On the distortion of twin building lattices

We show that twin building lattices are undistorted in their ambient group; equivalently, the orbit map of the lattice to the product of the associated twin buildings is a quasi-isometric embedding. As a consequence, we provide an estimate of the quasi-flat rank of these lattices, which implies that there are infinitely many quasi-isometry classes of finitely presented simple groups. In an appendix, we describe how non-distortion of lattices is related to the integrability of the structural cocycle

Ultimate decoherence border for matter-wave interferometry

Stochastic backgrounds of gravitational waves are intrinsic fluctuations of spacetime which lead to an unavoidable decoherence mechanism. This mechanism manifests itself as a degradation of the contrast of quantum interferences. It defines an ultimate decoherence border for matter-wave interferometry using larger and larger molecules. We give a quantitative characterization of this border in terms of figures involving the gravitational environment as well as the sensitivity of the interferometer to gravitational waves. The known level of gravitational noise determines the maximal size of the molecular probe for which interferences may remain observable. We discuss the relevance of this result in the context of ongoing progresses towards more and more sensitive matter-wave interferometry.Comment: 4 page

Inflation of the Aira Caldera (Japan) detected over Kokubu urban area using SAR interferometry ERS data

International audienceNine ERS-1 and ERS-2 descending orbit data acquired over Aira Caldera between June 1995 and November 1998 were used to create 36 differential interferograms. Although the interferograms exhibit a relatively low level of coherence, even for couples sampling short time intervals (6 months), Synthetique Aperture Radar (SAR) observations reveal a distinct range change pattern over Kokubu urban area whose amplitude increases with the time separation between SAR images. The analysis of the ground deformation time series relative to the earliest ERS images showed a maximum uplift of about 20 mm between the north and the south of the urban area during the period covered by our satellite observations. Taking the reduced surface of the coherent area into account, we performed a simple modeling of the deformation field assuming an inflating spherical source within an elastic half-space medium located beneath the centre of the Aira Caldera. This simple model predicts a maximum volume increase of 20–30×106 m3 between 1995 and 1998, which would produce an inflation of about 70 mm at the centre of the Aira Caldera and 40 mm in the Kokubu south urban area. These results are in good agreement with other geophysical observations carried out on the Aira caldera during this period. Despite the limited spatial extent of the coherent areas around the Aira Caldera, this study shows that DinSAR method using data collected in C band can be successfully used to detect subtle ground displacement changes of the volcanic complex and thus provides complementary information to ground-based geodetic monitoring of dynamic processes of the Aira Caldera and Sakurajima volcano

Non-Asymptotic Pure Exploration by Solving Games

Pure exploration (aka active testing) is the fundamental task of sequentially gathering information to answer a query about a stochastic environment. Good algorithms make few mistake

Resurgence, Stokes phenomenon and alien derivatives for level-one linear differential systems

A precise description of the singularities of the Borel transform of solutions of a level-one linear differential system is deduced from a proof of the summable-resurgence of the solutions by the perturbative method of J. Écalle. Then we compare the meromorphic classification (Stokes phenomenon) from the viewpoint of the Stokes cocycle and the viewpoint of alien derivatives. We make explicit the Stokes–Ramis matrices as functions of the connection constants in the Borel plane and we develop two examples. No assumption of genericity is made

Open subgroups of locally compact Kac-Moody groups

Let G be a complete Kac-Moody group over a finite field. It is known that G possesses a BN-pair structure, all of whose parabolic subgroups are open in G. We show that, conversely, every open subgroup of G is contained with finite index in some parabolic subgroup; moreover there are only finitely many such parabolic subgroups. The proof uses some new results on parabolic closures in Coxeter groups. In particular, we give conditions ensuring that the parabolic closure of the product of two elements in a Coxeter group contains the respective parabolic closures of those elements.Comment: Minor changes. Theorem A has been slightly improved and now contains an additional finiteness statemen

Generalized quasiperiodic Rauzy tilings

We present a geometrical description of new canonical $d$-dimensional codimension one quasiperiodic tilings based on generalized Fibonacci sequences. These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual Penrose and icosahedral tilings. Thanks to a natural indexing of the sites according to their local environment, we easily write down, for any approximant, the sites coordinates, the connectivity matrix and we compute the structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change

Anchorage of Conventional and High-Strength Headed Reinforcing Bars

Headed bars are often used to anchor reinforcing steel as a means of reducing congestion where member geometry precludes adequate anchorage with a straight bar. Currently, limited data on the behavior of headed bars are available, with no data on high-strength steel or high-strength concrete. Due to a lack of information, current design provisions for development length of headed reinforcing bars in ACI 318-14 limit the yield strength of headed reinforcing steel to 60,000 psi and the concrete compressive strength for calculating development length to 6,000 psi. Current design provisions for developing headed bars in ACI 349-13, which are based on ACI 318-08, apply the same limits on the material strengths (60,000 psi and 6,000 psi, respectively, for headed bars and concrete). These limits restrict the use of headed bars and prevent the full benefits of higher-strength reinforcing steel and concrete from being realized. The purpose of this study was to establish the primary factors that affect the development length of headed bars and to develop new design guidelines for development length that allow higher strength steel and concrete to be utilized. A total of 233 specimens were tested, with four specimen types used to evaluate heads across a variety of applications. Two hundred two beam-column joint specimens, 10 beam specimens with headed bars anchored near the support in regions that are known as compression-compression-tension (CCT nodes, 15 shallow embedment specimens (each containing one to three headed bars for a total of 32 tests), and 6 splice specimens were evaluated. No. 5, No. 6, No. 8, and No. 11 bars were evaluated to cover the range of headed bar sizes commonly used in practice. Concrete compressive strengths ranged from 3,960 to 16,030 psi. A range of headed bar sizes, with net bearing areas between 3.8 and 14.9 times the area of the bar, were also investigated. Some of these heads had obstructions larger than allowed under current Code requirements. In addition, the amount of confining reinforcement, number of heads in a specimen, spacing between heads, and embedment length were evaluated in this study. The results of this study show that provisions in ACI 318-14 and ACI 349-13 do not accurately account for the effect of bar size, compressive strength, or the spacing of headed bars in a joint. The effect of concrete compressive strength on the development length of headed bars is accurately represented by concrete strength raised to the 0.25 power, not the 0.5 power currently used in the ACI provisions. Confining reinforcement increases the anchorage strength of headed bars in proportion to the amount of confining reinforcement per headed bar being developed. Headed bars with obstructions not meeting the Class HA head requirements of ASTM A970 (heads permitted by ACI 318-14 and ACI 349-13) perform similarly to HA heads, provided the unobstructed bearing area of the head is at least 4.5 times the area of the bar. Headed bars exhibit a reduction in capacity for values of center-to-center spacing less than eight bar diameters. These results are used to develop descriptive equations for anchorage strength that cover a broad range of material strengths and member properties. The equations are used to formulate design provisions for development length that safely allow for the use of headed reinforcing bars for steels with yield strengths up to 120,000 psi and concretes with compressive strengths up to 16,000 psi. Adoption of the proposed provisions will significantly improve the constructability and economy of nuclear power plants and other building structures.Electric Power Research Institute, Concrete Steel Reinforcing Institute Education and Research Foundation, BarSplice Products, Incorporated, Headed Reinforcement Corporation, and LENTON® products from Pentair