Projective degenerations of K3 surfaces,Gaussian maps,and Fano threefolds

Summary In this article we exhibit certain projective degenerations of smoothK3 surfaces of degree 2g–2 in ^g (whose Picard group is generated by the hyperplane class), to a union of two rational normal scrolls, and also to a union of planes. As a consequence we prove that the general hyperplane section of suchK3 surfaces has a corank one Gaussian map, ifg=11 org13. We also prove that the general such hyperplane section lies on a uniqueK3 surface, up to projectivities. Finally we present a new approach to the classification of prime Fano threefolds of index one, which does not rely on the existence of a line.Oblatum 1-II-1993 & 24-V-1993Research supported in part by NSF grant DMS-9104058     

Experimental testing of Taylor's hypothesis by L.D.A. in highly turbulent flow

A new configuration for the transmitting optics of a laser Doppler anemometer has been developed in order to measure the velocity at two different points at the same time. From the simultaneous measurements at two points along the mean flow direction it is possible to evaluate the spatial correlations and to compare them with the temporal correlation to verify the validity limits of Taylor's hypothesis also known as the frozen turbulence hypothesis. The transfer function between the velocity signals at two different points has been introduced to better explain the differences between Taylor's hypothesis and non frozen flow. The analysis is carried out in a flow with high turbulence levels.     

Structure ofcatena-(2-amino-1,3,4-thiadiazolium, 2-amino-1,3,4-thiadiazole bis(μ-iodo)-di-iodo-bismuth(III)

[(C₂H₄N₃S) (C₂H₃N₃S) BiI₄]; [(HL) (L) BiI₄] (L=2-amino-1,3,4-thiadiazole),M _r=919.86. monoclinic, P 1 2₁/a 1,a=7.622(1),b=18.977(2),c=12.821(1) Å, =102.77(1)°, finalR=0.033. The crystals consist of HL⁺ cations, neutral L molecules and polymeric [BiI₄] ^– anions built up of edge-sharing [BiI₆]^3– octahedra, with Bi–I(bridging) distances in the range 3.320(1)–3.057(1) Å and Bi–I(terminal) distances in the range 2.917(1)–2.929(1) Å. The¹H and¹³C spectra in DMSO-d₆ solution are used in conjunction with the X-ray structural results to establish the preferred protonation site of the thiadiazole ring.     

Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian

We introduce various families of irreducible homaloidal hypersurfaces in projective space Pr, for all r?3. Some of these are families of homaloidal hypersurfaces whose degrees are arbitrarily large as compared to the dimension of the ambient projective space. The existence of such a family solves a question that has naturally arisen from the consideration of the classes of homaloidal hypersurfaces known so far. The result relies on a fine analysis of hypersurfaces that are dual to certain scroll surfaces. We also introduce an infinite family of determinantal homaloidal hypersurfaces based on a certain degeneration of a generic Hankel matrix. The latter family fit non-classical versions of de Jonquières transformations. As a natural counterpoint, we broaden up aspects of the theory of Gordan-Noether hypersurfaces with vanishing Hessian determinant, bringing over some more precision into the present knowledge.     

Micromorphic continua: non-redundant formulations

The kinematics of generalized continua is investigated and key points concerning the definition of overall tangent strain measure are put into evidence. It is shown that classical measures adopted in the literature for micromorphic continua do not obey a constraint qualification requirement, to be fulfilled for well-posedness in optimization theory, and are therefore termed redundant. Redundancy of continua with latent microstructure and of constrained Cosserat continua is also assessed. A simplest, non-redundant, kinematic model of micromorphic continua, is proposed by dropping the microcurvature field. The equilibrium conditions and the related variational linear elastostatic problem are formulated and briefly discussed. The simplest model involves a reduced number of state variables and of elastic constitutive coefficients, when compared with other models of micromorphic continua, being still capable of enriching the Cauchy continuum model in a significant way.     

Neutron enhancement from laser interaction with a critical fluid

We discuss experimentally and theoretically neutron production from the laser driven explosion of gas clusters prepared near the liquid-gas critical point. We let deuterated methane that was prepared very close to its critical temperature and pressure expand through a conical nozzle to create clusters, and then irradiated those clusters with a high intensity pulse from the Texas Petawatt Laser. After ionization, the clusters explode producing energetic ions, some of which fuse with resultant neutron emission. We show that the critical fluctuations present in the nozzle before the expansion influence the dynamics of neutron production. Neutron production near the critical point follows a power law, which is a signature of a second order phase transition and it is consistent with the Fisher model. This result might be relevant for energy production from fusion reactions.     

Evaluation of the performance of high-speed PIV compared to standard PIV in a turbulent jet

In this paper, a comparison between two particle image velocimetry (PIV) systems, one based on a standard cross-correlation charge coupled device (CCD) camera with pulsed laser and another using high-speed complementary metal oxide semiconductor (CMOS) camera with continuous laser is performed. The objective of the paper is to point out advantages and disadvantages of the two systems when computing large and small flow scale statistics. The comparison is performed on velocity measurements in the near and far fields of a circular water jet: on this flow several experimental data and empirical self-similarity laws are available for comparisons. The results show that both systems are suitable for measurements with a preference for the standard one when investigating small-scale statistics. This result depends on the lower number of effectively independent samples acquired by a high-speed system and on the higher noise levels of CMOS sensors in comparison to CCDs.     

Microstructuring of diamond bulk by IR femtosecond laser pulses

We report the fabrication of graphitic microstructures in the bulk of chemical vapor deposited (CVD) diamond using 120-fs laser pulses at 800-nm wavelength. The nature of the laser-modified region and generation of mechanical stresses in the surrounding diamond is studied with Raman spectroscopy. A spontaneous growth of the laser-modified region from the focal plane towards the laser has been visualized in the process of multipulse irradiation with different pulse energies. The formation of discrete or continuous graphitized structures is revealed depending on the varied local laser intensity. The physical processes governing the appearance of separate graphitic globules and continuous extension of the graphitized region are discussed. Controlling the laser irradiation conditions permits us to fabricate graphitic wires with typical length of 150 μm and diameter of 1.5 μm. The longer, 300-ps pulses, as applied to laser microstructuring of the CVD diamond bulk, are found to be inappropriate due to the stronger influence of structural defects on the damage threshold, the noticeable fluctuation of the structure diameter over the length and the pronounced cracking of the surrounding diamond. PACS 42.62.-b; 61.80.Ba     

Zinc oxide nanostructures grown by pulsed laser deposition

We report the use of PLD to grow different ZnO nanostructures. Very different film morphologies have been observed using different laser wavelengths to ablate the target. The influence of substrate temperature and oxygen background pressure on the film morphology has been investigated too. Smooth and rough films, hexagonal pyramids and columns have been obtained by using a KrF excimer laser (248 nm) for the target ablation, while hexagonal hierarchical structures and pencils have been obtained by using ArF (193 nm). Photoluminescence and X-ray diffraction measurements revealed the good quality of the samples, in particular of those deposited using the ArF laser beam.