Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Blaustein, Alain"'
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution $f_N(t)$ is gover
Externí odkaz:
http://arxiv.org/abs/2411.08614
Autor:
Blaustein, Alain
During the past century, biologists and mathematicians investigated two mechanisms underlying bacteria motion: the run phase during which bacteria move in straight lines and the tumble phase in which they change their orientation. When surrounded by
Externí odkaz:
http://arxiv.org/abs/2312.07121
Autor:
Blaustein, Alain, Filbet, Francis
We propose a numerical method for the Vlasov-Poisson-Fokker-Planck model written as an hyperbolic system thanks to a spectral decomposition in the basis of Hermite functions with respect to the velocity variable and a structure preserving finite volu
Externí odkaz:
http://arxiv.org/abs/2306.14605
Autor:
Blaustein, Alain
This work tackles the diffusive limit for the Vlasov-Poisson-Fokker-Planck model. We derive a priori estimates which hold without restriction on the phase-space dimension and propose a strong convergence result in a L2 space. Furthermore, we strength
Externí odkaz:
http://arxiv.org/abs/2210.10396
Autor:
Blaustein, Alain, Filbet, Francis
We propose and study a fully discrete finite volume scheme for the Vlasov-Fokker-Planck equation written as an hyperbolic system using Hermite polynomials in velocity. This approach naturally preserves the stationary solution and the weighted L 2 rel
Externí odkaz:
http://arxiv.org/abs/2210.02107
Autor:
Blaustein, Alain, Bouin, Emeric
In this paper we focus on a spatially extended FitzHugh-Nagumo model with interactions. In the regime where strong and local interactions dominate, we quantify how the probability density of neurons concentrates into a Dirac distribution. Previous wo
Externí odkaz:
http://arxiv.org/abs/2207.11010
Autor:
Blaustein, Alain
We consider a mesoscopic model for a spatially extended FitzHugh-Nagumo neural network and prove that in the regime where short-range interactions dominate, the probability density of the potential throughout the network concentrates into a Dirac dis
Externí odkaz:
http://arxiv.org/abs/2203.14558
Autor:
Blaustein, Alain, Filbet, Francis
We consider a spatially extended mesoscopic FitzHugh-Nagumo model with strong local interactions and prove that its asymptotic limit converges towards the classical nonlocal reaction-diffusion FitzHugh-Nagumo system. As the local interactions strongl
Externí odkaz:
http://arxiv.org/abs/2201.02363
Autor:
Blaustein, Alain, Filbet, Francis
Publikováno v:
In Journal of Computational Physics 1 February 2024 498
Autor:
Blaustein, Alain
Publikováno v:
In Journal of Differential Equations 25 November 2023 374:218-266