A finite-element approach in stream-tube method for solving fluid and solid mechanics problems

This paper presents a theoretical formulation in which the stream-tube method (STM) is examined through a variational approach for solving solid strain and fluid flow problems with finite elements. The analysis considers a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically. Mass conservation is automatically verified by STM. The variational approach leads to eliminate the pressure in fluid problems and avoids to set up a mixed displacement–pressure procedure in the case of incompressible solids. Examples are given for fluid flows, applications and comparisons are also provided in the bending problem in elasticity.     

The reaction of hexamethyl phosphoric triamide (HMPT) with phosphoryl chloride : A reexamination. Application to a novel preparation of BOP reagent for peptide coupling

The reaction of hexamethyl phosphoric triamide with phosphoryl chloride at R.T. gave actually a chlorophosphonium salt. This reaction is illustrated in a novel preparation of BOP reagent for peptide coupling in good conditions.     

Numerical simulation of complex flows of non-Newtonian fluids using the stream tube method and memory integral constitutive equations

In this paper a memory integral viscoelastic equation is considered for simulating complex flows of non-Newtonian fluids by stream tube analysis. A formalism is developed to take into account co-deformational memory equations in a mapped computational domain where the transformed streamlines are parallel and straight. The particle-tracking problem is avoided. Evolution in time and related kinematic quantities involved with a K-BKZ integral constitutive model are easily taken into account in evaluating the stresses. Successive subdomains, the stream tubes, may be considered for computing the main flow in abrupt axisymmetric contractions from the wall to the central flow region. The ‘peripheral stream tube’ close to the duct wall is determined by developing a non-conventional modified Hermite element. A mixed formulation is adopted and the relevant non-linear equations are solved numerically by the Levenberg-Marquardt algorithm. Although the singularity at the section of contraction is not involved explicitly, the results obtained for the peripheral stream tube clearly show the singularity effects and the extent of the recirculating zone near the salient corner. The algorithm is stable even at high flow rates and provides satisfactory solutions when compared with similar calculations in the literature.     

Vibrational Spectra of Anhydrous Lanthanum,Europium, Gadolinium,and Dysprosium Nitrates and Oxinitrates

IR. and Raman spectra of LnONO₃ (50–4,000 cm^?1, Ln?La, Gd, Eu, and Dy) are reported and discussed. The low frequency region of the spectra reflects the cubic structure of these compounds. The dimensions of the cubic unit cells determined by X-Ray powder diagrams are: 12.81 ± 0.05 Å for EuONO₃, 12.69 ± 0.05 Å for GdONO₃, and 12.67 ± 0.05 Å for DyONO₃. The vibrational frequencies of the nitrato group are consistent with a bidentate nitrate of C_2v symmetry. The synthesis of anhydrous Ln (NO₃)₃ (Ln?La, Gd, Eu, and Dy) by dehydration of the corresponding penta- or hexahydrates is described. The IR. and Raman spectra (50-4,000 cm^?1) are analysed. Splitting of the bands point to a complex structure of these compounds. All six vibrational modes of the nitrato group are observed and the data are again consistent with bidentate NO^?₃ moieties. Finally, an analytical control of the purity of Ln (NO₃)₃ is suggested.     

Etude par rmn de31p de la reaction de l'hexamethylphosphotriamide avec le trichlorure de phosphoryle

The reaction of HMPT with POCl₃ was studied by ³¹P NMR at various temperatures and stoechiometries. Progressive substitution of chlorine atoms of phosphoryl chloride by HMPT molecules was observed. Six new species were involved in the system. The main produce was the $\text{1}\text{1}$ adduct, (Me₂N)₃P⁺Cl, O₂PCl₂^?, analogous to Vilsmeier complex.     

A theoretical analysis of unsteady incompressible flows for time-dependent constitutive equations based on domain transformations

In this paper, we propose an analysis that allows calculation of kinematic histories in unsteady problems of continuum mechanics, in relation to the use of memory-integral constitutive equations. Such cases particularly concern flow conditions of processing rheology, requiring evaluation of strain or deformation rate tensors, for viscoelastic incompressible fluids as polymers. In two- and three-dimensional cases, we apply concepts of the stream-tube method (STM) initially given for stationary conditions, where unknown local or global mapping functions are defined instead of classic velocity-pressure formulations, leading to consider the flow parameters in domains where the streamlines and trajectories are parallel straight lines. The approach enables us to provide accurate formulae for evaluating the kinematics histories that can be used later for computing the stresses for a given memory-integral model.     

Two-threshold model for scaling laws of noninteracting snow avalanches

The sizes of snow slab failure that trigger snow avalanches are power-law distributed. Such a power-law probability distribution function has also been proposed to characterize different landslide types. In order to understand this scaling for gravity-driven systems, we introduce a two-threshold 2D cellular automaton, in which failure occurs irreversibly. Taking snow slab avalanches as a model system, we find that the sizes of the largest avalanches just preceding the lattice system breakdown are power-law distributed. By tuning the maximum value of the ratio of the two failure thresholds our model reproduces the range of power-law exponents observed for land, rock, or snow avalanches. We suggest this control parameter represents the material cohesion anisotropy.