On the elastic fibre pull-out problem: asymptotic and numerical results

Summary In this paper we present some asymptotic results for the pull out of a nearly-rigid fibre from an elastic matrix. The asymptotic results are accurate toO( ²), where=(ln 2l/R)^–1, if the fibre is pull-out from a semi-infinite matrix, and toO(h ²/l ²) if the fibre is pull-out from a matrix contained in a cylindrical container of radiush. Here R andl are the fibre radius and length, respectively. An interpolation formula is suggested which yields correct asymptotic behaviour at bothh/l=0 andh/l . These asymptotic results are confirmed by numerical methods to at least an aspect ratio ofl/R9. We also report some numerical confirmation of a previous approximate result for the pull out of a rigid fibre with an enlarged spherical end.

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Zusammenfassung In der vorliegenden Arbeit geben wir einige asymptotische Ergebnisse für das Ausziehen einer beinahe starren Faser aus einer elastischen Matrix. Die asymptotischen Resultate sind aufO( ²) genau, wo=(ln 2l/R)^–1 bedeutet, falls die Faser aus einer halbunendlichen Matrix ausgezogen wird. Sie sind aufO(h ²/l ²) genau, falls die Faser aus einer Matrix ausgezogen wird, welche einen Zylinder vom Radiush füllt. Eine Interpolationsformel, die das richtige asymptotische Verhalten fürh/l=0 undh/l aufweist, wird vorgeschlagen. Diese asymptotischen Ergebnisse werden durch numerische Methoden mindestens bis geometrische Verhältnisse vonl/R9 bestätigt. Wir berichten ebenfalls über eine gewisse numerische Bestätigung eines früheren approximativen Resultats für das Ausziehen einer starren Faser mit einem vergrößerten sphärischen Kopf.

     

1H MRS detection of glycine residue of reduced glutathione in vivo

Glutathione (GSH) is a powerful antioxidant found inside different kinds of cells, including those of the central nervous system. Detection of GSH in the human brain using ¹H MR spectroscopy is hindered by low concentration and spectral overlap with other metabolites. Previous MRS methods focused mainly on the detection of the cysteine residue (GSH-Cys) via editing schemes. This study focuses on the detection of the glycine residue (GSH-Gly), which is overlapped by glutamate and glutamine (Glx) under physiological pH and temperature. The first goal of the study was to obtain the spectral parameters for characterization of the GSH-Gly signal under physiological conditions. The second goal was to investigate a new method of separating GSH-Gly from Glx in vivo. The characterization of the signal was carried out by utilization of numerical simulations as well as experiments over a wide range of magnetic fields (4.0–14 T). The proposed separation scheme utilizes J-difference editing to quantify the Glx contribution to separate it from the GSH-Gly signal. The presented method retains 100% of the GSH-Gly signal. The overall increase in signal to noise ratio of the targeted resonance is calculated to yield a significant SNR improvement compared to previously used methods that target GSH-Cys residue. This allows shorter acquisition times for in vivo human clinical studies.     

Ketopiperazines: Conformationally Constrained Peptidomimetic of Arginine Amides

We have synthesized guanidine‐containing ketopiperazines designed to be conformational mimics of peptidomimetic arginine amides. D‐Allylglycine was converted by an efficient approach to give enantiopure ketopiperazines in which the trans stereochemistry of the C‐substituents resulted from stereospecific enolate alkylation.     

Long-range magnetic order in Li<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Na<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Cu<Subscript>2</Subscript>O<Subscript>2</Subscript>

Single crystals of Li _x Na_{1 ? x} Cu₂O₂ solid solutions have been grown from the melt and crystal lattice parameters have been studied. It is found that the solid solution of this system exists in the region x ≤ 0.25. Specific heat and magnetic susceptibility are investigated on monocrystalline samples with x = 0.07, 0.14, and 0.21. Long-range magnetic order in these compounds is formed at T = 13.8, 4.1, and 14.8 K, respectively. It is found that the Néel temperature T _N in these compounds increases with Li content.     

Structural and magnetoelectric properties of MFe<Subscript>2</Subscript>O<Subscript>4</Subscript>–PZT (M = Ni,Co) and La<Subscript>x</Subscript>(Ca,Sr)<Subscript>1-x</Subscript>MnO<Subscript>3</Subscript>–PZT multilayer composites

Thick-film layered magnetoelectric composites consisting of ferromagnetic and ferroelectric phases have been synthesized with nickel ferrite (NFO), cobalt ferrite, La_0.7Sr_0.3MnO₃ (LSMO), or La_0.7Ca_0.3MnO₃ (LCMO) and lead zirconate titanate (PZT). Structural, magnetic, and ferromagnetic resonance characterization shows evidence for defect-free ferrites, but deterioration of manganite parameters. The resistivity and dielectric constants are smaller than expected values. The magnetoelectric effect (ME) is stronger in ferrite–PZT than in manganite–PZT. The ME voltage coefficient _E at room temperature is the highest in NFO–PZT and the smallest for LCMO–PZT. The transverse ME effect is an order of magnitude stronger than the longitudinal effect. The magnitude of _E correlates well with magnetic permeability for the ferrites. PACS 75.80.+q; 75.70.Gg; 75.60.-d     

Heat capacity of the Pb<Subscript>5</Subscript>(Ge<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>x</Subscript>)<Subscript>3</Subscript>O<Subscript>11</Subscript> ferroelectric system

The temperature dependences of the molar heat capacity at constant pressure, C_p, of Pb₅(Ge_1?xSi_x)₃O₁₁ crystals with x=0, 0.39, and 0.45 in the range 5–300 K, as well as of their permittivity, dielectric losses, and the pyroelectric effect, have been measured. Experimental data on the temperature behavior of the heat capacity are presented in the form of a sum of two Debye and one Einstein terms, C_p(T)=0.405C_D1(Θ_D1=160 K, T)+0.53C_D2(Θ_D2=750 K, T)+0.046C_E(Θ_E=47 K, T). Besides a peak in the region of the ferroelectric Curie point T_c=450 K for crystals with x=0, the temperature dependences of the heat capacity did not reveal any other pronounced anomalies.     

Composition-induced transition of spin-modulated structure into a uniform antiferromagnetic state in a Bi<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>La<Subscript>x</Subscript>FeO<Subscript>3</Subscript> system studied using <Superscript>57</Superscript>Fe NMR

By analyzing the NMR line shape, the transformation of a spatially spin-modulated magnetic structure in BiFeO₃ into an ordinary spatially uniform structure of the LaFeO₃ orthoferrite in Bi_1?xLa_xFeO₃ solid solutions is studied. The measurements are made using a spin-echo technique at temperatures of 77 and 4.2 K on ceramics with compositions x=0, 0.1, 0.2, 0.61, 0.9, and 1.0 enriched by the ⁵⁷Fe isotope. It is shown that the spin-modulated structure disappears near the concentration x=0.2, which corresponds, according to the published data, to the phase transition with a change in the unit-cell symmetry R3c → C222. A formula is obtained describing the NMR absorption line shape for the spin-modulated structure with account of local line-width. Theoretical spectra adequately describe the evolution of the experimental spectrum in the concentration range 0≤x≤0.2. Highly nonuniform local magnetic fields in the intermediate compositions make it impossible to detect NMR signals in a sample with x=0.61. A uniform magnetic structure characterized by a single narrow line arises in the range of existence of a phase with the symmetry Pnma typical of the pure orthoferrite LaFeO₃.     

Synthesis of functionalized sulfonamides via 1,3-dipolar cycloaddition of pentafluorophenyl vinylsulfonate

[reaction: see text] An efficient intermolecular 1,3-dipolar cycloaddition of a variety of nitrones to pentafluorophenyl (PFP) vinylsulfonate is described. The transformation produces stable "reversed" cycloadducts of unprecedented stereo- and regioselectivity. Subsequent amine displacement of the PFP moiety furnished functionalized sulfonamide products in good yields.