Hyperbolic outer billiards : a first example

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit

Remodeling by fibroblasts alters the rate-dependent mechanical properties of collagen

The ways that fibroblasts remodel their environment are central to wound healing, development of musculoskeletal tissues, and progression of pathologies such as fibrosis. However, the changes that fibroblasts make to the material around them and the mechanical consequences of these changes have proven difficult to quantify, especially in realistic, viscoelastic three-dimensional culture environments, leaving a critical need for quantitative data. Here, we observed the mechanisms and quantified the mechanical effects of fibroblast remodeling in engineered tissue constructs (ETCs) comprised of reconstituted rat tail (type I) collagen and human fibroblast cells. To study the effects of remodeling on tissue mechanics, stress-relaxation tests were performed on ETCs cultured for 24, 48, and 72 h. ETCs were treated with deoxycholate and tested again to assess the ECM response. Viscoelastic relaxation spectra were obtained using the generalized Maxwell model. Cells exhibited viscoelastic damping at two finite time constants over which the ECM showed little damping, approximately 0.2 s and 10-30 s. Different finite time constants in the range of 1-7000 s were attributed to ECM relaxation. Cells remodeled the ECM to produce a relaxation time constant on the order of 7000 s, and to merge relaxation finite time constants in the 0.5-2 s range into a single time content in the 1 s range. Results shed light on hierarchical deformation mechanisms in tissues, and on pathologies related to collagen relaxation such as diastolic dysfunction. Statement of Significance As fibroblasts proliferate within and remodel a tissue, they change the tissue mechanically. Quantifying these changes is critical for understanding wound healing and the development of pathologies such as cardiac fibrosis. Here, we characterize for the first time the spectrum of viscoelastic (rate-dependent) changes arising from the remodeling of reconstituted collagen by fibroblasts. The method also provides estimates of the viscoelastic spectra of fibroblasts within a three-dimensional culture environment. Results are of particular interest because of the ways that fibroblasts alter the mechanical response of collagen at loading frequencies associated with cardiac contraction in humans. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved

A characterization of quasi-rational polygons

The aim of this paper is to study quasi-rational polygons related to the outer billiard. We compare different notions introduced, and make a synthesis of those.Comment: 15 pages, 9 figure

Photon Self-Induced Spin to Orbital Conversion in TGG crystal at high laser power

In this paper, we present experimental evidence of a newly discovered third-order nonlinear optical process Self-Induced Spin-to-Orbital Conversion (SISTOC) of the photon angular momentum. This effect is the physical mechanism at the origin of the depolarization of very intense laser beams propagating in isotropic materials. The SISTOC process, like self-focusing, is triggered by laser heating leading to a radial temperature gradient in the medium. In this work we tested the occurrence of SISTOC in a terbium gallium garnet (TGG) rod for an impinging laser power of about 100~W. To study the SISTOC process we used different techniques: polarization analysis, interferometry and tomography of the photon orbital angular momentum. Our results confirm, in particular, that the apparent depolarization of the beam is due to the occurrence of maximal entanglement between the spin and orbital angular momentum of the photons undergoing the SISTOC process. This explanation of the true nature of the depolarization mechanism could be of some help in finding novel methods to reduce or to compensate for this usually unwanted depolarization effect in all cases where very high laser power and good beam quality are required.Comment: 6 pages, 10 figures, submitte

Contact complete integrability

Complete integrability in a symplectic setting means the existence of a Lagrangian foliation leaf-wise preserved by the dynamics. In the paper we describe complete integrability in a contact set-up as a more subtle structure: a flag of two foliations, Legendrian and co-Legendrian, and a holonomy-invariant transverse measure of the former in the latter. This turns out to be equivalent to the existence of a canonical $\R\ltimes \R^{n-1}$ structure on the leaves of the co-Legendrian foliation. Further, the above structure implies the existence of $n$ contact fields preserving a special contact 1-form, thus providing the geometric framework and establishing equivalence with previously known definitions of contact integrability. We also show that contact completely integrable systems are solvable in quadratures. We present an example of contact complete integrability: the billiard system inside an ellipsoid in pseudo-Euclidean space, restricted to the space of oriented null geodesics. We describe a surprising acceleration mechanism for closed light-like billiard trajectories

High-vacuum-compatible high-power Faraday isolators for gravitational-wave interferometers

Faraday isolators play a key role in the operation of large-scale gravitational-wave detectors. Second-generation gravitational-wave interferometers such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and Advanced Virgo will use high-average-power cw lasers (up to 200 W) requiring specially designed Faraday isolators that are immune to the effects resulting from the laser beam absorption–degraded isolation ratio, thermal lensing, and thermally induced beam steering. In this paper, we present a comprehensive study of Faraday isolators designed specifically for high-performance operation in high-power gravitational-wave interferometers

The Álvaro Siza’s master plan, the architectural and structural projects for the reconstruction of Chiado, in Lisbon

On 1988 a frightful fire broke out in Chiado, destroying 18 buildings, of which most part only the facades remained. A reconstruction plan was committed to Álvaro Siza, who fulfilled the request to preserve the existing buildings. The bibliography is mainly devoted to historical events, and architectural design options. There are few publications on the constructive and structural interventions, the objective of this study, to allow a broader knowledge about the intervention at various levels and disciplines. This is of particular interest in the scope of the research project “Siza Atlas. Filling the gaps for World Heritage” which aims to contribute to the nomination of a group of Siza's works for the World Heritage List. The subject is analyzed trough complementary readings: research of bibliography, documentation from the archive and in situ observations. A comparative analysis of the interventions proves a common method of construction with reinforced concrete structure built in situ. The principal improvement of the plan concerned the public space, recreating paths between the blocks, connecting the lower and upper levels of Chiado.info:eu-repo/semantics/publishedVersio

Sensitivity Studies for Third-Generation Gravitational Wave Observatories

Advanced gravitational wave detectors, currently under construction, are expected to directly observe gravitational wave signals of astrophysical origin. The Einstein Telescope, a third-generation gravitational wave detector, has been proposed in order to fully open up the emerging field of gravitational wave astronomy. In this article we describe sensitivity models for the Einstein Telescope and investigate potential limits imposed by fundamental noise sources. A special focus is set on evaluating the frequency band below 10Hz where a complex mixture of seismic, gravity gradient, suspension thermal and radiation pressure noise dominates. We develop the most accurate sensitivity model, referred to as ET-D, for a third-generation detector so far, including the most relevant fundamental noise contributions.Comment: 13 pages, 7 picture

The Álvaro Siza’s master plan, the architectural and structural projects for the reconstruction of Chiado, in Lisbon

On 1988 a frightful fire broke out in Chiado, destroying 18 buildings, of which most part only the facades remained. A reconstruction plan was committed to Álvaro Siza, who fulfilled the request to preserve the existing buildings. The bibliography is mainly devoted to historical events, and architectural design options. There are few publications on the constructive and structural interventions, the objective of this study, to allow a broader knowledge about the intervention at various levels and disciplines. This is of particular interest in the scope of the research project “Siza Atlas. Filling the gaps for World Heritage” which aims to contribute to the nomination of a group of Siza's works for the World Heritage List. The subject is analyzed trough complementary readings: research of bibliography, documentation from the archive and in situ observations. A comparative analysis of the interventions proves a common method of construction with reinforced concrete structure built in situ. The principal improvement of the plan concerned the public space, recreating paths between the blocks, connecting the lower and upper levels of Chiado.info:eu-repo/semantics/publishedVersio