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

Displacement noise from back scattering and specular reflection of input optics in advanced gravitational wave detectors

The second generation of ground-based interferometric gravitational wave detectors are currently being built and installed. They are designed to be better in strain sensitivity by about a factor 10 with respect to the first generation. Light originating from the laser and following unintended paths, called stray light, has been a major problem during the commissioning of all of the first generation detectors. Indeed, stray light carries information about the phase of the emitting object. Therefore, in the next generation all the optics will be suspended in the vacuum in order to mitigate their associated stray light displacement noise. Despite this additional precaution, the challenging target sensitivity at low frequency which is partially limited by quantum radiation pressure combined with up-conversion effects, requires more detailed investigation. In this paper, we turn our attention to stray light originating from auxiliary optical benches. We use a dedicated formalism to compute the re-coupling of back-reflected and back-scattered light. We show, in particular, how much care should be taken in designing and setting requirements for the input bench optics

A conceptual model for building design coordination using open source tools

Building Design Coordination is the process of communicating and integrating multidisciplinary designs into a single, coherent set of information that can be used for construction, to anticipate problems that would otherwise only be raised on the construction site. As projects grow in complexity and size, digital communication tools and other technological improvements have made it possible for physically distant design teams to collaborate in novel ways. More recently, BIM (Building Information Modelling), has opened even greater possibilities, although the design process nevertheless is often one of trial and error, demanding on each small change multiple possibilities to be considered, with decisions requiring to be validated among designers and other project stakeholders. Regardless of all the advantages that BIM has brought to the industry, testing for design changes in BIM models often requires a big effort and is a time-consuming activity that should be avoided whenever simpler processes can be used. Further developments on this study will propose a framework for building design coordination, using a non-relational graph database. The system can track design issues between unlimited users, organized into teams, handling formal project documents and keeping an historical record of the design development timeline. Since all the information regarding the design development process is stored in the form of Nodes and Relationships these can be intuitively be manipulated making it easier for teams to provide input on design decisions in real time with least cost impact to the project, providing at the same time access to pertinent information on the status of design issues and how the various stakeholders are contributing to the project. Through the use of reliable open source tools, a prototype can be implemented and made available to the industry professionals for testing, providing guidelines for modelling a Building Design Coordination system.info:eu-repo/semantics/publishedVersio

Comparison of Structure and Properties of Femtosecond and Nanosecond Laser-Structured Silicon

We compare the optical properties, chemical composition, and crystallinity of silicon microstructures formed in the presence of SF6 by femtosecond laser irradiation and by nanosecond laser irradiation. In spite of very different morphology and crystallinity, the optical properties and chemical composition of the two types of microstructures are very similar. The structures formed with femtosecond (fs) pulses are covered with a disordered nanocrystalline surface layer less than 1 um thick, while those formed with nanosecond (ns) pulses have very little disorder. Both ns-laser-formed and fs-laser-formed structures absorb near-infrared (1.1 – 2.5 um) radiation strongly and have roughly 0.5% sulfur impurities.Engineering and Applied Science

Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings

Hafnium-silica multilayer mirrors and polarizers were deposited by e-beam evaporation onto BK7 glass substrates. The mirrors and polarizers were coated for operation at 1053 nm at 45{degree} and at Brewster`s angle (56{degree}), respectively. They were tested with a single 3-ns laser pulse. Morphology of the laser-induced damage was characterized by optical and scanning electron microscopy. Four distinct damage morphologies were found: pits, flatbottom pits, scalds, and delaminates. The pits and flat bottom pits (<30{mu}m dia) were detected at lower fluences (as low as 5 J/cm{sup 2}). The pits seemed to result from ejection of nodular defects by causing local enhancement of the electric field. Scalds and delaminates could be observed at higher fluences (above 13 J/cm{sup 2}) and seemed to result from the formation of plasmas on the surface. These damage types often originated at pits and were less than 300 {mu}m diameter; their size increased almost linearly with fluence. Finally, effects of the damage on the beam (reflectivity degradation and phase modulations) were measured

Differential Adaptive Stress Testing of Airborne Collision Avoidance Systems

The next-generation Airborne Collision Avoidance System (ACAS X) is currently being developed and tested to replace the Traffic Alert and Collision Avoidance System (TCAS) as the next international standard for collision avoidance. To validate the safety of the system, stress testing in simulation is one of several approaches for analyzing near mid-air collisions (NMACs). Understanding how NMACs can occur is important for characterizing risk and informingdevelopment of the system. Recently, adaptive stress testing (AST) has been proposed as a way to find the most likely path to a failure event. The simulation-based approach accelerates search by formulating stress testing as a sequential decision process then optimizing it using reinforcement learning. The approach has been successfully applied to stress test a prototype of ACAS Xin various simulated aircraft encounters. In some applications, we are not as interestedin the system's absolute performance as its performance relative to another system. Such situations arise, for example, during regression testing or when deciding whether a new system should replace an existing system. In our collision avoidance application, we are interested in finding cases where ACAS X fails but TCAS succeeds in resolving a conflict. Existing approaches do not provide an efficient means to perform this type of analysis. This paper extends the AST approach to differential analysis by searching two simulators simultaneously and maximizing the difference between their outcomes. We call this approach differential adaptive stress testing (DAST). We apply DAST to compare a prototype of ACAS X against TCAS and show examples of encounters found by the algorithm

Performance of a thermally deformable mirror for correction of low-order aberrations in laser beams

The thermally deformable mirror is a device aiming at correcting beam-wavefront distortions for applications where classical mechanical methods are precluded by noise considerations, as in advanced gravitational wave interferometric detectors. This moderately low-cost technology can be easily implemented and controlled thanks to the good reproducibility of the actuation. By using a flexible printed circuit board technology, we demonstrate experimentally that a device of 61 actuators in thermal contact with the back surface of a high-reflective mirror is able to correct the low-order aberrations of a laser beam at 1064 nm and could be used to optimize the mode matching into Fabry-Perot cavities

Influence of carbon and nitrogen on electronic structure and hyperfine interactions in fcc iron-based alloys

Carbon and nitrogen austenites, modeled by Fe8N and Fe8C superstructures are studied by full-potential LAPW method. Structure parameters, electronic and magnetic properties as well as hyperfine interaction parameters are obtained. Calculations prove that Fe-C austenite can be successfully modeled by ordered Fe8C superstructure. The results show that chemical Fe-C bond in Fe8C has higher covalent part than in Fe8N. Detailed analysis of electric field gradient formation for both systems is performed. The calculation of electric field gradient allow us to carry out a good interpretation of Moessbauer spectra for Fe-C and Fe-N systems.Comment: 8 pages, 3 figures, IOP-style LaTeX, submitted to J. Phys. Condens. Matte

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