Acoustic streaming and heat transfer in a vibrating rectangular two-dimensional channel filled with gas, the vertical walls of which are thermally insulated and the horizontal walls are maintained at different temperatures, are numerically investigated. The features of the wave motion of the gas are studied. The influence of the temperature difference of the walls, amplitude and frequency of vibration on acoustic streaming and the period average temperature is determined.
Since the second half of the twentieth century, wide studies of Sobolev-type equations are undertaken. These equations contain items that are derivatives with respect to time of the second order derivatives of the unknown function with respect to space variables. They can describe nonstationary processes in semiconductors, in plasm, phenomena in hydrodinamics and other ones. Notice that wide studies of qualitative properties of solutions of Sobolev-type equations exist. Namely, results about existence and uniqueness of solutions, their asymptotics and blow-up are known. But there are few results about exact solutions of Sobolev-type equations. There are books and papers about exact solutions of partial equations, but they are devoted mainly to classical equations, where the first or second order derivative with respect to time or the derivative with respect to time of the first order derivative of the unknown function with respect to the space variable is equal to a stationary expression. Therefore it is interesting to study exact solutions of Sobolev-type equations. In the present paper, a third order model nonlinear partial equation is studied. Six classes of its exact solutions are built. They are expressed in terms of elementary and special functions (solutions of some ordinary differential equations).
The analysis of the Taylor–Couette problem in the small gap limit is extended to the of nearly columnar (NC) solutions. The theoretical results are derived in the small-gap approximation which is not always well approximated in experiments. Despite this studies in the Cartesian frame work when compared with theoretical results and observations yield good agreement. For higher values of the axial wavenumber, (beta), up to (betasim 3) rather narrow Taylor vortices may be realized for Reynolds number (R<80). These vortices will become unstable to states with columnar components with increasing (R). We show that for low (R), ((R,beta)sim(62.2,3.5)), a state with a strong columnar component drifting in stream-wise direction exists for azimuthal wavenumbers (alphasim 0.17) with (beta=3.5). We examine the bifurcation sequence of these states.
SLAV is a mathematical model of the Earth’s atmosphere that predicts weather in future based on current weather conditions. This paper describes and evaluates the numerical algorithm based on the energy balance for implementing the LAKE model into SLAV. LAKE is an extended one-dimensional model of lake that has been tested in respect to thermal and ice regime at a number of lakes in contrasting climate conditions in a standalone mode. The results obtained from numerical simulations for lead times up to 4 month and retrospective forecasts of weather anomalies with the same lead time indicate the applicability of the developed approach to reproduce lake-atmosphere coupling.
This work is devoted to the study of the interaction of acoustic waves with a layer of multifractional vapor–gas–droplet mixture with polydispersed inclusions of different sizes and materials. A mathematical model that determines the oblique incidence of an acoustic wave on a layer of finite thickness is presented.The calculations results of acoustic wave reflection from a layer of multifractional vapor–gas–droplet mixture are presented. The influence of layer thickness, mass concentration, inclusion sizes, phase transitions, and the angle of wave incidence on the reflection of acoustic waves from the layer of multifractional polydispersed vapor–gas–droplet mixture has been analyzed.
In this paper, a mathematical model of real gas filtration to a vertical well in naturally fractured reservoir is constructed. The curves of bottomhole pressure and pressure derivative depending on the filtration parameters of the reservoir are analyzed. A method for well test analysis is proposed based on solving an ill-posed inverse problem.
Configurations and deformations are the homeomorphisms that relate material manifold and shapes of a solid in conventional non-linear elasticity. They play fundamental role in kinematic description of deformable media and seem to be an essential part of non-linear continuum mechanics. These concepts nevertheless are rooted in Euclidean nature of space and time, adopted in non-relativistic physics, and their direct application in relativistic case is impossible. The paper develops the generalization for them within General Relativity. To this end the concept of relativistic shape is introduced, which is defined as an element of foliation over a congruence of worldlines that constitute the world-tube of the solid. This makes it possible to define displacements as a field of translations along elements of congruence beginning on one element of foliation and ending on another. Geometrically this is similar to Fermi–Walker transport. Each relativistic shape can be endowed with two metrics, one induced by ambient space, and another, given by pushforwarding of the metric induced on another shape (another element of foliation). These metrics are relativistic counterpart of Cauchy–Green measures of deformation. The conditions under which the foliation of congruence of worldlines exists are specified. When these conditions are violated, the natural generalization of the shape leads to a set that cannot be represented by the Riemann submanifold. This situation is similar to that which arises in the continuum theory of defects when trying to find a globally stress-free shape. To solve this problem, it is proposed to construct a material manifold whose elements represent shapes locally. The method of determination of geometry on material manifold, which turns out to be Weyl geometry, is proposed. All constructions are carried out within the framework of a variational approach to the derivation of field equations and Noether symmetries.
The probability distribution of several characteristics, in particular, sea surface and subsurface temperature and sea salinity simulated by the ocean circulation model of Nucleus for European Modeling of the Ocean in conjunction with data assimilation are determined. The data assimilation method, called as the Generalized Kalman filter method developed by the authors earlier and published in a number of studies is used. For assimilation the Agro drifter data have been applied for different model levels from sea surface until 2000 m. In order to define the probability distribution of sought model characteristics the Karhunen–Loeve decomposition of the covariance function has been utilized. The results of numerical experiments have been presented and analyzed.
The paper is focused on mathematical modeling of heat transfer in an anisotropic plate with heat energy drain due to various physical and chemical transformations inside the material and under conditions of exponential heat transfer at the boundary. The analytical solution of the second initial boundary value problem of heat conduction with nonlinear heat energy flow is obtained and investigated.
In this paper, an economical unconditionally stable method of variable directions with extrapolation of numerical solutions of problems for parabolic equations containing mixed derivatives is proposed and justified by approximation and stability, which, in comparative analysis with other numerical methods, showed the highest accuracy and a unique margin of stability when changing grid characteristics.
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