Collaborative Research: Topological Dynamics of Hyperbolic and Fractal Lattices

合作研究：双曲和分形格子的拓扑动力学

• 批准号: 2131759
• 负责人: Camelia Prodan
• 金额: $ 32.72万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-11-01 至 2024-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2131759&HistoricalAwards=false
• 关键词: Collaborative; Research; Topological; Dynamics; Hyperbolic

This grant will fund research that dramatically enlarges the design space for future vibration absorbing materials and structural designs, with applications to energy harvesting and acoustic panel technologies, thereby promoting the progress of science and advancing the national prosperity. The wave guiding properties of such materials depend on an underlying spatial pattern of individual oscillator elements. While the behavior associated with simple patterns that tessellate the plane using regular polygons is well understood, there is a gap in our knowledge of the ability of other classes of patterns to steer, guide, and localize waves. This project will fill this gap by discovering radically new wave-guiding physics associated with such new classes of patterns, including fractals with self-similar features at multiple scales. The experimental part of this work will uncover solutions to the problems of fabricating acoustic crystals with a desired pattern, as well as characterizing the pattern of a given crystal, opening up new research directions in materials science, acoustics, and mechanics. The project’s collaborative research ecosystem, where pure mathematics meets computational modeling and physical validation, will provide unique training opportunities for both undergraduate and graduate students, as well as for postdoctoral researchers. Outreach programs will expose middle- and high-school students and teachers to advanced topics in geometry, topology, and dynamics through dedicated and hands-on activities.This research aims to make fundamental contributions to the mathematical theory of wave-guiding metamaterials that can be characterized as hyperbolic or fractal lattices, as well as to the ability to physically realize such structures for experimental validation or design. It will achieve this outcome by formulating a theoretical framework for the classification of topological dynamics and of the possible manifestations of the bulk-boundary principle in hyperbolic and fractal lattices. The research will further demonstrate how intrinsic degrees of freedom of such lattices may be controlled to achieve new forms of wave steering, phase control, edge and bulk mode localization, and topological pumping. The experimental effort will demonstrate bioinspired packing and design solutions for large-scale fabrication of aperiodic lattices. The project will expand our knowledge about the collective dynamics of lattices, and will deliver analysis tools, mathematical models, and experimental platforms that will help chart the complex landscape of novel lattice geometries and their possible application for future material and structural designs.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.

这项赠款将资助研究，从而大幅度地增加了未来振动材料和结构设计的设计空间，并应用于能源收集和声学面板技术，从而促进了科学的进步并促进了国家繁荣。此类材料的波浪引导特性取决于单个振荡器元件的潜在空间模式。虽然对使用常规多边形对平面进行镶嵌的简单模式相关的行为有充分的理解，但我们了解其他类别模式的茎，引导和定位波的能力存在差距。该项目将通过发现与此类新模式相关的根本新的Wave引导物理（包括具有多个尺度上具有自相似特征的分形）来填补这一空白。这项工作的实验部分将发现解决具有所需模式的声学晶体问题的解决方案，以及表征模式外展计划的表征将使中等和高中生的学生和老师在几何学，拓扑，拓扑和动态方面通过几何学，拓扑，拓扑，拓扑，拓扑，拓扑，以及通过专门和动态活动进行狂潮，以促进基本的狂潮，以实现基础，以实现基础，以实现基本的贡献，以实现精通的狂潮，以实现狂潮，从而实现基本的贡献，以实现狂潮。可以将其特征在于双曲线或分形晶格，以及实现实验验证或设计结构的能力。它将通过制定一个理论框架来实现这一结果，以分类拓扑动力学以及双曲线和分形晶格中构成原理的可能表现。该研究将进一步证明如何控制这种晶格的内在自由度，以实现新形式的波动转向，相控制，边缘和散装模式定位以及拓扑泵送。实验性的工作将展示生物启发的填料和设计解决方案，用于大规模制造上的植物。该项目将扩大我们对晶格集体动态的知识，并将提供分析工具，数学模型和实验平台，以帮助绘制新型晶格几何形状的复杂格局及其在未来的材料和结构设计中的应用。这奖反映了NSF的法定任务，并通过使用基础的知识来评估来评估NSF的法定任务，并以基础的智力效果和广泛的评估来进行评估。

项目成果

Observation of Majorana-like bound states in metamaterial-based Kitaev chain analogs

基于超材料的基塔耶夫链类似物中类马约拉纳束缚态的观察

• DOI: 10.1103/physrevresearch.5.l012012
• 发表时间: 2023
• 期刊: Physical Review Research
• 影响因子: 4.2
• 作者: Qian, Kai;Apigo, David J.;Padavić, Karmela;Ahn, Keun Hyuk;Vishveshwara, Smitha;Prodan, Camelia
• 通讯作者: Prodan, Camelia