AYMARD , Benjamin

In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self-and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and orbits of the latter. Special attention is paid to accuracy, a necessary condition when one wants to catch...

In this article we study reaction-diffusion systems containing self and cross-diffusion using a free energy approach. This framework naturally leads to the formulation of an energy law, and to a numerical method respecting a discrete version of the latter (a linear second order finite-element method with adaptive mesh refinement). Applying this...

In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Monte Carlo method for the simulation of the microscopic system, and a finite volume method (based on an upwind implicit scheme) for the mean-field model. The finite...

After injury, while regeneration can be observed in hydra, planaria and some vertebrates,regeneration is rare in mammals and particularly in humans. In this paper, we investigatethe mechanisms by which biological tissues recover after injury. We explore this question onadipose tissue, using the mathematical framework recently ...

We propose a new model for the emergence of blood capillary networks. We assimilate the tissue and extra cellular matrix as a porous medium, using Darcy's law for describing both blood and intersticial fluid flows. Oxygen obeys a convection-diffusionreaction equation describing advection by the blood, diffusion and consumption by the tissue....

We propose a new model for the emergence of blood capillary networks. We assimilate the tissue and extra cellular matrix as a porous medium, using Darcy's law for describing both blood and intersticial fluid flows. Oxygen obeys a convection-diffusionreaction equation describing advection by the blood, diffusion and consumption by the tissue....