Regression analysis with missing data and unknown colored noise: application to the MICROSCOPE space mission

The analysis of physical measurements often copes with highly correlated noises and interruptions caused by outliers, saturation events or transmission losses. We assess the impact of missing data on the performance of linear regression analysis involving the fit of modeled or measured time series. We show that data gaps can significantly alter the precision of the regression parameter estimation in the presence of colored noise, due to the frequency leakage of the noise power. We present a regression method which cancels this effect and estimates the parameters of interest with a precision comparable to the complete data case, even if the noise power spectral density (PSD) is not known a priori. The method is based on an autoregressive (AR) fit of the noise, which allows us to build an approximate generalized least squares estimator approaching the minimal variance bound. The method, which can be applied to any similar data processing, is tested on simulated measurements of the MICROSCOPE space mission, whose goal is to test the Weak Equivalence Principle (WEP) with a precision of $10^{-15}$. In this particular context the signal of interest is the WEP violation signal expected to be found around a well defined frequency. We test our method with different gap patterns and noise of known PSD and find that the results agree with the mission requirements, decreasing the uncertainty by a factor 60 with respect to ordinary least squares methods. We show that it also provides a test of significance to assess the uncertainty of the measurement.Comment: 12 pages, 4 figures, to be published in Phys. Rev.

An extremal model for amorphous media plasticity

An extremal model for the plasticity of amorphous materials is studied in a simple two-dimensional anti-plane geometry. The steady-state is analyzed through numerical simulations. Long-range spatial and temporal correlations in local slip events are shown to develop, leading to non-trivial and highly anisotropic scaling laws. In particular, the plastic strain is shown to statistically concentrate over a region which tends to align perpendicular to the displacement gradient. By construction, the model can be seen as giving rise to a depinning transition, the threshold of which (i.e. the macroscopic yield stress) also reveal scaling properties reflecting the localization of the activity.Comment: 4 pages, 5 figure

Leonardo's rule, self-similarity and wind-induced stresses in trees

Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads

Analyse expérimentale de l'effet de l'inharmonicité des instruments a anche simple -Cas du saxophone alto

National audiencePour les instruments de musiquè a vent, l'inharmonicité des fréquences de résonance est une des grandeurs considérées , en facture instrumentale, comme représentatives de la qualité d'un instrument. L'inharmonicité peut altérer le timbre ainsi que la justesse de l'instrument. Pour les saxophones, l'inharmonicité des fréquences de résonances est principalement causée par la troncature de la perce conique ainsi que par la présence des trous latéraux. Le but de ce travail est de mettre en avant expérimentalement l'effet de l'inharmonicité des fréquences de résonances sur la nature des régimes d'oscillation produits par un instrument a anche simple. Un piston est fixé au niveau du bocal d'un saxophone alto afin de diminuer progressivement lapremì ere fréquence de résonance , ce qui permet de modifier l'inharmonicité de l'instrument. Une bouche artificielle est utilisée afin de mettre en oscillation l'instrument avec des param etres de contrôle constants (param etre d'embouchure et pression statique dans la bouche). Ces param etres sont evalués expérimentalement par le biais d'une mesure de la caractéristique non linéaire. Par modification des param etres de contrôle et de l'inharmonicité, une grande diversité de régimes d'oscillation est observée expérimentalement. Ces régimes sont identifiés par l'analyse du signal de pression a l' intérieur du bec. En particulier, des régimes d'oscillation quasi-périodiques sont produits sous forme de sons multiphoniques

Eclipses of the inner satellites of Jupiter observed in 2015

During the 2014-2015 campaign of mutual events, we recorded ground-based photometric observations of eclipses of Amalthea (JV) and, for the first time, Thebe (JXIV) by the Galilean moons. We focused on estimating whether the positioning accuracy of the inner satellites determined with photometry is sufficient for dynamical studies. We observed two eclipses of Amalthea and one of Thebe with the 1 m telescope at Pic du Midi Observatory using an IR filter and a mask placed over the planetary image to avoid blooming features. A third observation of Amalthea was taken at Saint-Sulpice Observatory with a 60 cm telescope using a methane filter (890 nm) and a deep absorption band to decrease the contrast between the planet and the satellites. After background removal, we computed a differential aperture photometry to obtain the light flux, and followed with an astrometric reduction. We provide astrometric results with an external precision of 53 mas for the eclipse of Thebe, and 20 mas for that of Amalthea. These observation accuracies largely override standard astrometric measurements. The (O-C)s for the eclipse of Thebe are 75 mas on the X-axis and 120 mas on the Y-axis. The (O-C)s for the total eclipses of Amalthea are 95 mas and 22 mas, along the orbit, for two of the three events. Taking into account the ratio of (O-C) to precision of the astrometric results, we show a significant discrepancy with the theory established by Avdyushev and Ban'shikova in 2008, and the JPL JUP 310 ephemeris.Comment: 7 pages, 10 figures, 4 table

Quantum oscillations and decoherence due to electron-electron interaction in metallic networks and hollow cylinders

We have studied the quantum oscillations of the conductance for arrays of connected mesoscopic metallic rings, in the presence of an external magnetic field. Several geometries have been considered: a linear array of rings connected with short or long wires compared to the phase coherence length, square networks and hollow cylinders. Compared to the well-known case of the isolated ring, we show that for connected rings, the winding of the Brownian trajectories around the rings is modified, leading to a different harmonics content of the quantum oscillations. We relate this harmonics content to the distribution of winding numbers. We consider the limits where coherence length $L_\varphi$ is small or large compared to the perimeter $L$ of each ring constituting the network. In the latter case, the coherent diffusive trajectories explore a region larger than $L$, whence a network dependent harmonics content. Our analysis is based on the calculation of the spectral determinant of the diffusion equation for which we have a simple expression on any network. It is also based on the hypothesis that the time dependence of the dephasing between diffusive trajectories can be described by an exponential decay with a single characteristic time $\tau_\varphi$ (model A) . At low temperature, decoherence is limited by electron-electron interaction, and can be modelled in a one-electron picture by the fluctuating electric field created by other electrons (model B). It is described by a functional of the trajectories and thus the dependence on geometry is crucial. Expressions for the magnetoconductance oscillations are derived within this model and compared to the results of model A. It is shown that they involve several temperature-dependent length scales.Comment: 35 pages, revtex4, 25 figures (34 pdf files

Oscillation threshold of a clarinet model: a numerical continuation approach

This paper focuses on the oscillation threshold of single reed instruments. Several characteristics such as blowing pressure at threshold, regime selection, and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion. Previous works have shown interesting tendencies, using analytical expressions with simplified models. In the present study, a more elaborated physical model is considered. The influence of several parameters, depending on the reed properties, the design of the instrument or the control operated by the player, are studied. Previous results on the influence of the reed resonance frequency are confirmed. New results concerning the simultaneous influence of two model parameters on oscillation threshold, regime selection and playing frequency are presented and discussed. The authors use a numerical continuation approach. Numerical continuation consists in following a given solution of a set of equations when a parameter varies. Considering the instrument as a dynamical system, the oscillation threshold problem is formulated as a path following of Hopf bifurcations, generalizing the usual approach of the characteristic equation, as used in previous works. The proposed numerical approach proves to be useful for the study of musical instruments. It is complementary to analytical analysis and direct time-domain or frequency-domain simulations since it allows to derive information that is hardly reachable through simulation, without the approximations needed for analytical approach

Speckle Control with a remapped-pupil PIAA-coronagraph

The PIAA is a now well demonstrated high contrast technique that uses an intermediate remapping of the pupil for high contrast coronagraphy (apodization), before restoring it to recover classical imaging capabilities. This paper presents the first demonstration of complete speckle control loop with one such PIAA coronagraph. We show the presence of a complete set of remapping optics (the so-called PIAA and matching inverse PIAA) is transparent to the wavefront control algorithm. Simple focal plane based wavefront control algorithms can thus be employed, without the need to model remapping effects. Using the Subaru Coronagraphic Extreme AO (SCExAO) instrument built for the Subaru Telescope, we show that a complete PIAA-coronagraph is compatible with a simple implementation of a speckle nulling technique, and demonstrate the benefit of the PIAA for high contrast imaging at small angular separation.Comment: 6 figures, submitted to PAS