This CAREER award supports theoretical and computational research and education to advance understanding of how complex, functional organization arises in living and lifelike systems from the interactions of many similar units. From the cytoskeleton within cells up to animal swarms and flocks, nature abounds with examples of collective organization and collective motion with critically important functions, such as cell division and foraging for food. Recently, insights from statistical and soft materials physics have helped to uncover general principles underlying such collective behaviors across many size scales and species. This physics of active matter, because of its wide applicability, is guiding the design of new, advanced materials that mimic functionalities of living systems, such as the capability to sense their environment, internally rearrange, move, divide, or self-heal.
Active nematics constitute one prominent class of active matter, with examples including intracellular biofilament assemblies, colonies of growing or swarming bacteria, and tissues of epithelial or neural stem cells. Two basic factors unite these diverse systems: the active forces exerted by each unit, for example a cell or biofilament, along an axis of extension or contraction, and the tendency for neighboring units to align their long axes in parallel, like a crowded collection of tree logs floating on a river. This latter phenomenon, known as nematic order, can be interrupted at certain locations by topological defects, which are point-like or thread-like places within the nematic where the neighboring units unavoidably fail to align. Like a vexing bump in a rug, topological defects can be moved around or combined, but cannot be smoothed out of existence except by special operations such as moving them out to a boundary. In active nematics, far from being vexatious, topological defects are fundamental to the emergent collective motion: Active forces continually produce and destroy topological defects, whose chaotic motions continually rearrange the underlying, force-exerting units.
Therefore, in order to understand active nematics in biology and exploit these phenomena in life-mimicking technologies, it is imperative to understand the creation, motions, and effective interactions of topological defects. Significant progress has been made in recent years on this front for thin layers of active nematics. However, the behavior of topological defects becomes substantially more complicated in fully three-dimensional systems, which presents a challenge for developing robust technologies based on active nematic physics. To address this challenge, the principal investigator and his research team will develop a computationally guided theoretical understanding of active nematic dynamics in 3D, with topological defects as the central focus. This research will uncover the rules governing how thread-like topological defects are born, reshape themselves, and eventually merge with other defects or disappear. In turn, these findings will reveal the defect-driven rearrangements of active nematic material, illuminating how the material responds to stimuli such as damage or a change of chemical environment. The understanding gained from this project will guide experimental investigations of phenomena universal to diverse 3D active nematic systems in nature, and will enable design of advanced materials capable of autonomous functional responses with a wide range of applications in biomedical, industrial, and consumer devices.
The PI and his research group will design and lead education and outreach activities closely integrated with the research project. Modeling of nematics is incorporated into a new graduate course on Advanced Soft Matter and Statistical Physics at the University of California, Merced. Professional development workshops build undergraduates’ skills in critically analyzing, visualizing, and writing about scientific data. Additionally, outreach to high-school students in California’s San Joaquin Valley employs soft matter computer simulation activities as accessible, relatable, and visually appealing introductions to physics research and scientific computation.
This CAREER award supports theoretical and computational research on topological defect lines in three-dimensional (3D) nematic liquid crystals, together with an integrated program of education and outreach incorporating soft matter research. The research goal is to understand both equilibrium structure and non-equilibrium active dynamics of 3D nematics, through development of a coarse-grained theory for interaction and motion of curvilinear disclination defects. This goal is motivated in part by the recent demonstration of a bulk-3D active nematic model system, exhibiting creation and annihilation of topologically neutral disclination loops along with a network of disclination lines. This project, employing a coarse-grained framework for disclination geometry alongside relaxational and active-hydrodynamic computational modeling, will calculate effective pair potentials governing deformation and reorientation of nearby disclinations. Hydrodynamic calculations will illuminate how and why activity causes disclinations to curve, stretch, reconnect, and change winding character. Fundamental properties of the 3D active steady state will be determined, including chaotic self-mixing and the disclination network’s continual topological self-reconfiguration.
The perspective of disclinations as active quasiparticles has been central to understanding active nematic chaotic dynamics in 2D. As exploration begins of the 3D case, a major challenge is the far greater complexity of topological defects: While 2D disclinations have fixed winding numbers such as +1/2 and –1/2, in 3D these winding geometries can continuously transform into one another, as seen both in active defect loops and in heterogeneous defects of equilibrium nematics frustrated by surface anchoring. There is a need for theoretical tools to predict and characterize such geometrically variable but topologically robust features in complex 3D orientation data. Addressing this need, this research applies a new definition of disclination orientation and winding character via an orthonormal frame construction directly computable from the nematic director field. This frame provides a set of unambiguous coarse-grained variables to systematically generalize recent findings on disclination translation and reorientation from 2D into 3D. The project will produce a widely applicable framework for effective interactions and active dynamics of 3D disclinations.
The PI and research group will design and lead education and outreach activities closely integrated with the research project. Liquid crystals modeling is incorporated into a new graduate course on Advanced Soft Matter and Statistical Physics emphasizing computational techniques alongside theoretical methods. Professional development workshops build undergraduates’ skills in critically analyzing, visualizing, and writing about scientific data as they engage in research projects in various scientific and engineering disciplines. Additionally, outreach to high-school students in California’s San Joaquin Valley employs soft matter computer simulation activities as accessible, relatable, and visually appealing introductions to physics research and scientific computation.
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.
