A quasi-static Signorini contact problem for a thermoviscoelastic beam

This paper is concerned with the existence, uniqueness and numerical solution of a system of equations modelling the evolution of a quasi-static thermoviscoelastic beam that may be in contact with two rigid obstacles. A finite element approximation is proposed and analysed and some numerical results are given. Work partially supported by the Brazilian institution CNPq.     

A note on Schweizer–Smital chaos

In this paper, we consider a continuous map f:X→X$f:X\to X$, where X$X$ is a compact metric space, and prove that for any positive integer N$N$, f$f$ is Schweizer–Smital chaotic if and only if f^N$f^N$ is too.     

A MUSCL smoothed particles hydrodynamics for compressible multi‐material flows

By incorporating the Monotone Upwind Scheme of Conservation Law (MUSCL) scheme into the smoothed particles hydrodynamics (SPH) method and making use of an interparticle contact algorithm, we present a MUSCL–SPH scheme of second order for multifluid computations, which extends the Riemann‐solved‐based SPH method. The numerical tests demonstrate high accuracy and resolution of the scheme for both shocks, contact discontinuities, and rarefaction waves in the one‐dimensional shock tube problem. For the two‐dimensional cylindrical Noh and shock‐bubble interaction problems, the MUSCL–SPH scheme can resolve shocks well. Copyright © 2015 John Wiley & Sons, Ltd.     

Simultaneous determination of phosphonate, phosphate, and diphosphate by capillary electrophoresis using in-capillary complexation with Mo(VI)

This study describes the simultaneous determination of phosphonate, phosphate, and diphosphate by CE with direct UV detection, based on in-capillary complexation with Mo(VI). When a mixture of phosphonate, phosphate, and diphosphate was injected into a capillary containing 3.0 mM Mo(VI), 0.05 M malonate buffer (pH 3.0) and 45% v/v CH3CN, three well-defined peaks, due to the migration of the corresponding polyoxomolybdate anions, were separated. The respective calibration graphs were linear in the concentration range of 2 x 10(-6)-2 x 10(-4) M for phosphonate, 1 x 10(-6)-5 x 10(-5) M for phosphate, and 1 x 10(-6)-2 x 10(-4) M for diphosphate; the correlation coefficients were better than 0.9990. The present CE method is successfully applied to the simultaneous determination of phosphonate, phosphate, and diphosphate in tap water.     

Strain gradient plasticity solution for an internally pressurized thick-walled cylinder of an elastic linear-hardening material

An elastic-plastic solution is presented for an internally pressurized thick-walled plane strain cylinder of an elastic linear-hardening plastic material. The solution is derived in a closed form using a strain gradient plasticity theory. The inner radius of the cylinder enters the solution not only in non-dimensional forms but also with its own dimensional identity, which differs from that in classical plasticity based solutions and makes it possible to capture the size effect at the micron scale. The classical plasticity solution of the same problem is recovered as a special case of the current solution. To further illustrate the newly derived solution, formulas and numerical results for the plastic limit pressure are provided. These results reveal that the load-carrying capacity of the cylinder increases with decreasing inner radius at the micron scale. It is also seen that the macroscopic behavior of the pressurized cylinder can be well described by using classical plasticity based solutions.     

The Hertz contact problem,coupled Volterra integral equations and a linear complementarity problem

This paper is concerned with the indentation of an elastic half-space by an axisymmetric punch under a monotonically applied normal force and under the assumption of Coulomb friction with coefficient μ$\mu$ in the region of contact. Within an inner (unknown) circle the contact is adhesive, while in the surrounding annulus the surface moves inwards with increasing load. In this paper it is shown how this problem is equivalent to two coupled Abel's equations with an unknown free point, the inner circumference of the annulus. It is further shown that a product integration finite difference approximation of those integral equations leads to a mixed linear complementarity problem (mixed LCP). A method based on Newton's method for solving non-smooth nonlinear equations is demonstrated to converge under restrictive assumptions on the physical parameters defining the system; and numerical experimentation verifies that it has much wider applicability. The method is also validated against the approach of Spence. The advantage of the mixed LCP formulation is that it provides the radius of the inner adhesive circle directly using the physical parameters of the problem.     

Darstellung,Isolierung und Charakterisierung von Ba@C74

Preparation, Isolation, and Characterization of Ba@C₇₄ For the first time Ba@C₇₄ has been isolated in pure form. The title compound has been isolated from a raw material, produced in a radio‐frequency‐furnace, consisting of a mixture of fullerenes and endohedral Bariumfullerenes. Ba@C₇₄ was separated by two stage sublimation and subsequent high‐performance liquid chromatography (HPLC) using a Buckyprep column. The capacity factor for Ba@C₇₄ is 6.0. Its endohedral character has been deduced from the fragmentation pattern obtained by time‐of‐flight mass spectroscopy while the composition has been confirmed by comparison of calculated and measured isotopic pattern of the parent peak. Further characterization was performed by VIS/NIR‐spectroscopy and electron‐paramagnetic‐resonance spectroscopy (EPR).     

High-selectivity Detection of 2,4,6-Trinitrophenol Based on Fluorescent Mg-MOF-74 in Ethanol Solution

Mg-MOF-74 has adsorption capacity while less research is about its luminescent properties. In this work, the fluorescent properties of Mg-MOF-74 were studied and characterized. The results show that Mg-MOF-74 exhibits excellent fluorescent properties and, most strikingly, selective sensing detection for nitroaromatic compounds(NACs), 2,4,6-trinitrophenol(PA) in particular, making it a promising PA-selective luminescent probe. This work demonstrates the application of MOFs in the detection of NACs with good selectivity.     

A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods

Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green’s functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated.     

A variational approach to the local character of G-closure: the convex case

This article is devoted to characterize all possible effective behaviors of composite materials by means of periodic homogenization. This is known as a G-closure problem. Under convexity and p  -growth conditions (p>1$p>1$), it is proved that all such possible effective energy densities obtained by a Γ-convergence analysis, can be locally recovered by the pointwise limit of a sequence of periodic homogenized energy densities with prescribed volume fractions. A weaker locality result is also provided without any kind of convexity assumption and the zero level set of effective energy densities is characterized in terms of Young measures. A similar result is given for cell integrands which enables to propose new counter-examples to the validity of the cell formula in the nonconvex case and to the continuity of the determinant with respect to the two-scale convergence.