A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

Finite element analysis of fluid flow with moving free surface has been performed in 2‐D and 3‐D. The new VOF‐based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2‐D and 3‐D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby‐cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2‐D and 3‐D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non‐uniform grid systems and can be extended to 3‐D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd.     

A Tandem Queue with Coupled Processors: Computational Issues

In Resing and Örmeci [16] it is shown that the two-stage tandem queue with coupled processors can be solved using the theory of boundary value problems. In this paper we consider the issues that arise when calculating performance measures like the mean queue length and the fraction of time a station is empty. It is assumed that jobs arrive at the first station according to a Poisson process and require service at both stations before leaving the system. The amount of work that a job requires at each of the stations is an independent, exponentially distributed random variable. When both stations are nonempty, the total service capacity is shared among the stations according to fixed proportions. When one of the stations becomes empty, the total service capacity is given to the nonempty station. We study the two-dimensional Markov process representing the numbers of jobs at the two stations. The problem of finding the generating function of the stationary distribution can be reduced to two different Riemann-Hilbert boundary value problems, where both problems yield a complete analytical solution. We discuss the similarities and differences between the two problems, and relate them to the computational aspects of obtaining performance measures.     

Searching for new conditions for fermion N-representability

New elements of the dual cone of the set of fermion N-representable 2-density operators are proposed. So far, the explicit form of the corresponding necessary conditions for N-representability is obtained for N = 3. In this case the new condition is stronger than the known B- and C-conditions for 3-representability. The results provide evidence that in the spectral decomposition of the N-representable 2-density operator there exists an intrinsic relation between the eigenvalue and the corresponding eigenfunction.     

液态金属流的表面张力问题中的两点边值问题解的存在性

本文讨论了在区域提纯过程中，研究液态金属流的表面张力时提出的一个带有非负参数Ｑ的两点边值问题．利用上、下解方法和Ｓｃｈａｕｄｅｒ不动点定理，证明了当０Ｑ８５１时，该问题至少有一个解，对已有结果０Ｑ＜１进行了重要的改进．     

The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values. Received: August 2001 / Accepted: January 2002?Published online March 27, 2002     

Clifford分析中的多周期和准多周期Riemann边值问题

本文考虑了R^n 1空间中椭圆函数和准椭圆函数的一些性质，然后分别讨论了周期和准周期Riemann边值问题，给出了解的表达式和可解条件。     

在局部区域上的奇摄动反应扩散方程初始边值问题

本文是讨论一类在局部区域上的奇摄动反应扩散初始边值问题.利用算子理论和 不动点原理,得到了相应问题解的存在性和唯一性.     

Nonlinear degenerate parabolic equations with Neumann boundary condition

We study Neumann problem for a class of nonlinear degenerate parabolic PDE. A typical nonlinearity we have in mind is, for instance, β(u)=−1/u(u>0). We establish a necessary and sufficient condition on given data for existence of solution.