ESPCI web site
PMMH’s weekly seminar is held every Friday at 11 am (map)
Stéphane Perrard
Etienne Reyssat
Virgile Thiévenaz
PMMH
BARRE CASSAN
BAT A 1ER ETAGE CASE 18
7 QUAI SAINT BERNARD
75005 PARIS
France
Tel : (33) 1 40 79 45 22
Séminaire PMMH - Leonid Berlyand, Penn State
Asymptotic Stability in a free boundary model of cell motion
We introduce a free boundary model of the onset of motion of a living cell (e.g. a keratocyte) driven by myosin contraction, with focus on a transition from unstable radial stationary states to stable asymmetric moving states. This model generalizes a previous 1D model (Truskinovsky et al.) by combining a Keller-Segel model, a Hele-Shaw boundary condition and the Young-Laplace law with a nonlocal regularizing term, which precludes blow-up or collapse by ensuring that membrane-cortex interaction is sufficiently strong. We show that this model has a family of asymmetric traveling wave solutions bifurcating from a family of stationary states. Our goal is to establish observable steady cell motion with constant velocity. Mathematically, this amounts to proving stability of the traveling wave solutions, which requires generalization of the standard notion of stability. Our main result is establishing nonlinear asymptotic stability of traveling solutions. To this end, we derive an explicit asymptotic formula for the stability-determining eigenvalue from asymptotic expansions in small speed. This formula greatly simplifies the numerical computation of the sign of this eigenvalue and reveals the physics underlying onset of the cell motion and stability of moving states. If time permits, we will discuss work in progress on fingering instability in multicellular tissue spreading
The audience is composed of people with rather heterogeneous backgrounds including specialists in solids, fluids, granular flows, statistical physics... so the idea is to keep your talk understandable by people not necessarily working in your field... The seminar time slot runs from 11am to noon so the best is to make the talk last around 45 minutes to leave some time for discussion.
- Séminaires ESPCI-ENS de biophysique
- Séminaires du Département de Physique de l’ENS
- Séminaires du Laboratoire d’Hydrodynamique de l’X
- Séminaire de Mécanique d’Orsay (page web FAST)
- Séminaire de Mécanique d’Orsay (page web LIMSI)
- Séminaire de Mécanique des Fluides de l’Institut Jean le Rond d’Alembert
- Séminaires du laboratoire MSC, Paris VII
- Séminaires Gulliver
Link to cofee seminar (internal, every Thursday)
