Base manifolds for fibrations of projective irreducible symplectic manifolds

Given a projective irreducible symplectic manifold $M$ of dimension $2n$, a projective manifold $X$ and a surjective holomorphic map $f:M \to X$ with connected fibers of positive dimension, we prove that $X$ is biholomorphic to the projective space of dimension $n$. The proof is obtained by exploiting two geometric structures at general points of $X$: the affine structure arising from the action variables of the Lagrangian fibration $f$ and the structure defined by the variety of minimal rational tangents on the Fano manifold $X$

Experimental evidence on the development of scale invariance in the internal structure of self-affine aggregates

It is shown that an alternative approach for the characterization of growing branched patterns consists of the statistical analysis of frozen structures, which cannot be modified by further growth, that arise due to competitive processes among neighbor growing structures. Scaling relationships applied to these structures provide a method to evaluate relevant exponents and to characterize growing systems into universality classes. The analysis is applied to quasi-two-dimensional electrochemically formed silver branched patterns showing that the size distribution of frozen structures exhibits scale invariance. The measured exponents, within the error bars, remind us those predicted by the Kardar-Parisi-Zhang equation.Comment: 11 pages, 4 figure

Evidence for a charge Kondo effect in Pb(1-x)Tl(x)Te from measurements of thermoelectric power

We report measurements of the thermoelectric power (TEP) for a series of Pb(1-x)Tl(x)Te crystals with x = 0.0 to 1.3%. Although the TEP is very large for x = 0.0, using a single band analysis based on older work for dilute magnetic alloys we do find evidence for a Kondo contribution of 11 - 18 uV/K. This analysis suggests that Tk is ~ 50 - 70 K, a factor 10 higher than previously thought.Comment: 4 pages, 3 figure

Single crystal MgB2 with anisotropic superconducting properties

The discovery of superconductor in magnesium diboride MgB2 with high Tc (39 K) has raised some challenging issues; whether this new superconductor resembles a high temperature cuprate superconductor(HTS) or a low temperature metallic superconductor; which superconducting mechanism, a phonon- mediated BCS or a hole superconducting mechanism or other new exotic mechanism may account for this superconductivity; and how about its future for applications. In order to clarify the above questions, experiments using the single crystal sample are urgently required. Here we have first succeeded in obtaining the single crystal of this new MgB2 superconductivity, and performed its electrical resistance and magnetization measurements. Their experiments show that the electronic and magnetic properties depend on the crystallographic direction. Our results indicate that the single crystal MgB2 superconductor shows anisotropic superconducting properties and thus can provide scientific basis for the research of its superconducting mechanism and its applications.Comment: 7 pages pdf fil

A spinor approach to Walker geometry

A four-dimensional Walker geometry is a four-dimensional manifold M with a neutral metric g and a parallel distribution of totally null two-planes. This distribution has a natural characterization as a projective spinor field subject to a certain constraint. Spinors therefore provide a natural tool for studying Walker geometry, which we exploit to draw together several themes in recent explicit studies of Walker geometry and in other work of Dunajski (2002) and Plebanski (1975) in which Walker geometry is implicit. In addition to studying local Walker geometry, we address a global question raised by the use of spinors.Comment: 41 pages. Typos which persisted into published version corrected, notably at (2.15

Fibrations on four-folds with trivial canonical bundles

Four-folds with trivial canonical bundles are divided into six classes according to their holonomy group. We consider examples that are fibred by abelian surfaces over the projective plane. We construct such fibrations in five of the six classes, and prove that there is no such fibration in the sixth class. We classify all such fibrations whose generic fibre is the Jacobian of a genus two curve.Comment: 28 page

SMA/PdBI multiple line observations of the nearby Seyfert2 galaxy NGC 1068: Shock related gas kinematics and heating in the central 100pc?

We present high angular resolution (0.5-2.0") observations of the mm continuum and the 12CO(J=3-2), 13CO(J=3-2), 13CO(J=2-1), C18O(J=2-1), HCN(J=3-2), HCO+(J=4-3) and HCO+(J=3-2) line emission in the circumnuclear disk (r=100pc) of the proto-typical Seyfert type-2 galaxy NGC1068, carried out with the Submillimeter Array. We further include in our analysis new 13CO(J=1-0) and improved 12CO(J=2-1) observations of NGC1068 at high angular resolution (1.0-2.0") and sensitivity, conducted with the IRAM Plateau de Bure Interferometer. Based on the complex dynamics of the molecular gas emission indicating non-circular motions in the central ~100pc, we propose a scenario in which part of the molecular gas in the circumnuclear disk of NGC1068 is radially blown outwards as a result of shocks. This shock scenario is further supported by quite warm (Tkin>=200K) and dense (nH2=10^4cm^-3) gas constrained from the observed molecular line ratios. The HCN abundance in the circumnuclear disk is found to be [HCN]/[12CO]=10^-3.5. This is slightly higher than the abundances derived for galactic and extragalactic starforming/starbursting regions. This results lends further support to X-ray enhanced HCN formation in the circumnuclear disk of NGC1068, as suggested by earlier studies. The HCO+ abundance ([HCO+]/[12CO]=10^-5) appears to be somewhat lower than that of galactic and extragalactic starforming/starbursting regions. When trying to fit the cm to mm continuum emission by different thermal and non-thermal processes, it appears that electron-scattered synchrotron emission yields the best results while thermal free-free emission seems to over-predict the mm continuum emission.Comment: accepted for publication by ApJ; 35pages, 22 figures and 6 tables (at the end of the file); 3 figures have been decreased in quality to match size limi

Magnetic Properties of 2-Dimensional Dipolar Squares: Boundary Geometry Dependence

By means of the molecular dynamics simulation on gradual cooling processes, we investigate magnetic properties of classical spin systems only with the magnetic dipole-dipole interaction, which we call dipolar systems. Focusing on their finite-size effect, particularly their boundary geometry dependence, we study two finite dipolar squares cut out from a square lattice with $\Phi=0$ and $\pi/4$, where $\Phi$ is an angle between the direction of the lattice axis and that of the square boundary. Distinctly different results are obtained in the two dipolar squares. In the $\Phi=0$ square, the ``from-edge-to-interior freezing'' of spins is observed. Its ground state has a multi-domain structure whose domains consist of the two among infinitely (continuously) degenerated Luttinger-Tisza (LT) ground-state orders on a bulk square lattice, i.e., the two antiferromagnetically aligned ferromagnetic chains (af-FMC) orders directed in parallel to the two lattice axes. In the $\Phi=\pi/4$ square, on the other hand, the freezing starts from the interior of the square, and its ground state is nearly in a single domain with one of the two af-FMC orders. These geometry effects are argued to originate from the anisotropic nature of the dipole-dipole interaction which depends on the relative direction of sites in a real space of the interacting spins.Comment: 21 pages, 13 figures, submitted to Journal of Physical Society Japa