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The electronic structure of the Sigma 5(210) grain boundary in silicon was calculated by the first-principles, self-consistent, linear muffin-tin orbitals/tight-binding representation method on the basis of the atomic structure simulated by the bond orbital model. The calculated electronic structure is found to have localized and resonant defect states, which are caused by the distortions of the atomic structure at the grain boundary. Sharply localized states in the pseudo-gap were observed along with splitting of s states and dissipation of s-p mixed states. A rehybridization effect was revealed at the grain boundary on the atoms with strongly distorted bonds. However, there are no states inside the band gap. The increase of the s-state occupancy in comparison with the p-state occupancy appeared on the atoms with strongly distorted bonds at the grain boundary. The relationship between local electronic structure and local arrangement of the atoms is discussed.

A problem of surface waves simulation is considered there in the context of combating oil spills. Being independent of waves penetrating into water, oil is disposed in sea as floating surface slicks and as drops suspended in water thickness. An oil surface slick incurs of transferring by wind and current actions, on the one hand, and of a variety of transforming processes, on the other hand. Gravitational spreading is one of the most influent transforming processes for oil on the sea surface. Among physical problems, there are dynamics of thin films of petroleum products on the sea surface and the need to consider moving on the waved sea-atmosphere border. The oil penetration into the water thickness occurs during the dispersion process --- of the transfer of oil from the water surface to the water phase as a result of wave collapse. The carried away oil splits into drops of different sizes which spread and diffuse into the water thickness. The factors such as droplet size, buoyancy, and turbulence affect dispersion stability. The main sources of dispersion energy are collapsing waves formed by wind on the surface of a water body. We suggest using a 2D surface wave model based on the dynamics of interacting particles. In contrast to complex hydrodynamic and spectral models, that makes it possible to estimate quite simply and effectively the proportion of dispersed oil pollution carried from the surface to the depth of the sea area.

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