Seepage-Diffusion Model of Brine Migration in Inhomogeneous Aquifers

A new phenomenological mathematical model of the propagation of high- and low-salinity solutions through inhomogeneous aquifers is proposed. The model consists of interrelated equations of two-phase flow and diffusive mass transfer through a porous medium in a region with a traveling boundary. Features of different contamination scenarios of are analyzed with reference to particular examples.     

双振子模型手性分子介质的二次谐波理论

推导了在二次谐波条件下耦合双振子模型手性分子的一阶超极化率，给出了薄膜手性介质的二阶极化率，分析了分子的微观参量对二次谐波产生效率的影响.理论计算所得的偏振旋转角谱和已有的实验结果相符. 关键词： 手性分子 分子极化率 介质极化率 二次谐波     

Disappearance of interfaces in finite time

For the solution of filtration equation with a density which is decreasing at infinity fast enough we found that the interface disappears in finite time.

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Sommario Si considera un problema di filtrazione con densità che decresce all'infinito in modo sufficientemente rapido. Si dimostra che il contorno libero sparisce in tempo finito.

     

Numerical simulation of plate autorotation in a viscous fluid flow

A general formulation of the plane coupled dynamical and aerodynamical problem of the motion of a rigid body with a rotational degree of freedom in a viscous incompressible fluid flow is given. A computation technique for solving the Navier-Stokes equations based on the meshless viscous vortex domain method is used. The autorotation of a single plate and a pair of plates is investigated. The effect of the reduced moment of inertia and the Reynolds number on the angular rotation velocity is determined. The time dependences of the hydrodynamic loads are compared with the corresponding instantaneous flow patterns. The increased the autorotation velocity of two plates in tandem is detected.     

On the stochastic porous medium equation

In this paper, we discuss an initial-boundary value problem and a Cauchy problem for the stochastic porous medium equation. Our basic estimates are based on the known results due to (Math. Sbornik 67 (1965) 609-642, Arch. Rational Mech. Anal. 25 (1967) 64-80). By the procedure developed in (Trans. Amer. Math. Soc. 354 (2001) 1117-1135), we obtain solutions over the given probability space rather than martingale solutions. We will also establish the existence of invariant measures when the space domain is bounded.     

Three-dimensional numerical simulation of the inverse problem of thermal convection using the quasi-reversibility method

Inverse (time-reverse) simulation of three-dimensional thermoconvective flows is considered for a highly viscous incompressible fluid with temperature-dependent density and viscosity. The model of the fluid dynamics is described by the Stokes equations, the incompressibility and heat balance equations subject to the appropriate initial and boundary conditions. To solve the problem backward in time, the quasi-reversibility method is applied to the heat balance equation. The numerical solution is based on the introduction of a two-component vector potential for the velocity of the medium, on the application of the finite element method with a special tricubic spline basis for computing this potential, and on the application of the splitting method and the method of characteristics for computing the temperature. The numerical algorithm is designed to be executed on parallel computers. The proposed numerical algorithm is used to reconstruct the evolution of diapiric structures in the Earth’s upper mantle. The computational efficiency of the algorithm is analyzed on the basis of the appropriate functionals of residuals.     

Mass optimization of a compressed cylindrical shell with limited life

A new optimization model is proposed to design corrosion-affected structures with limited life. The optimization problem is stated as a nonlinear-programming problem. The mass of the structure is minimized. The design is considered optimal when physical wear and obsolescence arrive simultaneously. A smooth cylindrical shell compressed in the longitudinal direction is used to illustrate the model __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 97–101, March 2006.     

On the existence of weak solutions to the equations of non‐stationary motion of heat‐conducting incompressible viscous fluids

This paper is concerned with the equations of non‐stationary motion in 3D of heat‐conducting incompressible viscous fluids with temperature‐dependent viscosity. The conservation of internal energy includes the usual dissipation term. We prove the existence of a ‘weak solution with defect measure’ to the system of PDEs under consideration. Our method of proof is based on a regularization of the equations of conservation of momentum. Copyright © 2006 John Wiley & Sons, Ltd.     

Mathematical analysis of radionuclides displacement in porous media with nonlinear adsorption

This paper is devoted to the mathematical analysis of the miscible displacement of a set of radionuclides in a flow occurring in a heterogeneous porous medium. The flow is governed by Darcy's law, and the motion of the chemical species is given by a nonclassical advection-diffusion-reaction equations system. The novelty of the model lies in the adsorption phenomenon that leads to a time derivative of a nonlinear term in these equations. A semi-discretization method is used to establish the existence of weak solutions to this system. Uniform L^∞-estimates on the solutions are specified.