PECASE: Self-Sustained Interfacial Motions: Dynamics, Instabilities, and Singularities

这个教师早期职业发展（CAREER）计划奖的目的是调查和理解的物理起源和量化的自我维持的运动，奇点形成的动态，和复杂的流体界面的拓扑变化的Marangoni效应的背景下驱动的表面活性物质（表面活性剂）。实现这些目标将需要开发新的理论工具，以确定发生的条件，表面驱动的不稳定性和由此产生的自诱导动力学运动，并揭示界面奇点在维持这种运动的作用。拟议中的研究将导致新的几何启发的理论方法的基础上的协同动力系统，微分几何，几何流和奇异性理论的阐述。如果成功的话，这个研究项目也将帮助人们理解奇异性和不稳定现象之间的相互作用，从而使人们在结合Cartan理论和奇异性理论的Arnold问题上取得进展。界面的自我维持运动是生物体中所有马达的基础。揭示和人工创造这些功能从基本和实际的角度来看都是重要的，例如在人工细胞的开发中。解决这些问题将推动科学和工程的新领域。特别是，拟议的研究计划将加强理论基础，以了解某些类型的生物马达在中观和宏观尺度上的机制，并人工创造生物功能。由于复杂的界面是无处不在的，这个研究计划的结果应该提供的想法，在众多的应用程序中的表面活性剂与所需的功能，从工程到生物学的最有效的设计。在传播一级，所研究的现象提供了一个很好的机会，向人们介绍不同复杂程度的科学和技术，并鼓励科学培训。研究生，本科生和地区高中学生将受益不仅通过课堂教学，但也将获得第一手的研究经验。

The objective of this Faculty Early Career Development (CAREER) Program award is to investigate and understand the physical origin and quantify the dynamics of self-sustained motions, singularity formation, and topological changes of complex fluid interfaces in the context of Marangoni effects driven by surface-active substances (surfactants). Achieving these objectives will require developing new theoretical tools in order to identify the conditions for the occurrence of surfactant-driven instabilities and resulting self-induced dynamical motions, and uncover the role of interfacial singularities in sustaining such motions. The proposed research will lead to the elaboration of new geometrically inspired theoretical methods based on the synergy of dynamical systems, differential geometry, geometric flows, and singularity theories. If successful, this research program will also help one to understand the interplay between singularity and instability phenomena and thus allow one to make progress on Arnold's problem of combining Cartan's and singularity theories.Self-sustained motions of interfaces are at the basis of all motors in living organisms. Revealing and artificially creating such functions is important both from the fundamental and practical points of view, e.g. in the development of artificial cells. Addressing these questions will advance new fields in science and engineering. In particular, the proposed research program will enhance the theoretical basis for understanding mechanisms of certain types of biological motors at meso- and macroscopic scales and for creating biological functions artificially. Since complex interfaces are ubiquitous, the outcome of this research program should provide ideas for the most efficient designs in numerous applications of surfactants with desired functions ranging from engineering to biology. At the dissemination level, the studied phenomena provide a great opportunity to introduce people to science and technology at varying degrees of complexity and to encourage scientific training. Graduate, undergraduate, and regional high-school students will benefit not only through classroom instruction, but will also receive firsthand research experience.