Growth by laser ablation of Ti-based oxide films with different valency states

x La_2/3+yTiO_3-δ perovskite (with δ≤0.5) were deposited by the laser ablation technique from Li_0.33La_0.56TiO₃ targets. Their growth onto MgO substrateswas studied as a function of the oxygen pressure. For films grown in vacuum (10^-6 mbar), a La_0.63TiO_2.5 composition was obtained, meaning that Ti³⁺ alone is present in the films, while Li ions are not incorporated under these conditions. This material shows good electric conductivity (ρ=500 mΩ cm). By contrast, insulating films with a Li_0.1La_0.70TiO₃ composition corresponding to the Ti⁴⁺ species were obtained at high oxygen pressures (>0.05 mbar). For all conditions, textured films were grown with different orientations depending on the temperature and the oxygen pressure. Received: 10 September 1997/Accepted: 24 November 1997     

Stationary axisymmetric solutions of three-dimensional Einstein gravity

Einstein theory in three space-time dimensions is studied in the stationary, rotationally symmetric regime. Explicit interior solutions for various types of matter sources are found and their properties discussed.     

Molecular view of copper deposition chemistry: (Hexafluoroacetylacetonate)Cu(vinyltrimethylsilane) on a Si(1 0 0)-2 × 1 surface

The chemistry of a common copper deposition precursor, (hexafluoroacetylacetonate)Cu(vinyltrimethylsilane), (hfac)Cu(VTMS), on a single crystal Si(1 0 0)-2 × 1 surface is described at the molecular level using a combination of experimental surface analytical techniques under ultra-high vacuum conditions with computational analysis. At a cryogenic temperature of 100 K, (hfac)Cu(VTMS) adsorbs on this surface molecularly, without noticeable decomposition. Upon surface annealing, VTMS is easily released into the gas phase below the room temperature, while the hfac ligand is bound to the surface through the copper atom. When (hfac)Cu(VTMS) is adsorbed at room temperature, VTMS is released into the gas phase immediately, leaving surface adsorbate analogous in structure to the one formed by adsorption at cryogenic temperature and a brief annealing to room temperature. Upon surface annealing, the hfac ligand decomposes and constitutes the main source of impurities in copper deposition process.     

An asymptotic-preserving well-balanced scheme for the hyperbolic heat equationsUn schema « équilibre » et « asymptotic-preserving » pour les equations de la chaleur hyperboliques

We propose here a well-balanced numerical scheme for the one-dimensional Goldstein–Taylor system which is endowed with all the stability properties inherent to the continuous problem and works in both rarefied and diffusive regimes. To cite this article: L. Gosse, G. Toscani, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 337–342.     

Growth Series and Random Walks on Some Hyperbolic Graphs

 Consider the tessellation of the hyperbolic plane by m-gons, ℓ per vertex. In its 1-skeleton, we compute the growth series of vertices, geodesics, tuples of geodesics with common extremities. We also introduce and enumerate holly trees, a family of proper loops in these graphs. We then apply Grigorchuk’s result relating cogrowth and random walks to obtain lower estimates on the spectral radius of the Markov operator associated with a symmetric random walk on these graphs. Received 19 September 2001; in revised form 23 December 2001     

A Hamiltonian Model for Linear Friction in a Homogeneous Medium

 We introduce and study rigorously a Hamiltonian model of a classical particle moving through a homogeneous dissipative medium at zero temperature in such a way that it experiences an effective linear friction force proportional to its velocity (at small speeds). The medium consists at each point in a space of a vibration field modelling an obstacle with which the particle exchanges energy and momentum in such a way that total energy and momentum are conserved. We show that in the presence of a constant (not too large) external force, the particle reaches an asymptotic velocity proportional to this force. In a potential well, on the other hand, the particle comes exponentially fast to rest in the bottom of the well. The exponential rate is in both cases an explicit function of the model parameters and independent of the potential. Received: 18 July 2001 / Accepted: 20 April 2002 Published online: 12 August 2002     

A New Implicit Method for Surface Segmentation by Minimal Paths in 3D Images

We introduce a novel implicit approach for single-object segmentation in 3D images. The boundary surface of this object is assumed to contain two known curves (the constraining curves), given by an expert. The aim of our method is to find the wanted surface by exploiting as much as possible the information given in the supplied curves and in the image. As for active surfaces, we use a cost potential that penalizes image regions of low interest (most likely areas of low gradient or too far from the surface to be extracted). In order to avoid local minima, we introduce a new partial differential equation and use its solution for segmentation. We show that the zero level set of this solution contains the constraining curves as well as a set of paths joining them. We present a fast implementation that has been successfully applied to 3D medical and synthetic images.     

Infinite groups with large balls of torsion elements and small entropy

We exhibit infinite, solvable, virtually abelian groups with a fixed number of generators, having arbitrarily large balls consisting of torsion elements. We also provide a sequence of 3-generator non-virtually nilpotent polycyclic groups of algebraic entropy tending to zero. All these examples are obtained by taking appropriate quotients of finitely presented groups mapping onto the first Grigorchuk group. Received: 3 August 2005     

The cutoff phenomenon for randomized riffle shuffles

We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffled together. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008