Publications

2015

• Solutions of the time-harmonic wave equation in periodic waveguides : asymptotic behaviour and radiation condition
  
  • Fliss Sonia
  • Joly Patrick
  Archive for Rational Mechanics and Analysis, Springer Verlag, 2015, 219 (1), pp.10.1007/s00205-015-0897-3. In this paper, we give the expression and the asymptotic behaviour of the physical solution of a time harmonic wave equation set in a periodic waveguide. This enables us to define a radiation condition and show well-posedness of the Helmholtz equation set in a periodic waveguide. (10.1007/s00205-015-0897-3)
  DOI : 10.1007/s00205-015-0897-3
• Asymptotic analysis for the multiscale modeling of defects in mechanical structures
  
  • Marenić Eduard
  • Brancherie Delphine
  • Bonnet Marc
  , 2015. This research is a first step towards designing a numerical strategy capable of assessing the nocivity of a small defect in terms of its size and position in the structure with low computational cost, using only a mesh of the defect-free reference structure. The proposed strategy aims at taking into account the modification induced by the presence of a small defect through displacement field correction using an asymptotic analysis. Such an approach would allow to assess the criticality of defects by introducing trial micro-defects with varying positions, sizes and mechanical properties.
• A Wideband Fast Multipole Method for the Helmholtz Kernel: Theoretical Developments
  
  • Chaillat Stéphanie
  • Collino Francis
  Computers & Mathematics with Applications, Elsevier, 2015, pp.to appear. This work presents a new Fast Multipole Method (FMM) based on plane wave expansions (PWFMM), combining the advantages of the low and high frequency formulations. We revisit the method of Greengard et al. [1] devoted to the low frequency regime and based on the splitting of the Green's function into a propagative and an evanescent part. More precisely, we give an explicit formula of the filtered translation function for the propagative part, we derive a new formula for the evanescent part and we provide a new interpolation algorithm. At all steps, we check the accuracy of the method by providing error estimates. These theoretical developments are used to propose a wideband FMM based entirely on plane wave expansions. The numerical efficiency and accuracy of this broadband PWFMM are illustrated with a numerical example. (10.1016/j.camwa.2015.05.019)
  DOI : 10.1016/j.camwa.2015.05.019
• Local controllability of the two-link magneto-elastic swimmer
  
  • Giraldi Laetitia
  • Pomet Jean-Baptiste
  , 2015. A recent promising technique for moving a robotic micro-swimmers is to apply an external magnetic field. This paper focuses on a simple micro-swimmer model with two magnetized segments connected by an elastic joint, which is able to move in a plane by using a magnetic field. By considering the latter as control functions, we prove that the swimmer is locally controllable around the straight position.
• Probabilistic representation of a class of non conservative nonlinear Partial Differential Equations
  
  • Lecavil Anthony
  • Oudjane Nadia
  • Russo Francesco
  , 2015. We introduce a new class of nonlinear Stochastic Differential Equations in the sense of McKean, related to non conservative nonlinear Partial Differential equations (PDEs). We discuss existence and uniqueness pathwise and in law under various assumptions. We propose an original interacting particle system for which we discuss the propagation of chaos. To this system, we associate a random function which is proved to converge to a solution of a regularized version of PDE.
• On some stochastic control problems with state constraints
  
  • Picarelli Athena
  , 2015. This thesis deals with Hamilton-Jacobi-Bellman (HJB) approach for some stochastic control problems in presence of state-constraints. This class of problems arises in many challenging applications, and a wide literature has already analysed such problems under some strong compatibility conditions. The main features of the present thesis is to provide new ways to face the presence of constraints without assuming any controllability condition. The first contribution of the thesis in this direction is obtained by exploiting the existing link between backward reachability and optimal control problems. It is shown that by considering a suitable auxiliary unconstrained optimal control problem, the level set approach can be extended to characterize the backward reachable sets under state-constrained. On the other hand the value function associated with a general state constrained stochastic optimal control problem is characterized by means of a state constrained backward reachable set, enabling the application of the level set method for handling the presence of the state constraints. This link between optimal control problems and reachability sets led to the theoretical and numerical analysis of HJB equations with oblique derivative boundary conditions and problems with unbounded controls. Error estimates for Markov-chain approximation represent another contribution of this manuscript. Furthermore, the properties of asymptotic controllability of a stochastic system have also been studied. A generalization of the Zubov method to state constrained stochastic systems is presented. In the last part of the thesis an ergodic optimal control problems in presence of state-constraints are considered.
• Complexity of control-affine motion planning
  
  • Jean Frédéric
  • Prandi Dario
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2015, 53 (2), pp.816-844. In this paper we study the complexity of the motion planning problem for control- affine systems. Such complexities are already defined and rather well-understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time- rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quanti- tative estimates on the cost of stabilizing the system near a non-equilibrium point of the drift. (10.1137/130950793)
  DOI : 10.1137/130950793
• Perfectly matched layers in negative index metamaterials and plasmas
  
  • Bécache Eliane
  • Joly Patrick
  • Kachanovska Maryna
  • Vinoles Valentin
  ESAIM: Proceedings, EDP Sciences, 2015, pp.Vol. 50, p. 113-132. This work deals with the stability of Perfectly Matched Layers (PMLs). The first part is a survey of previous results about the classical PMLs in non-dispersive media (construction and necessary condition of stability). The second part concerns some extensions of these results. We give a new necessary criterion of stability valid for a large class of dispersive models and for more general PMLs than the classical ones. This criterion is applied to two dispersive models: negative index metamaterials and uniaxial anisotropic plasmas. In both cases, classical PMLs are unstable but the criterion allows us to design new stable PMLs. Numerical simulations illustrate our purpose. (10.1051/proc/201550006)
  DOI : 10.1051/proc/201550006
• Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Chesnel Lucas
  • Nazarov Sergei
  Inverse Problems, IOP Publishing, 2015. We investigate a time harmonic acoustic scattering problem by a penetrable inclusion with compact support embedded in the free space. We consider cases where an observer can produce inci-dent plane waves and measure the far field pattern of the resulting scattered field only in a finite set of directions. In this context, we say that a wavenumber is a non-scattering wavenumber if the associated relative scattering matrix has a non trivial kernel. Under certain assumptions on the physical coeffi-cients of the inclusion, we show that the non-scattering wavenumbers form a (possibly empty) discrete set. Then, in a second step, for a given real wavenumber and a given domain D, we present a construc-tive technique to prove that there exist inclusions supported in D for which the corresponding relative scattering matrix is null. These inclusions have the important property to be impossible to detect from far field measurements. The approach leads to a numerical algorithm which is described at the end of the paper and which allows to provide examples of (approximated) invisible inclusions.
• A Wideband Fast Multipole Method for the Helmholtz kernel: Theoretical developments
  
  • Chaillat Stéphanie
  • Collino Francis
  , 2015, pp.28. This work presents a new Fast Multipole Method (FMM) based on plane wave expansions, combining the advantages of the low and high frequency formulations. We revisit the method of Greengard et al. devoted to the low frequency regime and based on the splitting of the Green's function into a propagative and an evanescent part. More precisely, we give an explicit formula of the filtered translation function for the propagative part, we derive a new formula for the evanescent part and we provide a new interpolation algorithm. At all steps, we check the accuracy of the method by providing error estimates. These theoretical developments are used to propose a wideband FMM based entirely on plane wave expansions. The numerical efficiency and accuracy of this broadband are illustrated with a numerical example.
• Pattern selection in a biomechanical model for the growth of walled cells
  
  • Calvez Vincent
  • Giraldi Laetitia
  , 2015. In this paper, we analyse a model for the growth of three-dimensional walled cells. In this model the biomechanical expansion of the cell is coupled with the geometry of its wall. We consider that the density of building material depends on the curvature of the cell wall, thus yield-ing possible anisotropic growth. The dynamics of the axisymmetric cell wall is described by a system of nonlinear PDE including a nonlin-ear convection-diffusion equation coupled with a Poisson equation. We develop the linear stability analysis of the spherical symmetric config-uration in expansion. We identify three critical parameters that play a role in the possible instability of the radially symmetric shape, namely the degree of nonlinearity of the coupling, the effective diffusion of the building material, and the Poisson's ratio of the cell wall. We also investigate numerically pattern selection in the nonlinear regime. All the results are also obtained for a simpler, but similar, two-dimensional model.
• Infinite horizon problems on stratifiable state-constraints sets
  
  • Hermosilla Cristopher
  • Zidani Hasnaa
  Journal of Differential Equations, Elsevier, 2015, 258 (4), pp.1430–1460. This paper deals with a state-constrained control problem. It is well known that, unless some compatibility condition between constraints and dynamics holds, the value function has not enough regularity, or can fail to be the unique constrained viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. Here, we consider the case of a set of constraints having a stratified structure. Under this circumstance, the interior of this set may be empty or disconnected, and the admissible trajectories may have the only option to stay on the boundary without possible approximation in the interior of the constraints. In such situations, the classical pointing qualification hypothesis are not relevant. The discontinuous value function is then characterized by means of a system of HJB equations on each stratum that composes the state constraints. This result is obtained under a local controllability assumption which is required only on the strata where some chattering phenomena could occur. (10.1016/j.jde.2014.11.001)
  DOI : 10.1016/j.jde.2014.11.001
• Comparison of mean and osculating stability in the vicinity of the (2:1) tesseral resonant surface
  
  • Daquin Jérôme
  • Deleflie Florent
  • Perez Jérôme
  Acta Astronautica, Elsevier, 2015, 111, pp.170-177. We confront stability results over long time scales, considering alternately the averaged and the non-averaged theory to propagate the equations of motion of a celestial body orbiting the vicinity of the (2:1) tesseral resonant surface. This confrontation is performed using Fast Lyapunov Indicator stability maps. The benefit of such maps is threefold: (i) to reveal the whole phase space architecture and the consequences of the resonance overlap when several combinations of tesseral resonant parameters are accounted for, (ii) to perform a stability analysis on a whole phase space region, and (iii) to have a clear view of the possible impacts of the short-periodic effects removed during the averaging procedure. Our detailed numerical investigations conclude that the tesseral chaos is robust to the averaging procedure and the numerical methods used to propagate the equations of motion over such long time scales. (10.1016/j.actaastro.2015.02.014)
  DOI : 10.1016/j.actaastro.2015.02.014
• Optimal control problems on well-structured domains and stratified feedback controls
  
  • Hermosilla Cristopher
  , 2015. The aim of this dissertation is to study some issues in Control Theory of ordinary differential equations. Optimal control problems with tame state-constraints and feedback controls with stratified discontinuities are of special interest. The techniques employed along the manuscript have been chiefly taken from control theory, nonsmooth analysis, variational analysis, tame geometry, convex analysis and differential inclusions theory. The first part of the thesis is devoted to provide general results and definitions required for a good understanding of the entire manuscript. In particular, a strong invariance criterion adapted to manifolds is presented. Moreover, a short insight into manifolds and stratifications is done. The notions of relatively wedged sets is introduced and in addition, some of its properties are stated. The second part is concerned with the characterization of the Value Function of an optimal control problem with state-constraints. Three cases have been taken into account. The first one treats stratifiable state-constraints, that is, sets that can be decomposed into manifolds of different dimensions. The second case is focused on linear systems with convex state-constraints, and the last one considers convex state-constraints as well, but from a penalization point of view. In the latter situation, the dynamics are nonlinear and verify an absorbing property at the boundary. The third part is about discontinuous feedbacks laws whose singularities form a stratified set on the state-space. This type of controls yields to consider stratified discontinuous ordinary differential equations, which motivates an analysis of existence of solutions and robustness with respect to external perturbation for these equations. The construction of a suboptimal continuous feedback from an optimal one is also addressed in this part. The fourth part is dedicated to investigate optimal control problems on networks. The main feature of this contribution is that no controllability assumption around the junctions is imposed. The results can also be extended to generalized notions of networks, where the junction is not a single point but a manifold.
• On the Convergence of Decomposition Methods for Multistage Stochastic Convex Programs
  
  • Girardeau Pierre
  • Leclere Vincent
  • Philpott A. B.
  Mathematics of Operations Research, INFORMS, 2015, 40 (1). We prove the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions , and uncertainty is modelled by a scenario tree. As special cases, our results imply the almost-sure convergence of SDDP, CUPPS and DOASA when applied to problems with general convex cost functions. (10.1287/moor.2014.0664)
  DOI : 10.1287/moor.2014.0664
• Formulations par équations intégrales de surface pour la simulation numérique du contrôle non destructif par courants de Foucault
  
  • Vigneron Audrey
  , 2015. Cette thèse s'inscrit dans le contexte de la simulation numérique pour le contrôle non destructif (CND) par courants de Foucault et concerne le calcul des champs électromagnétiques induits par un capteur émetteur dans une pièce saine. Ce calcul constitue la première étape de la modélisation complète d'un procédé de contrôle dans la plateforme logicielle CIVA développée au CEA LIST. Aujourd'hui les modèles intégrés dans CIVA sont restreints à des pièces de géométrie canonique (calcul modal) ou axisymétriques. La demande de configurations plus diverses et complexes nécessite l'introduction de nouveaux outils numériques de modélisation. En pratique les capteurs peuvent être constitués d'éléments aux propriétés physiques et aux formes variées. Quant aux pièces à contrôler, elles sont conductrices et peuvent contenir des éléments diélectriques ou magnétiques. Du fait des différents matériaux présents dans une même configuration, différents régimes de modélisation (statique, quasi-statique, voire dynamique) peuvent cohabiter. Sous l'hypothèse de travail de milieux à propriétés linéaires, isotropes et homogènes par morceaux, l'approche par équations intégrales de surface (SIE) permet de ramener le problème volumique à un problème surfacique équivalent. Cependant les formulations SIE usuelles pour le problème de Maxwell souffrent en général d'un problème de robustesse numérique pour certains cas asymptotiques, en particulier à basse fréquence. L'objectif de cette étude est de déterminer une version stable pour une gamme de paramètres physique typique du CND. C'est dans ce cadre qu’un schéma itératif par blocs basé sur une décomposition liée à la physique du problème est proposé. Ce schéma est précis et bien conditionné pour le calcul des champs primaires. Une étude asymptotique du problème intégral de Maxwell est de plus effectuée. Celle-ci permet de formuler le problème intégral de l'approximation courants de Foucault comme une forme asymptotique de celui de Maxwell.
• A regularization approach to functional Itô calculus and strong-viscosity solutions to path-dependent PDEs
  
  • Cosso Andrea
  • Russo Francesco
  , 2015. First, we revisit functional Itô/path-dependent calculus started by B. Dupire, R. Cont and D.-A. Fournié, using the formulation of calculus via regularization. Relations with the corresponding Banach space valued calculus introduced by C. Di Girolami and the second named author are explored. The second part of the paper is devoted to the study of the Kolmogorov type equation associated with the so called window Brownian motion, called path-dependent heat equation, for which well-posedness at the level of classical solutions is established. Then, a notion of strong approximating solution, called strong-viscosity solution, is introduced which is supposed to be a substitution tool to the viscosity solution. For that kind of solution, we also prove existence and uniqueness. The notion of strong-viscosity solution motivates the last part of the paper which is devoted to explore this new concept of solution for general semilinear PDEs in the finite dimensional case. We prove an equivalence result between the classical viscosity solution and the new one. The definition of strong-viscosity solution for semilinear PDEs is inspired by the notion of "good" solution, and it is based again on an approximating procedure.
• Éléments de physique statistique - 2e édition
  
  • Perez Jérôme
  • Chardin Gabriel
  • Debu Pascal
  , 2015, pp.268 pages. Cet ouvrage aborde le thème classique de la physique statistique par la méthode pédagogique du dénombrement des états d’énergie microscopiques. Après avoir passé en revue les divers résultats de la théorie des systèmes sans interactions, divers cas plus généraux sont abordés comme la transition gaz-liquide, le ferromagnétisme ou la théorie du proche équilibre. Ce cours s’insère parfaitement dans la suite logique de l’enseignement de la physique de premier cycle et met en œuvre les résultats essentiels de la théorie quantique. Il permet d’appréhender l’origine microscopique d’un grand nombre de propriétés macroscopiques essentielles d’un système qui caractérisent son état d’équilibre (température, énergie, pression, etc.). La prise en compte des interactions à l’échelle microscopique et l’étude du proche équilibre viennent compléter ce panorama pour préparer des cours plus avancés comme l’étude physique des solides ou celle des plasmas. Cet ouvrage est le fruit d’un cours donné par les auteurs à L’École Nationale Supérieure de Techniques Avancées (ENSTA ParisTech). Il contient de nombreux exercices et une synthèse des points essentiels en fin de chaque chapitre.
• Monotone numerical schemes and feedback construction for hybrid control systems
  
  • Ferretti Roberto
  • Zidani Hasnaa
  Journal of Optimization Theory and Applications, Springer Verlag, 2015, 165 (2), pp.507-531. Hybrid systems are a general framework which can model a large class of control systems arising whenever a collection of continuous and discrete dynamics are put together in a single model. In this paper, we study the convergence of monotone numerical approximations of value functions associated to control problems governed by hybrid systems. We discuss also the feedback reconstruction and derive a convergence result for the approximate feedback control law. Some numerical examples are given to show the robustness of the monotone approximation schemes. (10.1007/s10957-014-0637-0)
  DOI : 10.1007/s10957-014-0637-0
• Value iteration convergence of "-monotone schemes for stationary Hamilton-Jacobi equations
  
  • Bokanowski Olivier
  • Falcone Maurizio
  • Ferretti Roberto
  • Grüne Lars
  • Kalise Dante
  • Zidani Hasnaa
  Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, 2015, 35 (9), pp.4041 - 4070. We present an abstract convergence result for the xed point approximation of stationary Hamilton{Jacobi equations. The basic assumptions on the discrete operator are invariance with respect to the addition of constants, "-monotonicity and consistency. The result can be applied to various high-order approximation schemes which are illustrated in the paper. Several applications to Hamilton{Jacobi equations and numerical tests are presented. (10.3934/dcds.2015.35.4041)
  DOI : 10.3934/dcds.2015.35.4041
• La mécanique des Sphères de Lie: un futur pour la CAO?
  
  • Arber Christian
  • Jean Frédéric
  , 2015, 28. La plupart des pièces ou ensembles de pièces de la vie courante sont conçus maintenant en CAO (Conception Assistée par Ordinateur): voiture, avion bien sûr, mais aussi savon, emballage de savon, machine à emballer les savons,... On peut se douter que la modélisation géométrique y joue un grand rôle. Mais quelle géométrie? Et finalement quels ressorts mathématiques sont employés dans ce qui est utilisé tous les jours par des centaines de milliers de concepteurs à travers le monde (et des millions d'utilisateurs de jeux vidéo!)? A leur insu et pour leur bonheur. Géométrie cartésienne bien sûr, mais aussi de belles vieilles idées de la grande école de géométrie franco-allemande de la fin du XXIème siècle revivent actuellement. Rangées dans les réserves du musée de l'algèbre triomphante, elles sont exhumées régulièrement par quelques archéologues des mathématiques (les géomètres!). Maintenant combinées avec les progrès fantastiques portés par la géométrie Riemannienne sur les groupes de Lie, elles permettent des avancées importantes dans le codage d'un logiciel de CAO. En seront-elles le futur? On illustrera cela avec l'espace des Sphères de Lie, pour traiter le problème du solveur d'esquisses (construction naturelle de géométries sous contraintes), un des problèmes centraux de la modélisation.
• A modified error in constitutive equation approach for frequency-domain viscoelasticity imaging using interior data
  
  • Diaz Manuel I.
  • Aquino Wilkins
  • Bonnet Marc
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2015, 296, pp.129-149. This paper presents a methodology for the inverse identification of linearly viscoelastic material parameters in the context of steady-state dynamics using interior data. The inverse problem of viscoelasticity imaging is solved by minimizing a modified error in constitutive equation (MECE) functional, subject to the conservation of linear momentum. The treatment is applicable to configurations where boundary conditions may be partially or completely underspecified. The MECE functional measures the discrepancy in the consti-tutive equations that connect kinematically admissible strains and dynamically admissible stresses, and also incorporates the measurement data in a quadratic penalty term. Regularization of the problem is achieved through a penalty parameter in combination with the discrepancy principle due to Morozov. Numerical results demonstrate the robust performance of the method in situations where the available measurement data is incomplete and corrupted by noise of varying levels. (10.1016/j.cma.2015.07.025)
  DOI : 10.1016/j.cma.2015.07.025
• Classical homogenization to analyse the dispersion relations of spoof plasmons with geometrical and compositional effects
  
  • Mercier Jean-François
  • Cordero Maria-Luisa
  • Félix Simon
  • Ourir Abdelwaheb
  • Maurel Agnes
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2015, 471 (2182). We show that the classical homogenization is able to describe the dispersion relation of spoof plasmons in structured thick interfaces with periodic unit cell being at the subwavelength scale. This is because the interface in the real problem is replaced by a slab of an homogeneous birefringent medium, with an effective mass density tensor and an effective bulk modulus. Thus, explicit dispersion relation can be derived, corresponding to guided waves in the homogenized problem. Contrary to previous effective medium theories or retrieval methods, the homogenization gives effective parameters depending only on the properties of the material and on the geometry of the microstructure. Although resonances in the unit cell cannot be accounted for within this low-frequency homogenization, it is able to account for resonances occurring because of the thickness of the interface and thus, to capture the behaviour of the spoof plasmons. Beyond the case of simple grooves in a hard material, we inspect the influence of tilting the grooves and the influence of the material properties. (10.1098/rspa.2015.0472)
  DOI : 10.1098/rspa.2015.0472
• Effective birefringence to analyze sound transmission through a layer with subwavelength slits
  
  • Maurel Agnes
  • Félix Simon
  • Mercier Jean-François
  • Ourir Abdelwaheb
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2015, 343 (12). We analyze the transmission of sound through a sound hard film or layer with periodic subwavelength slits. For wavelength comparable to or larger than the slit spacing, the transmission spectra are revisited in terms of the transmission through an equivalent birefringent layer. It is shown that the Fano-type resonances can be understood by means of the dispersion relations of guided waves within the birefringent layer in the homogenized problem, equivalent to spoof plasmons for gratings. This is done by extending the homogenization to the evanescent waves being excited in the near field of the actual perforated layer. (10.1016/j.crme.2015.07.006)
  DOI : 10.1016/j.crme.2015.07.006
• Solving the hypersingular boundary integral equation for the Burton and Miller formulation
  
  • Langrenne Christophe
  • Garcia Alexandre
  • Bonnet Marc
  Journal of the Acoustical Society of America, Acoustical Society of America, 2015, 138 (3332-3340). This paper presents an easy numerical implementation of the Burton and Miller (BM) formulation, where the hypersingular Helmholtz integral is regularized by identities from the associated Laplace equation and thus needing only the evaluation of weakly singular integrals. The Helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes not used when the surface is not smooth. The hypersingular operators arising in this process are regularized and then evaluated by an indirect procedure based on discretized versions of the Calderón identities linking the integral operators for associated Laplace problems. The method is valid for acoustic radiation and scattering problems involving arbitrarily shaped three-dimensional bodies. Unlike other approaches using direct evaluation of hypersingular integrals, collocation points still coincide with mesh nodes, as is usual when using conforming elements. Using higher-order shape functions (with the boundary element method model size kept fixed) reduces the overall numerical integration effort while increasing the solution accuracy. To reduce the condition number of the resulting BM formulation at low frequencies, a regularized version α = ik/(k2 + λ) of the classical BM coupling factor α = i/k is proposed. Comparisons with the combined Helmholtz integral equation Formulation method of Schenck are made for four example configurations, two of them featuring non-smooth surfaces. (10.1121/1.4935134)
  DOI : 10.1121/1.4935134