Properties of fine-grained graphites based on two-component fillers

The effect of the nature of two-component fillers on the physical and mechanical properties of finegrained graphites was studied using highly oriented needle coke and nearly isotropic synthetic graphite as components of fillers. Each filler was prepared in the form of coarse (-120 µm) and fine (-10 µm) powders. Different mixtures of these components were used in producing graphite samples, which were then characterized by density, thermal expansion, compressive strength, and modulus of elasticity measurements. The results demonstrate that the thermal expansion, compressive strength, and modulus of elasticity of the graphites thus prepared depend on the microtexture, size, and shape of the filler particles.Translated from Neorganicheskie Materialy, Vol. 40, No. 12, 2004, pp. 1448–1454.Original Russian Text Copyright © 2004 by Samoilov.     

Bifurcation points and bifurcated branches by an asymptotic numerical method and Padé approximants

The aim of this work is to develop a reliable and fast algorithm to compute bifurcation points and bifurcated branches. It is based upon the asymptotic numerical method (ANM) and Padé approximants. The bifurcation point is detected by analysing the poles of Padé approximants or by evaluating, along the computed solution branch, a bifurcation indicator well adapted to ANM. Several examples are presented to assess the effectiveness of the proposed method, that emanate from buckling problems of thin elastic shells. Especially problems involving large rotations are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

On strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method

We consider a problem stemming from recent models of phase transitions in stimulus‐responsive hydrogels, wherein a sharp interface separates swelled and collapsed phases. Extended finite element methods that approximate the local solution with an enriched basis such that the mesh need not explicitly ‘fit’ the interface geometry are emphasized. Attention is focused on the weak enforcement of the normal configurational force balance and various options for evaluating the jump in the normal component of the solute flux at the interface. We show that as the reciprocal interfacial mobility vanishes, it plays the role of a penalty parameter enforcing a pure Dirichlet constraint, eventually triggering oscillations in the interfacial velocity. We also examine alternative formulations employing a Lagrange multiplier to enforce this constraint. It is shown that the most convenient choice of basis for the Lagrange multiplier results in oscillations in the multiplier field and a decrease in accuracy and rate of convergence in local error norms, suggesting a lack of stability in the discrete formulation. Under such conditions, neither the direct evaluation of the gradient of the approximation at the phase interface nor the interpretation of the Lagrange multiplier field provide a robust means to obtain the jump in the normal component of solute flux. Fortunately, the adaptation and use of local, domain‐integral methodologies considerably improves the flux evaluations. Several example problems are presented to compare and contrast the various techniques and methods. Copyright © 2004 John Wiley & Sons, Ltd.     

New two‐dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes

In this paper, we introduce an extension of Van Leer's slope limiter for two‐dimensional discontinuous Galerkin (DG) methods on arbitrary unstructured quadrangular or triangular grids. The aim is to construct a non‐oscillatory shock capturing DG method for the approximation of hyperbolic conservative laws without adding excessive numerical dispersion. Unlike some splitting techniques that are limited to linear approximations on rectangular grids, in this work, the solution is approximated by means of piecewise quadratic functions. The main idea of this new reconstructing and limiting technique follows a well‐known approach where local maximum principle regions are defined by enforcing some constraints on the reconstruction of the solution. Numerical comparisons with some existing slope limiters on structured as well as on unstructured meshes show a superior accuracy of our proposed slope limiters. Copyright © 2004 John Wiley & Sons, Ltd.     

Optimization of support positions to maximize the fundamental frequency of structures

In this paper, the position optimization of simple supports is implemented to maximize the fundamental frequency of a beam or plate structure. Both elastic and rigid supports are taken into account. First, the frequency sensitivity with respect to the movement of a simple support is derived using the discrete method. By means of the shape functions of the finite element method, closed‐form sensitivity formulations are developed straightforwardly. Then, a heuristic approach, called evolutionary shift method, is presented for optimizing support positions with a fixed grid mesh scheme. Based on the design sensitivity analysis, the support with the highest efficiency is shifted in priority along the elementary edges with the interval (step) of the elementary size. To facilitate the convergence of the process, the interpolation technique is employed to evaluate the solution more accurately. Finally, three numerical examples are presented to demonstrate the validity of the sensitivity analysis and the effectiveness of the optimization method. Copyright © 2004 John Wiley & Sons, Ltd.     

Thomas Fincke und die <Emphasis Type="Italic">Geometria rotundi</Emphasis>

Thomas Fincke (January 6^th, 1561–April 24^th, 1656), born in Flensburg (Germany), was one of the very most important and significant scientists in Denmark during the seventeenth century, a mathematician and astrologer and physician in the beginning of modern science, a representative of humanism and an influentual academic organizer. He studied in Strasbourg (since 1577) and Padua (since 1583) and received his M.D. in Basel (1587), he practised as a physician throughout his life (since 1587 or 1590) and became a professor at Copenhagen (1591). But he was best known because of his Geometriae rotundi libri XIIII (1583), a famous book on plane and spherical trigonometry, based not on Euclid but on Petrus Ramus. In this influentual work, in which Fincke introduced the terms tangent and secant and probable first noticed the Law of Tangents and the so-called Newton-Oppel-Mauduit-Simpson-Mollweide-Gauss-formula, he showed himself to be „abreast of the mathematics of his time“.      

Local Strain Measurement within Tendon

Abstract:  Tendon is a dense connective tissue, responsible for transmitting the forces generated by muscles to the skeleton. It is composed of a hierarchical arrangement of crimped collagen fibres, interspersed with proteoglycan matrix and cells, known as tenocytes. During physiological loading, tendons are subjected to strains in the region of 5–6%, which result in the straightening and realignment of the collagen fibres, generating variable local strain fields within the tendon. This study demonstrates a technique for analysing local strains within viable tendon explants, during both loading and unloading of the tissue. Samples were strained in a custom-designed rig, allowing real-time visualisation of cell nuclei, used as local discrete markers, on a confocal microscope. Results indicated that local strains within the fascicle are smaller than the applied strains, never exceeding 1.2%, even at 8% gross applied strain. By contrast, the sliding of adjacent collagen units was recorded at each strain increment in this study, reaching a mean maximum of 3.9% of the applied displacement. Loading–unloading studies indicated that sliding behaviour is reversible up to strains of 5%, and provides the major extension mechanism within the rat-tail tendon. This technique can be extended to further analyse shearing behaviour within the matrix.     

Auto-correlation function analysis of phase formation in iron ion-implanted amorphous silicon layers

High-resolution transmission electron microscopy (HRTEM) in conjunction with autocorrelation function (ACF) analysis have been applied to investigate the evolution of structural order in iron ion-implanted amorphous silicon layers. β-FeSi₂ nanocrystallites as small as 5 nm in size were detected in 600 °C annealed for 60 min a-Si layers. The embedded nanocrystalline β-FeSi₂ was found to grow in the interlayer with annealing temperature.     

Electrosprayed and selenized Cu/In metal particle films

Nano-particulate copper and indium metal layers of 1-2 μm have been deposited by non-vacuum techniques such as doctor blade, screen printing and electrospray using alcoholic suspension pastes. Electrospray showed a high efficiency of material usage and yielded the most uniform morphology. The metal precursor layers were subjected to a thermal treatment (500-600 °C) in selenium vapor to convert the porous metal layers into CuInSe₂ compound layers. The chemical conversion, investigated by X-ray diffraction, showed the presence of the In₂O₃ impurity phase in the precursor as well as in the selenized layers.