Presentations: from Kac-Moody groups to profinite and back

We go back and forth between, on the one hand, presentations of arithmetic and Kac-Moody groups and, on the other hand, presentations of profinite groups, deducing along the way new results on both

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

Dynamical properties across a quantum phase transition in the Lipkin-Meshkov-Glick model

It is of high interest, in the context of Adiabatic Quantum Computation, to better understand the complex dynamics of a quantum system subject to a time-dependent Hamiltonian, when driven across a quantum phase transition. We present here such a study in the Lipkin-Meshkov-Glick (LMG) model with one variable parameter. We first display numerical results on the dynamical evolution across the LMG quantum phase transition, which clearly shows a pronounced effect of the spectral avoided level crossings. We then derive a phenomenological (classical) transition model, which already shows some closeness to the numerical results. Finally, we show how a simplified quantum transition model can be built which strongly improve the classical approach, and shed light on the physical processes involved in the whole LMG quantum evolution. From our results, we argue that the commonly used description in term of Landau-Zener transitions is not appropriate for our model.Comment: 7 pages, 5 figures; corrected reference

Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mRbh/m_{Rb}

We use Bloch oscillations in a horizontal moving standing wave to transfer a large number of photon recoils to atoms with a high efficiency (99.5% per cycle). By measuring the photon recoil of $^{87}Rb$, using velocity selective Raman transitions to select a subrecoil velocity class and to measure the final accelerated velocity class, we have determined $h/m_{Rb}$ with a relative precision of 0.4 ppm. To exploit the high momentum transfer efficiency of our method, we are developing a vertical standing wave set-up. This will allow us to measure $h/m_{Rb}$ better than $10^{-8}$ and hence the fine structure constant $\alpha$ with an uncertainty close to the most accurate value coming from the ($g-2$) determination

Strength and Deformation of Reinforced Concrete Squat Walls with High-Strength Materials

The behavior of reinforced concrete (RC) squat walls constructed with conventional- and high-strength materials was evaluated through tests of 10 wall specimens subjected to reversed cyclic loading. Primary variables included specimen height-to-length aspect ratio, steel grade, concrete compressive strength, and normalized shear stress demand. Specimens were generally in compliance with ACI 318-14. Test results showed that specimens containing conventional- and high-strength steel had similar strength and deformation capacities when designed to have equivalent steel force, defined as total steel area times steel yield stress. The lateral strength of walls with aspect ratios of 1.0 and 1.5 can be estimated using their nominal flexural strength when the nominal shear strength exceeds Vmn. For specimens with an aspect ratio of 0.5, the lateral strength was close to the force required to cause flexural reinforcement yielding and less than the nominal shear strength calculated per ACI 318-14. Specimen deformation capacity decreased as the normalized shear stress increased. The use of high-strength concrete, which led to a reduced normalized shear stress demand, resulted in larger specimen deformation capacity

Critical Point and Percolation Probability in a Long Range Site Percolation Model on Zd\Z^d

Consider an independent site percolation model with parameter $p \in (0,1)$ on $\Z^d,\ d\geq 2$ where there are only nearest neighbor bonds and long range bonds of length $k$ parallel to each coordinate axis. We show that the percolation threshold of such model converges to $p_c(\Z^{2d})$ when $k$ goes to infinity, the percolation threshold for ordinary (nearest neighbour) percolation on $\Z^{2d}$. We also generalize this result for models whose long range bonds have several lengths.Comment: 5 pages; Acepted in Stochastic Processes and their Applications 201

Deformation Capacity and Strength of RC Frame Members with High-Strength Materials

Some implications of using high-strength concrete and steel materials in reinforced concrete frame members are discussed in terms of both flexural design and behavior. Through an example, it is demonstrated that the computed sectional curvature is highly sensitive to the choice of rectangular stress block used to model compression zone stresses of high-strength concrete. Comparison of various models suggests that the use of the stress block model defined in the ACI Building Code tends to overestimate curvature for concrete strengths exceeding 12 ksi (83 MPa). In addition, recent test data are presented for flexure-dominated concrete members reinforced with high-strength steel bars. The effects of replacing Grade 60 (410) flexural reinforcement with Grade 100 (690) steel on deformation capacity, stiffness, and strength are examined. Test data support the viability of using Grade 100 (690) longitudinal reinforcement to resist loads that induce force-displacement response well into the nonlinear range