Cluster sets for sobolev functions and quasiminimizers

In this paper, we study cluster sets and essential cluster sets for Sobolev functions and quasiharmonic functions (i.e., continuous quasiminimizers). We develop their basic theory with a particular emphasis on when they coincide and when they are connected. As a main result, we obtain that if a Sobolev function u on an open set Ω has boundary values f in Sobolev sense and f |_∂Ω is continuous at x ₀ ∈ ∂Ω, then the essential cluster set (u, x ₀,Ω) is connected. We characterize precisely in which metric spaces this result holds. Further, we provide some new boundary regularity results for quasiharmonic functions. Most of the results are new also in the Euclidean case.     

Atomic Layer Deposition of ZnO on CuO Enables Selective and Efficient Electroreduction of Carbon Dioxide to Liquid Fuels

Electrochemical reduction of carbon dioxide, if powered by renewable electricity, could serve as a sustainable technology for carbon recycling and energy storage. Among all the products, ethanol is an attractive liquid fuel. However, the maximum faradaic efficiency of ethanol is only ≈10 % on polycrystalline Cu. Here, CuZn bimetallic catalysts were synthesized by in situ electrochemical reduction of ZnO‐shell/CuO‐core bi‐metal‐oxide. Dynamic evolution of catalyst was revealed by STEM‐EDS mapping, showing the migration of Zn atom and blending between Cu and Zn. CuZn bimetallic catalysts showed preference towards ethanol formation, with the ratio of ethanol/ethylene increasing over five times regardless of applied potential. We achieved 41 % faradaic efficiency for C₂₊ liquids with this catalyst. Transitioning from H‐cell to an electrochemical flow cell, we achieved 48.6 % faradaic efficiency and ?97 mA cm^?2 partial current density for C₂₊ liquids at only ?0.68 V versus reversible hydrogen electrode in 1 m KOH. Operando Raman spectroscopy showed that CO binding on Cu sites was modified by Zn. Free CO and adsorbed *CH₃ are believed to combine and form *COCH₃ intermediate, which is exclusively reduced to ethanol.     

Fast XANES fluorescence imaging using a Maia detector

A new fast X‐ray absorption spectroscopy scanning method was recently implemented at the Hard X‐ray Microprobe endstation P06, PETRA III, DESY, utilizing a Maia detector. Spectromicroscopy maps were acquired with spectra for X‐ray absorption near‐edge structure (XANES) acquisition in the sub‐second regime. The method combines XANES measurements with raster‐scanning of the sample through the focused beam. The order of the scanning sequence of the axes, one beam energy axis and two (or more) spatial axes, is a variable experimental parameter and, depending on it, the dwell at each location can be either single and continuous (if the energy axis is the inner loop) or in shorter discontinuous intervals (if a spatial axis is innermost). The combination of improved spatial and temporal resolution may be necessary for rapidly changing samples, e.g. for following in operando chemical reactions or samples highly susceptible to beam damage where the rapid collection of single XANES spectra avoids issues with the emergence of chemical changes developing from latent damage. This paper compares data sets collected on a specially designed test pattern and a geological thin‐section scanning the energy as inner, middle and outer axis in the sequence. The XANES data of all three scanning schemes is found to show excellent agreement down to the single‐pixel level.     

Regular Strongly Typical Blocks of $${\mathcal{O}^{\mathfrak {q}}}$$

We use the technique of Harish-Chandra bimodules to prove that regular strongly typical blocks of the category for the queer Lie superalgebra are equivalent to the corresponding blocks of the category for the Lie algebra .     

Optimizing the mapping of finger areas in primary somatosensory cortex using functional MRI

Functional magnetic resonance imaging mapping of the finger somatotopy in the primary somatosensory cortex requires a reproducible and precise stimulation. The highly detailed functional architecture in this region of the brain also requires careful consideration in choice of spatial resolution and postprocessing parameters. The purpose of this study is therefore to investigate the impact of spatial resolution and level of smoothing during tactile stimulation using a precise stimuli system. Twenty-one volunteers were scanned using 2³ mm³ and 3³ mm³ voxel volume and subsequently evaluated using three different smoothing kernel widths. The overall activation reproducibility was also evaluated. Using a high spatial resolution proved advantageous for all fingers. At 2³ mm³ voxel volume, activation of the thumb, middle finger and little finger areas was seen in 89%, 67% and 50% of the volunteers, compared to 78%, 61% and 33% at 3³ mm³, respectively. The sensitivity was comparable for nonsmoothed and slightly smoothed (4 mm kernel width) data; however, increasing the smoothing kernel width from 4 to 8 mm resulted in a critical decrease (50%) in sensitivity. In repeated measurements of the same subject at six different days, the localization reproducibility of all fingers was within 4 mm (1 S.D. of the mean). The precise computer-controlled stimulus, together with data acquisition at high spatial resolution and with only minor smoothing during evaluation, could be a very useful strategy in studies of brain plasticity and rehabilitation strategies in hand and finger disorders and injuries.     

Water polarization under thermal gradients

We investigate the response of bulk liquid water to a temperature gradient using nonequilibrium molecular dynamics simulations. It is shown that the thermal gradient polarizes water in the direction of the gradient, leading to a non-negligible electrostatic field whose origin lies in the water reorientation under nonequilibrium conditions. The dependence of the magnitude of the electrostatic field with the temperature gradient is in agreement with nonequilibrium thermodynamics theory. We conclude that temperature gradients of the order of 10(8) K/m could result in fairly large polarizations approximately 10(6) V/m.     

On the homogeneity range of the κ phases in the Hf-Mo-{Si,P, S,Ge, As,Se} systems

A survey of the various two- and three-phase equilibria involving the κ phases in the subsolidus regions of the ternary Hf-Mo-{Si, P, S, Ge, As, Se} systems has been made. The κ phases have homogeneity ranges, accompanied by variations in the unit-cell volumes. The hexagonal κ-phase structure is composed of a transition metal sublattice with triangular prismatic and octahedral interstices. The nonmetal atoms may occupy one or both types of interstices. Phase-analytical and crystallographic results suggest a variable degree of hafnium substitution on the molybdenum sites in the metal sublattice as the major cause of the variations in composition observed. The κ phase in the Hf-Mo-S system exhibits a particularly large extension of the homogeneity range. This fact might be interpreted in terms of an enhanced thermodynamic stability of this phase, connected with the filling of both octahedral and triangular prismatic sites by sulfur in the structure, in contrast to the empty octahedral sites in the remaining κ phases.     

Deformation of liquid droplets during collisions with hot walls: Experimental and Numerical Results

Measurements of droplet deformation during wall impingement were performed for ethanol droplets and water droplets with diameters ranging from 100 to 200 μm. The wall temperature is well above the Leidenfrost temperature of the droplet liquid. With monodisperse droplet streams and a special illumination technique, slow motion images of the phenomena can be obtained. Measurements with high temporal resolution below 1 μs are possible using a standard video camera. The experimental results are compared with numerical results, which were obtained by solving the three-dimensional Navier-Stokes equations for incompressible fluids including surface tension effects. The fluids are treated with the volume-of-fluid method and the free surface is modeled according to the continuum-surface-force model. Numerical and experimental results show good agreement.