The long‐time behaviour of the thermoconvective flow in a porous medium

For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd.     

Some non‐standard problems in viscous flow

Energy bounds are derived for Dirichlet type boundary value problems for the Navier–Stokes and Stokes equations when a combination of the solution values initially and at a later time is prescribed. The bounds are obtained by means of a differential inequality and imply uniqueness and continuous data dependence of the solutions for a range of values of the parameter in the non‐standard auxiliary condition. Copyright © 2004 John Wiley & Sons, Ltd.     

Diffusion in poro‐plastic media

A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial‐boundary‐value problem is a system that consists of the diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto‐visco‐plastic type. The variational form of this problem in Hilbert space is a non‐linear evolution equation for which the existence and uniqueness of a global strong solution is proved by means of monotonicity methods. Various degenerate situations are permitted, such as incompressible fluid, negligible porosity, or a quasi‐static momentum equation. The essential sufficient conditions for the well‐posedness of the system consist of an ellipticity condition on the term for diffusion of fluid and either a viscous or a hardening assumption in the constitutive relation for the porous solid. Copyright © 2004 John Wiley & Sons, Ltd.     

工程施工中运输网络优化方案

施工工地运输方案的优化设计可以归结为 :按施工期要求设计运输线路或验证已有线路通行能力 ,计算总线路中影响提高流量的关键路段 ,取得最小费用最大流 .本文运用图论理论这一数学工具把实际问题抽象为有向网络 ,进而建立数学模型 .此方法理论上严密 ,解题步聚直观清晰 ,对水利、公路、水路、铁路等其它运输系统有普遍意义 .     

Electromagnetic energy flow near nanoparticles—I: single spheres

The electromagnetic (EM) energy flow near single spheres is investigated by applying Mie theory. From the patterns of the energy flow, the absorption and the scattering of light can be understood in the microscopic point of view. In the absorption profiles of metallic particles, most absorbed energy is consumed on the surface of the particles, which indicates that the resonance of surface plasmon is different from that of the bulk plasmon. Two mechanisms to enhanced local EM field are also distinguished. One is the surface plasmon resonance, and another one is the intensified energy flow.     

A compact shock-assisted free-piston driver for impulse facilities

A free-piston driver that employs entropy-raising shock processes with diaphragm rupture has been constructed, which promises significant theoretical advantages over isentropic compression. Results from a range of conditions with helium and argon driver gases are reported. Significant performance gains were achieved in some test cases. Heat losses are shown to have a strong effect on driver processes. Measurements compare well with predictions from a quasi-one-dimensional numerical code. Received 7 September 1996 / Accepted 5 October 1996     

The Nonexistence of Procedures with Bounded Performance Characteristics in Certain Parametric Inference Problems

This paper gives a condition which implies the nonexistence of parametric statistical procedures with bounded risk or error performance characteristics. Many examples for which such a condition is satisfied are considered.     

The multiple-scale wave equation

An analytic and numerical study of the behavior of the linear nonhomogeneous wave equation of the form ε²u_tt = Δu + tf with high wave speed (ε 1) is carried out. This study was initially motivated by meteorological observations which have indicated the presence of large spatial scale gravity waves in the neighborhood of a number of summer and winter storms, mainly from visible images of ripples in clouds in satellite photos. There is a question as to whether the presence of these waves is caused by the nearby storms. Since the linear wave equation is an approximation to the full system describing pressure waves in the atmosphere, yet is considerably more tractable, we have chosen to analyze the behavior of the linear nonhomogeneous wave equation with high wave speed. The analysis is shown to be valid in one, two, and three space dimensions. Partly because of the high wave speed, the solution is known to consist of behavior which changes on two different time scales, one rapid and one slow. Additionally, because of the presence of the nonhomogeneous forcing term tf, we show that there is a component of the solution which will vary only on a very large spatial scale. Since even the linearized wave equation can give rise to persistent large spatial scale waves under the right conditions, the implication is that certain storms could be responsible for the generation of large-scale waves. Numerical simulations in one and two dimensions confirm analytic results.     

Adaptive remeshing for ductile fracture prediction in metal formingRemaillage adaptatif pour la prévision de la rupture ductile en mise en forme

The analysis of mechanical structures using the Finite Element Method in the framework of large elastoplastic strain, needs frequent remeshing of the deformed domain during computation. Indeed, the remeshing is due to the large geometrical distortion of finite elements and the adaptation to the physical behavior of the solution. This paper gives the necessary steps to remesh a mechanical structure during large elastoplastic deformations with damage. An important part of this process is constituted by geometrical and physical error estimates. The proposed method is integrated in a computational environment using the ABAQUS/Explicit solver and the BL2D-V2 adaptive mesher. To cite this article: H. Borouchaki et al., C. R. Mecanique 330 (2002) 709–716.     

高功率激光驱动器中小尺度自聚焦和噪声模型

 建立了一套线性的近似分析方法，研究高功率激光驱动器中强激光传输的小尺度自聚焦效应和相位噪声对光束传输和光束质量的影响，给出了系统噪声强度、B积分值与光束近场调制对比度之间的定量关系。研究表明,为保证输出光束质量，即近场调制对比度小于给定值，系统内的噪声强度必须符合一定的谱分布。