<!?tlsb=‐0.06pt>Zigzag polymer chains in catena‐poly[[[triaqua(isobutyrato‐κO)magnesium(II)]‐μ‐isobutyrato‐κ2O:O′] monohydrate]

The structure of the title compound, {[Mg(C₄H₇O₂)₂(H₂O)₃]·H₂O}_n, features one‐dimensional ...(μ₂‐ib)Mg(μ₂‐ib)Mg... zigzag chains (ib is isobutyrate) parallel to the c axis. The octahedral Mg environment is completed by three fac‐oriented terminal water ligands, as well as one further monodentate end‐on coordinated ib ligand. In the crystal structure, the hydrophobic ib groups are all oriented within one half of the coordination perimeter of each chain, whereas the water ligands, together with hydrogen‐bonded noncoordinated solvent water molecules, define the other half. Along the a axis, neighbouring strands are oriented so that both the hydrophilic and hydrophobic sides are adjacent to each other. This results in an extensive hydrogen‐bonding network within the hydrophilic areas, also involving an additional solvent water molecule per formula unit. There are van der Waals contacts between the aliphatic isopropyl groups of the hydrophobic areas.     

An adaptive enrichment algorithm for advection‐dominated problems

We are interested in developing a numerical framework well suited for advection–diffusion problems when the advection part is dominant. In that case, given Dirichlet type boundary condition, it is well known that a boundary layer develops. To resolve correctly this layer, standard methods consist in increasing the mesh resolution and possibly increasing the formal accuracy of the numerical method. In this paper, we follow another path: we do not seek to increase the formal accuracy of the scheme but, by a careful choice of finite element, to lower the mesh resolution in the layer. Indeed the finite element representation we choose is locally the sum of a standard one plus an enrichment. This paper proposes such a method and with several numerical examples, we show the potential of this approach. In particular, we show that the method is not very sensitive to the choice of the enrichment and develop an adaptive algorithm to automatically choose the enrichment functions.Copyright © 2012 John Wiley & Sons, Ltd.     

The inverse phase sequence SmA-SmC in symmetric dimeric liquid crystals

Seven homologous symmetric dimeric liquid crystals are presented where two three-ring mesogenic units are connected by a bis(carbonyloxy)alkylene spacer. For homologues with terminal heptyloxy, octyloxy and nonyloxy chains, the unusual phase sequence SmA-SmC with increasing temperature was detected by the study of the optical textures and by X-ray diffraction measurements. This unusual behaviour is discussed on the basis of the molecular structure of these compounds.     

The Orion Water-Hardness Electrode: An Unexpected Response to Magnesium Ion

Abstract

The Orion water-hardness electrode, while being used to measure magnesium ion activity in a series of calcium-free solutions, displayed some unanticipated changes in potential. As the overall potential change observed for one solution was 183 mV (equivalent to more than six orders of magnitude changes in magnesium-ion activity), several precautions are suggested which should be observed when using this electrode for specific purposes. In particular, it is recommended that the exchanger be pre-equilibrated with an appropriate solution if the electrode is to be used in restricted systems of known chemical composition.     

Numerical methods for light propagation in large LC cells: a new approach

Accurate numerical methods for the propagation of light in large 3D samples with strong lateral variation of the director field require prohibitive amounts of time. We consider and compare a standard spectral method and the Finite Difference in Frequency Domain method, showing that the CPU time can be reduced by one or two orders of magnitude using a perturbation approach or a recently developed Reduced Order Method. The equations obtained are applied to liquid crystal cells with in-plane switching, illuminated by a large incoherent source. The developed formalism, based on numerically exact equations, is particularly suitable for treating magnetic or optically active media and for extending to such media the well known approximations based on the 4 × 4 (Berreman) or 2 × 2 (Jones) matrices.     

Reductive Ring Opening of Ephedrine and Pseudo-Ephedrine-Derived Oxazolidinium Methiodides by Sodium Borohydride. A Direct Access to New Chiral Amine-Borane Adducts

Sodiun borohydride reacts with oxazolidinium methiodides derived from ephedrine and pseudoephedrine, in ethereal solvents, cleaving regioselectively the C-N bond of the ring and leading, in good yields, to chiral amine-borane adducts of know absolute configuration. The ¹HNMR data allow to predict the most stable conformation.     

Protein dielectrophoresis: Key dielectric parameters and evolving theory

Globular proteins exhibit dielectrophoresis (DEP) responses in experiments where the applied field gradient factor ∇E² appears far too small, according to standard DEP theory, to overcome dispersive forces associated with the thermal energy kT of disorder. To address this a DEP force equation is proposed that replaces a previous empirical relationship between the macroscopic and microscopic forms of the Clausius–Mossotti factor. This equation relates the DEP response of a protein directly to the dielectric increment δε⁺ and decrement δε⁻ that characterize its β-dispersion at radio frequencies, and also indirectly to its intrinsic dipole moment by way of providing a measure of the protein's effective volume. A parameter Γ_pw, taken as a measure of cross-correlated dipole interactions between the protein and its water molecules of hydration, is included in this equation. For 9 of the 12 proteins, for which an evaluation can presently be made, Γ_pw has a value of ≈4600 ± 120. These conclusions follow an analysis of the failure of macroscopic dielectric mixture (effective medium) theories to predict the dielectric properties of solvated proteins. The implication of a polarizability greatly exceeding the intrinsic value for a protein might reflect the formation of relaxor ferroelectric nanodomains in its hydration shell.     

Numerical simulation and convergence analysis for a system of nonlinear singularly perturbed differential equations arising in population dynamics

In this article, we consider a system of nonlinear singularly perturbed differential equations with two different parameters. To solve this system, we develop a weighted monotone hybrid scheme on a nonuniform mesh. The proposed scheme is a combination of the midpoint scheme and the upwind scheme involving the weight parameters. The weight parameters enable the method to switch automatically from the midpoint scheme to the upwind scheme as the nodal points start moving from the inner region to the outer region. The nonuniform mesh in particular the adaptive grid is constructed using the idea of equidistributing a positive monitor function involving the solution gradient. The method is shown to be second order convergent with respect to the small parameters. Numerical experiments are presented to show the robustness of the proposed scheme and indicate that the estimate is optimal.