the development of overburden water-flowing fracture zone height (DHOWFFZ) was proposed based on the characteristics of overburden rock in No. 3 coal seam of Xin’an Coal Mine. First, the stope of No. 3 coal seam exhibits a rock stratum structure of mudstone and sandstone overlapping. Considering this characteristic, the overburden strata of No. 3 coal seam are divided into several “mudstone-sandstone” rock stratum groups. Furthermore, the ultimate tensile deformation of soft rock is greater than that of hard rock. It is proposed to judge the development degree of penetrating fracture in each rock stratum by adopting the elongation rate of mudstone intermediate layer. Meanwhile, the DHOWFFZ of “mudstone sandstone” composite rock stratum structure in the 3402 working face of No. 3 coal seam is calculated to be smaller than 43.1 m according to the actual situation. Finally, the DHOWFFZ in the 3402 working face was measured in the field, which verifies the rationality of the new DHOWFFZ prediction method. The research results provide new ideas for the prediction of DHOWFFZ and are helpful for future research in related fields.

scholarly journals Superclustering: Theory Versus Observations

1988 ◽  
Vol 130 ◽  
pp. 245-254
Author(s):  
Jaan Einasto ◽  
Maret Einasto ◽  
Enn Saar ◽  
Bernard J. T. Jones ◽  
Vicent J. Martinez
Keyword(s):  
Dark Matter ◽  
Spatial Distribution ◽  
Fractal Dimension ◽  
Galaxy Formation ◽  
Multifractal Analysis ◽  
Cold Dark Matter ◽  
Dwarf Galaxies ◽  
Local Supercluster ◽  
Theory Versus

The spatial distribution of galaxies is compared with model distributions. It is demonstrated that giant and dwarf galaxies in the Local Supercluster occupy statistically identical regions. Various tests suggest that galaxy formation is biased since all unbiased model distributions are in conflict with observed distribution of galaxies. Multifractal analysis shows that a cold dark matter dominated universe with biased galaxy formation has a fairly constant fractal dimension over a broad range of scales. This contrasts with the observed distribution which does not show simple fractal features.

scholarly journals Correlation between the fractal of aftershock spatial distribution and active fault on Sumatra

2019 ◽  
Author(s):  
Bahary Setyawan ◽  
Benyamin Sapiie
Keyword(s):  
Spatial Distribution ◽  
Fractal Dimension ◽  
Active Fault ◽  
Fault System ◽  
Counting Method ◽  
Correlation Integral ◽  
Box Counting ◽  
Point Correlation ◽  
Box Counting Method ◽  
Earthquake Doublet

Abstract. This study discusses the correlation between the fractal of spatial epicentre distribution of aftershock (D2) and active fault (D0) in the Sumatra region. We identified 15 earthquakes in this region that were followed by aftershock cluster and related to the Sumatra Fault Zone or Southern Andaman West Fault. The spatial epicentre distribution of the aftershock was estimated by using two-point correlation integral and the D2 values found were varying from 1.03 ± 0.03 to 1.68 ± 0.08. We estimated the fractal dimension of the active fault by using Box–Counting Method and found that the variation of D0 values in the range of 0.95 ± 0.03 to 1.16 ± 0.01. Positive correlation was found in this study and two patterns were identified that had similar slope with different intercept. However, there was also a correlation that had steeper slope. The steeper slope was related to earthquake doublet mechanism that could generate more random spatial distribution of the aftershock in the fault system.

scholarly journals Abstract Description of Internet Traffic of Generalized Cauchy Type

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Fractal Dimension ◽  
Fundamental Problem ◽  
Internet Traffic ◽  
Similar Process ◽  
Hurst Parameter ◽  
Cauchy Type ◽  
Self Similarity ◽  
Abstract Description ◽  
The One ◽  
Traffic Theory

Self-similar process with long-range dependence (LRD), that is, fractional Gaussian noise (fGn) with LRD is a widely used model of Internet traffic. It is indexed by its Hurst parameterHfGnthat linearly relates to its fractal dimensionDfGn. Note that, on the one hand, the fractal dimensionDof traffic measures local self-similarity. On the other hand, LRD is a global property of traffic, which is characterized by its Hurst parameterH. However, by using fGn, both the self-similarity and the LRD of traffic are measured byHfGn. Therefore, there is a limitation for fGn to accurately model traffic. Recently, the generalized Cauchy (GC) process was introduced to model traffic with the flexibility to separately measure the fractal dimensionDGCand the Hurst parameterHGCof traffic. However, there is a fundamental problem whether or not there exists the generality that the GC model is more conformable with real traffic than single parameter models, such as fGn,irrelevant of traffic traces used in experimental verification. The solution to that problem remains unknown but is desired for model evaluation in traffic theory or for model selection against specific issues, such as queuing analysis relating to the autocorrelation function (ACF) of arrival traffic. The key contribution of this paper is our solution to that fundamental problem (see Theorem 3.17) with the following features in analysis. (i) Set-valued analysis of the traffic of the fGn type. (ii) Set-valued analysis of the traffic of the GC type. (iii) Revealing the generality previously mentioned by comparing metrics of the traffic of the fGn type to that of the GC type.

Experimental study on the effects of fractures on elastic wave propagation in synthetic layered rocks

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. D441-D451 ◽  
Author(s):  
Tianyang Li ◽  
Ruihe Wang ◽  
Zizhen Wang ◽  
Yuzhong Wang
Keyword(s):  
Wave Propagation ◽  
Fractal Dimension ◽  
Power Spectrum ◽  
Elastic Wave ◽  
Power Law ◽  
Layered Media ◽  
Physical Models ◽  
P Wave ◽  
Fracture Density ◽  
S Wave

Fractures greatly increase the difficulty of oil and gas exploration and development in reservoirs consisting of interlayered carbonates and shales and increase the uncertainty of highly efficient development. The presence of fractures or layered media is also widely known to affect the elastic properties of rocks. The combined effects of fractures and layered media are still unknown. We have investigated the effects of fracture structure on wave propagation in interlayered carbonate and shale rocks using physical models based on wave theory and the similarity principle. We have designed and built two sets of layered physical models with randomly embedded predesigned vertically aligned fractures according to the control variate principle. We have measured the P- and S-wave velocities and attenuation and analyzed the effects of fracture porosity and aspect ratio (AR) on velocity, attenuation, and power spectral dimension of the P- and S-waves. The experimental results indicated that under conditions of low porosity ([Formula: see text]), Han’s empirical velocity-porosity relations and Wang’s attenuation-porosity relation combined with Wyllie’s time-average model are a good prediction for layered physical models with randomly embedded fractures. When the porosity is constant, the effect of different ARs on elastic wave properties can be described by a power law function. We have calculated the power spectrum fractal dimension [Formula: see text] of the transmitted signal in the frequency domain, which can supplement the S-wave splitting method for estimating the degree of anisotropy. The simple power law relation between the power spectrum fractal dimension of the P-waveform and fracture density suggests the possible use of P-waves for discriminating fracture density. The high precision and low error of this processing method give new ideas for rock anisotropy evaluation and fracture density prediction when only P-wave data are available.

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