CAREER: Correlated Percolation Approaches to Jamming

Syracuse University, Syracuse NY

Investigators

Abstract

TECHNICAL SUMMARY: 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.