Critical Phenomena in Coherent Structure Formation

相干结构形成的关键现象

基本信息

批准号：
2205663
负责人：
Arnd Scheel
金额：
$ 28.5万
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：
2022
资助国家：
美国
起止时间：
2022-07-15 至 2025-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2205663&HistoricalAwards=false
关键词：
Critical Phenomena Coherent Structure Formation

项目摘要

Large complex dynamical systems often self-organize into simple coherent behavior. Describing, analyzing, and computing the dynamics of these self-organized structures is at the center of understanding processes ranging from crystallization, self-assembly, or material hardening, to the emergence of patterns and function in living organisms. The principal investigator (PI) studies the role of coherent structures both in organizing the dynamics of systems through the selection of patterns and shape, but also in their role for validating models through quantitative predictions. The first part of the project is concerned with invasion processes, where a new structure propagates in the system after a sudden change in parameters. This invasion process is poorly understood and computationally challenging. The PI will develop new analytical and computational tools to systematically analyze, predict, and thus validate models. The second part of the project is concerned with point defects that arise in soft matter. Point defects both organize the system dynamics, but also present challenges to macroscopic, homogenized descriptions of large systems. The proposed work further develops analytical and computational methods that aim at a fine description of the shape of the core of point defects and their effect on the medium far away from the core. Graduate and undergraduate students will be engaged in the research of the project.The PI will analyze invasion fronts and point defects. Invasion fronts describe the propagation into an unstable state across many scientific areas, from material science to ecology and epidemiology. Propagation speeds and the novel state created in the wake of the invasion process can often be well predicted from linear analysis at the unstable state, through a marginal pointwise stability analysis. The PI will first develop novel computational tools for the associated linear questions, complemented by a rigorous convergence analysis. In a second step, the PI will addresse the validity of these linear predictions in nonlinear systems, in particular questions associated with the marginal stability conjecture that postulates that critical, only marginally stable fronts are selected in the invasion process. A second part of the proposal studies dislocations in striped phases and creases in elastic media. In both situations, analysis of the existence of these point defects will yield a deeper understanding of the role of the core of the defect in the large-scale deformation of the medium. The interaction between core and farfield is analyzed using analytical, perturbative tools and computational methods that rely on rigorous approximations of unbounded by finite-size domains.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

大型复杂动力系统通常会自组织为简单的相干行为。描述，分析和计算这些自组织结构的动力学是理解从结晶，自组装或材料硬化到生物中模式和功能的出现的过程。首席研究者（PI）研究了相干结构在通过选择模式和形状的选择中组织系统动力学方面的作用，并且还可以通过定量预测来验证模型。该项目的第一部分与入侵过程有关，在参数突然变化后，新结构在系统中传播。这种入侵过程知之甚少，并且在计算上具有挑战性。 PI将开发新的分析和计算工具，以系统地分析，预测，从而验证模型。该项目的第二部分与软物质中出现的点缺陷有关。点缺陷都组织了系统动力学，但也对大型宏观，同质化的描述提出了挑战。提出的工作进一步开发了分析和计算方法，旨在对点缺陷核心的形状进行精心描述及其对远离核心的培养基的影响。研究生和本科生将从事该项目的研究。PI将分析入侵方面和点缺陷。入侵阵线描述了从材料科学到生态学和流行病学的许多科学领域中传播到不稳定状态的传播。传播速度和在入侵过程之后创建的新型状态通常可以通过边缘稳定性分析在不稳定状态的线性分析中得到很好的预测。 PI将首先为相关线性问题开发新颖的计算工具，并通过严格的合并分析进行补充。在第二步中，PI将解决这些线性预测在非线性系统中的有效性，特别是与边缘稳定性猜想相关的问题，这些问题假设在入侵过程中选择了关键的，只有略有稳定的前沿。提案的第二部分研究弹性介质中的条纹相和折痕中的位错。在这两种情况下，对这些点缺陷的存在的分析将对缺陷核心在培养基的大规模变形中的作用有更深入的了解。使用分析，扰动工具和计算方法分析了核心与Farfield之间的相互作用，这些工具和计算方法依赖于有限尺寸域无限的严格近似值。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和知识分子的优点和评估来支持的。更广泛的影响审查标准。