Research Interests

With competencies in both Theoretical Physics and Mathematics, I am interested in the modeling and numerical simulation of complex physical systems on powerful parallel computers.
Phenomena of interest include, for example, the quantum (ab initio) simulation of nano-materials, the aging of the tanks of nuclear reactors under prolonged irradiation, the atomic-scale simulation of fractures in novel materials such as metallic glasses, protein foldings, fundamental understanding of hydrodynamic turbulence, plasma and laser physics, morpho-hydrodynamics…

I often need to develop new mathematical methods, based on numerical analysis and computational physics, to enable the optimal development and implementation of numerical simulation programs that can help in the development of physical understanding of the indicated phenomena (global optimization, data mining, …).

I defended my PhD thesis in theoretical and computational physics. I tried in the first part to develop linear-scaling and near-linear-scaling algorithms for ab initio calculations of small gap systems in the framework of Density Functional Theory (DFT, Kohn-Sham scheme), by using the Energy Renormalization Group, which permits to couple different spatial and energy scales. In the second part, I showed how to obtain the effective hydrodynamic motion equation (Navier- Stokes) from a quantum liquid model in the framework of Current Density Functional Theory. I obtained an improvement of the Navier-Stokes equations which depend on the scale of observation.

Since the PhD, I worked on several topics including molecular dynamics and DFT calculations for different kind of material systems, and on some problems in quantum theory fundations. I developed also algorithms using classical molecular dynamics in order to optimize geometry of material systems and to study shear band appearance in bulk metallic glasses. I have studied hybrid methods such as QM/MM and QM/QM’ for studying zeolithe materials for example.

On the other hand, I created and developed new mathematical methods :

  • Probabilist Set Inversion (PSI) using pseudo-intervals arithmetic to solve inverse problems. PSI permits to solve numerically many inverse problems.
  • (min,+)-wavelets are very useful to perform multi-resolution (multi-scale) analysis of phenomena involving fractal or multi-fractal properties (turbulence, DNA, …).

Moreover, I developed algorithms using classical molecular dynamics in order to optimize geometry of material systems and to study shear band appearances in bulk metallic glasses.

I use computer systems such as Linux/UNIX, Windows and Mac OS X, even if have a strong preference for Linux. I master parallel and distributed programming (MPI, OpenMP), and I have used already some middlewares for cloud and grid computing (GLOBUS, EGEE). I am used to use langages such as python or ruby, and compilers C/C++, JAVA, FORTRAN 77/90/95. My knowledge of numerical analysis and scientific computing in general permits me to develop robust and efficient codes for scientific computing.

I have written as well codes in python and ruby to perform PSI and Genetic Programming and a complete MPI library for ruby which was not available at that time.

Actually, my main research interests are devoted to :

  • Tropical Mathematics, especially algebra and analysis in idempotent structures such as (min,+), (max+), and (min,max) dioids linked to Quantum and Statistical Physics.
  • Multifractal Analysis based on (min,+)-wavelets for hydrodynamical turbulence.
  • Improvement of Nature-inspired algorithms for Artificial Intelligence :
    • Evolutionnary Programming.
    • Neural Networks.
    • Swarm, Ants…

I have a strong experience of scientific consulting for industry, and worked with several companies such as EDF R&D (OSIRIS, Energy Optimization Department), PSA Peugeot-Citroën (Vehicle Dynamics Department, Scientific Facilities Service) in various types of complex problems such as continuous or combinatorial optimization, parameters identification, operations research, data mining

As member of the Interdisciplinary European Academy of Sciences (IEAS), I try to be eclectic and I am always interested by new topics.