PIRE: Science at the Triple Point Between Mathematics, Mechanics and Materials Science

许多当代的问题在新的先进材料涉及到变化的长度，时间尺度，和变化内在的变化在他们的制造和功能。解决这些问题需要针对这些复杂系统的预测理论，而这反过来又需要数学上的进步。在这个项目中，一个由来自四个美国机构、五个欧洲机构和一个跨国工业伙伴的杰出数学家组成的国际网络，将建立在几十年来在数学和材料科学界面的合作和培训的基础上，这些合作和培训在复杂的新数学和模拟方法的前沿取得了许多成就。该项目将集中在四个主要研究领域：1。基于能量最小化的模式形成，2。3.原子到连续体建模与计算的挑战。预测迟滞（具有“记忆”的系统，使刺激的影响在时间上延迟）；材料微观结构的模式动力学与发展。美国和欧洲的学生将受益于国际化的教育和研究培训，在国际教育合作框架内，促进包括文化层面在内的研究合作和教育的新模式。高级研究生课程将在网络上开发和共享，提供真正国际化的课程，并普遍获得与数学主题相关的最佳材料。美国研究生和博士后将沉浸在密集的多顾问指导模式中，加强他们的跨学科和全球研究技能。感兴趣的研究生将能够参加国际工业研究实习。此外，年度研讨会和暑期学校将把研究扩展到项目之外的更广泛的学生和博士后社区。该奖项将通过将美国机构与一个充满活力的国际应用数学家网络联系起来，帮助他们国际化，这些数学家将材料科学相关的研究与一个连贯的计划相结合，以培养下一代在快速发展的数学领域从事全球科学领导。团队的互补优势和专业知识将推动应用分析的前沿，并为材料研究的新应用扫清道路。美国将通过设在两个欧洲研究中心的基地，获得对第一个主要研究领域至关重要的变分学领域的专业知识和实力。与欧洲伙伴合作将有助于统一和扩展美国在材料科学问题建模、计算和分析方面的专业知识。在网络的几个节点上，模式动力学研究的进展揭示了新的建模和分析机会，这些机会有可能被该奖项所利用。该项目的合作者包括四所美国机构：卡内基梅隆大学、加州理工学院、纽约大学和明尼苏达大学；5个欧洲机构：安特卫普大学（比利时）、波恩大学（德国）、马克斯·普朗克科学数学研究所（德国）、国际高等研究学院（SISSA）（意大利）和牛津大学（英国）；和一个工业合作伙伴：博世公司（德国和美国）。该项目由美国国家科学基金会国际科学与工程办公室和数学科学部支持。

Many contemporary problems in new advanced materials relate to variation in length, time scales, and variations inherent in their fabrication and function. Resolution of these problems requires predictive theories for these complex systems that in turn require advances in mathematics. In this PIRE project an international network of prominent mathematicians from four U.S. institutions, five European institutions, and a multinational industrial partner, will build on decades of collaboration and training at the interface of mathematics and materials sciences that have yielded many achievements at the forefront of sophisticated new mathematics and simulation methods. The project will focus on four principal research areas: 1. Pattern formation from energy minimization, 2. Challenges in atomistic to continuum modelling and computing, 3. Prediction of hysteresis (systems that have "memory" such that effects of stimuli are temporally delayed), and 4. Pattern dynamics and development of material microstructure. U.S. and European students will benefit from internationalized education and research training within a PIRE framework promotes new patterns in research collaboration and education that includes cultural dimensions. Advanced graduate courses will be developed and shared across the network providing a truly internationalized curriculum and universal access to the best materials-relevant mathematics topics. U.S. graduate students and postdoctoral fellows will be immersed in intensive multi-advisor mentoring models strengthening their interdisciplinary and global research skills. Interested graduate students will be able to partake in an international industrial research internship. In addition, annual workshops and summer schools will extend the research to a much wider community of students and postdoctoral fellows outside the project. This award will help to internationalize US institutions by linking them in a vibrant international network of applied mathematicians who integrate research relevant to materials science with a coherent program for training the next generation of globally-engaged scientific leaders in fast-developing areas of mathematics. The complementary strengths and expertise of the team will push the frontiers of applied analysis and clear the pathway for new applications in materials research. The U.S. will gain expertise and strength in the field of calculus of variations, essential to the first principal research area, through its base at two of the European research centers. Working with European partners will help unify and extend U.S. expertise in the modelling, computation, and analysis on problems arising in materials science. Advances in pattern dynamics research at several nodes of the network have revealed new modelling and analysis opportunities with the potential to be leveraged by this award. Collaborators on this PIRE project include four U.S. institutions: Carnegie Mellon University (PA), California Institute of Technology, New York University, and University of Minnesota; five European institutions: University of Antwerp (Belgium), University of Bonn (Germany), Max Planck Institute for Mathematics in the Sciences (Germany), International School for Advanced Studies (SISSA)(Italy), and University of Oxford (UK); and an industrial partner: Robert Bosch GmbH (Germany and USA). This project is supported by NSF's Office of International Science and Engineering and the Division of Mathematical Sciences.