Many contemporary problems in new advanced materials relate to variation in length, time scales, and variations inherent in their fabrication and function. Resolution of these problems requires predictive theories for these complex systems that in turn require advances in mathematics. In this PIRE project an international network of prominent mathematicians from four U.S. institutions, five European institutions, and a multinational industrial partner, will build on decades of collaboration and training at the interface of mathematics and materials sciences that have yielded many achievements at the forefront of sophisticated new mathematics and simulation methods. The project will focus on four principal research areas: 1. Pattern formation from energy minimization, 2. Challenges in atomistic to continuum modelling and computing, 3. Prediction of hysteresis (systems that have "memory" such that effects of stimuli are temporally delayed), and 4. Pattern dynamics and development of material microstructure.
U.S. and European students will benefit from internationalized education and research training within a PIRE framework promotes new patterns in research collaboration and education that includes cultural dimensions. Advanced graduate courses will be developed and shared across the network providing a truly internationalized curriculum and universal access to the best materials-relevant mathematics topics. U.S. graduate students and postdoctoral fellows will be immersed in intensive multi-advisor mentoring models strengthening their interdisciplinary and global research skills. Interested graduate students will be able to partake in an international industrial research internship. In addition, annual workshops and summer schools will extend the research to a much wider community of students and postdoctoral fellows outside the project.
This award will help to internationalize US institutions by linking them in a vibrant international network of applied mathematicians who integrate research relevant to materials science with a coherent program for training the next generation of globally-engaged scientific leaders in fast-developing areas of mathematics. The complementary strengths and expertise of the team will push the frontiers of applied analysis and clear the pathway for new applications in materials research. The U.S. will gain expertise and strength in the field of calculus of variations, essential to the first principal research area, through its base at two of the European research centers. Working with European partners will help unify and extend U.S. expertise in the modelling, computation, and analysis on problems arising in materials science. Advances in pattern dynamics research at several nodes of the network have revealed new modelling and analysis opportunities with the potential to be leveraged by this award.
Collaborators on this PIRE project include four U.S. institutions: Carnegie Mellon University (PA), California Institute of Technology, New York University, and University of Minnesota; five European institutions: University of Antwerp (Belgium), University of Bonn (Germany), Max Planck Institute for Mathematics in the Sciences (Germany), International School for Advanced Studies (SISSA)(Italy), and University of Oxford (UK); and an industrial partner: Robert Bosch GmbH (Germany and USA).
This project is supported by NSF's Office of International Science and Engineering and the Division of Mathematical Sciences.
