Asymptotic ordination of artificial satellite Hamiltonian

Spatial Agencies’ projects for future artificial satellites continue to grow in number and complexity. These projects need the development of analytical theories in order to place the satellites in the most suitable orbit. The most common technique for constructing analytical theories is the Lie–Deprit method, which requires to expand in series of a small parameter the Hamiltonian of the problem. This expansion is not trivial but, usually, it is made without care. In this paper we provide a unified and systematic framework to get that development in a rigorous way.     

Synthesis of novel ionic polymers containing arsonic acid group

Synthesis of ortho‐ and para‐acryloylaminophenylarsonic acids (o‐AAPHA and p‐AAPHA) monomers and their homopolymers, useful as ion‐exchange materials, are reported. Both the monomers and homopolymers are synthesized with >90% yield. The structures of the new compounds are determined by NMR and FTIR spectroscopy. Molecular weights of the polymers are determined from light scattering measurements and found to be M_w = 38,759 g/mol for o‐AAPHA polymer and M_w = 31,347 g/mol for p‐AAPHA polymer. Good thermal stability of the new compounds derived from their intra‐ or intermolecular hydrogen bondings suggests their applications as proton‐exchange membrane at high temperatures. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1627–1634, 2006     

Interaction between water and polymer chains in poly(hydroxyethyl acrylate) hydrogels

Polymer networks of different cross-linking densities were prepared by copolymerisation of hydroxyethyl acrylate and ethylene glycol dimethacrylate. The average molecular weight between cross-links as well as the polymer chain mobility were characterised by means of dynamic–mechanical spectroscopy. Equilibrium sorption isotherms and the water uptake in immersion in liquid water allowed the determination of the Flory–Huggins interaction parameter between water molecules and polymer chain segments, which decreased with the water activity in the hydrogel and increased with the cross-linking density as a consequence of the hydrophobic character of the cross-linking agent. Dynamic sorption and desorption experiments were used to determine the diffusion coefficient. Received: 11 November 1999 Accepted: 28 July 2000     

Optical study and structure modelling of PPI liquid crystalline dendrimer derivatives

Optical study of two families of poly(propylene imine) (PPI) dendrimers (G = 1–5) are reported. The enlarging of the chain number (generations) of the PPI dendrimer leads to the spectra shift to IR region in solvent until 8 and 19 nm for both families, respectively. The theoretical modelling of the dendrimer structure was performed. The geometric characterization of dendrimer structure demonstrates that the preferable free space for encapsulation is periphery of the PPI dendrimer.     

-convergence of quadratic functionals with oscillating linear perturbations

We explore the Γ-convergence of quadratic functionals perturbed by linear terms with oscillatory coefficients. In particular, we are interested in understanding the interaction between the oscillations of the quadratic part and the linear term. We also look at this issue from the perspective of the associated equations of optimality as in homogenization.     

Wavelength dispersive x‐ray fluorescence spectrometry for the analysis of laser active lanthanides (Ln) in NaT1−xLnx(WO4)2 crystals

Four crystals with nominal compositions, NaLa_0.95Tm_0.05(WO₄)₂ (1.32 wt% of Tm), NaGd_1?xTm_x(WO₄)₂ x = 0.05, 0.07 (1.24 and 1.32 wt% of Tm, respectively) and NaY_0.9Yb_0.1(WO₄)₂ (2.81 wt% of Yb), were analyzed by wavelength dispersive x‐ray fluorescence spectrometry. A procedure for sample preparation was developed using lithium tetraborate as flux to obtain glass disks and to circumvent precipitation problems of lanthanides and tungsten experienced in their dissolution by wet routes. For this purpose three specific calibration standards with pure oxides were prepared for each analyzed element with near to constant W and Na concentrations, so that matrix effects could be properly addressed. The procedure allows measurement of the Tm and Yb concentrations above the determination limits of 0.017 wt% and 0.042 wt% for Tm in the first two crystals, respectively, and of 0.039 wt% of Yb in the last one. Further analyses show an excess with regard to the nominal formula of ≈5 mol% in the total concentration of trivalent ions incorporated to the crystal and some deficiency of Na (≈10 mol%) and W (≈2 mol%) ions. Copyright © 2009 John Wiley & Sons, Ltd.     

New Approaches to the Propagation of Nonlinear Transients in Porous Media

Many problems in regional groundwater flow require the characterization and forecasting of variables, such as hydraulic heads, hydraulic gradients, and pore velocities. These variables describe hydraulic transients propagating in an aquifer, such as a river flood wave induced through an adjacent aquifer. The characterization of aquifer variables is usually accomplished via the solution of a transient differential equation subject to time-dependent boundary conditions. Modeling nonlinear wave propagation in porous media is traditionally approached via numerical solutions of governing differential equations. Temporal or spatial numerical discretization schemes permit a simplification of the equations. However, they may generate instability, and require a numerical linearization of true nonlinear problems. Traditional analytical solutions are continuous in space and time, and render a more stable solution, but they are usually applicable to linear problems and require regular domain shapes. The method of decomposition of Adomian is an approximate analytical series to solve linear or nonlinear differential equations. It has the advantages of both analytical and numerical procedures. An important limitation is that a decomposition expansion in a given coordinate explicitly uses the boundary conditions in such axis only, but not necessarily those on the others. In this article we present improvements of the method consisting of a combination of a partial decomposition expansion in each coordinate in conjunction with successive approximation that permits the consideration of boundary conditions imposed on all of the axes of a transient multidimensional problem; transient modeling of irregularly-shaped aquifer domains; and nonlinear transient analysis of groundwater flow equations. The method yields simple solutions of dependent variables that are continuous in space and time, which easily permit the derivation of heads, gradients, seepage velocities and fluxes, thus minimizing instability. It could be valuable in preliminary analysis prior to more elaborate numerical analysis. Verification was done by comparing decomposition solutions with exact analytical solutions when available, and with controlled experiments, with reasonable agreement. The effect of linearization of mildly nonlinear saturated groundwater equations is to underestimate the magnitude of the hydraulic heads in some portions of the aquifer. In some problems, such as unsaturated infiltration, linearization yields incorrect results.     

Fast prediction of the fatigue behavior of short-fiber-reinforced thermoplastics based on heat build-up measurements: application to heterogeneous cases

Short-fiber-reinforced thermoplastics components for structural applications are usually very complex parts as stiffeners, ribs and thickness variations are used to compensate the quite low material intrinsic stiffness. These complex geometries induce complex local mechanical fields but also complex microstructures due to the injection process. Accounting for these two aspects is crucial for the design in regard to fatigue of these parts, especially for automotive industry. The aim of this paper is to challenge an energetic approach, defined to evaluate quickly the fatigue lifetime, on three different heterogeneous cases: a classic dog-bone sample with a skin-core microstructure and two structural samples representative of the thickness variations observed for industrial components. First, a method to evaluate dissipated energy fields from thermal measurements is described and is applied to the three samples in order to relate the cyclic loading amplitude to the fields of cyclic dissipated energy. Then, a local analysis is detailed in order to link the energy dissipated at the failure location to the fatigue lifetime and to predict the fatigue curve from the thermomechanical response of one single sample. The predictions obtained for the three cases are compared successfully to the Wöhler curves obtained with classic fatigue tests. Finally, a discussion is proposed to compare results for the three samples in terms of dissipation fields and fatigue lifetime. This comparison illustrates that, if the approach is leading to a very relevant diagnosis on each case, the dissipated energy field is not giving a straightforward access to the lifetime cartography as the relation between fatigue failure and dissipated energy seems to be dependent on the local mechanical and microstructural state.