Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories

The most general action, quadratic in the B fields as well as in the curvature F, having SO(3,1) or SO(4) as the internal gauge group for a four-dimensional BF theory is presented and its symplectic geometry is displayed. It is shown that the space of solutions to the equations of motion for the BF theory can be endowed with symplectic structures alternative to the usual one. The analysis also includes topological terms and cosmological constant. The implications of this fact for gravity are briefly discussed.Comment: 13 pages, LaTeX file, no figure

HD 169142 in the eyes of ZIMPOL/SPHERE

We present new data of the protoplanetary disc surrounding the Herbig Ae/Be star HD 169142 obtained in the very broad-band (VBB) with the Zurich imaging polarimeter (ZIMPOL), a sub-system of the Spectro-Polarimetric High-contrast Exoplanet REsearch instrument (SPHERE) at the Very Large Telescope (VLT). Our Polarimetric Differential Imaging (PDI) observations probe the disc as close as 0.03" (3.5au) to the star and are able to trace the disc out to ~1.08" (~126au). We find an inner hole, a bright ring bearing substructures around 0.18" (21au), and an elliptically shaped gap stretching from 0.25" to 0.47" (29-55au). Outside of 0.47", the surface brightness drops off, discontinued only by a narrow annular brightness minimum at ~0.63"-0.74" (74-87au). These observations confirm features found in less-well resolved data as well as reveal yet undetected indications for planet-disc interactions, such as small-scale structures, star-disk offsets, and potentially moving shadows.Comment: Accepted for publication in MNRA

Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty

We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the application of Dirac's quantization rule to the various symplectic structures recently reported for this classical system. It is pointed out that that these quantum theories are inequivalent in the sense that the mean values for the operators (observables) associated with the same physical classical observable do not agree with each other. The inequivalence does not arise from ambiguities in the ordering of operators but from the fact of having several symplectic structures defined with respect to the same set of coordinates. It is also shown that the uncertainty relations between the fundamental observables depend on the particular quantum theory chosen. It is important to emphasize that these (somehow paradoxical) results emerge from the combination of two paradigms: Dirac's quantization rule and the usual Copenhagen interpretation of quantum mechanics.Comment: 8 pages, LaTex file, no figures. Accepted for publication in Phys. Rev.

Interpreting the extended emission around three nearby debris disc host stars

Cool debris discs are a relic of the planetesimal formation process around their host star, analogous to the solar system's Edgeworth-Kuiper belt. As such, they can be used as a proxy to probe the origin and formation of planetary systems like our own. The Herschel Open Time Key Programmes "DUst around NEarby Stars" (DUNES) and "Disc Emission via a Bias-free Reconnaissance in the Infrared/Submillimetre" (DEBRIS) observed many nearby, sun-like stars at far-infrared wavelengths seeking to detect and characterize the emission from their circumstellar dust. Excess emission attributable to the presence of dust was identified from around $\sim$ 20% of stars. Herschel's high angular resolution ($\sim$ 7" FWHM at 100 $\mu$m) provided the capacity for resolving debris belts around nearby stars with radial extents comparable to the solar system (50 to 100 au). As part of the DUNES and DEBRIS surveys, we obtained observations of three debris disc stars, HIP 22263 (HD 30495), HIP 62207 (HD 110897), and HIP 72848 (HD 131511), at far-infrared wavelengths with the Herschel PACS instrument. Combining these new images and photometry with ancilliary data from the literature, we undertook simultaneous multi-wavelength modelling of the discs' radial profiles and spectral energy distributions using three different methodologies: single annulus, modified black body, and a radiative transfer code. We present the first far-infrared spatially resolved images of these discs and new single-component debris disc models. We characterize the capacity of the models to reproduce the disc parameters based on marginally resolved emission through analysis of two sets of simulated systems (based on the HIP 22263 and HIP 62207 data) with the noise levels typical of the Herschel images. We find that the input parameter values are recovered well at noise levels attained in the observations presented here.Comment: 13 pages, 5 figures, 5 tables, accepted for publication in A&

Industrial steel heat treating: Numerical simulation of induction heating and aquaquenching cooling with mechanical effects

This paper summarizes a mathematical model for the industrial heating and cooling processes of a steel workpiece corresponding to the steering rack of an automobile. The general purpose of the heat treatment process is to create the necessary hardness on critical parts of the workpiece. Hardening consists of heating the workpiece up to a threshold temperature followed by a rapid cooling such as aquaquenching. The high hardness is due to the steel phase transformation accompanying the rapid cooling resulting in non-equilibrium phases, one of which is the hard microconstituent of steel, namely martensite. The mathematical model describes both processes, heating and cooling. During the first one, heat is produced by Joule’s effect from a very high alternating current passing through the rack. This situation is governed by a set of coupled PDEs/ODEs involving the electric potential, the magnetic vector potential, the temperature, the austenite transformation, the stresses and the displacement field. Once the workpiece has reached the desired temperature, the current is switched off an the cooling stage starts by aquaquenching. In this case, the governing equations involve the temperature, the austenite and martensite phase fractions, the stresses and the displacement field. This mathematical model has been solved by the FEM and 2D numerical simulations are discussed along the paper

Gas and dust in the Beta Pictoris Moving Group as seen by the Herschel Space Observatory

Context. Debris discs are thought to be formed through the collisional grinding of planetesimals, and can be considered as the outcome of planet formation. Understanding the properties of gas and dust in debris discs can help us to comprehend the architecture of extrasolar planetary systems. Herschel Space Observatory far-infrared (IR) photometry and spectroscopy have provided a valuable dataset for the study of debris discs gas and dust composition. This paper is part of a series of papers devoted to the study of Herschel PACS observations of young stellar associations. Aims. This work aims at studying the properties of discs in the Beta Pictoris Moving Group (BPMG) through far-IR PACS observations of dust and gas. Methods. We obtained Herschel-PACS far-IR photometric observations at 70, 100 and 160 microns of 19 BPMG members, together with spectroscopic observations of four of them. Spectroscopic observations were centred at 63.18 microns and 157 microns, aiming to detect [OI] and [CII] emission. We incorporated the new far-IR observations in the SED of BPMG members and fitted modified blackbody models to better characterise the dust content. Results. We have detected far-IR excess emission toward nine BPMG members, including the first detection of an IR excess toward HD 29391.The star HD 172555, shows [OI] emission, while HD 181296, shows [CII] emission, expanding the short list of debris discs with a gas detection. No debris disc in BPMG is detected in both [OI] and [CII]. The discs show dust temperatures in the range 55 to 264 K, with low dust masses (6.6*10^{-5} MEarth to 0.2 MEarth) and radii from blackbody models in the range 3 to 82 AU. All the objects with a gas detection are early spectral type stars with a hot dust component.Comment: 12 pages, 7 figures, 6 table

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

Gravity inversion by means of growing bodies

This paper presents a gravity inversion method for determining the volumes of bodies with pre-established density contrasts. The method works step-by-step on a prismatic partition of the subsurface volume, expanding the anomalous bodies to fit the observed gravity values in a systematic exploration of model possibilities. The process is treated in a 3-D context; at the same time, it can determine a simple regional trend. Moreover, positive and negative density contrasts are simultaneously accepted. The solution is obtained by a double condition: (1) the e(2)-fitness to the observed gravity data (model fitness) and (2) the minimization of the total (weighted) anomalous mass (model smoothness). A positive parameter is used to balance the two minimization terms. The method is applied to a simulated example and also to a real example: the volcanic island of Gran Canaria (Canary Islands, Spain). In both cases, the results obtained show the possibilities of the method

Far-UV Emissions of the Sun in Time: Probing Solar Magnetic Activity and Effects on Evolution of Paleo-Planetary Atmospheres

We present and analyze FUSE observations of six solar analogs. These are single, main-sequence G0-5 strs selected as proxies for the Sun at several stages of its main-sequence lifetime. The emission features in the FUSE 920-1180 A wavelength range allow for a critical probe of the hot plasma over three decades in temperature. Using the flux ratio CIII 1176/977 as diagnostics, we investigate the dependence of the electron pressure of the transition region as a function of the rotation period, age and magnetic activity. The results from these solar proxies indicate that the electron pressure of the stellar ~10^5-K plasma decreases by a factor of about 70 between the young, fast-rotating magnetically active star and the old, slow-rotating inactive star. Also, the observations indicate that the average surface fluxes of emission features strongly decrease with increasing stellar age and longer rotation period. The emission flux evolution with age or rotation period is well fitted by power laws, which become steeper from cooler chromospheric (10^4 K) to hotter coronal (10^7 K) plasma. The relationship for the integrated (920-1180 A) FUSE flux indicates that the solar far-ultraviolet emissions were about twice the present value 2.5 Gyr ago and about 4 times the present value 3.5 Gyr ago. Note also that the FUSE/FUV flux of the Zero-Age Main Sequence Sun could have been higher by as much as 50 times. Our analysis suggests that the strong FUV emissions of the young Sun may have played a crucial role in the developing planetary system, in particular through the photoionization, photochemical evolution and possible erosion of the planetary atmospheres. (abridged)Comment: 15 pages, 8 figures, accepted for publication in Ap