Laboratoire d'Acoustique de l'Université du Maine

Centre National de la Recherche Scientifique

Ph.D. Research Position, “Acoustic propagation in fluid-saturated porous metamaterials” A Ph.D. position on theoretical, numerical and experimental aspects of sound propagation in fluidsaturated porous materials [1] is offered at the Acoustic Laboratory of Le Mans University (LAUM, UMR CNRS 6613), starting September 2014. The thesis advisor is Denis Lafarge (CNRS, Associate Editor of the Journal Acustica united with Acta Acustica); a short description is as follows. The main subject is a follow-up question raised by Navid Nemati’s recent thesis (2012) entitled: “Macroscopic theory of sound propagation in rigid–framed porous materials allowing for spatial dispersion: principle and validation” [2]. In electromagnetism, “metamaterials” -- materials having anomalous macroscopic behaviours, e.g. negative permittivities leading to negative refraction -- can arise as a result of a proper microstructuration; their anomalous properties explain through spatial dispersion effects (nonlocal responses) trigged by the microstructuration, meaning that the material constitutive properties depend not only on temporal variations, but also on spatial variations of the wavefield. In acoustics and in similar manner, “metamaterials” presenting anomalous macroscopic behaviours such as negative compressibility [3] also arise as a result of spatial dispersion effects trigged by specific microstructures (Helmholtz’s resonators in particular). A question then is raised: how to express the spatial dispersion effects and deduce, from microstructure, the macroscopic acoustic wave propagation properties? We have been able to rigorously answer this question through a thermodynamic analysis inspired by a deep electromagnetic analogy in [2, 4, 5]. The answer, however, has been so far limited to the special case of macroscopically homogeneous and isotropic fluid-saturated materials having rigid-framed structures. In the new thesis we propose to relax the restriction and extend the treatment to anisotropic and macroscopically inhomogeneous materials, hence obtaining a complete solution of macroscopic reflection-transmission problems within nonlocal theory. Our hope is to arrange the microstructure in such a way as to produce new acoustic materials. The subject is sufficiently rich and new to allow putting more emphasis on the theoretical, numerical, or experimental aspects, depending on the skills of the candidate. The position is fully funded by the French “Ministère de l’Enseignement Supérieur et de la Recherche” for three years, with possible extensions. Salary is in accordance with the Ph-D funding scale which offers approximately between $27,000 for entry level Ph.D. students, and $33,000 for entry level Ph.D. students with additional teaching or consulting activities. Applicants should contact Dr. Denis Lafarge (Email: [email protected]). [1] J.-F. Allard and N. Atalla, Propagation of sound in porous media, Wiley, Second Ed., 2009. [2] N. Nemati, Macroscopic theory of sound propagation in rigid–framed porous materials allowing for spatial dispersion: principle and validation, Doctoral thesis in acoustics, 2012, Le Mans, http://tel.archivesouvertes.fr/docs/00/84/86/03/PDF/thesis_Navid_Nemati_2012.pdf; Navid is currently in a Post-Doc position in N. Fang’s group, at MIT, Cambridge, Massachusets, USA. [3] N. Fang et al., Ultrasonic metamaterials with negative modulus, Nature Materials 5, 452-456 (2006). [4] D. Lafarge, N. Nemati, Nonlocal Maxwellian theory of sound propagation in fluid saturated rigid-framed porous media, Wave Motion 50, 1016-1035 (2013). [5] N. Nemati, D. Lafarge, Check on a nonlocal Maxwellian theory of sound propagation in fluid-saturated rigidframed porous media, Wave Motion, In Press, Available online 8 January 2014.