Duality,area-considerations,and the Kalai–Smorodinsky solution

We introduce a new solution concept for $2$-person bargaining problems, which can be considered as the dual of the Equal-Area solution (EA) (see Anbarc? and Bigelow (1994)). Hence, we call it the Dual Equal-Area solution (DEA). We show that the point selected by the Kalai–Smorodinsky solution (see Kalai and Smorodinsky (1975)) lies in between those that are selected by EA and DEA. We formulate an axiom–area-based fairness–and offer three characterizations of the Kalai–Smorodinsky solution in which this axiom plays a central role.     

On eight-dimensional unital division algebras over finite fields

The purpose of this paper is to investigate the eight-dimensional non-associative unital division algebras {0}≠A over finite fields, admitting elementary abelian 2-group of automorphisms E≤Aut(A), of order 8, using tools from algebraic geometry.     

Existence and Exponential Decay of Solutions for a Wave Equation with Integral Nonlocal Boundary Conditions of Memory Type

In this paper, we consider a wave equation with integral nonlocal boundary conditions of memory type. First, we establish two local existence theorems by using Faedo–Galerkin method and standard arguments of density. Next, we give a su?cient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results.     

Instability and friction

A review on the stability analysis of solids in unilateral and frictional contact is given. The presentation is focussed on the stability of an equilibrium position of an elastic solid in frictional contact with a fixed or moving obstacle. The problem of divergence instability and the obtention of a criterion of static stability are discussed first for the case of a fixed obstacle. The possibility of flutter instability is then considered for a steady sliding equilibrium with a moving obstacle. The steady sliding solution is generically unstable by flutter and leads to a dynamic response which can be chaotic or periodic. This dynamic response leads to the generation of stick–slip–separation waves on the contact surface in a similar way as Schallamach waves in statics. Illustrating examples and principal results recently obtained in the literature are reported. Some problems of friction-induced vibration and noise emittence, such as brake squeal for example, can be interpreted in this spirit. To cite this article: Q.S. Nguyen, C. R. Mecanique 331 (2003).     

后台阶流动的数值模拟

访述了大涡模拟的基本思想，指出大涡模拟的效率主要取决于四个因素，即流动中须有大尺度涡存在、合理的计算格式、合适的滤波器和亚格子应力模型。在深入考虑粘性不可压缩流Navier—Stokes方程各个子项作用的基础上，提出二阶全展开Euler—Taylor—Galerkin有限元方法作为大涡模拟的离散格式，并采用Gauss滤波器，对典型算例——后台阶处的流动进行大涡模拟，计算结果与相关文献符合的很好。从计算结果还可以看出大涡模拟与二阶全展开ETG有限元方法的结合在捕捉涡系及反映涡动时变过程方面具有明显的优势，说明大涡模拟适合于边界几何形状复杂区域流动的模拟。同时应用二阶全展开ETG有限元方法对低雷诺数粘性不可压缩后台阶流动进行了计算，得到与相关文献符合良好的计算结果，即该方法也可独立用于对低雷诺数粘性不可压缩流动的计算。     

Dispersion de Taylor généralisée à un fluide à propriétés physiques variablesGeneralized Taylor dispersion for heterogeneous fluid

The investigation of non-reactive miscible solute dispersion in a vertical Hele–Shaw cell is considered. An asymptotic method is used to extend Taylor model to the case of the fluid density, the dynamic viscosity and the molecular diffusion coefficient are solute concentration-dependent. It is demonstrated that the averaged variables over the gap are governed by a convection–dispersion equation in which the dispersion tensor is concentration-dependent. To cite this article: C. Felder et al., C. R. Mecanique 332 (2004).     

Experimental investigations on the dynamic behavior of a 2-DOF airfoil in the transitional Re number regime based on digital-image correlation measurements

The present paper investigates the fluid–structure interaction (FSI) of a wing with two degrees of freedom (DOF), i.e., pitch and heave, in the transitional Reynolds number regime. This 2-DOF setup marks a classic configuration in aeroelasticity to demonstrate flutter stability of wings. In the past, mainly analytic approaches have been developed to investigate this challenging problem under simplifying assumptions such as potential flow. Although the classical theory offers satisfying results for certain cases, modern numerical simulations based on fully coupled approaches, which are more generally applicable and powerful, are still rarely found. Thus, the aim of this paper is to provide appropriate experimental reference data for well-defined configurations under clear operating conditions. In a follow-up contribution these will be used to demonstrate the capability of modern simulation techniques to capture instantaneous physical phenomena such as flutter. The measurements in a wind tunnel are carried out based on digital-image correlation (DIC). The investigated setup consists of a straight wing using a symmetric NACA 0012 airfoil. For the experiments the model is mounted into a frame by means of bending and torsional springs imitating the elastic behavior of the wing. Three different configurations of the wing possessing a fixed elastic axis are considered. For this purpose, the center of gravity is shifted along the chord line of the airfoil influencing the flutter stability of the setup. Still air free-oscillation tests are used to determine characteristic properties of the unloaded system (e.g. mass moment of inertia and damping ratios) for one (pitch or heave) and two degrees (pitch and heave) of freedom. The investigations on the coupled 2-DOF system in the wind tunnel are performed in an overall chord Reynolds number range of $9.66\times 10^3\le \text{Re}\le 8.77\times 10^4$. The effect of the fluid-load induced damping is studied for the three configurations. Furthermore, the cases of limit-cycle oscillation (LCO) as well as diverging flutter motion of the wing are characterized in detail. In addition to the DIC measurements, hot-film measurements of the wake flow for the rigid and the oscillating airfoil are presented in order to distinguish effects originating from the flow and the structure.