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The article describes an experimental study aimed at identifying the peculiarities of cognitive processing of Russian emotional words – diminutives as well as the influence of the bilingualism factor on this process. The purpose was solved in two stages: a survey and an RT-experiment. Each of the stages was carried out sequentially first in a group of native Russian speakers, then in Turkic-Russian bilinguals. Based on the data obtained during the first stage, we found that emotionality interacts with the psycholinguistic parameters (age of acquisition, type of evaluation, contextual implementation, subjective frequency) in the perception of words by native speakers and bilinguals. It was demonstrated by the presence of correlations between the parameters. The results of the RT-experiment showed that both groups of participants had significant differences in the cognitive processing of neutral and emotional words. Summing up the results, it can be concluded that the bilingualism type – unbalanced with the dominance of the L2 has influence on the perception and cognitive processing of emotional words.

The authors analyze implementation of the Strategy of development of the information society, determine the recent changes in the exiting civil & legal and anti-monopoly regulation of relations in the sphere of the digital economy, and present suggestions for improving the law in this spheres for the purpose of optimal normative legal regulation of the digital economy.

In this work, we consider the elasticity problem in fractured media. For the efficient numerical solution, we present a Generalized Multiscale Finite Element Method (GMsFEM). GMsFEM is used for the construction of a coarse grid approximation of the problem by solution of the local spectral problems. We consider two types of the multiscale basis functions: (1) CG-GMsFEM with continuous multiscale basis functions and (2) DG-GMsFEM with discontinuous multiscale basis functions. The result of the numerical solution for the two-dimensional model problem is presented to show the performance of the presented multiscale method for fractured media. We compute error between the multiscale solution with the fine-scale solutions by choosing different numbers of multiscale basis functions.

In this paper, we consider a mixed dimensional discrete fracture model with highly conductive fractures. Mathematically the problem is described by a coupled system of equations consisting a d - dimensional equation for flow in porous matrix and a \((d-1)\) - dimensional equation for fracture networks with a specific exchange term for coupling them. For the numerical solution on the fine grid, we construct unstructured mesh that is conforming with fracture surface and use the finite element approximation. Fine grid approximation typically leads to very large systems of equations since it resolves the fracture networks, and therefore some multiscale methods or upscaling methods should be applied. The main contribution of this paper is that we propose a new upscaled model using Non-local multi-continuum (NLMC) method and construct an effective coarse grid approximation. The upscaled model has only one additional coarse degree of freedom (DOF) for each fracture network. We will present results of the numerical simulations using our proposed upscaling method to illustrate its performance.

We consider a mathematical model for simulation of the unsaturated flow problems in heterogeneous porous medium that describes by the Richards equation. To resolve all heterogeneity, we construct fine grid and construct finite element approximation. For dimension reduction of the discrete system, we construct multiscale solver for coarse grid solution using Generalized Multiscale Finite Element Method (GMsFEM). We generate multiscale basis functions by solution of the local spectral problems. We present numerical result and compare relative error for different number of the multiscale basis functions for 2D and 3D model problems.

In this work, we consider the poroelasticity problems in heterogeneous porous media. Mathematical model contains coupled system of the equations for pressure and displacements. For the numerical solution, we present a Generalized Multiscale Finite Element Method (GMsFEM). This method solves a problem on a coarse grid by construction of the local multiscale basic functions. The procedure begins with construction of multiscale bases for both displacement and pressure in each coarse block. Using a snapshot space and local spectral problems, we construct a basis of reduced dimension. Finally, after multiplying by a multiscale partitions of unity, the multiscale basis is constructed in the online phase and the coarse grid problem then can be solved for arbitrary forcing and boundary conditions. We compare the solutions by choosing different numbers of multiscale basis functions. The results show that GMsFEM can provide good accuracy for two and three dimensional problems in heterogeneous domains.

In this work, we consider wave propagation in fractured media. The mathematical model is described by Helmholtz problem related to wave propagation with specific interface conditions on the fracture in the frequency domain. We use a discontinuous Galerkin method for the approximation by space that help to weakly impose interface conditions on fractures. Such approximations lead to the large system of equations and computationally expensive. In this work, we construct a coarse grid approximation for effective solution using Generalized Multiscale Discontinuous Galerkin Method (GMsDGM). In this method, we construct a multiscale space using solution of the local spectral problems in each coarse elements. The results of the numerical solution for the two-dimensional problem are presented for model problems of the wave propagation in fractured media.

In this work, we consider the coupled systems of a partial differential equations, which arise in the modeling of thermoelasticity processes in heterogeneous domains. Heterogeneity of the properties requires a high resolution solve that adds many degrees of freedom that can be computationally costly. For the numerical solution, we use a Generalized Multiscale Finite Element Method (GMsFEM) that solves problem on a coarse grid by constructing local multiscale basis functions [1, 2, 3]. We construct multiscale basis functions for the temperature and for the displacements on the offline stage in each coarse block using local spectral problems [4, 5, 6, 7]. On the online stage we construct coarse scale system using precalculated multiscale basis functions and solve problem with any forcing and boundary conditions. The numerical results are presented for heterogeneous and perforated domains.

In this work we consider the numerical simulation of the dynamics of soil temperature in a permafrost area. The mathematical formulation of the problem with appropriate initial and boundary conditions is presented. A computational algorithm is based on the finite element approximation in space. To approximate in time we use the standard fully implicit scheme with linearisation from previous time layer. We present results of research of temperature stabilization time and the impact of presence of piles on the temperature of the surrounding soil. Numerical comparisons of two-dimensional and three-dimensional model problems are presented.

We consider an unconditionally stable splitting scheme for solving coupled systems of equations arising in poroelasticity and thermoelasticity problems. The scheme is based on splitting the systems of equation into physical processes, which means the transition to the new time level is associated with solving separate sub-problems for displacement and pressure/temperature. The stability of the scheme is achieved by switching to three-level finite-difference scheme with weight. We present stability estimates of the scheme based on Samarskii’s theory of stability for operator-difference schemes. We provide numerical experiments supporting the stability estimates of the splitting scheme.

Among inverse problems for PDEs we distinguish coefficient inverse problems, which are associated with the identification of the right-hand side of an equation using some additional information. When considering time-dependent problems, the identification of the right-hand side dependences on space and on time is usually separated into individual problems. We have linear inverse problems; this situation essentially simplify their study. This work deals with the problem of determining in a multidimensional parabolic equation the right-hand side that depends on time only. To solve numerically a inverse problem we use standard finite difference approximations in space. The computational algorithm is based on a special decomposition, where the transition to a new time level is implemented via solving two standard elliptic problems.

In this work we consider the coupled linear system of equations for temperature and displacements which describes the thermoelastic behaviour of the body. For numerical solution we approximate our system using finite element method. As model problem for simulation we consider the thermomechanical state of the ceramic substrates with metallization, which are used for the manufacturing of light-emitting diode modules. The results of numerical simulation of the 3D problem in the complex geometric area are presented.