Cellular Models of Nonlinear Flux Flow, Vortex Rivers, and Noise

University Of Houston, Houston TX

Investigators

Abstract

0074613 Bassler Many granular systems that are driven out of equilibrium exhibit nonlinear transport, where the dynamics is intermittent, or punctuated by avalanches. These breakdown events can be small, or catastrophic (system-wide), or the avalanches can exhibit scaling behavior. Understanding the dynamics of avalanches of granular objects is of fundamental theoretical and technological importance to a variety of subjects including magnetic fusion, superconductivity, and internet traffic. Much of the theoretical effort to describe avalanche phenomena has focussed on the behavior of discrete, cellular models, such as sandpile models, which naturally incorporate both the granularity of the objects and the threshold nature of the breakdown process. These models often have the added benefit of being numerically tractable, so that it is possible to study their behavior over a range of length and time scales, which is necessary to detect the presence or absence of scaling, and to determine universality. However, there has been little success, thus far, connecting those simple models with real physical systems to assess their accuracy, generality, and predictive power. This grant aims to address this fundamental problem by constructing discrete, cellular models to study the nonlinear transport properties of vortices driven through a type II superconductor, and making specific, quantifiable connection with experiments. As is well known, the repulsive interaction of vortices combined with attractive pinning due to disorder leads to a pile of quantized vortices in the superconductor, reminiscent of a pile of sand. So it is natural to ask if a sandpile type of cellular model can accurately describe the large scale behavior of the vortex pile. Furthermore, vortex dynamics provides an ideal test bed because of the large body of experimental work characterizing the internal magnetic field profile, the distribution of internal avalanches using micro-Hall probes, longitudinal and traverse noise measurements, current-voltage characteristics, thermally activated flux creep dynamics, magnetic relaxation, dynamical transitions at high currents, etc. This research is complementary to molecular dynamics simulations that have been performed on this same system. The results generated here can be compared quantitatively with the valuable results obtained using MD, but a microscopically realistic model is not sought here; instead, coarse grained, discrete models will be developed to try to capture the same large scale behavior. From a practical viewpoint, the models used here can be studied numerically at significantly larger length and time scales, enabling the use of finite size scaling methods, and the classification into universality classes. From a theoretical viewpoint, if such cellular models can be shown to be accurate, they provide a more general description of the phenomena associated with vortex dynamics, which can possibly be observed in other systems, and lead to a better understanding of nonlinear transport phenomena associated with avalanches. This research involves collaborations between the University of Houston and Imperial College, London. %%% Many granular systems that are driven out of equilibrium exhibit nonlinear transport, where the dynamics is intermittent, or punctuated by avalanches. These breakdown events can be small, or catastrophic (system-wide), or the avalanches can exhibit scaling behavior. Understanding the dynamics of avalanches of granular objects is of fundamental theoretical and technological importance to a variety of subjects including magnetic fusion, superconductivity, and internet traffic. Much of the theoretical effort to describe avalanche phenomena has focussed on the behavior of discrete, cellular models, such as sandpile models, which naturally incorporate both the granularity of the objects and the threshold nature of the breakdown process. These models often have the added benefit of being numerically tractable, so that it is possible to study their behavior over a range of length and time scales, which is necessary to detect the presence or absence of scaling, and to determine universality. However, there has been little success, thus far, connecting those simple models with real physical systems to assess their accuracy, generality, and predictive power. This grant aims to address this fundamental problem by constructing discrete, cellular models to study the nonlinear transport properties of vortices driven through a type II superconductor, and making specific, quantifiable connection with experiments. As is well known, the repulsive interaction of vortices combined with attractive pinning due to disorder leads to a pile of quantized vortices in the superconductor, reminiscent of a pile of sand. So it is natural to ask if a sandpile type of cellular model can accurately describe the large scale behavior of the vortex pile. Furthermore, vortex dynamics provides an ideal test bed because of the large body of experimental work characterizing the internal magnetic field profile, the distribution of internal avalanches using micro-Hall probes, longitudinal and traverse noise measurements, current-voltage characteristics, thermally activated flux creep dynamics, magnetic relaxation, dynamical transitions at high currents, etc. This research is complementary to molecular dynamics simulations that have been performed on this same system. The results generated here can be compared quantitatively with the valuable results obtained using MD, but a microscopically realistic model is not sought here; instead, coarse grained, discrete models will be developed to try to capture the same large scale behavior. From a practical viewpoint, the models used here can be studied numerically at significantly larger length and time scales, enabling the use of finite size scaling methods, and the classification into universality classes. From a theoretical viewpoint, if such cellular models can be shown to be accurate, they provide a more general description of the phenomena associated with vortex dynamics, which can possibly be observed in other systems, and lead to a better understanding of nonlinear transport phenomena associated with avalanches. This research involves collaborations between the University of Houston and Imperial College, London. ***