Homogenization and concentrated capacity in reticular almost disconnected structuresHomogénéisation et capacité concentrée dans les structures réticulaires presque déconnectées

We compute the homogenized-concentrated limit for a pair of non-linearly coupled diffusion equations in a perforated cylindric domain with coaxial cylindric holes periodically distributed along its axis. This problem arises from visual transduction. To cite this article: D. Andreucci et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 329–332.     

A Wiener-type condition for boundary continuity of quasi-minima of variational integrals

A Wiener-type condition for the continuity at the boundary points of Q-minima, is established, in terms of the divergence of a suitable Wiener integral.     

High T(c) superconductivity in MgB2 by nonadiabatic pairing

The evidence for the key role of the sigma bands in the electronic properties of MgB2 points to the possibility of nonadiabatic effects in the superconductivity of these materials. These are governed by the small value of the Fermi energy due to the vicinity of the hole doping level to the top of the sigma bands. We show that the nonadiabatic theory leads to a coherent interpretation of T(c) = 39 K and the boron isotope coefficient alphaB = 0.30 without invoking very large couplings and it naturally explains the role of the disorder on T(c). It also leads to various specific predictions for the properties of MgB2 and for the material optimization of these types of compounds.     

Nonadiabatic superconductivity in fullerene-based materials

Fullerene compounds have phonon frequencies up to ω_max=0.2 eV and a Fermi energy of the order E_F=0.3 eV. It is, therefore, expected that the adiabatic parameter λω_ph/E_F (where λ is the electron-phonon coupling constant and ω_ph is a typical phonon frequency) is not a priori negligible and the conventional theory of phonon-mediated superconductivity is inapplicable in this case. Here, we discuss how the conventional theory is inconsistent with a number of experimental data and provide a generalization of the theory in order to include nonadiabatic electron-phonon effects. We show that the inclusion of nonadiabatic channels in the electron-phonon interaction is a key element for the high values of T_c in these materials. We make several predictions regarding the superconducting and normal-state properties of fullerene compounds that can be tested experimentally.     

Polaronic and nonadiabatic phase diagram from anomalous isotope effects

Isotope effects (IEs) are powerful tools to probe directly the dependence of many physical properties on lattice dynamics. In this Letter we investigate the onset of anomalous IEs in the spinless Holstein model by employing the dynamical mean field theory. We show that the isotope coefficients of the electron effective mass and of the dressed phonon frequency are sizable also far away from the polaronic crossover and mark the importance of nonadiabatic lattice fluctuations. We draw a nonadiabatic phase diagram in which we identify a novel crossover, not related to polaronic features, where the IEs attain their largest anomalies.     

On complemented copies of c 0 and ℓ ∞

We furnish examples of pairs of Banach spaces X, Y so that none of c ₀ and l _∞ live inside X ^? and Y, but they embed complementably into the space DP(X,Y) of the Dunford–Pettis operators from X into Y.     

Study of temperature dependent atomic correlations in MgB2

We have studied temperature evolution of the local as well as the average crystal structure of MgB₂ using real-space atomic pair distribution function (PDF) measured by high resolution neutron powder diffraction in a wide temperature range of T=10–600 K. We find small positive correlation factors for the B–B and B–Mg pairs, determined by mean-square displacements (MSD) and the mean-square relative displacements (MSRD). We analyze the PDF using both Einstein and force constant models finding a good agreement between the experimental data and the two models. This indicates that B and Mg atomic correlations are not sensitive to the details of phonon dispersion.     

A linear hyperbolic system and an optimal control problem

We prove a theorem of existence, uniqueness, and continuous dependence for a linear hyperbolic system with Darboux-type conditions under assumptions on the coefficients, which are in a sense the most general possible. Moreover, an application of this result to an optimal control problem is given.     

Spin-Hall conductivity in electron-phonon coupled systems

We derive the ac spin-Hall conductivity sigmasH(omega) of two-dimensional spin-orbit coupled systems interacting with dispersionless phonons of frequency omega0. For the linear Rashba model, we show that the electron-phonon contribution to the spin-vertex corrections breaks the universality of sigmasH(omega) at low frequencies and provides a nontrivial renormalization of the interband resonance. On the contrary, in a generalized Rashba model for which the spin-vertex contributions are absent, the coupling to the phonons enters only through the self-energy, leaving the low-frequency behavior of sigmasH(omega) unaffected by the electron-phonon interaction.