Special Session 1: ODEs and Applications

Self-organization and criticality in martensite

pierluigi cesana
kyushu university
Japan
Co-Author(s):    John M. Ball; Ben Hambly
Abstract:
A martensitic phase-transformation is a first-order diffusionless transition occurring in elastic crystals and characterized by an abrupt change of shape of the underlying crystal lattice. It is the basic activation mechanism for the Shape-Memory effect. In this talk we present a probabilistic model for the description of martensitic microstructure as an avalanche process. Our approach to the analysis of the model is based on an associated general branching random walk process. Comparisons are reported for numerical and analytical solutions and experimental observations.