Non‐Lipschitzian control algorithms: application to a nanofriction model

Recently we proposed a new feedback control algorithm for quantities describing global features of non‐linear dynamical systems. The performance of the algorithm, which is based on the concepts of non‐Lipschitzian dynamics and global targeting, has been successfully demonstrated for systems confined to one spatial dimension and for a specific targeted global quantity, namely the velocity of the centre of mass. In this paper we extend the scope of the non‐Lipschitzian control scheme to multi‐dimensional systems and different targeted quantities. We illustrate the efficiency of the non‐Lipschitzian feedback w.r.t. the ordinary (Lipschitzian) feedback, as well as the robustness and accuracy of the algorithm in a broad variety of control scenarios on the 2‐d Frenkel‐Kontorova model for nanofriction. Published in 2005 by John Wiley & Sons, Ltd.     

A general approximate‐state Riemann solver for hyperbolic systems of conservation laws with source terms

An approximate‐state Riemann solver for the solution of hyperbolic systems of conservation laws with source terms is proposed. The formulation is developed under the assumption that the solution is made of rarefaction waves. The solution is determined using the Riemann invariants expressed as functions of the components of the flux vector. This allows the flux vector to be computed directly at the interfaces between the computational cells. The contribution of the source term is taken into account in the governing equations for the Riemann invariants. An application to the water hammer equations and the shallow water equations shows that an appropriate expression of the pressure force at the interface allows the balance with the source terms to be preserved, thus ensuring consistency with the equations to be solved as well as a correct computation of steady‐state flow configurations. Owing to the particular structure of the variable and flux vectors, the expressions of the fluxes are shown to coincide partly with those given by the HLL/HLLC solver. Computational examples show that the approximate‐state solver yields more accurate solutions than the HLL solver in the presence of discontinuous solutions and arbitrary geometries. Copyright © 2006 John Wiley & Sons, Ltd.     

Synthesis of Ionic Liquids Using Non Conventional Activation Methods: An Overview

Summary. The synthesis of ionic liquids under non conventional activation methods is historically reviewed and completed with the recent developments of “one-pot” synthesis and combination of these activation methods.     

Commutation relations for Schramm‐Loewner evolutions

Schramm‐Loewner evolutions (SLEs) describe a one‐parameter family of growth processes in the plane that have particular conformal invariance properties. For instance, SLE can define simple random curves in a simply connected domain. In this paper we are interested in questions pertaining to the definition of several SLEs in a domain (i.e., several random curves). In particular, we derive infinitesimal commutation conditions, discuss some elementary solutions, study integrability conditions following from commutation, and show how to lift these infinitesimal relations to global relations in simple cases. The situation in multiply connected domains is also discussed. © 2007 Wiley Periodicals, Inc.     

Convergence of finite volume monotone schemes for scalar conservation laws on bounded domains

Summary. This paper is devoted to the study of the finite volume methods used in the discretization of conservation laws defined on bounded domains. General assumptions are made on the data: the initial condition and the boundary condition are supposed to be measurable bounded functions. Using a generalized notion of solution to the continuous problem (namely the notion of entropy process solution, see [9]) and a uniqueness result on this solution, we prove that the numerical solution converges to the entropy weak solution of the continuous problem in for every . This also yields a new proof of the existence of an entropy weak solution. Received May 18, 2000 / Revised version received November 21, 2000 / Published online June 7, 2001     

Note Equilibrium payoffs in stochastic games of incomplete information: the general symmetric case

We prove that the existence of equilibrium payoffs for stochastic games of incomplete symmetric information follows from the same result for stochastic games with complete information. Received January 1999/Revised October 2001     

N-complexes et algèbres de Hopf

We show that the category of N-complexes is monoidally equivalent to the category of comodules over a well chosen Hopf algebra. This generalizes Pareigis' previous result for N=2. To cite this article: J. Bichon, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Structural transitions in positive electrodes for Li-ion batteries the vibronic approach

We present the vibrational properties of manganese dioxides and lithiated oxides with either spinel-type and layered-type structure used as positive electrodes in Li-ion batteries. The local structure in γ-MnO₂ is investigated as a function of the intergrowth rate, Pr, of pyrolusite in the ramsdellite matrix and the phase evolution as a function of the degree of intercalation or deintercalation in 4-volt electrode materials Li_1−xCoO₂ and Li_1−xMn₂O₄. Lattice dynamics are studied using either a classical group theoretical analysis or a local environment model. Raman and FTIR bands are identified on the basis of vibrational modes of polyhedral units which are building the structure. Structural modifications induced by intercalation-deintercalation process are examined. Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, Sept. 16–22, 2001.     

Solid-state lithium microbatteries

Batteries of the size of microelectronic devices, less than 10 μm thick, are now being developed and built, using thin-film deposition technologies, i.e., flash-evaporation, rf-sputtering and sol-gel technique, that are compatible with integrated circuits. Their use in future micro-devices, microsensors, intergrated circuits, memories and very large-scale integration are envisaged. Advances have been made particularly in the engineering of lithium/amorphous inorganic electrolyte/layered compound cells. Physics of the solid-state microbatteries are reviewed and the latest advances presented. The adequacy and efficiency of materials is examined. New optimized lithium microbatteries including transition-metal oxides as intercalation cathodes, i.e., MoO₃, V₂O₅, and V₆O₁₃ films are presented and their advantages are discussed in detail. Paper presented at the 2nd Euroconference on Solid State Ionics, Funchal, Madeira, Portugal, 10–16 Sept. 1995.