Synthesis, characterization, and thermal degradation studies on group VIA derived weak-link polymers

Polymers containing group VIA derived weak links, viz. poly(styrene disulfide) (PSD), poly- (styrene tetrasulfide) (PST), and poly(styrene diselenide) (PSDSE), have been synthesized. The polymers PSD and PST were characterized by NMR, IR, UV, TGA, and fast atom bombardment m w spectrometric (FABMS) techniques. The presence of different configurational sequences in PSD and PST were identified by *3C NMR spectroscopy. PSDSE, being insoluble in common organic solvents, was characterized using solid-state lac NMR (CP-MAS) spectroscopy. Thermal degradation of polymers under direct pyrolysis-mass spectrometric (DP-MS) conditions revealed that all the polymers undergo degradation through the weaklink scission. A comparative study of the pyrolysis products of these polymers with that of poly(styrene peroxide) (PSP) revealed a smooth transformation down the group with no monomer (styrene or oxygen) formation in PSP to only styrene and selenium metal in PSDSE. This trend of group VIA is explained from the energetics of the C-X bond (X = 0, S, and Se) which also seems to be important in addition to the weak X-X bond cleavage. In PSP and PSD, the behavior is also explained from the energetics of the alkoxy and thiyl radicals. The unique exothermic degradation in PSP compared to endothermic degradation in PSD and PSDSE is explained from the nature of the producta of degradation.

A note on the slow rotation of a disc in a bounded fluid with a surfactant surface layer

A method involving eigenfunction expansion and collocation is employed to solve the axisymmetric problem of a slowly and steadily rotating circular disc in a fluid of finite extent whose surface is covered with a surfactant film. The present method (originally described by Wang (Acta Mech. 94, 97, 1992)) is observed to produce results of practical importance associated with the problem more quickly and more easily than the one used earlier by Shail and Gooden (Int. J. Multiphase Flow 7, 245, 1992). (C) 1994 Academic Press, Inc.

CM defect and Hilbert functions of monomial curves

In this article we consider a semigroup ring R = KGamma] of a numerical semigroup Gamma and study the Cohen- Macaulayness of the associated graded ring G(Gamma) := gr(m), (R) := circle plus(n is an element of N) m(n)/m(n+1) and the behaviour of the Hilbert function H-R of R. We define a certain (finite) subset B(Gamma) subset of F and prove that G(Gamma) is Cohen-Macaulay if and only if B(Gamma) = empty set. Therefore the subset B(Gamma) is called the Cohen-Macaulay defect of G(Gamma). Further, we prove that if the degree sequence of elements of the standard basis of is non-decreasing, then B(F) = empty set and hence G(Gamma) is Cohen-Macaulay. We consider a class of numerical semigroups Gamma = Sigma(3)(i=0) Nm(i) generated by 4 elements m(0), m(1), m(2), m(3) such that m(1) + m(2) = mo m3-so called ``balanced semigroups''. We study the structure of the Cohen-Macaulay defect B(Gamma) of Gamma and particularly we give an estimate on the cardinality |B(Gamma, r)| for every r is an element of N. We use these estimates to prove that the Hilbert function of R is non-decreasing. Further, we prove that every balanced ``unitary'' semigroup Gamma is ``2-good'' and is not ``1-good'', in particular, in this case, c(r) is not Cohen-Macaulay. We consider a certain special subclass of balanced semigroups Gamma. For this subclass we try to determine the Cohen-Macaulay defect B(Gamma) using the explicit description of the standard basis of Gamma; in particular, we prove that these balanced semigroups are 2-good and determine when exactly G(Gamma) is Cohen-Macaulay. (C) 2011 Published by Elsevier B.V.

Stretch effects extracted from inwardly and outwardly propagating spherical premixed flames

Unsteady propagation of spherical flames, both inward and outward, are studied numerically extensively for single-step reaction and for different Lewis numbers of fuel/oxidizer. The dependence of flame speed ratio (s) and flame temperature ratio are obtained for a range of Lewis numbers and stretch (kappa) values. These results of s versus kappa show that the asymptotic theory by Frankel and Sivashinsky is reasonable for outward propagation. Other theories are unsatisfactory both quantitatively and qualitatively. The stretch effects are much higher for negative stretch than for positive stretch, as also seen in the theory of Frankel and Sivashinsky. The linearity of the flame speed ratio vs stretch relationship is restricted to nondimensional stretch of +/-0.1. It is shown further that the results from cylindrical flames are identical to the spherical flame on flame speed ratio versus nondimensional stretch plot thus confirming the generality of the concept of stretch. The comparison of the variation of (ds/dkappa)kappa=0 with beta(Lc - 1) show an offset between the computed and the asymptotic results of Matalon and Matkowsky. The departure of negative stretch results from this variation is significant. Several earlier experimental results are analysed and set out in the form of s versus kappa plot. Comparison of the results with experiments seem reasonable for negative stretch. The results for positive stretch are satisfactory qualitatively for a few cases. For rich propane-air, there are qualitative differences pointing to the need for full chemistry calculations in the extraction of stretch effects.

Stretch effects extracted from propagating spherical premixed flames with detailed chemistry

This paper is concerned with extracting stretch effects from outward propagating spherical flames with full chemistry. It is a continuation of a recently published study from this laboratory where it is shown that single-step chemistry is insufficient to explain the experimental results on methane, propane and hydrogen-air systems. Comparisons of the present full chemistry calculations with the experimental results for several fuel/air systems are good/excellent, with the exception of rich propane-air for which it is argued that soot chemistry with attendant radiation loss need to be invoked. The reversal in trends of stretch effects due to change in pressure, initial temperature and N-2 dilution (observed in experiments) can be predicted well by full chemistry but not with simple single-step chemistry. Analysis of the results shows the important role played by many intermediate species and explains why full chemistry is needed to predict stretch effects.

Covariant differentials lead to the design of a novel self-tuning power system stabilizer

Application of differential geometry to study the dynamics of electrical machines by Gabriel Kron evoked only theoretical interest among the power system engineers and was considered hardly suitable for any practical use. Extension of Kron's work led to a physical understanding of the processes governing the small oscillation instability in power system. This in turn has made it possible to design a self-tuning Power System Stabilizer to contain the oscillatory instability over arm extended range of system and operating conditions. This paper briefly recounts the history of this development and touches upon the essential design features of the stabilizer. It presents some results from simulation studies, laboratory experiments and recently conducted field trials at actual plants-all of which help to establish the efficacy of the proposed stabilizer and corroborate the theoretical findings.

Chemical Degradation of Poly(styrene disulfide) and Poly(styrene tetrasulfide) by Triphenylphosphine

The chemical degradation of polysulfide polymers, viz., poly(styrene disulfide), PSD, and poly(styrene tetrasulfide), PST, has been achieved using triphenylphosphine, TPP. The reaction was monitored using P-31 NMR spectroscopy. The solubility analysis of the reaction residues reveals that while PSD degrades completely, PST on the other hand, undergoes complete degradation only when the concentration of TPP is increased. Moreover, the reaction of PST with TPP occurs at room temperature whereas PSD requires a higher temperature. The reaction products were analyzed using the direct pyrolysis mass spectrometric (DP-MS) technique, and their formation has been explained through an ionic mechanism.

Primary pyrolysis products of thiokol liquid polysulfide

An analysis of the primary degradation products of the widely used commercial polysulfide polymer Thiokol LP-33 by direct pyrolysis-mass spectrometry (DP-MS) is reported. The mechanism of degradation is through a radical process involving the random cleavage of a formal C-O bond followed by backbiting to form the cyclic products.

Magnetic field-induced metal-insulator transitions in graphite and diluted magnetic semiconductors - Discussion

Two topical subjects related with the effect of magnetic field on electrical conduction and the metal-insulator transition are discussed. The first topic is an electronic phase transition in graphite, which is interpreted as a manifestation of a nestingtype instability inherent to a one-dimensional narrow Landau sub-band. The second topic is spin-dependent tranport in III-V based diluted magnetic semiconductors; in particular, a large negative magnetoresistance observed in the vicinity of metal-nonmetal transition.

Stabilization of thermal degradation of poly(methyl methacrylate) by polysulfide polymers

The thermal degradation of poly(methyl methacrylate) (PMMA) in the presence of polysulfide polymers, namely, poly( styrene disulfide) (PSD) and poly(styrene tetrasulfide) (PST) was studied using thermogravimetry (TG) and direct pyrolysis-mass spectrometric (DP-MS) analysis. Both PSD and PST were found to stabilizethe PMMA degradation, which was explained by both radical recombination and a chain-transfer mechanism. (C) 1997 John Wiley & Sons, Inc.

Minimal set of generators for the derivation module of certain monomial curves

Let K be a field of characteristic zero and let m(0),..., m(e-1) be a sequence of positive integers. Let C be an algebroid monomial curve in the affine e-space A(K)(e) defined parametrically by X-0 = T-m0,..., Xe-1 = Tme-1 and let A be the coordinate ring of C. In this paper, we assume that some e - 1 terms of m(0),..., m(e-1) form an arithmetic sequence and construct a minimal set of generators for the derivation module Der(K)(A) of A and write an explicit formula for mu (Der(K)(A)).

Shape optimization of RC flexural members

A natural velocity field method for shape optimization of reinforced concrete (RC) flexural members has been demonstrated. The possibility of shape optimization by modifying the shape of an initially rectangular section, in addition to variation of breadth and depth along the length, has been explored. Necessary shape changes have been computed using the sequential quadratic programming (SQP) technique. Genetic algorithm (Goldberg and Samtani 1986) has been used to optimize the diameter and number of main reinforcement bars. A limit-state design approach has been adopted for the nonprismatic RC sections. Such relevant issues as formulation of optimization problem, finite-element modeling, and solution procedure have been described. Three design examples-a simply supported beam, a cantilever beam, and a two-span continuous beam, all under uniformly distributed loads-have been optimized. The results show a significant savings (40-56%) in material and cost and also result in aesthetically pleasing structures. This procedure will lead to considerable cost saving, particularly in cases of mass-produced precast members and a heavy cast-in-place member such as a bridge girder.

The Herzog-Vasconcelos conjecture for affine semigroup rings

Let S be a simplicial affine semigroup such that its semigroup ring A = k[S] is Buchsbaum. We prove for such A the Herzog-Vasconcelos conjecture: If the A-module Der(k)A of k-linear derivations of A has finite projective dimension then it is free and hence A is a polynomial ring by the well known graded case of the Zariski-Lipman conjecture.