Geometric representation of interval exchange maps over algebraic number fields

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.Comment: 34 pages, 8 postscript figure

Geometrical Models for Substitutions

International audienceWe consider a substitution associated with the Arnoux-Yoccoz interval exchange transformation (IET) related to the tribonacci substitution. We construct the so-called stepped lines associated with the fixed points of the substitution in the abelianization (symbolic) space. We analyze various projections of the stepped line, recovering the Rauzy fractal, a Peano curve related to work in [Arnoux 88], another Peano curve related to the work of [McMullen 09] and [Lowenstein et al. 07], and also the interval exchange transformation itself

Symbolic approach and induction in the Heisenberg group

We associate a homomorphism in the Heisenberg group to each hyperbolic unimodular automorphism of the free group on two generators. We show that the first return-time of some flows in "good" sections, are conjugate to niltranslations, which have the property of being self-induced.Comment: 18 page

Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

An algorithm to identify automorphisms which arise from self-induced interval exchange transformations

We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self-induced interval exchange transformation. The algorithm effectively yields the interval exchange transformation in case of success.Comment: 26 pages, 8 figures. v2: the article has been reorganized to make for a more linear read. A few paragraphs have been added for clarit

Describing the set of words generated by interval exchange transformation

Let $W$ be an infinite word over finite alphabet $A$. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.Comment: 17 pages, this paper was submitted at scientific council of MSU, date: September 21, 200

Next-generation seismic experiments – II: wide-angle, multi-azimuth, 3-D, full-waveform inversion of sparse field data

3-D full-waveform inversion (FWI) is an advanced seismic imaging technique that has been widely adopted by the oil and gas industry to obtain high-fidelity models of P-wave velocity that lead to improvements in migrated images of the reservoir. Most industrial applications of 3-D FWI model the acoustic wavefield, often account for the kinematic effect of anisotropy, and focus on matching the low-frequency component of the early arriving refractions that are most sensitive to P-wave velocity structure. Here, we have adopted the same approach in an application of 3-D acoustic, anisotropic FWI to an ocean-bottom-seismometer (OBS) field data set acquired across the Endeavour oceanic spreading centre in the northeastern Pacific. Starting models for P-wave velocity and anisotropy were obtained from traveltime tomography; during FWI, velocity is updated whereas anisotropy is kept fixed. We demonstrate that, for the Endeavour field data set, 3-D FWI is able to recover fine-scale velocity structure with a resolution that is 2–4 times better than conventional traveltime tomography. Quality assurance procedures have been employed to monitor each step of the workflow; these are time consuming but critical to the development of a successful inversion strategy. Finally, a suite of checkerboard tests has been performed which shows that the full potential resolution of FWI can be obtained if we acquire a 3-D survey with a slightly denser shot and receiver spacing than is usual for an academic experiment. We anticipate that this exciting development will encourage future seismic investigations of earth science targets that would benefit from the superior resolution offered by 3-D FWI

Optical Coatings as Mirrors for Optical Diagnostics

The aim of this work was to provide a comprehensive insight concerning coated films which might be used for first mirrors in ITER. The influence of the mirror crystallite size has been addressed as well as the coating techniques to provide nanocrystalline films. Tests of coated mirrors both in laboratories and in tokamaks are reviewed. For the tokamak tests a wide angle camera system has been installed in JET-ILW which is composed of a mirror box with 3 stainless steel mirrors coated with rhodium viewing the torus through a conically shaped aperture. The system delivered the required image quality for plasma monitoring and wall protection. No or insignificant degradation of the optical transmittance has been observed during the experimental campaign in 2014 with about 3000 plasma pulses in different magnetic field configurations