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.

非技术摘要这一奖项支持理论研究和教育，以提高对“丝状物质”中的结构和反应的理解，该概念涵盖了生物学和合成纳米结构材料，范围从碳纳米管以及一些相互连接的长链分子的组装到内部和周围的生物细胞中。项目研究将开发和研究从通用但知之甚少的多丝材料结构和相关现象的理论模型，这是方向和空间组织模式之间的相互作用。开发的理论将进一步了解结构形成和重要类型的生物材料的机械运动，包括丝状蛋白质的网络，束和纤维，以及技术有价值的材料，例如基于纳米管的纱线和纺织品。除了现有材料之外，研究还将为设计和工程设计新的合成，响应式丝状材料的基础奠定基础，该材料通过发现新的原理来操纵其结构，这些原理跨越了跨组件的单丝。该项目将在各种定量方法中，从机械和几何形状到统计和计算物理学来推进对博士后和研究生研究人员的培训。正在进行的研究目标将与本科研究项目和软材料理论中研究生课程的发展融合。该项目还涉及与马萨诸塞州北安普敦的Pre-K Pre-K教育者进行新的合作，以开发一流的课程，该课程围绕形状和材料之间的联系，这将激发K级别的STEM中的兴趣和好奇心，并与4-5岁的学生在4-5岁年龄范围内的新兴数学思维互动。该研究重点关注两个原型组装架构，有序束和各向同性网络的通用模型，研究将研究由丝状物质的通用，几何非线性及其相关的多尺度几何，几何学，几何学，几何性非线性构成的多丝组件的新型集体行为。该项目是由将多丝结构的几何和机械原理与薄的2D结构（包括弹性板和晶体膜）连接的几何和机械原理的新兴框架建立的。 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局部稳定性的变化以及最终的不均匀和非线性行为的新类别：1）基于对细丝阵列的度量几何形状的新兴理解，该项目将研究不兼容的捆绑包的结构性不稳定性，在这种捆绑中，均匀的衬里间距均匀的衬里间距会感到沮丧。将研究两个通用模型：i）内聚束的缺陷驱动的形状 - 构造性和ii）横向限制下的远程排斥细丝的地面秩序和几何形状。 2）该项目将在束束的串联配置中推进丝间填料的几何描述，其中度量属性必然会沿捆绑包变化。目前对度量约束的理解仅限于简化的几何形状（直，扭曲的束束），这项研究将使最佳的最佳丝间组织的知识转化为与观察到的现象相关的弯曲，环形和折叠捆的模型，从生物聚合物的凝结到“在dsdna Chinains of viro callo”中的现象。 3）该项目借鉴了受到空间不均匀压缩的2D弹性板的应力爆发行为之间的相似之处，该项目将调查各向素质网络模型中成分细丝的压缩（屈曲）不稳定性的通用后果，驱动到远远超出屈曲阈值的范围。这个“远程阈值”制度揭示了新的普遍行为，包括由于网络附近的网络压缩崩溃而导致远场应力的重新归一化。正在进行的研究目标将与本科研究项目和软材料理论中研究生课程的发展融合。该项目还涉及与马萨诸塞州北安普敦的Pre-K Pre-K教育工作者的新合作，以开发一门课程，以形状和材料之间的联系为中心，这些课程将激发KT型在K级的STEM的兴趣和培养好奇心，并与4-5岁学生的新兴数学思维相互动。