Workshops

Within the focus of the workshop are three categories of multiscale problems with simultaneous scalings of time, space and further quantities that are characteristic for the case at hand: Discrete lattice models and their continuum limits, Discrete and continuum descriptions of nucleation and subsequent evolutions and Sharp interface limits of phase field systems.

Discrete lattice models serve as prototypes to study various possible limiting cases where a discrete ODE system can be substituted by a single or at least a few PDEs that describe the discrete dynamics on a continuum level.

During the first stages of a phase transition small clusters of the new phase with α particles may grow or shrink by adding or subtracting a single particle. The evolution of the number of clusters is described by an ODE system of Becker-Döring type, which, however, should be substituted by a PDE if clusters above a certain size appear.

Phase field systems resolve the interfacial region so that their evolution may be described by smooth fields. On the scale of microscopic observations the interfacial region mostly appears as a singular surface, where the observable fields change discontinuously. Thus the physical relevance of phase field systems is tested by their sharp interface limits.