According to modern physical notions, the transition of a material to the nanostructural state is accompanied by dimensional effects in its physical (in particular, mechanical) properties [1, 2]. By the dimensional effects, we imply the entire complex of phenomena associated with the modification of material properties due to a change in the particle size and an increase in the contribution of boundaries to the system properties with decreasing particle size, which becomes comparable with the wavelength of elastic waves. In the mathematical simulation of nanostructural media, two approaches can be distinguished. The first approach consists in the passage from atomic-level models to mesoscale models and is based on the laws of quantum theory. In this case, the medium is considered as a discrete system of particles coupled by the interaction forces determined from the first principles [3]. This approach allows one to understand the nature of physical laws and to explain the origin of a number of the properties having no substantiation in the classical theory.
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