Dynamics of liquid membranes. II: Adaptive finite difference methods

Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.     

Complexation of 6-Deoxy-6-(aminoethyl)amino-β-cyclodextrin with Sodium Cholate and Sodium Deoxycholate

In order to study its guest binding and the inclusion phenomena, 6-deoxy-6-(aminoethyl)amino--cyclodextrin (CDN) was synthesised and its binding properties examined. The complexation phenomena of sodium cholate (NaC) and sodium deoxycholate (NaDC) with CDN has been monitored by the NMR method using ¹³C chemical shift data. The method of continuous variation Job's method has been used to determine the stoichiometry of these supramolecular complexes. The Job's plot confirms the 1 : 1 supramolecular complex for NaC: CDN and the 1 : 2 supramolecular complex for NaDC: CDN. The interaction of NaC and NaDC with CDN has been obtained through two-dimensional Rotational Nuclear Overhauser Effect Spectroscopy (ROESY) NMR. Equilibrium constants were also obtained from ¹³C chemical shift data (C-1, C-3 & C-4) at different pH values (7, 9, & 11).     

A one-parameter family of hamiltonian structures for the KP hierarchy and a continuous deformation of the nonlinear WKP algebra

The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting W-algebra is a one-parameter deformation of W_KP admitting a central extension for generic values of the parameter, reducing naturally to W _n for special values of the parameter, and contracting to the centrally extended W₁₊, W and further truncations. In the classical limit, all algebras in the one-parameter family are equivalent and isomorphic tow _KP. The reduction induced by setting the spin-one field to zero yields a one-parameter deformation of which contracts to a new nonlinear algebra of the W-type.Address after October 1993: Queen Mary and Westfield College, UK     

The algebra of differential operators on the circle and W KP (q)

Radul has recently introduced a map from the Lie algebra of differential operators on the circle of W _n . In this Letter, we extend this map to W _KP ^(q) , a recently introduced one-parameter deformation of W_KP - the second Hamiltonian structure of the KP hierarchy. We use this to give a short proof that W is the algebra of additional symmetries of the KP equation.     

UV filter 2‐ethylhexyl 4‐methoxycinnamate: a structure,energetic and UV–vis spectral analysis based on density functional theory

2‐Ethylhexyl 4‐methoxycinnamate (EHMC) is a very commonly used UVB filter that is known to isomerize from the (E) to the (Z) isomer in the presence of light. In this study, we have performed high level quantum chemical calculations using density functional theory (DFT) with the B3LYP density functional and extended basis sets to study the gas‐phase molecular structure of EHMC and its energetic stability. Calculations were also performed for related smaller molecules cinnamic acid and 4‐methoxycinnamic acid. Charge delocalization has been analyzed using natural charges and Wiberg bond indexes within the natural bond orbital analysis and using nucleus independent chemical shifts. Density functional theory calculations reveal that the (E) isomer of EHMC is more stable than the (Z) by about 20 kJ mol^?1 in both the gas and aqueous phases. The enthalpy of formation in the gas phase of (E)‐EHMC was derived from an isodesmic bond separation reaction. Long‐range corrected DFT calculations in implicit water were made in order to understand the excited state properties of the (E) and (Z) isomers of EHMC. Copyright © 2013 John Wiley & Sons, Ltd.     

The use of vibrational spectroscopy to study the pathogenesis multiple sclerosis and other neurological conditions

Spectroscopy techniques are valuable tools in biomedical research and have been used extensively in the study of disease. However, neurological conditions such as multiple sclerosis (MS) have received little attention and the available spectroscopy studies are limited, both in overall numbers of patients studied and the disease samples considered. MS is a complex immune-mediated disease, with variable clinical courses and limited therapeutic options. This review aims to summarize current literature in the area, demonstrating how spectroscopy techniques can provide valuable information to inform and advance research into the most common neurological condition affecting young adults.     

Aza‐Diels–Alder reaction between cyclopentadiene and protonated N‐phenylethyliminoacetates of 8‐phenylmenthol and 8‐phenylneomenthol: a density functional theory study

The cycloaddition between glyoxylate imines possessing two chiral auxiliaries, N‐(R)‐ or N‐(S)‐1‐phenylethyl and 8‐phenylmenthyl or 8‐phenylneomenthyl, and cyclopentadiene is described. Computational calculations using density functional theory with the Becke, three‐parameter, Lee–Yang–Parr functional and the 6‐31G(d) basis set were performed to better understand the highly diastereoselective mechanism and the exo‐selectivity observed experimentally for these ionic aza‐Diels–Alder reactions. Copyright © 2011 John Wiley & Sons, Ltd.     

Dentinal tubules driven wetting of dentin: Cassie-Baxter modelling

We investigate the wetting properties of dentin surfaces submitted to a phosphoric acid etching followed by an air drying procedure, as in clinical situations of adhesive dentistry. The surface topography of the etched surfaces was characterized by AFM, and the wetting properties of water on these rough and heterogeneous surfaces were studied, by contact angle measurements. We showed that the contact angle increases with the acid exposure time and consequently with both surface roughness and the organic-mineral ratio of the dentin components. From the whole results, obtained on dentin and also on synthesized hydroxyapatites samples, we inferred a water contact angle of ∼ 133^° on the dentinal tubule. These experimental results may be described by the Cassie-Baxter approach, and it is suggested that small air pockets could be formed inside the dentinal tubules.     

Monte Carlo simulation of ion–material interactions in nuclear fusion devices

One of the key aspects regarding the technological development of nuclear fusion reactors is the understanding of the interaction between high-energy ions coming from the confined plasma and the materials that the plasma-facing components are made of. Among the multiple issues important to plasma–wall interactions in fusion devices, physical erosion and composition changes induced by energetic particle bombardment are considered critical due to possible material flaking, changes to surface roughness, impurity transport and the alteration of physicochemical properties of the near surface region due to phenomena such as redeposition or implantation. A Monte Carlo code named MATILDA (Modeling of Atomic Transport in Layered Dynamic Arrays) has been developed over the years to study phenomena related to ion beam bombardment such as erosion rate, composition changes, interphase mixing and material redeposition, which are relevant issues to plasma-aided manufacturing of microelectronics, components on object exposed to intense solar wind, fusion reactor technology and other important industrial fields. In the present work, the code is applied to study three cases of plasma material interactions relevant to fusion devices in order to highlight the code’s capabilities: (1) the Be redeposition process on the ITER divertor, (2) physical erosion enhancement in castellated surfaces and (3) damage to multilayer mirrors used on EUV diagnostics in fusion devices due to particle bombardment.