Center for Nonlinear Analysis: Research and Training in Applied Mathematics

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Proposal: DMS-0405343PI: Irene FonsecaInstitution: Carnegie-Mellon UniversityTitle: Center for Nonlinear Analysis: Research and Training in Applied MathematicsABSTRACTThe Center for Nonlinear Analysis (CNA), founded in 1991 in the Department of Mathematical Sciences at Carnegie Mellon University, is a center for research and advanced training in applied mathematics. The Center target areas are nonlinear analysis, mechanics, scientific computation, and stochastic analysis. Central issues in the CNA program are: modeling, analysis and computation to study the behavior of novel man-made materials, such as shape memory alloys, ferroelectric, electromagnetic and magnetostrictive (nano)materials, interfaces in heterogeneous materials, including polycrystals and foams, thin films, and more recently modeling and simulation areas of systemic and cellular biology. Multiscale issues are prominent in the challenges of these areas. Many of today's problems in advanced materials, for example, are related to the large range of length and time scales inherent in their fabrication and function. The multiscale aspect further implies that the applications range in dimension from bulk material through thin films and nanostructured materials. Bridging this multitude of scales requires examination of interconnected analytical and computational approaches, and this is where the CNA strength is realized. Contributions of CNA members to the understanding of these issues are broadly recognized, and several methods standard in these fields nowadays were initiated by CNA researchers. CNA accomplishments in these arenas have led to participation in and the creation of projects with high institutional and cross-institutional impact, and including the CMU MRSEC (Materials Research Science and Engineering Center), an ITR, an NIH(pre-NPEBC) grant, a European network (RTN), and the Center for Computational Finance. This involvement is strongly exploited in the CNA itself by enhancing and broadening training opportunities for post-docs.The Center for Nonlinear Analysis (CNA), founded in 1991 in the Department of Mathematical Sciences at Carnegie Mellon University, is a center for research and advanced training in applied mathematics. Central areas of activity concern: the behavior of novel man-made materials, often referred to as 'smart materials,' the role of interfaces in the behavior of polycrystals and in foams, and a developing focus in cellular and systemic biology. The Center seeks to identify and develop cutting-edge applications of mathematical sciences, to promote collaborations between applied mathematicians and allied scientists, and to respond to mathematical challenges in science and engineering. Its special focus is materials and manufacturing, nanotechnology, and biotechnology. There are also environmental concerns. The Center will maintain its scientific leadership in these areas and its position as a worldwide asset in the training of young scientists at the interface between mathematics and science and engineering. The CNA is more than the sum of its parts. Combined expertise in nonlinear analysis and computation, the wealth of interdisciplinary activity and collaboration worldwide, and especially across Carnegie Mellon research units, renders this one of the strongest groups in applied mathematics in the US and on the globe. The CNA serves as a vehicle to exploit these scientific resources with its training of postdoctoral fellows, its visitors program, summer schools and conferences. Funding is dedicated exclusively to the promotion of these training missions.