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PhD Position in Wave Propagation for Hyperbolic Media

Il y a 2 mois


Palaiseau, Île-de-France INRIA Temps plein
Context and Advantages

Hyperbolic metamaterials are artificially engineered anisotropic materials that exhibit unusual properties, such as negative refraction and backward wave propagation. The name 'hyperbolic' comes from the dispersive curves, which relate the frequency and wave vector of plane waves propagating in such media. This property enables them to support an arbitrary large wavenumber, with applications including enhanced particle absorption, emission, and collection, super-resolution imaging, stealth technologies, and rogue wave generation.

Unlike isotropic metamaterials, media with hyperbolic dispersion exist in nature, examples including crystals of hexagonal boron nitride, bismuth telluride, or even cold plasma. From a mathematical point of view, the main particularity of the corresponding models lies in the fact that in the frequency domain, the respective problem is elliptic, at least for a range of frequencies. This is strikingly different from classical frequency-domain problems, which are elliptic.

Main Activities

The hyperbolicity of the PDE has serious implications on the well-posedness of underlying boundary-value problems. For example, it is well-known that the Dirichlet problem for the wave equation is in general ill-posed in bounded domains. However, not much is known for the Klein-Gordon equation, especially when considered in the following settings: 1) unbounded domains, except for the free space case; 2) transmission problems, where the hyperbolic media interacts with vacuum, either in bounded or unbounded domains.

Requirements

We are looking for a candidate with a strong background in numerical analysis for wave propagation, solid complex analysis skills, and some knowledge of programming (MATLAB or C++).

Benefits
  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave
  • Possibility of teleworking and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural, and sports events and activities
  • Access to vocational training
Salary

Gross salary: 2,100 euros/month