Interfacial tension of a nematic liquid crystal/water interface with homeotropic surface alignment

Pendant drop experimental results are presented for the temperature dependence of the interfacial tension between water and the immiscible nematic liquid crystal 4'-pentyl-4-biphenylcarbonitrile (5CB) in the presence of the adsorbed surfactant cetyltrimethylammonium bromide (CTAB). Adsorption of the surfactant lowers the interfacial tension value and is also known from earlier work to induce a transition in liquid crystal surface alignment from planar to homeotropic [Brake et al. Langmuir 2003, 19, 6436.]. Discrepancies exist in the literature regarding the density of 5CB, and the density difference between 5CB and water in any case is very small. However, from the ability to form pendant 5CB drops, one may infer that the density of 5CB exceeds that of water over the entire temperature range studied (28-41 degrees C), in disagreement with the predictions of one earlier report on 5CB. The interfacial tension is shown to exhibit a relative maximum near the bulk 5CB nematic-isotropic transition temperature T(NI), regardless of which published data set of 5CB density values is used to analyze the measurements, with a possible discontinuity in tension occurring at T(NI). The anomalous shape of the interfacial tension curve, depending on the choice of the 5CB density data set, may be quite similar to that recently reported for the interface between 5CB and a hydrophobic, isotropic molten polymer (Rai et al. Langmuir 2003, 19, 7370).     

Predator–Prey model with Holling response function of type II and SIS infectious disease

We analyze the influence of a SIS infectious disease affecting Preys or both Predators and Preys in a Predator–Prey model. The response function used here is Holling function type II. Many thresholds are computed and used to investigate the global stability results. The disease can disappear from the community, persist in one or two populations of the community. At least one population can disappear from the community because of disease. In some cases, the model exhibits periodic solutions with persistence of the disease or without disease. Numerical simulations are used with nonstandard numerical schemes to illustrate our results.     

Exponential Decay of Correlations for a Real-Valued Dynamical System Generated by a $k$ Dimensional System

As a first step towards modelling real time-series, we study a class of real-variable, bounded processes \(\{X_{n}, n\in \mathbb{N}\}\) defined by a deterministic \(k\)-term recurrence relation \(X_{n+k} = \varphi (X _{n}, \ldots , X_{n+k-1})\). These processes are noise-free. We immerse such a dynamical system into \(\mathbb{R}^{k}\) in a slightly distorted way, which allows us to apply the multidimensional techniques introduced by Saussol (Isr. J. Math. 116:223–248, 2000) for deterministic transformations. The hypotheses we need are, most of them, purely analytic and consist in estimates satisfied by the function \(\varphi \) and by products of its first-order partial derivatives. They ensure that the induced transformation \(T\) is dilating. Under these conditions, \(T\) admits a greatest absolutely continuous invariant measure (ACIM). This implies the existence of an invariant density for \(X_{n}\), satisfying integral compatibility conditions. Moreover, if \(T\) is mixing, one obtains the exponential decay of correlations.

     

The 3-D electrostatic potential surrounding a square array of surface charges

Simple scaling laws have been derived which relate the 3-D potential to the inter-surfacestate spacing, the field-plate spacing, the dielectric constants of both insulators bordering the interface, and the dimensions x,y,z. This 3-D potential, obtained by using a pair of images and Neumann boundary conditions, contains the usual 1-D potential as the zeroth harmonic in a Fourier series. The 3-D and 1-D potentials give equivalent densities of conduction electrons in an accumulation layer only for a surface state density σ < 3 × 10¹¹/cm². For higher σ, the 1-D potential seriously underestimates the amount of space charge possible. There is a low saddle point in the 3-D potential configuration which allows surface conduction electrons to transport laterally in the presence of a transverse field.     

Chemical and mechanical properties of snake fangs

The composition of dental tissues and their interaction determines its mechanical properties. The mechanical properties and chemical composition of the teeth of extant reptiles are still poorly studied areas. As a preliminary study the fangs of four species of snakes and a human tooth were investigated through nanoindentation and Raman spectroscopy. The average elastic modulus values for the main body of the fangs ranged from 15.3 GPa to 24.6 GPa, and 19.1 GPa for the human dentine. Raman spectroscopy and principal component analysis (PCA) showed that snake fangs are similar in composition to human dentine, both of which comprised of hydroxyapatite and an organic matrix. The elastic modulus and hardness data were correlated to the Raman spectra using partial least squares regression (PLS). The spectral features which correlated with the elastic modulus would suggest that elastic modulus is dependent on the relative protein to mineral amounts in the tooth. The form of the phosphate and the relative levels of phosphate to organic components also appear to be governing factors for elastic modulus. The PLS of Raman spectra against the hardness gave very similar results. The small differences between snake fangs and human dentine appeared to be because of carbonate content, with higher levels of carbonate in the human tooth than the snake fangs. Snake fangs should be able to withstand large lateral forces. Human dentine aids in dissipating imposed loads. This similarity in the chemical composition of the snake fangs and human dentine supported the findings of the similarities in mechanical properties, which may be attributed to the similar functional demands of these biocomposites. Copyright © 2016 John Wiley & Sons, Ltd.