EVENT DETAILS AND ABSTRACT

Title: Phase-Field Asymptotics for Unequal Diffusivities
Speaker: Professor R. Almgren
Speaker Info: U. Chicago
Brief Description:
Special Note:
Abstract:

The phase field method is a reaction-diffusion system whose solutions contain thin boundary layers; in the asymptotic limit of a sharp interface, these layers move according to the modified Stefan problem describing solidification of a pure material from its melt. Recently, Karma and Rappel have constructed a more careful asymptotic analysis, to give dramatically better performance by controlling the "kinetic term." I show that their method may be described formally as continuing the standard asymptotic expansion to an additional order, and I show how it may be extended to the asymmetric case of unequal diffusivities, important for modeling alloy solidification.