A comparison of different contractions for molecular calculations with gaussian-type functions

The effect of various possible contractions of a gaussian basis set is investigated for atomic and molecular calculations. The gaussian basis set used consists of 11s-type functions and 7p-type functions. Atomic calculations for the atoms Li to F are reported with fourteen different contractions of the s orbitals. The effect of the same contractions has also been investigated for molecular calculations of LiH, BH, CH₂, NH ₂ ^– , H₂O, and FH, together with the effect of the contraction for the p orbitals and for the s orbitals of the hydrogen atom. It is shown that the contraction in itself does not affect seriously the quality of a molecular calculation, but that a wrong choice of the contraction can produce a poor result.

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Zusammenfassung Der Einfluß der verschiedensten Kontraktionen einer Basis von Gauß-Funktionen bei Berechnung atomarer oder molékularer Systeme wird untersucht. Diese Basis besteht zunächst aus 11 s-Funktionen und 7 p-Funktionen. 14 verschiedene Kontraktionen werden für die Atome Li bis F sowie für die Moleküle LiH, BH, CH₂, NH ₂ ^– , H₂O und FH getestet. Wie zu erwarten wird die Genauigkeit nicht wesentlich beeinflußt, solange man nur die richtigen Kontraktionen wählt.

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Résumé On étudie l'effet des différentes contractions possibles d'une base de fonctions gaussiennes dans le cas d'atomes et de molécules. La base de fonctions gaussiennes comprend 11 fonctions du type s et 7 fonctions du type p. On donne les résultats de quatorze différentes contractions des orbitales s pour les atomes du Li à F ainsi que pour les molécules LiH, BH, CH₂, NH _- ² , H₂O et FH. L'effet de la contraction des orbitales p ainsi que des orbitales s des atomes d'hydrogène est également discuté pour les molécules CH₂ et H₂O. On montre que la contraction par elle-même n'affecte pas sensiblement les résultats obtenus a condition d'effectuer un choix judicieux parmi les contractions possibles.

     

Lamb wave reflection at the free edge of a plate

This study concentrates on the reflection of Lamb waves at the free end of a plate. The conversion phenomena are examined in detail over a large frequency range and the energy conversion coefficients are obtained by three different ways: theoretically, numerically (finite element method) and experimentally. The experimental energy determination is obtained from the measurement of the plate normal displacements, by mean of a laser interferometer. All results are in relatively good agreement and the energy balance between incident and reflected waves is discussed in each case.     

Isotopic study of post-anthesis foliar incorporation of sulphur and nitrogen in wheat

Nitrogen (N) and sulphur (S) supplies have a strong influence on the quality and quantity of wheat storage proteins, which play an important role in the bread-making process. In order to relate the incorporation and distribution of foliar N and S fertilisers at the post-anthesis stage to the quality of wheat, 15N and 34S isotopes were used as tracers. The incorporation of these tracers in different plant parts (leaves, stems, ears) and in each storage protein fraction (gliadins, HMW and LMW glutenin subunits) was determined by isotopic ratio mass spectrometry coupled with an elemental analyser (EA-IRMS). By this means, the true recovery coefficient of N and S (TRCNfertiliser and TRCSfertiliser) and the N and S derived from fertilisers (Ndff and Sdff) could be determined. The TRCNfertiliser and TRCSfertiliser values of the different plant parts provide evidence of the applied N and S assimilation and translocation from wheat leaves to the seeds. The determination of Ndff and Sdff incorporated into storage proteins shows the efficiency and the influence of N and S incorporation into each storage protein fraction. Moreover, a favourable stage for fertiliser application can be determined by the TRCNfertiliser values in the grain and in the whole plant. The fertilisers enriched in stable isotope used in the culture techniques can be a means of understanding the effectiveness of fertilisers in the expression of wheat quality.     

Three-and two-dimensional calculations for the interface anisotropy dependence of magnetic properties of exchange-spring Nd2Fe(14)B/α-Fe multilayers with out-of-plane easy axes

Hysteresis loops,energy products and magnetic moment distributions of perpendicularly oriented Nd2Fe(14)B/α-Fe exchange-spring multilayers are studied systematically based on both three-dimensional(3D)and one-dimensional(1D)micromagnetic methods,focused on the influence of the interface anisotropy.The calculated results are carefully compared with each other.The interface anisotropy effect is very palpable on the nucleation,pinning and coercive fields when the soft layer is very thin.However,as the soft layer thickness increases,the pinning and coercive fields are almost unchanged with the increment of interface anisotropy though the nucleation field still monotonically rises.Negative interface anisotropy decreases the maximum energy products and increases slightly the angles between the magnetization and applied field.The magnetic moment distributions in the thickness direction at various applied fields demonstrate a progress of three-step magnetic reversal,i.e.,nucleation,evolution and irreversible motion of the domain wall.The above results calculated by two models are in good agreement with each other.Moreover,the in-plane magnetic moment orientations based on two models are different.The 3D calculation shows a progress of generation and disappearance of vortex state,however,the magnetization orientations within the film plane calculated by the 1D model are coherent.Simulation results suggest that negative interface anisotropy is necessarily avoided experimentally.     

A Control Volume Radial Basis Function Techniques for the Numerical Simulation of Saturated Flows in Semi-confined Aquifer

In this work, a Control Volume Radial Basis Function technique (CV-RBF) is adapted to solve ground water flow in the saturated zone of the semi-confined aquifer. The CV-RBF method differs from classical CV methods in the way that the flux at the cell surfaces is computed. A local RBF interpolation of the field variable is performed at the centres of the cell being integrated and its neighbours. This interpolation is then used to reconstruct the solution and its gradient in the integration points which support the flux computation. In addition, it is required that such interpolation satisfies the governing equation in a certain number of points placed around the cell centres. In this way, the local interpolations become equivalent to local boundary-value problems. The CV-RBF method is combined with a local remeshing technique in order to track the phreatic surface, where the gradients required to satisfy the kinematic condition are computed by the same local RBF interpolations used for the flux computation. The proposed numerical approach is validated in a series of three-dimensional groundwater flow problems where the operations of recharging and extracting water from a semi-confined aquifer are modelled.     

Numerical simulation of two‐dimensional Kelvin–Helmholtz instability using weakly compressible smoothed particle hydrodynamics

The growth of the Kelvin–Helmholtz instability generated at the interface between two ideal gases is studied by means of a Smoothed Particle Hydrodynamics (SPH) scheme suitable for multi‐fluids. The SPH scheme is based on the continuity equation approach where the densities of SPH particles are evolved during the simulation, in combination with a momentum equation previously proposed in the literature. A series of simulations were carried out to investigate the influence of viscosity, smoothing, the thickness of density and velocity transition layers. It was found that the effective viscosity of the presented results are strongly dependent on the artificial viscosity parameter α_AV, with a linear dependence of 0.15. The utilisation of a viscosity switch is found to significantly reduce the spurious viscosity dependence to 1.68 × 10^?4 and generated qualitatively improved behaviour for inviscid fluids. The linear growth rate in the numerical solutions is found to be in satisfactory agreement with analytical expectations, with an average relative error 〈η_smooth〉=13%. In addition, the role played by velocity and density transition layers is also in general agreement with the analytical theory, except for the sharp‐velocity, finite‐density gradient cases where the larger growth rate than the classical growth rate is expected. We argue the inherited smoothing properties of the velocity field during the simulations are responsible for causing this discrepancy. Finally, the SPH results are in good agreement for finite velocity and density gradient scenarios, where an average relative error of 〈η_smooth〉=11.5% is found in our work. Copyright © 2015 John Wiley & Sons, Ltd.     

Flax fibers: assessing the non-cellulosic polysaccharides and an approach to supramolecular design of the cell wall

Due to their particular tensile properties and composition, flax cellulosic fibres are widely used in various applications and are important in the stem architecture, as a source of mechanical support. Here, we have examined how various chemical extractions of cell-wall polysaccharides might improve our understanding of the structure and composition of these fibres. A set of chemical extractions, which had previously been independently studied on fibres of different origins and by different laboratories, was run on the same batch of technical fibres, variety Eden, and the released non-cellulosic polysaccharides were analyzed in terms of sugar composition and size exclusion chromatography. No single-step protocol was able to extract all the non-cellulosic polysaccharides estimated to be in the range of 130–140 mg per g of dry fibres. The major polymers consisted of rhamnogalacturonan and glucomannan, while the minor ones were xyloglucan and xylan. Several types of stepwise extractions helped to elucidate the subfractions of each polymer that are differently retained within cell wall. From our data, we have pointed out a new model which might help to approach the supramolecular design of the flax cellulosic fibres and, afterwards, the relationships between their chemical composition and their mechanical properties.     

Numerical Simulation of Coherent Structures over Plant Canopy

This paper reports large eddy simulations of the interaction between an atmospheric boundary layer and a canopy (representing a forest cover). The problem is studied for a homogeneous configuration representing the situation encountered above a continuous forest cover, as well as for a heterogeneous configuration representing the situation similar to an edge or a clearing in a forest. The numerical results reproduces correctly all the main characteristics of this flow as reported in the literature: the formation of a first generation of coherent structures aligned transversally with the wind flow direction, the reorganization and the deformation of these vortex tubes into horse-shoe structures. The results obtained when introducing a discontinuity in the canopy (reproducing a clearing or a fuel break in a forest), are compared with the experimental data collected in a wind tunnel; here, the results confirm the existence of a strong turbulence activity inside the canopy at a distance equal to 8 times the height of the canopy, referenced in the literature as the Enhance Gust Zone (EGZ) characterized by a local peak of the skewness factor.