Linear free divisors and Frobenius manifolds

We study linear functions on fibrations whose central fibre is a linear free divisor. We analyse the Gauß–Manin system associated to these functions, and prove the existence of a primitive and homogenous form. As a consequence, we show that the base space of the semi-universal unfolding of such a function carries a Frobenius manifold structure

A quasi-static nonlinear analysis for assessing the fire resistance of 3d frames exploiting time-dependent yield surface

In this work an automatic procedure for evaluating the axial force-biaxial bending yield surface of reinforced concrete sections in fire is proposed. It provides an accurate time-dependent expression of the yield condition by a section analysis carried out once and for all, accounting for the strength reduction of the materials, which is a function of the fire duration. The equilibrium state of 3D frames with such yield conditions, once discretized using beam finite elements, is formulated as a nonlinear vectorial equation defining a curve in the hyperspace of the discrete variables and the fire duration. A generalized path-following strategy is proposed for tracing this curve and evaluating, if it exists, the limit fire duration, that is the time of exposure which leads to structural collapse. Compared to the previous proposals on the topic, which are limited to local sectional checks, this work is the first to present a global analysis for assessing the fire resistance of 3D frames, providing a time history of the fire event and taking account of the stress redistribution. Numerical examples are given to illustrate and validate the proposal

Is ALT control really necessary for routine ART monitoring in resource poor settings?

2006 AIDS Conference in Toront

Fossil biomass preserved as graphitic carbon in a late paleoproterozoic banded iron formation metamorphosed at more than 550°C

Metamorphism is thought to destroy microfossils, partly through devolatilization and graphitization of biogenic organic matter. However, the extent to which there is a loss of molecular, elemental and isotope signatures from biomass during high-temperature metamorphism is not clearly established. We report on graphitic structures inside and coating apatite grains from the c. 1850 Ma Michigamme silicate banded iron formation from Michigan, metamorphosed above 550°C. Traces of N, S, O, H, Ca and Fe are preserved in this graphitic carbon and X-ray spectra show traces of aliphatic groups. Graphitic carbon has an expanded lattice around 3.6 Å, forms microscopic concentrically-layered and radiating polygonal flakes and has homogeneous δ13C values around −22‰, identical to bulk analyses. Graphitic carbon inside apatite is associated with nanometre-size ammoniated phyllosilicate. Precursors of these metamorphic minerals and graphitic carbon originated from ferruginous clayrich sediments with biomass. We conclude that graphite coatings and inclusions in apatite grains indicate fluid remobilization during amphibolite-facies metamorphism of precursor biomass. This new evidence fills in observational gaps of metamorphosed biomass into graphite and supports the existence of biosignatures in the highly metamorphosed iron formation from the Eoarchean Akilia Association, which dates from the beginning of the sedimentary rock record

Caesar II: An Italian decision support tool for the seismic risk. The case study of Torre Pellice, Villar Pellice and Pinerolo municipalities

Italy is a country with high seismic risk; however, a broad seismic classification of the national territory has been introduced only in the last twenty years. Therefore, most of the existing buildings stock do not comply with the current anti-seismic codes. In recent years, the seismic events that occurred in Italy have highlighted the complexity of emergency management and the great challenge for public authorities called to answer to the post-event reconstruction and the planning of effective risk prevention and mitigation measures implemented in "peacetime". In this perspective, the CAESAR II project (Controlling, Mitigating and Managing Earthquake Emergency: Cost-Benefit and Multi-criteria Analysis of Impact Scenarios for Risk Reduction and Increased Resilience) has been developed as a decision support system for public authorities engaged in the development of seismic disaster risk reduction plans. CAESAR II includes a module for the simulation of retrofitting measures applied at the municipal scale, integrating different categories of anti-seismic and energy improvement measures based on the vulnerability analysis of the existing buildings stock. The CAESAR II tool's core is the module for evaluating "seismic impact scenarios" based on the end-users' hazard. The output of the model includes information on expected damage levels for buildings (from D0-no damage to D5- total collapse) and population (dead, injured and homeless). Impact scenarios can be customised according to the minimum unit of analysis assumed (municipality or 250x250m square mesh grid) and the availability of exposure data (from national census data or survey on the spot building by building according to the PLINIVS form). Scenarios include geo-referenced data managed by geo-servers to exchange data in a format compliant with OGC (Open Gis Consortium) standards and the European INSPIRE Directive. Simulation results can be further processed through the Multi-Criteria and Cost-Benefit Analysis modules to support the comparative assessment of alternative seismic and energy measurements. In this work, the procedures included in CAESAR II are described and a case study is reported. It concerns the analysis of the expected damage assessment on buildings and population for three municipalities in northern Italy, Torre Pellice, Villar Pellice and Pinerolo (Piedmont Region)

On Singularity Formation of a Nonlinear Nonlocal System

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the nonlocal system for a large class of smooth initial data with finite energy. We also prove the global regularity for a class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model.Comment: 28 pages, 9 figure

The Molecular Hydrogen Deficit in Gamma-Ray Burst Afterglows

Recent analysis of five gamma-ray burst (GRB) afterglow spectra reveal the absence of molecular hydrogen absorption lines, a surprising result in light of their large neutral hydrogen column densities and the detection of H$_2$ in similar, more local star-forming regions like 30 Doradus in the Large Magellanic Cloud (LMC). Observational evidence further indicates that the bulk of the neutral hydrogen column in these sight lines lies 100 pc beyond the progenitor and that H$_2$ was absent prior to the burst, suggesting that direct flux from the star, FUV background fields, or both suppressed its formation. We present one-dimensional radiation hydrodynamical models of GRB host galaxy environments, including self-consistent radiative transfer of both ionizing and Lyman-Werner photons, nine-species primordial chemistry with dust formation of H$_2$, and dust extinction of UV photons. We find that a single GRB progenitor is sufficient to ionize neutral hydrogen to distances of 50 - 100 pc but that a galactic Lyman-Werner background is required to dissociate the molecular hydrogen in the ambient ISM. Intensities of 0.1 - 100 times the Galactic mean are necessary to destroy H$_2$ in the cloud, depending on its density and metallicity. The minimum radii at which neutral hydrogen will be found in afterglow spectra is insensitive to the mass of the progenitor or the initial mass function (IMF) of its cluster, if present.Comment: 12 pages, 7 figures, accepted for Ap