Center for Nonlinear Analysis: Research and Training in Applied Mathematics

题目：Center for Nonlinear Analysis: Research and Training in Applied mathematics摘要：非线性分析中心（Center for Nonlinear Analysis，简称CNA）成立于1991年，隶属于卡耐基梅隆大学数学科学系，是一个应用数学研究和高级培训中心。本中心的研究方向为非线性分析、力学、科学计算和随机分析。CNA计划的核心问题是：建模、分析和计算以研究新型人造材料的行为，如形状记忆合金、铁电、电磁和磁致伸缩（纳米）材料、非均质材料中的界面，包括多晶和泡沫、薄膜，以及最近系统和细胞生物学的建模和模拟领域。多尺度问题是这些领域面临的突出挑战。例如，当今先进材料的许多问题都与它们的制造和功能中固有的大范围长度和时间尺度有关。多尺度方面进一步意味着应用范围从块状材料到薄膜和纳米结构材料。弥合这众多的尺度需要检查相互关联的分析和计算方法，这就是CNA的优势所在。CNA成员对理解这些问题的贡献得到了广泛认可，目前这些领域的一些方法标准是由CNA研究人员发起的。CNA在这些领域的成就导致参与和创建具有高机构和跨机构影响的项目，包括CMU MRSEC（材料研究科学与工程中心），ITR， NIH（npebc前）拨款，欧洲网络（RTN）和计算金融中心。通过加强和扩大博士后的培训机会，这种参与在中央研究中心本身得到了强有力的利用。非线性分析中心（CNA）于1991年在卡耐基梅隆大学数学科学系成立，是一个应用数学研究和高级培训中心。活动关注的中心领域：新型人造材料的行为，通常被称为“智能材料”，界面在多晶和泡沫行为中的作用，以及细胞和系统生物学的发展焦点。该中心旨在确定和发展数学科学的前沿应用，促进应用数学家和相关科学家之间的合作，并应对科学和工程中的数学挑战。它的特别重点是材料和制造，纳米技术和生物技术。还有环境问题。该中心将保持其在这些领域的科学领导地位，并保持其在培养数学、科学和工程之间的年轻科学家方面的全球资产地位。CNA不仅仅是各部分的总和。结合非线性分析和计算方面的专业知识，丰富的跨学科活动和全球合作，特别是在卡内基梅隆大学的研究单位，使这成为美国和全球应用数学领域最强大的团队之一。中央研究中心通过培养博士后、访客计划、暑期学校和会议，发挥了开发这些科学资源的作用。资金专门用于促进这些训练任务。

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.