Stability of rarefaction waves in viscous media

We study the time-asymptotic behavior of weak rarefaction waves of systems of conservation laws describing one-dimensional viscous media, with strictly hyperbolic flux functions. Our main result is to show that solutions of perturbed rarefaction data converge to an approximate, Burgers rarefaction wave, for initial perturbations w ₀ with small mass and localized as w ₀(x)= The proof proceeds by iteration of a pointwise ansatz for the error, using integral representations of its various components, based on Green's functions. We estimate the Green's functions by careful use of the Hopf-Cole transformation, combined with a refined parametrix method. As a consequence of our method, we also obtain rates of decay and detailed pointwise estimates for the error.This pointwise method has been used successfully in studying stability of shock and constant-state solutions. New features in the rarefaction case are time-varying coefficients in the linearized equations and error waves of unbounded mass (log (t)). These diffusion waves have amplitude (t ^-1/2logt) in linear degenerate transversal fields and (t ^-1/2logt) in genuinely nonlinear transversal fields, a distinction which is critical in the stability proof.     

Determination of stability constants of chelate complexes: Part II. Applications

The proposed simplified method for calculating the stability constants of chelate complexes from pH and pM measurements (Part I) is applied to two systems. On the basis of data reported by Österberg, the stability constants of copper o-phosphorylserylglutamic acid are calculated and good agreement is achieved. In addition, the stability constants of the mononuclear, binuclear and trinuclear silver complexes of TTHA (triethylenetetraminehexaacetic acid) were calculated from potentiometric pAg data. These calculations yielded the following values of the cumulative constants: log β_AgL=8.7, log β_AgHL= 17.6, log β_AgH2L= 23.8, log β_Ag2L= 14.0, log β_Ag2HL = 20.5, log β_Ag2H2L = 25.6, log β_Ag2L =17.0.     

Conducting polymers containing in-chain metal centers: electropolymerization of oligothienyl-substituted {M(tpy)2} complexes and in situ conductivity studies, M = Os(II), Ru(II)

The electropolymerization of a series of Ru and Os bis-terpyridine complexes that form rodlike polymers with bithienyl, quaterthienyl, or hexathienyl bridges has been studied. Absorption spectroscopy, scanning electron microscopy, and cyclic voltammetry have been used to characterize the monomers and resulting polymer films. The absolute dc conductivity of the quaterthienyl-bridged {Ru(tpy)2} and {Os(tpy)2} polymers is unusually large and independent of the identity of the metal center at 1.6 x 10(-3) S cm(-1). The maximum conductivity occurs at the formal potential of each redox process, which typically is observed for systems where redox conduction is the dominant charge transport mechanism. Significantly, the dc conductivity of the metal-based redox couple observed in these polymers is 2 orders of magnitude higher thanthat of a comparable nonconjugated system.     

Synthesis of 5-alkylidene-2,5-dihydropyrrol-2-ones and their ring-transformation into 5,6-dihydrobenzo[h]chromones, 5,6,7,8-tetrahydrochromones and pyran-4-ones

Acid-mediated ring-transformations of 5-alkylidene-2,5-dihydropyrrol-2-ones, available by cyclization of 1,3-diketone dianions with bis(imidoyl) dichlorides of oxalic acid, resulted in formation of functionalized pyran-4-ones, such as 5,6-dihydrobenzo[h]chromones and 5,6,7,8-tetrahydrochromones.     

Electrochemical reduction of heterocyclic enammonium salts

Four N,N-disubstituted 2-cyano-Δ⁷-hexahydroindolium salts, 1, have been reduced at a mercury cathode in aqueous buffered solutions at intermediate pH-values. From the catholyte the following products were isolated and identified: 2-(β-cyanoethyl)-cyclohexanone, 5, a secondary amine, 4, and a mixture of cis-trans isomeric tertiary 2-(β-cyanoethyl) cyclohexylamines, 6. A reaction path via the protonated enamine 3 is proposed based on the pH-dependence of the composition of the product mixture and a few reductions in DMF solution.     

Theoretical study on solvation effects in chemical reactions: A vibrational coupling model

A vibrational coupling model to treat the solvation effects in chemical reaction rate calculations is proposed and applied to the intramolecular hydrogen transfer reaction CH₃O· → ·CH₂OH in the condensed phase. The effect of solvation is taken into account in two ways: (1) the solvent effect on the activation energy of the reaction is simulated by including 39 surrounding water molecules, represented by fractional charges at the assumed atomic positions, in the potential energy surface calculation; and (2) the vibrational couplings between the 10 nearest solvent molecules and the molecules constituting the reaction system are explicitly included in a vibrational frequency calculation. RRKM theory with Miller's tunneling correction included is employed to calculate the rate constants. The effect of solvation causes a significant change in the chemical reaction rate, mainly through a lowering of the activation energy. The vibrational coupling causes a slight increase of the rate constant in the tunneling region by perturbing the vibrational frequencies of the reactant and transition states, which appear in the rate-constant expression, but has little effect at higher temperatures.