We investigate the distribution of the electron density and the potential in a quantum wire coupled to reservoirs, treating this structure as a unified quantum system and taking into account the Coulomb interaction of electrons. The chemical potential difference that exists between a decoupled, isolated quantum wire and the reservoirs gives rise to charge transfer in the coupled system. We show that the quantum wire can be charged positively or negatively or remain neutral as a whole, depending on such factors as the wire radius and the background charge density in the wire. The magnitude of the charge and its sign are to a large extent determined by the exchange interaction of the electrons in the wire. Using a Hartree-Fock approach, we develop a model of a quantum wire which includes the reservoirs. This model allows us to find the self-consistent distribution of the electron density and the potential in the wire both at equilibrium and in the presence of transport. The linear conductance is investigated as a function of the chemical potential. The nonadiabatic transition from the reservoirs to the wire leads to conductance oscillations caused by multiple scattering of electron waves. The period of the oscillations depends on the charge acquired by the wire and the exchange energy. We find that the exchange interaction strongly enhances the Friedel oscillations near the contacts. However, they do not noticeably suppress the conductance because the wire has a finite length and is charged. Under far from equilibrium conditions, which appear when the applied voltage exceeds the Fermi energy in the wire, the system becomes unstable with respect to fluctuations of the electric potential and the electron density. The instability results in the appearance of multistable electron states.

An original numerical algorithm for calculating the gas parameters around a reentry vehicle was described and tested. It is based on a system of Quasi Gas Dynamics (QGD) equations and its approximations on hybrid meshes, which suppose adaptive, locally thickening meshes including both rectangular and triangular cells. The results of the calculations on a sequence of condensed meshes for Mach number values of 2, 5, and 12 are presented. These results correspond to well-known data and demonstrate the high efficiency of the algorithm.

Статья посвящена суперкомпьютерному моделированию термодинамического равновесия в микросистемах, содержащих разные вещества, находящиеся в различных агрегатных состояниях. В качестве примера нами рассмотрена система газ-металл, в которой в качестве газа используется азот, в качестве металла - никель. Такой выбор обусловлен тем, что рассматриваемая микросистема является основой многих технических приложений. В том числе, она используется в установках сверхзвукового холодного газодинамического напыления наночастиц на поверхности перспективных углеродсодержащих материалов. На первом этапе исследований представляет интерес равновесное состояние микросистемы азот-никель. Для моделирования процесса установления термодинамического равновесия в такой системе применен молекулярно-динамический подход. Выбранный численный алгоритм его реализации базируется на конечно-разностной схеме Верле. Для ускорения вычислений предложен параллельный алгоритм и выполнена его реализация в рамках технологий MPI и OpenMP. С помощью разработанной программы исследован процесс установления термодинамического равновесия как в чистых компонентах (азоте и никеле) при нескольких значениях температуры, включая комнатную, так и в системе азот-никель. В численных экспериментах определены как оптимальные параметры методики расчета, в том числе эффективность распараллеливания при использовании процессоров с различной архитектурой, так и физические параметры моделируемого процесса. This paper is devoted to the supercomputer modeling of thermodynamic equilibrium in microsystems containing different substances in various aggregate states. As an example, a nitrogen-nickel system is considered. This choice is due to the fact that such a microsystem is the basis of many technical applications, including the devices of supersonic cold gas-dynamic sputtering using nanoparticles on the surfaces of perspective carbonaceous materials. At the first stage of studies, the equilibrium state of a nitrogen-nickel microsystems is of interest. The molecular dynamic approach is used to model the thermodynamic equilibrium in this microsystem. The chosen numerical algorithm of its implementation is based on the Verlet finite-difference scheme. In order to increase the computational speedup, a parallel algorithm is proposed; its implementation is performed using the MPI and OpenMP technologies. The developed parallel solver is employed to study the establishment of thermodynamic equilibrium in the pure components (nitrogen and nickel) at several temperatures, including room temperature, and in the nitrogen-nickel microsystem. In the numerical experiments, the optimum parameters of the calculation procedure (including the efficiency of parallelization using processors of different architecture) and the physical parameters of the modeled process are found.

A model of the averaged quasihydrodynamic system of equations governing small-scale turbulence is proposed. In the case of plane geometry the model is tested against the problem of the flow past a rectangular cylinder. For this problem conservative finite-difference schemes on a rectangular grid are constructed and the algorithms of their numerical implementation are developed. Numerical experiments show that the model describes well the turbulent flow, both qualitatively and quantitatively. The results obtained are in good agreement with the results of other authors and the experimental data.