A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature

We consider the discretization in time of an inhomogeneous parabolicequation in a Banach space setting, using a representation ofthe solution as an integral along a smooth curve in the complexleft half-plane which, after transformation to a finite interval,is then evaluated to high accuracy by a quadrature rule. Thisreduces the problem to a finite set of elliptic equations withcomplex coefficients, which may be solved in parallel. The paperis a further development of earlier work by the authors, wherewe treated the homogeneous equation in a Hilbert space framework.Special attention is given here to the treatment of the forcingterm. The method is combined with finite-element discretizationin spatial variables.     

Selective Growth and Structural Analysis of Regular MnO Nanooctapods Bearing Multiple High‐Index Surface Facets

Although numerous morphologies of MnO nanostructures have been reported, an exact structural analysis and mechanistic study has been lacking. In the present study, the formation of regular MnO octapods was demonstrated in a simple procedure, comprising the thermal decomposition of manganese oleate. Because of their structural uniformity, an ideal three‐dimensional model was successfully constructed. The eight arms protruded from the cubic center with tip angles of 38° and surface facets of {311} and {533} with rounded edges. The concentrations of oleate and chloride ions were the determining factors for the octapod formation. Selective coordination of the oleate ions to the {100} faces led to edge growth along the <111> direction, which was then limited by the chloride ions bound to the high‐index surface facets. These structural and mechanistic analyses should be helpful for understanding the complex nanostructures and for tuning their structure‐related properties.     

Total synthesis and examination of three key analogues of ramoplanin: a lipoglycodepsipeptide with potent antibiotic activity

The total synthesis and evaluation of three key ramoplanin aglycon analogues are detailed. The first (5a) represents replacement of the labile depsipeptide ester with a stable amide (HAsn2 --> Dap2) with removal of the HAsn pendant carboxamide, and it was found to be slightly more potent than the natural aglycon in antimicrobial assays providing a new lead structure with an improved profile and a more stable and accessible macrocyclic template on which to conduct structure-function studies. In contrast, a second amide analogue 5b which contains a single additional methylene relative to 5a (HAsn2 --> Dab2) was found to be inactive in antimicrobial assays (>100-fold loss in activity). The third key analogue 5c in which the Asn1 lipid side chain was replaced with an acetyl group revealed that it contributes significantly to the antimicrobial activity (16-fold) of the ramoplanins, but is not essential.     

Growth of poly(pseudorotaxane) on gold using host-stabilized charge-transfer interaction

A novel supramolecular polymer (poly(pseudorotaxane)) in which the repeating units are linked by host-stabilized charge-transfer interaction between the guest molecules is grown on gold and characterized.     

A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature

We treat the time discretization of an initial-value problem for a homogeneous abstract parabolic equation by first using a representation of the solution as an integral along the boundary of a sector in the right half of the complex plane, then transforming this into a real integral on the finite interval , and finally applying a standard quadrature formula to this integral. The method requires the solution of a finite set of elliptic problems with complex coefficients, which are independent and may therefore be done in parallel. The method is combined with spatial discretization by finite elements.

     

Heat transfer measurements and correlations for air–water flow of different flow patterns in a horizontal pipe

Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the flow patterns was supplemented with photographic data, and the results were plotted on the flow regime map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.     

Surface roughness dependence of the first-order probability density function for integrated speckle

The surface roughness dependence of the first-order probability density function (PDF) of an integrated speckle pattern, produced in the condition of circular detection aperture and gaussian scattering spot, was theoretically investigated. The mutual intensity J_A(x₁, y₁; x₂, y₂) containing two roughness parameters, dispersion of surface height ø² lateral correlation length x_c, was calculated. The exact first-order probability density function was analytically derived and numerically calculated by means of the Karhunen-Loeve expansion and fast Fourier transform (FFT). As a diffuse object became smooth, the first order probability density function was changed from negative exponential to sharp peak gaussian centered around mean intensity.     

Alanine scan of [L-Dap(2)]ramoplanin A2 aglycon: assessment of the importance of each residue

In efforts that define the importance of each residue and that identify key regions of the molecule, an alanine scan of the ramoplanin A2 aglycon, a potent antibiotic that inhibits bacterial cell wall biosynthesis, is detailed. As a consequence of both its increased stability (lactam vs lactone) and its "relative" ease of synthesis, the alanine scan was conducted on [Dap2]ramoplanin A2 aglycon, which possesses antimicrobial activity equal to or slightly more potent than that of ramoplanin A2 or its aglycon. Thus, 14 key analogues of the ramoplanin A2 aglycon, representing a scan of residues 3-13, 15, and 17, were prepared enlisting a convergent solution-phase total synthesis that consolidated the effort to a manageable level. The antimicrobial activity of the resulting library of analogues provides insight into the importance and potential role of each residue of this complex glycopeptide antibiotic.     

A new cubic nonconforming finite element on rectangles

A new nonconforming rectangle element with cubic convergence for the energy norm is introduced. The degrees of freedom (DOFs) are defined by the 12 values at the three Gauss points on each of the four edges. Due to the existence of one linear relation among the above DOFs, it turns out the DOFs are 11. The nonconforming element consists of . We count the corresponding dimension for Dirichlet and Neumann boundary value problems of second‐order elliptic problems. We also present the optimal error estimates in both broken energy and norms. Finally, numerical examples match our theoretical results very well. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 691–705, 2015