A Virtual Element Method for elastic and inelastic problems on polytope meshes

We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a low-order approximation of the displacement field, as well as a suitable treatment of the displacement gradient. The proposed method allows for general polygonal and polyhedral meshes, it is efficient in terms of number of applications of the constitutive law, and it can make use of any standard black-box constitutive law algorithm. Some theoretical results have been developed for the elastic case. Several numerical results within the 2D setting are presented, and a brief discussion on the extension to large deformation problems is included

Lowest order Virtual Element approximation of magnetostatic problems

We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general decompositions of the computational domain (as is natural for Virtual Element Methods) and uses as unknowns the (constant) tangential component of the magnetic field $\mathbf{H}$ on each edge, and the vertex values of the Lagrange multiplier $p$ (used to enforce the solenoidality of the magnetic induction $\mathbf{B}=\mu\mathbf{H}$). In this respect the method can be seen as the natural generalization of the lowest order Edge Finite Element Method (the so-called "first kind N\'ed\'elec" elements) to polyhedra of almost arbitrary shape, and as we show on some numerical examples it exhibits very good accuracy (for being a lowest order element) and excellent robustness with respect to distortions

Spatially Resolved Spitzer-IRS Spectral Maps of the Superwind in M82

We have mapped the superwind/halo region of the nearby starburst galaxy M82 in the mid-infrared with $Spitzer-IRS$. The spectral regions covered include the H$_2 S(1)-S(3)$, [NeII], [NeIII] emission lines and PAH features. We estimate the total warm H$_2$ mass and the kinetic energy of the outflowing warm molecular gas to be between $M_{warm}\sim5-17\times10^6$ M$_{\odot}$ and $E_{K}\sim6-20\times10^{53}$ erg. Using the ratios of the 6.2, 7.7 and 11.3 micron PAH features in the IRS spectra, we are able to estimate the average size and ionization state of the small grains in the superwind. There are large variations in the PAH flux ratios throughout the outflow. The 11.3/7.7 and the 6.2/7.7 PAH ratios both vary by more than a factor of five across the wind region. The Northern part of the wind has a significant population of PAH's with smaller 6.2/7.7 ratios than either the starburst disk or the Southern wind, indicating that on average, PAH emitters are larger and more ionized. The warm molecular gas to PAH flux ratios (H$_2/PAH$) are enhanced in the outflow by factors of 10-100 as compared to the starburst disk. This enhancement in the H$_2/PAH$ ratio does not seem to follow the ionization of the atomic gas (as measured with the [NeIII]/[NeII] line flux ratio) in the outflow. This suggests that much of the warm H$_2$ in the outflow is excited by shocks. The observed H$_2$ line intensities can be reproduced with low velocity shocks ($v < 40$ km s$^{-1}$) driven into moderately dense molecular gas ($10^2 <n_H < 10^4$ cm$^{-3}$) entrained in the outflow.Comment: 19 pages and 12 figures; accepted in MNRA

Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition

In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order regularity estimates for the solutions to Prandtl's equation boundary layers. Furthermore, we prove that the strong solution to Navier-Stokes equations converges to the Eulerian one in $C([0,T];H^1(\Omega))$ and L^\infty((0,T)\times\o), where $T$ is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.Comment: 45page

A family of three-dimensional virtual elements with applications to magnetostatic

We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the formulation of F. Kikuchi. In doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of $H^1$-conforming ($0$-forms), $H({\rm {\bf curl}})$-conforming ($1$-forms), and $H({\rm div})$-conforming ($2$-forms) functional spaces in three dimensions, and they would surely be useful for other problems and in more general contexts.Comment: Submitted to SINU

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective

A nonsense mutation in the LIMP-2 gene associated with progressive myoclonic epilepsy and nephrotic syndrome

Abstract The main clinical features of two siblings from a consanguineous marriage were progressive myoclonic epilepsy without intellectual impairment and a nephrotic syndrome with a strong accumulation of C1q in capillary loops and mesangium of kidney. The biochemical analysis of one of the patients revealed a normal beta-glucocerebrosidase activity in leukocytes, but a severe enzymatic deficiency in cultured skin fibroblasts. This deficiency suggested a defect in the intracellular sorting pathway of this enzyme. The sequence analysis of the gene encoding LIMP-2 (SCARB2), the sorting receptor for beta-glucocerebrosidase, confirmed this hypothesis. A homozygous nonsense mutation in codon 178 of SCARB2 was found in the patient, whereas her healthy parents were heterozygous for the mutation. Besides lacking immunodetectable LIMP-2, patient fibroblasts also had decreased amounts of beta-glucocerebrosidase, which was mainly located in the endoplasmic reticulum, as assessed by its sensitivity to Endo H. This is the first report of a mutation in the SCARB2 gene associated with a human disease, which, contrary to earlier proposals, shares no features with Charcot-Marie-Tooth disease both at the clinical and neurophysiological levels.Projeto financiado pela Fundação para a Ciência e Tecnologia(SFRH/BD/19496/2004 to A.B.

Far-infrared line imaging of the starburst ring in NGC 1097 with the Herschel/PACS spectrometer

NGC 1097 is a nearby SBb galaxy with a Seyfert nucleus and a bright starburst ring. We study the physical properties of the interstellar medium (ISM) in the ring using spatially resolved far-infrared spectral maps of the circumnuclear starburst ring of NGC 1097, obtained with the PACS spectrometer on board the Herschel Space Observatory. In particular, we map the important ISM cooling and diagnostic emission lines of [OI] 63 μm, [OIII] 88 μm, [NII] 122 μm, [CII] 158 μm and [NII] 205 μm. We observe that in the [OI] 63 μm, [OIII] 88 μm, and [NII] 122 μm line maps, the emission is enhanced in clumps along the NE part of the ring. We observe evidence of rapid rotation in the circumnuclear ring, with a rotation velocity of ~220 km s-1 (inclination uncorrected) measured in all lines. The [OI] 63 μm/[CII] 158 μm ratio varies smoothly throughout the central region, and is enhanced on the northeastern part of the ring, which may indicate a stronger radiation field. This enhancement coincides with peaks in the [OI] 63 μm and [OIII] 88 μm maps. Variations of the [NII] 122 μm/[NII] 205 μm ratio correspond to a range in the ionized gas density between 150 and 400 cm-3