This PIRE (Partnerships for International Research and Education) project is a five-year National Science Foundation (NSF)-funded international collaboration program (NSF abstract) starting on January 2011. The scientific scope is directed to issues in applied mathematics and mechanics, including partial differential equations, calculus of variations, and scientific computation, which arise from the materials sciences.Four scientific themes, all at the interface where PDE and the calculus of variations meet mechanics and materials science:
- Pattern formation from energy minimization
- Challenges in atomistic to continuum modeling and computing
- Prediction of hysteresis
- Pattern dynamics and evolution of material microstructure
Many contemporary problems in new and advanced materials are related to the variety of length and time scales and heterogeneities inherent in their fabrication and function. Predictive theories for these complex systems require new advanced mathematics whose discovery will be enhanced by international collaboration.
The main international goals are:
- Nurture a group of internationally connected young scientists.
- Strengthen communication between groups, to accelerate scientific progress.
- Four US nodes
- Carnegie Mellon University
- California Institute of technology (Caltech)
- University of Minnesota
- New York University
- Seven foreign partners
- US-based students and postdocs acquire mentors at foreign partners, and spend semesters abroad (see http://www.math.cmu.edu/PIRE/training/abroad.html).
- Networking and outreach is achieved through summer schools and workshops (see http://www.math.cmu.edu/PIRE/activities/index.php).
PIRE-CNA 2016 Summer School
New Frontiers in Nonlinear Analysis for Materials: June 2–10, 2016, Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh, PA
PIRE NYU-Oxford Workshop
Mathematical Models of Defects and Patterns: January 5-8, 2016, Courant Institute of Mathematical Sciences, New York University
PIRE Researchers "Break the Rules"
PIRE CO-PI Richard James wrote commentary articles recently in Nature [vol. 521, 298-299 (21 May 2015)] and Science [29 May 2015 348 (6238): 968-969].