****Technical Abstract**** Materials that undergo a Jamming-unjamming transition are ubiquitous in nature: a pile of sand, a sack of marbles, and a raft of bubbles are examples of disordered particulate systems at the edge of stability. The transition from jammed to flowing, just like the glass-transition, has many of the hallmarks of a phase transition without fitting cleanly into any existing phase transitions theories. This project will pursue a multipronged approach, combining new experimental and simulational techniques to explore jammed systems in dimensions d=2, 3 and higher. If a mean-field theory of jamming exists, it is expected that its predictions should become increasingly exact with increasing dimension. Using newly developed simulations, this project will measure the scaling behavior of high-dimensional systems close to jamming. These results will be used both to test the validity of the recently proposed mean-field Gaussian Replica-Theory of jammed systems as well as to develop a renormalization approach towards understanding the geometric structures of such packings. If a full renormalization treatment is achieved, this will represent a true breakthrough in the study of jammed systems and would have broad impact for the study of jammed, glassy, and frustrated systems. This project will support the education and career development of a PhD student well versed in both cutting edge experimental and simulational science. The successful completion of these studies will provide a quantitative understanding of the geometric and mechanical phase transitions underlying the jamming transition in dimensions two, three, and higher.
Jamming is ubiquitous in nature and industry: a sand dune, a sack of grain, a pile of coal, and the powders that make medicines are all examples of disordered particulate systems at the edge of stability. They seem solid enough at first push, but give them a hard shove and they simply flow out of the way. Yet, for all of their ubiquity, they remain poorly understood. One of the ironies of nature is that often by imagining what the world would be like in much higher dimensions, we can better understand and explain the world as it is. Thus, studying the jamming of particles in (for example) 7 dimensions will shed light on such prosaic questions as "How does one design a better grain hopper?" This project will pursue a multipronged approach to explore jammed systems in the real world, in dimensions d=2, 3 and higher. This project will: measure the static and dynamic properties of a jammed emulsion, a model system for studies of jamming; drive the state of the art forward in high speed microscopy techniques; develop new computer programs and algorithms to harness cutting-edge supercomputers and simulate the interactions of an enormous number of particles in dimensions as high as the thirteenth dimension; and support the education and career development of a PhD student well versed in both cutting edge experimental and simulational science; pioneer a Visiting Artist program designed to spark public interest and appreciation in real science in ways that a purely scientific discourse cannot.
