On the Number of Balanced Words of Given Length and Height over a Two-Letter Alphabet

We exhibit a recurrence on the number of discrete line segments joining two integer points in the plane using an encoding of such segments as balanced words of given length and height over the two-letter alphabet $\{0,1\}$. We give generating functions and study the asymptotic behaviour. As a particular case, we focus on the symmetrical discrete segments which are encoded by balanced palindromes.Comment: 24 page

Environmental Noise Mapping as a Smart Urban Tool Development

Since the European Directive 2002/49, large transportation infrastructure along with large urban areas should have completed strategic noise maps (SNM) and the relative noise action plans (NAP). The majority of European Member States (MS) has enforced this directive and completed fully or, in some cases, partially, with European smart cities to use and share the same criteria and methodologies and along with transport operators to communicate to the public the relevant results and respective action plans by ensuring the citizen’s awareness about the environmental noise, the quality acoustic environment, and their effect to their professional and everyday lifestyle. Today, 18 years after its first edition, the European Directive 2002/49/EC is needed to be reformulated to take into account all defects that have been identified and to adapt as well as possible to contemporary constraints. New methodology tools have been developed especially regarding soundscaping and environmental acoustic rehabilitation of urban areas, and the respective chapter will describe the progress being made on these smart developments of cities and infrastructures. This chapter will also evoke criticisms of these smart tools and will present results from several—state of the art—case studies especially regarding the practical and theoretical limits they face

Assessment of field rolling resistance of manual wheelchairs

This article proposes a simple and convenient method for assessing the subject-specific rolling resistance acting on a manual wheelchair, which could be used during the provision of clinical service. This method, based on a simple mathematical equation, is sensitive to both the total mass and its fore-aft distribution, which changes with the subject, wheelchair properties, and adjustments. The rolling resistance properties of three types of front casters and four types of rear wheels were determined for two indoor surfaces commonly encountered by wheelchair users (a hard smooth surface and carpet) from measurements of a three-dimensional accelerometer during field deceleration tests performed with artificial load. The average results provided by these experiments were then used as input data to assess the rolling resistance from the mathematical equation with an acceptable accuracy on hard smooth and carpet surfaces (standard errors of the estimates were 4.4 and 3.9 N, respectively). Thus, this method can be confidently used by clinicians to help users make trade-offs between front and rear wheel types and sizes when choosing and adjusting their manual wheelchair.This material was based on work supported by the SACR-FRM project, French National Research Agency (ANR-06-TecSan-020) and the Centre d’Etudeset de Recherche sur l’Appareillage des Handicapés (loaned all MWCs required to fulfill this work

Pulsed high magnetic field measurement via a Rubidium vapor sensor

We present a new technique to measure pulsed magnetic fields based on the use of Rubidium in gas phase as a metrological standard. We have therefore developed an instrument based on laser inducing transitions at about 780~nm (D2 line) in a Rubidium gas contained in a mini-cell of 3~mm~x~3~mm cross section. To be able to insert such a cell in a standard high field pulsed magnet we have realized a fibred probe kept at a fixed temperature. Transition frequencies for both the $\pi$ (light polarization parallel to the magnetic field) and $\sigma$ (light polarization perpendicular to the magnetic field) configurations are measured by a commercial wavemeter. One innovation of our sensor is that in addition of monitoring the light transmitted by the Rb cell, which is usual, we also monitor the fluorescence emission of the gas sample from a very small volume with the advantage of reducing the impact of the field inhomogeneity on the field measurement. Our sensor has been tested up to about 58~T.Comment: Submitted to Review Scientific Instrument

Impact of inflated structures on a liquid free surface.

International audienceThere are many situations where inflated structures may hit violently a liquid free surface. One of them occurs during sea-landing of helicopters. As a matter of fact helicopters are equipped with inflated floaters. Those floaters are made of impermeable tissues which are almost inextensible and their flexural rigidity is small. These mechanical characteristics are difficult to reproduce at model scales, that is why we found more conventional inflated balloons like space hopper. Experiments have been carried out in the flume of Ecole Centrale Marseille. Only qualitative measurements have been performed. High speed camera provided the main features of the phenomenona. This abtract sums up this experimental campaign and the first attempts done in the numerical modellings thus yielding some comparisons. It is shown that simple linearized models- both structural and hydrodynamic models - can reproduce the early stage of penetration when impact occurs

Understanding the saturation power of Josephson Parametric Amplifiers made from SQUIDs arrays

We report on the implementation and detailed modelling of a Josephson Parametric Amplifier (JPA) made from an array of eighty Superconducting QUantum Interference Devices (SQUIDs), forming a non-linear quarter-wave resonator. This device was fabricated using a very simple single step fabrication process. It shows a large bandwidth (45 MHz), an operating frequency tunable between 5.9 GHz and 6.8 GHz and a large input saturation power (-117 dBm) when biased to obtain 20 dB of gain. Despite the length of the SQUID array being comparable to the wavelength, we present a model based on an effective non-linear LC series resonator that quantitatively describes these figures of merit without fitting parameters. Our work illustrates the advantage of using array-based JPA since a single-SQUID device showing the same bandwidth and resonant frequency would display a saturation power 15 dB lower.Comment: 12 pages, 9 figures, Appendices include

A photonic crystal Josephson traveling wave parametric amplifier

An amplifier combining noise performances as close as possible to the quantum limit with large bandwidth and high saturation power is highly desirable for many solid state quantum technologies such as high fidelity qubit readout or high sensitivity electron spin resonance for example. Here we introduce a new Traveling Wave Parametric Amplifier based on Superconducting QUantum Interference Devices. It displays a 3 GHz bandwidth, a -102 dBm 1-dB compression point and added noise near the quantum limit. Compared to previous state-of-the-art, it is an order of magnitude more compact, its characteristic impedance is in-situ tunable and its fabrication process requires only two lithography steps. The key is the engineering of a gap in the dispersion relation of the transmission line. This is obtained using a periodic modulation of the SQUID size, similarly to what is done with photonic crystals. Moreover, we provide a new theoretical treatment to describe the non-trivial interplay between non-linearity and such periodicity. Our approach provides a path to co-integration with other quantum devices such as qubits given the low footprint and easy fabrication of our amplifier.Comment: 6 pages, 4 figures, Appendixe