Investigation of the magnetic properties of the Gd1−xErx alloy system in the x < 0.62 composition range

The magnetic properties of the Gd---Er system (with erbium concentrations ranging from 0 to 62 at%) were investigated at temperatures between 4.2 and 350 K under external magnetic fields up to 1 T. The results show that, similar to other rare-earth systems, simple ferromagnetism prevails for concentrations with a de Gennes factor G higher than about 11.5 (≈ 30 at % Er) while complex magnetic structures are present for higher Er concentrations (G ≤ 11.5. The magnetic transition temperature decreases with increasing Er content, showing good agreement with phenomenological expectations. In the paramagnetic region, the Curie constant of the alloy corresponds to the linear combination of the constituent elements' contribution, thus proving that both Gd and Er maintain their individual magnetic moments. From magnetization data below the transition, the change in magnetic entropy for a 1 T field was calculated and this showed distinct differences between ferromagnetic-paramagnetic transitions and antiferromagnetic transitions. The Landau theory of second-order phase transitions can be well applied for evaluating the thermodynamic transition temperature and the specific heat anomaly in the ferromagnetic alloys but it fails for the more complex structures if the applied field is not far higher than the critical field. The magnetic entropy change displays well defined peaks at the transition temperature for both ferromagnetic and antiferromagnetic alloys. There is an indication that the spin-reorientation transition occurring in alloys with higher Er concentrations is also coupled with significant magnetic entropy changes.     

Energy dependence of multiplicity in proton-nucleus collisions and models of multiparticle production

This is a continuation of our earlier investigation (Gurtuet al 1974Phys. Lett. 50 B 391) on multiparticle production in proton-nucleus collisions based on an exposure of emulsion stack to 200 GeV/c beam at the NAL. It is found that the ratioR _em = 〈n _s〉/〈n _ch〉, where 〈n _ch〉 is the charged particle multiplicity in pp-collisions, increases slowly from about 1 at 10 GeV/c to 1·6 at 68 GeV/c and attains a constant value of 1·71 ± 0·04 in the region 200 to 8000 GeV/c. Furthermore,R _em = 1·71 implies an effectiveA-dependence ofR _A =A ^0.18,i.e., a very weak dependence. Predictions ofR _em on various models are discussed and compared with the emulsion data. Data seem to favour models of hadron-nucleon collisions in which production of particles takes place through adouble step mechanism,e.g., diffractive excitation, hydrodynamical and energy flux cascade as opposed to models which envisage instantaneous production.     

Glass Transition (T g) And Ftir Study Of Na2O-CuO-Bi2O3-P2O5 Glasses

(40?x)Na₂O-xCuO-10Bi₂O₃-50P₂O₅ glasses (0 h x h 40) were prepared and studied. Their density, molar volume, glass transition temperature and IR spectroscopy have been investigated in order to understand the structural role of Bi₂O₃ and CuO in these glasses. In the sodium bismo-phosphate glass, the structures consist of some phosphate chains linked together through P-O-Bi bonds. When copper oxide is added to sodium bismo-phosphate glass, phosphate chains are depolymerised by the incorporation of Cu through P-O-Cu bonds. The former bonds are the origin of the partial glass forming ability of Bi³⁺ and Cu²⁺.     

Experimental and asymptotic study of nonspherical bubble collapse

Observations of the behavior of spark-generated bubbles in the vicinity of solid and free boundaries are described. In all cases, the formation of a reentering region (microjet or constriction) occurs on the part of the bubble which has the most freedom of motion. Drag-reducing polymer additives are seen to significantly affect bubble departure from sphericity. Their presence weakens the influence of nearby solid boundaries, and seems to enhance that of a free surface. The relative importance of the acoustic pulses emitted during successive implosions and rebounds of the bubble is seen to be modified by the proximity of a solid wall. When the radius of the bubble is small compared to its distance from the closest boundary, a theoretical approach, using matched asymptotic expansion, is applied successfully to describe the nonspherical bubble behavior and the pressure field. This method is extended to the case of a multi-bubble system. It is very useful in determining the limiting distances of interaction. In the case of a free surface this distance is less than two bubble diameters. When applied to a solid wall covered with an elastic coating of finite thickness, or to a two-liquid interface this technique shows a selection process: bubbles closer than a limiting distance to the boundary are repelled during their collapse. The collapse is toward the boundary only for bubbles beyond this distance and is therefore less damaging.     

Selective interaction of lower rim calix[4]arene derivatives and bivalent cations in solution. Crystallographic evidence of the versatile behavior of acetonitrile in lead(II) and cadmium(II) complexes

The interaction of lower rim calix(4)arene derivatives containing ester (1) and ketone (2) functional groups and bivalent (alkaline-earth, transition- and heavy-metal) cations has been investigated in various solvents (methanol, N,N-dimethylformamide, acetonitrile, and benzonitrile). Thus, 1H NMR studies in CD3OD, C3D7NO, and CD3CN show that the interaction of these ligands with bivalent cations (Mg2+, Ca2+, Sr2+, Ba2+, Hg2+, Pb2+, Cd2+) is only observed in CD3CN. These findings are corroborated by conductance measurements in these solvents including benzonitrile, where changes upon the addition of the appropriate ligand (1 or 2) to the metal-ion salt only occur in acetonitrile. Thus, in this solvent, plots of molar conductance against the ligand/metal cation ratio reveal the formation of 1:1 complexes between these ligands and bivalent cations. Four metal-ion complex salts resulting from the interaction of 1 and 2 with cadmium and lead, respectively, were isolated and characterized by X-ray crystallography. All four structures show an acetonitrile molecule sitting in the hydrophobic cavity of the ligand. The mode of interaction of the neutral guest in the cadmium(II) complexes differs from each other and from that found in the lead(II) complexes and provides evidence of the versatile behavior of acetonitrile in binding processes involving calix(4)arene derivatives. The thermodynamics of complexation of these ligands and bivalent cations in acetonitrile is reported. Thus, the selective behavior of 1 and 2 for bivalent cations is for the first time demonstrated. The role of acetonitrile in the complexation process in solution is discussed on the basis of 1H NMR and X-ray crystallographic studies. It is suggested that the complexation of 1 and 2 with bivalent cations is likely to involve the ligand-solvent adducts rather than the free ligand. Plots of complexation Gibbs energies against the corresponding data for cation hydration show a selectivity peak which is explained in terms of the predominant role played by cation desolvation and ligand binding energy in complex formation involving metal cations and macrocycles in solution. A similar peak is found in terms of enthalpy suggesting that for most cations (except Mg2+) the selectivity is enthalpically controlled. The ligand effect on the complexation process is quantitatively assessed. Final conclusions are given highlighting the role of the solvent in complexation processes involving calix(4)arene derivatives and metal cations.     

Solvation effect of guest, supramolecular host, and host-guest compounds on the thermodynamic selectivity of calix(4)arene derivatives and soft metal cations

This paper reports thermodynamic data for the transfer of calixarene derivatives and their metal-ion complexes in dipolar aprotic solvents. These data are used to assess the effect of solvation of these compounds on the selective complexation shown by these macrocycles for soft metal cations in different media. Thus, solubilities and derived Gibbs energies of solution of 5,11,17,23-tetra-tert-butyl[25,27-bis(hydroxyl)-26,28-bis(ethylthioethoxy)]calix(4)arene, 1, and 5,11,17,23-tetra-tert-butyl-[25,27-bis(ethylenethanoate)-26,28-bis(ethylthioethoxy)]-calix(4)arene, 2, in various solvents at 298.15 K are reported. Solvation of these ligands in one medium relative to another is analyzed from their standard transfer Gibbs energies using acetonitrile as the reference solvent. These data are combined with transfer enthalpies (derived from standard solution enthalpies obtained calorimetrically) to calculate the corresponding entropies of transfer of these calix(4)arene derivatives from acetonitrile to methanol and N,N-dimethylformamide. As far as the metal-ion salts (silver and mercury) in their free and complex forms are concerned, standard solution enthalpies were determined in acetonitrile, methanol, and N,N-dimethylformamide. These data are used to derive their transfer enthalpies from one medium to another. It is concluded that the extent of complexation of these macrocycles with soft metal cations is controlled by not only the solvation changes that the free cation undergoes in moving from one medium to another but also those for the ligand and its complex cation in these solvents.     

A non-conformal eXtended Finite Element approach: Integral matching Xfem

This work is dedicated to the mathematical and numerical analysis of a new Xfem approach: the integral maching Xfem. It is known that the quality of the approximation and the convergence rate of Xfem type methods is broadly influenced by the transition layer between the singular enrichment area and the rest of the domain. In the presented method, this transition layer is replaced by an interface associated with an integral matching condition of mortar type. We prove an optimal convergence result for such a non-conformal approximation method and we perform some numerical experiments showing the advantages of the integral matching Xfem with respect to former Xfem approaches.     

Détermination de la résonance de Bragg et des largeurs des bandes interdites par le modèle d'onde plane corrigéDetermination of the Bragg resonance and line width of forbidden bands using the corrected plane wave model

During the interaction of the swell with a sea bottom composed of a set of steps, using the model of plane wave corrected by the effective length: (1) We determine the exact position of the Bragg resonance in case of a periodic bottom or containing a periodic part; (2) The determination of forbidden band widths is brought back to the study of the sign of the discriminant of the polynomial characteristic of the matrix of transfer of the generating motive of the periodic part of the bottom; (3) One can increase the width of the forbidden band while using some slightly increasing or decreasing length steps. To cite this article: S. Naasse et al., C. R. Mecanique 331 (2003).     

Advanced lattice Boltzmann scheme for high-Reynolds-number magneto-hydrodynamic flows

Is the lattice Boltzmann method suitable to investigate numerically high-Reynolds-number magneto-hydrodynamic (MHD) flows? It is shown that a standard approach based on the Bhatnagar–Gross–Krook (BGK) collision operator rapidly yields unstable simulations as the Reynolds number increases. In order to circumvent this limitation, it is here suggested to address the collision procedure in the space of central moments for the fluid dynamics. Therefore, an hybrid lattice Boltzmann scheme is introduced, which couples a central-moment scheme for the velocity with a BGK scheme for the space-and-time evolution of the magnetic field. This method outperforms the standard approach in terms of stability, allowing us to simulate high-Reynolds-number MHD flows with non-unitary Prandtl number while maintaining accuracy and physical consistency.