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

该职业奖支持理论和计算研究，以及促进设计材料模仿生命系统的适应性及其操纵能量流的能力的教育活动。一种材料的特性源于它的组成部分之间的集体相互作用。在传统材料中，原子或分子的相互作用是由它们之间的化学键的性质决定的。在制造复杂组件方面的现代技术进步，如3D打印和生物启发自组装，已经使由主动构建块组成的人工材料成为可能，例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节。通过加入动态元素，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量组装的集体行为，从而扩展针对特定技术需求定制动态材料响应的能力。PI和他的研究团队将开发新的理论和计算模型来预测建筑模块组件的机械和结构响应，这些组件的相互作用被调制成在空间和时间上形成周期性模式。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，并提出弹簧刚度将受外部驱动因素的正弦变化。新模型将用于提出具有理想材料性能的动态材料的设计，这些材料的目标是诸如振动控制、减震和声学信号处理等技术应用。例如，时变的弹簧刚度可以使结构放大在特定方向上穿过材料的声波，或者在施加规定压力时将静态固体转化为自发流动的液体。此外，这项研究活动将促进对电子、光子学和量子信息等不同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，以促进非传统学术途径的学生、K-12学生、研究生初学者和公众的材料科学知识。PI和他的研究小组将开发新的实践活动，向尤金青年数学节、俄勒冈国家博览会和俄勒冈大学主办的高中生暑期项目的参与者传达该项目的物理原理。该奖项将支持正在考虑转到四年制学位课程的社区大学学生的研究实习，以及开发新的学习模块，这些模块使用科学教学实践来提高研究生物理课程的公平性和包容性。这些教育活动旨在提高来自STEM中代表性不足群体的学生的参与度、成就和持久性，同时改善来自所有背景的学生的成果。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，动态材料旨在以惰性结构无法实现的方式引导机械能。技术突破使相互作用的构建块的集合的制造成为可能，这些构建块的局部属性可以根据需要被外部场或内部驱动机制调制。这为机械能的非平衡操纵开辟了新的可能性。然而，通常使用平面波和Magnus展开等近似方法来研究这些动态材料的正态模态，这些方法无法正确捕获激发光谱的对称约束和拓扑特征。本项目将建立一个精确的理论框架来计算具有广义耦合的时空调制机械系统的能带结构。该框架将用于非平衡力学和相行为的严格评估和新探索，包括激发光谱的拓扑性质和活性物质中晶体有序态之间的相变。除此之外，该框架将广泛适用于具有二阶时间动力学的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，该研究将推进与操纵量子凝聚态物质、冷原子和光学中的能量流动相关的非厄米物理的基本理解。基础概念和研究问题将整合到教育活动和计划中，以提高基础材料科学及其在K-12学生，本科和研究生物理学生以及公众技术进步中的作用的认识。将为社区大学学生创造材料科学研究的新机会，从而加强非传统背景的学生进入STEM职业的途径。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。该奖项反映了美国国家科学基金会的法定使命，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。

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.