Euler configurations and quasi-polynomial systems

Consider the problem of three point vortices (also called Helmholtz’ vortices) on a plane, with arbitrarily given vorticities. The interaction between vortices is proportional to 1/r, where r is the distance between two vortices. The problem has 2 equilateral and at most 3 collinear normalized relative equilibria. This 3 is the optimal upper bound. Our main result is that the above standard statements remain unchanged if we consider an interaction proportional to r ^b, for any b < 0. For 0 < b < 1, the optimal upper bound becomes 5. For positive vorticities and any b < 1, there are exactly 3 collinear normalized relative equilibria. The case b = −2 of this last statement is the well-known theorem due to Euler: in the Newtonian 3-body problem, for any choice of the 3 masses, there are 3 Euler configurations (also known as the 3 Euler points). These small upper bounds strengthen the belief of Kushnirenko and Khovanskii [18]: real varieties defined by simple systems should have a simple topology. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.     

X-ray diffuse scattering from incommensurable structures

X-Ray diffuse scattering from a series of examples where the reason for the existence of incommensurable features is fairly well understood, is described. They include in particular non stoichiometric compounds such as [DIPS Φ₄(l₃)0.76] and such as intercalated graphite RbC₂₄. and quasi one dimensional conductors. A particular emphasis is given on various 1 - D conductors and to the relation of the incommensurability to the characteristics of the electron conduction bands.     

Résolution des équations de dispersion–diffusion en présence de forts gradientsResolution of advection–diffusion equation in presence of sharp gradient

In order to resolve the convection terms in the simulation of coastal flows, we propose a numerical method based on the Total Variation Diminishing scheme completed with the Artificial Compression Method to reduce the artificial diffusion and to sharpen the tracer profile in strong gradient regions. This method was applied successfully at discontinuous regions, but out of these regions a limitation of its application is necessary. An application is made to estimate the width of the fresh water band in the Eastern English Channel. To cite this article: C. Sart et al., C. R. Mecanique 330 (2002) 159–165.     

A First Insight in the Mechanisms Involved in the Self-Assembly of 2D-Hexagonal Templated SiO2 and TiO2 Mesostructured Films During Dip-Coating

Since mesoporous materials can be prepared by combining the sol-gel chemistry and the structuring effect of surfactants, they have attracted attention for application in various high technology fields. The present work deals with the analyses of the mechanisms involved in the formation of SiO₂ and TiO₂ highly organised 2D-hexagonal meso-structured films using Brij 58 as surfactant. The preparation of such films by dip-coating involves rapid evaporation which makes the different steps difficult to control. Simultaneous in-situ SAXS (synchrotron) and interferometry analyses have been performed to get a first understanding of the self-assembly process. SiO₂ and TiO₂ materials have a different chemical reactivity (kinetics and coordination aspects). However, we show that the mechanisms involved during dip-coating are quite similar : the self-assembly leading to the organised phase takes place at a final stage of the drying process, involves the formation of a disorganised intermediate phase and depends also on the presence of micellar interfaces in addition to film/air and film/substrate interfaces.     

Détermination par RMN 1H et 13C de la Conformation Favorisée des Ozonides d'Acènes

The preferred conformation of 9,10-dimethylanthracene ozonide has been established by ¹³C and ¹H NMR. Results hold for other anthracenic ozonides such as those of 9,10-dimethoxyanthracene and anthracene. The latter compound, resulting from the ozonolysis of anthracene, has for the first time been shown to exist in solution.     

Magnetic moments of the 12+ isomeric states in 194, 196, 198Pb

The g-factor of the 12⁺ isomeric state in lead isotopes with A = 194, 196, 198 was measured using the time-differential perturbed angular distribution method (TDPAD). The values obtained are respectively g(194) = ?0.158(6); g(196) = ?0.157(7); g(198) = ?0.144(11). A more precise determination of the 12⁺ level half-life is also made. The g-factprs of these nuclear states, which are described with v(i_{$\text{13}\text{2}$})^?2 as the main configuration, are surprisingly constant over a large mass range (between A = 206 and 194). A core polarization analysis explains this trend: the polarization induced on neutrons in i_{$\text{13}\text{2}$} orbit decreases with the mass number A (blocking effect), but a compensation is provided by the other spin-orbit partners f_{$\text{7}\text{2}$}-f_{$\text{5}\text{2}$} and P_{$\text{3}\text{2}$}-P_{$\text{1}\text{2}$}.     

Experimental determination and modelization of a unique phase diagram: solid solutions of antiferromagnetic organometallic radical cation salts

The physical properties of paramagnetic Mo(V) organometallic radical cation salts, , are investigated through the study of two series of solid solutions incorporating two kinds of anions ( or ). The combination of EPR and X-ray diffraction is used to specify the nature of the structural phase transitions which occur in the paramagnetic phase and to determine the corresponding ( T , x ) phase diagrams. Finally, antiferromagnetic resonance is studied to probe the low temperature antiferromagnetic ground state. In the last part of the paper, the observed complex phase diagram is analyzed by considering a compressible model with at least two independent modes of compression. We conclude that the larger compressibilities are associated with the smaller anions. Received 5 August 1998     

Phase proportioning in CuAlBe shape memory alloys during thermomechanical loadings using electric resistance variation

The microstructure of shape memory alloys changes with the thermomechanical history of the material. During thermomechanical loading, austenite, thermally-induced martensite or stress-induced martensite can be simultaneously present in the material. In applications integrating SMA parts, utilization conditions seriously affect the microstructure and can generate macroscopic strain or stress. Consequently, during thermomechanical loadings, it is important to be able to proportion the different phases and consequently to understand the kinetic transformation. This is very useful in the development of constitutive equations. This study shows, by a series of tests, that the proposed experimental method, based on the measurement of the variation of electric resistance of CuAlBe wires, permits to determine the volume fraction of the different phases present in the material (i.e., austenite, stress-induced martensite and thermally-induced martensite). The proposed method is applied to the most common thermomechanical behavior met in engineering applications of shape memory alloys: pseudoelasticity, pseudoplasticity, recovery-stress and stress-assisted two-way shape memory effect. The proportioning method based on a mixture law integrating the resistivity of pure phases present in the SMA is first performed on different two-phase mixture cases and then applied to a three phase mixture case.