Generic Syzygy Schemes

For a finite dimensional vector space G we define the k-th generic syzygy scheme Gensyz_k(G) by explicit equations. We show that the syzygy scheme Syz(f) of any syzygy in the linear strand of a projective variety X which is cut out by quadrics is a cone over a linear section of a corresponding generic syzygy scheme. We also give a geometric description of Gensyz_k(G) for k=0,1,2. In particular Gensyz_2(G) is the union of a Pl"ucker embedded Grassmannian and a linear space. From this we deduce that every smooth, non-degenerate projective curve C which is cut out by quadrics and has a p-th linear syzygy of rank p+3 admits a rank 2 vector bundle E with det E = O_C(1) and h^0(E) at least p+4.Comment: 12 Pages. This paper is a completely rewritten version of the first part of math.AG/0108078. It also contains several new result

Internal-wave radiation by a horizontally oscillating body in a uniformly stratified fluid

International audienceIn this experimental-theoretical study we consider the waves emitted by a horizontally oscillating sphere in a linearly stratified fluid. In contrast to former investigations, the thus generated wave pattern is a-symmetric and three-dimensional. We consider large and small amplitude horizontal oscillations for different size spheres. The spatial structure of internal waves has a non-trivial dependence on the body geometry, direction and frequency of oscillations. The flowfield is measured quantitatively, using an alternative version of the synthetic schlieren technique. In addition we exploit the technique to visualise internal waves with fluorescein dye planes used by Hopfinger et al (Exp. in Fluids, 11, 1991) to measure the displacement field of the internal waves. For the theory a uniformly stratified viscous Boussinesq fluid of infinite extent is considered, with small viscosity and the boundary layer on the body surface neglected. For small amplitude oscillations, the comparison with the theory is good, with the near-field theory being in very good agreement with the experimental results and the far field theory slightly overestimating the wave amplitude

Internal wave structure emitted by a horizontally oscillating sphere

International audienceAn oscillating body in a stratified fluid generates a double cone-shaped internal-wave pattern, the 3D analogue of the classic St.Andrew-cross. For sufficiently low frequency and large amplitude oscillations, higher-order wave harmonics may be generated along with the fundamental one. We present an experimental study of the 3D structure of first- and second-order wave fields emitted by a horizontally oscillating sphere. In contrast to the axisymmetric wave pattern found for a vertically oscillating sphere, for horizontal oscillations, the first- and higher-order-harmonic waves have different distributions of wave amplitudes in the azimuthal direction. The amplitude of the first-order waves is shown to follow the cosine dependence on the azimuthal angle, in accordance with theoretical predictions. The azimuthal distribution of the amplitude of the second-order waves gives evidence of a quadrupolar distribution, with four preferential directions of wave radiation in a horizontal plane, along the direction of oscillation and normal to it. Noteworthy is that the amplitudes of these second-order waves may exceed the amplitude of first-order waves

First and second harmonic internal waves from a horizontally oscillating sphere

International audienceA horizontally oscillating sphere in a density-stratified fluid is studied experimentally and theoretically, as a paradigm of the generation of three-dimensional internal tides by supercritical topography. The experiments implement a novel technique for the measurement of the spatial structure of internal wave fields, based on horizontal fluorescent dye planes and a mobile vertical laser sheet; they are compared with an original linear theory. Spectral analysis reveals the presence of two harmonics, namely a first harmonics at the fundamental frequency and a second harmonics at twice this frequency. The first harmonics has a dipolar structure, an amplitude varying linearly with the amplitude of oscillation, and is quantitatively described by the theory. The second harmonics is present at amplitudes of oscillation higher than one tenth of the sphere radius and has a quadrupolar structure. Its amplitude varies quadratically with the amplitude of oscillation, and may exceed the amplitude of the first harmonics. At frequencies smaller than half the buoyancy frequency, the second harmonics is evanescent and confined to the vicinity of the sphere; at frequencies larger than half the buoyancy frequency, it propagates away

Three dimensional internal-wave radiation by a horizontally oscillating body in a uniformly stratified fluid

International audienceThe energy radiated by a vertically oscillating sphere in a uniformly stratified fluid has, in shadowgraph and schlieren images, the well known "St. Andrew cross" ray pattern. Since the wave length does not appear in the dispersion relation, the spatial structure of internal waves has non-trivial dependence on the body geometry, direction and frequency of oscillations, and the viscosity. In contrast to former investigations, in the present investigation we consider the asymmetric 3D wave pattern for large and small amplitude horizontal oscillation of different size spheres. New experimental techniques are explored. For small oscillations good agreement is found with linear theory; in addition to comparison between experimental data and theoretical (near-field) solution we also present the comparison between the far-field and near-field solutions

A tunable, dual mode field-effect or single electron transistor

A dual mode device behaving either as a field-effect transistor or a single electron transistor (SET) has been fabricated using silicon-on-insulator metal oxide semiconductor technology. Depending on the back gate polarisation, an electron island is accumulated under the front gate of the device (SET regime), or a field-effect transistor is obtained by pinching off a bottom channel with a negative front gate voltage. The gradual transition between these two cases is observed. This dual function uses both vertical and horizontal tunable potential gradients in non-overlapped silicon-on-insulator channel

Efficient dynamical nuclear polarization in quantum dots: Temperature dependence

We investigate in micro-photoluminescence experiments the dynamical nuclear polarization in individual InGaAs quantum dots. Experiments carried out in an applied magnetic field of 2T show that the nuclear polarization achieved through the optical pumping of electron spins is increasing with the sample temperature between 2K and 55K, reaching a maximum of about 50%. Analysing the dependence of the Overhauser shift on the spin polarization of the optically injected electron as a function of temperature enables us to identify the main reasons for this increase.Comment: 5 pages, 3 figure

Focalisation linéaire d'ondes internes par un tore oscillant

Parmi les phénomènes susceptibles de provoquer localement une intensification de l'amplitude des ondes internes dans un fluide stratifié, et ainsi de conduire au mélange, figure un phénomène spécifiquement tridimensionnel : la focalisation géométrique causée par la forme de l'émetteu

Étale motivic cohomology and algebraic cycles

We consider etale motivic or Lichtenbaum cohomology and its relation to algebraic cycles. We give an geometric interpretation of Lichtenbaum cohomology and use it to show that the usual integral cycle maps extend to maps on integral Lichtenbaum cohomology. We also show that Lichtenbaum cohomology, in contrast to the usual motivic cohomology, compares well with integral cohomology theories. For example, we formulate integral etale versions of the Hodge and the Tate conjecture, and show that these are equivalent to the usual rational conjectures

Cohomology of skew-holomorphic Lie algebroids

We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.Comment: 16 pages. v2: Final version to be published in Theor. Math. Phys. (incorporates only very minor changes