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: 2225543
• 负责人: Daniel Beller
• 金额: $ 57万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-01-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2225543&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.

非技术摘要这一职业奖支持理论和计算研究和教育，以促进对许多类似单位的互动中生活和栩栩如生系统中如何复杂，功能组织产生的理解。从细胞内的细胞骨架到动物群和羊群，自然界充斥着集体组织和集体运动的例子，具有至关重要的功能，例如细胞分裂和食物觅食。最近，来自统计和软材料物理学的见解有助于揭示了在许多尺寸尺度和物种上进行此类集体行为的一般原则。由于其广泛的适用性，这种主动物质物理学正在指导设计新的先进材料的设计，这些材料模仿了生活系统的功能，例如感知环境的能力，内部重新排列，移动，分裂或自我修理。活性耶数构成了一个重要的活性物质类别，其中包括细胞内生物丝组件，生长或蜂群细菌的菌落以及上皮或神经干细胞的组织。这些潜水系统的两个基本因素：每个单元施加的主动力，例如沿延伸或收缩轴的轴线或生物丝，以及相邻单元并行对齐的长轴的趋势，例如河流上浮起的树木原木集合。现象被称为列的秩序，可以在某些位置被拓扑缺陷中断，拓扑缺陷是列在邻近单元不可避免地无法对齐的列明中的点状或类似线的位置。就像地毯中的烦恼颠簸一样，拓扑缺陷可以四处移动或组合，但不能使存在的舒适性降低，除非通过将它们移出边界等特殊操作。在主动的列明中，拓扑缺陷远非令人不快，对新兴集体运动至关重要：积极的力量不断产生和破坏拓扑缺陷，其混乱的运动继续重新安排了基本的，力量伸出的单位。因此，为了理解生物学中的主动命名，并利用这些现象在模仿生命的技术中，必须了解拓扑缺陷的创造，动作和有效的相互作用。近年来，在薄层活跃的鸟类方面，在这方面取得了重大进展。但是，拓扑缺陷的行为在完全三维系统中变得更加复杂，这给开发基于主动列的物理学的强大技术带来了挑战。为了应对这一挑战，首席研究员及其研究团队将在3D中对主动nematic Dynamics进行计算指导的理论理解，拓扑缺陷是中心焦点。这项研究将揭示有关线性拓扑缺陷如何诞生的规则，自身重塑，有时会与其他缺陷合并或消失。反过来，这些发现将揭示有效的列材料的缺陷驱动的重排，从而阐明材料对刺激（例如损伤或化学环境变化）的反应。从该项目中获得的理解将指导对自然界中潜水员3D主动列神经系统的普遍现象的实验研究，并能够设计能够在生物医学，工业和消费者设备中应用广泛应用的能够自主功能响应的高级材料。 PI及其研究小组将设计和领导教育和外展活动与研究项目紧密融合。近代的建模纳入了加利福尼亚大学默塞德分校的新研究生课程中。专业发展研讨会建立了本科生在批判性分析，可视化和撰写科学数据方面的技能。 Additionally, outreach to high-school students in California’s San Joaquin Valley employees 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 incorporate soft matter research.研究目标是通过开发粗粒理论来理解3D nematics的平衡结构和非平衡活性动力学，用于曲线披露缺陷的相互作用和运动。该目标的一部分是由于最近展示了一个散装3D主动的nematic模型系统，该模型表现出拓扑上中立的纪律以及纪念线网络的创造和an灭。该项目采用粗粒框架进行纪念几何形状以及放松和活跃的杂技计算建模，将计算有效的配对电位，这些势力是管理近乎分类的变形和重新定位的有效对电势。流体动力学计算将阐明如何以及为什么活动导致曲线弯曲，伸展，重新连接和改变绕组特征。将确定3D主动稳态的基本属性，包括混乱的自我混合和披露网络的连续拓扑自我恢复。作为活跃准粒子的脱节的观点对于理解2D中主动的诺神性混沌动力学是至关重要的。 As exploration begins of the 3D case, a major challenge is the far greater complexity of topological defects: While 2D disclosures 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 equivalent nematics frustrated by surface anchoring.在复杂的3D方向数据中，需要理论工具来预测和表征这种几何可变但拓扑功能强大的特征。在满足这一需求时，本研究通过直接从列表董事字段进行计算的正顺式构造应用了披露方向和绕组角色的新定义。该框架提供了一组明确的粗粒变量，可以系统地将有关披露翻译和重新定向的最新发现从2D概括为3D。该项目将为有效的互动和3D披露的主动动态提供一个广泛的适用框架。PI和研究小组将设计和领导教育和外展活动与研究项目紧密融合。液晶建模纳入了有关高级软物质和统计物理学的新研究生课程中，强调计算技术以及理论方法。专业发展研讨会在各种科学和工程学科的研究项目中，建立了本科生的批判性分析，可视化和文章的技能。此外，向加利福尼亚州圣华金河谷的高中生进行宣传，以访问，相关和视觉上吸引人的物理研究和科学计算介绍，这是NSF的法定任务，并以评估基金会的知识功能和广泛的影响来审查CRITERIA，这被认为是珍贵的。