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

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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.