This award supports theoretical research and education on jammed matter. The goal of this proposal is to develop the ensemble of volume fluctuations to describe the statistical mechanics of jammed matter with an aim of shedding light to the long-standing problem of characterizing the random close packing and random loose packing of particles.
The PI will work to develop a theoretical statistical approach with the aim of describing the jammed system with equations of state relating observables such as entropy, coordination number, volume fraction, elastic moduli as well as the probability distributions of volume and contacts. The PI will follow a systematic route to classify jammed packings into a phase diagram of jamming, from frictionless to frictional particles, from hard spheres to deformable particles, from monodisperse to polydisperse, from spherical particles to nonspherical convex particles such as ellipsoids, in an attempt to understand the packing problem from a unifying perspective. We will also generalize our studies of random close packing and random loose packing of particles to other dimensions such as 2d, nd, and the mean-field limit of infinite dimension.
An important impact of the project will be to attract underrepresented students to participate in the proposed research drawn from the excellent pool of underrepresented undergraduate and graduate students from physics and engineering at CCNY.
NON-TECHNICAL SUMMARY This award supports theoretical research and education on jamming. The phenomenon of jamming takes place in particulate systems when the density of particles is increased to a point where all particles are in close contact with one another and experience structural arrest. Once jammed, the system is able to withstand an applied stress. Jammed systems have very different properties, ranging from hard and rough granular materials, to deformable and frictionless emulsion droplets, to colloidal suspensions. Exploring the jamming transition for a variety of systems carries importance in both industrial processes and understanding of the fundamental theory of this type of structural arrest. The PI aims to develop a theoretical framework to describe this phenomenon. The PI envisions creating a phase diagram or ?road map? to concisely capture the conditions under which jamming occurs and the states of granular materials.
There is a growing realization that the study of granular media offers unexpected challenges in physics, having behavior unlike that of liquids or solids. Generally, it is believed that the jamming transition shares many features with the glass transition, taking place in liquids cooled down sufficiently fast. Therefore, progress in the field of jammed matter will advance the understanding of a variety of out of equilibrium phenomena.
From a practical perspective, granular matter and emulsions are widespread, finding applications in the food industry, cosmetics, pharmaceuticals and geomorphology. Often, the handling of granular materials is based on empirical methods due to a lack of understanding of these complex systems. A fundamental basis for these systems would make it possible to develop new procedures and reduce handling costs. An important impact of the project will be to attract underrepresented students to participate in the proposed research drawn from the excellent pool of underrepresented undergraduate and graduate students from physics and engineering at CCNY.
The intellectual merit of this project lies in the importance it has for both fundamental research and practical interests. There is a growing realization that the study of granular media offers unexpected challenges in physics, having behavior unlike that of liquids or solids. Generally, it is believed that the jamming transition shares many features with the glass transition, taking place in liquids cooled down sufficiently fast. Therefore, progress in the field of jammed matter will advance the understanding of a variety of out of equilibrium phenomena. During this project we have developed theories of random packings that allow us to understand the way spheres and other non-spherical objects occupy space in an optimal way. This problem has important ramification in a number of fields, from mathematics, physics and computer science of hard optimization problems. Our findings have extended the knowledge of random packings in 3d to higher dimensions and ordered packings. The problem of higher dimensional packings has been treated as well. This problem is important in communication theory as the packing problem in infinite dimensions can be mapped to the optimization problem of sending signals in a noisy channel. From a broarder perspective, granular matter and emulsions are widespread, finding applications in the food industry, cosmetics, pharmaceuticals and geomorphology. Often, the handling of granular materials is based on empirical methods due to a lack of understanding of these complex systems. A fundamental basis for these systems would make it possible to develop new procedures and reduce handling costs.
