Comparisons of the vector method and tensor method for simulating liquid crystal devices

In calculating the director configuration in a liquid crystal device, two methods are commonly employed: a vector model and a tensor model. In this paper, we compare and contrast these methods for liquid crystal devices consisting of a layer of liquid crystal sandwiched between two plates. We compare the reliability and accuracy of the results, the speed of computation and the complexity of implementations of each method.     

UVB irradiation of normal human skin favors the development of type-2 T-cells in vivo and in primary dermal cell cultures

To determine the effect of UVB exposure on the balance of type-1 or type-2 T-cells in skin, we examined the expression of key markers interferon (IFN)-gamma and interleukin (IL)-4 in cryostat sections. IFN-gamma mRNA was clearly detectable in nonirradiated control skin, and IFN-gamma protein was found in 2% of the dermal CD3pos T-cells, whereas IL-4 mRNA was hardly detectable, and no IL-4 protein was found. In contrast, IL-4 mRNA expression increased upon irradiation, and IL-4 was found in 2% of the T-cells at day 2 after UVB-exposure. Concomitantly, IFN-gamma mRNA expression decreased, and IFN-gamma protein became absent. We also analyzed T-cells present in primary dermal cell cultures, which were used as an in vitro equivalent of the in vivo situation. As compared with T-cells from control skin, T-cells in dermal cell cultures from UVB-exposed skin displayed an increased IL-4 and decreased IFN-gamma expression. No such skewing occurred when the T-cells from irradiated skin were cloned in the absence of a dermal microenvironment. Except for an occasional positive T-cell, type-1-associated cell-surface markers (CCR5, CXCR3) or type-2 markers (CCR3, CD30, CRTH2) were undetectable in situ. But these markers were expressed on cultured dermal T-cells from UVB-exposed and control skin at a comparable level, but did not correlate with the IFN-gamma and IL-4 production. Altogether, UVB-induced changes of the dermal microenvironment favor the development of type-2 T-cells.     

Comparison of different types of outlet frits in slurry‐packed capillary columns

Fused‐silica capillary columns for high‐performance liquid chromatography with 320 and 250 μm inner diameter were prepared by slurry packing with 5 and 3 μm Nucleosil C₁₈ stationary phase. Different types of mechanical and monolithic outlet frits were used and their influence on the resulting column performance was evaluated. Columns with quartz wool exhibited symmetrical peaks and low theoretical plate height, and the preparation time was short. The performance of monolithic frits varied based on type of monolith, length of the frit, and silanization procedure. The best frit performed similarly to the quartz wool ones, but the preparation took several hours. Their main advantage lies in the possibility of on‐column detection, because the detection window can be burnt immediately behind the frit.     

Coordination chemistry of 5,6,7-trimethyl-[1,2,4]triazolo[1,5-a]pyrimidine with first-row transition-metal salts: Synthesis, spectroscopy and single-crystal structures, with counter-anion dependence of the structures

A variety of new coordination compounds with transition-metal salts and the ligand trimethyl[1,2,4]triazolo[1,5-a]pyrimidine (abbreviated as tmtp) is described, together with several of their 3D crystal structures and spectroscopic and magnetic properties. The compounds were selected based on the coordination ability of the counterion, halide, nitrate, sulfate, thiocyanate and perchlorate. The formed coordination compounds and their coordination numbers were found to be strongly dependent on both the cation and the used counter-anion. The several compounds studied have the following structural formulae: [CuCl₂(tmtp)₂], [CuBr₂(tmtp)₂], [ZnBr₂(tmtp)₂], [Cu(NO₃)₂(tmtp)₂], [CuSO₄(tmtp)₂]₂(H₂O)(MeOH), [Cu(H₂O)(NCS)₂(tmtp)₂], [Zn(NCS)₂(tmtp)₂], [Cd(NCS)₂(tmtp)₂] and [M(H₂O)₂(tmtp)₄](BF₄)₂, in which M = Co, Ni, Zn.The new coordination compounds have been further characterized by NMR, (far-)IR and LF spectra, as well as by C, H, N element analyses, and EPR spectra for the Cu(II) compounds. The coordination around the metal varies from 4 (Zn, Cu), via 5 (Cu) to 6 (for Co, Cu and Cd). The anions usually complete the coordination sphere; only the Co and Zn compounds with the tetrafluoridoborate anions have no coordinated anions, but water ligands complete the octahedral coordination sphere. In the 5-coordinated [Cu(H₂O)(NCS)₂(tmtp)₂] water completes the square pyramid geometry.     

The crystal and molecular structure of cyclopentadienyltin(II) chloride. The bonding of the cyclopentadienyl group in tin(II) compounds

The crystal and molecular structure of cyclopentadienyltin(II) chloride has been determined from three-dimensional X-ray data. The crystals are orthorhombic, space group Pc2₁n. The unit cell, of dimensions a = 5.711(5), b = 6.225(5), c = 17.24(2) Å, contains four molecules. The structure has been refined by full matrix least squares techniques to a final R value of 0.083 for 717 independent reflections. In the crystal unsymmetrical tin-chlorine bridges are present between the units of C₅H₅SnCl.It is suggested that in cyclopentadienyltin(II) compounds the cyclopentadienyl group occupies more than one coordination site as a result of the donation of π electron density from the cyclopentadienyl ring into an empty acceptor orbital of the tin atom having π symmetry.     

Statistical and Numerical Considerations of Backus-Average Product Approximation

In this paper, we examine the applicability of the approximation, \(\overline{f g}\approx \overline{f}\,\overline{g}\), within Backus (J. Geophys. Res. 67(11):4427–4440, 1962) averaging. This approximation is a crucial step in the method proposed by Backus (J. Geophys. Res. 67(11):4427–4440, 1962), which is widely used in studying wave propagation in layered Hookean solids. According to this approximation, the average of the product of a rapidly varying function and a slowly varying function is approximately equal to the product of the averages of those two functions.Considering that the rapidly varying function represents the mechanical properties of layers, we express it as a step function. The slowly varying function is continuous, since it represents the components of the stress or strain tensors. In this paper, beyond the upper bound of the error for that approximation, which is formulated by Bos et al. (J. Elast. 127:179–196, 2017), we provide a statistical analysis of the approximation by allowing the function values to be sampled from general distributions.Even though, according to the upper bound, Backus (J. Geophys. Res. 67(11):4427–4440, 1962) averaging might not appear as a viable approach, we show that—for cases representative of physical scenarios modelled by such an averaging—the approximation is typically quite good. We identify the cases for which there can be a deterioration in its efficacy.In particular, we examine a special case for which the approximation results in spurious values. However, such a case—though physically realizable—is not likely to appear in seismology, where Backus (J. Geophys. Res. 67(11):4427–4440, 1962) averaging is commonly used. Yet, such values might occur in material sciences, in general, for which Backus (J. Geophys. Res. 67(11):4427–4440, 1962) averaging is also considered.     

On the Lebesgue constant of Berrut’s rational interpolant at equidistant nodes

It is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting. In this paper we confirm this observation by proving that the Lebesgue constant of Berrut’s rational interpolant grows only logarithmically in the number of interpolation nodes. Moreover, the numerical results suggest that the Lebesgue constant behaves similarly for interpolation at Chebyshev as well as logarithmically distributed nodes.