Genealogical particle analysis of rare events

In this paper an original interacting particle system approach is developed for studying Markov chains in rare event regimes. The proposed particle system is theoretically studied through a genealogical tree interpretation of Feynman--Kac path measures. The algorithmic implementation of the particle system is presented. An estimator for the probability of occurrence of a rare event is proposed and its variance is computed, which allows to compare and to optimize different versions of the algorithm. Applications and numerical implementations are discussed. First, we apply the particle system technique to a toy model (a Gaussian random walk), which permits to illustrate the theoretical predictions. Second, we address a physically relevant problem consisting in the estimation of the outage probability due to polarization-mode dispersion in optical fibers.Comment: Published at http://dx.doi.org/10.1214/105051605000000566 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Backpropagation Imaging in Nonlinear Harmonic Holography in the Presence of Measurement and Medium Noises

In this paper, the detection of a small reflector in a randomly heterogenous medium using second-harmonic generation is investigated. The medium is illuminated by a time-harmonic plane wave at frequency omega. It is assumed that the reflector has a non-zero second-order nonlinear susceptibility, and thus emits a wave at frequency two omega in addition to the fundamental frequency linear scattering. It is shown how the fundamental frequency signal and the second-harmonic signal propagate in the medium. A statistical study of the images obtained by migrating the boundary data is performed. It is proved that the second-harmonic image is more stable with respect to medium noise than the one obtained with the fundamental signal. Moreover, the signal-to-noise ratio for the second-harmonic image does not depend neither on the second-order susceptibility tensor nor on the volume of the particle.Comment: 36 pages, 18 figure

Entropy production and time asymmetry in nonequilibrium fluctuations

The time-reversal symmetry of nonequilibrium fluctuations is experimentally investigated in two out-of-equilibrium systems namely, a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current. The dynamical randomness of their nonequilibrium fluctuations is characterized in terms of the standard and time-reversed entropies per unit time of dynamical systems theory. We present experimental results showing that their difference equals the thermodynamic entropy production in units of Boltzmann's constant

Finite Element Simulation of Low Velocity Impact Damage on an Aeronautical Carbon Composite Structure

Low velocity barely visible impact damage (BVID) in laminated carbon composite structures has a major importance for aeronautical industries. This contribution leads with the development of finite element models to simulate the initiation and the propagation of internal damage inside a carbon composite structure due by a low velocity impact. Composite plates made from liquid resin infusion process (LRI) have been subjected to low energy impacts (around 25 J) using a drop weight machine. In the experimental procedure, the internal damage is evaluated using an infrared thermographic camera while the indentation depth of the face is measured by optical measurement technique. In a first time we developed a robust model using homogenised shells based on degenerated tri-dimensional brick elements and in a second time we decided to modelize the whole stacking sequence of homogeneous layers and cohesive interlaminar interfaces in order to compare and validate the obtained results. Both layer and interface damage initiation and propagation models based on the Hashin and the Benzeggagh-Kenane criteria have been used for the numerical simulations. Comparison of numerical results and experiments has shown the accuracy of the proposed models

Poésie spatiale = Raumpoesie. - Zweisprachig: Französisch / Deutsch

Ilse und Pierre Garnier haben ein umfangreiches lyrisches Werk geschaffen. Seit Beginn der sechziger Jahre sind sie Initiatoren und Hauptvertreter der poésie spatiale. Die von Pierre Garnier redigierte Zeitschrift ´Les Lettres´ bildet zwischen 1963 und 1967 eine internationale Plattform für konkrete, visuelle und spatiale Poesie. Das Ehepaar Garnier hat darüber hinaus in Übersetzungen und Aufsätzen deutsche Literatur in Frankreich bekannt gemacht. Die maßgebliche französische Benn-Übersetzung stammt von Pierre Garnier. Die poésie spatiale integriert, reflektiert und erneuert die Konstellationen der konkreten und visuellen Poesie. Sie betont die Materialität und räumliche Gestalt von Sprach- und Textzeichen. Nach und nach wurden die spatialen Werke von Pierre und Ilse Garnier zunehmend asketischer und nachdenklicher. Ihre fragilen Wort- und Bildkompositionen verflechten vielfältige literarische und philosophische Assoziationen und versuchen, die Räume jenseits des Sagbaren zu ergründen

Scattered wavefield in the stochastic homogenization regime

In the context of providing a mathematical framework for the propagation of ultrasound waves in a random multiscale medium, we consider the scattering of classical waves (modeled by a divergence form scalar Helmholtz equation) by a bounded object with a random composite micro-structure embedded in an unbounded homogeneous background medium. Using quantitative stochastic homogenization techniques, we provide asymptotic expansions of the scattered field in the background medium with respect to a scaling parameter describing the spatial random oscillations of the micro-structure. Introducing a boundary layer corrector to compensate the breakdown of stationarity assumptions at the boundary of the scattering medium, we prove quantitative $L^2$- and $H^1$- error estimates for the asymptotic first-order expansion. The theoretical results are supported by numerical experiments