# Analysis of a Lattice Model for Phase Transitions and Derivation of Kinetic Relations

Tuesday, July 24, 2007 - 4:00pm - 4:30pm

Johannes Zimmer (University of Bath)

A short overview over solid-solid phase transitions (martensitic

transformations) will be given, and a one-dimensional lattice model

will be analysed. The equations of motions are given by Newton's

law, where the force is given by the interaction of neighbouring atoms.

The challenge is that the interaction potential is nonconvex, to model

phase transitions. The existence of subsonic travelling waves can be

proved. We will explain how this information can be used to derive

so-called kinetic relations, which relate the velocity of the phase

boundary to a driving force. The interest in kinetic relations can

be explained by their relevance for a continuum modelling of phase

transitions; this will be briefly sketched.

This is joint work with Hartmut Schwetlick (Bath).

transformations) will be given, and a one-dimensional lattice model

will be analysed. The equations of motions are given by Newton's

law, where the force is given by the interaction of neighbouring atoms.

The challenge is that the interaction potential is nonconvex, to model

phase transitions. The existence of subsonic travelling waves can be

proved. We will explain how this information can be used to derive

so-called kinetic relations, which relate the velocity of the phase

boundary to a driving force. The interest in kinetic relations can

be explained by their relevance for a continuum modelling of phase

transitions; this will be briefly sketched.

This is joint work with Hartmut Schwetlick (Bath).