Utilisation de la phase stationnaire pour localiser la provenance du bruit sur l'axe d'une structure élastique à symétrie de révolutionUse of the stationary phase method to localize the source of noise on the axis of an axisymmetric elastic structure

Consider the problem numbered (1) in the text. Along the axis, the pressure may be expressed as a combination of axisymmetric modes only. For high wave numbers, the method of stationary phase may be used to show that the pressure on the axis comes only from the vicinities of a few parallels. Generally, only the parallel constituting the points nearest to this axis point is to be considered. For low circumferential mode numbers (especially $n=0$), the curvature greatly influences the wavelength of the modes of the structure in vacuo: thus, the method of stationary phase can be applied, for most aeronautical airborne structures, even from the first axisymmetric mode and not only above the coincidence frequency. Using an expression established earlier, we can give an expression for the pressure on the axis of an axisymmetric enclosure. To cite this article: D. Brenot, C. R. Mecanique 334 (2006).     

Large solutions to the Monge–Ampère equations with nonlinear gradient terms: Existence and boundary behavior

In this paper, we obtain conditions about the existence and boundary behavior of (strictly) convex solutions to the Monge–Ampère equations with boundary blow-up

$\det ?D^{2}u(x)=b(x)f(u(x))\pm |\mathrm{?}u{|}^q,x\in \mathrm{\Omega },u{|}_{?\mathrm{\Omega }}=+\infty ,$

and

$\det ?D^{2}u(x)=b(x)f(u(x))(1+|\mathrm{?}u{|}^q),x\in \mathrm{\Omega },u{|}_{?\mathrm{\Omega }}=+\infty ,$

where Ω is a strictly convex, bounded smooth domain in ${\mathbb{R}}^N$ with $N\ge 2$, $q\in [0,N]$ (or $q\in [0,N)$), $b\in C^{\infty }(\mathrm{\Omega })$ which is positive in Ω, but may vanish or blow up on the boundary, $f\in C[0,\infty )$, $f(0)=0$, and f is strictly increasing on $[0,\infty )$ (or $f\in C(\mathbb{R})$, $f(s)>0,?s\in \mathbb{R}$, and f is strictly increasing on $\mathbb{R}$).     

Elastic Half-Plane under Random Displacement Excitations on the Boundary

We study in this paper a respond of an elastic half-plane to random boundary excitations. We treat both the white noise excitations and more generally, homogeneous random fluctuations of displacements prescribed on the boundary. Solutions to these problems are inhomogeneous random fields which are however homogeneous with respect to the longitudinal coordinate. This is used to represent the displacements as series expansions involving a complete set of deterministic functions with corresponding random coefficients. We construct the Karhunen-Loève (K-L) series expansion which is based on the eigen-decomposition of the correlation operator. The K-L expansion can be used to calculate the statistical characteristics of other functionals of interest, in particular, the strain and stress tensors and the elastic energy tensor. This work is supported partly by the RFBR Grant N 06-01-00498. I. Shalimova acknowledges the host institute WIAS, Berlin, and the support of DFG, under Grant SA 861/6-1 of 2008.     

Thermoelectric Properties (Resistivity and Thermopower) in (Bi1.5Pb0.5Ca2−xMxCo2O8−δ (M=Sc, Y, or La)

In order to understand the origin of good thermoelectric (TE) properties in the transition metal oxides with the lattice structure isomorphous to the 232-structure, the bond nature between Co and O ions in Bi_1.5Pb_0.5Ca_2−xM_xCo₂O_8−δ-system has been tried to vary by replacing M with Sc³⁺, Y³⁺ or La³⁺ and by changing x from 0 to 0.3. The resistivity is minimum at x = 0.1 in Sc- and Y-systems, but very high in La-system. The large thermopower is obtained in every compound. The experimental TE properties have been discussed mainly within the framework of the charge-transfer scheme in which the ionic radii of Sc³⁺ and Y³⁺ smaller than Ca²⁺ reduce the energy between O 2p levels and Co e_g parentages but the large ionic radius of La³⁺ expands it. The oxygen solubility in the compounds and the lattice distortion peculiar to the 232-structure are also likely to contribute somewhat to the experimental results.     

Ettore Majorana’s Forgotten Publication on the Thomas-Fermi Model

We analyze the forgotten communication of Ettore Majorana (1906–1938?) on the Thomas-Fermi statistical model of the atom, which he presented on December 29, 1928, during the XXII General Meeting of the Italian Physical Society in Rome, and which was published in Il Nuovo Cimento, the Society’s journal, in 1929. His communication was not mentioned subsequently in any of the numerous publications of Enrico Fermi (1901–1954) and his group in Rome, nor in any of the later accounts of Majorana’s life and work. We place Majorana’s contribution within the context of contemporary research on the subject, point out its influence on the final formulation of the Thomas-Fermi statistical model by Fermi and Edoardo Amaldi (1908–1989) in 1934, and discuss Majorana’s other scientific contributions before his mysterious disappearance in 1938. Francesco Guerra is Professor of Theoretical Physics in the Department of Physics at the University of Rome “La Sapienza.” His main fields of research are quantum-field theory, statistical mechanics of complex systems, and the history of nuclear physics. Nadia Robotti is Professor of History of Physics in the Department of Physics at the University of Genoa. Her main fields of research are the history of atomic physics, quantum mechanics, and nuclear physics.     

Settling motion of interacting solid particles in the vicinity of a plane solid boundary

The sedimentation of $N?1$ small arbitrarily-shaped solid bodies near a solid plane is addressed by discarding inertial effects and using 6N boundary-integral equations. Numerical results for 2 or 3 identical spheres reveal that combined wall–particle and particle–particle interactions deeply depend on the cluster's geometry and distance to the wall and may even cancel for a sphere which then moves as it were isolated. To cite this article: A. Sellier, C. R. Mecanique 333 (2005).     

Groupe Des Inversibles Et Rayon Spectral Dans Les Algèbres Topologiques

We deal with the relationship between the spectral radius and the topological bihaviour of the group of invertible elements in a topological algebra, introducing accordingly several types of (generalized Q-) algebras. We then give properties and characterizations of such algebras. Applications to weighted algebras as well as several classes of examples are provided.

     

Data completion via an energy error functional

We propose, in this Note, a new procedure for data completion based on the minimization of an energy like error functional. The efficiency of the proposed method is illustrated by a thermostatic application. To cite this article: S. Andrieux et al., C. R. Mecanique 333 (2005).