Stability of algebraic multigrid for Stokes problems

An investigation is made of the performance of algebraic multigrid (AMG) solvers for the discrete Stokes problem. The saddle‐point formulations are based on the direct enforcement of the fundamental conservation laws in discrete spaces and subsequently stabilised with the aid of a regular splitting of the diffusion operator. AMG solvers based on an independent coarsening of the fields (the unknown approach) and also on a common coarsening (the point approach) are investigated. Both mixed‐order and equal‐order interpolations are considered. The dependence of convergence on the ‘degree of coarsening’ is investigated by studying the ‘convergence versus coarsening’ characteristics and their variation with mesh resolution. They show a consistency in shape, which reveals two distinct performance zones, one convergent the other divergent. The transition from the convergent to the divergent zones is discontinuous and occurs at a critical coarsening factor that is largely mesh independent. It signals a breakdown in the stability of the smoothing at the coarser levels of coarse grid approximation. It is shown that the previously observed, mesh‐dependent, scaling of convergence factors, which had suggested inconsistencies in the coarse grid approximation, is not a reliable marker of inconsistency. It is an indirect consequence of the breakdown in the stability of smoothing. For stable smoothing, reduction factors are shown to be largely mesh independent. The ability of mixed‐order interpolation to permit stable smoothing and therefore to deliver mesh‐independent convergence is explained. Two expedient options are suggested for obtaining mesh‐independent convergence for those AMG codes that are based on an equal‐order interpolation. Copyright © 2012 John Wiley & Sons, Ltd.     

Triphenylamine derivatized phenylacetylene macrocycle with large two-photon absorption cross-section

A phenylacetylene macrocycle (PAM) derivative containing triphenylamine as the framework was synthesized in one-step Sonogashira coupling. The photophysical and electrochemical properties were investigated in details. This hexamer shows significant enhancement in two-photon absorption cross-section relative to reported PAM derivatives.     

Mixed‐order interpolation for the Galerkin coarse‐grid approximations in algebraic multigrid solvers

An empirical investigation is made of AMG solver performance for the fully coupled set of Navier–Stokes equations. The investigation focuses on two different FV discretizations for the standard driven cavity test problem. One is a collocated vertex‐based discretization; the other is a cell‐centred staggered‐grid discretization. Both employ otherwise identical orthogonal Cartesian meshes. It is found that if mixed‐order interpolation is used in the construction of the Galerkin coarse‐grid approximation (CGA), a close‐to‐optimum mesh‐independent scaling of the AMG convergence is observed with similar convergence rates for both discretizations. If, on the other hand, an equal‐order interpolation is used, convergence rates are mesh‐dependent but the scaling differs in each case. For the collocated‐grid case, it depends both on the mesh size, h (or bandwidth Q～h^?1) and on the total number of grids, G, whereas for the staggered‐grid case it depends only on Q. Comparing the two characteristics reveals that the Q‐dependent parts are very similar; it is only in the G‐dependent convergence for the collocated‐grid case that they differ. This takes the form of stepped reductions in the AMG convergence rate (implying step reductions in the quality of the Galerkin CGA that correlate exactly with step increases in G). These findings reinforce previous evidence that, for optimum mesh‐independent performance, mixed‐order interpolations should be used in forming Galerkin CGAs for coupled Navier–Stokes problems. Copyright © 2010 John Wiley & Sons, Ltd.     

Long-lived mesoscopic entanglement outside the Lamb-Dicke regime

We create entangled states of the spin and motion of a single 40Ca+ ion in a linear ion trap. We theoretically study and experimentally observe the behavior outside the Lamb-Dicke regime, where the trajectory in phase space is modified and the motional coherent states become squeezed. We directly observe the modification of the return time of the trajectory, and infer the squeezing. The mesoscopic entanglement is observed up to Deltaalpha=5.1 with coherence time 170 micros and mean phonon excitation n = 16.     

Synthesis and hydrophobic binding studies on a water- soluble tritriptycene

The water soluble tritriptycene 1 was synthesized starting with triptycene trisquinone and anthracene. The hydrophobic binding of substrates to the benzene-walled cavities in 1 was studied by noting the up-field shift of substrate protons in the NMR of the substrate in the presence of aqueous 1. Small substrates, negatively charged substrates or substrates larger than the cavities do not bind as strongly as substrates about the same size as the cavities or those bearing a positive charge. Based on differences in AH_z'S, the bound substrates position themselves in the cavities so that polar groups are at the water interface.     

Structural studies of the phase, aggregation and surface behaviour of 1-alkyl-3-methylimidazolium halide + water mixtures

The surface, phase and aggregation behaviour of mixtures of 1-alkyl-3-methylimidazolium halide, [C(n)mim]X, where n is the alkyl chain length, with water has been explored using a variety of methods. Critical micelle concentrations (cmc) and micelle structures have been determined for aqueous [C(n)mim]Br solutions for n=2, 4, 6, 8, and 10. Small-angle neutron scattering (SANS) measurements reveal that for the n=8 and 10 systems, at concentrations just above the cmc, small near-spherical aggregates exist, which, after initial growth, possess core radii (aggregation numbers) at intermediate concentrations of 10.5+/-0.5 Angstrom (22+/-2) and 13.2+/-0.5 Angstrom (40+/-3), respectively, for n=8 and n=10. Towards higher concentrations, the aggregates appear to grow, with the aggregates in the [C(10)mim]Br system becoming increasingly elongated (prolate) with increasing concentration. No evident aggregates are formed in the systems with n=2 and 4. In the n=6 system, it appears that oblate aggregates with radius approximately 9 Angstrom form at the cmc and that the radius increases with increasing concentration. For longer alkyl chain lengths, at high concentrations lyotropic mesophases form in some systems. The mesophase region for the [C(8)mim]Cl system has been explored across the composition range using X-ray diffraction and (2)H NMR spectroscopy. Both techniques suggest that a major hexagonal phase with lattice parameter of 29.5+/-0.5 Angstrom coexists with a minor lamellar phase (23.5+/-0.3 Angstrom) or possibly a second hexagonal phase (27.1+/-0.4 Angstrom). The area per adsorbed molecule at the surface of [C(8)mim]Br solutions has been measured as a function of concentration using neutron reflectometry. A minimum in the area per molecule behaviour is coincident with a minimum identified in the surface tension isotherm occurring close to the cmc. The data suggest depletion of [C(8)mim]Br from the surface region occurs at concentrations immediately above the cmc.     

3D printing for aqueous and non-aqueous redox flow batteries

Additive manufacturing technologies, generally grouped under the name of 3D printing, are experiencing an explosion of interest during the last few years. The possibility of fast prototyping enabled by 3D printing has been recognized as a crucial booster for device fabrication and general scientific advancements. In this review, attention is focused on the latest developments in the field of redox flow batteries which are, similar to other energy related devices, characterized by the recent adoption of 3D printing methods for the fabrication of key components. Whether simply to investigate flow phenomena, test new designs or fabricate final-product components with custom features, the use of 3D printing can critically drive this field of research towards better performing energy-storage systems. The latest and most representative examples of redox flow battery studies will be discussed, categorized in relation to the electrolyte used and whether the devices are employed in aqueous or non-aqueous applications.