Phase transitions and hysteresis
in free boundary problems

Special session at the

Joint International Meeting UMI - DMV

Perugia 18-22 June 2007




PHASE TRANSITIONS AND HYSTERESIS IN FREE BOUNDARY PROBLEMS


Motivation and contents

In the last decades, free boundary problems, especially arising from models of phase transitions and hysteresis phenomena, have been the subject of an intense mathematical research, with contributions by applied mathematicians as experts in PDEs, as well as by scientists working in continuum mechanics and thermodynamics. These problems are strictly intercorrelated.

The classical Stefan problem, a simplified model for phase transitions, is such a free boundary problem. Actually, it is often referred to as the basic example of an evolution problem, where the free boundary is the moving interface between phases. In general, phase transitions may be represented by means of free boundary problems.

Often phase transitions are accompanied by hysteresis effects. In these phenomena, a proper choice of the length and time scales is especially relevant, and the study of composite materials leads to homogenization problems. The aim is to explain, describe and predict relevant phenomena like solid-liquid phase transitions or martensitic transformations or phase separation effects, while accounting for crucial aspects such as surface tension, motion of interfaces and, of course, hysteresis.

Hysteresis may be defined as a "rate-independent memory effect". It is also encountered in plasticity, in ferromagnetism, or in superconductivity.

The use of order parameters in the description of models, and the investigation of the related systems of PDEs, provide a common basis for developing new mathematical problems and results. The purpose of the session is thus to stimulate an interdisciplinary discussion on these topics and to bring phase transitions and hysteresis to the attention of the german and italian mathematical communities.


Speakers and program


Organizers