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

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

Impacts of changes in groundwater recharge on the isotopic composition and geochemistry of seasonally ice-covered lakes: insights for sustainable management

Lakes are under increasing pressure due to widespread anthropogenic impacts related to rapid development and population growth. Accordingly, many lakes are currently undergoing a systematic decline in water quality. Recent studies have highlighted that global warming and the subsequent changes in water use may further exacerbate eutrophication in lakes. Lake evolution depends strongly on hydrologic balance, and therefore on groundwater connectivity. Groundwater also influences the sensitivity of lacustrine ecosystems to climate and environmental changes, and governs their resilience. Improved characterization of groundwater exchange with lakes is needed today for lake preservation, lake restoration, and sustainable management of lake water quality into the future. In this context, the aim of the present paper is to determine if the future evolution of the climate, the population, and the recharge could modify the geochemistry of lakes (mainly isotopic signature and quality via phosphorous load) and if the isotopic monitoring of lakes could be an efficient tool to highlight the variability of the water budget and quality. Small groundwater-connected lakes were chosen to simulate changes in water balance and water quality expected under future climate change scenarios, namely representative concentration pathways (RCPs) 4.5 and 8.5. Contemporary baseline conditions, including isotope mass balance and geochemical characteristics, were determined through an intensive field-based research program prior to the simulations. Results highlight that future lake geochemistry and isotopic composition trends will depend on four main parameters: location (and therefore climate conditions), lake catchment size (which impacts the intensity of the flux change), lake volume (which impacts the range of variation), and lake G index (i.e., the percentage of groundwater that makes up total lake inflows), the latter being the dominant control on water balance conditions, as revealed by the sensitivity of lake isotopic composition. Based on these model simulations, stable isotopes appear to be especially useful for detecting changes in recharge to lakes with a G index of between 50 and 80 %, but response is non-linear. Simulated monthly trends reveal that evolution of annual lake isotopic composition can be dampened by opposing monthly recharge fluctuations. It is also shown that changes in water quality in groundwater-connected lakes depend significantly on lake location and on the intensity of recharge change

Critical connectedness of thin arithmetical discrete planes

An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its $2$-connectedness. This infimum thickness can be computed thanks to the fully subtractive algorithm. This multidimensional continued fraction algorithm consists, in its linear form, in subtracting the smallest entry to the other ones. We provide a characterization of the discrete planes with critical thickness that have zero intercept and that are $2$-connected. Our tools rely on the notion of dual substitution which is a geometric version of the usual notion of substitution acting on words. We associate with the fully subtractive algorithm a set of substitutions whose incidence matrix is provided by the matrices of the algorithm, and prove that their geometric counterparts generate arithmetic discrete planes.Comment: 18 pages, v2 includes several corrections and is a long version of the DGCI extended abstrac

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

Impacts of changes in groundwater recharge on the isotopic composition and geochemistry of seasonally ice-covered lakes: insights for sustainable management

Lakes are under increasing pressure due to widespread anthropogenic impacts related to rapid development and population growth. Accordingly, many lakes are currently undergoing a systematic decline in water quality. Recent studies have highlighted that global warming and the subsequent changes in water use may further exacerbate eutrophication in lakes. Lake evolution depends strongly on hydrologic balance, and therefore on groundwater connectivity. Groundwater also influences the sensitivity of lacustrine ecosystems to climate and environmental changes, and governs their resilience. Improved characterization of groundwater exchange with lakes is needed today for lake preservation, lake restoration, and sustainable management of lake water quality into the future. In this context, the aim of the present paper is to determine if the future evolution of the climate, the population, and the recharge could modify the geochemistry of lakes (mainly isotopic signature and quality via phosphorous load) and if the isotopic monitoring of lakes could be an efficient tool to highlight the variability of the water budget and quality. Small groundwater-connected lakes were chosen to simulate changes in water balance and water quality expected under future climate change scenarios, namely representative concentration pathways (RCPs) 4.5 and 8.5. Contemporary baseline conditions, including isotope mass balance and geochemical characteristics, were determined through an intensive field-based research program prior to the simulations. Results highlight that future lake geochemistry and isotopic composition trends will depend on four main parameters: location (and therefore climate conditions), lake catchment size (which impacts the intensity of the flux change), lake volume (which impacts the range of variation), and lake G index (i.e., the percentage of groundwater that makes up total lake inflows), the latter being the dominant control on water balance conditions, as revealed by the sensitivity of lake isotopic composition. Based on these model simulations, stable isotopes appear to be especially useful for detecting changes in recharge to lakes with a G index of between 50 and 80 %, but response is non-linear. Simulated monthly trends reveal that evolution of annual lake isotopic composition can be dampened by opposing monthly recharge fluctuations. It is also shown that changes in water quality in groundwater-connected lakes depend significantly on lake location and on the intensity of recharge change

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

Escape orbits and Ergodicity in Infinite Step Billiards

In a previous paper we defined a class of non-compact polygonal billiards, the infinite step billiards: to a given decreasing sequence of non-negative numbers $\{p_{n}$, there corresponds a table \Bi := \bigcup_{n\in\N} [n,n+1] \times [0,p_{n}]. In this article, first we generalize the main result of the previous paper to a wider class of examples. That is, a.s. there is a unique escape orbit which belongs to the alpha and omega-limit of every other trajectory. Then, following a recent work of Troubetzkoy, we prove that generically these systems are ergodic for almost all initial velocities, and the entropy with respect to a wide class of ergodic measures is zero.Comment: 27 pages, 8 figure

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

Triangulations and Severi varieties

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as a geometric version of the (putative) triangulations