Topic

The phase-field method is a compact and elegant tool for the numerical modelling of problems that involve moving boundaries. In recent years, it has been applied to a large variety of subjects, including microstructure evolution in materials (solidification, precipitation, grain growth), multi-phase flows (fingering, droplet coalescence), fracture, soft matter and biophysics (membrane dynamics, vesicles). The key idea of this method is to represent the moving surfaces by an auxiliary field, the phase field, which exhibits a steep but smooth (diffuse) interface. The evolution of this field is governed by equations that can be obtained from the fundamental principles of out-of-equilibrium thermodynamics.

Goal and scope

This school is the fourth edition; the previous schools took place in 2013, 2016 and 2022. It is mainly intended for Ph.D. students and young researchers that already have a first experience with the phase-field method (on any topic) and who wish to deepen their understanding of the fundamentals, and/or wish to see applications in other domains to broaden their knowledge about the possibilities of the method. Complete beginners in phase field can be accepted if they have a strong background in at least one of the following fields: statistical physics, materials science, thermodynamics and phase transitions. The school will last two weeks. In the first week, the focus will be on the fundamentals; in the second week, various advanced applications will be presented. Practical sessions on several numerical examples of model problems will also be offered. Participants will be given an opportunity to present their work by a poster. The lecturers will be available for discussions with the participants during the entire session.

Lecturers

The lecturers come from various european countries and have all contributed to new developments on phase-field models and their applications in recent years:

• Benoît Appolaire, Université de Lorraine, France
• Janin Eiken, Access, Aachen, Germany
• Hervé Henry, CNRS/Ecole Polytechnique, Palaiseau, France
• Yann Le Bouar, CNRS/ONERA, Châtillon, France
• Mathis Plapp, CNRS/Ecole Polytechnique, Palaiseau, France
• Tamás Pusztai, Wigner Research Center, Budapest, Hungary
• Marco Salvalaglio, Dresden University of Technology, Germany
• Axel Voigt, Dresden University of Technology, Germany