Periodic orbits and chain-transitive sets of C1-diffeomorphisms

We prove that the chain-transitive sets of C¹-generic diffeomorphisms are approximated in the Hausdorff topology by periodic orbits. This implies that the homoclinic classes are dense among the chain-recurrence classes. This result is a consequence of a global connecting lemma, which allows to build by a C¹-perturbation an orbit connecting several prescribed points. One deduces a weak shadowing property satisfied by C¹-generic diffeomorphisms: any pseudo-orbit is approximated in the Hausdorff topology by a finite segment of a genuine orbit. As a consequence, we obtain a criterion for proving the tolerance stability conjecture in Diff¹(M).     

Approximate controllability for a system of Schrödinger equations modeling a single trapped ion

In this article, we analyze the approximate controllability properties for a system of Schrödinger equations modeling a single trapped ion. The control we use has a special form, which takes its origin from practical limitations. Our approach is based on the controllability of an approximate finite dimensional system for which one can design explicitly exact controls. We then justify the approximations which link up the complete and approximate systems. This yields approximate controllability results in the natural space (L²(R))²$(L^2{(\mathbb{R}))}^2$ and also in stronger spaces corresponding to the domains of powers of the harmonic operator.     

On four-dimensionals-cobordisms,II

Partially supported by NSF grants.     

Rational matrix pseudodifferential operators

The skewfield $\mathcal{K }(\partial )$ of rational pseudodifferential operators over a differential field $\mathcal{K }$ is the skewfield of fractions of the algebra of differential operators $\mathcal{K }[\partial ]$ . In our previous paper, we showed that any $H\in \mathcal{K }(\partial )$ has a minimal fractional decomposition $H=AB^{-1}$ , where $A,B\in \mathcal{K }[\partial ],\,B\ne 0$ , and any common right divisor of $A$ and $B$ is a non-zero element of $\mathcal{K }$ . Moreover, any right fractional decomposition of $H$ is obtained by multiplying $A$ and $B$ on the right by the same non-zero element of $\mathcal{K }[\partial ]$ . In the present paper, we study the ring $M_n(\mathcal{K }(\partial ))$ of $n\times n$ matrices over the skewfield $\mathcal{K }(\partial )$ . We show that similarly, any $H\in M_n(\mathcal{K }(\partial ))$ has a minimal fractional decomposition $H=AB^{-1}$ , where $A,B\in M_n(\mathcal{K }[\partial ]),\,B$ is non-degenerate, and any common right divisor of $A$ and $B$ is an invertible element of the ring $M_n(\mathcal{K }[\partial ])$ . Moreover, any right fractional decomposition of $H$ is obtained by multiplying $A$ and $B$ on the right by the same non-degenerate element of $M_n(\mathcal{K } [\partial ])$ . We give several equivalent definitions of the minimal fractional decomposition. These results are applied to the study of maximal isotropicity property, used in the theory of Dirac structures.     

Carbon nanotubes as nanoparticles collector

This communication reports on a new method for the collection of nanoparticles using carbon nanotubes (CNT) as collecting surfaces, by which the problem of agglomeration of nanoparticles can be circumvented. CNT (10–50 nm in diameter, 1–10 μm in length) were grown by thermal CVD at 923 K in a 7 v/v% C₂H₂ in N₂ mixture on electroless nickel-plated copper transmission electron microscopy (TEM) grids and Monel coupons. These samples were then placed downstream of an arc plasma reactor to collect individual copper nanoparticles (5–30 nm in diameter). It was observed that the Cu nanoparticles preferentially adhere onto CNT and that the macro-particles (diameter >1 μm), a usual co-product obtained with metal nanoparticles in the arc plasma synthesis, are not collected. Cu–Ni nanoparticles, a catalyst for CNT growth, were deposited on CNT to grow multibranched CNT. CNT-embedded thin films were produced by re-melting the deposited nanoparticles.     

Effect of finite pixel size on optical coupling in QWIPs

We study the optical coupling in quantum well photodetectors, focusing on finite size effects. We introduced a finite-element model of the detector and we show experimentally that the optical coupling efficiency is strongly dependent on the pixel size and that in very small detectors diffraction dominates the grating coupling. A 640 × 512 QWIP focal plane array was characterized to show that the optical response of thinned samples may depend on the substrate thickness noticeably. These results are in much closer agreement with predictions obtained with our model than using standard techniques.     

Sound focusing in rooms: the time-reversal approach

New perspectives in audible range acoustics, such as virtual sound space creation and active noise control, rely on the ability of the rendering system to recreate precisely a desired sound field. This ability to control sound in a given volume of a room is directly linked to the capacity to focus acoustical energy both in space and time. However, sound focusing in rooms remains a complicated problem, essentially because of the multiple reflections on obstacles and walls occurring during propagation. In this paper, the technique of time-reversal focusing, well known in ultrasound, is experimentally applied to audible range acoustics. Compared to classical focusing techniques such as delay law focusing, time reversal appears to considerably improve quality of both temporal and spatial focusing. This so-called super-resolution phenomenon is due to the ability of time reversal to take into account all of the different sound paths between the emitting antenna and the focal point, thus creating an adaptive spatial and temporal matched filter for the considered propagation medium. Experiments emphasize the strong robustness of time-reversal focusing towards small modifications in the medium, such as people in motion or temperature variations. Sound focusing through walls using the time-reversal approach is also experimentally demonstrated.     

Reflection measurements in CO2 laser solid deuterium target interaction

Using a 60 nsec, 300 MW CO₂ TEA laser reflection measurements from solid deuterium targets have been investigated. Energy, reflected and scattered pulse shape are recorded at various angles: 0°, 45°, 90°, 135°. Reflection, X-ray measurements and ion mean kinetic energy are correlated at the focussing lens position with respect to the target position. The maximum plasma temperature varies from 20 to 35 eV for incident laser fluxes ranging from 5 × 10¹⁰ up to 5 × 10¹¹ W/cm². The cut-off density inside the deuterium ice has been observed and located. In each case reflection has been found to be weak less than 5% for each direction. For the maximum fluxes X-ray energies greater than 0.5 keV have been observed.     

Effect of multiphoton absorption and free carriers in slow-light photonic crystal waveguides

We examine the effects of multiphoton absorption, free carriers, and disorder-induced linear scattering in slow-light photonic crystal waveguides. We derive an analytic formulation for self-phase modulation including the group velocity scaling of the nonlinear phase shift in materials limited by three-photon absorption as a representative nonlinear process. We investigate the role of free carriers and derive an approximate critical intensity at which these effects begin to strongly modify the optical field. This critical intensity is employed to determine an optimal group index for the self-phase modulation in the slow-light devices. These observations are confirmed with numerical modeling.     

Melonic Phase Transition in Group Field Theory

Group field theories have recently been shown to admit a 1/N expansion dominated by so-called ‘melonic graphs’, dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher-dimensional generalization of the Kirchhoff tree-matrix theorem. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov–Ooguri models, which describe topological BF theories and are the basis for the construction of 4-dimensional models of quantum gravity.