Analytic and numerical solutions in the theory of elastic plates

ABSTRACT

Numerical approximations of the solution of a boundary value problem when an exact solution is not available can be constructed by means of a variety of methods. In this paper, we present a technique that is based on the integral representation of the solution of an elliptic problem and the properties of the associated layer potentials. The procedure is illustrated in application to the mathematical model of bending of plates with transverse shear deformation in a finite domain, in the presence of Dirichlet, Neumann, and Robin conditions prescribed on the boundary.     

On the Dual Phosphorescence of Xanthone and Chromone in Glassy Hydrocarbon Hosts

Trace quantities of hydrogen‐bonding impurities in otherwise highly purified and dried glassy hydrocarbon matrices at 77 K can modify the relative triplet state energy levels, and hence the photophysical properties of two aromatic ketones, xanthone and chromone, to the extent that the intrinsic spectroscopic properties are obscured. The intrinsic spectroscopic properties of each are revealed in multicrystalline n‐alkane Shpol'skii matrices, and also can be observed in rigorously purified and dried hydrocarbon glasses at 77 K. The extreme sensitivity to stoichiometric, and even substoichiometric quantities of hydrogen‐bonding impurities arises from the near‐degeneracy of the two lowest‐lying triplet states, and the sensitive nature of the n→π* blueshift phenomena to specific hydrogen‐bonding interactions.     

Chromatographic separation of americium from europium using bis-2,6-(5,6,7,8-tetrahydro-5,9,9-trimethyl-5,8-methano-1,2,4-benzotriazin-3-yl) pyridine

The separation of americium(III) from europium(III) was achieved utilizing a bis-2,6-(5,6,7,8-tetrahydro-5,9,9-trimethyl-5,8-methano-1,2,4-benzotriazin-3-yl) pyridine (CA-BTP) chromatographic resin. The extraction chromatographic materials were prepared using various concentrations of CA-BTP. This new, hydrolytically stable extractant was impregnated on an inert polymeric support at 40% loading. The uptake of Am(III) and Eu(III) by this material from 0.1 to 4.0 M aqueous HNO₃ solutions was measured. The resulting dry weight distribution ratios, D _w , indicated a strong preference for Am(III) with little affinity for Eu(III). These results are similar to recently reported solvent extraction studies indicating a maximum uptake of Am(III) in the 0.5–1.0 M HNO₃ range. The resin preparation, performance, and characterization of the Am/Eu separation are reported herein.

     

Effective Relative Permeabilities and Capillary Pressure for One-Dimensional Heterogeneous Media

The paper presents an analytical construction of effective two-phase parameters for one-dimensional heterogeneous porous media, and studies their properties. We base the computation of effective parameters on analytical solutions for steady-state saturation distributions. Special care has to be taken with respect to saturation and pressure discontinuities at the interface between different rocks. The ensuing effective relative permeabilities and effective capillary pressure will be functions of rate, flow direction, fluid viscosities, and spatial scale of the heterogeneities.The applicability of the effective parameters in dynamic displacement situations is studied by comparing fine-gridded simulations in heterogeneous media with simulations in their homogeneous (effective) counterparts. Performance is quite satisfactory, even with strong fronts present. Also, we report computations studying the applicability of capillary limit parameters outside the strict limit.     

Quantification of myo‐inositol, 1,5‐anhydro‐ D‐sorbitol,and D‐chiro‐inositol using high‐performance liquid chromatography with electrochemical detection in very small volume clinical samples

Inositol is a six‐carbon sugar alcohol and is one of nine biologically significant isomers of hexahydroxycyclohexane. Myo‐inositol is the primary biologically active form and is present in higher concentrations in the fetus and newborn than in adults. It is currently being examined for the prevention of retinopathy of prematurity in newborn preterm infants. A robust method for quantifying myo‐inositol (MI), D ‐chiro‐inositol (DCI) and 1,5‐anhydro‐ D ‐sorbitol (ADS) in very small‐volume (25 μL) urine, blood serum and/or plasma samples was developed. Using a multiple‐column, multiple mobile phase liquid chromatographic system with electrochemical detection, the method was validated with respect to (a) selectivity, (b) accuracy/recovery, (c) precision/reproducibility, (d) sensitivity, (e) stability and (f) ruggedness. The standard curve was linear and ranged from 0.5 to 30 mg/L for each of the three analytes. Above‐mentioned performance measures were within acceptable limits described in the Food and Drug Administration's Guidance for Industry: Bioanalytical Method Validation. The method was validated using blood serum and plasma collected using four common anticoagulants, and also by quantifying the accuracy and sensitivity of MI measured in simulated urine samples recovered from preterm infant diaper systems. The method performs satisfactorily measuring the three most common inositol isomers on 25 μL clinical samples of serum, plasma, milk, and/or urine. Similar performance is seen testing larger volume samples of infant formulas and infant formula ingredients. MI, ADS and DCI may be accurately tested in urine samples collected from five different preterm infant diapers if the urine volume is greater than 2–5 mL. Copyright © 2015 John Wiley & Sons, Ltd.     

NMR-assisted computational studies of peptidomimetic inhibitors bound in the hydrophobic pocket of HIV-1 glycoprotein 41

Due to the inherently flexible nature of a protein–protein interaction surface, it is difficult both to inhibit the association with a small molecule, and to predict how it might bind to the surface. In this study, we have examined small molecules that mediate the interaction between a WWI motif on the C-helix of HIV-1 glycoprotein-41 (gp41) and a deep hydrophobic pocket contained in the interior N-helical trimer. Association between these two components of gp41 leads to virus–cell and cell–cell fusion, which could be abrogated in the presence of an inhibitor that binds tightly in the pocket. We have studied a comprehensive combinatorial library of α-helical peptidomimetics, and found that compounds with strongly hydrophobic side chains had the highest affinity. Computational docking studies produced multiple possible binding modes due to the flexibility of both the binding site and the peptidomimetic compounds. We applied a transferred paramagnetic relaxation enhancement experiment to two selected members of the library, and showed that addition of a few experimental constraints enabled definitive identification of unique binding poses. Computational docking results were extremely sensitive to side chain conformations, and slight variations could preclude observation of the experimentally validated poses. Different receptor structures were required for docking simulations to sample the correct pose for the two compounds. The study demonstrated the sensitivity of predicted poses to receptor structure and indicated the importance of experimental verification when docking to a malleable protein–protein interaction surface.     

Adsorption kinetics of alkanethiol-capped gold nanoparticles at the hexane–water interface

The pendant drop technique was used to characterize the adsorption behavior of n-dodecane-1-thiol and n-hexane-1-thiol-capped gold nanoparticles at the hexane–water interface. The adsorption process was studied by analyzing the dynamic interfacial tension versus nanoparticle concentration, both at early times and at later stages (i.e., immediately after the interface between the fluids is made and once equilibrium has been established). A series of gold colloids were made using nanoparticles ranging in size from 1.60 to 2.85 nm dissolved in hexane for the interfacial tension analysis. Following free diffusion of nanoparticles from the bulk hexane phase, adsorption leads to ordering and rearrangement of the nanoparticles at the interface and formation of a dense monolayer. With increasing interfacial coverage, the diffusion-controlled adsorption for the nanoparticles at the interface was found to change to an interaction-controlled assembly and the presence of an adsorption barrier was experimentally verified. At the same bulk concentration, different sizes of n-dodecane-1-thiol nanoparticles showed different absorption behavior at the interface, in agreement with the findings of Kutuzov et al. (Phys Chem Chem Phys 9:6351–6358, 2007). The experiments additionally demonstrated the important role played by the capping agent. At the same concentration, gold nanoparticles stabilized by n-hexane-1-thiol exhibited greater surface activity than gold nanoparticles of the same size stabilized by n-dodecane-1-thiol. These findings contribute to the design of useful supra-colloidal structures by the self-assembly of alkane-thiol-capped gold nanoparticles at liquid–liquid interfaces.