One of the mechanisms of energy transfer between degrees of freedom of dusty plasma system is based on parametric resonance. Initial stage of this process can de described by equation similar to Mathieu equation. Such equation is studied by analytical and numerical approach. The numerical solution of the extended Mathieu equation is obtained for a wide range of parameter values. Boundaries of resonance regions, growth rates of amplitudes and times of onset are obtained. The energy transfer between the degrees of freedom of dusty plasma system can occur over a wide range of frequencies.

Molecular dynamics is applied to calculate diffusion coefficients of n-triacontane C30H62 using Einstein-Smoluchowski and Green-Kubo relations. The displacement 〈Δr2〉(*t*) has a subdiffusive part 〈Δr2〉 ~ *t* α, caused by molecular crowding at low temperatures. Longtime asymptotes of 〈v(0)v(t)〉 are collated with the hydrodynamic tail t-3/2 demonstrated for atomic liquids. The influence of these asymptotes on the compliance of Einstein-Smoluchowski and Green-Kubo methods is analyzed. The effects of the force field parameters on the diffusion process are treated. The results are compared with experimental data.

The development of multi-core processor systems is a demanded branch of science and technology. The appearance of processors with dozens and hundreds of cores poses to the developers the question of choosing the optimal topology capable to provide efficient routing in a network with a large number of nodes. In this paper, we consider the possibility of using multiplicative circulants as a topology for networks-on-chip. A specialized routing algorithm for networks with multiplicative circulant topology, taking into account topology features and having a high scalability, has been developed.

Particles interaction and value of the screening length in dusty plasma systems are of great interest in dusty plasma area. Three inter-particle potentials (Debye potential, Gurevich potential and interaction potential in the weakly collisional regime) are used to solve equilibrium equations for two dusty particles suspended in a parabolic trap. The inter-particle distance dependence on screening length, trap parameter and particle charge is obtained. The functional form of inter-particle distance dependence on ion temperature is investigated and compared with experimental data at 200–300 K in order to test used potentials applicability to dusty plasma systems at room temperatures. The preference is given to the Yukawa-type potential including effective values of particle charge and screening length. The estimated effective value of the screening length is 5–15 times larger than the Debye length.

The article describes the device for selective registration of electrons, protons and heavy ions fluxes from the solar and galactic cosmic rays in the twelve energy ranges, built on a base of diamond detector. The use of the diamond detectors allowed for the creation a device for registration of cosmic particles fluxes at the external spacecraft surface with the resource not less than 20 years. Selective detector is aimed for continuous monitoring of radiation situation on board the spacecrafts, in order to predict the residual life of their work and prompt measures to actively protect the spacecraft when the flow of cosmic particles is sharply increased.

Simulation of electron, ion and metastable excited atom motion and interactions in a low-current discharge between the flat electrodes of a gas- discharge device in argon-mercury mixture is fulfilled. Also influence of gas temperature on both densities and fluxes of particles has been investigated. Distributions of the particle densities along the discharge gap under different mixture temperatures are obtained. It has been demonstrated that the principal mechanism of mercury ion generation was the Penning ionization of mercury atoms by argon metastables, which contribution grows sharply with the mixture temperature due to mercury density increase. Calculations showed that both mercury and argon ion flow densities near the cathode where of the same order already under the relative mercury content of about 10^{-4} corresponding at the argon pressure 10^{3} Pa to the mixture temperature 30 C. Because the mean path length of a mercury ion in the mixture between the resonant charge exchanges on parent gas atoms is much more than that of an argon ion, the energies of mercury ions exceed considerably the energies of argon ions, and they make the main contribution to the physical electrode sputtering. which reduces the service time of the gas- discharge device.

**Abstract**. The article considers the features of super-scalar processors, their way of performing several operations on several pairs of operands simultaneously. The research focuses on the organization of processor pipeline execution operation of several machine instructions in one processor core. The simulating kit was developed for better understanding of a processor core microarchitecture. It includes two parts: program and methodical recommendations with multiple task options. The simulating kit demonstrates the pipeline architecture consisting of two clusters: front-end and back-end and the principle of translating complex multi-cycle CISC-like instructions into simpler RISC-like micro-operations. The main types of machine instructions are considered: data transfer between registers and memory cells (four variations), data processing of couple of operands from registers and memory cells (four variations), conditional jump to the specified address. The program-simulator makes it possible to conduct a more detailed simulation of one of the three mechanisms for calculations accelerating in the processor core: multi-functional (super-scalar) processing, out-of-order processing, speculative instructions execution after the branch prediction. The simulating kit is used in educational process when training masters of Higher School of Economics National Research University.

Object of this research are macroeconomic indicators, which are important to

descript economic situation in a country. Purpose of this work is to identify these indicators

and to analyze how the state can affect these figures with available instruments. Here was

constructed a model where the targets can be calculated from raw data – tools in the field of

economic policy. Software code that implements all relations among the indicators and allows

to analyze with high accuracy, sufficiently successful economic policies and with the help of

some tools, you can achieve better results. This model can be used to forecast macroeconomic

scenarios. The corresponding values of the objective (outcome) variables are set as a

consequence of the configuration data of the previous period, subject to external influences and

depend on the instrumental variables. The results may be useful in economical predictions. The

results were successfully checked on real scenarios of Russian, European and Chinese

economics. Moreover, the results can be applied in the field of education. Program is available

to use as “economical game” the educational process of the University, in which you can

virtually implement various macroeconomic scenarios, draw conclusions about their success.

We study an optimal control problem for a nonlinear spherical inverted pendulum on a movable base. As the cost functional, the mean-squared deviation of the pendulum from the upper equilibrium is considered, so optimal controls stabilize the pendulum at the unstable upper position. We show that the problem under consideration posses a singular point of the second order and there are spiral-similar solution which attains the singular point in finite time.

Optimal control problem for the system of partial differential equations of hyperbolic type is considered. By using the Fourier method this problem is reduced to the optimal control problem for the corresponding Fourier coefficients. For some special initial data we prove the existence of optimal solutions with a countable number of switchings on a finite time interval and optimal spiral-like solutions which attain the origin in a finite time making a countable number of rotations. The problem of controlling the vibrations of the Timoshenko beam is considered as an example of the optimal control problem for linear system of PDE.

Dynamics of solitons is considered in an extended nonlinear Schrödinger equation, including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term (scattering on damping low-frequency waves, nonlinear dispersion and inhomogeneity of the spatial second-order dispersion (SOD). It is shown that wave-number downshift by the pseudo-SRS may be compensated by upshift provided by spatially increasing SOD with taking into account nonlinear dispersion. The equilibrium state is stable for negative parameter of nonlinear dispersion and unstable for positive one. The analytical solutions are verified by comparison with numerical results

This paper discusses the results of the application method of spatial correlation functions on a glass-forming liquid of a pure metal melt by performing molecular dynamics simulations. We define a high-order correlation function that quantifies a spatial correlation of single-particle displacements in liquids and amorphous systems. Time dependencies of the different 4-point spatial functions for supercooled and normal melt are obtained.

Molecular dynamics study of shear viscosity behavior of liquid aluminum is performed. The embedded atom method potential is used at the simulation of isobaric cooling. The viscosity is calculated using the Green–Kubo formula. The stress autocorrelation functions are obtained in the range 300–1200 K. The calculated kinematic viscosity is in agreement with the experimental data for the temperatures above melting temperature. The steep change of the shear viscosity is found below 650 K which we associate with the glass transition and is in a good agreement with the temperature which is obtained using the calorimetric criterion Kolotova et al (2015 J. Non-Cryst. Solids 429 98). The viscosity coefficient can not be calculated using the direct atomistic simulations below that temperature

We have developed the deposition technology of WSi thin films 4 to 9 nm thick with high temperature values of superconducting transition (Tc∼4 K). Based on deposed films there were produced nanostructures with indicative planar sizes ∼100 nm, and the research revealed that even on nanoscale the films possess of high critical temperature values of the superconducting transition (Tc∼3.3-3.7 K) which certifies high quality and homogeneity of the films created. The first experiments on creating superconducting single-photon detectors showed that the detectors' SDE (system detection efficiency) with increasing bias current (I b) reaches a constant value of ∼30% (for X=1.55 micron) defined by infrared radiation absorption by the superconducting structure. To enhance radiation absorption by the superconductor there were created detectors with cavity structures which demonstrated a practically constant value of quantum efficiency >65% for bias currents Ib>0.6-Ic. The minimal dark counts level (DC) made 1 s-1 limited with background noise. Hence WSi is the most promising material for creating single-photon detectors with record SDE/DC ratio and noise equivalent power (NEP).

We have developed the deposition technology of WSi thin films 4 to 9 nm thick with high temperature values of superconducting transition (Tc~4 K). Based on deposed films there were produced nanostructures with indicative planar sizes ~100 nm, and the research revealed that even on nanoscale the films possess of high critical temperature values of the superconducting transition (Tc~3.3-3.7 К) which certifies high quality and homogeneity of the films created. The first experiments on creating superconducting single-photon detectors showed that the detectors‟ SDE (system detection efficiency) with increasing bias current (Ib) reaches a constant value of ~30% (for =1.55 micron) defined by infrared radiation absorption by the superconducting structure. To enhance radiation absorption by the superconductor there were created detectors with cavity structures which demonstrated a practically constant value of quantum efficiency >65% for bias currents Ib0.6Ic. The minimal dark counts level (DC) made 1 s-1 limited with background noise. Hence WSi is the most promising material for creating single-photon detectors with record SDE/DC ratio and noise equivalent power (NEP).

We demonstrate superconducting niobium nitride nanowires folded on top of lithium niobate substrate. We report of 6% system detection efficiency at 20 s-1 dark count rate at telecommunication wavelength (1550 nm). Our results shown great potential for the use of NbN nanowires in the field of linear and nonlinear integrated quantum photonics.

The new version of the software system DASS designed to solve multicriteria problems using methods of the criteria importance theory is described. A new approach has been developed by the authors, allowing to take into account inaccurate and fuzzy information about preferences of decision makers.

A research of the diffusion of an ion in a liquid is carried out. Dependences of the diffusion coefficient on the ion-molecule potential, ion mass, liquid temperature and density are defined. The results are related to the ion solvation. The classical molecular dynamics method is applied. The effect of the ion solvation is discovered. Firstly, ion mass has no influence on the diffusion coefficient. This is because the total mass of the cluster formed by the ion and the ion solvation shell varies slightly while the mass of the ion changes significantly. In addition, the dependence on short-range interaction is found to be rather weak. The dependence of the diffusion coefficient on long-range interaction is found to be really stronger than on short- range. The ion velocity autocorrelation function calculated reveals a strong oscillatory character superimposed on the conventional functional liquid-type form. It reflects the oscillations of the ion inside the solvation shell. The relation between the ion mobility and temperature is found to be of the Arrhenius-type form.

Using the analytical approach introduced in our previous papers we analyse the possibilities of optimization of size and structure of active region of semiconductor quantum dot lasers emitting via ground-state optical transitions. It is shown that there are optimal length' dispersion and number of QD layers in laser active region which allow one to obtain lasing spectrum of a given width at minimum injection current. Laser efficiency corresponding to the injection current optimized by the cavity length is practically equal to its maximum value.

For the modern software that uses network communication protocols the problem of the ensuring reliability is acute. To solve such an important problem the stress testing is used. This type of the testing involves the generation of a large number of the test data, including sets of network packets. Reducing the stored data after the testing process is the main task. This task can be solved by clustering the set of received packets. To solve this problem it is proposed to use the clustering algorithm for categorical data of CLOPE. This algorithm allows to cluster datasets without the information about the source clusters. It has the low computational complexity and ease of implementation. The article describes the preparation and results of sets of the network packets processing experiments. The article shows that the CLOPE algorithm can be effectively used for the clustering network packets received during stress testing. The results of the research extend the toolkit for the SW stress testing process.

The paper presents the automated system intended to prevent industrial-caused diseases of workers, the basis of which is represented by algorithms of preventing several negative functional conditions (stress, monotony). The emergence of such state shall be determined based on an analysis of bioelectric signals, in particular, skin-galvanic reactions. Proceeding from the dynamics of the functional state, the automated system offers to perform an optimized set of measures to restore the health of the worker. Implementation of an automated system is presented in Visual Programming system LabVIEW.