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

Preparation and cycling performance of iron or iron oxide containing amorphous Al-Li alloys as electrodes

Crystalline phase transitions cause volume changes, which entails a fast destroying of the electrode. Non-crystalline states may avoid this circumstance. Herein we present structural and electrochemical investigations of pre-lithiated, amorphous Al39Li43Fe13Si5-powders, to be used as electrode material for Li-ion batteries. Powders of master alloys with the compositions Al39Li43Fe13Si5 and Al39Li43Fe13Si5 + 5 mass-% FeO were prepared via ball milling and achieved amorphous/nanocrystalline states after 56 and 21.6 h, respectively. In contrast to their Li-free amorphous pendant Al78Fe13Si9, both powders showed specific capacities of about 400 and 700 Ah/kgAl, respectively, after the third cycle

Confinement Effects for Efficient Macrocyclization Reactions with Supported Cationic Molybdenum Imido Alkylidene N -Heterocyclic Carbene Complexes

For entropic reasons, the synthesis of macrocycles via olefin ring-closing metathesis (RCM) is impeded by competing acyclic diene metathesis (ADMET) oligomerization. With cationic molybdenum imido alkylidene N-heterocyclic carbene (NHC) complexes confined in tailored ordered mesoporous silica, RCM can be run with macrocyclization selectivities up to 98% and high substrate concentrations up to 0.1 M. Molecular dynamics simulations show that the high conversions are a direct result of the proximity between the surface-bound catalyst, proven by extended X-ray absorption spectroscopy, and the surface-located substrates. Back-diffusion of the macrocycles decreases with decreasing pore diameter of the silica and is responsible for the high macrocyclization efficiency. Also, Z-selectivity increases with decreasing pore diameter and increasing Tolman electronic parameter of the NHC. Running reactions at different concentrations allows for identifying the optimum substrate concentration for each material and substrate combination

APRIL limits atherosclerosis by binding to heparan sulfate proteoglycans.

Atherosclerotic cardiovascular disease causes heart attacks and strokes, which are the leading causes of mortality worldwide1. The formation of atherosclerotic plaques is initiated when low-density lipoproteins bind to heparan-sulfate proteoglycans (HSPGs)2 and become trapped in the subendothelial space of large and medium size arteries, which leads to chronic inflammation and remodelling of the artery wall2. A proliferation-inducing ligand (APRIL) is a cytokine that binds to HSPGs3, but the physiology of this interaction is largely unknown. Here we show that genetic ablation or antibody-mediated depletion of APRIL aggravates atherosclerosis in mice. Mechanistically, we demonstrate that APRIL confers atheroprotection by binding to heparan sulfate chains of heparan-sulfate proteoglycan 2 (HSPG2), which limits the retention of low-density lipoproteins, accumulation of macrophages and formation of necrotic cores. Indeed, antibody-mediated depletion of APRIL in mice expressing heparan sulfate-deficient HSPG2 had no effect on the development of atherosclerosis. Treatment with a specific anti-APRIL antibody that promotes the binding of APRIL to HSPGs reduced experimental atherosclerosis. Furthermore, the serum levels of a form of human APRIL protein that binds to HSPGs, which we termed non-canonical APRIL (nc-APRIL), are associated independently of traditional risk factors with long-term cardiovascular mortality in patients with atherosclerosis. Our data reveal properties of APRIL that have broad pathophysiological implications for vascular homeostasis.Hell