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

Accuracy of Approximate Eigenstates

Besides perturbation theory, which requires, of course, the knowledge of the exact unperturbed solution, variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum theory. For a reasonable choice of the employed trial subspace of the domain of H, the lowest eigenvalues of H usually can be located with acceptable precision whereas the trial-subspace vectors corresponding to these eigenvalues approximate, in general, the exact eigenstates of H with much less accuracy. Accordingly, various measures for the accuracy of the approximate eigenstates derived by variational techniques are scrutinized. In particular, the matrix elements of the commutator of the operator H and (suitably chosen) different operators, with respect to degenerate approximate eigenstates of H obtained by some variational method, are proposed here as new criteria for the accuracy of variational eigenstates. These considerations are applied to that Hamiltonian the eigenvalue problem of which defines the "spinless Salpeter equation." This (bound-state) wave equation may be regarded as the most straightforward relativistic generalization of the usual nonrelativistic Schroedinger formalism, and is frequently used to describe, e.g., spin-averaged mass spectra of bound states of quarks.Comment: LaTeX, 14 pages, Int. J. Mod. Phys. A (in print); 1 typo correcte

Instantaneous Bethe-Salpeter equation: improved analytical solution

Studying the Bethe-Salpeter formalism for interactions instantaneous in the rest frame of the bound states described, we show that, for bound-state constituents of arbitrary masses, the mass of the ground state of a given spin may be calculated almost entirely analytically with high accuracy, without the (numerical) diagonalization of the matrix representation obtained by expansion of the solutions over a suitable set of basis states.Comment: 7 page

Impact of snow state variation for design flood simulations in glacierized catchments

A continuously running hydrological energy balance model was used to analyse the influence of different snow covers on the formation of large floods within glacierized catchments. Model outputs from three different catchments in the Austrian Alps with glacierizations ranging from 30 to 39% were statistically interpreted to cover a wide range of possible combinations of areal snow cover distribution and mean snow water equivalent (SWE_m) and to define initialisation values for extreme runoff scenarios. These model states consider snow conditions between less than 10% snow coverage up to almost complete snow coverage, with different snow depths represented by minimum, mean or maximum levels of SWE_m. For the utilization of extreme runoffs, these snow cover states were combined with design storm input data. An analysis of the resulting flood hydrographs showed that the maximum runoff values occur with minimal snow cover conditions. With increasing snow coverage and SWE_m, flow magnitudes tend to decrease while the relevant precipitation time increases significantly. The influence of topographical catchment features, snow cover and SWE_m on the simulated scenario discharge is discussed. The contribution of the different runoff components to the modelled peak flows confirms the assumption that floods in glacierized catchments are a combination of directly discharging rain and ice melt

Visual snow syndrome after start of citalopram-novel insights into underlying pathophysiology

Purpose!#!Chronic pain is common in the older population and a significant public health concern. However, comprehensive studies on analgesics use in this age group from Germany are scarce. This study aims to give a comprehensive overview on the use of the most common therapeutic groups of analgesics in community-dwelling older adults from Germany.!##!Methods!#!A cross-sectional study was carried out using data from a German cohort of 2038 community-dwelling adults aged 63-89 years. Descriptive statistics and logistic regression models were applied to assess the utilization of analgesics by age, sex, pain severity, pain duration, and locations.!##!Results!#!One out of four study participants was suffering from high-intensity or disabling pain. Approximately half of those taking analgesics still reported to suffer from high-intensity or disabling pain. Among analgesics users, occasional non-steroidal anti-inflammatory drugs (NSAIDs) use was the most frequent pain therapy (in 43.6% of users), followed by metamizole (dipyrone) use (16.1%), regular NSAIDs use (12.9%), strong opioids use (12.7%), and weak opioids use (12.0%). In multivariate logistic regression models, higher age, higher pain severity, longer pain duration, abdominal pain, and back pain were statistically significantly associated with opioids use. Metamizole use was also statistically significantly associated with higher pain severity but inversely associated with pain duration.!##!Conclusions!#!A significant number of older German adults are affected by high-intensity and disabling chronic pain despite receiving analgesics. Long-term studies are needed to compare the effectiveness and safety of different treatments for chronic pain in older adults

A Variational Approach to the Spinless Relativistic Coulomb Problem

By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some Coulomb-type interaction.Comment: 7 pages, HEPHY-PUB 606/9

Instantaneous Bethe-Salpeter Equation: Analytic Approach for Nonvanishing Masses of the Bound-State Constituents

The instantaneous Bethe-Salpeter equation, derived from the general Bethe-Salpeter formalism by assuming that the involved interaction kernel is instantaneous, represents the most promising framework for the description of hadrons as bound states of quarks from first quantum-field-theoretic principles, that is, quantum chromodynamics. Here, by extending a previous analysis confined to the case of bound-state constituents with vanishing masses, we demonstrate that the instantaneous Bethe-Salpeter equation for bound-state constituents with (definitely) nonvanishing masses may be converted into an eigenvalue problem for an explicitly - more precisely, algebraically - known matrix, at least, for a rather wide class of interactions between these bound-state constituents. The advantages of the explicit knowledge of this matrix representation are self-evident.Comment: 12 Pages, LaTeX, 1 figur

Age- and frequency-dependent changes in dynamic contrast perception in visual snow syndrome

OBJECTIVE Patients with visual snow syndrome (VSS) suffer from a debilitating continuous (\textquotedblTV noise-like\textquotedbl) visual disturbance. They report problems with vision at night and palinopsia despite normal visual acuity. The underlying pathophysiology of VSS is largely unknown. Currently, it is a clinical diagnosis based on the patient's history, an objective test is not available. Here, we tested the hypothesis that patients with VSS have an increased threshold for detecting visual contrasts at particular temporal frequencies by measuring dynamic contrast detection-thresholds. METHODS Twenty patients with VSS were compared to age-, gender-, migraine- and aura-matched controls in this case-control study. Subjects were shown bars randomly tilted to the left or right, flickering at six different frequencies (15 Hz, 20 Hz, 25 Hz, 30 Hz, 35 Hz, 40 Hz). The contrast threshold (CT) for detection of left or right tilt was measured in a two-alternative adaptive forced-choice procedure (QUEST). The threshold was defined as the Michelson contrast necessary to achieve the correct response in 75% of the cases. RESULTS The CT increased for higher flicker frequencies (ANOVA: main effect frequency: F (5,180) = 942; p < 0.001), with an additional significant frequency*diagnosis interaction (ANOVA: F (5,180) = 5.00; p < 0.001). This interaction effect was due to an increased CT at a flicker frequency of 15 Hz in the VSS cohort (VSS: MC = 1.17%; controls: MC = 0.77%). At the other frequencies, group comparisons revealed no differences. Furthermore, in the VSS cohort we observed an increase of CT with higher age (r = 0.69; p < 0.001), which was not seen in controls (r = 0.30; p = 0.20). CONCLUSIONS This study demonstrates a lower visual contrast sensitivity exclusively at 15 Hz in VSS patients and demonstrates frequency-dependent differences in dynamic contrast vision. The peak sensitivities of both parvo- and magnocellular visual pathways are close to a frequency of about 10 Hz. Therefore, this frequency seems to be of crucial importance in everyday life. Thus, it seems plausible that the impairment of contrast sensitivity at 15 Hz might be an important pathophysiological correlate of VSS. Furthermore, the overall age-related decrease in contrast sensitivity only in VSS patients underscores the vulnerability of dynamic contrast detection in VSS patients. Dynamic CT detection seems to be a promising neurophysiological test that may contribute to the diagnosis of VSS