Fractal Structure Characteristics Research Articles

Multifractal characteristics of soil particle size distribution of abandoned homestead reclamation under different forest management modes

In this study, fast-growing poplar reclaimed from abandoned homestead in Xixian New District, Xi’an City, Shaanxi Province, was used as the research object to explore the multi-fractal characteristics of soil particle size distribution under different management modes of abandoned land (control), irrigation, fertilizer irrigation and mixed fertilizer irrigation. The results showed that the mean values of soil clay, silt and sand in abandoned land were 14.58%, 81.21% and 4.22% respectively, 14.08%, 79.92% and 5.99% under irrigation, 15.17%, 81.19% and 3.64% under fertilizer irrigation, and 16.75%, 80.20% and 3.05% in mixed fertilizer treatment. From 40 cm, with increasing soil depth, soil clay particles increase under irrigation, fertilizer irrigation, and mixed fertilizer irrigation modes. The single fractal dimension of soil particle size distribution (D) in each treatment ranges from 2.721 to 2.808. At 60–100 cm, D shows fertilizer irrigation > mixed fertilizer irrigation > irrigation > abandoned land, indicating that fertilization and irrigation can increase the fine-grained matter of deep soil particles and reduce soil roughness. Compared with abandoned land, under irrigation, fertilizer irrigation and mixed fertilizer modes the capacity dimension (D0), entropy dimension (D1), correlation dimension(D2), shape characteristics of the multifractal spectrum (Δf) and overall inhomogeneity of the soil particle size distribution (D0–D10) indicate an uneven distribution of soil particle size; fractal structure characteristics of soil (D−10–D0) indicate a simplified soil structure, and degree of dispersion of soil particle size distribution (D1/D0) indicates that soil particle size is distributed in dense areas. Pearson correlation analysis showed that D was significantly correlated with clay, sand, D0–D10, soil organic matter (SOM) and soil available phosphorus (SAP) (P < 0.05). Stepwise regression analysis showed that clay was the main controlling factor of D and D0–D10 changes. The research results can provide some potential indicators for the quality evaluation of abandoned homestead reclamation.

Study on surface erosion threshold and erosion mass of bentonite applied in nuclear waste repository based on fractal structure characteristics

Bentonite exhibits good self-sealing performance and low permeability after hydration, and therefore is selected as a buffer material for high-level radioactive waste repositories, isolating the canisters containing nuclear waste from the external environment. The bentonite cushion directly contacts the surrounding rock and generates gels at the contact interface with fracture water. Surface erosion occurs once the shear stress exerted by the flowing water exceeds the erosion threshold of the bentonite gel, resulting in gel particle detachment from the soil–water interface and transport through fissure. The mass loss of the buffer by erosion will weaken its functionality as designed and directly endanger the long-term safety of the repository. The erosion behavior of bentonite is related to the structure of the gel formed by bentonite hydration. In this paper, the X-ray small-angle scattering experiments were used to prove that the gel structure has fractal characteristics and to obtain the mass fractal dimension. Based on the fractal structure of the bentonite gel, the erosion threshold that determines whether erosion will occur was quantified as a function of the solid volume fraction of the gel by taking the inter-particle attractive bond as the primary source of resistance. Furtherly, the cumulative erosion mass model that evaluates the extent of erosion was constructed to reveal the relationship between the cumulative erosion mass and cumulative water flow after the erosion has achieved stability. The proposed relations are verified by the experimental results from published literature and are of great significance for judging whether erosion will occur and evaluating the degree of erosion.

A new model for coal gas seepage based on fracture-pore fractal structure characteristics

Coal reservoir is a typical double pore medium, and the magnitude of its permeability is controlled by the parameters of the fracture pore structure. However, the relationship between fracture-pore parameters and permeability is not yet clear. Based on the fractal geometry theory, the fracture-pore morphology of coal body is characterized by tree bifurcation network and tortuous capillary bundle. This study also established a coal gas seepage flow model based on the fracture-pore fractal structure characteristics. The model includes the influence of coal structure parameters, different levels of original coal seam stress, and gas pressure on the gas seepage characteristics. Each parameter in the model has definite physical meaning and does not contain any empirical constants. Finally, the applicability of the model is evaluated by gas radial seepage experiment. It is shown that the gas permeability in the model is a function of fractal dimensions and structural parameters, and based on the sensitivity analysis of each parameter in the model, it is found that the tree diameter ratio β and length ratio γ of the bifurcation network have a significant impact on the permeability. When β increases from 0.1 to 0.9, the model permeability increases by 12 orders of magnitude. However, changes in the characteristic parameters of the pore structure have little effect on gas permeability. For dual porous media such as coal, the permeability of the fracture network dominates the overall permeability of the model, and small changes in the geometric structure of the fracture bifurcation network can lead to significant changes in permeability. The construction of this theoretical model provides a reliable basis for further improving coal-rock porous medium structure seepage models, as well as to better characterize the effect of gas drainage.

Fractal characterization of polyester based standard and single walled carbon nanotube modified composites

Abstract The electrical properties of composite materials over a wide frequency range are of great interest, not only for experimental applications, but also for theoretical studies such as fractal analysis. This study presents comparative analysis of alternating current (ac) conductivity and fractal structure characteristics in standard and single walled carbon nanotube (SWCNT) reinforced polymer composites based unsaturated polyester resin (UPR). The electrical characteristics of polymer matrices at 320 K have been analyzed as a function of frequency by impedance analysis method. It was found that the conductivity of the nanotube doped material in the dc conductivity region, which is the low frequency region, is independent of the frequency and takes a constant value. It was proved that conductivity obeys Jonscher’s power law toward the high frequency region. The standard sample showed an insulating behavior that exhibits continuous increase with increasing frequency. The images of the samples were obtained by scanning electron microscope (SEM) to reveal the relationship between the conductivity of the materials and their fractal properties. All samples were converted to binary format for calculations. Cellular particle density for each sample was determined according to scaling theory. Then, the surface coverage ratio, fractal dimensions, cluster densities, average cluster sizes and critical interface exponent values of the samples were calculated and compared with different samples in the literature. It was determined that the coverage ratio and fractal dimension increased when carbon nanotubes were added. In addition, it was observed that the interface critical exponent decreased when the carbon nanotube was doped.

Fractal Structure Characteristics and Prospecting Direction of Dispersed Metals in the Eastern Guizhou Pb–Zn Metallogenic Belt, SW China

The eastern Guizhou Pb–Zn metallogenic belt (EGMB) is an important source of Pb–Zn resources and other critical minerals (including dispersed metals, such as Ge, Cd and Ga) in China. In order to ensure the continuous resource supply of Pb–Zn and associated dispersed metals, it is urgent to explore the direction of further prospecting for them. Fractal theory can realize the fractal structure characterization of fault structures and the spatial distribution of mineral deposits, which is helpful for mineral exploration. However, the fault fractal research and prospecting application are still seldom covered in the EGMB. We used fractal theory to determine fine-scale fractal structure characteristics of fault structures and ore deposits in the EGMB, and Fry analysis to delineate favorable metallogenic areas. The results show that within a scale range of 3.670–58.716 km, the integrated faults capacity dimension (CPD) is 1.5095, the information dimension (IND) is 1.5391, and the correlation dimension (CRD) is 1.5436, indicating fault structures with high maturity, which are conducive to the migration and accumulation of ore-forming fluids. The multi-fractal spectrum width and height are 0.3203 and 1.5355, respectively, implying a significant metallogenic potential. The spatial distribution fractal dimensions (SDD) of Pb–Zn specifically and metal deposits in general are 1.0193 and 1.0709, respectively; the quantity distribution fractal dimensions (QDD) are 1.4225 and 1.4716, respectively, and the density distribution fractal dimensions (DDD) are 1.422 and 1.472, respectively, indicating strong clustering. Hence, the favorable metallogenic regions can be divided into four grades, among which grade I region is continuously distributed in space and has the greatest prospecting potential.

Preliminary Study of 2D Fracture Upscaling of Geothermal Rock Using IFS Fractal Model

Fractured rock plays important role in reservoir production. In larger scale, fractures are more likely to be heterogeneous and considered to be fractal in its nature. One of the characteristics of fractal structure is the scale independence. An investigation of fractal properties on natural fractured rock is therefore needed for modelling larger fracture. We have investigated the possibilities of fractal upscaling method to produce a larger geothermal fracture model based on smaller fracture data. We generate Iterated Function System (IFS) fractal model using parameters e.g. scale factor, angle between branch, initial line direction, and branch thickness. All the model parameters are obtained from smaller fracture data. We generate higher iteration model to be compared with larger geothermal fracture. The similarity between the IFS fractal model and natural fracture is measured by 2D box counting fractal dimension (D). The fractal dimension of first to fourth generation fractal model is (1.86 ± 0.02). The fractal dimension of the reference geothermal site is (1.86 ± 0.04). Besides of D, we found significant similarity of fracture parameters there are intensity and density between fracture model and natural fracture. Based on these result, we conclude that fractal upscaling using IFS fractal model is potential to model larger scale of 2D fracture.

Study of Fractal Structure Characteristics of Urban System in Northern Shaanxi

Based on the fractal theory,a quantitative research of the hierarchical structure of urban system, spatial structure and spatial agglomeration characteristics in Northern Shaanxi was made. Working on a major database of Northern Shaanxi non-agricultural population over 2012,traffic map of Shaanxi Province. The results indicate that Yanan and Yulin urban system scale is more concentrated and distribution is more balanced. The Transport accessibility between towns is better. Towns can develop economic cooperation by using infrastructure. The spatial distribution features of urban system in two cities is relatively concentrated. Towns is mainly in the valley along the river which is the main development axes of the urban system. The spatial distribution of urban system in Northern Shaanxi is decreasing from the center to the periphery .The town system presents a cluster distribution.

The Effect of the Fracture Surface for Stress Sensitivity in Shale Reservoir

Due to the characteristics of the ultra-low permeability, facture system becomes the key to the deployment of shale gas, and the following stress sensitivity damage will restrict the engineering effect. The essay takes the Niutitang group of black shale as the research object, which carried out for natural fracture rock sample and artificial fracture rock sample study of stress sensitivity evaluation in order to compare differences between them. The experimental results show that the natural fracture rock sample is medium to strong stress sensitivity, while the artificial fracture rock sample is from strong to the extreme strong stress sensitivity. Natural fracture is more flattening than the artificial fracture formation because of leaching action. The processed SEM image can reflect structure information on the two-dimensional surface. Its surface structure conforms to the fractal structure characteristics. Whats more, fracture it can also reflect the three-dimensional information of the fracture surface through grey value, which provides a new imaging method for the research of surface microstructure for fracture.

Construction of fractal nanostructures based on Kepler-Shubnikov nets

A system of information codes for deterministic fractal lattices and sets of multifractal curves is proposed. An iterative modular design was used to obtain a series of deterministic fractal lattices with generators in the form of fragments of 2D structures and a series of multifractal curves (based on some Kepler-Shubnikov nets) having Cantor set properties. The main characteristics of fractal structures and their lacunar spectra are determined. A hierarchical principle is formulated for modules of regular fractal structures.

ПЕРСПЕКТИВИ ДОСЛІДЖЕННЯ КРИСТАЛОГЕНЕЗУ РОТОВОЇ РІДИНИ В ДОКАЗОВІЙ ОРТОДОНТІЇ

The article provides a historic overview of research of micro-crystallization of saliva in complex diagnostics of dental diseases. Proceeding from results of their own and borrowed research, the authors demonstrate the principal qualitative parameters of comprehensive characteristics of fractal structures in the main layer of saliva facies. The article offers the algorithm of their evaluation and marks prospective trends in using software packages for objective qualitative assessment of fractals of micro-crystallograms of saliva in the case of norm or dental pathology.

334 セルオートマトンによるフラクタル構造のモデル化とその音響特性に関する考察

In the present study, acoustic characteristics of fractal structures are modeled and studied using Cellular Automata (CA). CA is a discrete system which consists of finite state variables arranged on uniform grid (cell). The dynamics of CA is expressed by temporary updating the states of cells according to the local interaction rules, defined among a cell and its neighbors. In this paper, the influence of the fractal shaped structures to the property of wave propagation phenomena in free field is investigated. Local rules are provided for the construction of three-dimensional fractal structures as well as representation of wave propagation phenomena.

Dynamics of the generalized 3 x + 1 function determined by its fractal images

Two different complex maps were obtained by generalizing 3 x + 1 function to the complex plane, and fractal images for these two complex maps were constructed by using escape time, stopping time and total stopping time arithmetic. The dynamics of the generalized 3 x + 1 function based on the structural characteristics of the fractal images was studied. We found that: (1) the size and structure of the stable regions, stopping regions, total stopping regions, and divergent regions for the three types of fractal images depend on convergence rate of the map on the x and y axes. (2) The black stable regions constructed, respectively, by escape time and total stopping time are almost overlapped, demonstrating that 3 x + 1 function converged steadily. (3) All of the three fractal images are symmetric to the real axis. The structures on the neighborhood of positive integer number are symmetric to a perpendicular line, which is corresponding to the point or its nearby points on the x axis. And the structures have complicated fractal structure characteristics. These findings indicate that the generalized 3 x + 1 function on integer number and its neighborhood contains plentiful information in the complex plane.

Fractals control in particle’s velocity

Julia set, a fractal set of the literature of nonlinear physics, has significance for the engineering applications. For example, the fractal structure characteristics of the generalized M–J set could visually reflect the change rule of particle’s velocity. According to the real world requirement, the system need show various particle’s velocity in some cases. Thus, the control of the nonlinear behavior, i.e., Julia set, has attracted broad attention. In this work, an auxiliary feedback control is introduced to effectively control the Julia set that visually reflects the change rule of particle’s velocity. It satisfies the performance requirement of the real world problems.

Visualizing generalized 3 x + 1 function dynamics based on fractal

We generalize 3 x + 1 function to the complex plane, gain two different complex maps, and construct fractal images for this two complex maps using escape time, stopping time and total stopping time arithmetic respectively, study the dynamics for generalized 3 x + 1 function on the base of the structure characteristics of the fractal images. We find that: ▪ The sizes and structures of the stable regions, stopping regions, total stopping regions, divergent regions for the three types of fractal images depend on convergence rate of the map on the x- and y-axis. ▪ The black stable regions constructed by escape time and total stopping time are almost similar, which show that 3 x + 1 function converged steadily. ▪ All of the three types of fractal images are symmetric about the real axis. The structures on the neighborhood of positive integer number are symmetric about a perpendicular line. The perpendicular line is corresponding to the point or its nearby points on the x-axis. And the structures have complicated fractal structure characteristics. These indicate that generalized 3 x + 1 function on the neighborhood of integer number contain plentiful information in the complex plane, which need research further.

Abrasion-resistant solgel antireflective films with a high laser-induced damage threshold for inertial confinement fusion

To prepare abrasion-resistant antireflective (AR) films for inertial confinement fusion, four solgel routes have been investigated on polysiloxane-modified and polyvinylalcohol- (PVA-) modified SiO2 sols. As confirmed with a transmissive electron microscope, different fractal structure characteristics of the modified SiO2 particles are disclosed by small-angle x-ray scattering technology. And it is these special fractal characteristics that determine the performance of AR films on the level of internal microstructure. A Si29 magic angle spinning and nuclear magnetic resonance study has been successfully applied in explaining the fractal microstructure and its relation to the laser-induced damage threshold (LIDT) of AR films. The films modified by PVA120000 or acetic acid-catalyzed polysiloxane have higher LIDTs than those films modified by PVA16000 or hydrochloride acid-catalyzed polysiloxane. The films from PVA-modified SiO2 sols have a stronger abrasion resistance but lower antireflection than those films from polysiloxane-modified SiO2 sols. In addition, the films from polysiloxane-modified SiO2 sols can possess high transmittance and high LIDT if the polysiloxane synthesis condition is appropriately chosen, but the abrasion resistance is not as good as that from PVA modification. If strong abrasion resistance is necessary, a possible resolution may be to choose a more appropriate hydrophilic polymer than PVA. If not, polysiloxane-modified silica sol can also work when polysiloxane is synthesized under acetic acid catalysis.

Behavior of fractal structure characteristics for neutral silica aerogels during the sintering process

physica status solidi (a)Volume 144, Issue 2 p. K59-K63 Short Note Behavior of fractal structure characteristics for neutral silica aerogels during the sintering process Ivana Hinic, Ivana Hinic Institute of Physics, Center for Experimental Physics, Belgrade Search for more papers by this author Ivana Hinic, Ivana Hinic Institute of Physics, Center for Experimental Physics, Belgrade Search for more papers by this author First published: 16 August 1994 https://doi.org/10.1002/pssa.2211440232Citations: 5 P. O. Box 57, 11 000 Belgrade, Yugoslavia. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume144, Issue216 August 1994Pages K59-K63 RelatedInformation

Time-resolved light scattering studies on protein precrystallization fractal clusters

X-ray diffraction is one of the most important methods for determining the three-dimensional structure of biological macromolecules. However, obtaining biological crystals is a lengthy and painstaking endeavour. Therefore, no universal recipes exist ;thus the field of protein crystallization can be judged as highly empirical. Hen-egg white lysozyme has served as a prototype to study the early stages of protein crystallization. Crystallization is initiated by addition of simple salts and the growth of fractal aggregates formed during the process is monitored with light scattering techniques. The evolution of those aggregates obeys the dynamic scaling characteristics of fractal structures in the diffusion, cross-over or reaction limited aggregation regimes. Protein concentration, type and concentration of the employed precipitant and temperature are intimately related with the kinetics of the growth process. The derived quasi-stationary sizes of the aggregates provide observables that correlate with the appearance of lysozyme crystals. The possibility that protein crystallization could be dynamically controlled in its very initial stage, is more than academic. Several difficulties and shortcomings involved in the envisaged approach are discussed.

Formation dynamics of protein precrystallization fractal clusters

The enzyme lysozyme served as a prototype to study the early stages of protein crystallization or precipitation. The crystallization and precipitation aggregates reactions were initiated by supersaturating the lysozyme solutions through addition of NaCl and (NH 4) 2SO 4 respectively and monitored via photon correlation spectroscopy. Laplace inversion of the spectra revealed in general bimodal particle distributions consisting of monomeric and high molecular weight protein species. The time evolution of the formation of large aggregates obeys the dynamic scaling characteristics of fractal structures in the diffusion, crossover or reaction limited aggregation regimes; it is a function of the protein concentration, and of the concentration and type of the employed precipitant. The derived scaling exponents provide estimates which correlate with the various parameters inducing crystallization in the very early stages of the process. Rules quite similar to those governing the aggregation of inorganic colloids seem to be applicable and provide assistance in dynamically controlling the crystallization process.