Geometric Instabilities of Filamentous Matter

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，“丝状物质”是一个包括生物和合成纳米结构材料的概念，范围从碳纳米管和一些相互连接的长链状分子的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多丝材料结构和相关现象的理论模型，这些理论模型源于定向模式和空间组织模式之间的一般但鲜为人知的相互作用。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，以及具有技术价值的材料，如基于纳米管的纱线和纺织品。在目前现有材料的基础上，研究将通过揭示操纵其结构的新原理，为设计和设计新型合成、响应性丝状材料奠定基础。该项目将推进博士后和研究生研究人员在从力学和几何到统计和计算物理的各种定量方法方面的培训。正在进行的研究目标将与本科生研究项目和软材料理论研究生课程的开发相结合。该项目还涉及与马萨诸塞州北安普顿的Pre-K教育者进行新的合作，开发一门以形状和材料之间的联系为中心的课堂课程，将激发Pre-K水平的兴趣和培养对STEM的好奇心，并参与4-5岁学生新兴的数学思维。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。这项研究聚焦于两种典型组装结构的通用模型，有序束和各向同性网络，研究源于丝状物质的通用几何非线性的多丝组装的新颖集体行为，以及它们相关的多尺度几何不稳定性。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力学原理与包括弹性薄片和结晶膜在内的薄2D结构的几何和力学原理联系起来。虽然2D膜的几何非线性原理现在已经在软物质物理中得到了很好的确立，但对多纤维束或网络的相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，其中内部或外部应力在整个结构中的大小、符号和方向不同，导致局部稳定性的变化，并最终产生新的非均匀和非线性行为：1)基于对纤维阵列的公制几何的新兴理解，该项目将研究不相容的纤维束的结构不稳定性，在这种情况下，均匀的细丝间距受到阻碍。我们将研究两个一般模型：i)缺陷驱动的内聚束形状不稳定性；ii)横向约束下长程排斥丝的基态有序性和几何形状。2)该项目将推进对束束扭曲配置中的长丝间堆积的几何描述，其中度量属性必然沿束变化。目前对度量约束的理解仅限于简化的几何形状(直束、恒扭束)，本研究将把最佳细丝间组织的知识推进到弯曲、环形和折叠束的模型中，这些模型与观察到的从生物聚合物凝聚到dsDNA链的“病毒”堆积的现象有关。3)利用二维弹性薄板在空间非均匀压缩下的应力崩溃行为之间的相似性，该项目将研究各向同性网络模型中组成纤维的压缩(屈曲)不稳定性的一般后果，远远超过屈曲阈值。这一“远离阈值”的机制揭示了新的普遍行为，包括由于靠近局部载荷的网络的压缩坍塌而导致的远场应力的重整化。该项目将推进博士后和研究生研究人员在从力学和几何到统计和计算物理的各种定量方法方面的培训。正在进行的研究目标将与本科生研究项目和软材料理论研究生课程的开发相结合。该项目还涉及与马萨诸塞州北安普顿的幼儿园前教育工作者进行新的合作，开发以形状和材料之间的联系为中心的课堂课程，将激发学生在幼儿园之前对STEM的兴趣和好奇心，并参与4-5岁学生新兴的数学思维。

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.