Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy最新文献

Analytical formulas are presented describing a generic singularity inside static spherically symmetric black holes in the SU(2) Einstein—Yang—Mills—Higgs theory with a triplet and/or doublet Higgs field. The singularity is spacelike and exhibits a ‘power-low mass inflation’. Alternatively this asymptotic behavior may be interpreted as a pointlike singularity in the Kantowski-Sachs closed anisotropic cosmology.

We propose here a systematic analysis of the boundary layer models describing the influence of a small geometrical perturbation of a wall on a Couette flow. The size scales of the boundary layer thickness and of the perturbation term of the longitudinal velocity are different for the boundary layer of the moving wall, whence the originality of this model.

The magnetic structure of neutron vortices in the superfluid cores of neutron stars is determined assuming that the proton condensate forms a type-I superconductor. It is shown that the entrainment currents induced by the neutron vortex circulation cause the proton superconductor to break into normal and superconducting domains of cylindrical form coaxial with the neutron vortex. The minimum of the energy functional corresponds to a tube radius a(0.1 – 0.5) b, where b is the outer radius of the neutron vortex. The magnetic field within the tube is of the order of 5 × 10¹⁴ G.

The Cepheids are relatively young, bright, periodic supergiant variable stars showing a correlation between their periods and luminosities. Since the beginning of the century the Cepheid Period -Luminosity relation has been the corner stone of distance determination, and of the measure of the correlation between the apparent relative expansion velocity to the relative distance (the Hubble constant, H₀). Using data obtained from the EROS project, we empirically found a small effect of metallicity on the Period-Luminosity relation which has important consequences for the inferred Cepheid distances and the determination of H₀.

The polymer film blowing process has been extensively studied in the literature. In most of the numerical models, the freezing line is arbitrarily fixed. In our anisothermal Newtonian and viscoelastic models, the freezing line is not set but results from the sharp increase of the viscosity. A precise computation of the bubble shape requires a careful determination of the initial angle of the bubble at the die exit. This has not been achieved yet. The existence of multiple solutions for the bubble and of an unattainable zone are underlined in the viscoelastic case.

In the previous paper we expressed the Euler-Lagrange variational equation for the non-relativistic energy of spin multiplicities of a multifermionic system, implicit in the charge distribution ρ(r), and showed how to solve it iteratively — and derive optimal values of observables, including the spin distribution σ(r) — through using the scalar function f(r) of the local-scaling transformation of the orbit. In the present paper we derive a similar equation, more explicit but also more complex, for the total energy expressed as a functional of f(r), and compare the problems raised by the different approaches.

The rate of spreading of a drop on a rigid substrate is governed by viscous dissipation in the liquid, the capillary driving force being compensated by the braking force resulting from viscous shearing in the liquid. In the case where the liquid is not newtonian but shear thinning or pseudoplastic, a deviation from the law of P.-G. de Gennes is observed, in particular a slower spreading kinetics corresponding to an increase of the liquid viscosity as the spreading speed decreases. In this study, this result is interpreted from the rheological behaviour of the non-newtonian liquid and a modified equation describing the spreading dynamics is proposed. This equation is obtained from two different calculations, either in considering an average viscosity or in expressing the distribution of speed in a shear thinning liquid wedge. The shape, slightly aspherical, of non-newtonian liquid drops having a size smaller than the capillary length, is also very simply interpreted, observing that the liquid viscosity increases from the edge to the center of drops during spreading, near the solid surface.