Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection-diffusion problems: insights into spectral vanishing viscosity

AbstractThis study addresses linear dispersion–diffusion analysis for the spectral/hp continuous Galerkin (CG) formulation in one dimension. First, numerical dispersion and diffusion curves are obtained for the advection–diffusion problem and the role of multiple eigencurves peculiar to spectral/hp methods is discussed. From the eigencurves' behaviour, we observe that CG might feature potentially undesirable non-smooth dispersion/diffusion characteristics for under-resolved simulations of problems strongly dominated by either convection or diffusion. Subsequently, the linear advection equation augmented with spectral vanishing viscosity (SVV) is analysed. Dispersion and diffusion characteristics of CG with SVV-based stabilization are verified to display similar non-smooth features in flow regions where convection is much stronger than dissipation or vice-versa, owing to a dependency of the standard SVV operator on a local Péclet number. First a modification is proposed to the traditional SVV scaling that enforces a globally constant Péclet number so as to avoid the previous issues. In addition, a new SVV kernel function is suggested and shown to provide a more regular behaviour for the eigencurves along with a consistent increase in resolution power for higher-order discretizations, as measured by the extent of the wavenumber range where numerical errors are negligible. The dissipation characteristics of CG with the SVV modifications suggested are then verified to be broadly equivalent to those obtained through upwinding in the discontinuous Galerkin (DG) scheme. Nevertheless, for the kernel function proposed, the full upwind DG scheme is found to have a slightly higher resolution power for the same dissipation levels. These results show that improved CG-SVV characteristics can be pursued via different kernel functions with the aid of optimization algorithms

Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods

We investigate the potential of linear dispersion–diffusion analysis in providing direct guidelines for turbulence simulations through the under-resolved DNS (sometimes called implicit LES) approach via spectral/hp methods. The discontinuous Galerkin (DG) formulation is assessed in particular as a representative of these methods. We revisit the eigensolutions technique as applied to linear advection and suggest a new perspective to the role of multiple numerical modes, peculiar to spectral/hp methods. From this new perspective, “secondary” eigenmodes are seen to replicate the propagation behaviour of a “primary” mode, so that DG's propagation characteristics can be obtained directly from the dispersion–diffusion curves of the primary mode. Numerical dissipation is then appraised from these primary eigencurves and its effect over poorly-resolved scales is quantified. Within this scenario, a simple criterion is proposed to estimate DG's effective resolution in terms of the largest wavenumber it can accurately resolve in a given hp approximation space, also allowing us to present points per wavelength estimates typically used in spectral and finite difference methods. Although strictly valid for linear advection, the devised criterion is tested against (1D) Burgers turbulence and found to predict with good accuracy the beginning of the dissipation range on the energy spectra of under-resolved simulations. The analysis of these test cases through the proposed methodology clarifies why and how the DG formulation can be used for under-resolved turbulence simulations without explicit subgrid-scale modelling. In particular, when dealing with communication limited hardware which forces one to consider the performance for a fixed number of degrees of freedom, the use of higher polynomial orders along with moderately coarser meshes is shown to be the best way to translate available degrees of freedom into resolution power

Spin precession and inverted Hanle effect in a semiconductor near a finite-roughness ferromagnetic interface

Although the creation of spin polarization in various non-magnetic media via electrical spin injection from a ferromagnetic tunnel contact has been demonstrated, much of the basic behavior is heavily debated. It is reported here for semiconductor/Al2O3/ferromagnet tunnel structures based on Si or GaAs that local magnetostatic fields arising from interface roughness dramatically alter and even dominate the accumulation and dynamics of spins in the semiconductor. Spin precession in the inhomogeneous magnetic fields is shown to reduce the spin accumulation up to tenfold, and causes it to be inhomogeneous and non-collinear with the injector magnetization. The inverted Hanle effect serves as experimental signature. This interaction needs to be taken into account in the analysis of experimental data, particularly in extracting the spin lifetime and its variation with different parameters (temperature, doping concentration). It produces a broadening of the standard Hanle curve and thereby an apparent reduction of the spin lifetime. For heavily doped n-type Si at room temperature it is shown that the spin lifetime is larger than previously determined, and a new lower bound of 0.29 ns is obtained. The results are expected to be general and occur for spins near a magnetic interface not only in semiconductors but also in metals, organic and carbon-based materials including graphene, and in various spintronic device structures.Comment: Final version, with text restructured and appendices added (25 pages, 9 figures). To appear in Phys. Rev.

TREX-DM: a low background Micromegas-based TPC for low-mass WIMP detection

Dark Matter experiments are recently focusing their detection techniques in low-mass WIMPs, which requires the use of light elements and low energy threshold. In this context, we describe the TREX-DM experiment, a low background Micromegas-based TPC for low-mass WIMP detection. Its main goal is the operation of an active detection mass $\sim$0.3 kg, with an energy threshold below 0.4 keVee and fully built with previously selected radiopure materials. This work describes the commissioning of the actual setup situated in a laboratory on surface and the updates needed for a possible physics run at the Canfranc Underground Laboratory (LSC) in 2016. A preliminary background model of TREX-DM is also presented, based on a Geant4 simulation, the simulation of the detector's response and two discrimination methods: a conservative muon/electron and one based on a neutron source. Based on this background model, TREX-DM could be competitive in the search for low-mass WIMPs. In particular it could be sensitive, e.g., to the low-mass WIMP interpretation of the DAMA/LIBRA and other hints in a conservative scenario.Comment: Proceedings of the XIV International Conference on Topics in Astroparticle and Underground Physics (TAUP 2015), 7-11 September 2015, Torino, Ital

New Marker of Colon Cancer Risk Associated with Heme Intake: 1,4-Dihydroxynonane Mercapturic Acid

Background: Red meat consumption is associated with an increased risk of colon cancer. Animal studies show that heme, found in red meat, promotes preneoplastic lesions in the colon, probably due to the oxidative properties of this compound. End products of lipid peroxidation, such as 4-hydroxynonenal metabolites or 8-iso-prostaglandin-F2 (8-iso-PGF2), could reflect this oxidative process and could be used as biomarkers of colon cancer risk associated with heme intake. Methods: We measured urinary excretion of 8-iso-PGF2 and 1,4-dihydroxynonane mercapturic acid (DHN-MA), the major urinary metabolite of 4-hydroxynonenal, in three studies. In a short-term and a carcinogenesis long-term animal study, we fed rats four different diets (control, chicken, beef, and blood sausage as a high heme diet). In a randomized crossover human study, four different diets were fed (a 60 g/d red meat baseline diet, 120 g/d red meat, baseline diet supplemented with heme iron, and baseline diet supplemented with non-heme iron). Results: DHN-MA excretion increased dramatically in rats fed high heme diets, and the excretion paralleled the number of preneoplastic lesions in azoxymethane initiated rats (P < 0.0001). In the human study, the heme supplemented diet resulted in a 2-fold increase in DHN-MA (P < 0.001). Urinary 8-iso-PGF2 increased moderately in rats fed a high heme diet (P < 0.0001), but not in humans. Conclusion: Urinary DHN-MA is a useful noninvasive biomarker for determining the risk of preneoplastic lesions associated with heme iron consumption and should be further investigated as a potential biomarker of colon cancer risk. (Cancer Epidemiol Biomarkers Prev 2006;15(11):2274–9

Size quantization of Dirac fermions in graphene constrictions

Quantum point contacts (QPCs) are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wave-length in high-quality bulk graphene can be tuned up to hundreds of nanometers, the observation of quantum confinement of Dirac electrons in nanostructured graphene systems has proven surprisingly challenging. Here we show ballistic transport and quantized conductance of size-confined Dirac fermions in lithographically-defined graphene constrictions. At high charge carrier densities, the observed conductance agrees excellently with the Landauer theory of ballistic transport without any adjustable parameter. Experimental data and simulations for the evolution of the conductance with magnetic field unambiguously confirm the identification of size quantization in the constriction. Close to the charge neutrality point, bias voltage spectroscopy reveals a renormalized Fermi velocity ($v_F \approx 1.5 \times 10^6 m/s$) in our graphene constrictions. Moreover, at low carrier density transport measurements allow probing the density of localized states at edges, thus offering a unique handle on edge physics in graphene devices.Comment: 24 pages including 20 figures and 1 table. Corrected typos. To appear in Nature Communication