The uniqueness property for networks with several origin–destination pairs

We consider congestion games on networks with nonatomic users and user-specific costs. We are interested in the uniqueness property defined by Milchtaich (2005) as the uniqueness of equilibrium flows for all assignments of strictly increasing cost functions. He settled the case with two-terminal networks. As a corollary of his result, it is possible to prove that some other networks have the uniqueness property as well by adding common fictitious origin and destination. In the present work, we find a necessary condition for networks with several origin–destination pairs to have the uniqueness property in terms of excluded minors or subgraphs. As a key result, we characterize completely bidirectional rings for which the uniqueness property holds: it holds precisely for nine networks and those obtained from them by elementary operations. For other bidirectional rings, we exhibit affine cost functions yielding to two distinct equilibrium flows. Related results are also proven. For instance, we characterize networks having the uniqueness property for any choice of origin–destination pairs.     

Optimization of flow diverters for cerebral aneurysms

A modern technique to treat cerebral aneurysms is to insert a flow diverter in the parent artery. In order to produce an optimal design of such devices, we consider a methodology combining simulated annealing optimization and lattice Boltzmann simulations. Our results surpass, in terms of stent efficiency, those obtained in the recent literature with an other optimization method. Although our approach is still in 2D, it demonstrates the potential of the method. We give some hint on how the 3D cases can be investigated.     

Measuring the interactions among variables of functions over the unit hypercube

By considering a least squares approximation of a given square integrable function f:n[0,1]→R by a multilinear polynomial of a specified degree, we define an index which measures the overall interaction among variables of f. This definition extends the concept of Banzhaf interaction index introduced in cooperative game theory. Our approach is partly inspired from multilinear regression analysis, where interactions among the independent variables are taken into consideration. We show that this interaction index has appealing properties which naturally generalize several properties of the Banzhaf interaction index. In particular, we interpret this index as an expected value of the difference quotients of f or, under certain natural conditions on f, as an expected value of the derivatives of f. Finally, we discuss a few applications of the interaction index in aggregation function theory.     

Interference theory: Moment solution for two component adsorption chromatography

Summary Moment analysis is used to study two component perturbation chromatography with linear non-equilibrium adsorption. The interference between components is included through the adsorption equilibrium. In this work, the expressions for the first and second moments of two component pertubations have been obtained for the first time. They are just the vectorization of those for the single component system, and they clearly show the interference between components. These results could be applied to establish an experimental procedure to measure adsorption equilibrium and kinetic data.     

Remarques sur les m\'ethodes de projection pour l'approximation des \'equations de Navier--Stokes

Summary. L'objet de cet article est de montrer que les estimations de convergence sur la pression pour les m\'ethodes de projection d\'ecrites dans \cite{Shen1} et \cite{Shen2} ne sont pas obtenues correctement car elles sont toutes bas\'ees sur une in\'egalit\'e fausse. Il semble qu'on ait besoin d'une convergence en de la vitesse dans pour d\'emontrer les estimations de convergence sur la pression en . La question de savoir si la m\'ethode de projection a un taux de convergence pour la pression plus \'elev\'e que reste ouverte. Received June 1, 1993     

Sur le theoreme de Stone-Weierstrass en Algebre commutative

We show that the sufficient conditions given by Cahen, Grazzini and Haouat for a version of the Stone-Weierstrass theorem in commutative algebra are the widest. More precisely, letA be a Noetherian ring andI a proper ideal ofA such thatA is Hausdorff with respect to theI-adic topology. Note the completion ofA andC(Â,Â) the ring of continuous functions from to with uniform convergence topology. The subset of polynomial functions is dense inC(Â,Â) if and only if the radical ofI is a maximal idealm ofA and the local ringA _m is a one-dimensional analytically irreducible domain with finite residue field.     

Transient dynamical behavior and phase transitions in magnetic systems

It was recently suggested that transient dynamical properties were of some use to predict equilibrium critical properties of 2D and 3D models of statistical mechanics on the lattice. We investigate such dynamical properties for three related models with competitive interactions, namely the ANNNI model, the brickwork model, and the BNNNI model. In spite of known differences in their equilibrium phase diagrams, our simulations display similar transient dynamical behaviors for all three models. The reliability of this method for probing equilibrium properties seems therefore questionable even for rather simple magnetic models without any structural disorder.On leave from Centre de Physique Théorique, Ecole Polytechnique, 91128, Palaiseau Cedex, France.     

Chlorzahl

Ohne Zusammenfassung     

Analysis and treatment of errors due to high velocity gradients in particle image velocimetry

This paper deals with errors occurring in two-dimensional cross-correlation particle image velocimetry (PIV) algorithms (with window shifting), when high velocity gradients are present. A first bias error is due to the difference between the Lagrangian displacement of a particle and the real velocity. This error is calculated theoretically as a function of the velocity gradients, and is shown to reach values up to 1 pixel if only one window is translated. However, it becomes negligible when both windows are shifted in a symmetric way. A second error source is linked to the image pattern deformation, which decreases the height of the correlation peaks. In order to reduce this effect, the windows are deformed according to the velocity gradients in an iterative process. The problem of finding a sufficiently reliable starting point for the iteration is solved by applying a Gaussian filter to the images for the first correlation. Tests of a PIV algorithm based on these techniques are performed, showing their efficiency, and allowing the determination of an optimum time separation between images for a given velocity field. An application of the new algorithm to experimental particle images containing concentrated vortices is shown.