Scientific Activities
Graduate Courses
21-820 Perspectives on Microstructure - Spring 2012
David Kinderlehrer: (PIRE senior personnel, CMU). Videotaped , T Th 11:30am - 12:45pm
Instructions for accessing the live stream and course materials will be posted on http://mm.math.cmu.edu/
Abstract: Cellular networks are ubiquitous in nature. They exhibit behavior on many di®erent length and time scales and are generally metastable. Most technologically useful materials are polycrystalline microstructures composed of a myriad of small monocrystalline grains separated by grain boundaries, and thus comprise cellular networks. The energetics and connectivity of the grain boundary network plays a crucial role in determining the properties of a material across a wide range of scales.
A central problem in materials is to develop technologies capable of producing an arrangement of grains that provides for a desired set of material properties. In this course we will investigate properties of these microstructures and the theories that are employed to characterize them. There will be opportunities for student participation and further research. We anticipate a number of guest lectures.
MATH 8450 Topics in Numerical Analysis: Multiscale Numerical Analysis for Materials - Spring 2012
Mitchell Luskin: (PI, Minnesota). MWF 02:30 P.M. - 03:20 P.M., Vincent Hall 20
Abstract: Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long-range elastic fields with a much larger region that cannot be computed atomistically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform on the atomistic scale.
During the past several years, a mathematical structure has been given to the description and formulation of atomistic-to-continuum coupling methods, and corresponding numerical analysis has clarified the relation between the various methods and their sources of error. This course will begin by introducing the physical and mathematical background and then presenting the current state of numerical analysis for atomistic-to-continuum coupling methods. More information: 8450_AtC.pdf
Minicourse on "A mathematical perspective on the structure of matter"
Date: May 14 - 18, 2012, 10:00 a.m. - 12:00 noon There will be no talk on Thursday, May 17, because of holiday.
Venue: HIM lecture hall, Poppelsdorfer Allee 45
Speaker: Richard D. James (Co-PI, University of Minnesota)
Abstract: Beginning with some observations about the periodic and nonperiodic structures commonly adopted by elements in the periodic table, I will introduce a definition ("objective structures") of a mathematically small but physically well represented class of molecular structures. This definition will be seen to have an intimate relation to the invariance of the equations of quantum mechanics, statistical mechanics and continuum mechanics. The resulting framework can be used to design various multiscale methods, and offers an unusual perspective on experimental science. Open mathematical problems will be highlighted. More information.
