This 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.
This 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.
