Collaborative Research: Unified Field Theory of Soft Amorphous Solids

非技术概述从颗粒集合到蛋白质、胶体或聚合物的聚集体，软固体具有各种结构并表现出广泛的物理响应。它们通常存在于机械稳定性的边缘，这导致了它们在应用中的适应性。 例子包括玻璃，水泥，压实的沙子，甚至酸奶或巧克力慕斯。该奖项支持专注于软固体物理学的理论和计算研究和教育，旨在开发和测试其动力学的新理论框架。与晶体不同，软固体的结构一般不表现出任何有序性。 因此，它们的机械响应不能用定义晶体行为的对称性破缺和长程有序的传统范式来描述。 传统的弹性理论是建立在动量（力学平衡）和能量守恒的原则上的，从这些原则中出现了对称性、序参量、几何形状和拓扑结构。在边缘软固体中能量守恒的缺乏，耗散或活性过程可以发挥作用，使这些理论无效。在这里提出的新框架中，守恒原理仅仅来自于力学平衡的约束。这种方法提供了一种自然的方式，将应力和结构重排之间的耦合固有的软固体，这是在现有的理论中缺少的，构建一个有效的场理论的非晶材料的应力和变形场的异质性。 PI将作为榜样参与，通过促进宣传活动，交流和讨论理论如何建立，如何连接到现象和实验，以及理论家开发的具体技能，来激励更多样化的学生群体理论凝聚态物理学。推广活动也将传播凝聚态物理的兴奋K-12学生和公众。技术摘要该奖项支持旨在了解无定形软固体，如堵塞的颗粒，凝胶，甚至生物组织的结构和功能关系的研究和教育。越来越清楚的是，局部的，亚维的，从机械平衡的约束出现的应力模式，确定了广泛的软物质的非平衡机械响应。次维激发也出现在张量规范理论中，这是最近为量子自旋液体发展的一类场论。 最近发现的严格映射这样一个张量规范理论的力学无定形固体形式的基础上提出的研究。 这种映射有可能解决应力如何传递以及为什么它们局限于软的无定形固体的问题。在非晶系统中的一个突出的挑战是确定一个序参数，区分不同的应力承载状态。 值得注意的是，没有序参量也是量子自旋液体的一个特征，其中拓扑指数（如缠绕数）可以区分状态。对于机械结构，拓扑力学提供了一个索引，可以做到这一点。有趣的是，软物质的弹性理论和量子自旋液体的张量规范理论是在某种程度上粗粒化的场论，而拓扑力学明确考虑了机械约束作用的网络结构，这表明拓扑力学可能是正确的工具，以建立在软非晶中起作用的微观力学约束之间的联系。材料和适当的张量规范理论框架。理论和数值模拟的结合将被用来探索从张量规范理论出现的软非晶材料的新范式的影响，并建立这种连续理论和拓扑力学之间的联系，它提供了一个网络特定的非晶固体的能力，以维持和发展外部应力下的描述。鉴于软无定形固体的普遍存在，其机械响应的统一场论将是软凝聚态物理学的变革，以及材料科学，化学和结构工程的相关应用学科。该合作将开发新的计算工具，以补充和通知理论，并确定新的实验测试。理论和模拟之间的反馈将反映在博士后，研究生和本科生的研究培训。 通过张量规范理论的共享框架在软凝聚态物理和硬凝聚态物理之间建立的桥梁为软凝聚态物理和硬凝聚态物理之间的接口提供了新的培训机会。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Non-technical summaryFrom collections of grains to aggregates of proteins, colloids or polymers, soft solids have a variety of structures and exhibit a broad range of physical response. They often exist at the margin of mechanical stability, which leads to the adaptability exploited in their applications. Examples include glass, cement, compacted sand, and even yogurt or chocolate mousse. This award supports theoretical and computational research and education focused on the physics of soft solids, with the objective to develop and test a new theoretical framework for their dynamics. Distinct from crystals, the structures of soft solids, generically, do not exhibit any order. Therefore, their mechanical response cannot be described by the conventional paradigm of broken symmetry and long-range order that define the behavior of crystals. Conventional elasticity theories are built on principles of momentum (mechanical equilibrium) and energy conservation, from which symmetries, order parameters, geometry and topology of patterns emerge. The absence of energy conservation in marginal soft solids, where dissipative or active processes can be at play, invalidates these theories. In the new framework proposed here, conservation principles emerge from just the constraints of mechanical equilibrium. This approach provides a natural way of incorporating the coupling between stress and structural rearrangements inherent in soft solids, which is missing in existing theories, to construct an effective field theory for amorphous materials with heterogeneities in stress and deformation fields. The PIs will engage as role models to inspire a more diverse population of students to theoretical condensed matter physics by promoting outreach activities that communicate and discuss how theories are built, how they connect to phenomena and experiments, and what specific skills theorists develop. Outreach activities will also disseminate the excitement of condensed matter physics to K-12 students and the general public.Technical SummaryThis award supports research and education aimed at understanding the structure-function relationship in amorphous soft solids such as jammed grains, gels, and even biological tissues. It has become increasingly clear that localized, sub-dimensional, stress patterns emerging from the constraints of mechanical equilibrium, determine the non-equilibrium mechanical response of a wide range of soft matter. Sub-dimensional excitations have also emerged in tensor gauge theories, a class of field theories recently developed for quantum spin liquids. A recently discovered rigorous mapping of such a tensor gauge theory to mechanics of amorphous solids forms the basis of the proposed research. This mapping has the potential to solve the problem of how stresses get transmitted and why they localize in soft, amorphous solids. An outstanding challenge in amorphous systems is identifying an order parameter that distinguishes between different stress-carrying states. Remarkably, the absence of an order parameter is also a feature of quantum spin liquids, where topological indices such as winding numbers can distinguish between the states. For mechanical structures, topological mechanics provides an index that can do precisely that. Interestingly enough, the elasticity theories of soft matter and tensor gauge theories for quantum spin liquids are field theories that emerge at some level of coarse-graining, whereas topological mechanics explicitly takes into account the network architecture in which the mechanical constraints operate, suggesting that topological mechanics may be the right tool to establish the connection between the microscopic mechanical constraints at play in soft amorphous materials and the appropriate tensor gauge theory framework. A combination of theory and numerical simulations will be used to explore the implications of a new paradigm emerging from tensor gauge theory for soft amorphous materials, and establish connections between this continuum theory and topological mechanics, which provides a network-specific description of the ability of amorphous solids to sustain and evolve under external stresses. Given the ubiquitous presence of soft amorphous solids, a unified field theory of their mechanical response will be transformative for soft condensed matter physics, and the associated applied disciplines of materials science, chemical and structural engineering. The collaboration will develop new computational tools to complement and inform theory and identify new experimental tests. The feedback between theory and simulations will be reflected in the research training of postdocs, graduate and undergraduate students. The bridge created between soft and hard condensed matter physics through the shared framework of tensor gauge theories offers new opportunities for training at the interface between soft and hard condensed matter physics.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.