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.

该奖项将在2016年7月18日至20日在匹兹堡卡内基·梅隆大学（Carnegie Mellon University）的非线性分析中心（CNA）举行的关于“应用非线性分析主题：最新进步和新趋势”会议的参与者，2016年7月18日至20日。会议将在许多方面进行了构图和材料的构图，这些材料将在许多方面进行了革新的构图，以革新材料的构图和行为，并将其革命性地进行了革新。这些领域对于维持美国在科学和技术领域的领导至关重要，例如，通过最近发起的多机构材料基因组计划所证明的。该会议将继续为学生和初级研究人员提供非凡的网络和培训机会的CNA传统，以与一群非凡的国家和国际研究人员进行应用分析。这次会议将为应用数学和材料科学领域的顶级研究人员提供一个杰出的场所，以与多​​样化的受众互动并分享最新进展。会议的影响是在数学和工程社区中的影响。已经制定了详细的计划，以帮助招募包括妇女和少数民族在内的科学界的一群参与者。科学和社会活动将组织起来，以使年轻的学员接触并促进他们的卓越表现。其中包括一个海报会议，并获得了四个最佳海报的奖项，该海报由一组从两个领域的高级专家选出的法官确定。会议的结果将通过一个专门的网站进行分解，其中包含所有受邀演示文稿的视频录制：https：//wwwww.math.cmu.edu/cna/cna/kinderlehrer75/index.html本次会议将在非线性分析中的一个班级和班级之间的班级和班级之间的班级，并强调两者相互分析，并强调两者的班级。在分析中特别突出：（1）最佳运输和（2）材料的数学。 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方法。可能会从这项活动中出现的新协作将有可能在理论/应用偏微分方程和各种工程学科之间催化研究，并导致思想交叉授粉。