CAREER: Transition Pathways in Complex Systems. Theory and Numerical Methods.

职业：复杂系统中的过渡途径。

• 批准号: 0239625
• 负责人: Eric Vanden-Eijnden
• 金额: $ 54万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-04-15 至 2009-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0239625&HistoricalAwards=false
• 关键词: CAREER; Transition; Pathways; Complex; Systems.

Abstract of NSF Proposal 0239625PI: Eric Vanden-Eijnden, Courant Institute of Mathematical SciencesTitle: Transition pathways in complex systemsThe description of complex system driven by rare events, orconformations, is a major challenge in applied mathematics andcomputational sciences. Well-known examples of conformations includenucleation events during phase transition, conformational changes inmolecules, thermal activated switching of magnetic materials, andchemical reactions. The disparity between the execution time of theconformation event and the waiting time between these events istypically so large that it impossible to simulate the dynamics ofthese processes by solving directly the underlying dynamic equations.This project is a combined theorical and numerical effort to describeand simulate these rare conformation changes. The theoreticaldescription of transition pathways in complex systems leads tochallenging problem in probability and stochastic processes theorywhich require to go beyond the standard tools of large deviationtheory and extensions thereof. These new theoretical tools will bedeveloped so as to naturally lead to efficient algorithms, well-suitedfor the numerical investigation of the transition pathways required inrealistic complex systems.Applied mathematics has much to contribute, and much to gain inunderstanding via a coordinate program of analysis, simulation, andeducation the mechanisms by which rare conformation changes arise incomplex systems. Topics to be addressed include: (a) the developmentof appropriate theoretical tools for the description of the transitionpathways in complex systems; (b) the development of efficientnumerical algorithms for the identification of these pathways; and,(c) the development of courses at undergraduate and graduate levels inapplied stochastic methods which will provide the students with thenecessary background to do research on these topics at the interfacebetween mathematics, computer science, and the natural sciences.Successful pursuit of these issues requires a multidisciplinaryeffort, drawing expertise from computational sciences, appliedmathematics, in the multiple fields in the natural sciences whichinvolve complex dynamical systems. The students and postdoctoralscientists participating this effort will gain flexibility andperspective through exposure to these many disciplines.

美国国家科学基金会提案0239625摘要：Eric Vanden-Eijnden，Courant数学科学研究所题目：复杂系统中的跃迁路径描述由稀有事件或构象驱动的复杂系统是应用数学和计算科学中的一个主要挑战。 众所周知的构象例子包括相变过程中的无核化事件、分子中的构象变化、磁性材料的热激活转换和化学反应。 构象事件的执行时间和等待时间之间的差距通常是如此之大，以至于不可能通过直接求解基本的动力学方程来模拟这些过程的动力学，本项目是理论和数值相结合的努力来描述和模拟这些罕见的构象变化。复杂系统中跃迁路径的理论描述导致了概率和随机过程理论中的挑战性问题，这需要超越大偏差理论及其扩展的标准工具.这些新的理论工具将得到发展，从而自然地导致有效的算法，以及suitedfor所需的过渡pathways在现实的复杂系统的数值研究。应用数学有很大的贡献，并获得通过分析，模拟和推理的协调程序在复杂系统中出现罕见的构象变化的机制的理解。研究的主题包括：（a）发展适当的理论工具来描述复杂系统中的过渡路径;（B）发展有效的数值算法来识别这些路径;并且，在本发明中，（c）第（1）款在本科和研究生水平的课程的发展应用随机方法，这将为学生提供必要的背景做研究，在这些问题的接口之间数学、计算机科学和自然科学。成功解决这些问题需要多学科的努力，从涉及复杂动力系统的自然科学多个领域的计算科学、应用数学中汲取专业知识。 参与这项工作的学生和博士后科学家将通过接触这些学科获得灵活性和视角。