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Information × Registration Number 0224U002472, 0121U110154 , R & D reports Title Technologies and Tools for Mathematical Modeling, Optimization and System Analysis of Nonequilibrium Physical Processes popup.stage_title Head Sokolovskyi Yaroslav I., Доктор технічних наук Registration Date 15-02-2024 Organization Ukrainian national forestry university popup.description2  Report on the research work: 158 pages, 58 figures, 20 tables and 239 references. The work is devoted to solving the scientific problem of developing mathematical modeling and software for the study of interconnected physical and mechanical fields in capillary-porous materials with a fractal structure, including models of cellular automata. Based on the laws of thermodynamics of irreversible processes, mechanics of hereditary media and the finite element method, new mathematical models for calculating strain-relaxation and heat and mass transfer processes were developed. Such fractional-order mathematical models describe the evolution of physical systems with residual memory, which are intermediate states between Markov systems and systems characterized by full memory. In particular, the fractionality index indicates the fraction of the system's states that are preserved throughout the entire process of its functioning. Additionally, cellular automata models are used in this work to more accurately describe the microstructure of capillary-porous materials. These cellular automata allow to take into account the internal geometry of materials and their interaction at the micro level, which is important for obtaining more accurate modeling results. Based on object-oriented programming technologies, algorithms and a package of application programs were developed for the automated calculation of strain-relaxation and heat and mass transfer fields in capillary-porous materials with a fractal structure, including the consideration of cellular automata for a more detailed analysis of the system microstructure. The tools for software implementation of operator algorithms for numerical realization of equations describing physical fields in fractal systems and their interaction at the level of cellular automata have been developed. Key words: mathematical model, fractal structure, fractional integro-differentiation, non-isothermal moisture transfer, viscoelastic deformation. Product Description popup.authors Boretska Iryna B. Kroshnyi Ihor M. Storozhuk Oleksandr L. Yatsyshyn Svitlana I. popup.nrat_date 2024-02-15 Close