Deformation of canonical morphisms and the moduli of surfaces of general type

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite map can be deformed to a one--to--one map. We use this criterion to construct new simple canonical surfaces with different $c_1^2$ and $\chi$. Our general results enable us to describe some new components of the moduli of surfaces of general type. We also find infinitely many moduli spaces $\mathcal M_{(x',0,y)}$ having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism.Comment: 32 pages. Final version with some simplifications and clarifications in the exposition. To appear in Invent. Math. (the final publication is available at springerlink.com

Selfsimilar Domain Growth, Localized Structures and Labyrinthine Patterns in Vectorial Kerr Resonators

We study domain growth in a nonlinear optical system useful to explore different scenarios that might occur in systems which do not relax to thermodynamic equilibrium. Domains correspond to equivalent states of different circular polarization of light. We describe three dynamical regimes: a coarsening regime in which dynamical scaling holds with a growth law dictated by curvature effects, a regime in which localized structures form, and a regime in which polarization domain walls are modulationally unstable and the system freezes in a labyrinthine pattern.Comment: 13 pages, 6 figure

Ferromagnetism in defect-ridden oxides and related materials

The existence of high-temperature ferromagnetism in thin films and nanoparticles of oxides containing small quantities of magnetic dopants remains controversial. Some regard these materials as dilute magnetic semiconductors, while others think they are ferromagnetic only because the magnetic dopants form secondary ferromagnetic impurity phases such as cobalt metal or magnetite. There are also reports in d0 systems and other defective oxides that contain no magnetic ions. Here, we investigate TiO2 (rutile) containing 1 - 5% of iron cations and find that the room-temperature ferromagnetism of films prepared by pulsed-laser deposition is not due to magnetic ordering of the iron. The films are neither dilute magnetic semiconductors nor hosts to an iron-based ferromagnetic impurity phase. A new model is developed for defect-related ferromagnetism which involves a spin-split defect band populated by charge transfer from a proximate charge reservoir in the present case a mixture Fe2+ and Fe3+ ions in the oxide lattice. The phase diagram for the model shows how inhomogeneous Stoner ferromagnetism depends on the total number of electrons Ntot, the Stoner exchange integral I and the defect bandwidth W; the band occupancy is governed by the d-d Coulomb interaction U. There are regions of ferromagnetic metal, half-metal and insulator as well as nonmagnetic metal and insulator. A characteristic feature of the high-temperature Stoner magnetism is an an anhysteretic magnetization curve which is practically temperature independent below room temperature. This is related to a wandering ferromagnetic axis which is determined by local dipole fields. The magnetization is limited by the defect concentration, not by the 3d doping. Only 1-2 % of the volume of the films is magnetically ordered.Comment: 22 pages, 6 figure

On the Effective Description of Large Volume Compactifications

We study the reliability of the Two-Step moduli stabilization in the type-IIB Large Volume Scenarios with matter and gauge interactions. The general analysis is based on a family of N=1 Supergravity models with a factorizable Kaehler invariant function, where the decoupling between two sets of fields without a mass hierarchy is easily understood. For the Large Volume Scenario particular analyses are performed for explicit models, one of such developed for the first time here, finding that the simplified version, where the Dilaton and Complex structure moduli are regarded as frozen by a previous stabilization, is a reliable supersymmetric description whenever the neglected fields stand at their leading F-flatness conditions and be neutral. The terms missed by the simplified approach are either suppressed by powers of the Calabi-Yau volume, or are higher order operators in the matter fields, and then irrelevant for the moduli stabilization rocedure. Although the power of the volume suppressing such corrections depends on the particular model, up to the mass level it is independent of the modular weight for the matter fields. This at least for the models studied here but we give arguments to expect the same in general. These claims are checked through numerical examples. We discuss how the factorizable models present a context where despite the lack of a hierarchy with the supersymmetry breaking scale, the effective theory still has a supersymmetric description. This can be understood from the fact that it is possible to find vanishing solution for the auxiliary components of the fields being integrated out, independently of the remaining dynamics. Our results settle down the question on the reliability of the way the Dilaton and Complex structure are treated in type-IIB compactifications with large compact manifold volumina.Comment: 23 pages + 2 appendices (38 pages total). v2: minor improvements, typos fixed. Version published in JHE

Acute febrile illness is associated with Rickettsia spp infection in dogs

BACKGROUND: Rickettsia conorii is transmitted by Rhipicephalus sanguineus ticks and causes Mediterranean Spotted Fever (MSF) in humans. Although dogs are considered the natural host of the vector, the clinical and epidemiological significance of R. conorii infection in dogs remains unclear. The aim of this prospective study was to investigate whether Rickettsia infection causes febrile illness in dogs living in areas endemic for human MSF. METHODS: Dogs from southern Italy with acute fever (n = 99) were compared with case–control dogs with normal body temperatures (n = 72). Serology and real-time PCR were performed for Rickettsia spp., Ehrlichia canis, Anaplasma phagocytophilum/A. platys and Leishmania infantum. Conventional PCR was performed for Babesia spp. and Hepatozoon spp. Acute and convalescent antibodies to R. conorii, E. canis and A. phagocytophilum were determined. RESULTS: The seroprevalence rates at first visit for R. conorii, E. canis, A. phagocytophilum and L. infantum were 44.8%, 48.5%, 37.8% and 17.6%, respectively. The seroconversion rates for R. conorii, E. canis and A. phagocytophilum were 20.7%, 14.3% and 8.8%, respectively. The molecular positive rates at first visit for Rickettsia spp., E. canis, A. phagocytophilum, A. platys, L. infantum, Babesia spp. and Hepatozoon spp. were 1.8%, 4.1%, 0%, 2.3%, 11.1%, 2.3% and 0.6%, respectively. Positive PCR for E. canis (7%), Rickettsia spp. (3%), Babesia spp. (4.0%) and Hepatozoon spp. (1.0%) were found only in febrile dogs. The DNA sequences obtained from Rickettsia and Babesia PCRs positive samples were 100% identical to the R. conorii and Babesia vogeli sequences in GenBank®, respectively. Febrile illness was statistically associated with acute and convalescent positive R. conorii antibodies, seroconversion to R. conorii, E. canis positive PCR, and positivity to any tick pathogen PCRs. Fourteen febrile dogs (31.8%) were diagnosed with Rickettsia spp. infection based on seroconversion and/or PCR while only six afebrile dogs (12.5%) seroconverted (P = 0.0248). The most common clinical findings of dogs with Rickettsia infection diagnosed by seroconversion and/or PCR were fever, myalgia, lameness, elevation of C-reactive protein, thrombocytopenia and hypoalbuminemia. CONCLUSIONS: This study demonstrates acute febrile illness associated with Rickettsia infection in dogs living in endemic areas of human MSF based on seroconversion alone or in combination with PCR

The formation history of our Galaxy's nuclear stellar disc constrained from HST observations of the Quintuplet field

Until recently it was thought that the nuclear stellar disc at the centre of our Galaxy was formed via quasi-continuous star formation over billions of years. However, an analysis of GALACTICNUCLEUS survey data indicates that >80% of the mass of the stellar disc formed at least 8 Gyr ago and about 5% roughly 1 Gyr ago. Our aim is to derive new constraints on the formation history of the nuclear stellar disc. We analysed a catalogue of HST/WFC3-IR observations of the Quintuplet cluster field. From this catalogue, we selected about 24000 field stars that probably belong to the nuclear stellar disc. We used red clump giants to deredden the sample and fit the resulting F153M luminosity function with a linear combination of theoretical luminosity functions created from different stellar evolutionary models. We find that >70% of the stellar population in the nuclear disc probably formed more than 10 Gyr ago, while ~15% formed in an event (or series of events) ~1Gyr ago. Up to 10% of the stars appear to have formed in the past tens to hundreds of Myr. These results do not change significantly for reasonable variations in the assumed mean metallicity, sample selection, reddening correction, or stellar evolutionary models. We confirm previous work that changed the formation paradigm for stars in the Galactic Centre. The nuclear stellar disc is indeed a very old structure. There seems to have been little star formation activity between its formation and about 1 Gyr ago.Comment: Accepted for publication in A&

Steel heat treating: Mathematical modelling and numerical simulation of a problem arising in the automotive industry

We describe a mathematical model for the industrial heating and cooling processes of a steel workpiece representing the steering rack of an automobile. The goal of steel heat treating is to provide a hardened surface on critical parts of the workpiece while keeping the rest soft and ductile in order to reduce fatigue. The high hardness is due to the phase transformation of steel accompanying the rapid cooling. This work takes into account both heating-cooling stage and viscoplastic model. Once the general mathematical formulation is derived, we can perform some numerical simulations