Virtual Elements for the Navier-Stokes problem on polygonal meshes

A family of Virtual Element Methods for the 2D Navier-Stokes equations is proposed and analysed. The schemes provide a discrete velocity field which is point-wise divergence-free. A rigorous error analysis is developed, showing that the methods are stable and optimally convergent. Several numerical tests are presented, confirming the theoretical predictions. A comparison with some mixed finite elements is also performed

The Schizophrenic Spectrum of LSR 1610-0040: a Peculiar M Dwarf/Subdwarf

We present a moderate resolution (R=2000), 0.8-4.1 micron spectrum of LSR 1610-0040, a high proper motion star classified as an early-type L subdwarf by Lepine and collaborators based on its red-optical spectrum. The near-infrared spectrum of LSR 1610-0040 does not fit into the (tentative) M/L subdwarf sequence but rather exhibits a mix of characteristics found in the spectra of both M dwarfs and M subdwarfs. In particular, the near-infrared spectrum exhibits a Na I doublet and CO overtone bandheads in the K band, and Al I and K I lines and an FeH bandhead in the H band, all of which have strengths more typical of field M dwarfs. Furthermore the spectrum of Gl 406 (M6 V) provides a reasonably good match to the 0.6-4.1 micron spectral energy distribution of LSR 1610. Nevertheless the near-infrared spectrum of LSR 1610 also exhibits features common to the spectra of M subdwarfs including a strong Ti I multiplet centered at ~0.97 microns, a weak VO band at ~1.06 microns, and possible collision-induced H_2 absorption in the H and K bands. We discuss a number of possible explanations for the appearance of the red-optical and near-infrared spectrum of LSR 1610-0040. Although we are unable to definitively classify LSR 1610-0040, the preponderance of evidence suggests that it is a mildly metal-poor M dwarf. Finally, we tentatively identify a new band of TiO at ~0.93 microns in the spectra of M dwarfs.Comment: Accepted for publication in the Astronomical Journa

FeH Absorption in the Near-Infrared Spectra of Late M and L Dwarfs

We present medium-resolution z-, J-, and H-band spectra of four late-type dwarfs with spectral types ranging from M8 to L7.5. In an attempt to determine the origin of numerous weak absorption features throughout their near-infrared spectra, and motivated by the recent tentative identification of the E 4\Pi- A ^4\Pi system of FeH near 1.6 microns in umbral and cool star spectra, we have compared the dwarf spectra to a laboratory FeH emission spectrum. We have identified nearly 100 FeH absorption features in the z-, J-, and H-band spectra of the dwarfs. In particular, we have identified 34 features which dominate the appearance of the H-band spectra of the dwarfs and which appear in the laboratory FeH spectrum. Finally, all of the features are either weaker or absent in the spectrum of the L7.5 dwarf which is consistent with the weakening of the known FeH bandheads in the spectra of the latest L dwarfs.Comment: accepted by Ap

Effectiveness of a soil mapping geomatic approach to predict the spatial distribution of soil types and their properties

A soil map (1:50,000 scale) was recently produced in Sardinia (Italy) using a cost-effective GIS approach. In this study we aimed to verify, in two pilot areas and by means of statistical analysis, the effectiveness of the adopted methodology in representing and predicting the spatial distribution of soil types and properties. We focused on evaluation of 1) the influence of landforms and parent materials on soil types (WRB Reference Soil Groups) and selected soil properties and 2) the suitability of the adopted methodology for calibrating a model to predict land unit composition in terms of different soil types. Leptosols, Regosols and Cambisols were prevalent on slopes, with Leptosols being more frequent on convex slopes and Regosols and Cambisols on concave slopes. In flat areas, soil types mainly depended on the type and age of parent material, with Regosols and Cambisols prevailing on Holocene deposits and highly developed soils (mainly Luvisols) largely prevailing on Pleistocene deposits. On hard rock, Leptosols were very frequent on terrigenous metamorphic rock and frequent on granite. Besides Leptosols, Regosols occurred more frequently than Cambisols on both parent materials. Landforms strongly influenced soil depth and available water capacity. Soils on plains were deeper than those on slopes, where convex forms had shallower soils than concave forms. A similar trend applied to the available water capacity. The parent material had a significant effect on topsoil properties (thickness, texture, pH and organic carbon content) of soils belonging to the same WRB Reference Soil Group (analysis done on the most relevant WRB Reference Soil Groups, i.e. Leptosols, Regosols and Cambisols). We calibrated and tested stepwise multiple linear regressions (MLR) and general linear models (GLM) to predict the composition of map units in terms of different WRB Reference Soil Groups. The two models gave very similar results, with distinct distribution patterns that were coherent with the relationships observed between soil groups and specific combination of terrain attributes and parent materials. Results showed that both models were more reliable in predicting the absence rather than presence of a given soil type

A Strategy for Passive Control of Natural Roll-Waves in Power-Law Fluids through Inlet Boundary Conditions

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Applicability of Kinematic and Diffusive models for mud-flows: a steady state analysis

The paper investigates the applicability of Kinematic and Diffusive Wave models for mud-flows with a power-law shear-thinning rheology. In analogy with a well-known approach for turbulent clear-water flows, the study compares the steady flow depth profiles predicted by approximated models with those of the Full Dynamic Wave one. For all the models and assuming an infinitely wide channel, the analytical solution of the flow depth profiles, in terms of hypergeometric functions, is derived. The accuracy of the approximated models is assessed by computing the average, along the channel length, of the errors, for several values of the Froude and kinematic wave numbers. Assuming the threshold value of the error equal to 5%, the applicability conditions of the two approximations have been individuated for several values of the power-law exponent, showing a crucial role of the rheology. The comparison with the clear-water results indicates that applicability criteria for clear-water flows do not apply to shearthinning fluids, potentially leading to an incorrect use of approximated models if the rheology is not properly accounted for