THEORETICAL, PRACTICAL, SOFTWARE AND TECHNICAL BASES OF THE COURSE «METHODS OF FRACTAL ANALYSIS»

This paper describes three bases of the course «Methods of fractal analysis», developed in the department of ‘Standardization, metrology and certification’ of the Moscow State University of Mechanical Engineering (MAMI). The theoretical basis includes academic papers in the field of fractals, fractal analysis and fractal geometry, which form the basis of lectures on the course. The program includes four computer programs: «Nova», «Gwyddion», «Fractan», «MyTestX». The first two are used for a scanning probe microscope and applied as tools of fractal analysis of the material surface layer. The paper presents features of their work and identifies strengths and weaknesses. Moreover, it presents analysis of algorithm of fractal processing, embedded in the program «Nova» due to which the high accuracy of fractal analysis of mathematical and physical structures are revealed. The program «Fractan» is recommended for practice work on the analysis of time series data on basis of Hurst’s method. A set of educational resources forming practical basis has been developed for seminars. The program «MyTestX» has been selected for computer evaluation of students’ knowledge in the form of a computer test. This program and the previously mentioned software products are included in the block diagram of the practical session on the discipline «Methods of fractal analysis». Arranging and conducting classes on the discipline «Methods of fractal analysis» considering the proposed basis and the block diagram allow students to master the general cultural and professional competences in major 221700.62 «Standardization and Metrology» (for example, research, analysis of vital information, technical data, indicators and results, their generalization and systematization; making calculations with the use of modern hardware; conducting experiments according to preset processing methods and results analysis; making descriptions and data preparation for scientific reviews and publications). In prospect we are planning to include in the course «Methods of fractal analysis» practical classes on fractal analysis of samples using scan multi-microscope SMM-2000, which is at the disposal of the University of mechanical engineering within the framework of implementation of the strategic development Program. This makes it possible to study the influence of fractal dimension on service properties of materials obtained by modern processing methods.

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