Rigidity and Shape Transitions in Living and Nonliving Matter

该奖项支持理论和计算研究和教育，以研究粒子和细胞系统从类流体状态到刚性状态的转换。从咖啡豆轻易地流出料斗到恼人地卡在料斗里，从一堆沙子最初支撑着一个人的体重到突然坍塌，从生物组织中的细胞轻易地相互移动到固定在原地，颗粒（豆子、沙子或细胞）的无序集合从流动的液体转变为刚性的、无序的固体（反之亦然）的现象在我们周围无处不在。PI和她的团队将对刚性转变进行分析和数值研究-从流动或松软的系统（如液体）到刚性系统（如无序固体）的转变-能够预测转变如何以及何时出现。更具体地说，他们将研究摩擦颗粒填料和可变形多边形的随机平铺作为细胞组织，以了解颗粒间和细胞间摩擦在刚度转变中的作用。为了做到这一点，他们将继续开发算法，在这样的系统中绘制出刚性集群或刚性区域。局部刚性簇在软盘/流动阶段生长，并最终在刚性过渡阶段连接成一个跨系统的刚性簇。因此，对刚性团簇空间结构的研究将允许预测如何通过在单个粒子/细胞水平上去除或增加粒子间接触和/或相互作用来机械地破坏或稳定系统。这种方法将使过渡更可控，从而更安全，如果系统需要继续支持重量，例如。PI和她的团队还将研究系统中的刚性转变如何影响无序弹簧网络和无序粒子堆积之间的界面形状。这种情况与细胞内的细胞骨架（模拟为无序的弹簧网络）和细胞核内的DNA（模拟为颗粒堆积）之间的界面特别相关。PI和她的团队还将研究软物质表面的形状转变，比如折痕转变——从平坦表面到具有非常局部褶皱的表面的转变。这些形状的研究将导致对影响DNA转录的机械因素的理解取得新的进展，并且通过皱褶研究发育中的大脑作为一种材料可能有助于我们最终了解它是如何运作的。除了为非生命系统的刚性开始提供一个通用的微观框架外，拟议的工作还将物理学的范围扩展到生命系统，以帮助推动定量生物学的新兴领域。此外，PI还提议，通过讨论将生物时钟和终身教职时钟与高级研究生和博士后脱钩的科学进步，招收更多的女性进入物理学领域。PI还将向参观印第安克里克农场的学生介绍农场物理，这是纽约州伊萨卡的一个u采摘苹果园/农场。这是一个将物理与果园/农场结合起来的独特机会，使物理具有互动性和趣味性。该奖项支持理论和计算研究和教育，以研究各种颗粒和生物系统的刚性转变。无序的弹簧网络，无定形的颗粒堆积，以及可变形多边形对平面的随机平铺，都表现出软盘/类流体状态和刚性/无定形固体状态之间的刚性转变。在每一个刚性转变的核心是一个跨越刚性簇的开始，这已经在无序弹簧网络中研究了几十年。2016年，PI和她的合作者使用了一种基于（3,3）卵石游戏的算法来识别摩擦盘数值生成填料中的刚性簇。刚性过渡附近的跨越刚性簇表现出部分刚性，或软盘区域被刚性区域包围，这是在无摩擦圆盘填料中没有发现的特征。PI和她的团队将继续在数值上探索摩擦（3,3）卵石游戏应用于摩擦颗粒填料的优点和缺点，以更好地理解非生命颗粒物质在2- 3维摩擦填料中的旋转与平移是如何耦合的。刚性的出现也大量存在于生命体中。生物细胞的融合（无间隙）单层表现出刚性过渡，这可以在顶点模型中捕获，其中首选细胞周长变化，同时保持统一的包装分数。由于刚性过渡的调节在材料意义和生物学意义上都很重要，因此有必要问：顶点模型中刚性过渡的位置和性质是如何随着模型的变化而变化的？PI和她的团队将构建先前研究的顶点模型的二聚体版本，并通过分析和数值方法检查刚性过渡的位置和性质。以顶点模型耦合到底层弹簧网络的形式来模拟细胞-细胞粘附的机械敏感活性也将被研究，这些新顶点模型的刚性集群描述也将被研究。刚性转变通常是整体分析的。PI和她的团队将在数值上探索两种耦合无序材料之间的界面形状，每种材料都可以独立地经历刚性转变。当两个系统通过各自的刚度转变进行调整时，界面是否经历了从平面到皱褶的形状转变？这种情况与细胞内的细胞骨架和细胞核内的DNA之间的界面以及它们之间的机械耦合特别相关。将此应用于生物物质，通过ATP水解的活性驱动这两个系统，因此PI和她的团队将确定活跃的弹簧网络（细胞骨架）和活跃的粒子样模型（DNA）如何相互作用，从而使细胞核外的变形可能导致细胞核内的变形。形状转变也发生在表面上。最近，PI和她的团队将进一步研究软物质表面上被称为折痕的形状转变的分析微观理论，以揭示平坦和弯曲表面上的折痕图案是如何产生的。这里提出的想法有助于建立一个通用的微观框架，不仅在弹簧网络和粒子填充中，而且在顶点模型中也是如此。此外，将物理学扩展到生命系统有助于推动定量生物学这一新兴领域的发展。机械耦合的细胞骨架- dna系统可能会导致理解影响转录的机械因素的新进展，而通过皱褶理解发育中的大脑作为一种材料将促进对其功能的理解。为了招募更多的女性进入物理学领域，以帮助推动该领域达到新的高度，PI将为高级研究生和博士后举办一个研讨会，讨论用于将生物钟和终身教职时钟脱钩的科学进展。PI还将向参观印第安克里克农场的学生介绍农场物理，这是纽约州伊萨卡的一个u采摘苹果园/农场。这是一个独特的机会，将物理学与果园/农场结合起来，使物理学变得有趣，并帮助培养下一代物理学家。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 research and education to study transformations of particle and cellular systems from fluid-like states to rigid states. From coffee beans easily flowing out of a hopper to annoyingly getting stuck within it, from a pile of sand initially supporting a person's weight to suddenly collapsing beneath them, and from cells in a biological tissue readily moving past each other to remaining fixed in place, the phenomenon of a disordered collection of particles (beans, sand, or cells) transitioning from a flowing liquid to a rigid, disordered solid (or vice-versa) is ever present around us. The PI and her group will conduct analytical and numerical studies of the rigidity transition---a transition from a system that is flowing or floppy, such as a liquid, to one that is rigid, such as a disordered solid---to be able to predict how and when the transition emerges. More specifically, they will study frictional particle packings and random tilings of deformable polygons as cellular tissues to understand the role of inter-particle and intercellular friction on the rigidity transition. To do so, they will continue to develop algorithms to map out rigid clusters, or regions of rigidity, in such systems. Localized rigid clusters grow in the floppy/flowing phase and eventually connect to become a system-spanning rigid cluster at the rigidity transition. Study of the spatial structure of the rigid clusters will therefore allow for predictions as to how to mechanically destabilize or stabilize the system by removing or adding inter-particle contacts and/or interactions at the individual particle/cell level. This approach will make the transition more controllable and thus safer should the system need to continue to support weight, for example.The PI and her group will also investigate how rigidity transitions in the bulk of a system affect the shape of an interface between a disordered network of springs and a disordered particle packing. This situation is particularly relevant to the interface between the cellular cytoskeleton inside the cell, modeled as a disordered spring network, and the DNA inside the cell nucleus, modeled as a particle packing. The PI and her group will also study shape transitions at soft matter surfaces, such as the creasing transition---a transition from a flat surface to one with very localized folds. These shape studies will lead to new inroads in the understanding of mechanical factors affecting the transcription of DNA, and studying the developing brain as a material via creasing may help us ultimately understands how it functions. In addition to contributing towards a generic, microscopic framework for the onset of rigidity in nonliving systems, the proposed work extends the reach of physics to living systems to help drive the emerging field of quantitative biology. Moreover, the PI proposes to recruit more women to physics by discussing the scientific advances used to decouple the biological clock and the tenure clock to senior graduate students and post-docs. The PI will also introduce farm physics to school children visiting Indian Creek Farm, a u-pick apple orchard/farm in Ithaca, NY. It is a unique opportunity to combine physics with orchardry/farming to make physics interactive and fun. TECHNICAL SUMMARYThis award supports theoretical and computational research and education to study the rigidity transition in various particulate and biological systems. Disordered spring networks, amorphous packings of particles, and random tilings of the plane by deformable polygons all exhibit a rigidity transition between a floppy/fluid-like state and a rigid/amorphous solid state. At the heart of every rigidity transition is the onset of a spanning rigid cluster, which has been studied in disordered spring networks for several decades now. In 2016, an algorithm based on the (3,3) pebble game was used by the PI and her collaborators to identify rigid clusters in numerically-generated packings of frictional discs. The spanning rigid cluster near the rigidity transition exhibited partial rigidity, or floppy regions surrounded by rigid regions, which is a feature not found in frictionless disc packings. The PI and her group will continue to numerically explore the strengths and weaknesses of the frictional (3,3) pebble game as applied to frictional particle packings to better understand how rotations couple to translations in frictional packings of nonliving granular matter in 2- and ultimately 3-dimensions.The emergence of rigidity abounds in living matter as well. Confluent (no gap) monolayers of biological cells exhibit a rigidity transition, which can be captured in a vertex model where a preferred cell perimeter is varied while maintaining a packing fraction of unity. Since regulation of a rigidity transition is important in both a materials sense and a biological sense, it behooves one to ask: How does the location and the nature of the rigidity transition in vertex models change with variations in the model? The PI and her group will construct a dimerized version of the vertex model studied previously and analytically and numerically examine the location and nature of the rigidity transition. Mechanosensitive activity in the form of a vertex model coupled to an underlying spring network to model cell-cell adhesion will also be investigated as will a rigid cluster description for these new vertex models. Rigidity transitions are typically analyzed in bulk. The PI and her group will numerically explore the shape of an interface between two coupled disordered materials that can each undergo a rigidity transition independently. Does the interface undergo a shape transition from flat to crumpled as the two systems are tuned through their respective rigidity transitions? This situation is particularly relevant to the interface between the cellular cytoskeleton inside the cell and the DNA inside the cell nucleus, along with mechanical coupling between them. With this application to living matter, activity via ATP hydrolysis drives the two systems and so the PI and her group will determine how an active spring network, the cytoskeleton, and an active particle-like model, the DNA, interact such that deformations outside the cell nucleus potentially cause deformations inside it. Shape transitions also occur at surfaces. A recent analytical microscopic theory for the shape transition known as creasing in soft matter surfaces will be studied further by the PI and her group to uncover how crease patterns arise on flat and curved surfaces. The ideas presented here contribute towards a generic, microscopic framework for the onset of rigidity in not just spring networks and particle packings, but in vertex models as well. Moreover, extending the reach of physics to living systems helps drive the emerging field of quantitative biology. The mechanically coupled cytoskeleton-DNA system may lead to new inroads in the understanding of mechanical factors affecting transcription, while understanding the developing brain as a material via creasing will advance understanding of how it functions. To recruit more women into physics to help propel the field to new heights, the PI will give a seminar discussing the scientific advances used to decouple the biological clock and the tenure clock to senior graduate students and post-docs. The PI will also introduce farm physics to school children visiting Indian Creek Farm, a u-pick apple orchard/farm in Ithaca, NY. It is a unique opportunity to combine physics with orchardry/farming to make physics fun and help create a future generation of physicists.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.