Mathematics of Multiscale and Multiphysics Phenomena in Materials Science (24w5159)


(University of Utah)

Rustum Choksi (McGill University)

Chun Liu (Illinois Institute of Technology)


The Banff International Research Station will host the “Mathematics of Multiscale and Multiphysics Phenomena in Materials Science” workshop in Banff from June 16 - 21, 2024.

Tremendous progress has been made in the past century in materials science thanks to technological advances in experimental and industrial techniques. As was the case for mechanics, materials science is at a critical juncture where further advancements rely crucially on the development of theoretical and quantitative tools. Mathematics will inevitably play a fundamental role in the design and engineering of new materials that will revolutionize our future.

Many questions in materials science are characterized by the interplay of multiple scales and governed by different physical laws. Working on these problems requires the creation of innovative mathematical tools that can describe interactions of microstructures at the atomic and continuum scales. Such problems are inherently multi-disciplinary, and they present formidable challenges. On the other hand, they provide fantastic opportunities for modelers, analysts, as well as computational and experimental scientists.

In this workshop, we will focus on multiscale and multi-physics problems that emerge in various areas of materials science with the main focus on three interconnected themes: Polycrystals and Materials Microstructures; Smart Materials and Materials with Unusual Properties; and Complex Fluids and Biomaterials. For instance, the modeling of grain boundary evolution in polycrystalline materials will be discussed in detail. In particular, the important question of how to incorporate elasticity and temperature effects into the model of grain growth while considering other physical properties of the system will be considered. Such couplings can completely change the behavior of the grain boundary networks and have not yet been systematically studied. Using new approaches and tools, we are now in a better position to address some of these central problems in materials science.

Furthermore, as a part of the meeting, we will discuss current efforts and future ways to attract much more diverse participation in the cross-disciplinary areas and respective departments represented in the workshop.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines, and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta’s Advanced Education and Technology, and Mexico’s Consejo Nacional de Ciencia y Tecnología (CONACYT).