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Geometric Instabilities of Filamentous Matter

丝状物质的几何不稳定性

基本信息

批准号：
1608862
负责人：
Gregory Grason
金额：
$ 28.5万
依托单位：
University of Massachusetts Amherst
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2016
资助国家：
美国
起止时间：
2016-12-01 至 2020-11-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1608862&HistoricalAwards=false
关键词：
Geometric Instabilities Filamentous Matter

项目摘要

NONTECHNICAL ABSTRACTThis award supports theoretical research and education to advance understanding of the structure and response in "filamentous matter," a notion which encompasses biological and synthetic nanostructured materials, ranging from carbon nanotubes and some assemblies of interconnected long chainlike molecules to filamentous proteins within and around biological cells. Project research will develop and investigate theoretical models of multi-filament material structures and related phenomena that derive from the generic, yet poorly understood, interplay between patterns of orientation and spatial organization. Developed theories will advance understanding of structure formation and organized mechanical motion of important classes of biological materials, including networks, bundles and fibers of filamentous proteins, as well as technologically valuable materials, like nanotube-based yarns and textiles. Beyond currently existing materials, studies will lay the groundwork for designing and engineering new classes of synthetic, responsive filamentous materials by uncovering new principles for manipulating their structure spanning from single filaments across assemblies. The project will advance the training of a postdoctoral and graduate researcher in a diverse set of quantitative methods, from mechanics and geometry to statistical and computational physics. Ongoing research goals will be integrated with undergraduate research projects and development of graduate curriculum in soft materials theory. The project also involves new collaboration with pre-K educators in Northampton, MA to develop an in-class curriculum centered on the connections between shape and materials that will stimulate interest and foster curiosity in STEM at the pre-K level and engage with the emerging mathematical thinking of students at 4-5 age range.TECHNICAL ABSTRACTThis award supports theoretical research and education to advance understanding of the structure and response in "filamentous matter." Focusing on generic models of two prototypical assembly architectures, ordered bundles and isotropic networks, the research will study novel collective behaviors of multi-filament assemblies stemming from generic, geometric nonlinearities of filamentous matter, and their associated multi-scale, geometric instabilities. The project builds from emerging frameworks that connect geometric and mechanical principles of multi-filament structures to those of thin, 2D structures, including elastic sheets and crystalline membranes. While the geometrically-nonlinear principles of 2D membranes are now well-established in soft matter physics, an understanding of the basic methods and consequences of analogous principles for multi-filament bundles or networks, which this project seeks to develop, is in its infancy.Project research will consider physical models of multi-filament assemblies in which intrinsic or extrinsic stresses vary in magnitude, sign and direction throughout the structure, leading to variations in local stability, and ultimately, new classes of inhomogeneous and non-linear behaviors:1) Building on an emerging understanding of the metric geometry of filament arrays, the project will study structural instabilities of incompatible bundles, in which uniform inter-filament spacing is frustrated. Two generic models will be studied: i) defect driven shape-instabilities of cohesive bundles and ii) ground-state order and geometry of long-range repulsive filaments under lateral confinement. 2) The project will advance geometric descriptions of inter-filament packing in contorted configurations of bundles, where the metric properties necessarily vary along the bundle. The present understanding of metric constraints is limited to only simplified geometries (straight, constant-twist bundles), and this study will advance the knowledge of optimal inter-filament organization to models of bent, toroidal and folded bundles relevant to observed phenomena from condensation of biopolymers to "in viro" packing of dsDNA chains. 3) Drawing on parallels between the stress-collapse behavior of 2D elastic sheets subject to spatially non-uniform compression, the project will investigate generic consequences of the compressive (buckling) instability of constituent filaments in isotropic network models, driven far beyond the buckling threshold. This "far-from threshold" regime reveals new universal behaviors, including the renormalization of far-field stresses due to compressive collapse of networks near to locally-applied loads.The project will advance the training of a postdoctoral and graduate researcher in a diverse set of quantitative methods, from mechanics and geometry to statistical and computational physics. Ongoing research goals will be integrated with undergraduate research projects and development of graduate curriculum in soft materials theory. The project also involves new collaboration with pre-K educators in Northampton, MA to develop an in-class curriculum centered on the connections between shape and materials that will stimulate interest and foster curiosity in STEM at the pre-K level and engage with the emerging mathematical thinking of students at 4-5 age range.

非技术摘要该奖项支持理论研究和教育，以促进对“丝状物质”的结构和反应的理解，这一概念包括生物和合成纳米结构材料，从碳纳米管和一些相互连接的长链状分子组装到生物细胞内和周围的丝状蛋白质。项目研究将开发和研究复丝材料结构的理论模型和相关现象，这些理论模型和现象源于一般的，但知之甚少的方向和空间组织模式之间的相互作用。发展的理论将促进对重要类别生物材料的结构形成和有组织的机械运动的理解，包括丝状蛋白质的网络，束和纤维，以及技术上有价值的材料，如纳米管纱线和纺织品。除了目前现有的材料，研究将为设计和工程新类别的合成，响应丝状材料奠定基础，通过揭示新的原理来操纵它们的结构，从单丝跨越组件。该项目将推进博士后和研究生研究员的培训，从力学和几何学到统计和计算物理学等各种定量方法。正在进行的研究目标将与本科研究项目和软材料理论研究生课程的开发相结合。该项目还涉及与北安普顿学前教育工作者的新合作，MA开发一个以形状和材料之间的联系为中心的课堂课程，这将激发兴趣并培养对学前班STEM的好奇心，并与4- 5岁学生的新兴数学思维互动。技术摘要该奖项支持理论研究和教育，以促进对“丝状物质”结构和反应的理解。“专注于两个原型组装架构的通用模型，有序束和各向同性网络，该研究将研究源于丝状物质的通用几何非线性及其相关的多尺度几何不稳定性的复丝组装的新颖集体行为。该项目建立在新兴框架的基础上，这些框架将多丝结构的几何和机械原理与薄的2D结构（包括弹性片材和结晶膜）联系起来。虽然二维膜的几何非线性原理现在在软物质物理学中已经得到了很好的建立，但是对于本项目所寻求开发的多纤维束或网络的类似原理的基本方法和结果的理解还处于起步阶段。项目研究将考虑多纤维组件的物理模型，其中内在或外在应力的大小不同，符号和方向的变化，导致局部稳定性的变化，并最终导致新的非均匀和非线性行为：1）建立在对细丝阵列的度量几何的新兴理解的基础上，该项目将研究不相容束的结构不稳定性，其中均匀的细丝间间距是失败的。我们将研究两个一般模型：i）缺陷驱动的内聚束的形状不稳定性和ii）横向约束下长程排斥细丝的基态有序性和几何结构。2)该项目将推进几何描述的扭曲配置的纤维束，其中的公制属性必然会发生变化沿着束。目前对度量约束的理解仅限于简化的几何形状（直的，恒定的扭曲束），本研究将推进最佳的细丝间组织的知识模型的弯曲，环形和折叠束相关的观察到的现象，从生物聚合物的缩合的dsDNA链的“体内”包装。3)该项目利用受到空间非均匀压缩的2D弹性片材的应力-塌陷行为之间的相似性，研究各向同性网络模型中组成细丝的压缩（屈曲）不稳定性的一般后果，远远超过屈曲阈值。这个“远离阈值”的制度揭示了新的普遍行为，包括由于压缩崩溃的网络附近的局部施加load.The项目将推进在一个多元化的定量方法，从力学和几何统计和计算物理的博士后和研究生研究人员的培训远场应力的重整化。正在进行的研究目标将与本科研究项目和软材料理论研究生课程的开发相结合。该项目还涉及与北安普顿的学前教育工作者的新合作，MA开发以形状和材料之间的联系为中心的课堂课程，这将激发兴趣并培养对学前阶段STEM的好奇心，并与4-5岁学生的新兴数学思维互动。