Displaying similar documents to “Analytical and numerical study of Kramers' exit problem. I.”

A stochastic phase-field model determined from molecular dynamics

Erik von Schwerin, Anders Szepessy (2010)

ESAIM: Mathematical Modelling and Numerical Analysis


The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation...

A zoology of boundary layers.

David Gérard-Varet, Emmanuel Grenier (2002)



In meteorology and magnetohydrodynamics many different boundary layers appear. Some of them are already mathematically well known, like Ekman or Hartmann layers. Others remain unstudied, and can be much more complex. The aim of this paper is to give a simple and unified presentation of the main boundary layers, and to propose a simple method to derive their sizes and equations.