Fractal model of thermal contact conductance of two spherical joint surfaces considering friction coefficient

Purpose The purpose of this study is to propose a fractal model of thermal contact conductance (TCC) of two spherical joint surfaces, considering friction coefficient based on the three-dimensional fractal theory. Design/methodology/approach The effects of friction coefficient, fractal parameters, radius of curvature and contact type on TCC were analyzed using numerical simulation. Findings The results indicate that the TCC decreases with the increase of friction coefficient and fractal roughness and increases with the increase of fractal dimension and radius of curvature; the contact type of two spherical joint surfaces has an important influence on the TCC, and the TCC of external contact is smaller than that of internal contact under the same contact load. Originality/value A fractal model of TCC of two spherical joint surfaces considering friction coefficient is proposed in this paper. Achievements of this work provide some theoretical basis for the research of TCC of bearings and other curved surfaces.

Research On the Fractal Dimensions of the Organic-Rich Shale Pores Via Different Models

Fractal dimension can be used to the pore surface characterize. For pore structures in different sizes, the calculation models of fractal theory should be distinguished due to the different principles of the gas adsorption experiments. To further study the adaptability of the fractal model for gas adsorption experimental data, the author collected shale samples of Longmaxi formation from Well JY1, then CO2 and N2 adsorption provided the PSD curves. In addition, the fractal dimensions of micropore and mesopore were calculated by the Jaroniec fractal model and Frenkel–Halsey–Hill (FHH) fractal model respectively. The research shows that the Jaroniec model may be suitable to calculate CO2 adsorption data and could characterize the fractal dimension of micropore, while the FHH model may be suitable to calculate N2 adsorption data in the high relative pressure region. It suggests that the micropore and mesopore could have different dimensions and the evaluation of the structure in shale pores should consider both of them.

Dynamics research of Fangzhu’s nanoscale surface

In this paper, we mainly focus on a fractal model of Fangzhu’s nanoscale surface for water collection which is established through He’s fractal derivative. Based on the fractal two-scale transform method, the approximate analytical solutions are obtained by the energy balance method and He’s frequency–amplitude formulation method with average residuals. Some specific numerical experiments of the model show that these two methods are simple and effective and can be adopted to other nonlinear fractal oscillators. In addition, these properties of the obtained solution reveal how to enhance the collection rate of Fangzhu by adjusting the smoothness of its surfaces.

A FRACTAL-FRACTIONAL 2019-NCOV MODEL OF MAJOR DISASTER FOR HUMAN LIFE

The purpose of this research is to explore the spread dynamics of a novel coronavirus outbreak, or 2019-nCOV via a fractional approach of type fractal-fractional (FF) derivative. We considered the FF approach in sense of the Atangana–Baleanu derivative for the system 2019-nCOV. In the FF operator, when we choose fractional-order one, we achieve the fractal model and when choosing fractal order one then we obtain a fractional model and while considering both the operators together we obtain the fractal-fractional model. The obtained results show via graphics for the different collections of fractal and fractional orders. The graphical results show the new operator impacts on a practical situation in a more visual way.

Physical modeling of water-retention capacity of soils

The function of the water-retention capacity of the soil is necessary, for example, when calculating irrigation norms in irrigation agriculture. Various mathematical models are used to approximate the water-retention capacity, which have a number of disadvantages inherent in these models. For example, the absence of physically adequate analytical descriptions for the coefficients of a given function. The use of physical fractal models for predicting and calculating the water-retention capacity of soils seems promising. Application of the fractal model Pore-Solid-Fractal is necessary to perform the calculation of desorption curves of water-retention capacity of some types of alpha-humus and texture-differentiated soils of light particle size distribution has been performed. The calculated data for the drying branches of the WRC are compared with the experimental data. The study of statistical differences between samples (data convergence) was carried out using the Mann-Whitney test (U). The empirical values of the U-test are from 17.5 to 20. The critical value of the U-test for a given number of compared data series at a probability level of 0.99 is 8. The critical value of the U-test for a given sample size is less than the calculated one, respectively, the difference between the series of empirical and the calculated data in the sample are not statistically significant. The fractal model allows calculating the water-retention capacity function of soils with high accuracy.

Beading Mechanism and Performance of Porous Steel Slag Microbead Abrasive

The use of the gas-quenching process for preparing porous bead slag abrasive was investigated in this paper. An X-ray diffractometer, field emission scanning electron microscope, mercury intrusion porosimetry, and stereo microscope were used to analyze the microbead forming mechanism, pore structure, acid–alkali resistance, and polishing properties of porous steel slag microbead abrasives. Results show that the porous steel slag abrasives present a mono-disperse spherical shape with a hard shell and the porosity is 42.36%. The thermodynamic fractal model indicates that the fractal dimension of the abrasive is 2.226, which shows its simple pore structure. The sample has better chemical stability in the polishing fluid than in water, acid, and alkali solution. Therefore, aluminum and copper alloys are used as substrates for polishing tests. The results indicate that the abrasives could effectively improve the quality of the workpiece surface and the polishing efficiency for aluminum alloy was higher than that for copper alloy.

Application of Traditional Cultural Symbols in Art Design under the Background of Artificial Intelligence

In order to solve the declining influence of traditional cultural symbols, the research on traditional cultural symbols has become more meaningful. This article aims to study the application of traditional cultural symbols in art design under the background of artificial intelligence. In this paper, a fractal model with self-combined nonlinear function changes is constructed. By combining nonlinear transformations and multiparameter adjustments, various types of fractal models can be automatically rendered. The convolutional neural network algorithm is used to extract the characteristics of the style picture, and it is compared with the trained picture many times to avoid the problem of excessive tendency of the image with improper weight. The improved L-BFGS algorithm is also used to optimize the loss of the traditional L-BFGS, which improves the quality of the generated pictures and reduces the noise of the chessboard. The experimental results in this paper show that the improved L-BFGS algorithm has the least loss and the shortest time in the time used for more than 500 s. Compared with the traditional AdaGrad method, its loss is reduced by about 62%; compared with the traditional AdaDelta method, its loss is reduced by 46%. Its loss is reduced by about 8% compared with the newly optimized Adam method, which is a great improvement.

Simplified Relation Model of Soil Saturation Permeability Coefficient and Air-Entry Value and Its Application

Based on the Tao and Kong (TK) model and the fractal model of the soil–water characteristic curve, a simplified model of the relationship between the saturated permeability coefficient and the air-entry value is established in this study: ks = k0ψa−2. It is shown that the saturated permeability coefficient of soil is determined by its maximum pore size. In order to facilitate the mutual prediction of saturation permeability coefficient and air-entry value, based on the data of five types of soil in the UNSODA database, the comprehensive proportionality constant k0 of the five types of soil were obtained: sand k0 = 0.03051; clay k0 = 0.001878; loam k0 = 0.001426; sandy loam k0 = 0.009301; and silty clay loam k0 = 0.0007055. Based on the obtained comprehensive proportionality constant k0 and the relationship model between saturated permeability coefficient and air intake value, the air-entry value of five kinds of soils in the existing literature and the SoilVision database were calculated. Comparing the calculated air-entry value with the measured one, the results showed that the model simplifies the traditional air-entry value prediction method to some extent and can effectively predict the air-entry value of different types of soil. On the whole, the model better predicts the air-entry value for sandy, clay, and silty clay loam than loam and sandy loam.