Statistical stationary states for a two-layer quasi-geostrophic system

Existence of a family of locally invariant probability measures for large scale flows in enclosed temperate sea is proved. This model is extremely important for understanding the meso-scale phenomena in oceans. The techniques used are those developed by Albeverio and his collaborators.     

High‐order finite difference schemes for incompressible flows

This paper presents a new high‐order approach to the numerical solution of the incompressible Stokes and Navier–Stokes equations. The class of schemes developed is based upon a velocity–pressure–pressure gradient formulation, which allows: (i) high‐order finite difference stencils to be applied on non‐staggered grids; (ii) high‐order pressure gradient approximations to be made using standard Padé schemes, and (iii) a variety of boundary conditions to be incorporated in a natural manner. Results are presented in detail for a selection of two‐dimensional steady‐state test problems, using the fourth‐order scheme to demonstrate the accuracy and the robustness of the proposed methods. Furthermore, extensions to higher orders and time‐dependent problems are illustrated, whereas the extension to three‐dimensional problems is also discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal transport with convex obstacle

We consider the Monge transportation problem when the cost is the squared geodesic distance around a convex obstacle. We show that there exists at least one—and in general infinitely many—optimal transport maps.     

Linear-programming extended formulations for the single-item lot-sizing problem with backlogging and constant capacity

Recently, several authors [8, 10] have argued for the use of extended formulations to tighten production planning models. In this work we present two linear-programming extended formulations of the constant-capacity lot-sizing problem with backlogging. The first one applies to the problem with a general cost function and has O(n³) variables and constraints. This improves on the more straightforward O(n⁴) Florian and Klein [2] type formulation. The second one applies when the costs satisfy the Wagner-Whitin property but it has O(n²) variables and O(n³) constraints. As a by-product, we positively answer an open question of Miller and Wolsey [4] about the tightness of an extended formulation for the continuous mixing set. This text presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister's Office, Science Policy Programming. The research was carried out with financial support of the Growth Project G1RD-1999-00034 (LISCOS) of the European Community. The scientific responsibility is assumed by the author.     

Effect of numerical integration in the DGFEM for nonlinear convection‐diffusion problems

This paper is concerned with the effect of numerical integration applied to the discontinuous Galerkin finite element discretization of nonlinear convection‐diffusion problems in 2D. In the space semidiscretization the volume and line integrals are evaluated by numerical quadratures. Our goal is to estimate the error caused by the numerical integration and to show what numerical quadratures guarantee that the accuracy of the method with exact integration is preserved. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Time-harmonic acoustic propagation in the presence of a shear flow

This work deals with the numerical simulation, by means of a finite element method, of the time-harmonic propagation of acoustic waves in a moving fluid, using the Galbrun equation instead of the classical linearized Euler equations. This work extends a previous study in the case of a uniform flow to the case of a shear flow. The additional difficulty comes from the interaction between the propagation of acoustic waves and the convection of vortices by the fluid. We have developed a numerical method based on the regularization of the equation which takes these two phenomena into account. Since it leads to a partially full matrix, we use an iterative algorithm to solve the linear system.     

面积,行列式,积分因子和Green公式

利用二阶行列式的几何意义是有向面积及积分因子的存在性给Green公式一个新的证明.尽管技术上走得远了些,但从概念上揭示了Green公式异常简明的几何意义,即Green公式只是面积的两种不同表达方式.同时这也蕴含了一个更深刻的哲学含义,即一般性隐含于特殊性(或特例)之中.     

Study of LMDS Videoconferencing System

LMDS is one kind of fixed broadband wireless access network. It uses radio spectrum between 10GHz and 40GHz to transmit voice, video, and data signals within small cell 3-10 miles in diameter. This paper proposes some key technical scenarios to support videoconferencing services transported on LMDS. Firstly, two kinds of typical LMDS lower layer standards made by DAVIC and 802.16 separately are discussed from the angle of supporting video conferencing services. Then, H.323 is studied and recommended as the standard of LMDS video conferencing system. And some strategies are proposed to support H.323 services on LMDS. After that, IP multicast technology, the key supporting technology of H.323, is studied from the angle of running on LMDS. Scenarios for IGMP, RMTP protocol running on LMDS are suggested and analyzed with Markov network queuing theory. The technical scenarios proposed by this paper make use of the transporting property of LMDS to support LMDS videoconferencing system more effectively.     

The Hamilton formalism with fractional derivatives

Recently the traditional calculus of variations has been extended to be applicable for systems containing fractional derivatives. In this paper the passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. The Hamilton's equations of motion are obtained in a similar manner to the usual mechanics. In addition, the classical fields with fractional derivatives are investigated using Hamiltonian formalism. Two discrete problems and one continuous are considered to demonstrate the application of the formalism, the results are obtained to be in exact agreement with Agrawal's formalism.     

On streamline diffusion arising in Galerkin FEM with predictor/multi‐corrector time integration

In the present paper, the author shows that the predictor/multi‐corrector (PMC) time integration for the advection–diffusion equations induces numerical diffusivity acting only in the streamline direction, even though the equations are spatially discretized by the conventional Galerkin finite element method (GFEM). The transient 2‐D and 3‐D advection problems are solved with the PMC scheme using both the GFEM and the streamline upwind/Petrov Galerkin (SUPG) as the spatial discretization methods for comparison. The solutions of the SUPG‐PMC turned out to be overly diffusive due to the additional PMC streamline diffusion, while the solutions of the GFEM‐PMC were comparatively accurate without significant damping and phase error. A similar tendency was seen also in the quasi‐steady solutions to the incompressible viscous flow problems: 2‐D driven cavity flow and natural convection in a square cavity. Copyright © 2002 John Wiley & Sons, Ltd.