Papers by Keyword: Fractal Dimension

Abstract: New techniques for the analysis of complex images were advanced by the example of asurface microrelief of the Fe70Cr15B15 alloys, obtained by the melt-spinning at different linearvelocity of a quenching roller. Proposed techniques are based on the fast Fourier transform of theimage using digital signal processors. The degree of morphological ordering/disordering of ribbonswas determined due to the parameterization of mode spectra by entropy functionals. The best glassforming ability for alloys of the studied composition was obtained at 30 m/s.

Abstract: The work considers the approach determining suboptimal relation of strength and plasticity by the example of low-carbon constructional steel 3 (0.14...0.22 % С), which is widely used in metal structures. As parameters for the research, the elements of chemical composition and properties of ferrite-pearlite structure of steel were taken. For the reliability of the obtained results for the evaluation of structure, its quantitative analysis was carried out either by traditional methods or by fractal approach. Combining operating regions of the values of steel properties depending on the chemical composition and area and fractal dimension of pearlite, we got the diagram of the region of compromise for indices of strength limit σ_В, σ_0,2 and specific elongation δ. Areas with suboptimal relations σ_В/δ and σ_0.2/δ were defined in the region of compromise for quality criteria. The application of the given approach allows (while adhering to steel production process) to predict areas with stable suboptimal relations for strength and plasticity indices by selecting value range for the elements of chemical composition and analysis of structure.

Abstract: The article presents the fractal approach to the study of the five peat structure samples. Digital images from natural porous raw peat, intended for fractal studies of the porosity, are proposed. Peat active porosity is used in this study. In this study, the peat active porosity, fractal dimension (D), and their relationship with different peat samples were investigated in an experiment. The results of this study demonstrate that a fractal dimension analysis of peat compositions texture is a useful method for the quantitative description of the active porosity. The received results should be considered in the theoretical and pilot studies connected with physicomechanical processes occurring on the porous surfaces of peat raw materials during its mechanical processing.

Abstract: The superficial microstructure, received by laser processing, is characterized by a high density of defects of a crystal structure and incompleteness of thermal phase and structural transformations. The degree of a neravnovesnost of such a structure can be estimated by means of multifractal ranges. As a measure for calculation of multifractals, it is possible to use any quantitative structural index, in particular, the area of microstructural objects, their perimeter and density of borders. The most informative is density of borders, which considers the area and perimeter of structural object. Microstructures of stainless steel 12kh18n10t in an initial state, after laser processing and a local laser alloying by hard-alloy powder from BK8 were investigated. Calculations of complex indicators of the structural organization of material, which showed, are executed on the basis of the multifratalnykh of ranges, that laser processing leads to, increase of orderliness and frequency. It indicates high degree of a neravnovesnost with which increase hardening increases.

Abstract: Based on the particle size distribution test of 6 kinds of limestone powder, the fractal dimension of particle size distribution was calculated, and its influence on the surface area, median grain diameter and RR-B value was studied. In addition, 20% of the total mass of cement was replaced with limestone powder, and the effect of fractal dimension on fluidity of cement paste and 3, 7, 28d strength of mortar was investigated. The results showed that fractal dimension for limestone powder specific surface area has a good linear relationship with median grain diameter and RR-B value. The fractal dimension showed a quadratic function with the degree of the fluidity, and the maximum value was between 2.1-2.2. Mortar strength at the age of 3, 7, 28d value displayed a linear relationship with fractal dimension L4 had the greatest effect on strength. L1-L4 had more influence on the strength at the age of 3d and 7d than that of 28d. While the influence of L5-L7 on the strength at 3d, 7d and 28d was essentially similar to each other.

Abstract: In order to search the correlation between textural properties and geometrical heterogeneity in clays, as characterized by the surface fractal dimension, we used, three different cationic clays; namely Kaolin of Hamam Dbagh, Montmorillonite (Mt) of Maghnia and a sample prepared from Sodium Montmorillonte (Na-Mt)) and three different synthetic anionic clays, ZnAlCO3, MgAlCO₃ at a molar ratio equal to three (R=3), and NiAlCO₃ with different molar ratios (R=2, R=3 and R= 4). This D_S parameter was evaluated from nitrogen (N₂) analysis gas. the fractal Frenkel-Halsey-Hill (FHH) (D_S) models was used to estimate the surface fractal dimensions at two ranges of relative pressure, the first between 0.08 and 0.22, which were found Ds to be 2.59, 2.53 and 2.68 from Kaolin, Montmorillonite and Sodium Montmorillonte clays respectively and 2.33, 2.61, 2.53, 2.56 and 2.56 for ZnAlCO₃ and MgAlCO₃, NiAlCO₃ (2, 3 and 4) respectively, and other at medium relative pressure, which there was an excellent linear adjustment for F-H-H equation within the range between 0.37 and 0.82, which were found Ds to be 2.77, 2.64 and 2.82 for Kaolinite, Montmorillonite and Sodium Montmorillonte clays respectively, and 2.68, 2.64, 2.40, 2.60, 2.47 for ZnAlCO₃, MgAlCO₃, NiAlCO₃ (2, 3 and 4) respectively. SEM Characterization confirmed the heterogeneous distribution of the particles and the BET analysis confirmed the fractal nature of the surface of these materials. The zeta potential of the sample which is most used as an indicator of dispersion stability, show a proportionality between increases of zeta potential with increase of dimension fractal (D_S), for the same type of clays ( (NiAlCO₃) with (R=2, 3 and 4) and Mt, Na-Mt). Key words: Anionic clays; Cationic clays; Fractal dimension; geometrical heterogeneity; Frenkel-Halsey-Hill model.

Abstract: In present work the yield process of nanocomposites polypropylene/carbon nanotubes analysis has performed within the frameworks of fractional derivatives conception and fractal analysis. The mathematical model of a viscoelastic body based on derivatives of fractional order. It has been shown that the yield stress is defined by elasticity modulus and nanocomposite structural state. The fractional exponent structural identification has performed.

Abstract: This study was undertaken to compare chemically identical nanoparticles that have been synthesed by different methods. The methodology applied allows the identification of different characteristics in the structure and surface parameters of nanoparticles. The study shows that the structural parameters of nanoparticles are to a great extend related to the conditions in which nanoparticles are formed. This is demonstrated through the comparison of three oxides and their different methods of synthesis. The results show that the method of synthesis defines the structure of the nanoparticles; the surface and qualitative and quantitative parameters of the crystaline phases, energy shifts and changes in the internal electron levels. The examples of nanoliquids and the associated polymer strength identify that the interaction of nanoparticles with the environment is also depends on the synthesis method. It is proposed that a fractal dimension may be used as a basic parameter to classify nanoparticles and predict the properties in their interaction with various media.

Abstract: Capillary tree networks can be efficiently used for several applications. These trees display the same patterns at different levels of scale, which is a property found in fractal objects. This paper combines a thermodynamic formulation with the geometric characteristics of the tree fractal network, to describe the equilibrium capillary pressure. The model proposed here accounts for, in addition to physical properties of the fluids, the fractal dimension, the scale factor between the size of parent and daughter tubes, and the branching level. The effect of each of these properties on the capillary pressure is also investigated.

Abstract: The structure, distribution and evolution of micro-crack within the mud-shale are studied in this paper. The micro-fracture behavior of mud-shale has fractal characteristics. Fractal method is used to quantitative description of the damage evolution behavior of the mud-shale. The study shows that the variation of the fractal dimension in the domain of the bearing surface can reflect the internal damage evolution trend of the mud-shale. The fractal dimension has a nonlinear relationship with the applied stress.