Use of dynamic trees in a network simplex algorithm for the maximum flow problem

Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann-vertex,m-arc network in at mostnm pivots and O(n ² m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm logn). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.Research partially supported by a Presidential Young Investigator Award from the National Science Foundation, Grant No. CCR-8858097, an IBM Faculty Development Award, and AT&T Bell Laboratories.Research partially supported by the Office of Naval Research, Contract No. N00014-87-K-0467.Research partially supported by the National Science Foundation, Grant No. DCR-8605961, and the Office of Naval Research, Contract No. N00014-87-K-0467.     

Preparation of Papers

We motivate the study of a vector variational inequality by a practical flow equilibrium problem on a network, namely a generalization of the well-known Wardrop equilibrium principle. Both weak and strong forms of the vector variational inequality are discussed and their relationships to a vector optimization problem are established under various convexity assumptions.     

Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach

The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique. This work was supported by the National Natural Science Fund of China (No. 10371096) for ZM Gao and YC Ma.     

垂直上升管内液体横掠流动传热特性研究

本文对单相水和单相油横掠流动时的平均换热特性进行了实验研究,对试验的结果进行了分析和讨论,并对实验数据进行关联,得到了垂直上升管内单相水和单相油横掠流动时的换热准则关系式。结果表明,狭窄空间条件下的液体横掠柱体时的流动换热对液相Re数的依赖,较大空间条件下的流动换热相比明显减小,并对单相水和单相油横掠流动时的换热性能进行了比较。     

Three-dimensional steady supersonic duct flow using Lagrangian formulation

In this paper, numerical simulation of three-dimensional supersonic flow in a duct is presented. The flow field in the duct is complex and can find its applications in the inlet of air-breathing engines. A unique streamwise marching Lagrangian method is employed for solving the steady Euler equations. The method was first initiated by Loh and Hui (1990) for 2-D steady supersonic flow computations and then extended to 3-D computation by the present authors Loh and Liou (1992). The new scheme is shown to be capable of accurately resolving complicated shock or contact discontinuities and their interactions. In all the computations, a free stream of Mach numberM=4 is considered.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

存在滑移时两圆球间的幂律流体挤压流动

基于Reynolds润滑理论分析了壁面滑移对任意圆球颗粒间幂律流体的挤压流动的影响。研究表明有壁面滑移时挤压流动的粘性力可通过引进本文定义的滑移修正系数分离出无滑移解。推导出的挤压力滑移修正系数是一积分表达式，依赖于滑移参数、幂律指数、球间隙和积分上限。一般地壁面滑移导致粘性力减小，粘性力的减小量随幂律指数的增大而增大，表明壁面滑移对剪切增稠流变材料有更大的影响；粘性力的减小量还随着滑移参数的增大而增加，而这恰与假设相符合；粘性力的减小量又随球间隙减小或积分上限的增大（从液桥情况到完全浸渍）而减小直到趋于常数，这一特性在离散元模拟时可以有效地减少计算量。     

A new approach to potential flow around axisymmetric bodies

A new method is introduced to solve potential flow problems around axisymmetric bodies. The approach relies on expressing the infinite series expansion of the Laplace equation solution in terms of a finite sum which preserves the Laplace solution for the potential function under a Neumann-type boundary condition. Then the coefficients of the finite sum are calculated in a least squares approximation sense using the Gram-Schmidt orthonormalization method. Sample benchmark problems are presented and discussed in some detail. The solutions are accurate and converged faster when a rather small number of terms were used. The method is simple and can be easily programmed.     

Thermal characterisation of micro-hotplates used in sensor structures

Micro-hotplates operated at elevated temperature form the basic element in several sensor devices, such as integrated calorimetric or Taguchi-type gas sensors and flow-rate sensors. In all of these applications thermal properties of the sensing elements play a determining role in functional operation, therefore, their accurate characterisation is essential. The micro-hotplates investigated were developed by one side porous silicon micro-machining technology, forming Pt micro-filaments embedded in non-stoichiometric silicon nitride, and suspended across a cavity. This work is dealing with the accurate temperature detection in the micro-scale by different measurement methods for the deduction of steady state and transient thermal properties from the results. Transient properties of the structure were investigated by application of a simplified thermal equivalent circuit model.     

Interactions between kinetic and radiative processes inside moving absorbing fluids

The aim of this paper is to present several features of the couplings occurring between radiative transfer and the kinetics of a moving dielectric. After determining how the velocity field affects the apparent thermo-optical properties of matter, the energy transport problem is investigated in instationary regime and the general form of transient radiative transfer equation inside a moving medium is built. Then, the model is applied to the particular case of turbulent flows: a system of two equations for mean and fluctuating radiative energies is presented, and the resolution of this system is finally carried out.     

Operational characteristics and power scaling of a transverse flow transversely excited CW CO<Subscript>2</Subscript> laser

Transverse flow transversely excited (TFTE) CO₂ lasers are easily scalable to multikilowatt level. The laser power can be scaled up by increasing the volumetric gas flow and discharge volume. It was observed in a TFTE CW CO₂ laser having single row of pins as an anode and tubular cathode that the laser power was not increasing when the discharge volume and the gas volumetric flow were increased by increasing the electrode separation keeping the gas flow velocity constant. The discharge voltage too remained almost constant with the change of electrode separation at the same gas flow velocity. This necessitated revision of the scaling laws for designing this type of high power CO₂ laser. Experimental results of laser performance for different electrode separations are discussed and the modifications in the scaling laws are presented.