Springer publishes Theoretical and Practical Stefan Problems, by Tim Myers (CRM)

Springer has published Theoretical and Practical Stefan Problems, by Tim Myers, Senior Researcher at the CRM. The book appears as volume 63 of the Interdisciplinary Applied Mathematics series and is intended for graduate students and researchers in applied mathematics, engineering, physics and chemistry.

Stefan problems describe processes in which a material changes phase: ice melting into water, a liquid solidifying, a crystal growing. What makes them mathematically awkward is that the boundary between the two phases moves, and its position is not given in advance. It is part of the unknown. The heat equation must be solved in a domain whose shape depends on the very solution being sought. The class of problems takes its name from Josef Stefan, the Austrian physicist who studied the growth of polar ice at the end of the nineteenth century, and it has since become a standard framework for phase-change processes across the physical sciences and industry.

The first three chapters set out the formulation of the classical Stefan problem together with exact and approximate solution methods, and introduce the applied techniques used later in the text, among them non-dimensionalisation, perturbation methods and lubrication theory. The remaining chapters move beyond the classical setting to formulations where the material properties or the phase-change temperature are no longer constant.

Throughout, the theory is developed from physical situations. The book treats phase change in the presence of a flowing liquid, in the context of microvalves and of ice accretion on aircraft, as well as the solidification of a supercooled liquid and the melting and growth of nanoparticles and nanocrystals, where the smallness of the sample shifts the phase-change temperature itself. A closing chapter considers what happens when heat no longer flows according to Fourier’s law, a regime relevant at very small scales and very short times. A collection of hints to the exercises completes the volume, which runs to 200 pages.

Tim Myers is a Senior Researcher at the CRM, Adjunct Professor at the Universitat Politècnica de Catalunya and Adjunct Professor of Industrial Mathematics at the University of Limerick. He has worked at universities in the United Kingdom, South Africa, Australia, Canada, Argentina and South Korea, coordinates the European Study Groups with Industry, and is involved in several initiatives to bring practical mathematics to the Global South. His current research is focussed on environmental applications.

Theoretical and Practical Stefan Problems. Timothy G. Myers. Interdisciplinary Applied Mathematics 63, Springer, 2025. DOI: 10.1007/978-3-032-04826-4.