Publications

2025

• An operator approach to the analysis of electromagnetic wave propagation in dispersive media. Part 2: transmission problems.
  
  • Cassier Maxence
  • Joly Patrick
  , 2025. In this second chapter, we analyse transmission problems between a dielectric and a dispersive negative material. In the first part, we consider a transmission problem between two half-spaces, filled respectively by the vacuum and a Drude material, and separated by a planar interface. In this setting, we answer the following question: does this medium satisfy a limiting amplitude principle? This principle defines the stationary regime as the large time asymptotic behavior of a system subject to a periodic excitation. In the second part, we consider the transmission problem of an infinite strip made of a Drude material embedded in the vacuum and analyse the existence and dispersive properties of guided waves. In both problems, our spectral analysis elucidates new and unusual physical phenomena for the considered transmission problems due to the presence of the dispersive negative material. In particular, we prove the existence of an interface resonance in the first part and the existence of slow light phenomena for guiding waves in the second part.
• On the constitutive behavior of linear viscoelastic solids under the plane stress condition
  
  • Guzina Bojan B
  • Bonnet Marc
  Journal of Elasticity, Springer Verlag, 2025, 157, pp.45. Motivated by the recent experimental and analytical developments enabling high-fidelity material characterization of (heterogeneous) sheet-like solid specimens, we seek to elucidate the constitutive behavior of linear viscoelastic solids under the plane stress condition. More specifically, our goal is to expose the relationship between the plane-stress viscoelastic constitutive parameters and their (native) ``bulk'' counterparts. To facilitate the sought reduction of the three-dimensional (3D) constitutive behavior, we deploy the concept of projection operators and focus on the frequency-domain behavior by resorting to the Fourier transform and the mathematical framework of tempered distributions, which extends the Fourier analysis to functions (common in linear viscoelasticity) for which Fourier integrals are not convergent. In the analysis, our primary focus is the on class of linear viscoelastic solids whose 3D rheological behavior is described by a set of constant-coefficient ordinary differential equations, each corresponding to a generic arrangement of ``springs'' and ``dashpots''. On reducing the general formulation to the isotropic case, we proceed with an in-depth investigation of viscoelastic solids whose bulk and shear modulus each derive from a suite of classical ``spring and dashpot'' configurations. To enable faithful reconstruction of the 3D constitutive parameters of natural and engineered solids via (i) thin-sheet testing and (ii) applications of the error-in-constitutive-relation approach to the inversion of (kinematic) sensory data, we also examine the reduction of thermodynamic potentials describing linear viscoelasticity under the plane stress condition. The analysis is complemented by a set of analytical and numerical examples, illustrating the effect on the plane stress condition on the behavior of isotropic and anisotropic viscoelastic solids. (10.1007/s10659-025-10136-6)
  DOI : 10.1007/s10659-025-10136-6
• Efficient boundary integral method to evaluate the acoustic scattering from coupled fluid-fluid problems excited by multiple sources
  
  • Pacaut Louise
  • Chaillat Stéphanie
  • Mercier Jean-François
  • Serre Gilles
  Journal of Computational Physics, Elsevier, 2025, 524, pp.113736. In the naval industry many applications require to study the behavior of a penetrable obstacle embedded in water, notably in presence of a turbulent flow. Such configuration is encountered in particular when noise is scattered by two-phase fluids, e.g., turbulent flows with air bubbles. Fast and efficient numerical methods are required to compute this scattering in the presence of realistic 3D geometries, such as bubble curtains. In [1], we have developed a very efficient approach in the case of a rigid obstacle of arbitrary shape, excited by a turbulent flow. It is based on the numerical evaluation of tailored Green's functions. Here we extend this fast method to the case of a penetrable obstacle. It is not a straightforward extension and we propose two main contributions. First, tailored Green's functions for a fluid-fluid coupled problem are derived theoretically and determined numerically. Second, we show the need of a regularized Boundary Integral formulation to obtain these Green's functions accurately in all configurations. Finally, we illustrate the efficiency of the method on various applications related to the scattering by multiple bubbles. (10.1016/j.jcp.2025.113736)
  DOI : 10.1016/j.jcp.2025.113736