CAREER: Geometries of Topological Defects in 3D Nematics, from Equilibrium Structure to Active Dynamics

职业：3D 向列学中拓扑缺陷的几何形状，从平衡结构到主动动力学

• 批准号: 2046063
• 负责人: Daniel Beller
• 金额: $ 57万
• 依托单位: University of California - Merced
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-08-01 至 2022-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2046063&HistoricalAwards=false
• 关键词: CAREER; Geometries; Topological; Defects; 3D

NONTECHNICAL SUMMARYThis 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.TECHNICAL SUMMARYThis 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.

该职业奖支持理论和计算研究和教育，以促进对生命和类生命系统中许多相似单元相互作用产生的复杂功能组织的理解。从细胞内的细胞骨架到动物群和羊群，自然界充满了具有至关重要功能的集体组织和集体运动的例子，例如细胞分裂和觅食。最近，来自统计和软材料物理学的见解有助于揭示跨许多尺寸尺度和物种的这种集体行为的一般原理。这种活性物质的物理学，由于其广泛的适用性，正在指导设计新的、先进的材料，模仿生命系统的功能，如感知环境、内部重新排列、移动、分裂或自我修复的能力。活性向列体构成了一类突出的活性物质，其例子包括细胞内生物丝组合，生长或群集的细菌菌落，上皮细胞或神经干细胞组织。两个基本因素将这些不同的系统联系在一起：每个单元（例如细胞或生物丝）沿着延伸或收缩的轴施加的积极力量，以及相邻单元平行排列其长轴的趋势，就像漂浮在河上的拥挤的原木集合。后一种现象，被称为向列顺序，可以在某些位置被拓扑缺陷打断，拓扑缺陷是向列中的点状或线状位置，相邻单元不可避免地不能对齐。就像地毯上恼人的凸起一样，拓扑缺陷可以四处移动或组合，但除非通过特殊操作（例如将它们移出边界），否则无法消除存在。在主动向列中，拓扑缺陷远不是无理的，而是紧急集体运动的基础：主动力不断地产生和破坏拓扑缺陷，其混沌运动不断地重新排列底层的施力单元。因此，为了理解生物学中的主动向列数学，并在模拟生命的技术中利用这些现象，必须了解拓扑缺陷的产生、运动和有效的相互作用。近年来，薄层主动向列线在这方面取得了重大进展。然而，在全三维系统中，拓扑缺陷的行为变得更加复杂，这为开发基于主动向列物理的鲁棒技术提出了挑战。为了应对这一挑战，首席研究员和他的研究团队将以拓扑缺陷为中心，开发一种以计算为指导的三维主动向列动力学理论理解。这项研究将揭示控制线状拓扑缺陷如何产生、重塑自身并最终与其他缺陷合并或消失的规则。反过来，这些发现将揭示活性向列材料的缺陷驱动重排，阐明材料如何响应诸如损伤或化学环境变化等刺激。从该项目中获得的理解将指导对自然界中各种3D主动向列系统普遍现象的实验研究，并将使设计能够在生物医学，工业和消费设备中广泛应用自主功能响应的先进材料成为可能。PI及其研究小组将设计和领导与研究项目紧密结合的教育和外展活动。向列数学建模被纳入加州大学默塞德分校高级软物质和统计物理的新研究生课程。专业发展研讨会培养本科生批判性分析、可视化和撰写科学数据的技能。此外，向加州圣华金河谷的高中生推广软物质计算机模拟活动，将其作为物理研究和科学计算的可访问、相关和视觉上吸引人的介绍。该职业奖支持三维（3D）向列液晶拓扑缺陷线的理论和计算研究，以及结合软物质研究的综合教育和推广计划。研究目标是通过发展曲线偏斜缺陷相互作用和运动的粗粒度理论来理解三维向列图的平衡结构和非平衡主动动力学。这一目标的部分动机是由于最近的一个体- 3d主动向列模型系统的演示，展示了拓扑中性偏转环的产生和湮灭以及偏转线网络。该项目采用粗粒度的斜向几何框架以及松弛和主动流体动力学计算模型，将计算控制附近斜向变形和重新定向的有效对势。流体力学计算将阐明活动如何以及为什么会导致斜交弯曲、拉伸、重新连接和改变缠绕特性。三维有源稳态的基本性质将被确定，包括混沌自混合和发散网络的连续拓扑自重构。斜位作为活动准粒子的观点是理解二维活动向列混沌动力学的核心。随着3D情况的探索开始，主要的挑战是拓扑缺陷的复杂性：虽然2D斜向具有固定的绕组数，如+1/2和-1/2，但在3D中，这些绕组几何形状可以不断地相互转换，无论是在主动缺陷回路中，还是在平衡向列线的异构缺陷中，都可以看到表面锚定。在复杂的三维方向数据中，需要理论工具来预测和表征这些几何上可变但拓扑上健壮的特征。针对这一需求，本研究通过直接从向列指向域计算的标准正交框架结构，应用了一种新的衍射取向和缠绕特性的定义。该框架提供了一组明确的粗粒度变量，以系统地概括最近关于斜视转换和从2D到3D的重新定向的发现。该项目将产生一个广泛适用的框架，有效的相互作用和三维斜向的主动动力学。PI和研究小组将设计和领导与研究项目密切结合的教育和外联活动。液晶建模被纳入一个新的研究生课程的高级软物质和统计物理强调计算技术与理论方法。专业发展研讨会培养本科生在从事各种科学和工程学科的研究项目时批判性地分析、可视化和撰写科学数据的技能。此外，向加州圣华金河谷的高中生推广软物质计算机模拟活动，将其作为物理研究和科学计算的可访问、相关和视觉上吸引人的介绍。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。