A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry

We present a fourth-order finite-volume algorithm in space and time for low Mach number reacting flow with detailed kinetics and transport. Our temporal integration scheme is based on a Multi-Implicit Spectral Deferred Correction (MISDC) strategy that iteratively couples advection, diffusion, and reactions evolving subject to a constraint. Our new approach overcomes a stability limitation of our previous second-order method encountered when trying to incorporate higher-order polynomial representations of the solution in time to increase accuracy. We have developed a new iterative scheme that naturally fits within our MISDC framework and allows us to conserve mass and energy while simultaneously satisfying the equation of state. We analyse the conditions for which the iterative schemes are guaranteed to converge to the fixed point solution. We present numerical examples illustrating the performance of the new method on premixed hydrogen, methane, and dimethyl ether flames.     

Mates toE=mc 2 and to the Heisenberg uncertainty relations

E=mc ² is found to be a special case ofE= ^±1cⁿ, where is any one of four susceptibilities, namely electric, magnetic, gravitational, and elastic. Letl be length,t time,t time dilation, andl a measure of Fitzgerald-Lorentz contraction. A particle is stated to be the manifestation of a collection of susceptibilities which arise when(l)/1=(t)/t. Then(E)/E=5 (t)/2t=±()/. Corresponding to susceptibility, special energy particles are postulated which exhibitSU(3) symmetry, Related to the susceptibilities are five new Heisenberg uncertainty relations. Three new conservation laws for particles are proposed.     

Graft copolymers from poly(2,6-dimethylphenylene oxide) and pivalolactone

The copolyether-polyester system resulting from the anionic graft polymerization of pivalolactone onto poly(2,6-dimethylphenylene oxide) has been formulated with differing graft densities and graft segment lengths. Wide angle x-ray scattering studies on these materials indicated an increased crystalline order with increased PVL segments/graft for similarly annealed specimens and a decrease in such order with increasing carboxylation.     

A permeation method for the determination of average concentrations of carbon monoxide in the atmosphere

A simple, inexpensive and reliable method for the determination of average concentrations of carbon monoxide in the atmosphere is described. Silver p-sulfa-moylbenzoic acid is used as the colorimetric reagent in a specially designed permeation device. The calibration graphs are linear up to 80 p.p.m. carbon monoxide, and the limit of detection is 2 p.p.m. for a 24-h exposure. Tests under field conditions are discussed.     

Convenient approaches to heterocycles via copper-catalysed additions of organic polyhalides to activated olefins

An efficient method for the synthesis of 2,3-dichloro-5-substituted (Cl, CF₃, alkyl) pyridines $\text{29}$ starting from the 1:1 adducts of the copper-catalysed addition of chloral or the corresponding 2,2-dichloroaldehydes to acrylonitrile is presented. Proper choice of experimental conditions allows the preparation of $\text{29}$ in a one-pot process. Similarly, the CuCl-catalysed reaction of methyl itaconate with several trichloromethyl compounds R-CCl₃ gives 6-R-substituted 2-pyrone derivatives $\text{40}$ via dehalogenation and subsequent thermal ring closure of the primary 1:1-adducts. The new electrophilic 2-pyrone $\text{40b}$ undergoes [4+2]-cycloaddition reactions with inverse electron demand with a number olefins and acetylenes, allowing thereby regioselective transfer of a trifluoromethyl group from a simple Freon derivative (1,1,1-trichloro-2,2,2-trifluoroethane) into more complex organic molecules. Finally, the 1:1-adduct of trichloroacetylchloride with methyl acrylate allows a very convenient synthesis of novel N-substituted derivatives $\text{66}$ of pyroglutamic acid as well as of proline.     

Electron-impact induced fragmentation of 3-hydroxy quinazoline-2,4(1H,3H) dione,pyridopyrimidine-2,4(1H,3H)diones,lumazine and alloxazine

Electron-bombardment of the N-3-hydroxy derivatives of the above-mentioned condensed uracils revealed that the major fragmentations involved the heterocyclic ring. The most intense ion proved to be the M-32 ion which was created by the loss of the NHOH radical from the molecular ion. Mechanisms for this transition are presented. Other fragmentations common to these systems are discussed and compared with those reported for the corresponding N-3 deoxy analogs of the title compounds. The mass spectral fragmentations of the O-methyl-, N-methyl- and O,N-dimethyl derivatives of 3-hydroxyquinazoline-2,4(1H,3H)dione were analyzed and were consistent with those expected from these structures. Electron bombardment of the 3-benzenesulfonyloxy derivatives of the title compounds resulted primarily in the scission of the sulfonate group in preference to that of the heterocyclic dione ring. These sulfonates also showed ions which indicated that a Lossen rearrangement had taken place in the mass spectrometer.     

Aitken acceleration of some alternating series

Aitken's ²-process is applied to a convergent sequence {s _n }, wheres _n =u ₁ –u ₂+...+(–1) ^n–1 u _n . The improvement in the rate of convergence of {s _n } is measured in terms of the functionu and its derivatives and numerical examples are given. The paper concludes with a theorem showing that the Aitken process is well-conditioned in such problems and this theorem is shown to have wider applications.