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

这个跨学科的项目汇集了一位机械工程师，一位实验物理学家和一位理论物理学家，创造了一类新的工程材料和结构，这些材料和结构的特性来自几何排列-在这种情况下，对称排列-而不仅仅是材料组成。这些新型材料将能够响应传播的机械波或振动，其响应时间比散装材料更快。新材料系统将催生新兴技术，满足迫在眉睫的国家民用和国防需求。例子包括结构完整性的极其敏感的传感器，或者相反地，通过使用这些新型材料系统，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声音和开关，可以在运行中重新配置。除了工作的各种物理和工程框架的相关性，从机械和电磁物质和量子波，学生之间的协作互动从突出的工程和文科环境将灌输他们与跨学科的技能，在设计结构，数学建模，制造和实验表征。该团队将提供一个关于“工程机械波”的视频课程，并邀请当地社区学院的学生参加。演示本课程基本概念的互动动画将在网上发布，并向当地高中学生做广告，以吸引潜在的暑期实习生。对称性破坏是拟议设计的核心，与动力学对称性有关（例如时间反演，宇称，手征或任何组合），通常与非厄米特谱奇点有关。这些奇异点，即本征频率和相应的本征模合并的地方，被称为例外点。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。采用由实验现实指导的自下而上的策略，团队应首先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。其次，将这些单元组合成大型系统的设计应能实现额外形式的特殊点控制。这导致了不同的功能，例如通过拓扑保护配置对制造缺陷的鲁棒性，高度非互易传输或对小扰动的超敏感性。设想的应用包括监测结构完整性，可重构波传输，自激振动滤波器，和主动表面声波器件。项目？的重点在弹性动力学的目的是利用微妙的模式相互作用，以及在连续介质力学的团队？该奖项反映了NSF的法定使命，并通过使用基金会的知识价值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.