3 papers
math.NA2024
Numerical study of the Gross-Pitaevskii equation on a two-dimensional ring and vortex nucleation
Quentin Chauleur, Radu Chicireanu, Guillaume Dujardin +2
We consider the Gross-Pitaevskii equation with a confining ring potential with a Gaussian profile. By introducing a rotating sinusoidal perturbation, we numerically highlight the n…
math.AP2024
A numerical study of vortex nucleation in 2D rotating Bose-Einstein condensates
Guillaume Dujardin, Ingrid Lacroix-Violet, Anthony Nahas
This article introduces a new numerical method for the minimization under constraints of a discrete energy modeling multicomponents rotating Bose-Einstein condensates in the regime…
math.NA2024
Uniform estimates for a fully discrete scheme integrating the linear heat equation on a bounded interval with pure Neumann boundary conditions
Guillaume Dujardin, Pauline Lafitte
This manuscript deals with the analysis of numerical methods for the full discretization (in time and space) of the linear heat equation with Neumann boundary conditions, and it pr…