Research Interests :
- Mathematical models for biology
- Models for collective motion and more generally collective behaviour
- Emergence and self-organization in complex patterns
- Stochastic models for collective motion
But also (less recently but still interested !) :
- 3D Schrödinger-Poisson sysmtems
- Low dimensional systems for strongly confined Schrödinger-Poisson systems
Publications :
- P. Cattiaux, F. Delebecque, O. Hacquard, Some flocking properties for a model of collective dynamics with topological interactions, (preprint)
- P. Cattiaux, F. Delebecque, L. Pédèches, Stochastic Cucker-Smale models : old and new, Ann. Appl. Probab. 28(5): 3239–3286, 2018. (here)
- D. Peurichard, F. Delebecque, A. Lorsignol, C. Barreau, J. Rouquette, X. Descombes, L. Casteilla, P. Degond, Simple mechanical cues could explain adipose tissue morphology, Journal of Theoretical Biology, 429 (2017), 61-81, (here)
- F. Delebecque, S. Le Coz, R-M. Weishäupl : Multi-speed solitary waves of nonlinear Schrödinger systems : theoretical and numerical analysis, Commun. Math. Sci. 14 (2016), no. 6, 1599–1624. (here)
- P. Degond, F. Delebecque, D. Peurichard, Continuum model for linked fibers with alignment interactions, M3AS, 26 (2016), 269–318 , (here)
- F. Delebecque : An asymptotic model for the transport of a bidimensional electron gas in a slab, M3AS, 21, no. 7 (2011) 1443-1478 (here)
- F. Delebecque, F. Méhats : An effective mass theorem for the bidimensional electron gas in a strong magnetic field, Comm. Math. Phys. 292 (2009), 829–870 (here)
- N. Ben Abdallah, F. Castella, F. Delebecque-Fendt, F. Méhats : The strongly confined Schrödinger-Poisson system for the transport of electrons in a nanowire, SIAM J. Appl. Math., 69 (2009), no. 4,\ 1162-1173. (here)
PhD Manuscript : Modeling the transport of strongly confined quantum gas (dec 2009) (here)