Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

Geomorphological significance of lichen colonization in a present snow hollow: Hoya del Cuchillar de las Navajas, Sierra de Gredos (Spain)

18 páginas, 12 figuras y 1 tablaThis paper discusses the results of a lichenometrical and geomorphological study of one of the few remaining active snow hollows in the central region of the Iberian Peninsula. The study area, located on a glacial shoulder, is called Hoya del Cuchillar de las Navajas. A protalus rampart occurs at the base of the hollow. Our studies, conducted between 1992 and 1998, were designed to determine the geomorphological characteristics of Hoya, the mobility of the deposits, and the characteristics of the snow cover. These data formed the basis for a study of the lichen colonization on the blocks and on the wall surrounding the snow hollow. All of the lichen species found were analyzed according to their abundance, distribution and the extent of their surface cover. Measurements of the diameter of the thalli of the species Rhizocarpon geographicum were also obtained. Thalli of this species were found to require a mean snow-free growing season of at least 95 days 13.5 weeks per year. Maximum mean thallus diameters indicate that the protalus rampart was formed during the Little Ice Age and became inactive 130 years ago.The staff of the Refugio Jose Antonio Elola (Laguna Grande de Gredos) is thanked for its cooperation and hospitality. We are indebted to Alicia Ferrero for her careful revision of the English manuscript. Financial support was provided by the Proyecto de Investigacion Multidisciplinar PR218 / 94-5653 (Universidad Complutense de Madrid)Peer reviewe

Petrofacies of Eocene sand injectites of the Tumey Giant Injection Complex, California (USA)

The authors gratefully acknowledge support from Shell Brazil and CNPq through the “BG05: UoA-UFRGS-SWB Sedimentary Systems” project at UFRGS and UoA and the strategic importance of the support given by ANP through the R&D levy regulation. We thank all the support from the Sand Injection Research Group (SIRG). We also wish to thank the support of the Bureau of Land Management (CA - USA) providing legal access to the study area.Peer reviewedPostprin

Spatially resolved origin of mm-wave linear polarization in the nuclear region of 3C 84

We report results from a deep polarization imaging of the nearby radio galaxy 3C 84 (NGC 1275). The source was observed with the Global Millimeter VLBI Array (GMVA) at 86 GHz at an ultra-high angular resolution of 50μas (corresponding to 250R). We also add complementary multi-wavelength data from the Very Long Baseline Array (VLBA; 15 & 43 GHz) and from the Atacama Large Millimeter/submillimeter Array (ALMA; 97.5, 233.0, and 343.5 GHz). At 86 GHz, we measure a fractional linear polarization of ~ 2% in the VLBI core region. The polarization morphology suggests that the emission is associated with an underlying limb-brightened jet. The fractional linear polarization is lower at 43 and 15 GHz (~ 0.3-0.7% and < 0.1%, respectively). This suggests an increasing linear polarization degree towards shorter wavelengths on VLBI scales. We also obtain a large rotation measure (RM) of ~ 10⁵⁻⁶ rad/m² in the core at ≳43 GHz. Moreover, the VLBA 43 GHz observations show a variable RM in the VLBI core region during a small flare in 2015. Faraday depolarization and Faraday conversion in an inhomogeneous and mildly relativistic plasma could explain the observed linear polarization characteristics and the previously measured frequency dependence of the circular polarization. Our Faraday depolarization modeling suggests that the RM most likely originates from an external screen with a highly uniform RM distribution. To explain the large RM value, the uniform RM distribution, and the RM variability, we suggest that the Faraday rotation is caused by a boundary layer in a transversely stratified jet. Based on the RM and the synchrotron spectrum of the core, we provide an estimate for the magnetic field strength and the electron density of the jet plasma.Accepted manuscrip

Interacting coronae of two T Tauri stars: first observational evidence for solar-like helmet streamers

Context {The young binary system V773 Tau A exhibits a persistent radio flaring activity that gradually increases from a level of a few mJy at apoastron to more than 100 mJy at periastron. Interbinary collisions between very large (> 15 R) magnetic structures anchored on the two rotating stars of the system have been proposed to be the origin of these periodic radio flares. Magnetic structures extended over tens of stellar radii, that can also account for the observed fast decay of the radio flares, seem to correspond to the typical solar semi-open quite extended magnetic configurations called helmet streamers.} Aims {We aim to find direct observational evidence for the postulated, solar-like, coronal topologies.} Methods {We performed seven-consecutive-day VLBI observations at 8.4 GHz using an array consisting of the VLBA and the 100-m Effelsberg telescope.} Results {Two distintive structures appear in the radio images here presented. They happen to be associated with the primary and secondary stars of the V773 Tau A system. In one image (Fig.2-B) the two features are extended up to 18 R each and are nearly parallel revealing the presence of two interacting helmet streamers. One image (Fig.2-E) taken a few hours after a flare monitored by the 100-m Effelsberg telescope shows one elongated fading structure substantially rotated with respect to those seen in the B run. The same decay scenario is seen in Fig.2-G for the helmet streamer associated with the other star.} Conclusions {This is the very first direct evidence revealing that even if the flare origin is magnetic reconnection due to interbinary collision, both stars independently emit in the radio range with structures of their own. These structures are helmet streamers, observed for the first time in stars other than the Sun.}Comment: 7 pages, 3 figures, A&A in pres

PHOTONEUTRON SOURCE BY HIGH ENERGY ELECTRONS ON HIGH Z TARGET: COMPARISON BETWEEN MONTE CARLO CODES AND EXPERIMENTAL DATA

ne, in the National Laboratory of Frascati, near Rome (Italy). Neutrons are produced sending high energy electrons to impinge on an optimized Tungsten target. This source could be suitably used for calibration of neutron detectors as well as for material and nuclear science investigations. Moreover photoneutron processes are encountered in many physics domains: from accelerator to reactor physics, mainly related to neutron shielding issues in high Z materials, used for gamma shielding.This work presents the Monte Carlo simulations performed with different codes (FLUKA and MCNPX) to estimate the neutron rate and energy spectrum, obtained when 510 MeV electrons are sent against the designed target. Finally, the comparison of the Monte Carlo predictions of neutron and photon fluences around the target with the experimental values is discussed