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International audience; This paper considers the problem of fully distributed channel allocation in clustered wireless networks when the propagation medium is random. We extend here the existing Trial and Error (TE) framework developed in the deterministic case and for which strong convergence properties hold. We prove that using directly this solution in the random context leads to unsatisfactory solutions. Then we propose an adaptation of the original Trial and Error Learning (TEL) algorithm, called Robust TEL (RTEL), assuming that the random channel effects translate into a bounded stochastic disturbance of the utility function. The solution consists in introducing thresholds in the transitions of the TEL’s Finite State Controller (FSC). We prove that this new solution restores the good convergence property inherited from the TEL. Furthermore, we provide analysis of the stochastic utilities in the Rayleigh fading case in order to check the bounded assumption. Finally, we develop an online algorithm that dynamically estimates the optimal threshold values to adapt to the instantaneous disturbance. Numerical results corroborate our theoretical claims.

This paper considers wave-based imaging through a heterogeneous (random) scattering medium. The goal is to estimate the support of the reflectivity function of a remote scene from measurements of the backscattered wave field. The proposed imaging methodology is based on the coherent interferometric (CINT) approach that exploits the local empirical cross correlations of the measurements of the wave field. The standard CINT images are known to be robust (statistically stable) with respect to the random medium, but the stability comes at the expense of a loss of resolution. This paper shows that a two-point CINT function contains the information needed to obtain statistically stable and high-resolution images. Different methods to build such images are presented, theoretically analyzed and compared with the standard imaging approaches using numerical simulations. The first method involves a phase-retrieval step to extract the reflectivity function from the modulus of its Fourier transform. The second method involves the evaluation of the leading eigenvector of the two-point CINT imaging function seen as the kernel of a linear operator. The third method uses an optimization step to extract the reflectivity function from some cross products of its Fourier transform. The presentation is for the synthetic aperture radar data acquisition setup, where a moving sensor probes the scene with signals emitted periodically and records the resulting backscattered wave. The generalization to other imaging setups, with passive or active arrays of sensors, is discussed briefly., Comment: 31 pages, 5 figures

We study wave propagation in materials in which the refractive index varies in time. We compare the situations in which the variations are periodic and random. If the modulation period (in the peri...

International audience; The dynamic analysis of random fibrous networks (RFNs) is a novel topic, which has many applications since these networks are very often subjected to dynamical loading conditions such as mechanical vibrations. In order to bypass the complexity of performing dynamic computations at the microscopic scale of RFN, we develop and identify couple-stress and second gradient models as effective continua at the mesoscopic level of windows of analysis. The static mechanical properties which are at the basis of the dynamical analysis are computed thanks to FE simulations performed over windows of analysis subjected to mixed boundary conditions allowing to capture the classical and non-classical effective moduli. The acoustic properties are captured by the dispersion diagrams and phase velocity plots; we analyze the influence on the dynamic properties of the fiber bending length, and the fiber network density. The impact of these parameters is successively assessed for the couple-stress and strain gradient substitution continua. A comparison of the acoustic properties of the two effective media is provided, showing that the couple-stress medium is essentially non-dispersive for the longitudinal mode and dispersive for the shear mode, whereas the strain gradient medium behaves in a dispersive manner for both modes.

International audience; We address the question of estimating coherent scattering (weak scattering or coherent scatterer) by a time-evolving random medium. We consider two models of coherent scattering: homodyned K (HK) and generalized K (GK), and in both cases we derive stochastic differential equations for the scattered field. Approximate transition probabilities are computed using Euler–Maruyama scheme and the parameters for coherent scattering are estimated by maximum likelihood (ML). Using numerical simulations, we show that in the HK case, maximum likelihood estimation does not provide a significant advantage over a simplistic estimator based on the ergodicity property of the scattered field. On contrary, in GK scattering the transition probabilities carry significant information about the parameters, resulting in much better performance of the ML estimator.

International audience; Structures composed of repetitions of multiple identical cells are common and have been the object of a large body of literature on waveguides, periodic media, and cyclic symmetry. Starting from a cell model, possibly with a large number of Degrees of Freedom both inside the cell and on its edges, the objective of this paper is to propose a Ritz-Galerkin reduction procedure retaining the standard second order model form and periodicity properties of the original model, while controlling accuracy in terms of model bandwidth and reproduction of the forced response to applied loads. The procedure is classically decomposed in two phases: subspace learning and basis generation. For the learning phase, Wave Finite Element (WFE) and periodic computations are presented as alternatives. The latter are then preferred for their easier control on the reduced model accuracy using classical modal synthesis and the simple choice of few target wavelengths. For the basis generation phase, constraints needed to generate a periodic superelement are defined and numerical procedures to generate a basis verifying those constraints are proposed. The validity of the reduction is demonstrated for the case of a cell with random elastic properties presenting bandgaps, local modes and wavemode crossing. Accurate predictions of modes and damped forced response are given for both the infinite and finite cases, using frequency and time simulations. The proposed analysis illustrates tracking of waveshapes, evaluation of significant waves by computation of the forced response in the frequency/wavenumber domain and interpretation of the relation between the infinite and finite forced responses. The case of a railway track with edges and transitions between multiple periodic zones is finally used to illustrate scalability issues.

International audience; The paper focuses on the construction of one particle homogenization schemes for an ageing linear viscoelastic composite. The composite consists of an isotropic host matrix and randomly located spheroidal inhomogeneities. Both phases are assumed to be ageing linear viscoelastic. Expressions for the effective viscoelastic properties in the frameworks of Non Interaction Approximation as well as Maxwell and Mori-Tanaka-Benveniste homogenization schemes are derived. A special attention is paid to the far-field solution to the one-particle problem since it plays a major role in the Maxwell scheme.

International audience; We go back to the analysis of the transport of (classical or quantum) particles intime-dependent random media as proposed in [F. Poupaud and A. Vasseur,J. Math. Pures Appl.(9), 82 (2003), pp. 711–748], where the convergence of the expectation of solutions of the Liouvilleequation (resp., Wigner equation) to the solution of the Fokker-Planck equation (resp., Boltzmannequation) is established. Here we show that the convergence holds in probability. This result relieson certain scale separation properties of the scaling, as indicated by several counterexamples

We analyze sound propagation in a waveguide filled with a random medium modeled by small-amplitude spatial and temporal fluctuations of the mass density and wave speed. The time dependence of the m...

Nous etudions le comportement de la constante ergodique associee a une equation de Hamilton–Jacobi avec un hamiltonien convexe dans un environnement periodique, lorsque le hamiltonien est perturbe soit par une perturbation periodique avec une periode tendant vers l'infini, soit par une perturbation de type Bernoulli avec un petit parametre. Nous donnons un developpement de Taylor de la constante ergodique qui depend de la dimension. Lorsque d = 1 , le premier terme est non trivial, tandis que si d ≥ 2 , il est toujours nul. Bien que des questions similaires aient ete etudiees dans le cadre de l'homogeneisation d'equation elliptiques lineaires, notre resultat est le premier de cette nature dans un cas non-lineaire. Nos arguments, qui reposent sur des techniques de solutions de viscosite et de theorie KAM faible, soulevent de nombreuses questions nouvelles et stimulantes.

International audience; The effective wavenumber model of Linton and Martin [1] for the dilute monodisperse case (obstacles of identical sizes) is used to calculate the effective modulus and mass density of a polydisperse assembly of poroelastic spheres. We focus on the Rayleigh limit (low frequency regime) where the wavelengths can be considered very large compared to the size of the obstacles. In order to show the influence of the distribution in size of the obstacles, the special case of Schulz probability density function is considered.

International audience; The paper presents an analysis of acoustic wave propagation in a waveguide with random fluctuations of its sound speed profile. These random perturbations are assumed to have long-range correlation properties. In the waveguide, a monochromatic wave can be decomposed in propagating modes and evanescent modes, and the random perturbation couples all these modes. The paper presents an asymptotic analysis of the mode-coupling mechanism and uses this to characterize the transmitted wave. The paper presents the first fully rigorous characterization of wave propagation in long-range non-layered media.

TRIPOLI-4® is a registered trademark of CEA.; International audience; Assessing the impact of random media for eigenvalue problems plays a centralrole in nuclear reactor physics and criticality safety. In a recent work (Larmieret al., 2018a), we have applied a probabilistic model based on stochastic tessellationsin order to describe fuel degradation following severe accidents withpartial melting and re-arrangement of the resulting debris. The distribution ofthe multiplication factor and of the kinetics parameters as a function of the mixingstatistics model and of the typical correlation length of the tessellation wereexamined in detail for a benchmark configuration consisting in a fuel assemblywith UOX or MOX fuel pins. In this paper, we extend our previous findingsby including in the stochastic tessellation model the effects of anisotropy thatmight result from gravity and material stratification for this purpose, we adoptthe broad class of anisotropic Poisson geometries. We examine the evolution ofthe statistical properties of the tessellations, including the volume, surface andchord length of the cells for various anisotropy laws, and compare them to thecase of isotropic Poisson geometries. Then, we discuss the behaviour of the keyobservables of interest for eigenvalue problems in anisotropic tessellations byrevisiting the fuel assembly benchmark calculations proposed in (Larmier et al.,2018a). The effects of anisotropic random media on the multiplication factor andon the kinetics parameters will be carefully examined.

International audience; The microstructure studied in this paper is a Composite made up of Randomly oriented Short Fibers (RSFC) and a computational homogenization is performed to investigate its effective properties. The area fraction is also varied to study its effect on the size of the Deterministic Representative Volume Element (DRVE). It appeared that at certain area fractions, the RSFC does not respect the convergence of the apparent properties calculated under different boundary conditions. This indicates that it does not adhere to the definition of the DRVE in the studied range of scale. The concerned area fraction is found to be around the percolation threshold. The present work consists primarily in investigating the causes of this problem by studying an extreme example of a percolating medium which is a Composite made up of Randomly oriented Long Fibers (RLFC). By identifying the contributing factors, the calculability of the DRVE of a random composite can be predicted by simple verification of the microstructure morphology.

SpringerReference; International audience; The statistical inverse problem for the experimental identification of a non-Gauss-ian matrix-valued random field that is the model parameter of a boundary value problem, using some partial and limited experimental data related to a model observation, is a very difficult and challenging problem. A complete advanced methodology and the associated tools are presented for solving such a problem in the following framework: the random field that must be identified is a non-Gaussian matrix-valued random field and is not simply a real-valued random field; this non-Gaussian random field is in high stochastic dimension and is identified in a general class of random fields; some fundamental algebraic properties of this non-Gaussian random field must be satisfied such as symmetry, positiveness, invertibility in mean square, boundedness, symmetry class, spatial-correlation lengths, etc; the available experimental data sets correspond only to partial and limited data for a model observation of the boundary value problem. The developments presented are mainly related to the elasticity framework, but the methodology is general and can be used in many areas of computational sciences and engineering. The developments are organized as follows. The first part is devoted to the definition of the statistical inverse problem that has to be solved in high stochastic dimension. The second one deals with the construction of two possible parameterized representations for a non-Gaussian positive-definite matrix-valued random field that models the model parameter of a boundary value problem. The third part is devoted to the description of all the steps of the methodology allowing the statistical inverse problem to be solved in high stochastic dimension. These steps are based on the identification of a prior stochastic model of the Non-Gaussian random field by using the maximum likelihood method and then, on the identification of a posterior stochastic model of the Non-Gaussian random field by using the Bayes method.The fourth part presents the construction of an algebraic prior stochastic model of the model parameter of the boundary value problem, for a non-Gaussian matrix-valued random field. The generator of realizations for such an algebraic prior stochastic model for a non-Gaussian matrix-valued random field is presented.

International audience; Eigenvalue problems for neutron transport in random geometries are key for many applications, ranging from reactor design to criticality safety. In this work we examine the behaviour of the reactivity and of the kinetics parameters (the effective delayed neutron fraction and the effective neutron generationtime) for three-dimensional UOX and MOX assembly configurations where aportion of the fuel pins has been randomly fragmented by using various mixingstatistics. For this purpose, we have selected stochastic tessellations of the Poisson, Voronoi and Box type, which provide convenient models for the randompartitioning of space, and we have generated an ensemble of assembly realizations; for each geometry realization, criticality calculations have been performedby using the Monte Carlo code TRIPOLI-4 developed at CEA. We have then examined the evolution of the ensemble-averaged observables of interest as afunction of the average chord length of the random geometries, which is roughlyproportional to the correlation length of the fuel fragmentation. The methodology proposed in this work is fairly general and could be applied, e.g., to theassessment of re-criticality probability following severe accidents.

International audience; We explore the spatial profile of the ensemble average of the energy density of eigenchannels of the transmission matrix within random diffusive media using computer simulations and nonperturbative diagrammatic technique. A symmetrical profile with a peak in the middle of the sample is found for the fully transmitting eigenchannel and is shown to be closely related to a position dependent diffusion coefficient of the open media. We show that the average spatial profile of each transmission eigenchannel when normalized by the profile of the completely transmitting eigenchannel depends only upon the value of transmission through the corresponding eigenchannel. A universal expression for the average spatial profile is given in terms of the auxiliary localization lengths determined from transmission eigenvalues and position dependent diffusion coefficient. These lengths were first introduced by Dorokhov to describe the scaling of transmission and conductance through disordered media. Though direct measurement of energy distribution within a scattering medium is generally difficult, we demonstrate in microwave measurements that the integrated energy density stored in the media of each eigenchannel can be determined from the measurements of spectra of the transmission matrix. The derivative of the composite phase of the eigenchannels with respect to the angular frequency yields the contribution to the density of states (DOS) from the individual transmission eigenchannels. This is proportional to integrated energy stored and the dwell time of the transmission eigenchannel. The DOS determined from the transmission eigenchannel is shown to be in good agreement with DOS obtained by analyzing the field spectra into quasi-normal modes of the open medium. These results provide a path towards controlling the energy deposition within a scattering medium. © 2016 SPIE.

We study the probability $p \equiv p_\eta(t)$ that two directed polymers in a given random potential $\eta$ and with fixed and nearby endpoints, do not cross until time $t$. This probability is itself a random variable (over samples $\eta$) which, as we show, acquires a very broad probability distribution at large time. In particular the moments of $p$ are found to be dominated by atypical samples where $p$ is of order unity. Building on a formula established by us in a previous work using nested Bethe Ansatz and Macdonald process methods, we obtain analytically the leading large time behavior of {\it all moments} $\overline{p^m}\simeq \gamma_m/t$. From this, we extract the exact tail $\sim \rho(p)/t$ of the probability distribution of the non-crossing probability at large time. The exact formula is compared to numerical simulations, with excellent agreement., Comment: 16 pages + 6 pages of appendices, 2 figures

International audience; Modeling and simulation of two-phase flows in a porous random media is a highly challenging task due the non-linearity of the wetting process, the time and space scales at stake and the very large spatial variability and anisotropy of the intrinsic permeability. In the particular case of an injection problem being statistically invariant for any rotation around the axis of the well a coupled 3D/rotation-invariant probabilistic model is proposed following the methodology introduced in [1] and [2]. The idea of a variational coupling between a probabilistic local model and a deterministic or probabilistic model is developed here in the context of a coupling along a surface and not over a volume. 3D/2D coupling is also considered. The implementation in a general purpose Finite Element Code is then addressed and illustrated in the context of Risk assessment of geological storage of carbon dioxide.

We study the probability that two directed polymers in the same random potential do not intersect. We use the replica method to map the problem onto the attractive Lieb-Liniger model with generalized statistics between particles. We obtain analytical expressions for the first few moments of this probability, and compare them to a numerical simulation of a discrete model at high-temperature. From these observations, several large time properties of the non-crossing probabilities are conjectured. Extensions of our formalism to more general observables are discussed., Comment: 5 pages + 16 pages of supplemental material (Minor misprints corrected, references added)

International audience; We consider correlation-based imaging of a reflector located on one side of a passive array where the medium is homogeneous. On the other side of the array the illumination by remote impulsive sources goes through a strongly scattering medium. It has been shown in [J. Garnier and G. Papanicolaou, Inverse Problems, 28 (2012), 075002] that migrating the cross correlations of the passive array gives an image whose resolution is as good as if the array was active and the array response matrix was that of a homogeneous medium. In this paper we study the signal to noise ratio (SNR) of the image as a function of statistical properties of the strongly scattering medium, the signal bandwidth, and the source and passive receiver array characteristics. Using a Kronecker model for the strongly scattering medium we show that image resolution is as expected and that the SNR can be computed in an essentially explicit way. We show with direct numerical simulations using full wave propagation solvers in random media that the theoretical predictions based on the Kronecker model are accurate.

In this paper the reflection of an obliquely incident electromagnetic wave on a randomly layered multiscale half-space is analyzed. By using homogenization and diffusion approximation theorems it is possible to get a complete description of the reflectivity of the random half-space that depends on the effective reflectivity of the interface and on the random reflectivity of the bulk medium. Particular attention is devoted to the characterization of the Brewster anomalies that correspond to small or even zero reflectivity. It turns out that the interface reflectivity and the random medium reflectivity as functions of the incidence angle may both possess Brewster angles that minimize or even cancel them, but these two angles are in general different.

International audience; Some remarks are provided concerning the effects of geometrical transformations, such as those encountered in a manufacturing process, on the stochastic character of corresponding material properties. It is shown that, in general, even second-order statistical properties are transformed in a non-trivial manner as the material undergoes arbitrary transformation.

In Chapter 2, we describe the results obtained with Frank den Hollander about a model for a copolymer in an emulsion. This model was introduced by den Hollander and Whittington in \cite{dHW06}, and has subsequently being analyzed in details in \cite{dHP07b},\cite{dHP07c}, \cite{dHP07a}. In \cite{dHP13} it was extended to an even more realistic model which enters a new class consisting of those models for a polymer interacting with a random interface. Among the elements of this new class of models we can mention the random walk pinned at another random walk (see \cite{BerTon}, \cite{BS1} and \cite{BS2}) or the famous directed polymer with bulk disorder (see \cite{dH09} for a review). Most models for a copolymer at thermodynamic equilibrium had, up to the introduction of this new class of models, been built with a medium made of a single linear interface separating two solvents. The introduction of a random interface allows us to take into account some more complex media among which are the colloids (milk, ink, polluted water etc...)which are typically stabilized with polymers via the steric/depletion stabilization effect. The particularity of our model for a copolymer in an emulsionis that we managed to provide a variational characterization of its free energy. Such formulas are rarely available for disordered models in Statistical Mechanicsand they turn out to be a powerful tool to analyze the phase diagram of the system.Chapter 3 is dedicated to a completely different phenomenon, that is the collapse transition of a self-interacting partially directed self-avoiding walk. As mentioned above, this is a model for an homopolymer in a repulsive solvent. The model and its non directed counterpart have triggered a fair amount of activity within the physics community (see \cite{BDL09}, \cite{BOP95}, \cite{BGW92} and \cite{cf:Brak}). We studied this model with Philippe Carmona and Gia-Bao Nguyen in \cite{NGP13}, \cite{CNGP13} and \cite{CP}. We analyzed the model with a new probabilistic technic that relies on a random walk representation of the partition function. Our method turns out to be much more explicit and simple than what had been obtained previously with combinatorics techniques. We derive a fine asymptotic for the free energy close to criticality and we provide, for both the collapsed phase and the interior of the extended phase, a complete description of the path under the polymer measure when the system size is large but finite. In Chapter 4, we give a survey of the results obtained in \cite{Petr1}, \cite{Petr} and later in \cite{CP09a}, \cite{CP09b} with Francesco Caravenna and in \cite{CarCarPetr} with Francesco Caravenna and Philippe Carmona. The common point of the models studied in these papers is that they are elements of a wider class of models, i.e., the random walks in a random/deterministic potential. Many celebrated models enters this general framework such as the parabolic Anderson model via the Feynman Kac description of its solution,the pinning of a random walk by one or infinitely many horizontal interfaces, the polymer in a slit interacting with two walls but also the directed polymer in a random environment etc... Most of these models generate some phase transitions between very different regime corresponding to radically differentconformations of the path. We focus on three models that are (1) the discrete parabolic Anderson model, (2) the homogeneous polymer pinned/depinned at infinitely many interfaces and (3) the copolymer randomly pinned at a selective layer between two solvents. We will provide some results concerning the limiting free energy and the critical point for (3), the free energy and the scaling limits of the path in (2) and some strong localization results on the path for (1).

This thesis reports an experimental study of the modifications of the near-resonant light scattering properties of mesoscopic cold clouds of rubidium 87 which densities are tunable. for densities of the order of 1014 atoms/cm3, inter-atomic distances can be smaller than the wavelength of the radiation at resonance with the d2 line (780 nm) of rubidium 87. the magnitude of the dipole-dipole interactions between the scatters is such that they can no longer be considered as independent of each other: a phenomenon called collective scattering. the methods used to produce the studied samples are based on cooling (zeeman slower and magneto-optical trap) and trapping (optical tweezers) techniques for neutral atoms. they allow obtaining cold (100 µK) atomic ensembles containing from exactly one to several hundreds of atoms. the observations performed are based on the light scattered by these atoms which is collected thanks to a high numerical aperture optical system. in a first step, this study consists in characterizing the near-resonant light scattering by a single atom. it leads to the measurement of the delay in the scattering by an atom of a wave packet of light, called wigner delay, in conditions close to those of a gedanken experiment. in a second step, this study deals with the collective scattering of light by dense atomic ensembles. it especially reports a measurement of the suppression of the excitation of the nano-clouds versus their densities.; Cette thèse présente une étude expérimentale des modifications des propriétés de diffusion résonante de la lumière par des nuages mésoscopiques de rubidium 87 froids dont la densité peut être variée. pour des densités de l’ordre de 1014 atomes/cm3, les distances entre certains atomes deviennent bien plus petites que la longueur d’onde du rayonnement à résonance avec la transition d2 (780 nm) du rubidium 87. l’ampleur des interactions dipôle-dipôle entre ces diffuseurs empêche alors de les considérer comme étant indépendants les uns des autres: on parle de diffusion collective. les méthodes employées pour produire les échantillons étudiés s’appuient sur des techniques de refroidissement (ralentisseur zeeman et piège magnéto-optique) et de piégeage (pinces optiques) d’atomes neutres permettant d’obtenir des ensembles d’atomes froids (environ 100 µK) allant d’exactement un à plusieurs centaines d’entre eux. les observations réalisées portent sur la lumière diffusée par ces atomes, collectée grâce à un système optique de grande ouverture numérique. l’étude consiste dans un premier temps en la caractérisation la diffusion résonante de lumière par un unique atome. elle aboutit notamment à la mesure du retard dans la diffusion par un atome d’un paquet d’ondes lumineuses, appelé délai de wigner, dans des conditions proches d’une expérience de pensée. dans un second temps, cette étude porte sur les propriétés de diffusion collective de lumière par des ensembles denses d’atomes. elle rapporte en particuliers une mesure de la suppression de l’excitation des nano-nuages en fonction de leur densité.

We study the high-dimensional entanglement of a photon pair transmitted through a random medium. We show that multiple scattering in combination with the subsequent selection of only a fraction of outgoing modes reduces the average entanglement of an initially maximally entangled two-photon state. Entanglement corresponding to a random pure state is obtained when the number of modes accessible in transmission is much less than the number of modes in the incident light. An amount of entanglement approaching that of the incident light can be recovered by accessing a larger number of transmitted modes. In contrast, a pair of photons in a separable state does not gain any entanglement when transmitted through a random medium., Comment: 6 pages, 2 figures. Text slightly revised

Light propagation in matter is described by vibration eigenstates, called modes, which characterize the light-matter interaction. In the specific case of random media, according to the strength of the disorder, the modes can be either extended over the whole system or spatially localized. This disorder-based confinement is called Anderson’s localization.In the first part, we introduce basic notions used along this manuscript. In particular the light-matter interaction requires a semiclassical approach: The electromagnetic field is described by Maxwell’s equations while the quantum nature of matter must be considered. In this thesis open media are studied. In such systems the modal description requires a specific analytic treatment different from closed problems. In the second part, we focus on Anderson-localized modes in open passive random media. Any change of the disorder induces modifications of modes. Therefore, it enables the control over the light properties. Moreover, when inserting an emitter inside an Anderson-localized mode, strong light-matter interaction regimes can be reached. In the third part, active random media, commonly called random lasers, are introduced. Using our experimental achievements, characteristics of random lasers are presented. The notion of mode enables us to describe complex mechanisms involved in the lasing emission. Last, we demonstrate both experimentally and numerically that a non-uniform excitation of random lasers can lead to a control of the properties of the emission. In particular a multimode spectrum for a uniform pumping can be turned into single-mode using an adapted pumping.; La propagation de la lumière dans un milieu matériel est décrite par des états propres de vibration, communément appelés modes, qui caractérisent l'interaction lumière-matière. Dans le cas particulier des milieux aléatoires, en fonction de l'importance du désordre, ces modes peuvent être soit étendus à tout le système ou alors spatialement localisés. Ce confinement par le désordre est appelé localisation d'Anderson. Dans une première partie, nous introduisons les notions de base utilisées dans ce manuscrit. L'interaction lumière-matière requière une description semi-classique : le champ électromagnétique est décrit par les équations de Maxwell, tandis que la nature quantique de la matière est considérée. Les milieux étudiés dans cette thèse sont ouverts. La description des modes dans de tels systèmes nécessite une approche analytique différente de celle utilisée dans les milieux fermés. Dans une seconde partie, nous nous intéressons aux modes localisés dans des milieux ouverts et passifs. Au sein de tels systèmes, une modification du désordre affecte les modes. Il est ainsi possible de les faire interagir et de manipuler les propriétés du champ électrique. Par ailleurs, en plaçant un émetteur au sein d'un mode localisé, il est également possible d'atteindre des régimes de forte interaction lumière-matière. Dans une troisième partie, les milieux aléatoires actifs (ou lasers aléatoires) sont introduits. En partant de réalisations expérimentales, les principales propriétés de ces lasers sont étudiées. L'utilisation de la notion de mode permet de décrire les mécanismes complexes sur lesquels reposent ces systèmes.Enfin, nous démontrons à la fois expérimentalement et numériquement qu'une excitation non-uniforme des lasers aléatoires peut permettre de contrôler leurs propriétés. En particulier, un laser aléatoire ayant une émission multimode pour un pompage uniforme peut émettre une lumière monomode pour une excitation adaptée.

Light propagation in matter is described by vibration eigenstates, called modes, which characterize the light-matter interaction. In the specific case of random media, according to the strength of the disorder, the modes can be either extended over the whole system or spatially localized. This disorder-based confinement is called Anderson’s localization.In the first part, we introduce basic notions used along this manuscript. In particular the light-matter interaction requires a semiclassical approach: The electromagnetic field is described by Maxwell’s equations while the quantum nature of matter must be considered. In this thesis open media are studied. In such systems the modal description requires a specific analytic treatment different from closed problems. In the second part, we focus on Anderson-localized modes in open passive random media. Any change of the disorder induces modifications of modes. Therefore, it enables the control over the light properties. Moreover, when inserting an emitter inside an Anderson-localized mode, strong light-matter interaction regimes can be reached. In the third part, active random media, commonly called random lasers, are introduced. Using our experimental achievements, characteristics of random lasers are presented. The notion of mode enables us to describe complex mechanisms involved in the lasing emission. Last, we demonstrate both experimentally and numerically that a non-uniform excitation of random lasers can lead to a control of the properties of the emission. In particular a multimode spectrum for a uniform pumping can be turned into single-mode using an adapted pumping.; La propagation de la lumière dans un milieu matériel est décrite par des états propres de vibration, communément appelés modes, qui caractérisent l'interaction lumière-matière. Dans le cas particulier des milieux aléatoires, en fonction de l'importance du désordre, ces modes peuvent être soit étendus à tout le système ou alors spatialement localisés. Ce confinement par le désordre est appelé localisation d'Anderson. Dans une première partie, nous introduisons les notions de base utilisées dans ce manuscrit. L'interaction lumière-matière requière une description semi-classique : le champ électromagnétique est décrit par les équations de Maxwell, tandis que la nature quantique de la matière est considérée. Les milieux étudiés dans cette thèse sont ouverts. La description des modes dans de tels systèmes nécessite une approche analytique différente de celle utilisée dans les milieux fermés. Dans une seconde partie, nous nous intéressons aux modes localisés dans des milieux ouverts et passifs. Au sein de tels systèmes, une modification du désordre affecte les modes. Il est ainsi possible de les faire interagir et de manipuler les propriétés du champ électrique. Par ailleurs, en plaçant un émetteur au sein d'un mode localisé, il est également possible d'atteindre des régimes de forte interaction lumière-matière. Dans une troisième partie, les milieux aléatoires actifs (ou lasers aléatoires) sont introduits. En partant de réalisations expérimentales, les principales propriétés de ces lasers sont étudiées. L'utilisation de la notion de mode permet de décrire les mécanismes complexes sur lesquels reposent ces systèmes.Enfin, nous démontrons à la fois expérimentalement et numériquement qu'une excitation non-uniforme des lasers aléatoires peut permettre de contrôler leurs propriétés. En particulier, un laser aléatoire ayant une émission multimode pour un pompage uniforme peut émettre une lumière monomode pour une excitation adaptée.

International audience; We are interested in the averaged behavior of interfaces moving in stationary ergodic environments, with oscillatory normal velocity which changes sign. This problem can be reformulated, using level sets, as the homogenization of a Hamilton-Jacobi equation with a positively homogeneous non-coercive Hamiltonian. The periodic setting was earlier studied by Cardaliaguet, Lions and Souganidis (2009). Here we concentrate in the random media and show that the solutions of the oscillatory Hamilton-Jacobi equation converge in $L^\infty$-weak $*$ to a linear combination of the initial datum and the solutions of several initial value problems with deterministic effective Hamiltonian(s), determined by the properties of the random media.

Let Z_N be the number of self-avoiding paths of length N starting from the origin on the infinite cluster obtained after performing Bernoulli percolation on Z^d with parameter p>p_c(Z^d). The object of this paper is to study the connective constant of the dilute lattice \limsup_{N\to \infty} Z_N^{1/N}, which is a non-random quantity. We want to investigate if the inequality \limsup_{N\to \infty} (Z_N)^{1/N} \le \lim_{N\to \infty} E[Z_N]^{1/N} obtained with the Borel-Cantelli Lemma is strict or not. In other words, we want to know the the quenched and annealed versions of the connective constant are the same. On a heuristic level, this indicates whether or not localization of the trajectories occurs. We prove that when d is sufficiently large there exists p^{(2)}_c>p_c such that the inequality is strict for p\in (p_c,p^{(2)}_c)., 21 pages 3 figures

International audience; In this paper, we study the loss of coherence of a wave propagating according to the Schrödinger equation with a time-dependent random potential. The random potential is assumed to have slowly decaying correlations. The main tool to analyze the decoherence phenomena is a properly rescaled Wigner transform of the solution of the random Schrödinger equation. We exhibit anomalous wave decoherence effects at different propagation scales.

International audience; In this paper, we present a novel approach that allows to couple two stochastic continuum models describing the same random medium at different observation scales. The coupling strategy is performed in the Arlequin framework, which is based on a volume coupling and a partition of the energy. Suitable functional space and coupling operator are chosen for the weak enforcement of the continuity between the two models. This choice ensures that the resulting mixed problem is well posed. The Monte-Carlo based numerical strategy for the solution of the mixed problem is briefly outlined. An application is presented, emphasizing on the interest of the chosen coupling operator. Finally, some remarks are provided concerning a stochastic multi-model coupling.

We prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton--Watson trees. This provides the first example where the Einstein relation is proved for motion in random media with arbitrary deep traps., Minor errors corrected

We propose a simple, exactly solvable, model of interface growth in a random medium that is a variant of the zero-temperature random-field Ising model on the Cayley tree. This model is shown to have a phase diagram (critical depinning field versus disorder strength) qualitatively similar to that obtained numerically on the cubic lattice. We then introduce a specifically tailored random graph that allows an exact asymptotic analysis of the height and width of the interface. We characterize the change of morphology of the interface as a function of the disorder strength, a change that is found to take place at a multicritical point along the depinning-transition line., Comment: 7 pages, 6 figures

International audience; In this paper, we describe a multiscale strategy that allows to couple stochastic and deterministic models. The transition condition enforced between the two models is weak, in the sense that it is based on volume coupling in space (rather than more classical boundary coupling) and on a volume/sample average in the random dimension. The paper then concentrates on the application of this weak coupling technique for the development of a new iterative method for the homogenization of random media. The technique is based on the coupling of the stochastic microstructure to a tentative homogenized medium, the parameters of which are initially chosen at will. Based on the results of the coupled simulation, for which Dirichlet or Neumann boundary conditions are posed at the boundary of the tentative homogenized medium, the parameters of the homogenized medium are then iteratively updated. An example shows the efficiency of the proposed approach compared to the classical KUBC and SUBC approaches in stochastic homogenization.

The goal of this thesis is to develop morphological models of cementitious materials and use these models to study their local and effective response. To this aim, 3D images of cementitious materials (mortar and concrete), obtained by micro-tomography, are studied. First, the mortar image is segmented in order to obtain an image of a real microstructure, to be used for linear elasticity computations. The image of concrete is used, after being processed, to determine various morphological characteristics of the material. A random model of concrete is then developed and validated by means of morphological data. This model is made up of three phases, corresponding to the matrix, aggregates and voids. The aggregates phase is modelled by implantation of Poisson polyhedra without overlap. For this purpose, an algorithm suited to the vector generation of Poisson polyhedra is introduced and validated with morphological measurements. Finally, the effective linear elastic properties of the mortar and other simulated microstructures are estimated with the FFT (Fast-Fourier Transform) method, for various contrasts between the aggregates and matrix' Young moduli. To complete this work, focused on effective properties, an analysis of the local elastic response in the matrix phase is undertaken, in order to determine the spatial arrangement between stress concentration zones in the matrix and the phases of the microstructure (aggregates and voids). Moreover, a statistical fields characterization, in the matrix, is achieved, including the determination of the Representative Volume Element (RVE) size. Furthermore, a comparison between effective and local elastic properties obtained from microstructures containing polyhedra and spheres is carried out.; Cette thèse porte sur la modélisation morphologique de matériaux cimentaires, et sur l'analyse de leurs propriétés linéaires élastiques. Dans cet objectif, des images 3D, obtenues par micro-tomographie, de matériaux cimentaires (mortier et béton) sont étudiées. Dans un premier temps, l'image de mortier est segmentée afin d'obtenir une image de microstructure réelle pour des calculs en élasticité linéaire. L'image de béton est utilisée, après traitement, pour la détermination des caractéristiques morphologiques du matériau. Un modèle aléatoire de béton est ensuite développé et validé par des données morphologiques. Ce modèle comporte trois phases qui correspondent à la matrice, les granulats et les pores. La phase des granulats est modélisée par implantation sans recouvrement de polyèdres de Poisson. Pour cela, un algorithme de génération vectorielle de polyèdres de Poisson est mis en place et validé par des mesures morphologiques. Enfin, les propriétés linéaires élastiques effectives de la microstructure de mortier et de microstructures simulées sont déterminées par méthode FFT (Fast-Fourier Transform), pour différents contrastes entre le module de Young des granulats et de la matrice. Cette étude des propriétés effectives est complétée par une analyse locale des champs dans la matrice, afin de déterminer l'arrangement spatial entre les zones de concentration de contraintes dans la matrice, et les différentes phases de la microstructure (granulats et pores). Une caractérisation statistique des champs est de plus réalisée, avec notamment le calcul du Volume Élémentaire Représentatif (VER). Une comparaison des propriétés élastiques effectives et locales obtenues d'une part sur une microstructure simulée contenant des polyèdres et d'autre part sur une microstructure contenant des sphères est de plus effectuée.

The goal of this thesis is to develop morphological models of cementitious materials and use these models to study their local and effective response. To this aim, 3D images of cementitious materials (mortar and concrete), obtained by micro-tomography, are studied. First, the mortar image is segmented in order to obtain an image of a real microstructure, to be used for linear elasticity computations. The image of concrete is used, after being processed, to determine various morphological characteristics of the material. A random model of concrete is then developed and validated by means of morphological data. This model is made up of three phases, corresponding to the matrix, aggregates and voids. The aggregates phase is modelled by implantation of Poisson polyhedra without overlap. For this purpose, an algorithm suited to the vector generation of Poisson polyhedra is introduced and validated with morphological measurements. Finally, the effective linear elastic properties of the mortar and other simulated microstructures are estimated with the FFT (Fast-Fourier Transform) method, for various contrasts between the aggregates and matrix' Young moduli. To complete this work, focused on effective properties, an analysis of the local elastic response in the matrix phase is undertaken, in order to determine the spatial arrangement between stress concentration zones in the matrix and the phases of the microstructure (aggregates and voids). Moreover, a statistical fields characterization, in the matrix, is achieved, including the determination of the Representative Volume Element (RVE) size. Furthermore, a comparison between effective and local elastic properties obtained from microstructures containing polyhedra and spheres is carried out.; Cette thèse porte sur la modélisation morphologique de matériaux cimentaires, et sur l'analyse de leurs propriétés linéaires élastiques. Dans cet objectif, des images 3D, obtenues par micro-tomographie, de matériaux cimentaires (mortier et béton) sont étudiées. Dans un premier temps, l'image de mortier est segmentée afin d'obtenir une image de microstructure réelle pour des calculs en élasticité linéaire. L'image de béton est utilisée, après traitement, pour la détermination des caractéristiques morphologiques du matériau. Un modèle aléatoire de béton est ensuite développé et validé par des données morphologiques. Ce modèle comporte trois phases qui correspondent à la matrice, les granulats et les pores. La phase des granulats est modélisée par implantation sans recouvrement de polyèdres de Poisson. Pour cela, un algorithme de génération vectorielle de polyèdres de Poisson est mis en place et validé par des mesures morphologiques. Enfin, les propriétés linéaires élastiques effectives de la microstructure de mortier et de microstructures simulées sont déterminées par méthode FFT (Fast-Fourier Transform), pour différents contrastes entre le module de Young des granulats et de la matrice. Cette étude des propriétés effectives est complétée par une analyse locale des champs dans la matrice, afin de déterminer l'arrangement spatial entre les zones de concentration de contraintes dans la matrice, et les différentes phases de la microstructure (granulats et pores). Une caractérisation statistique des champs est de plus réalisée, avec notamment le calcul du Volume Élémentaire Représentatif (VER). Une comparaison des propriétés élastiques effectives et locales obtenues d'une part sur une microstructure simulée contenant des polyèdres et d'autre part sur une microstructure contenant des sphères est de plus effectuée.

International audience; When dealing with modal representations of the Green's function of a complex medium, the modal coefficients are often assimilated to random variables, where statistical independence is justified on heuristic arguments supported by the complexity of the propagation in multiple-scattering scenarios. This letter addresses this assumption when the randomness originates from an uncertain positioning of the sources, proving under what conditions the modal coefficients can be regarded as uncorrelated, showing that this special condition should not be taken for granted, even in complex media.

Array imaging in a strongly scattering medium is limited because coherent signals recorded at the array and coming from a reflector to be imaged are weak and dominated by incoherent signals coming from multiple scattering by the medium. If, however, an auxiliary passive array can be placed between the reflector to be imaged and the scattering medium then the cross correlations of the incoherent signals on this array can also be used to image the reflector. In this paper, we show both in the weakly scattering paraxial regime and in strongly scattering layered media that this cross-correlation approach produces images as if the medium between the sources and the passive array was homogeneous and the auxiliary passive array was an active one made up of both sources and receivers.

International audience; The aim of this paper is to develop new coherent interferometry (CINT) algorithms to correct the effect of an unknown cluttered sound speed (random fluctuations around a known constant) on photoacoustic images. By back-propagating the correlations between the preprocessed pressure measurements, we show that we are able to provide statistically stable photoacoustic images. The preprocessing is exactly in the same way as when we use the circular or the line Radon inversion to obtain photoacoustic images. Moreover, we provide a detailed stability and resolution analysis of the new CINT-Radon algorithms. We also present numerical results to illustrate their performance and to compare them with Kirchhoff-Radon migration functions.

We consider the random reversible Markov kernel K obtained by assigning i.i.d. nonnegative weights to the edges of the complete graph over n vertices and normalizing by the corresponding row sum. The weights are assumed to be in the domain of attraction of an $\alpha$-stable law, $\alpha\in(0,2)$. When $1\leq\alpha, Comment: Published in at http://dx.doi.org/10.1214/10-AOP587 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We study probability distributions of eigenvalues of Hermitian and non-Hermitian Euclidean random matrices that are typically encountered in the problems of wave propagation in random media., Comment: 29 pages, 10 figures

International audience; The propagation of dislocations in random crystals is evidenced to be governed by atomic-scale avalanches whose the extension in space and the time intermittency characterizingly diverge at the critical threshold. Our work is the very first atomic-scale evidence that the paradigm of second order phase transitions applies to the depinning of elastic interfaces in random media.

We consider a 1+1 dimensional directed continuum polymer in a Gaussian delta-correlated space-time random potential. For this model the moments (= replica) of the partition function, Z(x,t), can be expressed in terms of the attractive delta-Bose gas on the line. Based on a recent study of the structure of the eigenfunctions, we compute the generating function for Z(x_1,t), Z(x_2,t) under a particular decoupling assumption and thereby extend recent results on the one-point generating function of the free energy to two points. It is established that in the long time limit the fluctuations of the free energy are governed by the two-point distribution of the Airy process, which further supports that the long time behavior of the KPZ equation is the same as derived previously for lattice growth models., Comment: 25 pages

Co-encadrement de la thèse : Christine Delisée; This PhD thesis is carried out in the framework of the Silent Wall research program whose main objective consists of designing an acoustic and thermal insulating system for buildings, from fibrous materials. Since the acoustic insulation is the main issue of this work, several fields of research are prospected within the study of the microstructural properties of these media. The Thermisorel material, made of wooden fibres, is a reference fibrous medium for the Silent Wall project thanks to its good acoustic and thermal insulating properties. Volumic 3D X-Ray microtomographic images of this material are analyzed by mathematical morphology in order to characterize the microstructures of its fibrous and porous phases. A 3D Boolean model of random cylinders is proposed to simulate such a fibrous medium. Since the morphological measurements processed on real and simulated media are quite similar, this morphological model is validated. Finally, the thermo-acoustic properties of microscopic elementary periodic cells of simplified media, composed of parallel fibres, are estimated by the finite element method. The objective of this modelling is to link the coefficient of acoustic absorption to the radii of the fibres and to the thickness of the material. The absorption coefficient of the simulated fibrous media are similar to the experimental measurements made on Thermisorel. Therefore, our global method to characterize, and to model the morphology and the thermo-acoustic properties of fibrous media at the microscopic scale, is validated by the morphological and acoustic properties of wooden panels of Thermisorel, and is helpful for future optimisations of the acoustic performances of fibrous materials by modifying their microstructures.; Cette thèse se situe à l'interface de plusieurs disciplines, dans le cadre du programme de recherche Silent Wall qui a pour vocation d'élaborer un système isolant acoustique et thermique pour le bâtiment, à base de matériaux fibreux. La problématique d'isolation acoustique étant le fil rouge de ce travail, différents domaines de recherche sont abordés dans l'étude des propriétés microstructurales de ces matériaux. Un matériau fibreux de référence, le Thermisorel, élaboré par procédé papetier à base de fibres de bois, est retenu par le consortium Silent Wall pour ses bonnes propriétés d'isolation phonique et thermique. Des images 3D de ce matériau, réalisées par microtomographie aux rayons X, sont analysées par morphologie mathématique afin de caractériser la microstructure de ses phases fibreuse et porale. Un modèle booléen de cylindres aléatoires permet de simuler un tel matériau fibreux. L'adéquation des mesures morphologiques des milieux ainsi simulés, avec celles du Thermisorel valident ce modèle morphologique. Enfin, les propriétés thermo-acoustiques de cellules périodiques élémentaires microscopiques de milieux fibreux 3D simplifiés et composés de fibres parallèles, sont estimées par éléments finis, afin de relier leurs performances en absorption acoustique, à la taille des fibres et à l'épaisseur de l'échantillon. Après comparaison, les coefficients d'absorption acoustique des milieux fibreux simulés sont en adéquation avec les valeurs expérimentales mesurées sur des échantillons de Thermisorel. Ainsi, notre démarche globale de caractérisation, et de modélisations morphologique et thermo-acoustique à l'échelle de la microstructure, est validée par les propriétés morphologiques et acoustiques de panneaux de Thermisorel, et ouvre la voie à l'optimisation des performances acoustiques macroscopiques de tels matériaux fibreux par modification de leur microstructure.

Co-encadrement de la thèse : Christine Delisée; This PhD thesis is carried out in the framework of the Silent Wall research program whose main objective consists of designing an acoustic and thermal insulating system for buildings, from fibrous materials. Since the acoustic insulation is the main issue of this work, several fields of research are prospected within the study of the microstructural properties of these media. The Thermisorel material, made of wooden fibres, is a reference fibrous medium for the Silent Wall project thanks to its good acoustic and thermal insulating properties. Volumic 3D X-Ray microtomographic images of this material are analyzed by mathematical morphology in order to characterize the microstructures of its fibrous and porous phases. A 3D Boolean model of random cylinders is proposed to simulate such a fibrous medium. Since the morphological measurements processed on real and simulated media are quite similar, this morphological model is validated. Finally, the thermo-acoustic properties of microscopic elementary periodic cells of simplified media, composed of parallel fibres, are estimated by the finite element method. The objective of this modelling is to link the coefficient of acoustic absorption to the radii of the fibres and to the thickness of the material. The absorption coefficient of the simulated fibrous media are similar to the experimental measurements made on Thermisorel. Therefore, our global method to characterize, and to model the morphology and the thermo-acoustic properties of fibrous media at the microscopic scale, is validated by the morphological and acoustic properties of wooden panels of Thermisorel, and is helpful for future optimisations of the acoustic performances of fibrous materials by modifying their microstructures.; Cette thèse se situe à l'interface de plusieurs disciplines, dans le cadre du programme de recherche Silent Wall qui a pour vocation d'élaborer un système isolant acoustique et thermique pour le bâtiment, à base de matériaux fibreux. La problématique d'isolation acoustique étant le fil rouge de ce travail, différents domaines de recherche sont abordés dans l'étude des propriétés microstructurales de ces matériaux. Un matériau fibreux de référence, le Thermisorel, élaboré par procédé papetier à base de fibres de bois, est retenu par le consortium Silent Wall pour ses bonnes propriétés d'isolation phonique et thermique. Des images 3D de ce matériau, réalisées par microtomographie aux rayons X, sont analysées par morphologie mathématique afin de caractériser la microstructure de ses phases fibreuse et porale. Un modèle booléen de cylindres aléatoires permet de simuler un tel matériau fibreux. L'adéquation des mesures morphologiques des milieux ainsi simulés, avec celles du Thermisorel valident ce modèle morphologique. Enfin, les propriétés thermo-acoustiques de cellules périodiques élémentaires microscopiques de milieux fibreux 3D simplifiés et composés de fibres parallèles, sont estimées par éléments finis, afin de relier leurs performances en absorption acoustique, à la taille des fibres et à l'épaisseur de l'échantillon. Après comparaison, les coefficients d'absorption acoustique des milieux fibreux simulés sont en adéquation avec les valeurs expérimentales mesurées sur des échantillons de Thermisorel. Ainsi, notre démarche globale de caractérisation, et de modélisations morphologique et thermo-acoustique à l'échelle de la microstructure, est validée par les propriétés morphologiques et acoustiques de panneaux de Thermisorel, et ouvre la voie à l'optimisation des performances acoustiques macroscopiques de tels matériaux fibreux par modification de leur microstructure.

International audience; The biomechanical materials are among the most complex mechanical systems. Most often, their micro-structure are complex and random. This is the case for the human cortical bones which are considered in this paper. For such a system, the microstructure can be altered near its interface with the marrow (osteoporosis). A gradient of porosity is then observed in the thickness direction but, in this case, none usual theory of porous materials can be applied. For this reason, we present a simplified model with gradient for the elasticity tensor. The predictability of this model is improved by taking into account uncertainties. The elasticity tensor is then modeled by a random field. This random model is well adapted for the modeling of the random experimental measurements in ultrasonic range for the human cortical bone.

We study several models of directed polymers in random environments. For the classical model on Z^d, we study the convergence of the environments seen by the particle in the weak disorder region. We prove strong results for very high values of the temperature. We then give a complete treatment of the partition function of directed polymers on the diamond hierarchical lattice. Finally, we study the free energy of directed polymers in random environments on Z^d in very asymmetric boxes. We prove that, in a particular regime, it coincides with the free energy of a continuous time model in a Brownian environment. For d=1, the exact value of this free energy is known. We also study one-dimensional directed polymers with a huge drift. We give the exact value of the free energy and compute the order of fluctuations of the partition function.; Nous étudions plusieurs modèles de polymères dirigés en milieux aléatoires. Pour le modèle classique sur Z^d, nous étudions la convergence de l'environnement vu par la particule dans la région de faible désordre. Nous donnons des résultats très forts pour de très hautes valeurs de la température. Nous donnons ensuite un traitement complet de la fonction de partition pour un modèle de polymères dirigés en milieux aléatoires sur le réseau hiérarchique en diamant. Finalement, nous étudions l'énergie libre des polymères dirigés en milieux aléatoires sur Z^d dans des boites très asymétriques. Nous parvenons à prouver que, dans un régime approprié, elle coïncide avec l'énergie libre d'un modèle en temps continu dans un environnement Brownien. En dimension 1, la valeur exacte de cette énergie libre est connue. Nous étudions également des polymères dirigés en dimension 1 avec un drift qui tend vers l'infini. Nous donnons la valeur exacte de l'énergie libre et l'ordre des fluctuations de la fonction de partition.

We study several models of directed polymers in random environments. For the classical model on Z^d, we study the convergence of the environments seen by the particle in the weak disorder region. We prove strong results for very high values of the temperature. We then give a complete treatment of the partition function of directed polymers on the diamond hierarchical lattice. Finally, we study the free energy of directed polymers in random environments on Z^d in very asymmetric boxes. We prove that, in a particular regime, it coincides with the free energy of a continuous time model in a Brownian environment. For d=1, the exact value of this free energy is known. We also study one-dimensional directed polymers with a huge drift. We give the exact value of the free energy and compute the order of fluctuations of the partition function., Nous étudions plusieurs modèles de polymères dirigés en milieux aléatoires. Pour le modèle classique sur Z^d, nous étudions la convergence de l'environnement vu par la particule dans la région de faible désordre. Nous donnons des résultats très forts pour de très hautes valeurs de la température. Nous donnons ensuite un traitement complet de la fonction de partition pour un modèle de polymères dirigés en milieux aléatoires sur le réseau hiérarchique en diamant. Finalement, nous étudions l'énergie libre des polymères dirigés en milieux aléatoires sur Z^d dans des boites très asymétriques. Nous parvenons à prouver que, dans un régime approprié, elle coïncide avec l'énergie libre d'un modèle en temps continu dans un environnement Brownien. En dimension 1, la valeur exacte de cette énergie libre est connue. Nous étudions également des polymères dirigés en dimension 1 avec un drift qui tend vers l'infini. Nous donnons la valeur exacte de l'énergie libre et l'ordre des fluctuations de la fonction de partition.

A technique for selective cancellation of fully polarized light is presented. Within the context of imaging in random media the polarimetric behaviour of scattered light is addressed: a statistical signature of the scattering origins (surface or bulk) is experimentally demonstrated and then the polarization properties are deduced. In a last step, data are given to show the loss of polarization by spatial average process, which is induced by the microstructure of the scattering samples.