Spectrofluorimetric determination of phenyl-<Emphasis Type="Italic">β</Emphasis>-naphthylamine used as rubber antioxidant

Phenyl-74w86v/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-naphthylamine (PBN) used as rubber antioxidant was found to have native fluorescence. A spectrofluorimetric method for determination of PBN in multicomponent mixtures of polymer additives is described. The apparent excitation and fluorescence wavelengths used are 348 and 413.5 nm, respectively. Maximum fluorescence intensity is obtained by irradiating PBN dissolved in ethanol, at room temperature. The fluorescence varies linearly with the concentration of PBN in the range of 0.04–4 74w86v/xxlarge956.gif" alt="mgr" align="MIDDLE" BORDER="0">g mL^–1. The accuracy and precision of the method are reported.     

Excimer-laser-induced ablation of the high-T c superconductor Bi-Ca-Sr-Cu-O

The ablation of ceramic Bi-Ca-Sr-Cu-O by XeCl-excimer-laser projection has been investigated. In both air and vacuum, etching commences at about 2.4 J/cm² and then increases with fluence within the regime investigated ( <) 20 J/cm²). At 10 J/cm² the respective etch rates are around 1 m/pulse and 1.6 m/pulse.     

The minimum free energy for an electromagnetic conductor

We consider the linear theory of the electromagnetism characterized by a constitutive equation for the current density with memory effects. We find in the frequency domain a first expression of the minimum free energy, which is the maximum recoverable work we can obtain from a given state of the material. By using another equivalent formulation of the minimum free energy, we give the explicit formulae for the particular case of a discrete spectrum model material response.     

Instability of solitary waves on Euler’s elastica

Stability of solitary waves in a thin inextensible and unshearable rod of infinite length is studied. Solitary-wave profile of the elastica of such a rod without torsion has the form of a planar loop and its speed depends on a tension in the rod. The linear instability of a solitary-wave profile subject to perturbations escaping from the plane of the loop is established for a certain range of solitary-wave speeds. It is done using the properties of the Evans function, an analytic function on the right complex half-plane, that has zeros if and only if there exist the unstable modes of the linearization around a solitary-wave solution. The result follows from comparison of the behaviour of the Evans function in some neighbourhood of the origin with its asymptotic at infinity. The explicit computation of the leading coefficient of the Taylor series of the Evans function near the origin is performed by means of the symbolic computer language. Received: April 6, 2004; revised: December 12, 2004     

A Chebyshev spectral collocation method for solving Burgers’-type equations

In this paper, we elaborated a spectral collocation method based on differentiated Chebyshev polynomials to obtain numerical solutions for some different kinds of nonlinear partial differential equations. The problem is reduced to a system of ordinary differential equations that are solved by Runge–Kutta method of order four. Numerical results for the nonlinear evolution equations such as 1D Burgers’, KdV–Burgers’, coupled Burgers’, 2D Burgers’ and system of 2D Burgers’ equations are obtained. The numerical results are found to be in good agreement with the exact solutions. Numerical computations for a wide range of values of Reynolds’ number, show that the present method offers better accuracy in comparison with other previous methods. Moreover the method can be applied to a wide class of nonlinear partial differential equations.     

Global existence and decay estimate of solutions to magneto-micropolar fluid equations

We are concerned with magneto-micropolar fluid equations (1.3)–(1.4). The global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the magneto-micropolar-Navier–Stokes (MMNS) system, we obtain global existence and large time behavior of solutions near a constant states in ${\mathbb{R}}^3$. Appealing to a refined pure energy method, we first obtain a global existence theorem by assuming that the $H^3$ norm of the initial data is small, but the higher order derivatives can be arbitrary large. If the initial data belongs to homogeneous Sobolev norms ${\dot{H}}^{?s}$ $(0\le s<\frac{3}{2})$ or homogeneous Besov norms ${\dot{B}}_{2,\infty }^{?s}$ $(0<s\le \frac{3}{2})$, we obtain the optimal decay rates of the solutions and its higher order derivatives. As an immediate byproduct, we also obtain the usual $L^p?L^2$ $(1\le p\le 2)$ type of the decay rates without requiring that the $L^p$ norm of initial data is small. At last, we derive a weak solution to (1.3)–(1.4) in ${\mathbb{R}}^2$ with large initial data.     

A compatible‐incompatible decomposition of symmetric tensors in Lp with application to elasticity

In this paper, we prove the Saint‐Venant compatibility conditions in L^p for p∈(1,+∞), in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in L^p are provided. We also use the Helmholtz decomposition in L^p to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence‐free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami‐type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where 1 < p < 2. This justifies the need to generalize and prove these rather classical results in the Hilbertian case (p = 2), to the full range p∈(1,+∞). Copyright © 2015 John Wiley & Sons, Ltd.     

A priori time regularity estimates and a simplified proof of existence in perfect plasticity

We revisit the time‐incremental method for proving existence of a quasistatic evolution in perfect plasticity. We show how, as a consequence of a priori time regularity estimates on the stress and the plastic strain, the piecewise affine interpolants of the solutions of the incremental minimum problems satisfy the conditions defining a quasistatic evolution up to some vanishing error. This allows for a quicker proof of existence: furthermore, this proof bypasses the usual variational reformulation of the problem and directly tackles its original mechanical formulation in terms of an equilibrium condition, a stress constraint, and the principle of maximum plastic work.     

Structural stability and convergence in thermoelasticity and heat conduction with relaxation times

This article investigates the structural stability in several thermomechanics and heat conduction theories as well as the convergence of these theories to the classical versions of the thermoelasticity and heat conduction. We consider first the Lord–Shulman theory of thermoelasticity. We study the structural stability with respect to the relaxation parameter and the convergence of the solutions when the relaxation parameter tends to zero. Second we study the dual-phase-lag theory. Assuming that the relaxation parameters are small we consider the Taylor series in which only the first powers of the phase-lag parameters are retained. In this situation we consider the heat equation and study the structural stability and the convergence with respect to the phase-lag of the gradient of temperature. In the last part of the article, we consider the thermoelastic theory proposed by Chandrasekharaiah and Tzou. We study the structural stability and the convergence with respect to both relaxation parameters that describe this theory     

Thermo-chemical modelling of the formation of a composite material

We consider a composite material composed of carbon or glass fibres included in a resin which becomes solid when it is heated up (the reaction of reticulation).

A mathematical model of the cure process is given by a kinetic equation describing the evolution of the reaction of reticulation coupled with the heat equation. The geometry of the composite material is periodic, with a small period ? >0, thus we get a coupled system of nonlinear partial differential equations.

First we prove the existence and uniqueness of a solution by using a fixed point theorem and we obtain a priori estimates. Then we derive the homogenized problem which describes the macroscopic behaviour of the material. We prove the convergence of the solution of the problem to the solution of the homogenized problem when ? tends to zero as well as the estimates for the difference of the exact and the approximate solutions.