L'équation de Navier–Stokes avec mémoire et le transfert de quantité de mouvement dans un milieu poreuxThe Navier–Stokes equation with memory,and momentum transfer in a porous medium

This paper is concerned with the momentum transfer in a porous medium. The equations for the continuous equivalent medium are written by the averaging method but the closure is obtained using an extended thermodynamics. The resulting model corresponds to the Navier–Stokes equation, in which the force exerted by the solid matrix on the fluid satisfies of first order differential equation. This Navier–Stokes equation model with memory generalises the Darcy model with an integro-differential term. To cite this article: O. Séro-Guillaume, D. Calogine, C. R. Mecanique 330 (2002) 383–389.     

Estimations anisotropes dans les convexes de type fini

Let Ω be a smoothly bounded convex domain of finite type m and f be a (0,1)-form -closed in Ω. It is proved that the equation admits a solution u belonging to the space Λ1(Ω) (respectively to the anisotropic space Γ^α_(ρ) of McNeal-Stein, for all α,0<α<1/m) if the anisotropic norm - introduced by Bruna-Charpentier-Dupain - is finite (respectively if the Euclidian norm ‖f‖_∞ of the form f is finite).     

Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light

We review recent developments regarding the quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues, by analogy with atomic physics. We start with quantum impurity models addressing dissipative and driven systems. Both theorists and experimentalists are making efforts towards the characterization of these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect can be characterized by a renormalized light frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled with an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing one to engineer the Jaynes–Cummings lattice and Rabi lattice models through the presence of superconducting qubits in the cavities. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott–superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin–orbit couplings have been successfully implemented in quantum materials and with ultra-cold atoms in optical lattices — using time-dependent Floquet perturbations periodic in time, for example — as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose–Hubbard models in ladder and two-dimensional geometries, producing phase coherence and Meissner currents. The Bose–Hubbard model is related to the Jaynes–Cummings lattice model in the large detuning limit between light and matter (the superconducting qubits). In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.     

Dynamics of a particle with friction and delay

We are interested in the motion of a simple mechanical system having a finite number of degrees of freedom subjected to a unilateral constraint with dry friction and delay effects (with maximal duration $\tau >0$). At the contact point, we characterize the friction by a Coulomb law associated with a friction cone. Starting from a formulation of the problem that was given by Jean-Jacques Moreau in the form of a second-order differential inclusion in the sense of measures, we consider a sweeping process algorithm that converges towards a solution to the dynamical contact problem. The mathematical machinery as well as the general plan of the existence proof may seem much too heavy in order to treat just this simple case, but they have proved useful in more complex settings.     

D-brane models and flux supersymmetry breaking

We describe recent work on constructing four-dimensional string models with moduli stabilized by field strength fluxes and chiral gauge sectors close to the Standard Model from D-brane configurations. We discuss how the interplay of both ingredients relates to phenomenological issues, in particular the appearance of soft terms on the D-brane gauge sector induce from non-supersymmetric flux backgrounds. To cite this article: A.M. Uranga, C. R. Physique 5 (2004).

Résumé

Nous décrivons des travaux récents de constructions de modèles de cordes à 4 dimensions ayant des modules stabilisés par des flux, ainsi que des secteurs chiraux de jauge proches du modèle standard, réalisés à partir de configurations de D-branes. Nous expliquons comment les liens entre les différents ingrédients relient des aspects phénoménologiques, en particulier l'apparition de termes doux dans le secteur de jauge des D-branes à partir de champs de fonds non-supersymétriques avec flux. Pour citer cet article : A.M. Uranga, C. R. Physique 5 (2004).     

Non-linear dynamic of rotor–stator system with non-linear bearing clearanceDynamique non-linéaire d'un ensemble rotor–stator comportant un roulement non-linéaire avec jeu

The study deals with a rotor–stator contact inducing vibration in rotating machinery. A numerical rotor–stator system, including a non-linear bearing with Hertz contact and clearance is considered. To determine the non-linear responses of this system, non-linear dynamic equations can be integrated numerically. However, this procedure is both time consuming and costly to perform. The aim of this Note is to apply the Alternate Frequency/Time Method and the ‘path following continuation’ in order to obtain the non-linear responses to this problem. Then the orbits of rotor and stator responses at various speeds are investigated. To cite this article: J.-J. Sinou, F. Thouverez, C. R. Mecanique 332 (2004).     

Molecular vibrations of complexes with trigonal ligands. Part V. Symmetry coordinates for tetrahedral complexes

Ligands of C_3V symmetry are assumed to be a part of a T_d complex. Suitable combinations of C_3v (a₂ + e) symmetry coordinates, which fit into the T_d model, are studied. The results constitute a useful supplement to the C_3V (a₁ + e) type coordinates studied previously. Torsional coordinates in the Ni(PF₃)₄ type model are treated in particular.     

Etude des reactions pericycliques sous pression—IV: Cyclodimerisation thermique de l'acroleine et de la methylvinylcetone

The thermal cyclodimerization of acrolein with methyl vinyl ketone gives selectively only one substituted dihydropyran. The rate is only slightly sensitive to the nature of the solvent; however a slight decrease of the reaction rate with increasing solvent polarity was observed. Effects of high pressure give strong support for a one-step mechanism and the formation of a transition state more compact than the adduct.