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

荷兰莱顿的洛伦兹中心（Lorentz Center）批准了一项提案，举办一个名为？动力系统中的相干结构？2011年5月16日至5月20日。美国国家科学基金会的资助将部分支付本次研讨会美国参与者的旅费。研讨会的组织和大部分费用由洛伦兹中心（http://www.lorentzcenter.nl）提供。研讨会的重点是来自不同国家和领域的科学家之间的新合作，将30至40名初级和高级研究人员聚集在一个为所有参与者提供工作空间的激励环境中。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现状及其未来，并进行合作，建立新的国际联系，并发现未来的人才。动力系统研究的核心是寻找组织长期行为的不变量集或连贯结构。相干结构的例子包括周期轨道、不变流形、同斜轨道和不变环面。通过对这些连贯结构进行适当的局部分析，并研究它们是如何结合在一起的，就可以勾勒出动力学的“骨架”。近年来，新技术已经被设计出来，以帮助从有限的数据集中揭示动态骨架。这些技术主要应用于二维非定常流动，导致混合物理的重大突破；它们在非定常三维流动中的应用在很大程度上仍未被探索。例如，是否存在一种严谨的理论，可以作为这种流动背后的连贯结构的基础，还有待确定。随之而来的挑战是在三维空间和时间上对连贯结构进行适当的可视化。因此，研讨会的目的是将对动力系统方法的应用感兴趣的理论专家和研究人员聚集在一起。这样的聚会有望激发新的理论研究和新的应用领域。该研讨会将以《混沌》杂志最近一期关于“流体流动中的拉格朗日相干结构”的专题报道的成功为基础，该专题报道曾在《纽约时报》和《经济学人》上刊登。开发强大的方法来揭示流体系统中的相干结构，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引人注目的情景做出可靠预测的能力，这两种情况都具有巨大的社会影响。

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.