二阶流体在旋转坐标系中的三维管道流动

就两个水平板构成的旋转系统,在磁场作用下分析二阶磁流体在其间的流动.下表面是一块可伸展的平面,上面是一块多孔的固体平板.选用合适的变换,将质量和动量的守恒方程,简化为耦合的非线性常微分方程组.应用最强大的分析技术,即同伦分析法(HAM),得到该非线性耦合方程组的级数解.结果用图形给出,并详细地讨论了无量纲参数Re,λ,Ha2,α和K2对速度场的影响.     

On the Equivalence of Multiparameter Gaussian Processes

Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a special type of stochastic equation with linear noise.      

Some path properties of generalized Lévy sheet

Let X(t) be an N parameter generalized Lévy sheet taking values in ℝ^d with a lower index α, ℜ = {(s, t] = ∏ _i=1 ^N (s _i, t _i], s _i < t _i}, E(x, Q) = {t ∈ Q: X(t) = x}, Q ∈ ℜ be the level set of X at x and X(Q) = {x: ∃t ∈ Q such that X(t) = x} be the image of X on Q. In this paper, the problems of the existence and increment size of the local times for X(t) are studied. In addition, the Hausdorff dimension of E(x, Q) and the upper bound of a uniform dimension for X(Q) are also established.     

Diffusion of chemically reactive species in a porous medium over a stretching sheet

Solutions for a class of nonlinear second-order differential equations, arising in diffusion of chemically reactive species of a non-Newtonian fluid immersed in a porous medium over a stretching sheet, are obtained. Furthermore, using the Brouwer fixed point theorem, existence results are established. Moreover, the exact analytical solutions (for some special cases) are obtained. The results obtained for the diffusion characteristics reveal many interesting behaviors that warrant further study of the effects of reaction rate on the transfer of chemically reactive species.     

Three-dimensional flow of a Jeffery fluid over a linearly stretching sheet

This investigation reports the three-dimensional flow of Jeffrey fluid over a linearly stretching surface. Transformation method has been utilized for the reduction of partial differential equations into the ordinary differential equations. The solutions of the nonlinear systems are presented by a homotopy analysis method (HAM). The reported graphical results are analyzed. A comparative study with the previous results of viscous fluid in the literature is made.     

Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion

The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution; the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile at a given point, and the time history can be described by the fractional calculus.     

次分数布朗运动局部时的研究

设X^H={X^H(t),t∈R+}是一个取值于R^d参数为H的次分数布朗运动.本文给出了X^H在单参数情况下局部时的Holder条件和尾概率估计.同时,还给出了X^H在多参数情况下局部时的存在性及L^2表示.     

Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling

A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The goveming thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness changes.Here,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model components.The solvers are integrated through a well-designed coupler for the exchange of parametric data between components.The discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers.We demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.     

Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a non-uniform property micropolar liquid

A study of the hydromagnetic flow due to a stretching sheet and heat transfer in an incompressible micropolar liquid is made. Temperature-dependent thermal conductivity and a non-uniform heat source/sink render the problem analytically intractable and hence a numerical study is made using the shooting method based on Runge-Kutta and Newton-Raphson methods. The two problems of horizontal and vertical stretching are considered to implement the numerical method. The former problem involves one-way coupling between linear momentum and heat transport equations and the latter involves two-way coupling. Further, both the problems involve two-way coupling between the non-linear equations of conservation of linear and angular momentums. A similarity transformation arrived at for the problem using the Lie group method facilitates the reduction of coupled, non-linear partial differential equations into coupled, non-linear ordinary differential equations. The algorithm for solving the resulting coupled, two-point, non-linear boundary value problem is presented in great detail in the paper. Extensive computation on velocity and temperature profiles is presented for a wide range of values of the parameters, for prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions.     

三维不可压缩Euler方程的H1(R~3)轴对称解

在适当的初值条件下，对三维不可压缩Ｅｕｌｅｒ方程组，我们证明了Ｈ１（Ｒ３）轴对称解的存在性．