Dynamics of Disordered Non-Equilibrium Systems: Hysteresis, Noise, and Domain Wall Dynamics in Systems Ranging from Magnets to Earthquakes

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

Many systems "crackle"; when pushed slowly they respond with discrete events in a broad distribution of sizes and durations. The earth responds to slow tectonic motion with quakes ranging in size from tiny tremors to devastating multitude-nine quakes. Similarly, a magnetic tape in a slowly changing external magnetic field magnetizes in a series of jumps (Barkhausen noise) - avalanches of reorienting magnetic domains that range from microscopic to macroscopic in size. In the past few years there has been rapid progress in developing models and theories of scale-invariant, often-universal behavior in driven, disordered, nonlinear, dynamical systems. This theoretical project will carefully test some of these models against experimental results, extract universal predictions for future experiments, extend the models if necessary to adequately describe experiments, and explore the size of the corresponding universality classes. The methods employed range from numerical simulations to scaling theories, and draw on ideas ranging from hydrodynamics to dynamical and disordered systems theory. Intellectual merit: Barkhausen noise serves as an ideal experimental example system for studying collective "crackling" noise in hysteretic systems. It is relatively accessible to experiments and is also of commercial interest, as for non-destructive testing. The non-equilibrium zero temperature random field Ising model (RFIM) and recent variants (with applications far beyond magnetic systems) have been extraordinarily successful in modeling universal scaling exponents obtained from Barkhausen noise measurements in a large class of different materials. Adding temperature fluctuations to the model at finite field sweep rate, the entire experimentally relevant crossover regime from far-from equilibrium to close-to equilibrium will be explored and compared to recent experiments in magnetic and ferroelectric systems. The corresponding equilibrium and non-equilibrium universality classes will be compared in detail, to answer long-standing questions relevant to both experiments and applications. Broader impact is two-fold. Students involved with the project will gain a broad range of skills and learn to work with groups of theorists, experimentalists and possibly industrial representatives. Besides being of great fundamental importance, the results of this research hold promise of technological applications. %%% Many systems "crackle"; when pushed slowly they respond with discrete events in a broad distribution of sizes and durations. The earth responds to slow tectonic motion with quakes ranging in size from tiny tremors to devastating multitude-nine quakes. Similarly, a magnetic tape in a slowly changing external magnetic field magnetizes in a series of jumps (Barkhausen noise) - avalanches of reorienting magnetic domains that range from microscopic to macroscopic in size. In the past few years there has been rapid progress in developing models and theories of scale-invariant, often-universal behavior in driven, disordered, nonlinear, dynamical systems. This theoretical project will carefully test some of these models against experimental results, extract universal predictions for future experiments, extend the models if necessary to adequately describe experiments, and explore the size of the corresponding universality classes. The methods employed range from numerical simulations to scaling theories, and draw on ideas ranging from hydrodynamics to dynamical and disordered systems theory. ***