Scattering pour l'équation de Schrödinger en présence d'un potentiel répulsif

We study scattering theory for linear Schrödinger equations, when the reference Hamiltonian is ?Δ?〈x〉^α, in $\text{R}{}^{\mathrm{n}}$, with 0<α?2. The notion of short range perturbative potential is much weaker than for the usual reference Hamiltonian ?Δ. We also consider the case where 〈x〉² is replaced by a general second order polynomial. To cite this article: J.-F. Bony et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Electron charge density of alkali halides beyond the rigid-ion approximation

The dependence of the electron charge distribution in alkali halides on the lattice constant is examined. It is found that in the case of NaCl the non-rigid behavior of the electron charge density calculated from first principles can be well understood if one starts from the free-ion functions and takes into account the mutual overlap between them. The relevance of our results for the structural properties of alkali halides is pointed out in connection with recent ab-initio calculations.     

Poisson boundaries of discrete groups of matrices

If μ is a probability measure on a countable group there is defined a notion of the Poisson boundary for μ which enables one to represent all bounded μ-harmonic functions on the group. It is shown that for discrete groups of matrices this boundary can be identified with the boundary of the corresponding Lie group.     

On minimum congestion routing in rearrangeable multihop lightwave networks

In this article we consider the problem of minimizing the congestion in logically rearrangeable multihop lightwave networks. Namely, we consider a network in which each node is equipped with a small number of transmitters and receivers, and tuning a transmitter at nodei and a receiver at nodej to the same wavelength creates a logical link (i, j) through which traffic could be sent. For a given traffic matrix-the matrix of flows between nodes—the objective is to find the best connectivity diagram and the corresponding flow assignment so that the maximal flow on any link is minimized. We develop a tabu search heuristic that yields a suboptimal connectivity diagram and an optimal flow assignment on it. Computational experiments are conducted on some benchmark data sets, on a real-world traffic matrix, and on some randomly generated problems of larger dimension. The results are compared with known results from the literature and with a known greedy approach. The results suggest that a tabu search—based heuristic is a promising approach for handling this NP-hard combinatorial problem. In addition, we discuss the performance of the method in view of different patterns of input data.     

Interfacial tension between low molecular weight polymers from the static analysis of cylindrical drops and their break-up dynamics

A spinning drop tensiometer was used to measure the interfacial tension between the coexisting phases of mixtures of low molecular weight polypropylene glycol, M_w = 1000, and polyethylene glycol, M_w = 300, 400, or 550. Two types of experiments gave concordant interfacial tensions. First, the static analysis of the equilibrium diameter of cylindrical drops according to Vonnegut and, second, Tomotika's dynamic analysis of Rayleigh instabilities caused by a sharp decrease of the angular speed. The end-pinching process also lead to the break-up of the drops and it was characterized by a rapid expansion of the hemispherical ends followed by a slower pinching step. The pinching rate increases as the final angular speed decreases while the growth rate of Rayleigh instabilities shows no definite trends in the range 118-245 rad · s^?1. It is shown that the end-pinching of long cylindrical drops can be analyzed in terms of short fiber retraction to get the interfacial tension. © 1995 John Wiley & Sons, Inc.     

Crystal structures of high-T c oxides

A comprehensive review of structure work on high-T _c oxides as reported during the years 1987 and 1988 is given. Thirteen structures are refined from X-ray single-crystal and/or neutron powder diffraction data:I. (Ba_1–x ,K _x )BiO₃ (T _c =30 K),II. (La_2–x , Sr _x )CuO₄ (T _c =40 K),III. (Nd, Ce, Sr)₂CuO₄ (T _c =28 K),IV. (Nd_2–x , Ce _x )CuO₄ (T _c =24 K),V. YBa₂Cu₃O₇ (T _c =90 K),VI. YBa₂Cu₄O₈ (T _c =80 K),VII. Y₂Ba₄Cu₇O₁₄ (T _c =40 K),VIII. Pb₂Sr₂NdCu₃O₈ (T _c =70 K),IX. TlBa₂CaCu₂O₇ (T _c =103 K),X. TlBa₂Ca₂Cu₃O₉ (T _c =120 K),XI. Tl₂Ba₂CuO₆ (T _c =90 K),XII. Tl₂Ba₂CaCu₂O₈ (T _c =112 K),XIII. Tl₂Ba₂Ca₂Cu₃O₁₀ (T _c =125 K). Except forI (perovskite type),II (K₂NiF₄ type) andIV (Nd₂CuO₄ type) they represent new structure types. Structure data, bond distances, structure drawings and calculated X-ray powder diffraction patterns are given for each compound. Structural features and correlations with superconductivity are discussed. The review contains 301 citations.     

Rigidity Result for Certain Three-Dimensional Singular Spaces and Their Fundamental Groups

In this paper, we introduce a particularly nice family of locally CAT(−1) spaces, which we call hyperbolic P-manifolds. For X³ a simple, thick hyperbolic P-manifold of dimension 3, we show that certain subsets of the boundary at infinity of the universal cover of X³ are characterized topologically. Straightforward consequences include a version of Mostow rigidity, as well as quasi-isometry rigidity for these spaces.