Technical note: A fourth‐order finite difference scheme for a system of a 2D nonlinear elliptic partial differential equations

In this article we present a fourth‐order finite difference scheme, for a system of two‐dimensional, second‐order, nonlinear elliptic partial differential equations with mixed spatial derivative terms, using 13‐point stencils with a uniform mesh size h on a square region R subject to Dirichlet boundary conditions. The scheme of order h⁴ is derived using the local solution of the system on a single stencil. The resulting system of algebraic equations can be solved by iterative methods. The difference scheme can be easily modified to obtain formulae for grid points near the boundary. Computational results are given to demonstrate the performance of the scheme on some problems including Navier‐Stokes equations. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 43–53, 2001     

Fulleretic Well‐Defined Scaffolds: Donor–Fullerene Alignment Through Metal Coordination and Its Effect on Photophysics

Herein, we report the first example of a crystalline metal–donor–fullerene framework, in which control of the donor–fullerene mutual orientation was achieved through chemical bond formation, in particular, by metal coordination. The ¹³C cross‐polarization magic‐angle spinning NMR spectroscopy, X‐ray diffraction, and time‐resolved fluorescence spectroscopy were performed for comprehensive structural analysis and energy‐transfer (ET) studies of the fulleretic donor–acceptor scaffold. Furthermore, in combination with photoluminescence measurements, the theoretical calculations of the spectral overlap function, Förster radius, excitation energies, and band structure were employed to elucidate the photophysical and ET processes in the prepared fulleretic material. We envision that the well‐defined fulleretic donor–acceptor materials could contribute not only to the basic science of fullerene chemistry but would also be used towards effective development of organic photovoltaics and molecular electronics.     

Preference for a C3 conformation in tris-dimethylaminophosphonium cations: a comparison of the reactions of (Me2N)3P with I-X (X = Cl, Br, I, CN)

Tris-(dimethylamino)phosphine reacts with I(2) to form (Me(2)N)(3)PI(2), which when recrystallised from acetonitrile displays a structure of overall stoichiometry [{(Me(2)N)(3)PI}I](6).CH(3)CN . The asymmetric unit of consists of four different [(Me(2)N)(3)PI](+) cations, one of these exhibits a cation-anion interaction to an iodide ion, with an I-I contact distance of 3.6378(14) A, the longest yet observed for an R(3)PI(2) compound. Two of the other three cations display no interactions, whilst a cation-solvent interaction is observed for the fourth. When (Me(2)N)(3)PI(2) is recrystallised from dichloromethane the molecule abstracts chlorine from the solvent to form [(Me(2)N)(3)PCl]I this latter compound can also be synthesised directly from (Me(2)N)(3)P and ICl. The reaction of (Me(2)N)(3)P with IBr forms [(Me(2)N)(3)PBr]I, which when recrystallised from chlorinated solvents forms [(Me(2)N)(3)PCl(0.5)Br(0.5)]I. The analogous [(Me(2)N)(3)PCN]I, does not display CN-Cl exchange and can be recrystallised from dichloromethane. The structures of and have all been determined by X-ray diffraction. All of the (Me(2)N)(3)P groups in the cations in, and exhibit a C(3) conformation, in contrast to the majority of (R(2)N)(3)P systems where a C(s) conformation is usually preferred. This C(3) conformation appears to be favoured where there is increased positive charge on phosphorus, as is the case in the phosphorus(v) ionic species described herein. This conformation allows greater P-N pi-bonding, and as a result the P-N bonds are shortened, varying between 1.566(10) and 1.624(10) A in these compounds.     

Spin injection in mesoscopic silver wires: experimental test of resistance mismatch

The spin polarization of current injected from a Permalloy electrode into a mesoscopic Ag wire is measured for samples with very low interface resistance. The observed value of 22.3% +/- 1.6% at 79 K is an order of magnitude larger than values previously reported for low resistance interfaces and about 4 times larger than predictions of the common resistance mismatch model. These results demonstrate that high resistance barriers are not necessary for efficient spin injection.     

Metabolic monitoring of the electrically stimulated single heart cell within a microfluidic platform

A device based on five individually addressable microelectrodes, fully integrated within a microfluidic system, has been fabricated to enable the real-time measurement of ionic and metabolic fluxes from electrically active, beating single heart cells. The electrode array comprised one pair of pacing microelectrodes, used for field-stimulation of the cell, and three other microelectrodes, configured as an electrochemical lactate microbiosensor, that were used to measure the amounts of lactate produced by the heart cell. The device also allowed simultaneous in-situ microscopy, enabling optical measurements of cell contractility and fluorescence measurements of extracellular pH and cellular Ca2+. Initial experiments aimed to create a metabolic profile of the beating heart cell, and results show well defined excitation-contraction (EC) coupling at different rates. Ca2+ transients and extracellular pH measurements were obtained from continually paced single myocytes, both as a function of the rate of cell contraction. Finally, the relative amounts of intra- and extra-cellular lactate produced during field stimulation were determined, using cell electroporation where necessary.     

Novel 1,4-homofragmentation via an alpha-lactone

Conversion of an alpha,alpha-dichloroester to the corresponding alpha-keto acid was unexpectedly complicated by a novel 1,4-homofragmentation. Investigation of the kinetics of this reaction revealed a mechanism involving an alpha-lactone intermediate, which can lead to both the desired alpha-keto acid and the 1,4-homofragmentation, with the product distribution being dependent upon reaction conditions. This information allowed development of a process that affords the alpha-keto acid exclusively and should be generally applicable to the preparation of alpha-keto acids from alpha,alpha-dichloroesters or acids.     

Trapping photon-dressed Dirac electrons in a quantum dot studied by coherent two dimensional photon echo spectroscopy

We study the localization of dressed Dirac electrons in a cylindrical quantum dot (QD) formed on monolayer and bilayer graphene by spatially different potential profiles. Short lived excitonic states which are too broad to be resolved in linear spectroscopy are revealed by cross peaks in the photon-echo nonlinear technique. Signatures of the dynamic gap in the two-dimensional spectra are discussed. The effect of the Coulomb induced exciton-exciton scattering and the formation of biexciton molecules are demonstrated.