Collaborative Research: Engineering Dynamical Symmetries for Extreme Wave-Matter Interactions in Elastodynamics

这个跨学科的项目汇集了一名机械工程师、一名实验物理学家和一名理论物理学家，以创造一类新的工程材料和结构，它们的性质来自几何排列--在这种情况下，对称排列--而不仅仅是材料组成。这些新材料将能够以比块状材料更快的响应时间来响应传播的机械波或振动。新的材料系统将催生满足迫在眉睫的国家民用和国防需求的新兴技术。例子包括结构完整性的极其敏感的传感器，或者相反，通过使用这些新的材料系统，使结构对制造缺陷或不利的环境变化基本上不敏感。这些工程材料和结构将实现对传播的声波或弹性波的极端控制，应用于单向机械波传播和振动，或可动态重新配置的声音和开关。除了这项工作与各种物理和工程框架(从机械和电磁到物质和量子波)的相关性外，来自著名工程和文科环境的学生之间的协作互动将向他们灌输设计结构、数学建模、制造和实验表征方面的跨学科技能。该团队将提供一门名为“工程机械波浪”的视频课程，邀请当地社区大学生参与。演示本课程基本概念的互动动画将在网上发布，并向当地高中生做广告，以吸引潜在的暑期实习生。拟议设计的中心对称性违反与动力学对称性(例如，时间反转、宇称、手性或任何组合)有关，通常与非厄米光谱奇点有关。当本征频率和相应的本征模合在一起时，这些奇点称为异常点。将利用三种不同的方法来实现这些对称性：(A)空间安排，(B)相位安排，和(C)时间周期调制安排。采用以实验现实为导向的自下而上策略，团队首先应专注于开发在基本机械结构中实现这些极端响应点的策略。下一步，应设计将这些单元组合成大型系统，以实现额外形式的特殊点数控制。这导致了不同的功能，如通过拓扑保护配置对制造缺陷的稳健性，高度非互易传输，或对微小扰动的超级敏感。设想的应用包括监测结构完整性、可重新配置的波传输、自感应振动过滤器和有源表面声波设备。S强调弹性动力学的项目旨在利用连续介质力学中可用的模式相互作用的微妙以及S团队的不同经验。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This interdisciplinary project brings together a mechanical engineer, an experimental physicist, and a theoretical physicist to create a new class of engineered materials and structures, which derive their properties from geometric arrangements - in this case, symmetry arrangements - rather than the material composition alone. These novel materials will be capable of responding to propagating mechanical waves or vibrations with response times faster than possible with bulk materials. The new material systems will spawn emerging technologies addressing imminent national civil and defense needs. Examples include extremely sensitive sensors of structural integrity, or conversely, structures that are made essentially insensitive to fabrication defects or adverse environmental variations through the use of these novel material systems. These engineered materials and structures will enable extreme control of propagating sound or elastic waves, with applications to one-way mechanical wave propagation and vibration or sound and switches, which can be reconfigured on-the-fly. In addition to the work's relevance for a variety of physics and engineering frameworks, ranging from mechanical and electromagnetic to matter and quantum waves, the collaborative interaction among student peers from prominent engineering and liberal arts environments will instill them with interdisciplinary skill-sets in designing structures, mathematical modeling, fabrication, and experimental characterization. The team will offer a video-course on "Engineering Mechanical Waves", inviting participation from local community college students as well. Interactive animations demonstrating basic concepts of this course will be posted online and advertised to local high-school students to attract potential summer interns.The symmetry violations central to the proposed designs are associated with dynamical symmetries (e.g. time-reversal, parity, chiral, or any combination) and are typically connected with non-Hermitian spectral singularities. These singularities, where both eigenfrequencies and the corresponding eigenmodes coalesce, are known as exceptional points. Three distinct approaches for implementing these symmetries will be exploited: (a) spatial arrangements, (b) phase arrangements, and (c) time-periodic modulation arrangements. Adopting a bottom-up strategy guided by experimental realities, the team shall first focus on developing strategies that implement these extreme response points in basic mechanical structures. Next, combinations of these units into large-scale systems shall be designed to enable additional forms of exceptional point control. This leads to disparate functionalities such as robustness to fabrication imperfections via topologically protected configurations, highly non-reciprocal transport, or super-sensitivity to small perturbations. Applications envisioned include monitoring structural integrity, reconfigurable wave transport, self-induced vibration filters, and active surface acoustic wave devices. The project?s emphasis in elastodynamics aims to capitalize on the subtleties of mode interaction available in continuum mechanics as well as the team?s diverse experiences.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.