Our research team was able to undertake several research projects mainly in the following areas (statistical mechanics, magnetic susceptibility of the Ising model, dynamic systems, non-linear physics).
Our activities can be summarized as follows: the study of magnetic susceptibility of the Ising model, which is one of the most used models in the description of critical phenomena and phase transitions in physics and originating from lattice statistical mechanics. Some of the properties of the magnetic susceptibility of this Ising model whose exact analytical form is still unknown until now have been studied. The method we used consists of analyzing the very long series obtained for this susceptibility, determining the exact differential equations to which they obey and then determining the properties of these series via these differential equations. These studies will ultimately allow us to understand one of the most studied critical phenomena in statistical mechanics.
We plan to continue our work in this area of research in the coming years. This work began around the 1990s and led to several publications in international journals.
All the calculations that we developed during this work gave consistent exact results which show the existence of deep (algebro-differential) structures in the square two-dimensional lattice Ising model. These structures underline the deep link between the Ising model and the theory of elliptic functions (modular forms, special hypergeometric functions, modular curves, etc.).
Our current work consists of understanding these issues.
Another area of research that interests our team is that of applications in the field of energy, particularly renewable energies. We use mathematical and statistical tools for modeling, analysis and simulation in collaboration with the Optical Materials, Photonics and Systems laboratory (LMOPS) which brings together research teams from the University of Lorraine and CentraleSupélec.
Our research perspectives are also oriented towards applications in the field of aeronatics, in order to apply optimization theories and bifurcation theories and transition theories to turbulence.