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ПЕРЕВОД НА АНГЛИЙСКИЙ: MODERN METHODS OF MATHEMATICAL MODELING IN NANOMATERIALS SCIENCE

Silantev Danila Mikhailovich  (Graduate student MSTU «STANKIN» )

The article presents an overview of modern mathematical modeling methods in the field of nanomaterials and quantum systems. Key approaches are examined, including the solution of the Schrödinger equation for electronic structure analysis, quantum chemistry methods (Hartree–Fock, OVGF), molecular dynamics with embedded-atom potentials (EAM), finite element modeling of nonstationary thermal processes, and stochastic methods for describing mechanical effects. Special attention is paid to modeling heterogeneous systems such as mesoporous materials, doped nanocrystals, and two-dimensional metal–silicon structures. It is shown that combining various methods allows for a balance between calculation accuracy and computational efficiency. The research results demonstrate the importance of mathematical modeling for predicting material properties and optimizing technological processes.

Keywords:Schrödinger equation, quantum chemical calculations, molecular dynamics, finite element method, nanomaterials, mesoporous structures, doped nanocrystals, density functional theory (DFT), electronic structure, phase transitions, stochastic modeling, thermal processes, mechanical properties, computational efficiency.
 

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Citation link:
Silantev D. M. ПЕРЕВОД НА АНГЛИЙСКИЙ: MODERN METHODS OF MATHEMATICAL MODELING IN NANOMATERIALS SCIENCE // Современная наука: актуальные проблемы теории и практики. Серия: Естественные и Технические Науки. -2025. -№08. -С. 126-130 DOI 10.37882/2223-2966.2025.08.31
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