Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods

Recent works showed that pressure-robust modifications of mixed finite element methods for the Stokes equations outperform their standard versions in many cases. This is achieved by divergence-free reconstruction operators and results in pressure independent velocity error estimates which are robust with respect to small viscosities. In this paper we develop a posteriori error control which reflects this robustness. The main difficulty lies in the volume contribution of the standard residual-based approach that includes the $L^2$-norm of the right-hand side. However, the velocity is only steered by the divergence-free part of this source term. An efficient error estimator must approximate this divergence-free part in a proper manner, otherwise it can be dominated by the pressure error. To overcome this difficulty a novel approach is suggested that uses arguments from the stream function and vorticity formulation of the Navier--Stokes equations. The novel error estimators only take the $\mathrm{curl}$ of the right-hand side into account and so lead to provably reliable, efficient and pressure-independent upper bounds in case of a pressure-robust method in particular in pressure-dominant situations. This is also confirmed by some numerical examples with the novel pressure-robust modifications of the Taylor--Hood and mini finite element methods

Magneto-Roton Modes of the Ultra Quantum Crystal: Numerical Study

The Field Induced Spin Density Wave phases observed in quasi-one-dimensional conductors of the Bechgaard salts family under magnetic field exhibit both Spin Density Wave order and a Quantized Hall Effect, which may exhibit sign reversals. The original nature of the condensed phases is evidenced by the collective mode spectrum. Besides the Goldstone modes, a quasi periodic structure of Magneto-Roton modes, predicted to exist for a monotonic sequence of Hall Quantum numbers, is confirmed, and a second mode is shown to exist within the single particle gap. We present numerical estimates of the Magneto-Roton mode energies in a generic case of the monotonic sequence. The mass anisotropy of the collective mode is calculated. We show how differently the MR spectrum evolves with magnetic field at low and high fields. The collective mode spectrum should have specific features, in the sign reversed "Ribault Phase", as compared to modes of the majority sign phases. We investigate numerically the collective mode in the Ribault Phase.Comment: this paper incorporates material contained in a previous cond-mat preprint cond-mat/9709210, but cannot be described as a replaced version, because it contains a significant amount of new material dealing with the instability line and with the topic of Ribault Phases. It contains 13 figures (.ps files

Multiple sclerosis, the measurement of disability and access to clinical trial data

Background: Inferences about long-term effects of therapies in multiple sclerosis (MS) have been based on surrogate markers studied in short-term trials. Nevertheless, MS trials have been getting steadily shorter despite the lack of a consensus definition for the most important clinical outcome - unremitting progression of disability. Methods: We have examined widely used surrogate markers of disability progression in MS within a unique database of individual patient data from the placebo arms of 31 randomised clinical trials. Findings: Definitions of treatment failure used in secondary progressive MS trials include much change unrelated to the target of unremitting disability. In relapsing-remitting MS, disability progression by treatment failure definitions was no more likely than similarly defined improvement for these disability surrogates. Existing definitions of disease progression in relapsing-remitting trials encompass random variation, measurement error and remitting relapses and appear not to measure unremitting disability. Interpretation: Clinical surrogates of unremitting disability used in relapsing -remitting trials cannot be validated. Trials have been too short and/or degrees of disability change too small to evaluate unremitting disability outcomes. Important implications for trial design and reinterpretation of existing trial results have emerged long after regulatory approval and widespread use of therapies in MS, highlighting the necessity of having primary trial data in the public domain

A World Wide Web Primer for Small Business

The World Wide Web is growing very quickly. It offers small businesses the opportunity to reach a wider customer base. However, before deciding to launch a Web site, a small business manager needs an understanding of the Web and how to use it to achieve business goals. This article provides a foundation for using the Web to achieve them. It includes a brief history of the Web, its commercial demographics, and reasons for building a Web site. It also explains the key issues and steps for developing a Web site and assessing its success

Turnip crinkle virus coat protein mediates suppression of RNA silencing in nicotiana benthamiana

AbstractAll of the protein products of Turnip crinkle virus (TCV; Tombusviridae, Carmovirus) were tested for their ability to suppress RNA silencing of a reporter gene after transient expression in Agrobacterium-infiltrated Nicotiana benthamiana leaves. Only the capsid protein, P38, showed suppression activity, although this was not obvious when P38 was expressed as part of a TCV infection of the same tissues. When P38 was expressed from a PVX vector, symptoms with enhanced severity that correlated with increased PVX RNA accumulation were observed. This contradiction between ectopic expression of P38 and TCV infection could be accounted for if the active determinant of suppressor activity within P38 was sequestered within the capsid protein structure. The N-terminal 25 amino acids were shown to be important for this activity. This region forms part of the unexposed R-domain that interacts with the RNA within the virus particle. This observation throws light on some of the complex biology exhibited by TCV

Vortex stability in nearly two-dimensional Bose-Einstein condensates with attraction

We perform accurate investigation of stability of localized vortices in an effectively two-dimensional ("pancake-shaped") trapped BEC with negative scattering length. The analysis combines computation of the stability eigenvalues and direct simulations. The states with vorticity S=1 are stable in a third of their existence region, $0<N<(1/3)N_{\max}^{(S=1)}$, where $N$ is the number of atoms, and $N_{\max}^{(S=1)}$ is the corresponding collapse threshold. Stable vortices easily self-trap from arbitrary initial configurations with embedded vorticity. In an adjacent interval, $(1/3)N_{\max }^{(S=1)}<N<$ $\allowbreak 0.43N_{\max}^{(S=1)}$, the unstable vortex periodically splits in two fragments and recombines. At $N>$ $\allowbreak 0.43N_{\max}^{(S=1)}$, the fragments do not recombine, as each one collapses by itself. The results are compared with those in the full 3D Gross-Pitaevskii equation. In a moderately anisotropic 3D configuration, with the aspect ratio $\sqrt{10}$, the stability interval of the S=1 vortices occupies $\approx 40$ of their existence region, hence the 2D limit provides for a reasonable approximation in this case. For the isotropic 3D configuration, the stability interval expands to 65% of the existence domain. Overall, the vorticity heightens the actual collapse threshold by a factor of up to 2. All vortices with $S\geq 2$ are unstable.Comment: 21 pages, 8 figures, to appear in Physical Review

TAM and the World Wide Web

The purpose of this research-in-progress is to test the Technology Acceptance Model (TAM) with the World Wide Web as the users\u27 application. The investigation will validate, extend, or refute TAM. It will thus help identify guidelines for developing and using Web site

An alternative search for the electron capture of Te-123

A search for the electron capture of Te-123 has been performed using CdZnTe detectors. After a measuring time of 195 h no signal could be found resulting in a lower half-life limt of $T_{1/2} > 3.2 \cdot 10^{16}$ yrs (95 % CL) for this process. This clearly discriminates between existing experimental results which differ by six orders of magnitude and our data are in strong favour of the result with longer half-lifes.Comment: 2 pages, 2 eps-figures, reanalysis of data set

Ground-based follow-up observations of TRAPPIST-1 transits in the near-infrared

The TRAPPIST-1 planetary system is a favorable target for the atmospheric characterization of temperate earth-sized exoplanets by means of transmission spectroscopy with the forthcoming James Webb Space Telescope (JWST). A possible obstacle to this technique could come from the photospheric heterogeneity of the host star that could affect planetary signatures in the transit transmission spectra. To constrain further this possibility, we gathered an extensive photometric data set of 25 TRAPPIST-1 transits observed in the near-IR J band (1.2 $\mu$m) with the UKIRT and the AAT, and in the NB2090 band (2.1 $\mu$m) with the VLT during the period 2015-2018. In our analysis of these data, we used a special strategy aiming to ensure uniformity in our measurements and robustness in our conclusions. We reach a photometric precision of $\sim0.003$ (RMS of the residuals), and we detect no significant temporal variations of transit depths of TRAPPIST-1 b, c, e, and g over the period of three years. The few transit depths measured for planets d and f hint towards some level of variability, but more measurements will be required for confirmation. Our depth measurements for planets b and c disagree with the stellar contamination spectra originating from the possible existence of bright spots of temperature 4500 K. We report updated transmission spectra for the six inner planets of the system which are globally flat for planets b and g and some structures are seen for planets c, d, e, and f.Comment: accepted for publication in MNRA

Surfactant protein A and D polymorphisms and methylprednisolone pharmacogenetics in donor lungs

Objective: Surfactant proteins A and D are important molecules involved in lung allograft innate immunity. Genetic polymorphisms of surfactant proteins A and D are associated with various lung diseases. In this study, surfactant protein A and D expression responses were investigated during pharmacogenetics upon methylprednisolone treatment as observed during lung transplantation. Methods: A human cell line (NCI-H441) and precision-cut lung slices from 16 human donors were incubated with methylprednisolone, and surfactant protein A1, surfactant protein A2, and surfactant protein D messenger RNA and surfactant protein A protein expression were assayed. Surfactant protein A1, A2, and D polymorphisms and surfactant protein A gene and protein expressions were determined. Results: In NCI-H441 cells, methylprednisolone treatment at 10−5 M and 10−6 M reduced surfactant protein A1 and surfactant protein A2 messenger RNA and surfactant protein A protein expression (P &lt;.05). A pharmacogenetic relationship was observed in human donor precision-cut lung slices between the surfactant protein A2 (1Ax) variants: Surfactant protein A1, A2, and D messenger RNA expression were greater for 1A0 versus 1A1 (P &lt;.05); surfactant protein A1/surfactant protein A2 genotype 6A26A2/1A01A0 (n = 5) showed greater surfactant protein A1, A2, and D messenger RNA expression and surfactant protein A protein expression compared with the other surfactant protein A1/surfactant protein A2 genotypes (n = 11) (P &lt;.05). Conclusions: The surfactant protein A genotype and methylprednisolone stimuli influence donor lung surfactant protein A and D expression. Lungs carrying the surfactant protein A2 variant 1A0 have a greater expression of surfactant protein A when treated with methylprednisolone. Surfactant protein A polymorphisms could be used to personalize immunosuppressive regimens