119049, Москва, ул. Шаболовка, 26, офис 5414;
тел: +7 (495) 621 13 42,
+ 7(495) 772 95 90*26068, 26070;
Алескеров Фуад Тагиевич — руководитель департамента, доктор технических наук, ординарный профессор
Колотвина Оксана Альбертовна — менеджер
Питра Татьяна Георгиевна — cтарший администратор
Работа посвящена численному моделированию спирально-вихревых структур во вращающихся газовых дисках в рамках простой модели двумерных нестационарных баротропных уравнений Эйлера с массовой силой и указывает на возможность чисто гидродинамической основы формирования и эволюции таких структур. Выводятся новые аксиально симметричные стационарные решения уравнений, модифицирующие известные приближенные решения. Эти решения с малыми возмущениями используются как начальные данные в нестационарной задаче, для решения которой демонстрируется образование рукавов плотности с их раздвоением и анализируется перераспределение углового момента. Дополнительно подтверждается корректность лабораторных экспериментов с мелкой водой для описания формирования крупных вихревых структур в тонких газовых дисках. Расчеты основаны на специальной КГД регуляризации уравнений Эйлера в полярных координатах.
A new fast direct algorithm for implementing a finite element method (FEM) of order on rectangles as applied to boundary value problems for Poisson-type equations is described that extends a well-known algorithm for the case of difference schemes or bilinear finite elements (n = 1). Its core consists of fast direct and inverse algorithms for expansion in terms of eigenvectors of one-dimensional eigenvalue problems for an nth-order FEM based on the fast discrete Fourier transform. The amount of arithmetic operations is logarithmically optimal in the theory and is rather attractive in practice. The algorithm admits numerous further applications (including the multidimensional case).
The Arctic region is one of the most sensitive and vulnerable to climate change. The dramatic melting of Arctic ice has several negative consequences for the whole ecosystem as well as for a way of life of native people but it also creates new opportunities for the region. First, it opens up potential for exploitation of large deposits of natural resources such oil and gas. Second, it shrinks Arctic shipping routes which offer significant economic savings for many countries. These benefits has already attracted many countries, both Arctic and non-Arctic, thus resulting in potential conflict of interests. In our paper we present a mathematical approach to the problem of conflict resolution in the Arctic. First, we propose an approach how the level of interest in each part of the region should be evaluated with respect to main resources - oil, gas, fish and maritime routes. Second, we present several models of areas allocation to resolve the problem of conflict resolution. As a result, we applied several scenarios of areas allocation, evaluated their efficiency based on the total satisfaction level and identified conflict zones in the Arctic.
Entropy balance in the one-dimensional hyperbolic quasi-gasdynamic (HQGD) system of equations is analyzed. In regular flow regimes, it is shown that the behavior of entropy in the HQGD system is determined by terms involving the natural viscosity and thermal conductivity coefficients. The total entropy production differs from the Navier–Stokes equations for viscous compressible heat-conducting gases by the second order terms with respect to a relaxation parameter. Additionally, a similar analysis of energy balance is performed for the simpler case of the barotropic HQGD system, which is of interest for some applications.
Our study employs the network approach to the problem of international migration. During the last years, migration has attracted a lot of attention and has been examined from many points of view. However, very few studies considered it from the network perspective. The international migration can be represented as a network (or weighted directed graph) where the nodes correspond to countries and the edges correspond to migration flows. The main focus of our study is to reveal a set of critical or central elements in the network. To do it, we calculated different existing and new centrality measures. In our research the United Nations International Migration Flows Database (version 2015) was used. As a result, we obtained information on critical elements for the migration process in 2013.
We study a multidimensional hyperbolic quasi-gasdynamic (HQGD) system of equations containing terms with a regularizing parameter $\tau>0$ and 2nd order space and time derivatives; the body force is taken into account. We transform it to the form close to the compressible Navier-Stokes system of equations. Then we derive the entropy balance equation and show that the entropy production is like for the latter system plus a term of the order $O(\tau^2)$. We analyze an equation for the total entropy as well. We also show that the corresponding residuals in the HQGD equations with respect to the compressible Navier-Stokes ones are of the order $O(\tau^2)$ too. Finally we treat the simplified barotropic HQGD system of equations with the general state equation and the stationary potential body force and obtain the corresponding results for it.
We consider an application of power indices, which take into account preferences of agents for coalition formation proposed for an analysis of power distribution in elected bodies to reveal most powerful (central) nodes in networks. These indices take into account the parameters of the nodes in networks, a possibility of group influence from the subset of nodes to single nodes, and intensity of short and long interactions among the nodes.