Section: New Results

Variational modeling and analysis

Bose-Einstein condensates are a unique way to observe quantum effects at a (relatively) large scale. The fundamental state​s​ of such condensates ​are​ obtained as minimizer​s​ of a Gross-Pitaievskii functional.​ In [39] , M. Goldman and B. Merlet consider the case of a two component Bose-Einstein condensate in the strong segregation regime (the energy favors spatial segregation of the two different Boson species). They identify two different regimes in the strong segregation and small healing length limit. In one of these regimes, the relevant limit is an interesting weighted isoperimetric problem which explains some of the numerical simulations of [63] .

In [14] , C. Cancès et al. show that the equations that are classically used for modeling the motion of two incompressible immiscible phases in a porous medium can be formally reinterpreted as the gradient flow of the free energy in a degenerated geometry closely related to the Wasserstein metric. This extends to realistic models the seminal approach [65] and the more recent one [64] .