Energy spectrum of <Emphasis Type="Italic">p</Emphasis> electrons in a plane crystal lattice and in a strong magnetic field

Harper equations are derived for a _px, _py electronic system. Analysis is carried out for extreme points of the quasi-continuous spectrum in the cases when the number of magnetic flux quanta through a unit cell is a rational number and calculations are made for square and triangular lattices as well as for a honeycomb lattice with two nonequivalent atoms. The possibility of application of the results for explaining the fractional Hall effect is considered.     

Chern numbers for two families of noncommutative Hopf fibrations

We consider noncommutative line bundles associated with the Hopf fibrations of SU_q(2) over all Podle? spheres and with a locally trivial Hopf fibration of S³_pq. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SU_q(2) and S³_pq. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them. To cite this article: P.M. Hajac et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Longwave Marangoni convection in an inhomogeneously heated liquid

The supercritical Marangoni convection has been studied in a plane-parallel liquid layer, bounded by a free deformable gas-liquid interface from above and by a low-heat-conductivity wall from below, occurring under conditions of inhomogeneous heating in the horizontal plane. In a longwave approximation with a small inhomogeneity of heat flux, the process is described by a system of two-dimensional nonlinear equations for the temperature perturbations, vorticity, and free surface deformation. The concept of quasiequilibrium, implying stability of long-range flows, is introduced, which allows the inhomogeneous heat flux to be modeled by a step function. The linear stability is analyzed in the cases of planar and axisymmetric heat fluxes. The boundaries of stability of the convection regimes are determined on the plane of parameters characterizing the degree of supercriticity inside a heated spot and the depth of damping outside the spot. For an axisymmetric spot, the domains of stability with respect to perturbations for various azimuthal numbers are established.     

Temperature dependences of the low-frequency internal friction and shear modulus in a bulk amorphous alloy

The logarithmic decrement and shear modulus of a bulk amorphous Zr_52.5Ti₅Cu_17.9Ni_14.6Al₁₀ alloy were studied with an inverse torsion pendulum in the range from room temperature to the crystallization temperature and in the frequency range 5–40 Hz. The activation energy spectra of reversible and irreversible structural relaxation were estimated. The results obtained are discussed in the context of a two-energy-level model.     

Core-shell structure in fullerene-containing molecular complexes

A shell model that describes the formation of molecular complexes around a C₆₀ molecule upon the solid-phase interaction of the powders is considered. From the absorption spectra, it follows that a reacting particle is a fullerene dimer.     

Generation of angular momentum of fission fragments in a cluster model

Based on the dinuclear system concept, the role of bending vibrations in creation of the angular momentum of primary fission fragments is investigated. For ²⁵²Cf spontaneous fission, the angular momenta of the fragments are calculated as a function of the neutron multiplicity and compared with available experimental data. Different cluster compositions of the ²⁵²Cf fission modes at the scission point are considered.     

Some 3-manifolds with 2-generated fundamental group

We describe a family of graph manifolds that have 2-generated fundamental group but do not admit a Heegaard splitting of genus 2. They are closely related to the examples provided by Boileau and Zieschang if these are considered as (non-proper) graph manifolds.Received: 14 August 2002