Existence of standing waves for dirac fields with singular nonlinearities

International audienc

Nodal solutions for a sublinear elliptic equation

We consider radial solutions of Δu+u−|u|−2θu=0 in Image with d>1, Image and prove by a shooting method the existence of compactly supported solutions with any given number of nodes.ou

Nodal Solutions for a Sublinear Elliptic Equation

We consider radial solutions of \Deltau + u \Gamma juj u = 0 in IR with d ? 1, ` 2 (0; 2 ) and prove by a shooting method the existence of compactly supported solutions with any given number of nodes

Existence of excited states for a nonlinear Dirac field

International audienc

A complete model of keyhole and melt pool dynamics to analyze instabilities and collapse during laser welding

International audienceA complete modeling of heat and fluid flow applied to laser welding regimes is proposed. This model has been developed using only a graphical user interface of a finite element commercial code and can be easily usable in industrial R&D environments. The model takes into account the three phases of the matter: the vaporized metal, the liquid phase, and the solid base. The liquid/vapor interface is tracked using the Level-Set method. To model the energy deposition, a new approach is proposed which consists of treating laser under its wave form by solving Maxwell's equations. All these physics are coupled and solved simultaneously in Comsol Multyphysics®. The simulations show keyhole oscillations and the formation of porosity. A comparison of melt pool shapes evolution calculated from the simulations and experimental macrographs shows good correlation. Finally, the results of a three-dimensional simulation of a laser welding process are presented. The well-known phenomenon of humping is clearly shown by the model

A new approach to compute multi-reflections of laser beam in a keyhole for heat transfer and fluid flow modelling in laser welding

International audienceIt is widely accepted that laser reflections can play a critical role during keyhole laser welding. The energy concentration, the mask effects and the laser polarization can directly affect the molten pool dynamic. In this paper a new approach to compute laser reflections is proposed which consists of treating laser under its wave form by solving Maxwell's equations. The method has the advantage to be easily coupled with heat transfer and fluid flow equations and can be immediately transposable in any 2D, 2D axi or 3D configurations. The reliability and limits of this approach are discussed through different numerical examples. The complete model takes into account the three phases of the matter: the vaporized metal, the liquid phase and the solid base. To predict the evolution of these three phases, coupled equations of energy, continuity, momentum and Maxwell are solved. The liquid/vapour interface is tracked using the level-set method. All these physics are solved simultaneously with the commercial code COMSOL Multiphysics®. The calculated temperatures, velocities and free surface deformation are analysed. Examples of simulations leading to the formation of porosity are also presented. Finally, melt pool shapes evolution are compared to experimental macrographs