The high-energy critical minimum in elastic electron scattering by argon

The position of high-energy critical minimum in elastic electron-argon scattering was investigated both experimentally and theoretically. Differential cross-sections (DCSs) were measured as a function of both incident electron energy (40-150 eV) and scattering angle ( ), in small steps around the critical minimum. The position of the high-energy critical minimum in elastic electron-argon scattering was experimentally found to be at eV and . To cover the energy and angular ranges of the present experiment, relevant relativistic ab initio calculations were carried out, based on the Dirac-Hartree-Fock method with the exchange calculated exactly. Target polarization is described by an ab initio potential taken from relativistic polarized orbital calculations. The calculated position of the high-energy critical minimum is eV, . It was shown that even slight difference of fixed scattering angle close to the critical point could affect significantly the energy dependent DCS. Discussion of behavior of DCS in the vicinity of the critical minimum was performed including convolution analysis in both energy and angle.Received: 31 October 2003, Published online: 20 April 2004PACS: 31.15.Ar Ab initio calculations - 34.80.Bm Elastic scattering of electrons by atoms and molecules     

Analysis of viscoelastic contact with normal compliance,friction and wear diffusionAnalyse d'un problème viscoélastique avec compliance normale,frottement et diffusion d'usure

We consider a quasistatic problem of frictional contact between a viscoelastic body and a moving foundation. The contact is with wear and is modeled by normal compliance and a law of dry friction. The novelty in the model is that it allows for the diffusion of the wear debris over the potential contact surface. Such kind of phenomena arise in orthopaedic biomechanics and influence the properties of joint prosthesis. We derive a weak formulation of the problem and state that, under a smallness assumption on the problem data, there exists a unique weak solution for the model. To cite this article: M. Shillor et al., C. R. Mecanique 331 (2003).     

Modelling electron-N2 scattering in the resonant region

Quantum calculations of the resonant vibrational excitation of N₂ by electron impact are carried out using a model potential for exchange and correlation-polarization forces and exact static interaction. The inelastic process is treated within a coupled channel, space-frame formulation and final cross-sections are tested for convergence within less than of their values. Comparison with the experiments yields very good agreement with the latter data in the resonance region and suggests possible extension to calculations near the threshold openings for rovibrational inelastic processes induced by electron impact.     

Vibrational inelastic electron-H<Subscript>2</Subscript> scattering revisited: numerically converged coupled channels space frame calculations with model interactions

The collisional excitation of the lower vibrational levels of H₂(¹Σ_g⁺) molecules by low-energy electron impact is computed using an empirical model potential and by solving the coupled-channels scattering equations within a space-fixed (SF) frame of reference formulation. Numerically converged partial, integral inelastic and elastic cross-sections are obtained from what is an essentially exact treatment of the dynamics and the results are compared with measurements and with earlier calculations on the same system. The usefulness of the SF method for handling excitation processes at near-threshold collision energies is discussed and analyzed through the calculations of collisional superelastic partial cross-sections down to 10^-2 meV of collision energy.     

Effective Conductivity of Nonlinear Two-Phase Media: Homogenization and Two-Point Padé Approximants

The aim of this paper is a study of the quasilinear transport equation, for instance the stationary heat equation. For periodically microheterogeneous media asymptotic homogenization has been performed with the local problem formulated as a minimization problem. The Golden–Papanicolaou integral representation theorem and some bounds developed for the linear equation have been extended. Two-point Padé approximants have been used to calculate bounds. Examples are also provided.     

Asymptotic method of homogenization of fissured elastic plates

This paper deals with the homogenization of thin elastic plates weakened by periodically distributed fissures. The classical Kirchhoff theory of bending plates admits five different types of unilateral fissures. To derive effective properties of fissured plates we employ the asymptotic method. As a result we obtain five effective hyperelastic plates. An illustrative example concerns the homogenization of the plate with unidirectional fissures parallel to a straight line. The constitutive equation describing the effective plate is found provided that fissures are of the flexural type resembling that observed in reinforced concrete plates in bending.     

Piezoelectricity with polarization gradient: homogenization

The aim of this paper is to perform homogenization of the equation of linear piezoelectricity with the polarization gradient. We assume that the material coefficients are microperiodic. This assumption can be weakened. One can also consider nonuniform homogenization. Then the homogenized (macroscopic) moduli depend on macroscopic variable.