Labex MEC “Mechanics And Complexity”
Duration: 1 year
Period: 1/09/2019– 31/08/2020, earlier start possible
Location: IUSTI/LMA Marseille, France
Gross salary: from 2423 € to 2843 €/month depending on qualification and experience
Research project and job description
Title: Variational approach and homogenisation for dispersive waves in solids
This post-doc position is dedicated to the study of dispersive waves propagation. Dispersive shock waves and solitary waves are typical solutions of dispersive models. These waves appear in various applications such as quantum systems (ultra-cold atoms, semi-conductors, electron beams, nonlinear photonics, collision-less shocks in plasmas), hydrodynamics (surface waves) and in solid mechanics (phononic crystals, micro-structured materials). During this post-doc, only dispersive waves in solid mechanics will be investigated. These waves appear in isotropic materials as soon as geometrical effects are taken into account. The simplest example is bending waves in a bounded bar. Another example is the propagation of waves in a 1D multi-layered medium, for which dynamic homogenisation predicts a classical wave equation (second order derivative in space and time) but also dispersive terms with fourth order derivatives in space and time. In the 1D linear case, the equations can be rewritten in the following form:
where a, b, c, d are parameters to be determined through the homogenisation process. The choice of these parameters is not unique and it is possible, by introducing derivatives of higher order, to convert the fourth order derivatives in time to fourth order derivatives in space and time or only in space. The aim of this post-doc is to study the influence of this choice on the dispersion relations and to compare these relations with exact solutions or numerical approximations. In a second step, the simplest possible Lagrangian will be built to retrieve the equations using variational principles, and extensions will be proposed to take non-linearities into account. Finally, numerical schemes will be constructed for the dispersive equations and compared with direct numerical simulations. The multi-dimensional case will be treated at the end of the post-doc.
Profile: Candidates must hold a Ph.D. in mechanics, acoustics or applied mathematics.
Essential skills: homogenisation for heterogeneous materials. Generalised Continuum Mechanics.
Other skills: High order homogenisation. Numerical modelling. Experimental Validation.
Axis: Heterogeneity, multi-scale, change of scale
Action: Heterogeneity, homogenisation and multi-physics coupling
Modellking of heterogeneous media, waves, interfaces and multi-physics coupling
Contact IUSTI: Name, surname: Favrie Nicolas
Phone: +33 4 91 10 69 56
Contact LMA: Name, surname: Cottereau Régis
Phone: +33 4 84 52 42 49
How to apply
Send an application including:
- A detailed CV with a list of publications
- A cover letter
- A list of scientific personalities able to support the application
to both these addresses:
Relevant group leader (email@example.com)