Coherent Structures: Interaction and Propagation of Defects

相干结构：缺陷的相互作用和传播

• 批准号: 0504271
• 负责人: Arnd Scheel
• 金额: $ 9.4万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-15 至 2009-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0504271&HistoricalAwards=false
• 关键词: Coherent; Structures; Interaction; Propagation; Defects

We will investigate coherent structures in complex systems using a model-independent, dynamical systems approach. Among the phenomena that we will study are the spread of instabilities, the dynamics of wave trains in excitable and oscillatory media, line and corner defects in two-dimensional media, and the interaction of coherent structures. We exploit a detailed description of spectra to separate properties of defects from the background field. We isolate organizing centers where properties of the medium change and bifurcations occur.Important applications range from biology through material science to fluid dynamics and turbulence modeling. Prominent examples are spiral waves in cardiac tissue, spiking and bursting in nerve axons, giant vortices in superconductors, interface propagation in crystallization processes, or crack tip motion. In many of these examples, little is known about the exact microscopic mechanisms, or the mere size of the system does not allow for an accurate prediction of macroscopic behavior from microscopic laws. Coherent structures are the major obstruction to crude statistical approaches in complex systems. We intend to explore the properties of coherent structures using analytical methods and we project to develop reliable numerical tools. The results will further our ability to predict the behavior of complex systems in parameter ranges far from equilibrium by joining large-scale computations, based on a mean field theory, with small-scale information, based on a combined analytical and numerical description of coherent structures.

我们将使用模型独立的动力系统方法研究复杂系统中的相干结构。 在这些现象中，我们将研究的是不稳定性的传播，可激发和振荡介质中的波列动力学，二维介质中的线和角缺陷，以及相干结构的相互作用。 我们利用光谱的详细描述，从背景场中分离出缺陷的性质。 我们分离出了组织中心，在那里介质的性质发生变化和分叉。重要的应用范围从生物学到材料科学，再到流体动力学和湍流建模。 突出的例子是心脏组织中的螺旋波，神经轴突中的尖峰和爆裂，超导体中的巨大漩涡，结晶过程中的界面传播或裂纹尖端运动。 在许多这样的例子中，人们对精确的微观机制知之甚少，或者仅仅是系统的大小不允许从微观规律准确预测宏观行为。 相干结构是复杂系统中粗糙统计方法的主要障碍。 我们打算利用分析方法探索相干结构的性质，并计划开发可靠的数值工具。 这些结果将进一步提高我们的能力，预测复杂系统的行为参数范围内远离平衡加入大规模的计算，基于平均场理论，与小规模的信息，基于一个组合的分析和数值描述的相干结构。