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.

     

A method to obtain some similarity solutions to the generalized Newtonian fluid

It is shown that a similarity solution to the Rayieigh flow problem for a generalized Newtonian fluid exists if the fluid boundary (y=0) is given a velocityU(t) t ^1/2. Furthermore, if the fluid is of the power-law type then similarity solutions exist ifU(t) t (orU(t) e ^t), where is any real number.

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Zusammenfassung Eine Methode wird aufgezeigt, wonach eine Ähnlichkeitslösung für das Rayleigh Strömungsproblem für eine allgemeine Newtonische Flüssigkeit besteht, falls der Flüssigkeitsgrenze (y=0) eine GeschwindigkeitU (t) t ^1/2 zugeordnet wird. Für Flüssigkeiten von Potenz-Gesetz-Charakter gibt es außerdem Ähnlichkeitslösungen, fallsU(t) t (orU(t) e ^t) gilt, wobei eine beliebige reelle Zahl darstellt.

     

Organic Positive Materials for Magnesium Batteries: A Review

Magnesium batteries, like lithium-ion batteries, with higher abundance and similar efficiency, have drawn great interest for large-scale applications such as electric vehicles, grid energy storage and many more. On the other hand, the use of organic electrode materials allows high energy-performance, metal-free, environmentally friendly, versatile, lightweight, and economically efficient magnesium storage devices. In particular, the structural diversity and the simple activity of organic molecules make redox properties, and hence battery efficiency, easy to monitor. While organic magnesium batteries still in their infancy, this field becomes more and more promising because significant results were reported. To summarize the achievements in studies on organic cathodes for magnesium systems, their synthesis is discussed, combined with electrode design to provide the basis for controlling the electrochemical properties. Moreover, the techniques to synthesize organic materials with high-yield are mentioned. Finally, potential problems and prospects are explored to further improve organic cathodes.     

A boundary integral formulation for elastically deformable particles in a viscous fluid

This paper reports a formulation and implementation of a mixed (both direct and indirect) boundary element method using the double layer and its adjoint in a form suitable for solving Stokes flow problems involving elastically deformable particles. The formulation is essentially the Completed Double Layer Boundary Element Method for solving an exterior traction problem for the surrounding fluid or solid phase, followed by an interior displacement, and a mobility problem (if required) for the elastic particles. At the heart of the method is a deflation procedure that allows iterative solution strategies to be adopted, effectively opens the way for large-scale simulations of suspensions of deformable particles to be performed. Several problems are considered, to illustrate and benchmark the method. In particular, an analytical solution for an elastic sphere in an elongational flow is derived. The stresslet calculations for an elastic sphere in shear and elongational flows indicate that elasticity of the inclusions can potentially lead to positive second normal stress difference in shear flow, and an increase in the tensile resistance in elongational flow.This work is supported by a grant from the Australian Research Grant Council. X-J F wishes to acknowledge the support of the National Natural Science Foundation of China.     

The flow of a viscoelastic fluid in a wedge

Summary It is shown that the kinematics of the flow of a general viscoelastic fluid in a wedge, one plate of which is being stretched at a rate proportional to the distance from the wedge apex, is Newtonian in character. Existence proof is given when non-Newtonian effects are slight. Furthermore, the stress field is multivalued at the wedge apex and the pressure field is logarithmically singular there. The strength of this singularity increases with the Weissenberg number.     

The Development of a Sheathless Interface for Capillary Electrophoresis Electrospray Ionization Mass Spectrometry Using a Cellulose Acetate Cast Capillary

The fabrication of a novel sheathless interface for capillary electrophoresis–electrospray–mass spectrometry (CE–ESI–MS) is described. A programmable CO₂ laser was used to ablate small channels in the walls of a polyimide capillary near the terminus. Subsequent exposure of the channel region to a cellulose acetate solution followed by drying resulted in the formation of an electrically conductive semi-permeable membrane. Application of an appropriate voltage to the reservoir resulted in the simultaneous establishment of an electrical connection for CE and ESI. Interface viability was demonstrated by conducting a CE separation of a peptide mixture, with detection accomplished via positive ion mode ESI–MS. For the peptide Val-Tyr-Val, a limit of detection of 0.1 femtomole (S/N 3) was achieved using single reaction monitoring. Attributes of the interface include structural robustness, ease of fabrication, minimal interface dead volume, and the ability to alter post-separation analyte ionization status by use of appropriate buffers in the interface reservoir.     

Two acridones and two coumarins from the roots of Paramignya trimera

Two acridones, paratrimerins C (1) and D (2), and two coumarins, paratrimerins E (3) and F (4), were isolated from the CHCl₃ and EtOAc extracts of Paramignya trimera (Rutaceae), together with twelve known compounds (5–16). Their structures were elucidated on the basis of spectroscopic data. All isolated compounds possessed significant α-glucosidase inhibitory activity in a concentration-dependent manner, and showed more potent inhibitory activity, with IC₅₀ values ranging from 14.6 to 112.2 μM, than the positive control acarbose (IC₅₀, 214.5 μM). The biosynthesis of the isolated coumarins and acridones was proposed.     

Time-resolved spectroscopic measurements of shock-wave induced decomposition in cyclotrimethylene trinitramine (RDX) crystals: anisotropic response

Plate impact experiments on the (210), (100), and (111) planes were performed to examine the role of crystalline anisotropy on the shock-induced decomposition of cyclotrimethylenetrinitramine (RDX) crystals. Time-resolved emission spectroscopy was used to probe the decomposition of single crystals shocked to peak stresses ranging between 7 and 20 GPa. Emission produced by decomposition intermediates was analyzed in terms of induction time to emission, emission intensity, and the emission spectra shapes as a function of stress and time. Utilizing these features, we found that the shock-induced decomposition of RDX crystals exhibits considerable anisotropy. Crystals shocked on the (210) and (100) planes were more sensitive to decomposition than crystals shocked on the (111) plane. The possible sources of the observed anisotropy are discussed with regard to the inelastic deformation mechanisms of shocked RDX. Our results suggest that, despite the anisotropy observed for shock initiation, decomposition pathways for all three orientations are similar.     

CS-Rickart modules

We introduce a notion of CS-Rickart module being a modular analog of the ACS-ring concept. We describe the rings over which each finitely generated projective module is CS-Rickart module. The presented results yield the known results related to Rickart modules and semihereditary rings.