This CARRER award supports research and education on the statistical physics of condensed matter systems. Jamming is the transition in a disordered collection of objects from a state where motion is possible to one where it is not. With this definition, the seemingly unrelated systems of traffic, granular materials, glasses, and colloidal glasses all exhibit jamming behavior. Inspired by simple models of the glass transition, the PI and her collaborators have proposed a simple mechanism for the jamming of granular materials based on the model of k-core percolation. The definition of k-core percolation is ordinary percolation with an additional clustering constraint: each site in a percolation cluster must have a minimum number of contacts. While the mean field theory of this model quantitatively reproduces the critical exponents determined by simulations of granular jamming in finite-dimensions, finite-dimensional studies of k-core percolation so far do not. This raises the question: Is the k-core clustering constraint enough to describe the universality class of the jamming transition? Or do we need to consider other constraints, like force-balance? To answer this and related questions, the PI proposes to study various models of correlated percolation as simplified descriptions of jamming to determine which constraints are relevant in the renormalization group sense of the word and which constraints are not. Moreover, the PI will analyze systems where jamming arises due to the interplay between disorder resulting from intrinsic constraints and extrinsic, quenched disorder, with the goal of understanding jamming on rough surfaces. This avenue of investigation will also explore connections between jamming and depinning, where quenched disorder always plays a role. Finally, extension of the notion of jamming to quantum mechanical systems, by considering the jamming cluster as a medium for electronic transport, is introduced with an aim to broaden our understanding of conductivity in disordered materials. Since jamming is such an everyday phenomenon, whether occurring in traffic or coffee beans stuck in a dispenser, it is natural to have a broad outreach component to the educational part of the proposal. Furthermore, the geometrical concepts in jamming result in pictorial explanations that make it easy to convey to the general public. So the PI proposes to collaborate with Syracuse's Museum of Science and Technology (MOST) to give a series of lecture/demonstrations to children and design several stations on jamming and percolation with the ultimate goal of constructing an exhibit showcasing the theory and applications of soft matter. The PI also intends to give other public lectures on the subject. As for the university setting, the PI proposes to use percolation as a computer laboratory project in the undergraduate class "Science and Computing" and teach a graduate seminar on phase transitions with percolation and k-core as its focus.
NON-TECHNICAL SUMMARY:
This CARRER award supports research and education on the statistical physics of condensed matter systems. Diverse and seemingly unrelated systems of materials like sand, powders, glasses, and colloidal glasses can all exhibit jamming behavior, a transition from a state where motion is possible to one where it is not. The research focuses on understanding the fundamental science underlying this phenomenon. Since jamming is such an everyday and accessible phenomenon, whether occurring in traffic or coffee beans stuck in a dispenser, the PI will collaborate with Syracuse's Museum of Science and Technology (MOST) to give a series of lecture/demonstrations to children and design several stations on jamming and percolation with the ultimate goal of constructing an exhibit showcasing the theory and applications of soft matter. The PI also intends to give other public lectures on the subject. At the university level, the PI aims to use percolation as a computer laboratory project in the undergraduate class "Science and Computing" and teach a graduate seminar.
Normal 0 false false false EN-US X-NONE X-NONE We are all familiar with the formation of ice cubes, where water undergoes a phase transition from a liquid to an ordered solid. Ice is an ordered solid because the water molecules/particles form a regular, or ordered, structure. There also exist phase transitions from a liquid to a disordered solid, otherwise known as jamming, where the particles do not form an ordered structure in the solid phase. Such transitions are observed in beans getting stuck in a hopper or paint drying. Our current understanding of the jamming transition remains at the level of heuristic arguments along with a number of competing particle-based approaches. Until our understanding of the jamming transition progresses at the particle level, we will continue to have fast-drying paint developing cracks, hoppers that, at times, prevent the flow of particles, grain silos that collapse, and be unable to prevent avalanches of powdered snow. In addition, jamming can occur in living systems as well, most notably the cell cytoskeleton. The cell cytoskeleton consists of many filaments that solidify in a disordered way to give the cell structural integrity and also flow to allow the cell to change shape to begin to crawl. Therefore, a successful particle/filament-based approach to jamming will also help us address diseases in which cell motility plays an important role, for example. The difficulty in developing a particle-based approach to jamming is the disorder. And yet, there is a phase transition with disorder that is very well understood called percolation. Percolation is the study of connected structures in disordered networks. Such connected structures undergo a phase transition from a phase where they do not span (extend across) the system to a phase where the connected structures do span the system as their density is increased. The mission in this proposal was to extend the standard percolation model, where the structures are randomly assembled, to include constraints on their construction. These constraints encode properties of local and global mechanical stability required for solidification/rigidity. This approach is now known as correlated percolation. Using this correlated percolation approach we may ultimately bridge the gap between well understood standard percolation and far less understood jamming. This approach led to a number of discoveries, several of which are listed here: (1) Discovery of the first correlated percolation model allowing for a provably discontinuous percolation transition in two-dimensions and exhibiting at least one diverging lengthscale. This is the first time in the sixty years of percolation theory such a result has been obtained. Moreover, the jamming transition is also a discontinuous transition with more than one diverging lengthscale. 2) Discovery of a broader class of correlated percolation models, one of which has been dubbed the force-balance percolation model, demonstrating a discontinuous percolation transition and exhibiting at least two diverging lengthscales, again, indicating a link with jamming. (3) Construction of what is now known as the jamming graph, which contains both properties of global and local mechanical stability at the onset of jamming. The probing of how jamming graphs destabilize in response to deleting contacts/bonds led to the discovery of a potentially new diverging lengthscale associated with the destabilization of jammed systems. (4) The construction of a model cell cytoskeleton with both freely-rotating and angle-constraining crosslinks. The presence of angle-constraining crosslinks can cooperatively lower the onset of jamming to the standard percolation threshold---a result speculated for almost 30 years but never before obtained in a systematic framework. This result demonstrates that the cytoskeleton can attain rigidity at the lowest concentration of filament material possible. In addition to these highlights, which edge closer towards a particle-based understanding of jamming, the mission also led to a number of other discoveries in related systems with disorder such as the first discontinuous, disorder-driven, quantum metal-insulator transition via quantum correlated percolation. Quantum disordered systems are related to classical disordered systems in that one must investigate the statistics of the wavefunction in the former and the statistics of the forces, for instance, in the latter. Finally, in keeping with NSF's mission "to promote the progress of science", the PI mentored five graduate students during the course of this grant and two post-docs, one of which has just become an assistant professor equivalent in Europe. Moreover, the above discoveries (and related topics) were disseminated to the public at large by (i) giving public lectures at Syracuse's Museum of Science and Technology (MOST) and (ii) involvement in a summer camp for inner-city children also at the MOST for several summers. In addition, participation in a number of women-in-science events, such as the ``Expanding Your Horizons Career Conference'' at Syracuse's YWCA and the Sonya Kovalevsky Festival at Syracuse University, helped encourage young women to enter science and math.
