Study on the Distribution Law of the Crashed Coal Fragmentation

2011 ◽  
Vol 189-193 ◽  
pp. 1834-1839
Author(s):  
Jia Jia Zhang ◽  
Chang Long Du ◽  
Song Yong Liu ◽  
Hao Jiang
Keyword(s):  
Fractal Dimension ◽  
Weibull Distribution ◽  
Fractal Theory ◽  
Mathematic Model ◽  
Distribution Functions ◽  
Distribution Law ◽  
Characteristic Index ◽  
Fractal Distribution ◽  
The Relationship ◽  
Fragmentation Degree

In order to find the distribution law of coal fragmentation, mathematic model of size distribution was built according to fractal theory. Based on this, the experiments of impactive crash were carried out under different impact rate and different Protodikonov's hardness. The comparison between Weibull distribution and fractal distribution was done so as to find the relationship between the influence parameters and the coal fragmentation characteristic index, the coal fragmentation degree coefficient and the fractal dimension. The results indicate that both two types of distribution functions are suitable for the distribution discipline of coal fragmentation, but the relationship of the coal fragmentation degree and impact parameter is not reacted correctly by the coal fragmentation characteristic index and coal fragmentation degree coefficient in the Weibull distribution while the coal fragmentation degree could be expressed by the fractal dimension in fractal distribution. The relationships between the fractal dimension and the rate, the Protodikonov's hardness of coal are linear.

EFFECT OF FRACTAL FRACTURES ON PERMEABILITY IN THREE-DIMENSIONAL DIGITAL ROCKS

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940015 ◽  
Author(s):  
WEIFENG LV ◽  
GUOLIANG YAN ◽  
YONGDONG LIU ◽  
XUEFENG LIU ◽  
DONGXING DU ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Fractured Reservoirs ◽  
Three Dimensional ◽  
Absolute Permeability ◽  
Fracture Aperture ◽  
Fracture Networks ◽  
Discrete Fracture Networks ◽  
Discrete Fracture ◽  
The Relationship

The fracture has great impact on the flow behavior in fractured reservoirs. Fracture traces are usually self-similar and scale-independent, which makes the fractal theory become a powerful tool to characterize fracture. To obtain three-dimensional (3D) digital rocks reflecting the properties of fractured reservoirs, we first generate discrete fracture networks by stochastic modeling based on the fractal theory. These fracture networks are then added to the existing digital rocks of rock matrixes. We combine two low-permeable cores as rock matrixes with a group of discrete fracture networks with fractal characteristics. Various types of fractured digital rocks are obtained by adjusting different fracture parameters. Pore network models are extracted from the 3D fractured digital rock. Then the permeability is predicted by Darcy law to investigate the impacts of fracture properties to the absolute permeability. The permeability of fractured rock is subject to exponential increases with fracture aperture. The relationship between the permeability and the fractal dimension of fracture centers is exponential, as well as the relationship between permeability and the fractal dimension of fracture lengths.

scholarly journals Review about the Application of Fractal Theory in the Research of Packaging Materials

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 860
Author(s):  
Qingshan Duan ◽  
Jiejie An ◽  
Hanling Mao ◽  
Dongwu Liang ◽  
Hao Li ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Theory ◽  
Inorganic Materials ◽  
Packaging Materials ◽  
Analysis Method ◽  
Characteristic Parameters ◽  
Fractal Characteristic ◽  
Fractal Characteristics ◽  
The Relationship

The work is intended to summarize the recent progress in the work of fractal theory in packaging material to provide important insights into applied research on fractal in packaging materials. The fractal analysis methods employed for inorganic materials such as metal alloys and ceramics, polymers, and their composites are reviewed from the aspects of fractal feature extraction and fractal dimension calculation methods. Through the fractal dimension of packaging materials and the fractal in their preparation process, the relationship between the fractal characteristic parameters and the properties of packaging materials is discussed. The fractal analysis method can qualitatively and quantitatively characterize the fractal characteristics, microstructure, and properties of a large number of various types of packaging materials. The method of using fractal theory to probe the preparation and properties of packaging materials is universal; the relationship between the properties of packaging materials and fractal dimension will be a critical trend of fractal theory in the research on properties of packaging materials.

Study about Characteristics of Cement Paste on Fractal Theory

2013 ◽  
Vol 423-426 ◽  
pp. 1051-1054
Author(s):  
Tian Yang Zhai
Keyword(s):  
Compressive Strength ◽  
Fractal Dimension ◽  
Cement Paste ◽  
Permeability Coefficient ◽  
Fractal Theory ◽  
Fractal Model ◽  
Concrete Compressive Strength ◽  
Internal Pore Structure ◽  
The Relationship ◽  
Internal Pore

A fractal model to simulate cement paste internal pore structure, and on this basis deduce that fractal dimension is D and the corresponding pore is r, the relationship between porosity is P. MIP was measured test. Then calculated the different ages of the fractal dimension of cement and concrete compressive strength, tensile strength and permeability coefficient. The results showed that: compressive strength, permeability and fractal dimension has a good correlation. Whey in cement in the process of hydration of cement products continue to fill the pores, making the compressive strength increased 70%, permeability is declining.

Particles Gradation Optimization of Blasting Rockfill Based on Fractal Theory

2011 ◽  
Vol 366 ◽  
pp. 469-473 ◽  
Author(s):  
Sheng Zhu ◽  
Yan Ming Feng ◽  
Shu Rong Feng ◽  
Wu Yi Chen
Keyword(s):  
Fractal Dimension ◽  
Test Data ◽  
Fractal Theory ◽  
Average Diameter ◽  
Optimization Method ◽  
Dry Density ◽  
Rock Blasting ◽  
Rockfill Dam ◽  
Under Construction ◽  
The Relationship

Based on fractal theory, used the index of rockfill compaction characteristics(granularity fractal dimension) which conforms to Talbot curve distribution, combined with blasting schemes and rolling test data of several domestic rockfill dams, the relationship is established between compacted rockfill’s dry density and rock blasting parameters by rockfill granularity fractal dimension and its average diameter, and that provided the basis for rockfill particle grading optimization method. The method is applied by rockfill of JIANGPINGHE dam under construction, and the results show that this method can well reflect the intrinsic relation between rock blasting and rockfill compaction, which can be applied to particle grading design of rockfill dam.

scholarly journals A study on the effects of the fractal characteristics of aggregates on the mechanical behavior of cemented sand and gravel

2021 ◽  
Vol 71 (342) ◽  
pp. e250
Author(s):  
L. Guo ◽  
S. Li ◽  
L. Zhong ◽  
L. Guo ◽  
L. Wang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Elastic Modulus ◽  
Fractal Theory ◽  
Peak Stress ◽  
Aggregate Gradation ◽  
Cemented Sand ◽  
Ordinary Concrete ◽  
Fractal Characteristics ◽  
Sand And Gravel ◽  
The Relationship

Owing to complex aspects of cemented sand and gravel (CSG), such as included unscreened aggregates, CSG properties differ from those of ordinary concrete. Fractal theory is introduced to study the effects of aggregate characteristics on CSG properties, quantifying aggregate gradation and shape. Numerical simulation and analyses show that: (1) improved aggregate gradation decreases the gradation fractal dimension and increases the CSG peak stress and elastic modulus; (2) more irregularly shaped aggregates increase the shape fractal dimension and decrease the CSG peak stress and elastic modulus; (3) the relationship quantified between aggregate characteristics and CSG mechanical properties provides a theoretical basis for aggregate allocation in engineering design and construction. Mixing artificial aggregates can improve aggregate gradation but reduces CSG performance. Appropriately blending artificial and on-site aggregates achieves optimal CSG performance; in this study, this is attained using 20% artificial aggregates added under standard gradation.

scholarly journals Structure and breathability of silk/cashmere interwoven fabrics based on fractal theory

2020 ◽  
Vol 15 ◽  
pp. 155892502097930
Author(s):  
Ying Chen ◽  
Lifan Mei ◽  
Qiuyu Li
Keyword(s):  
Fractal Dimension ◽  
Structural Parameters ◽  
Fractal Theory ◽  
Air Permeability ◽  
Water Soluble ◽  
Weft Yarn ◽  
Warp Yarn ◽  
Moisture Permeability ◽  
And Performance ◽  
The Relationship

The fractal weave has a different appearance from the traditional weaves, and the fabric performances such as air and moisture comfort have not been studied. The relationship between the fabric structure and performance of the fractal weaves is not yet clear. In this paper, the corresponding fractal weaves were generated based on the fractal theory, and the corresponding fabrics were woven using raw silk as the warp yarn and cashmere/water-soluble vinylon as the weft yarn. The structural parameters, air permeability and moisture permeability were tested. The results show that fabric moisture permeability are not closely related with the three weave parameters of fractal dimension, average float length and weave coefficient. Its conduction mechanism is different from air permeability. The average floating length, fractal dimension, and its parameter combinations have a good fitting relationship with air permeability, and the polynomial fitting R2 can reach to 0.99938. The fitting formula 8 has guiding significance for the design of fabrics with certain air permeability requirements.

Experimental Research on Grading of Fine Aggregate in Frame Concrete

2010 ◽  
Vol 163-167 ◽  
pp. 1085-1089 ◽  
Author(s):  
Zhen Shuang Wang ◽  
Li Jiu Wang ◽  
Hao Lin Su
Keyword(s):  
Fractal Dimension ◽  
Coarse Aggregate ◽  
Design Method ◽  
Fractal Theory ◽  
Uniform Design ◽  
Fine Aggregate ◽  
N Value ◽  
Uniform Design Method ◽  
The Relationship ◽  
Mortar Matrix

According to frame concrete theory, Concrete was composed of mortar matrix, coarse aggregate, and transition zone between mortar matrix and coarse aggregate. Proper particle grading of fine aggregate can not only save cement, but also increase comprehensive properties of mortar matrix. Uniform design method was used to study the relationships between the grading of fine aggregate and workability, and the relationship with mechanic properties of mortar matrix and concrete. Based on fractal theory, the relationship between fractal dimension and modulus of fineness, and the relationship between fractal dimension and n value in Fuller equation were researched. It concluded that grading of fine aggregate affects the workability and mechanic properties of mortar matrix and concrete, significantly. There was a good linear relation between fractal dimension and n value in Fuller Equation, and fratatal dimension decreased with modulus of fineness increasing.

A Study on Land Use Scape Pattern Changes Based on Fractal Theory - Case Study of Mingcheng Town of Panshi City in Jilin

2014 ◽  
Vol 1044-1045 ◽  
pp. 1513-1516
Author(s):  
Rui Qing Qie
Keyword(s):  
Land Use ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Land Resource ◽  
Residential Areas ◽  
Gis Technology ◽  
Distribution Law ◽  
Unused Land ◽  
Land Use Types ◽  
Garden Plot

Based on the spatial land use database of Mingcheng town of Panshi City in Jilin, fractal dimension and stability of land use types are studied by using GIS technology and fractal theory. The land use is classified into 7 types: cropland, garden plot, wood land, water, road land, industrial and mining, residential areas, unused land, and other lands. The fractal dimension for the patches of the land use types is analyzed. Results showed that all the land use types have fractal characteristics and the fractal dimension (D) values vary from 1.1028 to 1.6638. In terms of the land use stability given by the fractal dimension, the order of the land use types from high to low is water, industrial and mining residential areas, cropland, wood land, unused land, road land, garden plot. And land use shape index, fragmentation index and the separation index in the spatial distribution law are largely affected by human activities influence and interference, then it can provided reference for the reason utilizing of land resource.

scholarly journals Blood physiological and flow characteristics within coronary artery circulatory network for human heart based on vascular fractal theory

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402093338
Author(s):  
Yan-li Chen ◽  
Gui-Qiang Bai ◽  
Liu-xing Ren ◽  
Yang Bai ◽  
Meng-yao Sun ◽  
...  
Keyword(s):  
Blood Flow ◽  
Fractal Dimension ◽  
Coronary Artery ◽  
Flow Resistance ◽  
Fractal Theory ◽  
Flow Characteristics ◽  
Fractal Dimensions ◽  
Vascular Network ◽  
Capillary Diameter ◽  
The Relationship

To analyze the fractal form of the vascular network in the human circulatory system, the optimal transport effect has been achieved from the point of view of biological evolution. The blood flow mathematical models based on the fractal theory for capillary network and arteriole–capillary vascular fractal network were established using theory derivation, and the blood flow characteristics, dynamic flow resistance effects, and vascular fractal physiology property based on the fractal porous medium theory for the coronary artery circulatory network were analyzed under the consideration of some influencing factors, namely, non-Newtonian fluid characteristics of blood, hemocoagulation and embolization effect in capillaries, and plasma mass flow effects. Moreover, the Poiseuille flow equation is modified by introducing the correction function, and the flow model of blood in the vascular network is established. Obviously, the relationship characteristics between blood flow and bifurcation grade in fractal vascular, fractal dimension in the arteriole–capillary vascular network, fractal dimensions of the diameter of capillary tubular diameter, fractal dimensions of capillary blood vessels, blood Casson yield stress, and ratio of red blood cell radius to capillary diameter can be obtained. And the relationship characteristics between blood flow resistance and ratio of erythrocyte radius to capillary diameter, ratios of the distance between adjacent red blood cells to the radius of red cells, and bifurcation grade can be obtained. Finally, the clinical verification tests were accomplished to verify the theory is worthy of authenticity and rationality where the curve tendencies are very similar with those obtained by numerical simulations based on the theoretical models and experimental test showed that the theoretical calculation and simulation analysis of blood circulation system of fractal vascular network were reasonable and applicable by means of experimental relative method because of the maximum relative error is less than 10%, whatever fractal dimension m changes under different conditions.

Analysis of Collapsible Loess Microstructure at Fractal Theory Based

2012 ◽  
Vol 204-208 ◽  
pp. 614-617
Author(s):  
Ming Yuan Shi ◽  
Zong Fang Chen ◽  
Hong Yan Zhang
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Linear Relationship ◽  
Pore Radius ◽  
Fractal Theory ◽  
Fractal Characteristic ◽  
Geological Age ◽  
Collapsible Loess ◽  
Fractal Character ◽  
The Relationship

On the basis of publicized data, the fractal character of pore structure in loess is studied. We have determined fractal characteristic pore radius and discussed the relationship between fractal character values and collapsibility. Results show that there is a good linear relationship between and collapsibility, and fractal dimension can reflect geological age of loess section.

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