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

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)

Empirical vulnerability curves for Italian mansory buildings: evolution of vulnerability model from the DPM to curves as a function of accelertion

In the framework of the emergency management in the case of seismic events, the evaluation of the expected damage represents a basic requirement for risk informed planning. Seismic risk is defined by the probability to reach a level of damage on given exposed elements caused by seismic events occurring in a fixed period and in a fixed area. To this purpose, the expected seismic input, the exposed elements and their vulnerability have to be correctly evaluated. The aim of the research is to define a correct model of vulnerability curves, in PGA, for masonry structures in Italy, by heuristic approach starting from damage probability matrices (DPMs). To this purpose, the PLINIVS database, containing data on major Italian seismic events, has been used and supported by “critical” assumption on missing data. To support the reliability of this assumption, two vulnerability models, considering or not the hypothesis on the missing data, have been estimated and used to calculate the seismic scenario of the L’Aquila 2009 earthquake through the IRMA (Italian Risk MAp) platform. Finally, a comparison between the outcomes elaborated by IRMA platform and the observed damage collected in the AEDES forms, has been done. © 2020, The Author(s)

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

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

Harmonic damped oscillators with feedback. A Langevin study

We consider a system in direct contact with a thermal reservoir and which, if left unperturbed, is well described by a memory-less equilibrium Langevin equation of the second order in the time coordinate. In such conditions, the strength of the noise fluctuations is set by the damping factor, in accordance with the Fluctuation and Dissipation theorem. We study the system when it is subject to a feedback mechanism, by modifying the Langevin equation accordingly. Memory terms now arise in the time evolution, which we study in a non-equilibrium steady state. Two types of feedback schemes are considered, one focusing on time shifts and one on phase shifts, and for both cases we evaluate the power spectrum of the system's fluctuations. Our analysis finds application in feedback cooled oscillators, such as the Gravitational Wave detector AURIGA.Comment: 17 page

A proto brown dwarf candidate in Taurus

Aims. We search for brown dwarfs at the Class 0/I evolutionary stage, or proto brown dwarfs. Methods. We present a multi wavelength study, ranging from optical at 0.8 μm to radio wavelengths at 6 cm, of a cool, very faint, and red multiple object, SSTB213 J041757, detected by Spitzer toward the Barnard 213 dark cloud, in Taurus. Results. The SED of SSTB213 J041757 displays a clear excess at long wavelengths resembling that of a Class I object. The mid-IR source has two possible counterparts, A and B, in the near-IR and optical images, and the 350 μm observations detect clear extended emission, presumably from an envelope around the two sources. The position of A & B in the (Ic− J) versus (J − [3.6]) colour-colour diagram is consistent with them being Galactic sources and not extragalactic contaminants. A proper-motion study confirms this result for A, while it is inconclusive for B. The temperature and mass of the two possible central objects, according to COND evolutionary models, range between 1550−1750 K and 3−4 M_(Jupiter), and 950−1300 K and 1−2 M_(Jupiter), for A and B, respectively. The integrated SED provides bolometric temperatures and luminosities of 280 K and 0.0034 L_⊙, assuming that the emission at wavelengths > 5 μm is associated with component A, and 150 K and 0.0033 L_⊙, assuming that the emission at wavelengths > 5 μm is associated with component B, which would imply the SSTB213 J041757 object has a luminosity well below the luminosity of other very low luminosity objects discovered up to date. Conclusions. With these characteristics, SSTB213 J041757 seems to be a promising, and perhaps double, proto brown dwarf candidate

A submillimeter search for pre- and proto-brown dwarfs in Chamaeleon II

Context. Chamaeleon II molecular cloud is an active star forming region that offers an excellent opportunity for studying the formation of brown dwarfs in the southern hemisphere. Aims. Our aims are to identify a population of pre- and proto- brown dwarfs (5 sigma mass limit threshold of ~0.015 Msun) and provide information on the formation mechanisms of substellar objects. Methods. We performed high sensitivity observations at 870 microns using the LABOCA bolometer at the APEX telescope towards an active star forming region in Chamaeleon II. The data are complemented with an extensive multiwavelength catalogue of sources from the optical to the far-infrared to study the nature of the LABOCA detections. Results. We detect fifteen cores at 870 microns, and eleven of them show masses in the substellar regime. The most intense objects in the surveyed field correspond to the submillimeter counterparts of the well known young stellar objects DK Cha and IRAS 12500-7658. We identify a possible proto-brown dwarf candidate (ChaII-APEX-L) with IRAC emission at 3.6 and 4.5 microns. Conclusions. Our analysis indicates that most of the spatially resolved cores are transient, and that the point-like starless cores in the sub-stellar regime (with masses between 0.016 Msun and 0.066 Msun) could be pre-brown dwarfs cores gravitationally unstable if they have radii smaller than 220 AU to 907 AU (1.2" to 5" at 178 pc) respectively for different masses. ALMA observations will be the key to reveal the energetic state of these pre-brown dwarfs candidates.Comment: 11 pages, 6 figure

Toward the Identification of Novel Antimicrobial Agents: One-Pot Synthesis of Lipophilic Conjugates of N-Alkyl d- and l-Iminosugars

In the effort to improve the antimicrobial activity of iminosugars, we report the synthesis of lipophilic iminosugars 10a-b and 11a-b based on the one-pot conjugation of both enantiomeric forms of N-butyldeoxynojirimycin (NBDNJ) and N-nonyloxypentyldeoxynojirimycin (NPDNJ) with cholesterol and a succinic acid model linker. The conjugation reaction was tuned using the established PS-TPP/I2/ImH activating system, which provided the desired compounds in high yields (94-96%) by a one-pot procedure. The substantial increase in the lipophilicity of 10a-b and 11a-b is supposed to improve internalization within the bacterial cell, thereby potentially leading to enhanced antimicrobial properties. However, assays are currently hampered by solubility problems; therefore, alternative administration strategies will need to be devised