In this paper, we present a new mathematical model of the interaction of two languages. In the model, we distinguish percentages of people who speak a non-target language, a target language with low ...and high proficiency, and both languages considering the low and high proficiency levels in the target language. Therefore, the solution consists of five fields. Furthermore, we assume the diffusive and convective spread of the languages, considering the overflow between them. Thus, the mathematical model is defined by a coupled system of partial differential equations for the five fields.
Since the mathematical model is coupled and the medium is heterogeneous, we have implemented a multiscale method. The proposed multiscale method is based on the Generalized Multiscale Finite Element Method (GMsFEM). In addition to offline multiscale basis functions, we also construct online multiscale basis functions. The online basis functions can account for changes in the heterogeneity of the medium caused by migration flows. Numerical results have shown that such online enrichment can significantly improve the accuracy of multiscale modeling.
In this paper, we propose a mathematical model of the interaction of two languages. In our model, we consider two languages, though it can be generalized to multiple languages, which compete in a ...heterogeneous environment, consisting of highly varying properties related to the dynamics of the interaction. We use coupled convection–diffusion–reaction equations to describe the processes. Each equation describes the dynamics of one of the languages and contains terms related to the stand-alone dynamics and some coupling terms. The coupling terms represent the interaction between languages. We propose a numerical approach for solving the proposed model equation. In particular, we consider various inhomogeneities associated with cities and countryside, where languages are used differently (e.g., Sakha republic). These dynamics are essential for understanding the evolution of languages (one being dominant) and linguistic ecology that studies languages and their use in real/social life. Because of heterogeneities associated with geography, we use a multiscale approach. The proposed multiscale approach designs special basis functions to represent the small-scale information on larger scales. This way, we can solve the problem on a much coarser grid. Numerical results are presented that describe the dynamics and interaction of two languages. The main novelty of the paper consists of the proposed model and a multiscale algorithm.
In this paper, we propose a new mathematical model of language interactions considering bilingualism. We assume diffusive and convective language spreads with language exchange terms. The resulting ...model consists of a coupled system of partial differential equations for three functions. We develop a finite element approximation of the mathematical model using implicit and partially explicit time schemes. In addition, we present a partial learning approach for this problem using a partially explicit discretization. In this method, we train a Deep Neural Network to predict the values of the difficult-to-compute (implicit) part of the solution at some observed points. We then perform linear temporal interpolation and spatial interpolation using the Proper Orthogonal Decomposition (POD) and the Discrete Empirical Interpolation Method (DEIM).
To test the proposed approach and the model, we consider two model problems. Each of them simulates different language situations. For each problem, we compute the relative errors of the proposed approach and define the different parts of the error. The numerical results show that the proposed approach can provide good accuracy while reducing computational costs.
In the Republic of Sakha (Yakutia), from 2001 to 2020, the incidence of asthma is increasing from 4.1 per 1000 population to 12.5 per 1000 population. Considering that currently one of the most ...effective modern methods of treating severe asthma is genetic engineering biological therapy, research on biologically active medications, as well as the lack of research on this problem in the Yakut population, our work seems relevant. The purpose of this study was to evaluate the effectiveness of treatment with genetic engineering biological drugs (GEBD) in patients with severe asthma in the Yakut population. The study included 17 patients suffering from severe asthma. In 5 patients with severe asthma, the effectiveness of the following GEBD was assessed: anti IL-4, IL-13 drug, in 6 patients – anti IL-5 drug, in 6 patients – anti IgE drug. The effectiveness of treatment was assessed using the ACQ-5 symptom control test, the number of exacerbations over the previous 12 months of asthma therapy, IgE levels, the absolute number of eosinophils, indicators of external respiratory function, and the need of patients for additional asthma therapy. Before initiation, 8 (47.10%) patients had exacerbations and sought medical help; 2 patients were hospitalized in the pulmonology department; after 6 and 12 months, no exacerbations or hospitalizations in specialized hospitals were registered. When using a GEBD for 12 months, the need for inhaled corticosteroids decreased in micrograms/day. Thus, treatment of severe asthma in the Yakut population with GEBD makes it possible to achieve control over its symptoms, reduce the risk of severe exacerbations and the number of hospitalizations, and prevent side effects from high doses of standard therapy.
Radial distributions of the electric potential and plasma density oscillations have been measured in the T-10 tokamak ohmic plasma. Radial distributions of the amplitude and frequency of the geodesic ...acoustic mode are plotted according to the data on the fluctuations of the electric potential of the plasma, and radial distributions of the amplitude and frequency of the quasi-coherent mode are plotted according to the data on the fluctuations of the plasma density. The quasi-coherent mode corresponds to the major part of the turbulent particle flow, the geodesic acoustic mode as a high-frequency branch of zonal flows is involved in the turbulence regulation, which makes these objects very important for plasma physics. The paper presents the results obtained in different operating modes of the T-10 tokamak.
Heavy ion beam probe (HIBP) is a unique plasma diagnostics that makes it possible to measure the electric potential φ of high-temperature plasma and its fluctuations
, as well as the density
and ...poloidal magnetic field
fluctuations. Position of the point of performing measurements in the plasma vertical cross-section depends on the beam energy and angle of its entrance into the plasma. The variation of these two parameters makes it possible to construct a two-dimensional (2D) detector grid, which covers the domain of possible measurements. The measurement results obtained in the detector grid points provide for constructing 2D distributions of plasma parameters. For the OH and ECRH stages of the T-10 tokamak shots, 2D distributions of the plasma electric potential are presented for the regime with the on-axis magnetic field of
B
t
= 2.2 T, plasma current of
I
pl
= 230 kA, line-average density of
≈ 1.1 × 10
19
m
–3
and off-axis ECRH power of
P
ECRH
= 1.7 MW.
The paper discusses the applicability of the horizontal-to-vertical spectral ratio for ground motion (H/V method) to estimate the seismic intensity increment and trace the bedrock surface covered by ...soil layers. The first issue is the classic seismic microzoning problem; the second is related to structural mapping of the upper part of the geological profile. The authors assess the possibility of using a single station to estimate the intensity increment without synchronization of data at a given point at a site with records based on reference rocks. It is shown that such an approach is invalid, because the maximum variations in the H/V ratio during a day may reach 2.7 times; a degree of intensity of 0.8 will correspond to such variation. At the same time, it is shown that the resonance frequencies of soil layers are stable. If the mean velocities of seismic waves are known at some points of profile surface, the position of the underlying bedrock top can be traced with confidence.
The development of the cryolithozone requires building and numerically implementing mathematical models of multiphysics thermoelastic processes involving with first-order phase transitions and ...occurring in the foundations of engineering structures and buildings. Numerical implementation of such models is associated with computational difficulties due to various types of heterogeneities in applied problems and the nonlinearity of governing equations, which require very fine grids, increasing computational costs. We develop a numerical method for solving a thermoelasticity problem with phase transitions based on the generalized multiscale finite-element method (GMsFEM). The main idea of the GMsFEM is to construct multiscale basis functions that take the medium heterogeneities into account. The approximation on a fine grid is carried out using the finite-element method with standard linear basis functions. To verify the accuracy of the proposed multiscale method, we solve two- and three-dimensional problems in heterogeneous media. Numerical results show that the multiscale method can provide a good approximation to the solution of the thermoelasticity problem with a phase transition on a fine grid with a significant reduction in the dimensionality of the discrete problem.
