Preconditioned conjugate gradients for solving the transient Boussinesq equations in three-dimensional geometries

In this paper we present a new version of the ‘modified finite element method’ (MFEM) presented by Gresho, Chan, Lee and Upson.¹ The main modification of the original algorithm is the introduction of a cost-effective and memory-saving iterative solver for the discretized Poisson equation for the pressure. The vectorization of the preconditioner has been especially considered. For low Prandtl number problems we also split the advection-diffusion operator of the energy equation into explicit and implicit parts. In that sense the present approach is related to the recent implicitization of the diffusive terms introduced by Gresho and Chan² and by Gresho.³ The algorithm is applied to the study of buoyancy-driven flow oscillations occuring in a horizontal crucible of molten metal under the action of a horizontal temperature gradient.     

Conjugate addition of organolithium reagents to acrylanilide anions

Phenyllithium, $\text{n}$-butyllithium, and $\text{t}$-butyllithium were found to add to substituted acrylanilide anions to give the 1,4-addition products in fair to good yields.     

Commutative free loop space models at large primes

Let p be a prime number and a natural number. If E is a r-connected finite CW-complex of dimension at most pr, then E is an example of a p -Anick space. For p > 2 we construct a commutative cochain algebra over that is an -model of the free loop space on a p-Anick space, i.e., its cohomology algebra is isomorphic to the mod p cohomology of the free loop space. For p-Anick spaces that are p-formal, such as spheres and projective spaces, we define an even simpler commutative free loop space model that applies for all primes p. We then use the simplified model to compute the cohomology algebras of a number of free loop spaces explicitly. Received: 23 June 1999; in final form: 8 September 2000 // Published online: 7 April 2003     

Finite element simulation of viscoelastic fluids of the integral type

In the present paper, we develop an algorithm for calculating the steady flow of viscoelastic fluids of the integral type. The calculation is based upon a simple integration of the strains along the streamlines, and the method remains valid for arbitrary elements. The technique is applied to the flow of a Maxwell fluid through a wedge and to the calculation of the hole-pressure error for the Doi-Edwards fluid.     

Electrochemical properties of a new cytostatic agent: 2-Formylpyridine thiosemicarbazone

Summary The electrochemical characteristics of 2-formylpyridine thiosemicarbazone (2-FPTS) have been studied by direct current, alternating current, and differential pulse polarography and cyclic voltammetry at a mercury electrode. This new cytostatic agent is reduced in a two-electron irreversible step at the nitrogen double bond of the side chain, in the pH range 0.2–12. A double anodic wave very close to the oxidation wave of mercury, corresponding to the formation of an organo-mercury compound, develops in neutral and alkaline media. These different electrochemical reactions are complicated by adsorption. In alkaline media, the carbon-nitrogen double bond reduction current decreases progressively with increasing pH due to formation of an electrochemically inactive species. Finally, a catalytic reduction wave of protons is developed in neutral solutions. Quantitative determination of the compound was possible in the range 1×10^–7 to 1×10^–3 M, using the diffusion controlled reduction wave at pH 7. The qualitative detection limit is 2×10^–8 M (4 ng/ml).

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Elektrochemische Eigenschaften einer neuen cytostatischen Substanz: 2-Formylpyridin-thiosemicarbazon

Zusammenfassung Die elektrochemischen Eigenschaften von 2-Formylpyridin-thiosemicarbazon wurden mit Hilfe der Gleichstrom-, Wechselstrom- und Differentialpuls-Polarographie sowie der cyclischen Voltammetrie an der Hg-Elektrode untersucht. Die neue cytostatische Substanz wird in einer irreversiblen Zweielektronen-Stufe an der Stickstoff-Kohlenstoff-Doppelbindung der Seitenkette reduziert (pH-Bereich 0,212). In neutralen und alkalischem Medium entwickelt sich eine anodische Doppelstufe dicht bei der Oxidationsstufe des Quecksilbers, entsprechend der Bildung einer quecksilberorganischen Verbindung. Diese elektrochemischen Reaktionen werden durch Adsorptionsvorgange verkompliziert. In alkalischem Medium nimmt der Reduktionsstrom der Kohlenstoff-Stickstoff-Doppelbindung mit zunehmendem pH ab, was der Bildung einer elektrochemisch inaktiven Substanz zugeschrieben wird. In neutraler Lösung wird eine katalytische protonische Reduktionsstufe gebildet. Die quantitative Bestimmung war im Bereich von 1·10^–7 bis 1·10^–3 M möglich, wobei die diffusionskontrollierte Reduktionsstufe bei pH 7 benutzt wurde. Die qualitative Nachweisgrenze liegt bei 2·10^–8 M (4 ng/ml).

     

Kinetics and mechanistic aspects of the Heck reaction promoted by a CN-palladacycle

In the Heck reaction between aryl halides and n-butyl acrylate, the palladacycle {Pd[kappa(1)-C, kappa(1)-N-C=(C(6)H(5))C(Cl)CH(2)NMe(2)](mu-Cl)}(2), 1, is merely a reservoir of the catalytically active Pd(0) species [1](Pd colloids or highly active forms of low ligated Pd(0) species) that undergoes oxidative addition of the aryl halide on the surface with subsequent detachment, generating homogeneous Pd(II) species. The main catalytic cycle is initiated by oxidative addition of iodobenzene to [1], followed by the reversible coordination of the olefin to the oxidative addition product. All the unimolecular subsequent steps are indistinguishable kinetically and can be combined in a single step. This kinetic model predicts that a slight excess of alkene relative to iodobenzene leads to a rapid rise in the Pd(0) concentration while when using a slight excess of iodobenzene, relative to alkene, the oxidative addition product is the resting state of the catalytic cycle. Competitive experiments of various bromoarenes and iodoarenes with n-butyl acrylate catalyzed by 1 and CS, CP, and NCN palladacycles gave the same rho value (2.4-2.5 for Ar-Br and 1.7-1.8 for Ar-I) for all palladacycles employed, indicating that they generate the same species in the oxidative addition step. The excellent fit of the slope with the sigma(0) Hammett parameter and the entropy of activation of -43 +/- 8 J mol(-1) K(-1) are consistent with an associative process involving the development of only a partial charge in the transition state for the oxidative step of iodobenzene.     

Galerkin methods for parabolic equations with nonlinear boundary conditions

A variety of Galerkin methods are studied for the parabolic equationu _t =(a(x) u),x ⁿ ,t (O,T], subject to the nonlinear boundary conditionu _v =g(x,t,u),x,t (O,T] and the usual initial condition. Optimal order error estimates are derived both inL ² () andH ¹ () norms for all methods treated, including several that produce linear computational procedures.The authors were partially supported by The National Science Foundation during the preparation of this paper.     

Mesoscopic resonating valence bond system on a triple dot

We theoretically introduce a mesoscopic pendulum from a triple dot. The pendulum is fastened through a singly occupied dot (spin qubit). Two other strongly capacitively coupled islands form a double-dot charge qubit with one electron in excess oscillating between the two low-energy charge states (1,0) and (0,1). The triple dot is placed between two superconducting leads. Under realistic conditions, the main proximity effect stems from the injection of resonating singlet (valence) bonds on the triple dot. This gives rise to a Josephson current that is charge- and spin-dependent and, as a consequence, exhibits a distinct resonance as a function of the superconducting phase difference.