A remarkable periodic solution of the three-body problem in the case of equal masses

Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is that the three bodies chase each other around a fixed eight-shaped curve. Setting aside collinear motions, the only other known motion along a fixed curve in the inertial plane is the ``Lagrange relative equilibrium" in which the three bodies form a rigid equilateral triangle which rotates at constant angular velocity within its circumscribing circle. Our orbit visits in turns every ``Euler configuration" in which one of the bodies sits at the midpoint of the segment defined by the other two (Figure 1). Numerical computations by Carles Sim\'o, to be published elsewhere, indicate that the orbit is ``stable" (i.e. completely elliptic with torsion). Moreover, they show that the moment of inertia I(t) with respect to the center of mass and the potential U(t) as functions of time are almost constant.Comment: 21 pages, published versio

The cost of exactly simulating quantum entanglement with classical communication

We investigate the amount of communication that must augment classical local hidden variable models in order to simulate the behaviour of entangled quantum systems. We consider the scenario where a bipartite measurement is given from a set of possibilities and the goal is to obtain exactly the same correlations that arise when the actual quantum system is measured. We show that, in the case of a single pair of qubits in a Bell state, a constant number of bits of communication is always sufficient--regardless of the number of measurements under consideration. We also show that, in the case of a system of n Bell states, a constant times 2^n bits of communication are necessary.Comment: 9 pages, LaTeX, no figure

Prior uncertainty investigation of density-viscosity dependent joint transport of heat and solute in alluvial sediments

Joint heat and solute tracer tests allow to add diffusion and conduction information to the solute advection-dispersion and help imaging preferential pathways in heterogeneous aquifers. We perform a joint interpretation of heat and solute tracer tests combining deterministic modeling and Bayesian Evidential Learning. The results show a strong influence of the water viscosity. The stochastic simulations highlight the influence of spatial and parameter uncertainty on the resulting breakthrough curves, stressing the need for realistic uncertainty quantification.Joint heat and solute tracer test inversion for imaging preferential pathway

Arctic HYCOS – 1st Workshop on Improved Monitoring, Accuracy and Data Availability in the Arctic Drainage Basin: Meeting Summary Report and Implementation Plan

The World Hydrological Cycle Observing System (WHYCOS) is a global programme, developed in response to the scarcity or absence of accurate, timely and accessible data and information in real or near real time on freshwater resources in many parts of the world. The programme is implemented through various components (HYCOSs) at the regional and/or basin scale. It is guided by the WHYCOS International Advisory Group (WIAG). The Arctic-HYCOS program is being promoted through this Workshop. For more information on the WHYCOS, please see http://www.whycos.org/cms/. The main goal of the Arctic-HYCOS program is to improve monitoring, data accuracy, availability and dissemination of information in the pan-arctic drainage basin. This project is science-driven and is aimed at monitoring freshwater fluxes and pollutants into the Arctic Ocean with the objective of improving climate predictions in the Northern Hemisphere and assessing the pollution of the Arctic coastal areas and the open Arctic Ocean. Arctic-HYCOS is currently organized along three main activities. 1. Develop and optimal design fro hydro-meteorological monitoring networks to capture the essential variability of the Arctic hydrological system and to enable accurate and efficient assessment of change 2. Estimate uncertainty of available in situ and possible remote sensing data including analysis of accuracy and systematic errors of new observation technology 3. Develop an integrated pan-arctic data consolidation and analysis system for the water cycle uniting data from various in-situ and other sources

Prévalence du trouble de stress post-traumatique chez des chauffeurs d’autobus

Plusieurs rapports indiquent que les employés du transport en commun constituent un groupe de travailleurs risquant de vivre des événements traumatiques. Cependant, il n'y a que peu de données scientifiques sur l'impact de tels événements dans cette population. Lors d'une enquête épidémiologique menée auprès des chauffeurs d'autobus de la STCUM, un peu plus du tiers des chauffeurs rapportent un événement traumatique au travail. De ces événements, les menaces graves et les agressions constituent la majorité. Les événements traumatiques sont plus fréquents au travail que dans la vie privée. La prévalence à vie du TSPT est de 10,7% pour les événements subis au travail et de 21,3 % pour ceux de la vie privée. Neuf chauffeurs sur 100 exposés à un événement au travail souffraient d'un TSPT dans le mois précédant l'enquête. Lorsque nous considérons les événements survenus dans la vie privée, près de 15% de ces exposés étaient victimes d'un TSPT. Lorsque les deux milieux d'exposition sont réunis, 12% présentaient un TSPT dans le mois précédant la recherche.Many recent reports indicate that public transport employees constitute a group of workers at high risk of going through a traumatic event. Yet, very few scientific data on the impact of these events on this population are available. The authors present results of an epidemiological study conducted among Montreal bus drivers. A little more than a third of bus drivers have reported a traumatic event at work. Among the whole of traumatic events occuring during the course of their work, serious threats and assault constitute the majority of these events. Traumatic events are more frequent at work than in their private lives. The prevalence of PTSD for those exposed to a traumatic event at work is of 10,7% and of 21,3% for those bus drivers exposed to traumatic events in their private lives. Nine out of 100 drivers exposed to a traumatic event at work suffered a PTSD in the month preceding the study. When the authors consider the events occuring in the private lives, alomost 15% of those exposed were victims of PTSD. When the two levels of expositions are reunited, 12% of those exposed presented a PTSD in the month preceding the research

Statistical Methods for Thermonuclear Reaction Rates and Nucleosynthesis Simulations

Rigorous statistical methods for estimating thermonuclear reaction rates and nucleosynthesis are becoming increasingly established in nuclear astrophysics. The main challenge being faced is that experimental reaction rates are highly complex quantities derived from a multitude of different measured nuclear parameters (e.g., astrophysical S-factors, resonance energies and strengths, particle and gamma-ray partial widths). We discuss the application of the Monte Carlo method to two distinct, but related, questions. First, given a set of measured nuclear parameters, how can one best estimate the resulting thermonuclear reaction rates and associated uncertainties? Second, given a set of appropriate reaction rates, how can one best estimate the abundances from nucleosynthesis (i.e., reaction network) calculations? The techniques described here provide probability density functions that can be used to derive statistically meaningful reaction rates and final abundances for any desired coverage probability. Examples are given for applications to s-process neutron sources, core-collapse supernovae, classical novae, and big bang nucleosynthesis.Comment: Accepted for publication in J. Phys. G Focus issue "Enhancing the interaction between nuclear experiment and theory through information and statistics

Transient Fields Radiated by Nonuniform Trasnducers in a Solid Calculated by an Approximate Model and the Finite-Difference Method

Nonuniform broadband transducers have been shown to radiate transient fields of simpler time and space structures than conventional uniform transducers by modifying transducer diffraction effects [1, 2]. The echo-structure arising from a defect as measured in pulse-echo methods of NDT is a fortiori simplified since transducer diffraction effects occur both in radiation and in reception [2]. Most of the theoretical and experimental works on nonuniform transducers dealt with the propagation of pulses of ultrasound in fluids. In solids, the transient field radiated by even a simple compression wave disk-transducer directly coupled with an elastic half-space is very complex because diffraction effects leads to complex mode-conversion phenomena [3–5]. Such a transducer not only radiates a complex compression wave-field (comparable with that radiated in fluids by a similar transducer) but also a complex shear wavefield. In the present paper, three different source profiles are considered (same as in Ref. [2] where echo-responses from targets in fluids were studied): a conventional uniform profile, a nondiffracting profile and a profile reinforcing diffraction effects. The two nonuniform profiles are not ideal as those considered in [6]. We have developed industrial prototypes vibrating with these profiles (in [2], only laboratory-made transducers were considered). The present paper aims to show how they simplify the wavefield structure radiated in solids. To do this, both waveform and amplitude of the transient velocity radiated at various field-points are calculated by means of two methods: a recently proposed approximate solution [4] (improved in [5]) and a pure numerical scheme based on the finite-difference method [7]. First, the approximate solution is recalled [4, 5]. Analytic formulas for a uniform source profile are explicitly given. They are combined with the superposition principle to allow the computation of the field radiated by nonuniform but axisymmetrical source profiles considered herein. Then, the finite-difference scheme originally developed for NDT modeling [7] is briefly recalled. It allows the computation of the field radiated by arbitrary axisymmetrical source profiles. Both methods are used to predict the particle velocity radiated by the three profiles considered at various field-points either on- or off-axis and at different ranges. The accuracy of both methods is shown by comparing predicted waveforms. Finally, all the results are discussed to show advantages and disadvantages of using nonuniformly excited transducers in the context of pulse-echo methods of NDT

Component retention in principal component analysis with application to cDNA microarray data

Shannon entropy is used to provide an estimate of the number of interpretable components in a principal component analysis. In addition, several ad hoc stopping rules for dimension determination are reviewed and a modification of the broken stick model is presented. The modification incorporates a test for the presence of an "effective degeneracy" among the subspaces spanned by the eigenvectors of the correlation matrix of the data set then allocates the total variance among subspaces. A summary of the performance of the methods applied to both published microarray data sets and to simulated data is given. This article was reviewed by Orly Alter, John Spouge (nominated by Eugene Koonin), David Horn and Roy Varshavsky (both nominated by O. Alter)