Computational and Theoretical Modeling of Active Nematics in 3D and Under Confinement

该奖项支持活性材料的理论和计算建模以及相关的教育活动。活性材料是由可以利用当地环境的能量来推动自身的组件制成的。这种能力使活性材料具有传统材料不可能具有的特性。在生物细胞中发现了天然存在的活性物质的例子，这些物质使细胞能够执行诸如移动、自我复制和伤口愈合等功能。最近的实验进展使人造活性材料成为可能，这种材料可能具有类似的能力。然而，目前对活性物质的理论认识是不完整的。改进这一理论将指导新型人工材料的设计，并将有助于理解生物过程，如有机体发育、细胞运动和癌症生长。该奖项将支持旨在朝着这一理论取得进展的研究。PI将为最近开发的一种由生物细丝和分子马达蛋白制成的实验性人工活性材料开发理论和计算模型。这些模型将描述当系统被限制在各种几何形状时的行为，例如在通道或球形液滴内。理论模型和计算模型的准确性将通过对相同约束几何的实验数据进行模型预测来评估。该研究的目标包括了解活性材料的各个组成部分如何共同工作以实现诸如大规模运动之类的行为，以及推进如何影响系统的结构顺序。支持的研究将在数学方法与理论和实验软物质物理之间的接口为本科生和研究生提供有价值的科学，技术，工程和数学（STEM）培训。研究活动包括训练计划，旨在让不同的学生参与计算研究，并向专业和非专业受众提供科学交流方面的指导。该奖项还支持利用活跃物质模拟和实验中产生的壮观视觉效果来激发外行观众对科学研究兴趣的公共宣传项目。该奖项支持活性材料的理论和计算建模以及相关的教育活动。活性物质描述本质上不平衡的物质，其组成元素消耗能量来产生力和运动。例如，生物细胞内分子对ATP的消耗使其能够执行各种功能，如运动、复制和自我修复。现在有可能从生物分子或合成胶体中构建人工活性材料，它们具有将能量转化为运动的类似能力。这些构建模块可以实现一类新的软材料，其功能目前仅在生物有机体中发现。然而，目前对活性物质的理论认识还远远不够完善。发展这样一种理论对于合理设计新型人工活性材料至关重要，并将阐明生物过程，如有机体发育、细胞运动和癌症生长，并将使新型人工活性材料的合理设计成为可能。该奖项将支持旨在推进这一理论的研究，通过开发由实验合作者开发的模型活性材料驱动的理论和计算模型-由微管和运动蛋白悬浮液构建的三维（3D）“活性向列”。PI将开发三维主动向列方程组的连续流体动力学模型，并使用最近开发的数值方法在各种约束几何中求解它们。连续体模型将与基于粒子的模拟相联系，以探索在粒子尺度上产生的能量如何消散到更大的尺度模式。研究的一个特别重点将是阐明三维拓扑缺陷的结构，以及它们如何推动新兴动力学。模型预测将针对实验性三维主动向列方程组进行广泛测试。该研究将建立在目前对活性物质的理论认识的基础上，克服以下局限性：(1)大多数实际应用需要3D材料，但迄今为止几乎所有可控的实验活性物质系统都是二维或准二维的。因此，目前对活性物质的理论认识主要局限于二维。(2)虽然边界在平衡理论中通常可以忽略，但它们对活性物质具有深远的、长期的影响。因此，活性物质的模型必须明确地处理边界，并具有适当的边界条件。(3)在有源系统中，粒子尺度上的能量输入不断级联到更大的尺度上，这使得很难确定一个可以用来简化理论描述的尺度分离。因此，需要将微尺度力产生单元与集体行为的大尺度描述联系起来的模型。支持的研究将在数学方法与理论和实验软物质物理之间的接口为本科生和研究生提供有价值的科学，技术，工程和数学（STEM）培训。研究活动包括训练计划，旨在让不同的学生参与计算研究，并向专业和非专业受众提供科学交流方面的指导。该奖项还支持利用活跃物质模拟和实验中产生的壮观视觉效果来激发外行观众对科学研究兴趣的公共宣传项目。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 award supports theoretical and computational modeling of active materials and related educational activities. Active materials are made from components that can use energy from their local environment to propel themselves. This capability enables active materials to have properties which are not possible in traditional materials. Examples of naturally occurring active materials are found within biological cells, and these materials enable cells to perform functions such as moving, replicating themselves, and healing of wounds. Recent experimental advances are now making it possible to construct artificial active materials, that potentially could have similar capabilities. However, the current theoretical understanding of active materials is incomplete. Improving this theory will guide the design of novel artificial materials, and will help to understand biological processes such as organismal development, cell motility, and cancer growth. This award will support research aimed at making progress towards such a theory. The PI will develop theoretical and computational models for a recently developed experimental artificial active material made from biological filaments and molecular motor proteins. The models will describe how the system behaves when it is confined in a variety of geometries, such as within channels or spherical droplets. The accuracy of the theoretical and computational models will be assessed by testing model predictions against data from experiments in the same confinement geometries. Goals of the research include understanding how the individual components of an active material work collectively to enable behaviors such as large-scale motions, and how propulsion affects the structural order of the system. The supported research will provide valuable science, technology, engineering, and mathematical (STEM) training for undergraduate and graduate students at the interface between mathematical methods and theoretical and experimental soft matter physics. Research activities include training programs that are designed to engage diverse students in computational research, and to provide instruction in scientific communication to specialized and non-specialized audiences. The award also supports public outreach programs that use the spectacular visual effects that arise in active matter simulations and experiments to excite the interest of lay audiences in scientific research. TECHNICAL SUMMARYThis award supports theoretical and computational modeling of active materials and related educational activities. Active matter describes intrinsically non-equilibrium materials whose constituent elements consume energy to generate forces and motion. For example, the consumption of ATP by molecules within a biological cell enables it to perform diverse functions such as motion, replication, and self-healing. It is now possible to construct artificial active materials from biomolecules or synthetic colloids which have a similar capability to convert energy to motion. These building blocks could enable a new class of soft materials, with functionalities currently found only in biological organisms. However, the current theoretical understanding of active matter is far from complete. Developing such a theory is crucial to enable rational design of novel artificial active materials, and would elucidate biological processes such as organismal development, cell motility, and cancer growth, and would enable rational design of novel artificial active materials.This award will support research aimed at progressing toward such a theory, by developing theoretical and computational models motivated by a model active material developed by experimental collaborators - a three-dimensional (3D) "active nematic" constructed from a suspension of microtubules and motor proteins. The PI will develop continuum hydrodynamic models of 3D active nematics, and use recently developed numerical methods to solve them in a variety of confinement geometries. The continuum models will be linked to particle-based simulations that probe how energy generated at the particle scale dissipates into larger scale modes. A particular focus of the research will be elucidating the structure of topological defects in 3D, and how they power emergent dynamics. Model predictions will be extensively tested against the experimental 3D active nematics system. The research will build on the current theoretical understanding of active matter by overcoming the following limitations: (1) Most real-world applications require 3D materials, but to date almost all controllable experimental active systems have been 2D or quasi-2D. Thus, the current theoretical understanding of active matter is largely limited to 2D. (2) While boundaries can usually be neglected in an equilibrium theory, they have profound, long-ranged effects on active matter. Thus, models for active matter must treat boundaries explicitly and with appropriate boundary conditions. (3) Energy input at the particle scale in an active system cascades continuously to larger scales, making it difficult to identify a separation of scales that can be exploited to simplify theoretical descriptions. Thus, models that link the microscale force generation units to large-scale descriptions of collective behaviors are needed. The supported research will provide valuable science, technology, engineering, and mathematical (STEM) training for undergraduate and graduate students at the interface between mathematical methods and theoretical and experimental soft matter physics. Research activities include training programs that are designed to engage diverse students in computational research, and to provide instruction in scientific communication to specialized and non-specialized audiences. The award also supports public outreach programs that use the spectacular visual effects that arise in active matter simulations and experiments to excite the interest of lay audiences in scientific research.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.