284 research outputs found
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 -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 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<sub>m</sub>) 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<sub>m</sub>. 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<sub>m</sub>, flow magnitudes tend to decrease while the relevant
precipitation time increases significantly. The influence of topographical
catchment features, snow cover and SWE<sub>m</sub> 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
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