On accurate boundary conditions for a shape sensitivity equation method

This paper studies the application of the continuous sensitivity equation method (CSEM) for the Navier–Stokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve flow derivatives at the boundary. Thus, accurate flow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate flow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least‐squares procedure to evaluate accurate first and second derivatives of the flow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The flow and sensitivity fields are solved using an adaptive finite‐element method. The proposed methodology is first verified on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity fields for realistic problems is then demonstrated. The flow and sensitivity fields for a NACA 0012 airfoil are used for fast evaluation of the nearby flow over an airfoil of different thickness (NACA 0015). Copyright © 2005 John Wiley & Sons, Ltd.     

Crystal and molecular structure of crenatine carbonate

The crystal and molecular structure of 1-ethyl-4-methoxy-9H-pyrido[3,4b]indole (crenatine) carbonate C₁₄H₁₄N₂O·H₂CO₃, (MS, m/z 226)M _R 288.3, a-carboline alkaloid, has been determined from X-ray diffraction data. The compound crystallizes in the space group Pbca with cell parameters:a=11.616(4),b=18.450(8),c=12.992(5)Å,V=2784(2)ų,Z=8,D _calc=1.375 g cm^–3, (MoK)=0.71069Å,(Mo K)=0.94 cm^–1,F(000)=1216,R/R _w =8.2/10.3% for 1099 reflections. The ring system of the-carboline nucleus is planar. The title compound shows a two center hydrogen bond between the indole N-H group and the oxygen atom of a carbonate group. The structure does not display hydrogen bonding between-carboline groups but rather a bonding network involving the carbonate group.     

On estimating a density using Hellinger distance and some other strange facts

Résumé On s'intéresse ici aux possibles vitesses d'estimation d'une densité à support compact dans ^m sous des hypothèses de régularité, lorsque la perte est mesurée par le carré de la distance de Hellinger (on regardera aussi le cas connu des normes pour 1q2) et le risque est le risque minimax sur la famille. On donne une méthode générale permettant de traiter les problèmes dans le cadre de la théorie de l'approximation sous des conditions concernant l'entropie métrique et l' -capacité des familles à estimer. Les rapports entre régularité et entropie métrique étant bien connus, nous pourrons aussi traiter les cas classiques et d'autres qui le sont moins. Sous des conditions de bornes inférieures les vitesses sont celles observées pour la norme mais elles diffèrent dans le cas général. On montre aussi que les restrictions sur la compacité du support ou la régularité sont indispensables et que leur absence mène à l'impossibilité d'obtenir une estimation raisonnable en ce sens que n'importe quelle suite d'estimateurs sera arbitrairement mauvaise en un point au moins. Un résultat analogue est vrai sous des conditions de régularité.

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This work was carried out during a visit of the author at the Mathematical Sciences Research Institute at Berkeley     

Effect of radial distribution functions and poisson reparatition of reactants on the analysis of reactions involving long distance energy transfer

Starting from a uniform distribution and knowing the space dependent rate constant, it is possible to express the fluorescence quenching effect. In the case of long distance energy transfer (Forster), we show that the introduction of radial distribution functions and of non-uniform repartition of quenchers has only small effects on the kinetics of such reactions.

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Computation of LCAO wave functions for ground states of polymers and solids

The LCAO form of the Hartree–Fock method is discussed in its application to crystals. General formulae are given for obtaining Fourier coefficient of electronic density (in direct space) as well as of the band structure (in momentum space). Finally, it is shown that in its LCAO form, Slater–Hartree–Fock equations are very simple and that this method is of interest for numerical applications. Special integrals occurring in this formalism are evaluated for a Gaussian basis in the last part of this paper.     

A new tri-orthogonal strategy for peptide cyclization

A solid phase tri-orthogonal protection/cleavage strategy that uses acidic, basic, and neutral conditions is described. Strategically protected alpha-azido-gamma-9-fluorenylmethyl-L-glutamate (1) and alpha-azido-epsilon-N-Fmoc-L-lysine (2) were incorporated into growing peptides on Wang resin using a novel azide protection strategy. These residues, separated by 1-3 monomers, were deprotected at the side chains and cyclized via lactam formation. The N-terminus was further functionalized to extend the chain. This method represents a straightforward protocol for peptide cyclization on solid support.     

Effect of actin concentration on the structure of actin-containing liposomes

Liposomes encapsulating monomeric actin (G-actin) were produced via extrusion through 400 and 600 nm pore diameter polycarbonate membranes in low ionic strength buffer (G-buffer). After actin-containing liposomes were subjected to high ionic strength polymerization buffer (F-buffer), morphological changes in the structure of actin-containing liposomes were studied using asymmetric flow field-flow fractionation (AFFF) coupled with multiangle static light scattering (MASLS). The general shape of these liposomes was initially determined by fitting three form factors, which describe the angular distribution of scattered light from a spherical thin shell, thin disk, and thin rod, to the experimentally measured light scattering spectra to regress the dimensions of the liposomes corresponding to the proposed geometry. Light scattering spectra that yielded a best fit to the thin disk model were analyzed further and fit to the ellipsoidal of revolution form factor to regress both the major and minor axis dimensions. The results of this analysis showed that actin-containing liposomes extruded through 400 and 600 nm pore diameter membranes in F-buffer, at a low actin concentration (0.1 mg/mL), assumed a spherical shape, which is also the case for plain liposomes (no actin present) in G-buffer and F-buffer. When the actin concentration was increased to 1 mg/mL, the polymerizing actin filaments stretched the initially spherical liposome into a disklike shape. However, when the actin concentration was further increased to 5 mg/mL, the liposomes reverted back to a spherical shape.     

Tuning of the alpha-terthiophene radical cation coupling reaction using mixed micelles with varying charge density.

The photophysics and photochemistry of alpha-terthiophene (alphaT), compartmentalized in mixed nonionic/anionic micelles, have been investigated with focus on the influence of the micellar surface charge density on the formation of the radical coupling product alpha-hexathiophene (alphaH). By varying the ratio of nonionic-to-anionic surfactants, and assuming ideal mixing, the charge density of the mixed micelles was varied. From Poisson-Boltzmann calculations, performed using the cell model, the electrostatic potential and the counterion activity were estimated as a function of the distance from the micellar surface. Upon excitation, the triplet state of alphaT is formed, from which the alphaT radical cation can be formed by absorption of a second photon. The radical cation can form alphaH if it encounters another alphaT radical cation. Under the experimental conditions used, this implies that the alphaH formation only occurs if the compartmentalized radical cation is able to migrate from its host micelle to another micelle, either via the surrounding bulk or by fusion of two micelles followed by mixing of their contents before micellar fission. The formation yield of the radical cation depends on the charge density of the mixed micelle; a lower charge density, that is, an increased amount of nonionic surfactant, lowers the yield. The yield of the coupling product alphaH, however, does not follow the same trend. A maximum yield of alphaH is found at intermediate nonionic surfactant molar ratios. This behavior is understood in terms of the Poisson-Boltzmann simulation results and by comparing charge-density changes as a function of molar fraction with the changes in counterion activity. The alphaH yield is a result of the balance between an increased possibility of radical cation bulk migration and a lowered electrostatic stabilization of the radical.     

Mean configurational distribution function for the steady state and stern-volmer representation

A slight discrepancy appears between the treatment of the steady state of diffusion controlled bimolecular quenching of excited species either by the pair model or by the continuum model. A simplifying assumption is pointed out which helps to solve the steady state case but which is responsible for the discrepancy. The error involved is of small importance considering the experimental accuracy.

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The synthesis of certain 11,14-dimethoxydeoxypodocarpic acid derivatives. an application to the synthesis of (+)-winterin from drimys winteri

This paper reports the synthesis of several 11,14-dimethoxydeoxypodocarpic acid derivatives from (+)-podocarpic acid. The synthesis of the naturally occurring sesquiterpene, (+)-winterin, from Drimys winteri illustrates a synthetic application of the 11,14-dimethoxy intermediates and establishes the absolute configuration for winterin.