scholarly journals Fractal Model for Acoustic Absorbing of Porous Fibrous Metal Materials

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Weihua Chen ◽  
Tianning Chen ◽  
Xiaopeng Wang ◽  
Jiuhui Wu ◽  
Suobin Li
Keyword(s):  
Sound Absorption ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Wave Number ◽  
Geometrical Parameters ◽  
Acoustic Model ◽  
Metal Materials ◽  
Flow Resistivity ◽  
Fibrous Metal ◽  
Static Flow

To investigate the changing rules between sound absorbing performance and geometrical parameters of porous fibrous metal materials (PFMMs), this paper presents a fractal acoustic model by incorporating the static flow resistivity based on Biot-Allard model. Static flow resistivity is essential for an accurate assessment of the acoustic performance of the PFMM. However, it is quite difficult to evaluate the static flow resistivity from the microstructure of the PFMM because of a large number of disordered pores. In order to overcome this difficulty, we firstly established a static flow resistivity formula for the PFMM based on fractal theory. Secondly, a fractal acoustic model was derived on the basis of the static flow resistivity formula. The sound absorption coefficients calculated by the presented acoustic model were validated by the values of Biot-Allard model and experimental data. Finally, the variation of the surface acoustic impedance, the complex wave number, and the sound absorption coefficient with the fractal dimensions were discussed. The research results can reveal the relationship between sound absorption and geometrical parameters and provide a basis for improving the sound absorption capability of the PFMMs.

scholarly journals Flow Simulation of Artificially Induced Microfractures Using Digital Rock and Lattice Boltzmann Methods

Energies ◽  
2018 ◽  
Vol 11 (8) ◽  
pp. 2145 ◽  
Author(s):  
Yongfei Yang ◽  
Zhihui Liu ◽  
Jun Yao ◽  
Lei Zhang ◽  
Jingsheng Ma ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Lattice Boltzmann ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Geometrical Parameters ◽  
Fracture Aperture ◽  
Berea Sandstone ◽  
Wide Range ◽  
Induced Fractures

Microfractures have great significance in the study of reservoir development because they are an effective reserving space and main contributor to permeability in a large amount of reservoirs. Usually, microfractures are divided into natural microfractures and induced microfractures. Artificially induced rough microfractures are our research objects, the existence of which will affect the fluid-flow system (expand the production radius of production wells), and act as a flow path for the leakage of fluids injected to the wells, and even facilitate depletion in tight reservoirs. Therefore, the characteristic of the flow in artificially induced fractures is of great significance. The Lattice Boltzmann Method (LBM) was used to calculate the equivalent permeability of artificially induced three-dimensional (3D) fractures. The 3D box fractal dimensions and porosity of artificially induced fractures in Berea sandstone were calculated based on the fractal theory and image-segmentation method, respectively. The geometrical parameters (surface roughness, minimum fracture aperture, and mean fracture aperture), were also calculated on the base of digital cores of fractures. According to the results, the permeability lies between 0.071–3.759 (dimensionless LB units) in artificially induced fractures. The wide range of permeability indicates that artificially induced fractures have complex structures and connectivity. It was also found that 3D fractal dimensions of artificially induced fractures in Berea sandstone are between 2.247 and 2.367, which shows that the artificially induced fractures have the characteristics of self-similarity. Finally, the following relations were studied: (a) exponentially increasing permeability with increasing 3D box fractal dimension, (b) linearly increasing permeability with increasing square of mean fracture aperture, (c) indistinct relationship between permeability and surface roughness, and (d) linearly increasing 3D box fractal dimension with increasing porosity.

Flow resistivity, characteristic impedance and complex wave number assessment of coconut fiber with thin thickness samples.

2017 ◽  
Author(s):  
Key Fonseca de Lima ◽  
Nilson Barbieri ◽  
Fernando Jun Hattori Terashima ◽  
Vinicius Antonio Grossl ◽  
Nelson Legat Filho
Keyword(s):  
Characteristic Impedance ◽  
Wave Number ◽  
Coconut Fiber ◽  
Complex Wave ◽  
Flow Resistivity ◽  
Complex Wave Number

scholarly journals Dynamic characteristics and fractal representations of crack propagation of rock with different fissures under multiple impact loadings

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bing Sun ◽  
Shun Liu ◽  
Sheng Zeng ◽  
Shanyong Wang ◽  
Shaoping Wang
Keyword(s):  
Fractal Dimension ◽  
Crack Propagation ◽  
Crack Growth ◽  
Impact Test ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Fractal Dimensions ◽  
Peak Stress ◽  
Dynamic Mechanical Properties ◽  
Gravitational Potential Energy

AbstractTo investigate the influence of the fissure morphology on the dynamic mechanical properties of the rock and the crack propagation, a drop hammer impact test device was used to conduct impact failure tests on sandstones with different fissure numbers and fissure dips, simultaneously recorded the crack growth after each impact. The box fractal dimension is used to quantitatively analyze the dynamic change in the sandstone cracks and a fractal model of crack growth over time is established based on fractal theory. The results demonstrate that under impact test conditions of the same mass and different heights, the energy absorbed by sandstone accounts for about 26.7% of the gravitational potential energy. But at the same height and different mass, the energy absorbed by the sandstone accounts for about 68.6% of the total energy. As the fissure dip increases and the number of fissures increases, the dynamic peak stress and dynamic elastic modulus of the fractured sandstone gradually decrease. The fractal dimensions of crack evolution tend to increase with time as a whole and assume as a parabolic. Except for one fissure, 60° and 90° specimens, with the extension of time, the increase rate of fractal dimension is decreasing correspondingly.

scholarly journals Development of Back-calculation Model for Aggregate Gradation Determination Using Fractal Theory

2018 ◽  
Vol 159 ◽  
pp. 01006
Author(s):  
Bagus Hario Setiadji ◽  
Supriyono ◽  
Djoko Purwanto
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Calculation Model ◽  
Careful Consideration ◽  
Upper And Lower Bounds ◽  
Aggregate Gradation ◽  
Fractal Characteristic ◽  
Fractal Characteristics

Several studies have shown that fractal theory can be used to analyze the morphology of aggregate materials in designing the gradation. However, the question arises whether a fractal dimension can actually represent a single aggregate gradation. This study, which is a part of a grand research to determine aggregate gradation based on known asphalt mixture specifications, is performed to clarify the aforementioned question. To do so, two steps of methodology were proposed in this study, that is, step 1 is to determine the fractal characteristics using 3 aggregate gradations (i.e. gradations near upper and lower bounds, and middle gradation); and step 2 is to back-calculate aggregate gradation based on fractal characteristics obtained using 2 scenarios, one-and multi-fractal dimension scenarios. The results of this study indicate that the multi-fractal dimension scenario provides a better prediction of aggregate gradation due to the ability of this scenario to better represent the shape of the original aggregate gradation. However, careful consideration must be observed when using more than two fractal dimensions in predicting aggregate gradation as it will increase the difficulty in developing the fractal characteristic equations.

scholarly journals FRACTAL APPROACH TO MECHANICAL AND ELECTRICAL PROPERTIES OF GRAPHENE/SIC COMPOSITES

2021 ◽  
Vol 19 (2) ◽  
pp. 271
Author(s):  
Yu-Ting Zuo ◽  
Hong-Jun Liu
Keyword(s):  
Carbon Nanotubes ◽  
Electrical Properties ◽  
Fractal Theory ◽  
Bright Light ◽  
Fractal Dimensions ◽  
Mechanical Analysis ◽  
New Era ◽  
Fractal Approach ◽  
Mechanical And Electrical Properties ◽  
Sic Composites

Graphene and carbon nanotubes have a Steiner minimum tree structure, which endows them with extremely good mechanical and electronic properties. A modified Hall-Petch effect is proposed to reveal the enhanced mechanical strength of the SiC/graphene composites, and a fractal approach to its mechanical analysis is given.  Fractal laws for the electrical conductivity of graphene, carbon nanotubes and graphene/SiC composites are suggested using the two-scale fractal theory. The Steiner structure is considered as a cascade of a fractal pattern. The theoretical results show that the two-scale fractal dimensions and the graphene concentration play an important role in enhancing the mechanical and electrical properties of graphene/SiC composites. This paper sheds a bright light on a new era of the graphene-based materials.

Application of Fractal Theory in Aggregate Gradation Research

2012 ◽  
Vol 204-208 ◽  
pp. 1923-1928
Author(s):  
Bo Tan ◽  
Rui Hua Yang ◽  
Yan Ting Lai
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Aggregate Gradation ◽  
Structure Characteristics ◽  
Aggregate Distribution ◽  
Dimension Formula ◽  
Mass Fractal ◽  
Fractal Characteristics

The paper presents the fractal dimension formula of distribution of asphalt mixture aggregate diameter by the deducing mass fractal characteristics function. Taking AC-20 and SMA-20 as examples, selected 6 groups of representative grading curves within the grading envelope proposed by the present specification, and calculated their fractal dimensions. The asphalt mixture gradation has fractal dimension D (D∈(1,3)), and the fractal of continuous gradation is single while the fractal of gap-gradation shows multi-fractal with 4.75 as the dividing point. Fractal dimension of aggregate gradation of asphalt mixture reflect the structure characteristics of aggregate distribution, that is, finer is aggregate, bigger is the fractal dimension.

Research On The Fractal and Percolation Characteristics of Coal-Based Porous Media For Filtration and Impregnation

2021 ◽  
Author(s):  
Qili Wang ◽  
Jiarui Sun ◽  
Yuehu Chen ◽  
Yuyan Qian ◽  
Shengcheng Fei ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Structure ◽  
Mercury Intrusion Porosimetry ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Infinite Cluster ◽  
Porous Graphite ◽  
Local Aggregation ◽  
Gradual Expansion ◽  
The Difference

Abstract In order to distinguish the difference in the heterogeneous fractal structure of porous graphite used for filtration and impregnation, the fractal dimensions obtained through the mercury intrusion porosimetry (MIP) along with the fractal theory were used to calculate the volumetric FD of the graphite samples. The FD expression of the tortuosity along with all parameters from MIP test was optimized to simplify the calculation. In addition, the percolation evolution process of mercury in the porous media was analyzed in combination with the experimental data. As indicated in the analysis, the FDs in the backbone formation regions of sample vary from 2.695 to 2.984, with 2.923 to 2.991 in the percolation regions and 1.224 to 1.544 in the tortuosity. According to the MIP test, the mercury distribution in porous graphite manifested a transitional process from local aggregation, gradual expansion, and infinite cluster connection to global connection.

Complexity-Based Analysis of the Relation between Human Muscle Reaction and Walking Path

2020 ◽  
Vol 19 (03) ◽  
pp. 2050025 ◽  
Author(s):  
Shahul Mujib Kamal ◽  
Sue Sim ◽  
Rui Tee ◽  
Visvamba Nathan ◽  
Hamidreza Namazi
Keyword(s):  
Fractal Dimension ◽  
Statistical Analysis ◽  
Fractal Theory ◽  
Contact Point ◽  
Fractal Dimensions ◽  
Human Muscle ◽  
Physiological Signals ◽  
Eeg Signal ◽  
Leg Muscles ◽  
Emg Signal

Legs are the contact point of humans during walking. In fact, leg muscles react when we walk in different conditions (such as different speeds and paths). In this research, we analyze how walking path affects leg muscles’ reaction. In fact, we investigate how the complexity of muscle reaction is related to the complexity of path of movement. For this purpose, we employ fractal theory. In the experiment, subjects walk on different paths that have different fractal dimensions and then we calculate the fractal dimension of Electromyography (EMG) signals obtained from both legs. The result of our analysis showed that the complexity of EMG signal increases with the increment of complexity of path of movement. The conducted statistical analysis also supported the result of analysis. The method of analysis used in this research can be further applied to find the relation between complexity of path of movement and other physiological signals of humans such as respiration and Electroencephalography (EEG) signal.

scholarly journals Impacts of Pore-Throat System on Fractal Characterization of Tight Sandstones

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Dengke Liu ◽  
Zhaolin Gu ◽  
Ruixiang Liang ◽  
Junwei Su ◽  
Dazhong Ren ◽  
...  
Keyword(s):  
Experimental Data ◽  
Prediction Models ◽  
Dominant Role ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Optical Observations ◽  
Reservoir Quality ◽  
Pore Throat ◽  
Tight Sandstone ◽  
Reservoir Type

The pore-throat structures play a dominant role in the evaluation of properties of tight sandstone, but it remains difficult to determine the related parameters and understand their impact on reservoir quality. Hence, toward this end, we analyze the experimental data that are indicative of the pore-throat system, then we investigate the effect of fractal dimensions of pore-throat structures on petrologic and physical properties, and finally, the optical observations, fractal theory, and prediction model were integrated to explore the qualities of various reservoir types in tight sandstones. The results show that the fractal dimensions of the mercury intrusion curve correspond to three pore-throat types and those of the mercury extrusion curve could correspond to two pore-throat types. Five types of reservoirs were identified, the best reservoir type has a high percentage of interparticle and dissolution pores but a low proportion of clay-related pores, and the differences in pore-throat connectivity of various types affect storage capacity significantly. The storage ability prediction models of various reservoir types are raised by integrated experimental data. This work employed a comprehensive fractal theory based on capillary pressure curves and helps to explore how pore-throat systems influence reservoir quality in tight sandstones.

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