Section: New Results

Modelling Polymerization Processes

Nucleation Phenomena.

A new stochastic model of polymerization including the nucleation has been analyzed in [4]. A Functional Central Limit Theorem for the Becker-Döring model in an infinite dimensional state space is established in [25].

An oscillatory model of polymerisation-depolymerisation.

In 2017, we evidenced the presence of several polymeric species by using data assimilation methods to fit experimental data from H. Rezaei's lab  [64]. In collaboration with Klemens Fellner from the university of Graz, we now propose a new model, variant of the Becker-Döring system but containing two monomeric species, capable of displaying sustained though damped oscillations [39].

Time asymptotics for nucleation, growth and division equations.

We revisited the well-known Lifshitz-Slyozov model, which takes into account only polymerisation and depolymerisation, and progressively enriched the model. Taking into account depolymerisation and fragmentation reaction term may surprisingly stabilisde the system, since a steady size-distribution of polymers may then emerge, so that “Ostwald ripening” does not happen [8].

Cell population dynamics and its control

The PhD thesis work of Camille Pouchol (co-supervisors Jean Clairambault, Michèle Sabbah, INSERM, and Emmanuel Trélat, Inria CAGE and LJLL) has been continued, leading after his first article published in the J. Maths Pures Appl.  [136], summarised in [31], to his PhD defence in June [1], and to a diversification of his research activities in various directions related to population dynamics and optimal control with Antoine Olivier, Emmanuel Trélat and Enrique Zuazua [51], [56] or to more general questions [55].

Measure solutions for the growth-fragmentation equation

As recalled in the section ”Foundations”, entropy methods for population dynamics have been successfully developed around B. Perthame and co-authors. We recently extend such methods to the growth-fragmentation equation, in collaboration with P. Gwiazda, E. Wiedemann and T. Debiec [40], using the framework of generalised Young measures.