CAREER: Non-Hermitian physics of spacetime-periodic soft matter

非技术性总结这个职业奖支持理论和计算研究，以及促进设计材料的教育活动，这些材料模仿生命系统的适应性及其操纵能量流的能力。材料的性质来自于其构建块的集体相互作用。在传统材料中，构建块是原子或分子，其相互作用由它们之间的化学键的性质决定。制造复杂组件的现代技术进步，如3D打印和生物启发自组装，已经使人工材料能够由主动构建模块组成，如驱动微机械谐振器，微型机器人，甚至细菌，其相互作用可以通过外部手段或内部电源动态调制。通过引入动态元素，这些新材料可以操纵机械能，并以惰性材料无法实现的方式改变其结构特性。该项目将开发定量模型，预测动态构建块的大规模组件的集体行为，PI及其研究团队将开发新的理论和计算模型，以预测积木组件的机械和结构响应，这些积木组件的相互作用被调制以形成周期性模式，空间和时间。这些模型将扩展物理理论，该理论将惰性材料建模为由弹簧连接的质量网络，具有弹簧刚度将通过外部驱动剂正弦变化的新进展。新模型将用于提出动态材料的设计，这些材料具有针对振动控制、减震和声信号处理等技术应用的理想材料特性。例如，随时间变化的弹簧刚度可以使结构能够放大在特定方向上穿过材料的声波，或者当施加规定的压力时将静态固体转化为自发流动的液体。此外，该研究活动还将促进对电子学、光子学和量子信息等领域中操纵能量流的系统的基本理解。该项目的教育部分将开发新的教学工具、活动和计划，以提高非传统学术途径的学生、K-12学生、开始研究生和公众的材料科学知识。PI和他的研究团队将开发新的实践活动，向尤金青年数学节、俄勒冈州乡村集市和俄勒冈州大学主办的高中生暑期课程的参与者传达项目背后的物理原理。该奖项将支持社区大学学生的研究实习，他们正在考虑转入四年制学位课程，并开发新的学习模块，使用科学的教学实践来提高研究生物理课程的公平性和包容性。该教育活动旨在提高学生的参与度，成就和坚持性，同时提高来自不同背景的学生的成果。技术总结该职业奖将支持研究和教育活动，以促进对动态材料的基本理解和公众意识，这些动态材料旨在以惰性结构无法实现的方式引导机械能。技术突破使得能够制造相互作用的构建块的集合，其局部性质可以根据需要通过外部场或内部动力机制进行调节。这为机械能的非平衡操纵开辟了新的可能性。然而，这些动态材料的正常模式通常使用近似的方法，如平面波和马格努斯展开，无法正确地捕捉对称性约束和拓扑特征的激发光谱的调查。本计画将发展一个精确的理论架构来计算具有广义耦合的时空调制力学系统的能带结构。该框架将用于严格的评估和新的探索非平衡力学和相行为，包括激发光谱的拓扑性质和活性物质中晶体有序状态之间的相变。除此之外，该框架将广泛适用于二阶时间动力学动力系统的谐波振荡。通过揭示控制经典系统中机械能流动的新方法，这项研究将推进对非厄米物理学的基本理解，这些物理学与操纵量子凝聚态、冷原子、基本的概念和研究问题将被整合到教育活动和计划中，这些活动和计划将提高人们对基础材料科学及其在技术进步中的作用的认识，K-12学生，本科生和研究生物理学生，以及公众。材料科学研究的新机会将为社区大学生创造，从而加强非传统背景学生的STEM职业途径。该研究和教育计划利用PI在软物质系统理论建模方面的专业知识以及与俄勒冈州尤金及其周围的教育和外展组织的现有关系。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

NONTECHNICAL SUMMARYThis CAREER award supports theoretical and computational research, and educational activities that advance designer materials that mimic the adaptability of living systems and their ability to manipulate energy flows. The properties of a material arise from the collective interactions of its building blocks. In traditional materials, the building blocks are atoms or molecules whose interactions are determined by the nature of the chemical bonds among them. Modern technical advances in fabricating complex assemblies, such as 3D printing and bio-inspired self-assembly, have enabled artificial materials composed of active building blocks such as driven micromechanical resonators, miniature robots, and even bacteria whose interactions can be dynamically modulated via external means or internal power sources. By incorporating dynamic elements, these new materials can manipulate mechanical energy and transform their structural properties in ways that are unattainable in inert materials. This project will develop quantitative models that predict the collective behavior of massive assemblies of dynamic building blocks, thereby expanding capabilities to tailor the response of dynamic materials towards specific technological needs.The PI and his research team will develop new theoretical and computational models to predict the mechanical and structural response of assemblies of building blocks whose interactions are modulated to form periodic patterns in both space and time. These models will extend physical theories which model inert materials as networks of masses connected by springs, with the novel advance that the spring stiffnesses will be varied sinusoidally by external driving agents. The new models will be used to propose designs for dynamic materials with desirable material properties targeted towards technological applications such as vibration control, shock absorption, and acoustic signal processing. For example, time-varying spring stiffnesses can enable structures that amplify sound waves traveling through the material in particular directions or transform a static solid to a spontaneously flowing liquid when a prescribed pressure is applied. In addition, this research activity will advance fundamental understanding of systems which manipulate energy flows in fields as diverse as electronics, photonics, and quantum information.The educational component of the project will develop new pedagogical tools, activities, and programs to advance materials science knowledge among students in non-traditional academic pathways, K-12 students, beginning graduate students, and the general public. The PI and his research team will develop new hands-on activities to convey the physical principles underlying the project to participants at the Eugene Youth Math Festival, the Oregon Country Fair, and summer programs for high school students hosted by the University of Oregon. This award will support research internships for community college students who are considering a transfer to a four-year degree program, and the development of new learning modules which use scientific teaching practices to improve equity and inclusion in graduate physics courses. The educational activities are designed to enhance participation, achievement, and persistence of students from underrepresented groups in STEM while improving outcomes for students from all backgrounds.TECHNICAL SUMMARYThis CAREER award will support research and educational activities to advance fundamental understanding and public awareness of dynamic materials that are designed to channel mechanical energy in ways unattainable by inert structures. Technological breakthroughs have enabled the fabrication of collections of interacting building blocks whose local properties can be modulated by external fields or internally powered mechanisms as desired. This opens new possibilities for non-equilibrium manipulation of mechanical energy. However, the normal modes of these dynamic materials are typically investigated using approximate methods such as plane-wave and Magnus expansions that fail to correctly capture symmetry constraints and topological features of the excitation spectra. This project will develop an exact theoretical framework to compute the band structures of spacetime-modulated mechanical systems with generalized couplings. The framework will be used for rigorous evaluations and new explorations of non-equilibrium mechanics and phase behavior, including topological properties of excitation spectra and phase changes between crystal-like ordered states in active matter. Beyond this work, the framework will be widely applicable to harmonic oscillations of dynamical systems with second-order time dynamics. By revealing new ways to control the flow of mechanical energy in classical systems, the research will advance fundamental understanding of non-Hermitian physics with relevance to manipulating energy flows in quantum condensed matter, cold atoms, and optics.The underlying concepts and research questions will be integrated into educational activities and programs that will improve awareness of fundamental materials science and its role in technological advancement in K-12 students, undergraduate and graduate physics students, and the general public. New opportunities for materials science research will be created for community college students, thereby reinforcing pathways to STEM careers for students with non-traditional backgrounds. The research and educational plans leverage the PI's expertise in theoretical modeling of soft matter systems and existing relationships with educational and outreach organizations in and around Eugene, Oregon.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.