Methodological Aspects of Fractal Dimension Estimation on the Basis of Particle Size Distribution

2013 ◽  
Vol 12 (1) ◽  
pp. vzj2012.0064 ◽  
Author(s):  
Andrzej Bieganowski ◽  
Tymoteusz Chojecki ◽  
Magdalena Ryżak ◽  
Agata Sochan ◽  
Krzysztof Lamorski
Keyword(s):  
Particle Size ◽  
Fractal Dimension ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Dimension Estimation ◽  
Methodological Aspects

scholarly journals Green Preparation, Spheroidal, and Superior Property of Nano-1,3,5,7-Tetranittro-1,3,5,7-Tetrazocane

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Xinlei Jia ◽  
Jingyu Wang ◽  
Conghua Hou ◽  
Yingxin Tan
Keyword(s):  
Activation Energy ◽  
Particle Size ◽  
Fractal Dimension ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Fractal Theory ◽  
Crystal Form ◽  
Decomposition Temperature ◽  
Scanning Calorimetry ◽  
The Impact

Herein, a green process for preparing nano-HMX, mechanical demulsification shearing (MDS) technology, was developed. Nano-HMX was successfully fabricated via MDS technology without using any chemical reagents, and the fabrication mechanism was proposed. Based on the “fractal theory,” the optimal shearing time for mechanical emulsification was deduced by calculating the fractal dimension of the particle size distribution. The as-prepared nano-HMX was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and differential scanning calorimetry (DSC). And the impact sensitivities of HMX particles were contrastively investigated. The raw HMX had a lower fractal dimension of 1.9273. The ideal shearing time was 7 h. The resultant nano-HMX possessed a particle size distribution ranging from 203.3 nm to 509.1 nm as compared to raw HMX. Nano-HMX particles were dense spherical, maintaining β-HMX crystal form. In addition, they had much lower impact sensitivity. However, the apparent activation energy as well as thermal decomposition temperature of nano-HMX particles was decreased, attributing to the reduced probability for hotspot generation. Especially when the shearing time was 7 h, the activation energy was markedly decreased.

scholarly journals Fractal dimension of particle-size distribution and their relationships with alkalinity properties of soils in the western Songnen Plain, China

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Yufeng Bai ◽  
Yan Qin ◽  
Xinrui Lu ◽  
Jitao Zhang ◽  
Guoshuang Chen ◽  
...  
Keyword(s):  
Particle Size ◽  
Fractal Dimension ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Linear Regression Analysis ◽  
Salt Content ◽  
Clay Content ◽  
Fine Sand ◽  
Alkaline Soil ◽  
Songnen Plain

AbstractThe purpose of this study was to identify the fractal dimension and their relationships with alkalinity properties of soils, and to evaluate the potential of fractal dimension as an indicator of alkalinity properties of soil. Six soils with an increasing salinity (electrical conductivity was 0.09, 0.18, 0.62, 0.78, 1.57 and 1.99 dS m−1, respectively) were selected from the western part of the Songnen Plain (China). Salt content, exchangeable sodium percentage, sodium adsorption ratio and other properties of the soils were determined and the soil particle-size distribution (0–2000 μm) was measured using a laser diffraction particle size analyser. Our results show that the overall fractal dimension of the selected soils ranged from 2.35 to 2.60. A linear regression analysis showed a significant negative correlation between fractal dimension and the amount of coarse sand and fine sand (r =  − 0.5452, P < 0.05 and r =  − 0.8641, P < 0.01, respectively), and a significant positive correlation with silt and clay (r = 0.9726, P < 0.01 and r = 0.9526, P < 0.01, respectively). Thus, soils with higher silt and clay content have higher fractal dimension values. Strong linear relationships between fractal dimension and salt content (P < 0.05), in particular a very significant positive relationship with HCO3− (P < 0.01), also exist. It is therefore possible to conclude that a soil’s fractal dimension could serve as a potential indicator of soil alkalization and the variability in alkaline soil texture.

Fractal Dimension of Floc Growth in Micro-Coagulation Stage II: Some Normal Influencing Factors

2011 ◽  
Vol 243-249 ◽  
pp. 4827-4830
Author(s):  
Hao Yu Li ◽  
Jun Nan ◽  
Wei Peng He
Keyword(s):  
Particle Size ◽  
Fractal Dimension ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Influencing Factors ◽  
Aluminum Chloride ◽  
Fractal Dimensions ◽  
Coagulation Time ◽  
On Line ◽  
Line Detector

The coagulation experiment, with Kaolin as objects, aluminum chloride (PAC) as coagulant and hydrated MnO2 as coagulant aid, were accomplished under different conditions. In the experiment, the particle size distribution and turbidity in water were detected by on-line detector. The results show that increase PAC dosage, original turbidity, hydrated MnO2 dosage and coagulation time will make the fractal dimensions of floc growth in micro-coagulation stage increase. The fractal dimensions of floc growth in micro-coagulation stage increasing means more particle size <5µm flocs are removed. Hydrated MnO2 can strengthen micro-coagulation.

A fractal kinetic model for heap leaching of uranium ore with fractal dimension of varied particle size distribution

2013 ◽  
Vol 136 ◽  
pp. 85-92 ◽  
Author(s):  
De-Xin Ding ◽  
Hai-Ying Fu ◽  
Yong-Jun Ye ◽  
Nan Hu ◽  
Guang-Yue Li ◽  
...  
Keyword(s):  
Particle Size ◽  
Fractal Dimension ◽  
Kinetic Model ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Heap Leaching ◽  
Uranium Ore

scholarly journals Permeability Evolution and Particle Size Distribution of Saturated Crushed Sandstone under Compression

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Yanlong Chen ◽  
Bangyong Yu ◽  
Kai Zhang ◽  
Mingwei Zhang ◽  
Guang Xu ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Particle Size ◽  
Fractal Dimension ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Axial Stress ◽  
Permeability Evolution ◽  
Particle Crushing ◽  
X Ray ◽  
X Ray Computed

In this research, the particle size distribution and permeability of saturated crushed sandstone under variable axial stresses (0, 2, 4, 8, 12, and 16 MPa) were studied. X-ray Computed Tomography results revealed that particle crushing is likely to occur considerably as the axial stress is approaching 4 MPa, which results in the change of pore structure greatly. During compression, the particle size distribution satisfies the fractal condition well, and the fractal dimension of particle size distribution is an effective method for describing the particle crushing state of saturated crushed sandstone. When the axial stress increases from 0 MPa to 4 MPa, the fractal dimension of the particle size distribution increases rapidly by over 60% of the total increase (0–16 MPa), and the permeability decreases sharply by about 85% of the total decrease. These results indicate that 4 MPa is a key value in controlling the particle size distribution and the permeability of the saturated crushed sandstone under axial compression. The permeability is influenced by the initial gradation of the specimens, and a larger Talbot exponent corresponds to a larger permeability.

Fractal Features of Cracked Backfill Particle Size Distribution

2012 ◽  
Vol 588-589 ◽  
pp. 1894-1898
Author(s):  
Yong Jian Zhu ◽  
Dai Qiang Deng ◽  
Ping Wang
Keyword(s):  
Particle Size ◽  
Fractal Dimension ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Negative Correlation ◽  
Fractal Structure ◽  
Fine Grained ◽  
Calculation Data ◽  
Relationship Of

Based on the taking sample by geological drilling, combined with the fractal principle, analysis on the cracked backfill particle size of its fractal features and strength correlation. Even each backfill sand specimen particle size is difference, but calculation data shows that the particle size of each sand specimen has preferable fractal feature, the sand specimen particle size distribution has remarkable fractal structure by the linear fitted results of the sand specimens. The fractal relationship of strength and particle size distribution shows that with the increased of fractal dimension, the strength of backfill is decreased, that is to say there is negative correlation, the main cause is that the higher parameter D of the fractal dimension, the higher fine-grained content and more non-uniform of the particle size distribution, especially for the thinner full tailings, if properly increasing the content of slightly crude particles, the strength of backfill will be certainly improved to some extent.

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