Section: New Results

Miscellaneous

Participants : Laurent Boudin, Irène Vignon-Clementel.

In [34] we develop a quantitative single cell-based model for multi-cellular tumor spheroids of a specific lung cancer cell line, growing under various nutrient conditions: we confront the simulations performed with this model with data on the growth kinetics and spatial labeling patterns for cell proliferation, extracellular matrix, cell distribution and cell death. We stepwise arrive at a model that mimics the spheroid growth under two conditions, and can predict two other ones. The number of mechanisms the model contains is necessary and sufficient to explain the data.

In [19] we consider a kinetic model describing some mechanisms of opinion formation in the framework of referendums, where the individuals, who can interact between themselves and modify their opinion by means of spontaneous self-thinking, are moreover under the influence of mass media. We study, at the numerical level, both the transient and the asymptotic regimes. In particular, we point out that a plurality of media, with different orientations, is a key ingredient to allow pluralism and prevent consensus. The forecasts of the model are compared to some surveys related to the Scottish independence referendum of 2014.

In [56] we review various results on the compactness of the linearized Boltzmann collision operator and of its generalization to mixtures of non-reactive monatomic gases.