Modeling of Soil Cutting at Different Attack Angles of the Ploughshare of the Rack Ripper Using Fractal Analysis Methods

The level of soil compaction is influenced by physical and mechanical properties, climatic conditions, the amount of annual precipitation, the type of cultivated crops, and other factors. Excessive compaction of the soil impairs water permeability and air access to the roots, resulting in reduced crop yields, increased soil erosion, reduced fertilizer efficiency, which leads to an increase in the cost of material and technical resources for tillage. Therefore, it is important to solve this problem with minimal energy and material costs. Such a solution is the loosening of the soil, which can be done naturally and with the help of mechanical loosening. (Research purpose) The research purpose is in evaluating the effectiveness of loosening the soil with a U-shaped ripper at different angles of the ploughshare using fractal analysis methods, which is necessary to reduce additional loads during further soil treatment. (Materials and methods) A dirt channel with a special cart was used to consider physical models of meliorative machines and specialized working equipment. (Results and discussion) Author conducted six experiments in a soil tray for each corner of the ploughshare separately. Nineteen ground sections were made. The structure of the soil before and after treatment depends on the mode of operation of the ripper model and the design features of its working bodies. (Conclusions) The more energy is spent on the treatment of homogeneous areas, the more the soil structure changes. To quantify the structural changes in the nature of the cultivated soil, we used its fractal characteristics, in particular, the fractal dimension. The soil sections have fractal properties, and, accordingly, fractal methods can be used for their analysis. The article proves the applicability of fractal methods in the analysis of the quality of tillage and the degree of its loosening.

A comparison of fractal methods for evaluation of hydraulic fracturing surface roughness

Surface roughness is a crucial parameter in the hydraulic fracturing process, affecting rock toughness, fluid flow and proppant transport; however, the scale-dependent nature of hydraulic fracture surfaces is not well studied. In this paper, we examined four fractal methods, compass, box-counting, variation and roughness-length, to evaluate and compare the fractal dimension of the surface roughness profiles created by laboratory hydraulic fracturing. Synthetic surface profiles were generated by the Weierstrass-Mandelbrot function, which was initially used to test the accuracy of the four methods. Each profile had a predefined fractal dimension that was revisited by these methods. Then, the fractal analysis was performed for experimental fracture surfaces, which were created by a hydraulic fracturing experiment in a true triaxial situation. By comparing fractal analysis results, we found that for both synthetic and laboratory fracture height profiles, the roughness-length method provides a relatively more reliable estimation of the fractal dimension. This method predicts the dimension for synthetic surface within an error of less than 1%, considering a wide range of surface heights from centimetres down to micrometres. By increasing the fractal dimension of surface profiles, the error of fractal estimation increased for all four methods. Among them, the variation method provided the closest results to the roughness-length method when considering both experimental and synthetic surfaces. The evaluated fractal dimension may provide a guideline for either field- or laboratory-scale hydraulic fracturing treatments to evaluate the effects of surface roughness on fracture growth.

Application of Fractal Methods to Ensure the Cyber-Resilience of Self-Organizing Networks

In the article the approach and methods of ensuring the security of VANET-networks based on automated counteraction to information security threats through self-regulation of the network structure using the theory of fractal graphs is provided.

Geochemical Anomaly Separation by Statistical and Fractal Methods in the Sehezar Valley of Tonekabon – Northern Iran

Sehezar area is located in southern Tonokabon in Mazandaran province, north of Iran, near the Tarom – Hashdtjin belt. The existence of granitoid masses in the region can be important in terms of the potential of mineralization. Geochemical anomaly separation from the background is one of the important steps in mineral exploration. In the past decades, geochemical anomalies have been identified by means of various methods. Some of these separation methods include: statistical analysis methods (like univariate, bivariate, multivariate statistics), spatial statistical methods and fractal and multi-fractal methods. To identify the anomalous area, 71 stream sediment samples were collected from the area and analyzed by the ICP-MS method, and then interpreted. Initially, data were normalized and afterwards, univariate analysis (threshold limit and screening (P.N) methods) was used, in which results of the probable and definite anomaly of the threshold method were confirmed by the P.N screening method. Finally, the maps of the anomal zones were drawn. Then, bivariate analysis (Pearson correlation coefficients) and multivariate analysis on normal data were performed on SPSS software, in which factor analysis and cluster analysis were used for multivariate analysis. As a result of using the factor analysis method, six factors were identified and factor maps were drawn by the Surfer software. Also, by using cluster analysis, the variables were divided into two groups. In order for a better separation of the geochemical anomaly from the background, in addition to the threshold method, the Concentration - Area fractal method was used. Here, the fractal geometry using full-logarithmic graphs of the Concentration - Area obtained is capable of separating the stairs of different sections (background, threshold, and anomaly) with respect to the angle coefficient of the Concentration - Area plot. Then, in conclusion, results of these methods were compared and investigated, and finally, the anomalies area maps of the Au, Ag, Cu, Fe, W elements were drawn by Concentration - Area fractal and threshold methods and anomalous zones were introduced.