Correction to: Finite Element Approximation of the Spectrum of the Curl Operator in a Multiply Connected Domain

Foundations of Computational Mathematics - In the published article, Figure 5 corresponds to an eigenfunction associated not with the first smallest positive eigenvalue.     

Stackelberg–Nash exact controllability for the Kuramoto–Sivashinsky equation

This paper deals with a hierarchical control problem for the Kuramoto–Sivashinsky equation following a Stackelberg–Nash strategy. We assume that there is a main control, called the leader, and two secondary controls, called the followers. The leader tries to drive the solution to a prescribed target and the followers intend to be a Nash equilibrium for given functionals. It is known that this problem is equivalent to a null controllability result for an optimality system consisting of three non-linear equations. One of the novelties is a new Carleman estimate for a fourth-order equation with right-hand sides in Sobolev spaces of negative order, which allows to relax some geometric conditions for the observation sets for the followers.     

Validity of the Electronic Transition Moment Functions for the B-X Transition of I2, From Radiative Lifetimes of the Vibrational Levels of the B State

Franck-Condon factors and R-centroids for the B-X transition of I₂ have been calculated from recent molecular parameters. From our radiative lifetimes and others reported in the literature, the validity of several proposed electronic transition moment functions has been checked. Acombination of the Bhale and Koffend functions seems to give the best fitting with the experimental radiative lifetimes.     

X‐ray absorption study of the local structure at the NiO/oxide interfaces

This work reports an X‐ray absorption near‐edge structure (XANES) spectroscopy study at the Ni K‐edge in the early stages of growth of NiO on non‐ordered SiO₂, Al₂O₃ and MgO thin films substrates. Two different coverages of NiO on the substrates have been studied. The analysis of the XANES region shows that for high coverages (80 Eq‐ML) the spectra are similar to that of bulk NiO, being identical for all substrates. In contrast, for low coverages (1 Eq‐ML) the spectra differ from that of large coverages indicating that the local order around Ni is limited to the first two coordination shells. In addition, the results also suggest the formation of cross‐linking bonds Ni—O—M (M = Si, Al, Mg) at the interface.     

Kinetic wavelength-pair method as an alternative approach to simultaneous multi-component analysis

The kinetic wavelength-pair method involves adapting a well established principle to the simultaneous kinetic-based determination of two or more compounds with diode-array detection. It relies on measuring the difference in the rate of change of the absorbance with time at two preset wavelength pairs such that the values of these measuring parameters are the result of the contribution of one or two components. The theoretical basis adapted to first-order kinetic-based determinations was established and checked on four systems. The method thus developed was compared with other differential kinetic methods and applied to the resolution of formaldehyde-acrolein mixtures.     

Types d'orbites et dynamique minimale pour les applications continues de graphesOrbit types and minimal dynamics for graph maps

We define the type of a periodic orbit of a graph map. We consider the class of ‘train-track’ representatives, that is, those graph maps which minimise the topological entropy of the topological representatives of a given free group endomorphism. We prove that each type of periodic orbit realised by an efficient representative is also realised by any representative of the same free group endomorphism. Moreover, the number of periodic orbits of a given type is minimised by the efficient representatives. To cite this article: Ll. Alsedà et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 479–482.     

A Mixed Heuristic for Circuit Partitioning

As general-purpose parallel computers are increasingly being used to speed up different VLSI applications, the development of parallel algorithms for circuit testing, logic minimization and simulation, HDL-based synthesis, etc. is currently a field of increasing research activity. This paper describes a circuit partitioning algorithm which mixes Simulated Annealing (SA) and Tabu Search (TS) heuristics. The goal of such an algorithm is to obtain a balanced distribution of the target circuit among the processors of the multicomputer allowing a parallel CAD application for Test Pattern Generation to provide good efficiency. The results obtained indicate that the proposed algorithm outperforms both a pure Simulated Annealing and a Tabu Search. Moreover, the usefulness of the algorithm in providing a balanced workload distribution is demonstrated by the efficiency results obtained by a topological partitioning parallel test-pattern generator in which the proposed algorithm has been included. An extented algorithm that works with general graphs to compare our approach with other state of the art algorithms has been also included.     

Predicting the Capillary Imbibition of Porous Rocks from Microstructure

The kinetics of capillary imbibition into porous rocks is studied experimentally and theoretically. The Washburn law is modified by introducing various corrections relating to the microstructure of the rocks, such as tortuosity, pore shape (obtained experimentally), and applying the effective medium approximation (EMA) in order to calculate the effective radius that defines the hydraulic conductance and the topology of the capillary imbibition. The application of the EMA shows that capillary imbibition is mainly produced in 1-D, and the pore structure is constituted by different pore throats in series, linked by chamber pores. The capillary process has been discussed as a function of their petrography and pore structure. Our study of the Washburn equation and the addition of correction factors for the pore structure allows a very accurate prediction of the weight rate.