This award supports theoretical research on fundamental condensed matter physics. The collective transport of granular objects driven through a disordered medium is often intermittent, governed by avalanches. The avalanches can be small, or system-wide, or they can exhibit scaling behavior. Understanding avalanche dynamics is of fundamental theoretical and technological importance to a variety of subjects including river hydrology, superconductivity, solar flares, and Internet traffic. Much of the theoretical effort to understand avalanche dynamics has focused on the behavior of cellular "sandpile" models. Cellular models provide a coarse-grained physical description that naturally incorporates both the granularity of the objects and the threshold nature of the breakdown process. They also often have the benefit of being numerically tractable, making it possible to study their behavior over a range of length and time scales, which is needed to detect the presence or absence of scaling, and to determine the universal features of the dynamics.
Discrete, cellular models will be used to study the nonlinear transport properties of magnetic vortices driven through a type II superconductor, and to make quantifiable connection with experiments. It has been suggested that, because of the repulsive interactions between vortices, and the attractive pinning between vortices and lattice defects or impurities, the dynamics of quantized vortices in a superconductor is analogous to that of grains in a pile of sand. Additionally, the over-damped motion of vortices in most experiments is captured by the threshold dynamics of most sandpile type cellular models. Therefore, the driven dynamics of magnetic vortices is an ideal physical system to attempt to model with cellular models. Furthermore, a number of experiments characterizing vortex dynamics present opportunities for establishing and exploring the connection between cellular models and the large-scale behavior of superconducting vortices. By establishing that connection, the universal aspects of the dynamics of a variety of other nonequilibrium systems may also become better understood.
This research builds on existing results that have developed a cellular model for vortex dynamics, and demonstrated that it captures at least some of the large-scale properties, including some quantitative results, of the nonlinear transport in superconductors that are observed experimentally. In the new work, large-scale numerical simulations will be used to further explore the connection between the universal dynamics of cellular models and of superconducting vortices by extending our existing model to study a variety of novel phenomena observed in type II superconductors. In particular, the existing model will be extended to account for thermal effects caused by the resistive heating of vortex motion, and to describe the three-dimensional nature of vortices. Studies are proposed to model experiments that measure the scaling properties of flux penetration, including the formation of dendrites, and of distributions of voltage noise and vortex flow. Additionally, studies exploring the relationship of the universal dynamics of the cellular model, and of vortex dynamics, to other physical systems are proposed. Novel numerical algorithms will be employed to achieve massively parallel simulations of the models. Collaborations with experimental groups are also planned.
Graduate students will be involved in the project and the research will enhance efforts to incorporate computation into the graduate physics curriculum. An interactive website will be developed to promote outreach. Talks will be given at local high schools. %%% This grant supports fundamental condensed matter physics. The research investigates, primarily using computational methods, the transport of magnetic vortices in superconductors. This problem is of interest for both basic and applied reasons. The theoretical approach utilizes the connection between this problem and that of the motions of grains of sand in a sandpile. A strong educational and outreach program is planned as part of this project. ***
