Séminaire Doctorants
organisé par l'équipe DOCT
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Lucas Bourgoin
Geometric quantization
5 juin 2025 - 16:30Salle de séminaires IRMA
In classical mechanics physical systems are described using Hamiltonian or Lagrangian formulations. In this settings the classical observables are functions defined on the phase space. On the other hand, in quantum mechanics observables are operators acting on quantum states. We will briefly introduce geometric quantization which is a method to try to connect this two physics using symplectic manifolds and line bundles. -
Livia Grammatica
TBA
19 juin 2025 - 16:30Salle de conférences IRMA
TBA -
Roxana Sublet
Mathematical modeling of apoptosis in cell collective dynamics: microscopic and macroscopic points of view
26 juin 2025 - 16:30Salle de conférences IRMA
In this work, we are interested in the mathematical modeling of the impact of apoptosis on the dynamics of cellular tissues, and in particular on cell tissue fluidity. Indeed, cell apoptosis corresponds to the programmed cell death: when they leave the tissue, they induce local contractions but also enable cells rearrangements.
We first propose an individual-based model that provides the dynamics of the positions, velocities and polarities of the cells, idealized as hard spheres. Cells interact with each other through contact forces, smooth attraction, and polarity alignment. The model also involves a microscopic description of apoptotic and proliferation events. The present work is an extension of the model proposed in [3] and validated by experiments on cellular rings. Numerical simulations are performed and several indicators of fluidity are analyzed.
Next, we derive a macroscopic description, following the methodology proposed in [1], [2]. We start from a mean-field dynamics of the kinetic distribution function in phase-space (position, polarity, radius), where contact forces have been replaced with repulsion forces. We then introduce a specific time and space rescaling and identify the equilibria distribution functions, which are parameterized by two macroscopic quantities: the density and the mean polarity. Based on the Generalized Collision Invariant (GCI) method [2], we are then able to identify their dynamics: the resulting description can be seen as a modified Self-Organized Hydrodynamics (SOH) model. We finally discuss the obtained model and highlight the effect of the apoptotic events on the dynamics.
This is a joint work with Laurent Navoret (Université de Strasbourg) and Marcela Szopos (Université Paris Cité). It has also been carried out in collaboration with Romain Levayer (Institut Pasteur) and Daniel Riveline (IGBMC, Université de Strasbourg) in the context of the ANR project MAPEFLU.
References
[1] Degond, P., Dimarco, G., Mac, T. B. N., and Wang, N. Macroscopic models of collective motion with repulsion. Communications in Mathematical Sciences, 13(6), 1615–1638 (2015).
[2] Degond, P., and Motsch, S. Continuum limit of self-driven particles with orientation interaction. Mathematical Models and Methods in Applied Sciences, 18(supp01), 1193–1215 (2008).
[3] Vecchio, S. L., Pertz, O., Szopos, M., Navoret, L., and Riveline, D. Spontaneous rotations in epithelia as an interplay between cell polarity and boundaries. Nature Physics (2024).