Analogue Models of and for Gravity

Condensed matter systems, such as acoustics in flowing fluids, light in moving dielectrics, or quasiparticles in a moving superfluid, can be used to mimic aspects of general relativity. More precisely these systems (and others) provide experimentally accessible models of curved-space quantum field theory. As such they mimic kinematic aspects of general relativity, though typically they do not mimic the dynamics. Although these analogue models are thereby limited in their ability to duplicate all the effects of Einstein gravity they nevertheless are extremely important—they provide black hole analogues (some of which have already been seen experimentally) and lead to tests of basic principles of curved-space quantum field theory. Currently these tests are still in the realm of gedanken-experiments, but there are plausible candidate models that should lead to laboratory experiments in the not too distant future.     

Labile Interactions Defined in Crystalline Metal Complexes

The problems involved in identifying and quantifying labile interactions considered to influence complex compound structures are highlighted through the assessment of four different families of metal complexes for which extensive crystallographic data are available. Modification of the charge distribution within a ligand molecule as a result of coordination is one factor with a number of ramifications. A detailed analysis of evidence for both intra- and inter-molecular attractions in dimethylsulfoxide complexes of metal perchlorates is used to provide a basis for the consideration of weak interactions between complex ions involving forces including phenyl-group attractions, hydrogen bonding and cavity inclusion.     

Spline collocation for strongly elliptic equations on the torus

Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4].     

A second-order accurate numerical method for a fractional wave equation

We study a generalized Crank–Nicolson scheme for the time discretization of a fractional wave equation, in combination with a space discretization by linear finite elements. The scheme uses a non-uniform grid in time to compensate for the singular behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assuming that the spatial domain is convex or smooth, we show that the error is of order k ² + h ², where k and h are the parameters for the time and space meshes, respectively.     

Correction: Phytol-based novel adjuvants in vaccine formulation: 1. assessment of safety and efficacy during stimulation of humoral and cell-mediated immune responses

This is a correction article.     

3D molecular imaging SIMS

Thin monolayer and bilayer films of spin cast poly(methyl methacrylate) (PMMA), poly(2-hydroxyethyl methacrylate) (PHEMA), poly(lactic) acid (PLA) and PLA doped with several pharmaceuticals have been analyzed by dynamic SIMS using SF₅⁺ polyatomic primary ion bombardment. Each of these systems exhibited minimal primary beam-induced degradation under cluster ion bombardment allowing molecular depth profiles to be obtained through the film. By combing secondary ion imaging with depth profiling, three-dimensional molecular image depth profiles have been obtained from these systems. In another approach, bevel cross-sections are cut in the samples with the SF₅⁺ primary ion beam to produce a laterally magnified cross-section of the sample that does not contain the beam-induced damage that would be induced by conventional focussed ion beam (FIB) cross-sectioning. The bevel surface can then be examined using cluster SIMS imaging or other appropriate microanalysis technique.     

Multifunctional Calix[4]arenes Containing Pendant Amide and Phosphoryl Groups: Their Use as Extracting Agents and Carriers for Alkali Cations

The complexing, extracting and mobile carrier properties of the tetra(phosphine oxide)-calix[4]arene 1 and the hybrid diamide-di(phosphine oxide)-calix[4]arene 2 were studied. Both ligands give 1 : 1 complexes with alkali cations in THF as shown by the picrate method. 1H NMR experiments were run to follow encapsulation of sodium and potassium cations. The corresponding spectra indicate C2-symmetrical structure. The observed extraction orders of the alkali picrates were as follows K+>Rb+>Li+>Cs+>Na+ for 1 and Li+>Na+>K+>Rb++ for 2. Transport kinetics was analysed by means of a model which assumes pure diffusion and which allows the evaluation of mass transfer coefficients in all systems. These coefficients and their influences on the transport rate are discussed in terms of size of the transporting species in the liquid membrane.