Flip-flop operation in opto-thermal bistable devices with localized absorption

We consider nonlinear interferometric devices based on opto-thermal bistability with localized absorption and show how the introduction of composite structures within the interferometer makes feasible its setting and resetting between stable outputs by applying positive light pulses on different parts of the bistable device. Experimental demonstration of all-optical flip-flop operation is reported for two interferometric configurations, one of them being extremely simple and well suited for parallel processing.     

Invariant manifolds of periodic orbits for piecewise linear three-dimensional systems

This paper analyses the existence of invariant manifolds ofperiodic orbits for a specific piecewise linear three-dimensionalsystem with two zones, whose linear parts share a pair of imaginaryeigenvalues. This degenerate situation is obtained from thelack of controllability. The analysis proceeds by its reductionto a periodic one-dimensional equation for which some resultsof the Ambrosetti–Prodi type are given.     

Polynomial decay and control of a 1−d model for fluid–structure interaction

We consider a linearized and simplified 1?d model for fluid–structure interaction. The domain where the system evolves consists in two bounded intervals in which the wave and heat equations evolve respectively, with transmission conditions at the point of interface. First, we develop a careful spectral asymptotic analysis on high frequencies. Next, according to this spectral analysis we obtain sharp polynomial decay rates for the whole energy of smooth solutions. Finally, we prove the null-controllability of the system when the control acts on the boundary of the interval where the heat equation holds. The proof is based on a new Ingham-type inequality, which follows from the spectral analysis we develop and the null controllability result in Zuazua (in: J.L. Menaldi et al. (Eds.), Optimal Control and Partial Differential Equations, IOS Press, 2001, pp. 198–210) where the control acts on the wave component. To cite this article: X. Zhang, E. Zuazua, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Kondo effect in a double quantum-dot molecule under the effect of an electric and magnetic field

Electron tunneling through a double quantum-dot molecule, in the Kondo regime, under the effect of a magnetic field and an applied voltage, is studied. This system possesses a complex response to the applied fields characterized by a tristable solution for the conductance. The different nature of the solutions are studied in and out thermodynamical equilibrium. It is shown that the interdot coupling and the fields can be used to control the region of multistability. The mean-field slave-boson formalism is used to obtain the solution for the problem.     

A boundedness result for twisted convolution

We consider twisted convolution operators with kernels having singularities on a sphere and having as Fourier transform the oscillatory symbol m_α(|ξ|) = |ξ|^–αe^i|ξ|, 0 ≤ ??α < 2n. We give integral representations for such operators and, as a principal result, we study L_p–L_q estimates for them.     

Derivation of the amplitude equation for a hydromagnetic convective problem

The amplitude equation for a convective system under a vertical magnetic field is derived. The coefficients in these equations have been numerically calculated for infinite Prandtl number fluids and for boundary conditions both free and rigid top and bottom. The results confirm that, for realistic parameter values only stationary convection can be present and the pattern is made by convective rolls.     

Triangular strictly cyclic operators

The title refers to an empty class of operators. Moreover, if T is a triangular Banach space operator, then either T is algebraic and the double commutant has infinite strict multiplicity, or T is not algebraic and the commutant has infinite strict multiplicity. A rationally strictly cyclic, but not strictly cyclic, operator cannot have finite strict multiplicity.This research was partially supported by a Grant of the National Science Foundation.     

Structure functions of nucleons with excited supersymmetric particles

We calculate the QCD evolution equations for structure functions with supersymmetric particles excited for the following models: light gluinos, g? and heavy squarks q? with $\text{m}{}_{\mathrm{<mtext>g</mtext><mtext>?</mtext>}}\text{? Q}{}^2\text{? m}{}_{\mathrm{<mtext>q</mtext><mtext>?</mtext>}}{}^2$; light squarks, and heavy gluinos with $\text{m}{}_{\mathrm{<mtext>g</mtext><mtext>?</mtext>}}\text{? Q}{}^2\text{? m}{}_{\mathrm{<mtext>g</mtext><mtext>?</mtext>}}{}^2\text{;}\text{and}\text{m}{}_{\mathrm{<mtext>g</mtext><mtext>?</mtext>}}{}^2\text{, m}{}_{\mathrm{<mtext>g</mtext><mtext>?</mtext>}}{}^2\text{? Q}{}^2$. The momentum sum rules and the behaviour of structure functions as x → 1 are particularly discussed.     

Acoustic fluid flow through holes and permeability of perforated walls

We first study the unsteady incompressible fluid flow through a hole in a wall in the two- and three-dimensional cases. In the first case, a convolution relation is obtained between the fluid flux through the hole and the difference of pressure between the far regions on the two sides of the wall. In the two-dimensional case, the pressure increases logarithmically with distance from the wall. In a second part, we study acoustic flow in a domain containing a wall with many small holes. The distance between two contiguous holes is of order η and the size of each hole, ε (η and ε are two small parameters). In the three-dimensional case the critical behaviour appears for ε = η²: it is described by a convolution relation between the flow through the wall and the jump of pressure. In the two-dimensional case, the critical behaviour appears if η log ε tends to a constant; there is a differential relation between the flow through the wall and the jump of pressure.     

Das Schwingungsspektrum des synthetischen Carnotits

The infrared and laser-Raman spectra of synthetic carnotite, K₂[(UO₂)₂V₂O₈], are reported and discussed. Force constants for the terminal V-O bonds as well as for the UO₂ ²⁺ ions are evaluated. From the spectroscopic data, a U-O bond length of 1.81 Å is estimated for the uranyl ion in this compound.

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15. Mitteilung der Reihe Orthovanadate und verwandte Verbindungen 14. Mitt:E. J. Baran, J. C. Pedregosa undP. J. Aymonino, Mh. Chem.106 1085 (1975).