I am interested in mathematical physics and particularly in fluid dynamics, statistical physics and soft matter.
Below are my past and current subjects of research.
At nano-scales, fluid transport exhibits quantum effects. In particular, friction at the interface between fluids and solids can only be explained properly using a quantum formalism. The coupling between the collective modes of the fluid and the electronic excitations at the surface of the solid gives a theoritical explanation to the interfacial phenomena. Recent theoretical and experimental results have proved the strength of such an approach [Kavokine2020, Marcotte2020]. Future theoretical studies include quantum friction for special material and interfaces, the coupling between electronic winds inside the solid and ionic currents inside the fluid (see diagram) and the quantum interfacial effects on thermal transfers. While the theory is still to complete, applications in quantum engineering for nano-hydrodynamics are already promising.
The metriplectic framework is a generalisation of Hamiltonian dynamics in which dissipation is included. The main ideas are to replace the use of the Hamiltonian by the use of the free energy and to generalise the Poisson bracket by subtracting another bracket, called dissipative. The dissipative bracket must be symmetric and positive. To unsure the principles of thermodynamics, the dissipative bracket must also fulfil a compatibility condition, namely that the Hamiltonian is a degeneracy of the bracket. With such a construction, the dynamics splits between the Hamiltonian part and the dissipative part, and both the conservation of the Hamiltonian and the growth of the entropy are implemented. For a given model, it remains to write the good dissipative bracket to generate the dynamics. For most of fluid models, which are derived from Onsager-like out-of-equilibrium thermodynamics, there exists a natural and direct way to get the physical dissipative bracket (see figure and Coquinot2020). For instance, the brackets for Navier-Stokes-Fourier hydrodynamics and resistive magnetohydrodynamics can be derived with this method. Finally, the whole dynamics is expressed in a geometrical formulation, which allows powerful tools and deep insight for the theory.