Equivalence of u–p and ζ–ψ formulations of the time-dependent Navier–Stokes equations

This paper deals with the non-stationary incompressible Navier--Stokes equations for two-dimensional flows expressed in terms of the velocity and pressure and of the vorticity and streamfunction. The equivalence of the two formulations is demonstrated, both formally and rigorously, by virtue of a condition of compatibility between the boundary and initial values of the normal component of velocity. This condition is shown to be the only compatibility condition necessary to allow for solutions of a minimal regularity, namely H¹ for the velocity, as in most current numerical schemes relying on spatial discretizations of local type.     

Calculation of impulsively started incompressible viscous flows

The paper's focus is the calculation of unsteady incompressible 2D flows past airfoils. In the framework of the primitive variable Navier–Stokes equations, the initial and boundary conditions must be assigned so as to be compatible, to assure the correct prediction of the flow evolution. This requirement, typical of all incompressible flows, viscous or inviscid, is often violated when modelling the flow past immersed bodies impulsively started from rest. Its fulfillment can however be restored by means of a procedure enforcing compatibility, consisting in a pre‐processing of the initial velocity field, here described in detail. Numerical solutions for an impulsively started multiple airfoil have been obtained using a finite element incremental projection method. The spatial discretization chosen for the velocity and pressure are of different order to satisfy the inf–sup condition and obtain a smooth pressure field. Results are provided to illustrate the effect of employing or not the compatibility procedure, and are found in good agreement with those obtained with a non‐primitive variable solver. In addition, we introduce a post‐processing procedure to evaluate an alternative pressure field which is found to be more accurate than the one resulting from the projection method. This is achieved by considering an appropriate ‘unsplit’ version of the momentum equation, where the velocity solution of the projection method is substituted. Copyright © 2004 John Wiley & Sons, Ltd.     

The search for a new model structure of β-Factor XIIa

We present the search for a new model of -factor XIIa, a blood coagulation enzyme, with an unknown experimental 3D-structure. We decided to build not one but three different models using different homologous proteins as well as different techniques and different modellers. Additional studies, including extensive molecular dynamics simulations on the solvated state, allowed us to draw several conclusions concerning homology modelling, in general, and -factor XIIa, in particular.     

Characterization of Mercury – Humic Acids Interaction by Potentiometric Titration with a Modified Carbon Paste Mercury Sensor

Stability constant for mercury binding by commercial and natural humic acids (HA) were determined using a new potentiometric mercury(II) sensor based on dithiosalicylic acid modified carbon paste electrode. The sensor present a high selective and sensitive response to mercury(II) ions, and a low detection limit of 1.8×10^?8 M. The potentiometric titrations curves of humic acids against mercury(II) ions were modeled. For 1.00×10^?7 to 3.00×10^?4 M mercury(II) ion concentration levels the results are consistent with the presence of two different binding sites in the humic acid macromolecule. The strongest binding sites (log K₁ ranging from 10.1 to 6.8) are probably due to interaction with carboxylic acid and amine groups in the molecule, whereas weakest binding sites (log K₂ ranging from 8.8 to 4.5) can be associated to phenolic groups.     

Effects of palmitic acid and cholesterol on proton transport across black lipid membranes

We studied the effect of palmitic acid (PA) and cholesterol (approximately 17 wt.%) on proton translocation across asolectin (charged) and diphytanoylphosphatidylcholine (DPhPC, neutral) black lipid membranes (BLMs). Potential difference (PD), short circuit current (SCC), and conductance (G(total)) were measured with a digital electrometer. Membranes were exposed to pH gradients (0.4-2.0 units), followed by PA addition to bath (symmetrically, 40-65 microM). The membrane conductive pathway was subdivided into an unspecific and a proton-related routes. A computer program estimated the conductances (G(un) and G(H)) of the two pathways from the measured parameters. No significant differences in proton selectivity were found between DPhPC membranes and DPhPC/cholesterol membranes. By contrast, cholesterol incorporation into asolectin increases membranes selectivity to proton. Cholesterol dramatically reduced G(un) reflecting, probably, its ability of inducing order in lipid chains. In asolectin membranes, PA increases proton selectivity, probably by acting as a proton shuttle according to the model proposed by Kamp and et al. [Biochemistry 34 (1995) 11928]. Cholesterol incorporation into asolectin membranes eliminates the PA-induced increase in proton selectivity. In DPhPC and DPhPC/cholesterol membranes, PA does not affect proton selectivity. These results are discussed in terms of the presence of cardiolipin (CL) in asolectin, cholesterol/PA interactions, and cholesterol order-inducing effects on acyl-chains.     

Separation of fuels,heavy fractions,and crude oils into compound classes: A review

Practically all the conventional chromatographic techniques are used in the characterization of the highly complex mixtures of organic compounds occurring in fuels, heavy fractions, and crude oils. This paper surveys the techniques employed for class determination, preparative fractionation of the main classes, and determination of subgroups after class fractionation.     

New designs for inhibitors of the NF-κB: DNA binding

We present a series of new inhibitors of the association between nuclear factor kappa B (NF-B) and the corresponding B site in DNA. They were designed using the lead compound 15-deoxy-^12,14 -prostaglandin J₂ (PGJ2), which is a natural product with demonstrated inhibitory efficiency for this system. First, the binding mode of PGJ2 to NF-B was unraveled by GOLD docking calculation. Subsequently, substitutions were made to PGJ2 to optimize its association with NF-B. Care was taken not to strongly increase the reactivity of the new compounds, and to keep the overall shape, size and hydrophilicity of the lead compound, which should render them a similar bioavailability. Molecular mechanics calculations were performed to decide on the suitability of the substitutions, and to evaluate the energies of association with NF-B. Density functional theory calculations were performed also to study the overall reactivity of the substituted drugs towards NF-B. Important general conclusions were obtained, concerning the improvement of these natural inhibitors; namely, a set of rational methodologies were deduced to improve the association between the PGJ2 derivatives and NF-B, and their efficiency demonstrated by generating a set of substituted complexes, some of them with a very much increased affinity for NF-B, opening new doors to enlarge the therapeutic capabilities of this class of drugs.     

Coordinating ability of the heterocycles 1,3-dithia-2-arsa and stiba-cyclopentanes toward sulfur containing ligands,part I. Dialkyl-dithiocarbamate complexes

Summary The heterocyclic compounds ClMS₂ (CH₂)₂ (M = As, Sb) are tested by first time as source of starting materials in the synthesis of complexes. The preparation and characterization of heterocyclic dithiocarbamatesR ₂NCS₂ MS₂ (CH₂)₂, (M = As, Sb;R =Me,Et,i-Pr) is reported. Spectroscopic and analytical data suggest a bidentate behavior of the dithiocarbamate entity and the presence of aMS₄ core.

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Die Koordinationsfähigkeit der Heterocyclen 1,3-Dithia-2-arsa- und-stiba-cyclopentan gegenüber Schwefel enthaltenden Liganden, I. Dialkyldithiocarbamat-Komplexe

Zusammenfassung Die heterocyclischen Verbindungen ClMS₂ (CH₂)₂ (M = As, Sb) werden erstmals als Quelle für Ausgangsmaterial zur Synthese von Komplexen herangezogen. Es wird über die Herstellung und Charakterisierung der heterocyclischen DithiocarbamateR ₂NCS₂ MS₂ (CH₂)₂ (M = As, Sb;R =Me,Et,i-Pr) berichtet. Spektroskopische und analytische Daten sprechen für ein bidentates Verhalten der Dithiocarbamat-Einheit und der Präsenz einerMS₄-Anordnung im Komplex.

     

Synthesis and reactivity of silyl ruthenium complexes: the importance of trans effects in C-H activation,Si-C bond formation,and dehydrogenative coupling of silanes

A series of octahedral ruthenium silyl hydride complexes, cis-(PMe(3))(4)Ru(SiR(3))H (SiR(3) = SiMe(3), 1a; SiMe(2)CH(2)SiMe(3), 1b; SiEt(3), 1c; SiMe(2)H, 1d), has been synthesized by the reaction of hydrosilanes with (PMe(3))(3)Ru(eta(2)-CH(2)PMe(2))H (5), cis-(PMe(3))(4)RuMe(2) (6), or (PMe(3))(4)RuH(2) (9). Reaction with 6 proceeds via an intermediate product, cis-(PMe(3))(4)Ru(SiR(3))Me (SiR(3) = SiMe(3), 7a; SiMe(2)CH(2)SiMe(3), 7b). Alternatively, 1 and 7 have been synthesized via a fast hydrosilane exchange with another cis-(PMe(3))(4)Ru(SiR(3))H or cis-(PMe(3))(4)Ru(SiR(3))Me, which occurs at a rate approaching the NMR time scale. Compounds 1a, 1b, 1d, and 7a adopt octahedral geometries in solution and the solid state with mutually cis silyl and hydride (or silyl and methyl) ligands. The longest Ru-P distance within a complex is always trans to Si, reflecting the strong trans influence of silicon. The aptitude of phosphine dissociation in these complexes has been probed in reactions of 1a, 1c, and 7a with PMe(3)-d(9) and CO. The dissociation is regioselective in the position trans to a silyl ligand (trans effect of Si), and the rate approaches the NMR time scale. A slower secondary process introduces PMe(3)-d(9) and CO in the other octahedral positions, most likely via nondissociative isomerization. The trans effect and trans influence in 7a are so strong that an equilibrium concentration of dissociated phosphine is detectable (approximately 5%) in solution of pure 7a. Compounds 1a-c also react with dihydrogen via regioselective dissociation of phosphine from the site trans to Si, but the final product, fac-(PMe(3))(3)Ru(SiR(3))H(3) (SiR(3) = SiMe(3), 4a; SiMe(2)CH(2)SiMe(3), 4b; SiEt(3), 4c), features hydrides cis to Si. Alternatively, 4a-c have been synthesized by photolysis of (PMe(3))(4)RuH(2) in the presence of a hydrosilane or by exchange of fac-(PMe(3))(3)Ru(SiR(3))H(3) with another HSiR(3). The reverse manifold - HH elimination from 4a and trapping with PMe(3) or PMe(3)-d(9) - is also regioselective (1a-d(9)() is predominantly produced with PMe(3)-d(9) trans to Si), but is very unfavorable. At 70 degrees C, a slower but irreversible SiH elimination also occurs and furnishes (PMe(3))(4)RuH(2). The structure of 4a exhibits a tetrahedral P(3)Si environment around the metal with the three hydrides adjacent to silicon and capping the P(2)Si faces. Although strong Si...HRu interactions are not indicated in the structure or by IR, the HSi distances (2.13-2.23(5) A) suggest some degree of nonclassical SiH bonding in the H(3)SiR(3) fragment. Thermolysis of 1a in C(6)D(6) at 45-55 degrees C leads to an intermolecular CD activation of C(6)D(6). Extensive H/D exchange into the hydride, SiMe(3), and PMe(3) ligands is observed, followed by much slower formation of cis-(PMe(3))(4)Ru(D)(Ph-d(5)). In an even slower intramolecular CH activation process, (PMe(3))(3)Ru(eta(2)-CH(2)PMe(2))H (5) is also produced. The structure of intermediates, mechanisms, and aptitudes for PMe(3) dissociation and addition/elimination of H-H, Si-H, C-Si, and C-H bonds in these systems are discussed with a special emphasis on the trans effect and trans influence of silicon and ramifications for SiC coupling catalysis.     

Structure and reactivity of bis(silyl) dihydride complexes (PMe(3))(3)Ru(SiR(3))(2)(H)(2): model compounds and real intermediates in a dehydrogenative C-Si bond forming reaction

A series of stable complexes, (PMe(3))(3)Ru(SiR(3))(2)(H)(2) ((SiR(3))(2) = (SiH(2)Ph)(2), 3a; (SiHPh(2))(2), 3b; (SiMe(2)CH(2)CH(2)SiMe(2)), 3c), has been synthesized by the reaction of hydridosilanes with (PMe(3))(3)Ru(SiMe(3))H(3) or (PMe(3))(4)Ru(SiMe(3))H. Compounds 3a and 3c adopt overall pentagonal bipyramidal geometries in solution and the solid state, with phosphine and silyl ligands defining trigonal bipyramids and ruthenium hydrides arranged in the equatorial plane. Compound 3a exhibits meridional phosphines, with both silyl ligands equatorial, whereas the constraints of the chelate in 3c result in both axial and equatorial silyl environments and facial phosphines. Although there is no evidence for agostic Si-H interactions in 3a and 3b, the equatorial silyl group in 3c is in close contact with one hydride (1.81(4) A) and is moderately close to the other hydride (2.15(3) A) in the solid state and solution (nu(Ru.H.Si) = 1740 cm(-)(1) and nu(RuH) = 1940 cm(-)(1)). The analogous bis(silyl) dihydride, (PMe(3))(3)Ru(SiMe(3))(2)(H)(2) (3d), is not stable at room temperature, but can be generated in situ at low temperature from the 16e(-) complex (PMe(3))(3)Ru(SiMe(3))H (1) and HSiMe(3). Complexes 3b and 3d have been characterized by multinuclear, variable temperature NMR and appear to be isostructural with 3a. All four complexes exhibit dynamic NMR spectra, but the slow exchange limit could not be observed for 3c. Treatment of 1 with HSiMe(3) at room temperature leads to formation of (PMe(3))(3)Ru(SiMe(2)CH(2)SiMe(3))H(3) (4b) via a CH functionalization process critical to catalytic dehydrocoupling of HSiMe(3) at higher temperatures. Closer inspection of this reaction between -110 and -10 degrees C by NMR reveals a plethora of silyl hydride phosphine complexes formed by ligand redistribution prior to CH activation. Above ca. 0 degrees C this mixture converts cleanly via silane dehydrogenation to the very stable tris(phosphine) trihydride carbosilyl complex 4b. The structure of 4b was determined crystallographically and exhibits a tetrahedral P(3)Si environment around the metal with the three hydrides adjacent to silicon and capping the P(2)Si faces. Although strong Si.HRu interactions are not indicated in the structure or by IR, the HSi distances (2.00(4) - 2.09(4) A) and average coupling constant (J(SiH) = 25 Hz) suggest some degree of nonclassical SiH bonding in the RuH(3)Si moiety. The least hindered complex, 3a, reacts with carbon monoxide principally via an H(2) elimination pathway to yield mer-(PMe(3))(3)(CO)Ru(SiH(2)Ph)(2), with SiH elimination as a minor process. However, only SiH elimination and formation of (PMe(3))(3)(CO)Ru(SiR(3))H is observed for 3b-d. The most hindered bis(silyl) complex, 3d, is extremely labile and even in the absence of CO undergoes SiH reductive elimination to generate the 16e(-) species 1 (DeltaH(SiH)(-)(elim) = 11.0 +/- 0.6 kcal x mol(-)(1) and DeltaS(SiH)(-)(elim) = 40 +/- 2 cal x mol(-)(1) x K(-)(1); Delta = 9.2 +/- 0.8 kcal x mol(-)(1) and Delta = 9 +/- 3 cal x mol(-)(1).K(-)(1)). The minimum barrier for the H(2) reductive elimination can be estimated, and is higher than that for silane elimination at temperatures above ca. -50 degrees C. The thermodynamic preferences for oxidative additions to 1 are dominated by entropy contributions and steric effects. Addition of H(2) is by far most favorable, whereas the relative aptitudes for intramolecular silyl CH activation and intermolecular SiH addition are strongly dependent on temperature (DeltaH(SiH)(-)(add) = -11.0 +/- 0.6 kcal x mol(-)(1) and DeltaS(SiH)(-)(add) = -40 +/- 2 cal.mol(-)(1) x K(-)(1); DeltaH(beta)(-CH)(-)(add) = -2.7 +/- 0.3 kcal x mol(-)(1) and DeltaS(beta)(-CH)(-)(add) = -6 +/- 1 cal x mol(-)(1) x K(-)(1)). Kinetic preferences for oxidative additions to 1 - intermolecular SiH and intramolecular CH - have been also quantified: Delta = -1.8 +/- 0.8 kcal x mol(-)(1) and Delta = -31 +/- 3 cal x mol(-)(1).K(-)(1); Delta = 16.4 +/- 0.6 kcal x mol(-)(1) and Delta = -13 +/- 6 cal x mol(-)(1).K(-)(1). The relative enthalpies of activation (-)(1) x K(-)(1)). Kinetic preferences for oxidative additions to 1 - intermolecular SiH and intramolecular CH - have been also quantified: Delta (H)SiH(add) = 1.8 +/- 0.8 kcal x mol(-)(1) and Delta S((SiH-add) =31+/- 3 cal x mol(-)(1) x K(-)(1); Delta S (SiH -add) = 16.4 +/- 0.6 kcal x mol(-)(1) and =Delta S (SiH -CH -add) =13+/- 6 cal x mol(-)(1) x K(-)(1). The relative enthalpies of activation are interpreted in terms of strong SiH sigma-complex formation - and much weaker CH coordination - in the transition state for oxidative addition.