Center for Nonlinear Analysis: Research and Training in Applied Mathematics

非线性分析中心：应用数学研究和培训

• 批准号: 0405343
• 负责人: Irene Fonseca
• 金额: --
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-01 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0405343&HistoricalAwards=false
• 关键词: Center; Nonlinear; Analysis; Research; Training

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.

提案：DMS-0405343PI：Irene Fonseca机构：卡内基梅隆大学标题：非线性分析中心：应用数学研究与培训摘要非线性分析中心（CNA）于1991年在卡内基梅隆大学数学科学系成立，是一个中心用于应用数学的研究和高级培训。 该中心的目标领域是非线性分析、力学、科学计算和随机分析。 CNA 项目的核心问题是：通过建模、分析和计算来研究新型人造材料的行为，例如形状记忆合金、铁电、电磁和磁致伸缩（纳米）材料、异质材料中的界面（包括多晶和泡沫）、薄膜，以及最近的系统和细胞生物学建模和模拟领域。 这些领域的挑战中，多尺度问题尤为突出。 例如，当今先进材料中的许多问题都与其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的尺寸范围从散装材料到薄膜和纳米结构材料。连接如此众多的尺度需要检查相互关联的分析和计算方法，而这正是 CNA 优势得以实现的地方。 CNA 成员对理解这些问题的贡献得到了广泛认可，目前这些领域的几种方法标准都是由 CNA 研究人员发起的。 CNA 在这些领域取得的成就导致参与和创建了具有较高机构和跨机构影响力的项目，包括 CMU MRSEC（材料研究科学与工程中心）、ITR、NIH（NPEBC 之前）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，CNA 本身充分利用了这种参与。非线性分析中心 (CNA) 于 1991 年在卡内基梅隆大学数学科学系成立，是一个研究和高级研究中心应用数学培训。 中心活动关注领域：新型人造材料（通常称为“智能材料”）的行为、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重点。 该中心致力于识别和开发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，并应对科学和工程领域的数学挑战。 其特别关注材料和制造、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，以及在数学与科学与工程交叉领域培养年轻科学家方面的全球资产地位。 CNA 不仅仅是各个部分的总和。 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，特别是卡内基梅隆大学研究单位的合作，使该小组成为美国乃至全球应用数学领域最强大的小组之一。 CNA 通过博士后培训、访客计划、暑期学校和会议作为开发这些科学资源的工具。 资金专门用于促进这些培训任务。