Topics in Applied Nonlinear Analysis: Recent Advances and New Trends

应用非线性分析主题：最新进展和新趋势

• 批准号: 1601475
• 负责人: Irene Fonseca
• 金额: $ 3.16万
• 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: 2016
• 资助国家: 美国
• 起止时间: 2016-04-01 至 2017-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1601475&HistoricalAwards=false
• 关键词: Topics; Applied; Nonlinear; Analysis; Recent

This award will provide support for participants of the conference on "Topics in Applied Nonlinear Analysis: Recent Advances and New Trends," to be held at the Center for Nonlinear Analysis (CNA) at Carnegie Mellon University, Pittsburgh, in July 18-20, 2016. The conference will be devoted to the topics of applied analysis that in many ways revolutionized the field, especially for our understanding of behavior of materials and design of materials with desired properties. These areas are of critical importance to maintaining US leadership in science and technology as evidenced, for instance, by the recently launched, multi-agency Materials Genome Initiative. The conference will continue the CNA tradition of offering extraordinary networking and training opportunities for students and junior researchers to interact with a remarkable group of leading national and international researchers in applied analysis. This conference will provide an exceptional venue for top researchers in applied mathematics and in materials science to interact and share recent advances with a diverse audience. The impact of the conference is expected in both the mathematical and engineering communities. Detailed plans have been made to help recruit a diverse group of participants from the scientific community, including women and minorities. Scientific and social activities will be organized to give young trainees exposure and promote their excellence. These include a poster session with awards for four best posters, identified by a group of judges selected from top experts in both fields. The results of the conference will be disseminated by means of a dedicated website featuring video recordings of all invited presentations: https://www.math.cmu.edu/CNA/kinderlehrer75/index.html This conference will bring under one umbrella contemporary trends in nonlinear analysis, emphasizing two scientific areas where the interplay between the classical and the modern, the theoretical and the applied in analysis has been especially prominent: (1) Optimal Transport and (2) Mathematics of Materials. Among others, the topics will include: - Recent advances in variational inequalities, non-convex variational problems, Gamma-convergence and optimal transport;- Applications to PDE;- Modeling and Analysis of Problems in Materials Science: materials microstructure and design of smart materials;- Computational Methods with Application to Problems in Materials Science and Mathematical Biology: recent developments in Finite Element Methods, Virtual Element Methods and Quasi-Continuum Methods.New collaborations that are likely to emerge from this activity will have a potential to catalyze research at the interface between theoretical/applied partial differential equations and various engineering disciplines, and will result in cross-pollination of ideas.

该奖项将为“应用非线性分析主题：最新进展和新趋势”会议的参与者提供支持，该会议将于 7 月 18 日至 20 日在匹兹堡卡内基梅隆大学非线性分析中心 (CNA) 举行， 2016 年。会议将专门讨论应用分析的主题，这些主题在许多方面彻底改变了该领域，特别是对于我们对材料行为的理解以及具有所需性能的材料的设计。这些领域对于维持美国在科学技术领域的领先地位至关重要，最近启动的多机构材料基因组计划就证明了这一点。此次会议将延续 CNA 的传统，为学生和初级研究人员提供非凡的交流和培训机会，让他们与应用分析领域的国内外领先研究人员进行互动。此次会议将为应用数学和材料科学领域的顶尖研究人员提供一个绝佳的场所，与不同的观众互动并分享最新进展。预计这次会议将在数学界和工程界产生影响。已经制定了详细的计划，以帮助招募来自科学界的多元化参与者，包括女性和少数族裔。将组织科学和社会活动，让年轻学员接触并促进他们的卓越表现。其中包括海报会议，由从两个领域的顶级专家中选出的一组评委评选出四张最佳海报。会议结果将通过一个专门网站传播，该网站包含所有受邀演讲的视频录制：https://www.math.cmu.edu/CNA/kinderlehrer75/index.html 本次会议将汇集当代趋势在非线性分析中，强调古典与现代、理论与应用分析之间相互作用尤为突出的两个科学领域：（1）最优传输和（2）材料数学。 其中，主题将包括： - 变分不等式、非凸变分问题、伽马收敛和最优输运方面的最新进展； - 偏微分方程的应用； - 材料科学问题的建模和分析：材料微观结构和智能材料设计;- 应用于材料科学和数学生物学问题的计算方法：有限元方法、虚拟元素方法和准连续方法的最新发展。可能出现的新合作这项活动将有可能促进理论/应用偏微分方程与各种工程学科之间的交叉研究，并将导致思想的交叉授粉。