A matrix‐free preconditioned Newton/GMRES method for unsteady Navier–Stokes solutions

The unsteady compressible Reynolds‐averaged Navier–Stokes equations are discretized using the Osher approximate Riemann solver with fully implicit time stepping. The resulting non‐linear system at each time step is solved iteratively using a Newton/GMRES method. In the solution process, the Jacobian matrix–vector products are replaced by directional derivatives so that the evaluation and storage of the Jacobian matrix is removed from the procedure. An effective matrix‐free preconditioner is proposed to fully avoid matrix storage. Convergence rates, computational costs and computer memory requirements of the present method are compared with those of a matrix Newton/GMRES method, a four stage Runge–Kutta explicit method, and an approximate factorization sub‐iteration method. Effects of convergence tolerances for the GMRES linear solver on the convergence and the efficiency of the Newton iteration for the non‐linear system at each time step are analysed for both matrix‐free and matrix methods. Differences in the performance of the matrix‐free method for laminar and turbulent flows are highlighted and analysed. Unsteady turbulent Navier–Stokes solutions of pitching and combined translation–pitching aerofoil oscillations are presented for unsteady shock‐induced separation problems associated with the rotor blade flows of forward flying helicopters. Copyright © 2000 John Wiley & Sons, Ltd.     

Enantioselective Synthesis of anti‐β‐Hydroxy‐α‐Amido Esters by Asymmetric Transfer Hydrogenation in Emulsions

Herein, we present two methods for an asymmetric transfer hydrogenation through the dynamic kinetic resolution of α‐amido‐β‐ketoesters. These procedures yield the corresponding anti‐β‐hydroxy‐α‐amido esters in good yields and with good diastereo‐ and enantioselectivities. First, the scope of the reduction of α‐amido‐β‐ketoesters by using triethylammonium formate azeotrope is examined. Then, an emulsion technology with sodium formate is explored, which allows for broader substrate scope, faster reaction times, and lower catalyst loading. Furthermore, these reactions are operationally simple and can be set up in air.     

Characterization of Metallosupramolecular Polymers by Top‐Down Multidimensional Mass Spectrometry Methods

Top‐down multidimensional mass spectrometry, interfacing electrospray ionization (ESI) with ion mobility mass spectrometry (IM‐MS), and energy resolved (gradient) tandem mass spectrometry (gMS²) are employed to characterize the stoichiometries, architectures, and intrinsic stabilities of coordinatively bound supramolecular polymers containing terpyridine functionalized ligands. As a soft ionization method, ESI prevents or minimizes unwanted assembly destruction. The IM dimension affords separation of the supramolecular ions by charge and collision cross‐section (a function of size and shape). The mobility separated ions are subsequently identified by their mass‐to‐charge‐ratios and isotope patterns in the orthogonal MS dimension. Finally, the gMS² dimension reveals bond breaking proclivities and disintegration pathways of the assemblies. The described methodology does not require high sample purity due to the dispersive nature of the IM and MS steps. Its utility is demonstrated with the comprehensive analysis of bisterpyridine‐based metallomacrocycle mixtures and a tristerpyridine based complex with 3‐D nanosphere‐like architecture.

     

Ultracold strontium clock: Applications to the measurement of fundamental constant variations

We describe the application of high accuracy Srspectroscopy to the measurement of the variation of thefundamental constants of nature. We first describe recent progressof the JILA Sr optical frequency standard, with a systematicuncertainty evaluation at the 10^-16 fractional frequencylevel. Using recent internationally based measurements of the Srclock frequency, we show improved constraints of gravitational andtemporal changes in the fine structure constant and theelectron-proton mass ratio. Finally, we describe how ultracoldatomic strontium, confined in an optical lattice, can beassociated into molecular dimers and be used for amodel-independent measurement of the variation of theelectron-proton mass ratio.     

Substituent effects on the vibronic coupling for the phenoxyl/phenol self-exchange reaction

The impact of substituents on the vibronic coupling for the phenoxyl/phenol self-exchange reaction, which occurs by a proton-coupled electron transfer mechanism, is investigated. The vibronic couplings are calculated with a grid-based nonadiabatic method and a nuclear-electronic orbital nonorthogonal configuration interaction method. The quantitative agreement between these two methods for the unsubstituted phenoxyl/phenol system and the qualitative agreement in the predicted trends for the substituted phenoxyl/phenol systems provides a level of validation for both methods. Analysis of the results indicates that electron-donating groups enhance the vibronic coupling, while electron-withdrawing groups attenuate the vibronic coupling. Thus, if all other aspects of the reaction are the same, then electron-donating groups will increase the rate, while electron-withdrawing groups will decrease the rate. Correlations between the vibronic coupling and physical properties of the phenol are also analyzed. Negative Hammett constants correspond to higher vibronic couplings, while positive Hammett constants correspond to similar or slightly lower vibronic couplings relative to the unsubstituted phenoxyl/phenol system. In addition, lower bond dissociation enthalpies, ionization potentials, and redox potentials, as well as higher pKa values, tend to correspond to higher vibronic couplings relative to the unsubstituted phenoxyl/phenol system. The observed trends enable the prediction of the impact of general substituents on the vibronic coupling, and hence the rate, for the phenoxyl/phenol self-exchange reaction. The fundamental physical insights obtained from these studies are applicable to other proton-coupled electron transfer systems.     

Amphiphilic [tpy-MII-tpy] metallotriangles: synthesis,characterisation and hierarchical ordering

Long chain (C₁₆) alkylated metallocycles are synthesised and characterised. Their ordered aggregation was studied via TEM to gauge to the effects of molecular topology, solvent, counterion and metal centre(s) on morphology and nanoscale structure. The results indicate that their amphiphilicity significantly enhanced their self-ordering characteristics relative to controls and enabled the formation of nanoscale structures. Similar ordering was observed for both labile and non-labile analogues with SAXD showing comparable d-spacing values, suggesting the presence of intramolecular π–π stacking. Effect of counterion and solvent was studied with the non-labile system. Nanotubular, ribbon, or sheet-like structures were afforded depending upon conditions.     

Preparation and characterization of MgB2 superconductor

The MgB₂ superconductor, synthesized using solid-state and liquid-phase sintering methods, have been characterized for various properties. The upper critical field, irreversibility line and critical current density have been determined using magnetization data. The current-voltage characteristics recorded under an applied magnetic field revealed the existence of vortex glass transition. The surface analysis using X-ray photoelectron spectroscopy shows that MgB₂ is sensitive to atmospheric degradation.     

Size-exclusion chromatography with on-line ultraviolet, proton nuclear magnetic resonance and mass spectrometric detection and on-line collection for off-line Fourier transform infrared spectroscopy.

The coupling of HPLC with UV detection and on-line NMR spectroscopy and mass spectrometry combined with a dedicated interface for the collection of the chromatographic eluent for subsequent Fourier transform (FT) IR has been investigated using a number of polymer additives as model compounds. Size-exclusion chromatography was performed using deuterated chloroform as eluent with the separation monitored on-line by UV detection at 254 nm and on-flow 1H-NMR and MS. The effluent from the NMR probe was directed to a dedicated HPLC interface where it was deposited on a germanium plate for subsequent FT-IR. NMR and MS spectra were successfully obtained for 2,6-di-tert.-butyl-4-methylphenol, octadecyl-3-(3,5-di-tert.-butyl-4-hydroxyphenyl) propionate (Irganox 1076) and diisooctyl phthalate on-line and FT-IR spectra for all three compounds were obtained off-line. Practical problems encountered with this multiple hyphenation are described.