Theoretical studies of smectic C liquid crystals confined in a wedge. Stability considerations and Frederiks transitions

Abstract

A general deformation of a smectic C liquid crystal is composed of five different distortions, each of which can be made independently. Here we show that to each of these distortions we can assign a simple vector operator. Use of these five basis operators enables us to write down the elastic free energy density as a quadratic form consisting of nine terms. We also discuss how the nine elastic constants defined by the elastic energy expansion must fulfil certain restrictions in terms of inequalities and a specific tilt angle dependence. Assuming the smectic layers to be incompressible, we examine how certain arrangements of the smectic layers can be stable due to an interplay between the incompressibility condition and the boundary conditions which we impose on the director. One such stable configuration is the wedge, where the smectic layers form parts of concentric cylinders with the common axis coinciding with the centre of the wedge. For such a system we discuss the different director configurations which can be achieved and their stability. We also discuss the possibility of inducing Frederiks transitions for some of these configurations and calculate the corresponding thresholds, thereby demonstrating the design of an experiment which would make it possible to measure those elastic constants which are related to the deformations of the smectic layers, constants which are normally difficult to determine experimentally.     

pH‐controlled reaction divergence of decarboxylation versus fragmentation in reactions of dihydroxyfumarate with glyoxylate and formaldehyde: parallels to biological pathways

The reactions of dihydroxyfumarate with glyoxylate and formaldehyde exhibit a unique pH‐controlled mechanistic divergence leading to different product suites by two distinct pathways. The divergent reactions proceed via a central intermediate (2,3‐dihydroxy‐oxalosuccinate, 3 , in the reaction with glyoxylate and 2‐hydroxy‐2‐hydroxymethyl‐3‐oxosuccinate, 14 , in the reaction with formaldehyde). At pH 7–8, products ( 7 , 8 , and 15 ) exclusively from a decarboxylation of the intermediate are observed, while at pH 13–14, products ( 9 , 10 , and 16 ) solely derived from a hydroxide‐promoted fragmentation of the intermediate are formed. The decarboxylative and fragmentation pathways are mutually exclusive and do not appear to coexist under the range of pH (7–14) conditions investigated. Herein, we employ a combination of quantitative ¹³C NMR measurements and density functional theory calculations to provide a rationale for this pH‐driven reaction divergence. These rationalizations also hold true for the reactions of dihydroxyfumarate produced in situ by the catalytic cyanide‐mediated dimerization of glyoxylate. In addition, the non‐enzymatic decarboxylation and fragmentation transformations of these central intermediates ( 3 and 14 ) appear to have intriguing parallels to the enzymatic reactions of oxalosuccinate and formation of glyceric acid derivatives in extant metabolism – the high and low pH mimicking the precise control exerted by the enzymes over reaction pathways. Copyright © 2016 John Wiley & Sons, Ltd.     

The effect of Fe doping on superconductivity in ZrRuP

This work reports the structure and superconducting properties of the superconductor ZrRuP doped with Fe; the ZrRu_1−xFe_xP solid solution was investigated by means of X-ray powder diffraction, SQUID magnetometry and Mößbauer spectroscopy. It is shown that the modification of the superconducting properties by doping with Fe is similar to the effect of chemical pressure and that the Fe doped compounds do not show any magnetic ordering.     

Empirical analysis of the evolution of a scientific collaboration network

We present an analysis of the temporal evolution of a scientific coauthorship network, the genetic programming network. We find evidence that the network grows according to preferential attachment, with a slightly sublinear rate. We empirically find how a giant component forms and develops, and we characterize the network by several other time-varying quantities: the mean degree, the clustering coefficient, the average path length, and the degree distribution. We find that the first three statistics increase over time in the growing network; the degree distribution tends to stabilize toward an exponentially truncated power-law. We finally suggest an effective network interpretation that takes into account the aging of collaboration relationships.     

A symmetry-adapted method for the determination of the lattice energy and properties of ionic crystals

An efficient symmetry-adapted algorithm is described for the calculation of the elastic and dielectric properties of perfect ionic crystals.     

On an integral method for backward boundary layers

Zusammenfassung Eine Integralmethode für die Lösung von zweidimensionalen Grenzschichtgleichungen wird entwickelt für Fälle, in denen die Lösungen sich anfänglich wie diejenigen von End-Grenzschichten benehmen. Diese Lösungen sind von Goldstein behandelt worden. Die bedeutendste Anwendung betrifft den Fall, wo ein zweidimensionaler Strom gegen eine Öffnung fliesst, durch welche die Flüssigkeit entleert wird. In erster Annäherung wird die Grenzschichtströmung für grosse Entfernungen von der Öffnung durch die Ähnlichkeitsgesetze der konvergenten Strömung in einem keilförmigen Kanal beschrieben. Um Strömungen dieser Art zu studieren, die über lange Entfernungen laufen, wird die Geschwindigkeit am Rande der Grenzschicht an Stelle der Entfernung längs der Grenzschicht als unabhängige Veränderliche eingeführt. Die beschriebene Methode wird auf den Fall der Strömung in Richtung eines Schlitzes angewendet, ausgehend von einem unendlichen Halbraum, ferner auf den Fall einer Strömung um eine endliche Platte, die senkrecht zur Strömungsrichtung steht. In beiden Beispielen ist die Potentialströmung in der Form des Kirchhoff-Rayleighschen Gesetzes angenommen, wobei die freien Stromlinien an die scharfen Kanten gebunden sind. Die Methode wird verallgemeinert, so dass sie für allgemeinere End-Grenzschichten benutzt werden kann. Die Resultate stimmen ausgezeichnet mit denen der Methode von Thwaites sowie mit den Ähnlichkeitslösungen von Falkner-Skan überein.     

The potential role of ultrasound in differentiating solid and cystic swellings of the true vocal fold

This study was designed to investigate the potential role of ultrasound in the diagnosis of cysts of the true vocal fold. Materials and Methods: Grayscale ultrasound of the larynx was carried out in 29 patients with a swelling of the true vocal fold and dysphonia. The findings were then compared with those at subsequent microlaryngoscopy, in the majority of cases. Results and Conclusions: Whereas preoperative laryngeal ultrasound correctly predicted the surgical findings of a cystic lesion in only 5 of 11 cases, it correctly identified that no cyst was present in 15 of 16 instances when this had been queried. This study suggests that ultrasound may have some role in investigation of unilateral vocal fold pathology, but that further fine-tuning of the technique may be necessary.     

Visual Speech Recognition with Lightweight Psychologically Motivated Gabor Features

Extraction of relevant lip features is of continuing interest in the visual speech domain. Using end-to-end feature extraction can produce good results, but at the cost of the results being difficult for humans to comprehend and relate to. We present a new, lightweight feature extraction approach, motivated by human-centric glimpse-based psychological research into facial barcodes, and demonstrate that these simple, easy to extract 3D geometric features (produced using Gabor-based image patches), can successfully be used for speech recognition with LSTM-based machine learning. This approach can successfully extract low dimensionality lip parameters with a minimum of processing. One key difference between using these Gabor-based features and using other features such as traditional DCT, or the current fashion for CNN features is that these are human-centric features that can be visualised and analysed by humans. This means that it is easier to explain and visualise the results. They can also be used for reliable speech recognition, as demonstrated using the Grid corpus. Results for overlapping speakers using our lightweight system gave a recognition rate of over 82%, which compares well to less explainable features in the literature.     

1H NMR Studies on the Methylation,Protonation, and Hydration Sites in Some Benzo[b]Naphthyridines (Azaacridines)

Abstract

The 300.13 MHz ¹H NMR spectra of the methylated and protonated 6(9)-methylbenzo[b][1,x] naphthyridines (x=5, 6, 7, 8) (5-methylazaacridines) were collected at 298 K in deuterated dimethyl sulfoxide and chloroform, respectively. The methylation and protonation sites were assigned by comparisons of these data with those of the free bases. The results were compared with similar data for related heterocycles and showed that both methylation and protonation occur at the nitrogen in the outer pyrido ring in all four series.

The hydration site in some 2-and 3-azaacridines was determined by specific line broadening in their ¹H NMR spectra to be the same nitrogen as that involved in methylation and protonation. Variable temperature ¹H NMR demonstrated that the specific line broadening results from some changes of ¹⁴N quadrupolar relaxation produced by the slow chemical exchange between unhydrated and hydrated species. Deuterium exchange experiments indicated that the direct spin-spin interaction of a water proton and the protons alpha to the hydrated nitrogen may also have some contribution.     

Finite time blowup of the <Emphasis Type="Italic">n</Emphasis>-harmonic flow on <Emphasis Type="Italic">n</Emphasis>-manifolds

In this paper, we generalize the no-neck result of Qing and Tian (in Commun Pure Appl Math 50:295–310, 1997) to show that there is no neck during blowing up for the n-harmonic flow as \(t\rightarrow \infty \). As an application of the no-neck result, we settle a conjecture of Hungerbühler (in Ann Scuola Norm Sup Pisa Cl Sci 4:593–631, 1997) by constructing an example to show that the n-harmonic map flow on an n-dimensional Riemannian manifold blows up in finite time for \(n\ge 3\).