Co-Segregation Effects on Boundary Migration

We analyze the effect of co-segregation on the mobility of grain boundaries within the framework of the impurity drag theory originally proposed by Cahn and Lücke and Stüwe for an ideal solution. The new derivation extends this model to the case where there are two types of impurities (or three components in the alloy). Since the resultant expression for the boundary mobility is complicated, numerical solutions were obtained for several cases to show how co-segregation affects the boundary mobility. Depending on the relative diffusivities of the two impurities which are both attracted to the boundary, the mobility may either increase or decrease with increasing concentration of one of the impurities. When one of the impurities is attracted to the boundary and the other repelled from the boundary, increasing the concentration of the attractive impurity can lead to a sharp decrease in the boundary mobility.     

Numerical analysis of turbulent structure in compound meandering open channel by algebraic Reynolds stress model

The turbulent flow in a compound meandering channel with a rectangular cross section is one of the most complicated turbulent flows, because the flow behaviour is influenced by several kinds of forces, including centrifugal forces, pressure‐driven forces and shear stresses generated by momentum transfer between the main channel and the flood plain. Numerical analysis has been performed for the fully developed turbulent flow in a compound meandering open‐channel flow using an algebraic Reynolds stress model. The boundary‐fitted coordinate system is introduced as a method for coordinate transformation in order to set the boundary conditions along the complicated shape of the meandering open channel. The turbulence model consists of transport equations for turbulent energy and dissipation, in conjunction with an algebraic stress model based on the Reynolds stress transport equations. With reference to the pressure–strain term, we have made use of a modified pressure–strain term. The boundary condition of the fluctuating vertical velocity is set to zero not only for the free surface, but also for computational grid points next to the free surface, because experimental results have shown that the fluctuating vertical velocity approaches zero near the free surface. In order to examine the validity of the present numerical method and the turbulent model, the calculated results are compared with experimental data measured by laser Doppler anemometer. In addition, the compound meandering open channel is clarified somewhat based on the calculated results. As a result of the analysis, the present algebraic Reynolds stress model is shown to be able to reasonably predict the turbulent flow in a compound meandering open channel. Copyright © 2005 John Wiley & Sons, Ltd.     

四阶非线性边值问题解的存在性与上下解方法

该文讨论四阶常微分方程边值问题u^(4)(t)=f(t,u,u″), t∈［0,1］,u(0)=u(1)=u″(0)=u″(1)=0解的存在性, 其中f(t,u,v):［0,1］×R×R→R为Carathéodory函数. 在不限制f关于u,v的增长阶, 不假定f关于u,v的单调性的一般情形下, 用上下解方法获得了解的存在性结果,并讨论了单调迭代求解的有效性.     

Absorbing boundary conditions for reaction-diffusion equations

We treat here of the question of absorbing boundary conditionsfor nonlinear diffusion equations. We use the conditions designedfor the linear equation, we prove them to be well posed forthe nonlinear problem, and through numerical experiments thatthey are well suited for reaction–diffusion equations.     

Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

On Brennan's Conjecture for a Special Class of Functions

In this paper, we prove Brennan's conjecture for conformal mappings f of the disk {z : | z| < 1} assuming that the Taylor coefficients of the function log(zf′(z)/f(z)) at zero are nonnegative. We also obtain inequalities for the integral means over the circle |z| = r of the squared modulus of the function zf′(z)/f(z).     

On a free boundary problem for the Reynolds equation derived from the Stokes system with Tresca boundary conditions

The asymptotic behaviour of a Stokes flow with Tresca free boundary friction conditions when one dimension of the fluid domain tends to zero is studied. A specific Reynolds equation associated with variational inequalities is obtained and uniqueness is proved.     

A note on the unsteady boundary layers over a flat plate

The unsteady boundary layer over a semi-infinite flat plate was investigated in this paper. The flow involves the unsteady flow over a flat plate with leading edge accretion or ablation. The momentum boundary layer was further analyzed and it was shown that the leading edge ablation had a similar effect to the wall mass injection or upstream wall movement making the fluid blown away from the wall. The thermal boundary layer of the same flow was also studied. Results show that the leading edge accretion or ablation can greatly change the fluid motion and the heat transfer characteristics.     

一类含有P-Laplacian算子的奇异边值问题解的确切个数

讨论了一类p-L ap lac ian算子型的奇异边值问题正解的确切个数以及解的性质.     

Numerical Prediction of the Strain State of Thermoset Matrix/Mineral Filler Composite Plates

The numerical prediction of the fields of inelastic strains (the linear invariant of the tensor of inelastic strains) in thermoset polyester/marble filler composite plates is discussed. A uniformly distributed load is applied to the plates, which lie on a steel base. The strain fields are predicted by means of the boundary element method by using creep test data for the composites and the polyester matrix itself. Identical creep tests were performed for two ages of the materials (1 month and 13 years), which allowed evaluating the aging effect. The study is carried out in two stages. At the first stage, the application of the generalized Maxwell-Gurevich equation to the thermoset matrix/mineral filler composite is demonstrated. The model parameters determined from the experimental creep data is used for the second stage, where the state of inelastic strains in the plates is predicted by applying the boundary element method. The influence of composite formulation (filler content) and physical aging of the polyester matrix on the state of inelastic strains in the plates is shown.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 145–156, March–April, 2005.