Electron impact ionization cross sections of beryllium and beryllium hydrides

We report calculated electron impact ionization cross sections (EICSs) for beryllium (Be) and some of its hydrides from the ionization threshold to 1 keV using the Deutsch-Märk (DM) and the Binary-Encounter-Bethe (BEB) formalisms. The positions of the maxima of the DM and BEB cross sections are very close in each case while the DM cross section values at the maxima are consistently higher. Our calculations for Be are in qualitative agreement with results from earlier calculations (convergent close-coupling, R matrix, distorted-wave and plane-wave Born approximation) in the low energy region. For the various beryllium hydrides, we know of no other available data. The maximum cross section values for the various compounds range from 4.0 × 10^?16 to 9.4 × 10^?16 cm² at energies of 44 to 56 eV for the DM cross sections and 3.0 × 10^?16 to 5.4 × 10^?16 cm² at energies of 40.5 to 60 eV for the BEB cross sections.     

Kinetics of the conversion reaction of gypsum with ammonium carbonate

The reactivity of flue gas desulphurization gypsum with ammonium carbonate has been studied in the temperature range (20–50) °C. Mechanism of this reaction was suggested and the kinetics parameters characterizing the reaction were determined. A mathematical model suitable for the prediction of the conversion of gypsum was proposed. The reaction is of the second order. Influence of the size of gypsum particles on the relationship between the surface and volume of the particles is not significant. From the obtained experimental results, it follows that the reaction does not proceed at the surface of the solid gypsum particles, but in the liquid phase between dissolved gypsum and ammonium carbonate. The diffusion of the dissolved gypsum through the liquid film formed at the surface of the solid gypsum particles is the rate-limiting step of the conversion reaction.     

Self-condensation of 2-(ethoxalylmethyl)chromones into new derivatives of isotetronic acid

2-(Ethoxalylmethyl)chromones undergo dimerization to dichromonyl derivatives of isotetronic acid in 62–89% yields on refluxing with 2,3-diaminopyridine in ethanol for 1–2 h.     

Localized strain waves in a nonlinearly elastic conducting medium interacting with a magnetic field

The influence of magnetic field on the generation of a localized wave in a nonlinearly elastic conducting medium is considered. The evolution equation for describing the wave beam propagation in the medium is derived. It is shown that the wave beam parameters depend on the value of the external magnetic field and on the field orientation in space.     

Mathematical modeling of volumetric material growth

Growth (resp. atrophy) describes the physical processes by which a material of solid body increases (resp. decreases) its size by addition (resp. removal) of mass. In the present contribution, we propose a sound mathematical analysis of growth, relying on the decomposition of the geometric deformation tensor into the product of a growth tensor describing the local addition of material and an elastic tensor, which is characterizing the reorganization of the body. The Blatz-Co hyperelastic constitutive model is adopted for an isotropic body, satisfying convexity conditions (resp. concavity conditions) with respect to the transformation gradient (resp. temperature). The evolution law for the transplant is obtained from the natural assumption that the evolution of the material is independent of the reference frame. It involves a modified Eshelby tensor based on the specific free energy density. The heat flux is dependent upon the transplant. The model consists of the constitutive equation, the energy balance, and the evolution law for the transplant. It is completed by suitable boundary conditions for the displacement, temperature and transplant tensor. The existence of locally unique solutions is obtained, for sufficiently smooth data close to the stable equilibrium. The question of the global existence is examined in the simplified situation of quasistatic isothermal equations of linear elasticity under the assumption of isotropic growth.