A posteriori error estimates for the virtual element method

An a posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is fully computable as it relies only on quantities available from the VEM solution, namely its degrees of freedom and element-wise polynomial projection. Upper and lower bounds of the error estimator with respect to the VEM approximation error are proven. The error estimator is used to drive adaptive mesh refinement in a number of test problems. Mesh adaptation is particularly simple to implement since elements with consecutive co-planar edges/faces are allowed and, therefore, locally adapted meshes do not require any local mesh post-processing

Thickness dependence of the integrated Bragg intensity for statistically disturbed silicon crystals

The thickness dependence of the integrated Bragg intensities for Czochralski-grown silicon was measured with the characteristic tungsten Kα1-line at 59.3 keV. In contrast to previous experiments the sample is wedge shaped, which allows to take data over a wide range of Pendellösung fringes in one exposure only and without any mechanical movement of the sample. The period length, the oscillation amplitude, and the mean value of the Bragg intensity can be explored to identify the presence of point defects, and the temperature dependence of the period length allows to quantify the thermal Debye-coefficient with high precision

Effects of A1 Milk, A2 Milk and the Opioid-like Peptide β-Casomorphin-7 on the Proliferation of Human Peripheral Blood Mononuclear Cells

Special attention is given to cow’s milk and its variants, with ongoing discussions about health-related impacts primarily focusing on the A1 variant in contrast to the A2 variant. The difference between these variants lies in a single amino acid alteration at position 67 of β-casein. This alteration is presumed to make the A1 variant more susceptible to enzymatic breakdown during milk digestion, leading to an increased release of the peptide β-casomorphin-7 (BCM-7). BCM-7 is hypothesized to interact with µ-opioid receptors on immune cells in humans. Although BCM-7 has demonstrated both immunosuppressive and inflammatory effects, its direct impact on the immune system remains unclear. Thus, we examined the influence of A1 and A2 milk on Concanavalin A (ConA)-stimulated human peripheral blood mononuclear cells (PBMCs), as well as the effect of experimentally digested A1 and A2 milk, containing different amounts of free BCM-7 from β-casein cleavage. Additionally, we evaluated the effects of pure BCM-7 on the proliferation of ConA-stimulated PBMCs and purified CD4+ T cells. Milk fundamentally inhibited PBMC proliferation, independent of the β-casein variant. In contrast, experimentally digested milk of both variants and pure BCM-7 showed no influence on the proliferation of PBMCs or isolated CD4+ T cells. Our results indicate that milk exerts an anti-inflammatory effect on PBMCs, regardless of the A1 or A2 β-casein variant, which is nullified after in vitro digestion. Consequently, we deem BCM-7 unsuitable as a biomarker for food-induced inflammation