Pattern dynamics and evolution of material microstructure
The macroscopic behavior of materials is often the result of the development and evolution of fine microstructure on one or several microscopic length and time scales. Examples include the structure of polycrystals, including processes of solidification and recrystallization; the formation of martensite in materials such as iron and shape-memory alloys; the formation of dislocation structures during plastic deformation of ductile crystals; and the formation of magnetic domains and domain wall structures in ferromagnetic materials, among others. Often, the roots of these phenomena are to be found at the quantum mechanical or atomistic level. However, a strictly atomistic viewpoint is impractical for many applications, and models of effective behavior must be used instead. The problem of formulating physics-based and accurate models of effective behavior through a systematic bridging of length and time scales remains a grand challenge of our time and one that sits squarely at the triple point between mathematics, mechanics and materials science. Due to this inherently multidisciplinary nature of the subject and to its importance in industrial applications involving the design and utilization of new materials, students will get exposed to important concepts from physics, mathematics and computation, ranging from the theoretical to the applied, which will confer them a competitive advantage for future careers in research and industry.