Parametric generation of twin photons in vertical triple microcavities

We report the realization of a monolithic vertical-cavity, surface emitting micro-optical parametric conversion nanostructure, triply resonant with the parametric frequencies, allowing parametric oscillation with ultra-low pump power threshold. The photonic phase-space naturally provides triple resonance for the parametric frequencies, together with built-in cavity phase-matching for the pump wave at normal incidence. Parametric oscillation is observed in both the strong and weak exciton–photon coupling regime, allowing a high operating temperature. Signal and idler beams can be collected at 0° or at finite angles. The OPO threshold is low enough to envisage the realization of an all-semiconductor electrically-pumped micro-parametric oscillator. To cite this article: C. Diederichs et al., C. R. Physique 8 (2007).     

Magnetic measurement of transport AC losses in Bi-2223/Ag tapes

Magnetic nature of the losses in superconducting wire carrying AC current implies that it should be possible to determine these losses in a contactless way. Ribbon-like samples are quite favorable for such an experiment, because a notable portion of magnetic flux related to losses ‘escapes' the sample volume and can be detected by an appropriate pick-up coil. In this case, a model describing the AC current penetration into the tape, based, e.g., on the critical state model, allows one to derive the losses from the pick-up coil signal. Because this signal is proportional to the number of coil turns, extension of the accessible range of measured voltages (and losses) can be achieved. We demonstrate the data obtained on a 1 cm long portion of a low-loss multifilamentary tape carrying AC current with frequency 35 Hz. The pick-up coil technique allowed us to reach loss level more than one order below the experimental limit for direct measurements.     

Chaos and unpredictability in evolutionary dynamics in discrete time

A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from those of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace the usual fixed-point population solutions. We observe the familiar period-doubling and chaotic-band-splitting attractor cascades of unimodal maps but in some cases more elaborate variations appear due to bimodality. Also unphysical stationary solutions can have unusual physical implications, such as the uncertainty of the final population caused by sensitivity to initial conditions and fractality of attractor preimage manifolds.     

Stable colloidal suspensions of nanostructured zirconium oxide synthesized by hydrothermal process

Nanocrystalline zirconium oxide was synthesized by hydrothermal treatment of ZrO(NO₃)₂ and ZrOCl₂ aqueous solutions at different temperatures and time in presence of hydrogen peroxide. Hydrothermal treatment of zirconium salts (0.25 and 0.50 mol L^?1) produced nanocrystalline monoclinic ZrO₂ powders with narrow size distribution, which were formed by the attachment of the smaller particles with crystallites size of 3.5 nm, estimated by means of the Scherrer’s equation and confirmed by transmission electronic microscopy. Typical monoclinic zirconium oxide X-ray powder diffraction patterns and Raman spectra were obtained for all the crystalline powders. It was observed that the crystallization depends strongly on the temperature, resulting in amorphous material when the synthesis was realized at 100 °C, and crystalline with monoclinic phase when synthesized at 110 °C, independently of the salt used. Zirconium oxide colloidal nanoparticles were formed only at hydrothermal treatments longer than 24 h. The stability of the colloids was successfully characterized of zeta potential, showing an initial value of + 59.2 mV in acid media and isoelectric point at pH = 5.2, in good agreement with previous studies.     

Algebraic models defined over Q of differential manifolds

Here we prove that every compact differential manifold has a smooth algebraic model defined over Q. In dimension 2 we find an algebraic model (may be singular) defined over Q and birational over Q to the projective plane.     

Positive\partial \bar \partial - closed currents and non-Kähler geometrycurrents and non-Kähler geometry

In this paper some new results on positive \(\partial \bar \partial - closed\) currents are applied to modifications \(f:\bar M \to M\) . The main result in this topic is that every smooth proper modification of a compact Kähler manifoldM is balanced. Moreover, under suitable hypotheses on the map, the Kähler degrees of \(\bar M\) corresponds to homological properties of the exceptional set of the modification. More examples ofp-Kähler manifolds are discussed in the last section of the paper.     

Ordinary differential operators in Hilbert spaces and Fredholm pairs

Let be a path of bounded operators on a real Hilbert space, hyperbolic at . We study the Fredholm theory of the operator . We relate the Fredholm property of to the stable and unstable linear spaces of the associated system . Several examples are included to point out the differences with respect to the finite dimensional case, in particular concerning the role of the spectral flow. We define a general class of paths A for which many properties typical of the finite dimensional framework still hold. Our motivation is to develop the linear theory which is necessary for the set-up of Morse homology on Hilbert manifolds. Received: 9 March 2001; in final form: 1 March 2002 / Published online: 2 December 2002     

Two exact algorithms for the capacitated p-median problem

The p-median problem has been widely studied in combinatorial optimisation, but its generalisation to the capacitated case has not. We propose a branch and price algorithm, comparing it with a standard MIP solver and a branch and bound algorithm based on Lagrangean relaxation. We present computational experience, using test instances drawn from the literature and new instances with higher ratio between the number of medians p and the number of nodes N. The branch and price algorithm shows very good performances and computational time robustness in solving problems for any ratio.Received: December 2002, Revised: August 2003AMS classification: 90C10, 90C27