Vortex dans les condensats de Bose Einstein
Vortex filament dynamics for Gross-Pitaevsky type equations
We study solutions of the Gross-Pitaevsky equation and similar equations in space dimensions in a certain scaling limit, with initial data for which the jacobian concentrates around an (oriented) rectifiable dimensional set, say , of finite measure. It is widely conjectured that under these conditions, the jacobian at later times continues to concentrate around some codimension submanifold, say , and that the family of submanifolds evolves by binormal mean curvature flow. We prove...
Vortex pinning with bounded fields for the Ginzburg–Landau equation
Vortex rings for the Gross-Pitaevskii equation
We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross–Pitaevskii (GP) equation in dimension . We also extend the asymptotic analysis of the free field Ginzburg–Landau equation to a larger class of equations, including the Ginzburg–Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if ).
Vortices for a variational problem related to superconductivity
Vortices in Ginzburg-Landau equations.
Vorticité dans les équations de Ginzburg-Landau de la supraconductivité
Vorticité dans les modèles de Ginzburg-Landau pour la supraconductivité
Vorticity dynamics and numerical resolution of Navier-Stokes equations
We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical data...
Vorticity dynamics and numerical Resolution of Navier-Stokes Equations
We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical data...
Vorticity dynamics and turbulence models for large-Eddy simulations
We consider in this paper the problem of finding appropriate models for Large Eddy Simulations of turbulent incompressible flows from a mathematical point of view. The Smagorinsky model is analyzed and the vorticity formulation of the Navier–Stokes equations is used to explore more efficient subgrid-scale models as minimal regularizations of these equations. Two classes of variants of the Smagorinsky model emerge from this approach: a model based on anisotropic turbulent viscosity and a selective...
Vorticity dynamics and turbulence models for Large-Eddy Simulations
We consider in this paper the problem of finding appropriate models for Large Eddy Simulations of turbulent incompressible flows from a mathematical point of view. The Smagorinsky model is analyzed and the vorticity formulation of the Navier–Stokes equations is used to explore more efficient subgrid-scale models as minimal regularizations of these equations. Two classes of variants of the Smagorinsky model emerge from this approach: a model based on anisotropic turbulent viscosity and...