Workshop: Coherent Structures in Dynamical Systems; Lorentz Center, Leiden, The Netherlands; 16-20 May 2011

研讨会：动力系统中的相干结构；

• 批准号: 1057412
• 负责人: Francisco Beron-Vera
• 金额: $ 3.65万
• 依托单位: University of Miami
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1057412&HistoricalAwards=false
• 关键词: Workshop; Coherent; Structures; Dynamical; Systems

A proposal has been approved by the Lorentz Center, Leiden, The Netherlands, to carry out a workshop entitled ?Coherent structures in dynamical systems? on 16 May 2011 - 20 May 2011. This NSF support will partially cover the travel cost of US participants in this workshop. The organization of the workshop and substantial part of the cost are provided by the Lorentz Center (http://www.lorentzcenter.nl) .The workshop focus on new collaborations between scientists from different countries and fields, bringing together groups of 30 to 40 junior and senior researchers in a stimulating environment with working space for all participants. Through a combination of informal talks, working sessions, and discussions, participants are able to assess the status of a field and its future, and to collaborate, establish new international contacts, and spot upcoming talent. Central in the study of dynamical systems is the search for invariant sets or coherent structures that organize long-term behavior. Examples of coherent structures include periodic orbits, invariant manifolds, homoclinic orbits, and invariant tori. By performing appropriate local analyses around these coherent structures and studying how they fit together, a "skeleton" of the dynamics may be sketched. In recent years, new techniques have been devised to help unveil dynamical skeletons from limited data sets. These techniques have been mainly applied to unsteady flows in two-space dimensions, leading to a major breakthrough in the physics of mixing; their application to unsteady three-dimensional flows remains largely unexplored. For instance, it remains to be determined if there exists a rigorous theory that can be used as a foundation for coherent structures underlying such flows. An accompanying challenge is the appropriate visualization of coherent structures evolving in three-space dimensions and time. The aim of the workshop, therefore, is to bring together theoretical experts and researchers with interests in the application of dynamical systems methods. Such a gathering is expected to inspire new theoretical research and new areas of application. The workshop will build on the success of the recent Focus Issue on "Lagrangian Coherent Structures in Fluid Flows" in the journal Chaos, which was featured in The New York Times and The Economist. Developing robust methods for uncovering coherent structures in fluid systems will directly influence our ability to make reliable predictions for such high-profile scenarios as the Deepwater Horizon oil spill and the Icelandic volcanic ash cloud, both of which have had tremendous societal impact.

荷兰莱顿的洛伦兹中心已批准一项建议，举办一个题为？动力系统中的相干结构2011年5月16日至2011年5月20日。国家科学基金会的支持将部分支付美国与会者参加研讨会的旅费。 讲习班的组织和大部分费用由洛伦兹中心（http：//www.example.com）提供。讲习班的重点是来自不同国家和领域的科学家之间的新合作，使30至40名初级和高级研究人员聚集在一个激励人心的环境中，为所有与会者提供工作空间。www.lorentzcenter.nl通过非正式会谈，工作会议和讨论的结合，参与者能够评估一个领域的地位及其未来，并进行合作，建立新的国际联系，并发现即将到来的人才。 动力系统研究的核心是寻找组织长期行为的不变集或相干结构。相干结构的例子包括周期轨道、不变流形、同宿轨道和不变环面。通过对这些相干结构进行适当的局部分析，并研究它们如何结合在一起，可以勾勒出动态的“骨架”。 近年来，新的技术已经被设计出来，以帮助从有限的数据集揭示动态骨架。这些技术主要应用于二维空间的非定常流动，导致混合物理学的重大突破;它们在非定常三维流动中的应用在很大程度上尚未探索。例如，还有待确定的是，是否存在一个严格的理论，可以作为基础的连贯结构的这种流动。一个随之而来的挑战是在三维空间和时间的相干结构演变的适当的可视化。因此，讲习班的目的是汇集对动力系统方法应用感兴趣的理论专家和研究人员。这样的聚会有望激发新的理论研究和新的应用领域。 讲习班将借鉴《混沌》杂志最近成功发表的焦点问题“流体流动中的拉格朗日相干结构”，《纽约时报》和《经济学家》对该问题作了专题报道。开发用于揭示流体系统中相干结构的强大方法将直接影响我们对深水地平线石油泄漏和冰岛火山灰云等高调场景进行可靠预测的能力，这两种情况都产生了巨大的社会影响。