Modeling the effect of electroporation-based therapies on tumours
Objective: To provide mathematical and numerical models of electroporation-based therapies at the macroscopic scale (tissue, spheroids) in order to fill the gap between cell- and tissue-scale models and broaden the scope of clinical applications. Model calibration with experimental data provided by IPBS (Toulouse, France) and computational optimisation in collaboration with the UCSB (USA).
Key words : mathematical and numerical modelling, finite-element method, electroporation, homogenization, calibration, high-performance scientific computing.
Programming : Python, Firedrake package.
Main collaborators : Clair Poignard and Frédéric Gibou (UCSB).
Variational water-wave models and pyramidal freak waves
Objective: Formulation and simulation of an accurate mathematical and numerical model of non-linear, steep waves to estimate their force and to design reliable and durable maritime structures.
Key words : Mathematical and numerical model, experimental validation, data analysis, PDEs, Finite Element method, discontinuous Galerkin method, geophysical fluid dynamics, variational principle, water waves, solitons.
Programming : Python, Firedrake package, Matlab.
Main collaborators : Onno Bokhove, Mark Kelmanson, Geert Kapseenberg and Tim Bunnik.
Real-time estimation of lung mechanics during breath under ventilation support
Objective : Implementation of the Extended Kalman Filter to estimate Lung Mechanics continuously for a patient under ventilation support. Validation of the models against real data.
Key words : Processing and signal analysis, modelling, (extended) Kalman filter, Lung mechanics, electrical engineering.
Programming : Python.
Main collaborators : Thomas Handzsuj, Philipp Rostalski and Marcus Eger.
Modeling of heat conduction in fractured rocks
Objective : Modelling of heat conduction in fractured rocks to determine their properties (conductivity, thermal diffusivity, porosity but also dimension and location of the fractures, their flow velocity, their aperture...) and thus predict the outcome of pollution in these rocks.
Key words : Semi-analytical modelling, heat conduction, fractured rocks.
Programming : Matlab.
Main collaborators : Delphine Roubinet and Pete Pehme
Fluid-wave-tank demonstrations to show various applications of maths to solve "real-world" problems (coastal errosion, freak-wave impacts on wind-turbine...)
Public lectures about the legendary freak waves and how they went from mariner tales to marine threat
Raising awareness among children in Togo (Africa) of the importance of education;
Interventions in schools to show the applications of mathematics in everyday life (France and Poland)
Sharing interventions, new findings, everyday-life applications. Visited from more than 30 countries: https://blogsurfsup.wordpress.com
10mn presentation about my PhD project and its impact: