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

University Of Oregon Eugene, Eugene OR

Investigators

Abstract

NONTECHNICAL SUMMARY This 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 SUMMARY This 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.