Exponential almost Runge-Kutta methods for semilinear problems

We present a new class of one-step, multi-value Exponential Integrator (EI) methods referred to as Exponential Almost Runge-Kutta (EARK) methods which involve the derivatives of a nonlinear function of the solution. In order to approximate such derivatives to a sufficient accuracy, the EARK methods will be implemented within the broader framework of Exponential Almost General Linear Methods (EAGLMs) to accommodate past values of this nonlinear function and becoming multistep in nature as a consequence. Established EI methods, such as Exponential Time Differencing (ETD) methods, Exponential Runge-Kutta (ERK) methods and Exponential General Linear Methods (EGLMs) become special cases of EAGLMs. We present order conditions which facilitate the construction of two- and three-stage EARK methods and, when cast in an EAGLM format, we perform a stability analysis to enable a comparison with existing EI methods. We conclude with some numerical experiments which confirm the convergence order and also demonstrate the computational efficiency of these new methods.     

Optically referenced broadband electronic synthesizer with 15 digits of resolution

Fundamental science, as well as all communications and navigation systems, are heavily reliant on the phase, timing, and synchronization provided by low‐noise and agile frequency sources. Although research into varied photonic and electronic schemes have strived to improve upon the spectral purity of microwave and millimeter‐wave signals, the reliance on conventional electronic synthesis for tuning has resulted in limited progress in broadband sources. Using a digital‐photonic synthesizer architecture that derives its time‐base from a high‐stability optical reference cavity, we generate frequency‐agile and wideband microwave signals with exceptional dynamic range and with a fractional frequency instability of 1 × 10⁻¹⁵ at 1 s. The presented architecture demonstrates digitally controlled, user defined and broadband frequency tuning from RF to 100 GHz with orders‐of‐magnitude improvement in noise performance over room‐temperature electronic wide‐bandwidth synthesis schemes.

     

Tristhiolatomolybdenum nitrides, (RS)(3)Mo[triple bond]N where R = (i)Pr and (t)Bu,preparation, characterization and comparisons with related trialkoxymolybdenumnitrides

The addition of thiols to ((t)BuO)(3)Mo[triple bond]N in toluene leads to the formation of (RS)(3)Mo[triple bond]N compounds as yellow, air-sensitive compounds, where R = (i)Pr and (t)Bu. The single-crystal structure of ((t)BuS)(3)Mo[triple bond]N reveals a weakly associated dimeric structure where two ((t)BuS)(3)Mo[triple bond]N units (Mo-N = 1.61 A, Mo-S = 2.31 A (av)) are linked via thiolate sulfur bridges with long 3.03 A (av) Mo-S interactions. Density functional theory calculations employing Gaussian 98 B3LYP (LANL2DZ for Mo and 6-31G* for N, O, S, and H) have been carried out for model compounds (HE)(3)Mo[triple bond]N and (HE)(3)MoNO, where E = O and S. A comparison of the structure and bonding within the related series ((t)BuE)(3)Mo[triple bond]N and ((t)BuE)(3)MoNO is made for E = O and S. In the thiolate compounds, the highest energy orbitals are sulfur lone-pair combinations. In the alkoxides, the HOMO is the N 2p lone-pair which has M-N sigma and M-O pi* character for the nitride. As a result of greater O p pi to Mo pi interactions, the M-N pi orbitals of the Mo-N triple bond are destabilized with respect to their thiolate counterpart. For the nitrosyl compounds, the greater O p pi to Mo d pi interaction favors greater back-bonding to the nitrosyl pi* orbitals for the alkoxides relative to the thiolates. The results of the calculations are correlated with the observed structural features and spectroscopic properties of the related alkoxide and thiolate compounds.     

Ultralow-noise mode-locked optical pulse trains from an external cavity laser based on a slab coupled optical waveguide amplifier (SCOWA)

We report the generation of optical pulse trains with 8.5 fs timing jitter (10 Hz to 10 MHz) from a mode-locked semiconductor laser, with a slab coupled optical waveguide amplifier used as the gain element. This is, to our knowledge, the lowest residual timing jitter reported to date from an actively mode-locked laser.     

Preparation of beta- and gamma-lactams from carbamoyl radicals derived from oxime oxalate amides

A general synthetic route to oxime oxalate amides was developed and applied to the preparation of molecules incorporating N-benzyl-N-alkenyl amides linked with acetone oxime or benzaldoxime units. In addition, 2-substituted-thiazolidine-4-carboxylic acid methyl ester amides of oxalyl benzaldoxime were also prepared. It was shown by EPR spectroscopy that the oxalyl benzaldoxime amides dissociated to produce benziminyl and carbamoyl (aminoacyl) radicals when photolysed with 4-methoxyacetophenone as a photosensitizer. Carbamoyl radicals derived from N-alk-3-enyl oxime oxalate amides underwent ring closure to afford pyrrolidin-2-ones. The analogous N-alk-2-enyl precursors afforded azetidin-2-ones. Reactions of the cyclohexenyl and cinnamyl oxime oxalate amides afforded a bicyclic beta-lactam and a 3-benzyl-substituted beta-lactam respectively. Interestingly, both products were isolated as hydroxylated compounds. A thiazolidine-derived oxime oxalate amide containing an isobutenyl side chain also dissociated with production of the corresponding thiazolidinyl-carbamoyl radical, as shown by EPR spectroscopy. GC-MS evidence indicated that this radical cyclised to afford some of the corresponding penicillin derivative     

Synthesis of P-stereogenic BINAP bissulfide analogues

A synthetic route to BINAP disulfide analogues with chirality on one of the phosphorus atoms was developed. The synthesis of these ligands was achieved by step-wise palladium and nickel-catalysed coupling reactions of the precursor binaphthyl triflate with secondary phosphines and phosphine oxides, respectively. C2-Unsymmeric BINAP bissulfide analogues with the same aryl substituents were also synthesized for the sake of comparison. Preliminary studies of the reduction of these sulfides to the free phosphines are also described.     

Measurements of the gas and particle flow within a converging-diverging nozzle for high speed powdered vaccine and drug delivery

A unique system has been developed based upon the concept of accelerating pharmaceutical agents in particle form with a gas flow to attain sufficient momentum to enter the epidermis of human skin and achieve a pharmacological endpoint. This paper presents an experimental investigation of the transient gas and particle dynamics within a transonic converging-diverging nozzle prototype. The primary gas flow regimes are identified through Pitot-static pressure surveys and schlieren images with a high frame rate. The action of the gas flow-field in imparting momentum to the drug particles is investigated through schlieren imaging and time-resolved Doppler global velocimetry (DGV).Abbreviations DGV Doppler global velocimetry - CCD Charge coupled device - CST Contoured shock tube M.A.F Kendall and N.J. Quinlan contributed equally to this paper. Some of this work was originally presented at the 22nd International Symposium on Shock Waves, Imperial College, London, UK.     

Evidence for Rydberg doorway states in photoion pair formation in bromomethane

The vacuum ultraviolet laser-excited photoion-pair formation spectrum of CH 3Br has been measured under high resolution in the threshold region. The (2 + 1) and (3 + 1) resonance-enhanced multiphoton ionization spectra in the same energy region are also reported. By comparison of the spectra in this and a more extended region, resonances in the photoion-pair formation spectrum are assigned to p and f Rydberg states. It is concluded that all the structure in the photoion-pair formation spectrum near threshold can be accounted for by members of the Omega = 0 subset of Rydberg states that act as doorway states to the ion channel.