Flows over edge-disjoint mixed multipaths and applications

For improving reliability of communication in communication networks, where edges are subject to failure, Kishimoto [Reliable flow with failures in a network, IEEE Trans. Reliability, 46 (1997) 308-315] defined a δ-reliable flow, for a given source-sink pair of nodes, in a network for δ∈(0,1], where no edge carries a flow more than a fraction δ of the total flow in the network, and proved a max-flow min-cut theorem with cut-capacites defined suitably. Kishimoto and Takeuchi in [A method for obtaining δ-reliable flow in a network, IECCE Fundamentals E-81A (1998) 776-783] provided an efficient algorithm for finding such a flow.When (1/δ) is an integer, say q, Kishimoto and Takeuchi [On m-route flows in a network, IEICE Trans. J-76-A (1993) 1185-1200 (in Japanese)] introduced the notion of a q-path flow. Kishimoto [A method for obtaining the maximum multi-route flows in a network, Networks 27 (1996) 279-291] proved a max-flow min-cut theorem for q-path flow between a given source-sink pair (s,t) of nodes and provided a strongly polynomial algorithm for finding a q-path flow from s to t of maximum flow-value.In this paper, we extend the concept of q-path flow to any real number q?1. When q(=1/δ) is fractional, we show that this general q-path flow can be viewed as a sum of some ⌈q⌉-path flow and some ⌊q⌋-path flow. We discuss several applications of this results, which include a simpler proof and generalization of a known result on wavelength division multiplexing problem.Finally we present a strongly polynomial, combinatorial algorithm for synthesizing an undirected network with minimum sum of edge capacities that satisfies (non-simultaneously) specified minimum requirements of q-path flow-values between all pairs of nodes, for a given real number q?1.     

A control-volume based finite element method for three-dimensional incompressible turbulent fluid flow,heat transfer,and related phenomena

A control-volume based finite element method of equal-order type for three-dimensional incompressible turbulent fluid flow, heat transfer, and related phenomena is presented. The discretization equations are based mainly on the physics of the phenomena under consideration, more than on mathematical arguments. Special emphasis is devoted to the discretization of the convective terms and the continuity equation, and to the treatment of the boundary conditions imposed by the use of a high Reynolds k-?, type turbulence model. The pressure-velocity coupling in the fluid flow calculation is made from a derivative of the original SIMPLER method, without pressure correction. The discretized equations are solved in a sequential, rather than a coupled, form with significant advantage in the required computer time and storage. The method is an extension of a former version proposed by us for two-dimensional, laminar problems, and is here successfully applied to the following situations: three-dimensional deflected turbulent jet, and flows in 90° and 45° junctions of ducts with rectangular cross sections. The calculated results are in very good agreement with the experimental and numerical (obtained with the well established finite difference method) data available in the literature.     

Interdiffusion in two-layer Pd/Ag films I. The effects of interphase boundaries

Interdiffusion processes in epitaxial single-crystal Pd/Ag thin films within the temperature range 20°–500°C are studied by transmission electron microscopy, electron diffraction and electrical resistance methods. Homogenization is investigated both during deposition and during annealing.The mass transfer kinetics is found to depend significantly on the original structure of the interphase boundary (dislocations present or not) and on its reconstruction due to interdiffusion. Regular networks of misfit dislocations at the interface can retard interdiffusion, while network failures lead to acceleration of homogenization process. The vacancy flows play a decisive role in these processes. The effects of interphase dislocations on the DIGM, DIR and RID processes are discussed.The numerical study of electrical resistance variations during annealing is carried out. The concentration profiles are plotted for a nontrivial dependence of interdiffusion coefficient on concentration. The numerical results are compared with the experimental data.     

Simulation of 2D external viscous flows by means of a domain decomposition method using an influence matrix technique

Two-dimensional external viscous flows are numerically approximated by means of a domain decomposition method which combines a vortex method and a finite difference method. The vortex method is used in the flow region which is dominated by convective effects, whereas the finite difference method is used in the flow region where viscous diffusion effects are dominant. An influence matrix technique combined with the uniformity condition of the pressure is used to enforce the tangential velocity boundary condition. Comparisons between numerical and experimental data show that the method is well adapted for simulating two-dimensional flows.     

Entropy and vorticity corrections for transonic flows

Different models for inviscid transonic flows are examined. The common assumptions that the flow is isentropic and irrotational are critically evaluated. Entropy and vorticity correction procedures for potential and stream function formulations are presented, together with the details of the treatment of shocks and wakes, and drag and lift calculations. The non-uniqueness problem of the potential formulation is studied using different artificial viscosity forms. Numerical results are compared with Euler solutions.     

New formulation of eddy diffusion thermocline models

One-dimensional thermal stratification models (for lakes, reservoirs, oceans, fjords), based on eddy diffusion concepts to represent vertical mixing of heat, have not found extensive application due to the lack of an adequate analytical representation of the neutral eddy diffusion coefficient, K_Ho. In this paper such an analytic expression is developed and shown to be in good agreement with various pieces of empirical evidence.     

Optimal Control for Traffic Flow Networks

We consider traffic flow models for road networks where the flow is controlled at the nodes of the network. For the analytical and numerical optimization of the control, the knowledge of the gradient of the objective functional is useful. The adjoint calculus introduced below determines the gradient in two ways. We derive the adjoint equations for the continuous traffic flow network model and derive also the adjoint equations for a discretized model. Numerical examples for the solution of problems of optimal control for traffic flow networks are presented.This author was supported by Deutsche Forschungsgemeinschaft (DFG), Grant KL 1105/5.     

水下爆炸过程的高精度数值计算

采用三阶精度的Parabolic Piecewise Method(PPM)方法和Volume Of Fluid(VOF)方法相结合，运用Lagrange-Remapping算法，数值计算爆轰产物、水、空气多种介质之间的相互作用过程，该方法可以用来处理界面两边高密度比可压缩流动以及强剪切滑移运动等问题。     

Mixing in a stably stratified medium by horizontal shear near vertical walls

Stratified environmental flows near boundaries can have a horizontal mean shear component, orthogonal to the vertical mean density gradient. Vertical transport, against the stabilizing force of gravity, is possible in such situations if three-dimensional turbulence is sustained by the mean shear. A model problem, water with a constant mean density gradient flowing in a channel between parallel vertical walls, is examined here using the technique of large eddy simulation (LES). It is found that, although the mean shear is horizontal, the fluctuating velocity field has significant vertical shear and horizontal vorticity, thereby causing small-scale vertical mixing of the density field. The vertical stirring is especially effective near the boundaries where the mean shear is large and, consequently, the gradient Richardson number is small. The mean stratification is systematically increased between cases in our study and, as expected, the buoyancy flux correspondingly decreases. Even so, horizontal mean shear is found to be more effective than the well-studied case of mean vertical shear in inducing vertical buoyancy transport as indicated by generally larger values of vertical eddy diffusivity and mixing efficiency.     

Non‐linear stability and convection for laminar flows in a porous medium with Brinkman law

The non‐linear stability of plane parallel shear flows in an incompressible homogeneous fluid heated from below and saturating a porous medium is studied by the Lyapunov direct method.In the Oberbeck–Boussinesq–Brinkman (OBB) scheme, if the inertial terms are negligible, as it is widely assumed in literature, we find global non‐linear exponential stability (GNES) independent of the Reynolds number R. However, if these terms are retained, we find a restriction on R (depending on the inertial convective coefficient) both for a homogeneous fluid and a mixture heated and salted from below. In the case of a mixture, when the normalized porosity ε is equal to one, the laminar flows are GNES for small R and for heat Rayleigh numbers less than the critical Rayleigh numbers obtained for the motionless state. Copyright © 2003 John Wiley & Sons, Ltd.